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[ "Muhammad Naeem (physicist)\n\nMuhammad Naeem, is a Pakistani nuclear scientist who is the current chairman of the Pakistan Atomic Energy Commission (PAEC). ", "He is also the current chairman of the Board of Governors of Pakistan Institute of Engineering and Applied Sciences (PIEAS).", "\n\nReferences\n\nExternal links \n Pakistan Atomic Energy Commission (PAEC) Website\n Pakistan Institute of Engineering and Applied Sciences (PIEAS) Website\n\nCategory:Living people\nCategory:Pakistani nuclear physicists\nCategory:Pakistan Institute of Engineering and Applied Sciences faculty\nCategory:21st-century Pakistani scientists\nCategory:20th-century Pakistani scientists\nCategory:1949 births" ]

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[ "Hurricane Harvey\n\nHouston is facing significant burdens in recovering from the unprecedented flooding brought by Hurricane Harvey, and our historic neighborhoods will have their own unique challenges. ", "Preservation Houston is here to provide professional advice and accurate, timely information about the resources available for the owners of flood-damaged historic properties. ", "We will be collecting some of that information here; if you have questions, please contact us.", "\n\nGeneral information for those wanting to volunteer/donate or those in need of help: harveyneeds.org\n\nNews and announcements\n\nOur fall Architecture Walks schedule has been shuffled. ", "We'll be offering a tour of Turner Addition on Sunday afternoon, Oct. 8, and a tour of Shadow Lawn and Waverly Court on Sunday afternoon, Nov. 12.", "\n\nOnline recovery resources\n\nPreservation Houston has been collecting information to help Houstonians begin the recovery process after Hurricane Harvey. ", "Some of the materials will be useful to all property owners, while others are geared toward the owners of historic homes and buildings.", "\n\nWhat we're doing\n\nHelping THC to identify potential National Register historic districts. ", "This is a very important task because FEMA is required to focus its preservation efforts on properties listed on the National Register of Historic Places and properties that are eligible for listing.", "\n\nSpeaking with representatives of historic neighborhoods and the owners of historic properties across Houston to help them assess their needs in the storm's wake.", "\n\nPreservation Houston is your local historic preservation organization. ", "Our members, volunteers, board and staff are your friends and neighbors. ", "We have shared your experiences in this life-changing event, and we will continue working on behalf of Houston's historic resources as the post-Harvey situation develops.", "\n\nThank you for your support, which allows us to continue our community-focused work." ]

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[ "\n\nLOVE'S\n\nBETRAYAL\n\nA NOVEL OF THE FREYODIN WARRIORS\n\nELIZABETTE REMON\nCopyright Information\n\nLove's Betrayal\n\nElizabeth Emmons\n\nCopyright 2016 Elizabeth Emmons\n\nPublished by HEA Scribe, LLC\n\nSmashwords Edition\n\nCover Art by Elizabeth Emmons; AdobeStock_56326260\n\neBooks are not transferrable. ", "They cannot be sold, shared or given away as it is an infringement of the copyright of these works.", "\n\nThis is a work of fiction. ", "Names, characters, businesses, places, events and incidents are either the products of the author's imagination or used in a fictitious manner. ", "Any resemblance to actual persons, living or dead, or actual events is purely coincidental.", "\n\nAll rights reserved. ", "This book or any portion thereof may not be reproduced or used in any manner whatsoever without the express written permission of the publisher except for the use of brief quotations in a book review.", "\n\nWarning: Adult Reading Material\n\nThis story, while purely fictional,\n\nis meant for adults and contains explicit\n\nmaterial including sex and violence.", "\n\nIt is not suitable for persons\n\nunder the age of 18.", "\n\nReaders, please be advised.", "\n\nBetrayed by her first love...\n\nDanielle is one tough female and vows only to believe in herself and her dedication to protect mortals. ", "In her past, she has several strikes against her and has had to prove herself time and again. ", "One, her lineage as the daughter of a Goddess who cares nothing for her. ", "Two, the painful betrayal of a male she was sacredly pledged to. ", "And three, just the fact that she's female and considered weak. ", "Even though times have changed, she still harbors the insecurities secretly deep within and strives to maintain the respect she is due as a member of the Freyodin Warriors.", "\n\nAaron is an archeologist searching for a mythical relic. ", "In the process, he blunders upon an ancient chain that causes problems he wasn't expecting and may change the course of his lifelong dreams and aspirations. ", "Maybe even against his will – if he can survive.", "\n\nThe unexpected connection between them is filled with inexplicable attraction, danger and adventure. ", "They learn truths of their past that neither one is prepared for and face a possible future neither one may want. ", "Can they overcome their differences, secrets and pasts, and work together to find a solution they both can live through?", "\n\nDedication\n\nTo us and our lasting friendship. ", "May we have many, many more years.", "\n\nTable of Contents\n\nChapter One\n\nChapter Two\n\nChapter Three\n\nChapter Four\n\nChapter Five\n\nChapter Six\n\nChapter Seven\n\nChapter Eight\n\nChapter Nine\n\nChapter Ten\n\nChapter Eleven\n\nChapter Twelve\n\nChapter Thirteen\n\nChapter Fourteen\n\nChapter Fifteen\n\nChapter Sixteen\n\nChapter Seventeen\n\nChapter Eighteen\n\nChapter Nineteen\n\nChapter Twenty\n\nAbout The Author\n\nUpcoming Release\n\nThey are guardian angels in a paranormal army who battle demons. ", "Demons that have succeeded in crossing over into the mortal realm. ", "Their crusade is endless, therefore they are immortal. ", "Not heavenly saints or divine angels, by far. ", "They are warriors. ", "Freyodin Warriors. ", "Chosen by the Gods Odin and Freya for their extraordinary honor, bravery and supreme sacrifice to their individual causes for the good of their own people. ", "Now, they fight side by side for the good of all mankind...\n\nChapter One\n\nThe pull is a painful ecstasy. ", "Her body and mind are neither here nor there, shifting like an apparition in an incorporeal, disembodied state. ", "Blindly floating through the colorful swirling wisps of misty fog with an unknown destination. ", "She feels anxious but excited. ", "Never knowing if what will be shown to her will be beneficial or malevolent, helpful or harmful. ", "But she does understand that whatever is shown to her, she must pay heed. ", "For the message she receives could mean the difference between life and death to someone...man, woman or child, alike. ", "Unbeknownst to them, no one was safe from the evil that penetrated the earth and her destiny was to aid in their safety and survival.", "\n\nSlowly, her vision clears, the ethereal fog rolls away and she can once again feel the solid ground beneath her spectral feet. ", "She knows this place. ", "The salty smell of the sea, the moisture floating on the air that strays from the forceful waves crashing into the cliffs below, the battering wind whipping around and through her, it's eternal beauty...home.", "\n\nImages of the past threaten to crush her spirit. ", "One of the worst days in her long, long memories happened here. ", "So much loss. ", "So much pain. ", "The Great Battle.", "\n\nShe quiets her grief and focuses on the task at hand. ", "Still an unseen observer, she watches as mortals labor around what appears to be a large ominous cavity in the earth. ", "She is immediately propelled forward by an invisible force and there in the hands of a young man is a sight she never thought to behold.", "\n\nThis can't be. ", "It shouldn't exist, unless...\n\nViolently startled, she is fiercely ripped from her vision, feeling as if she's falling into a free floating vortex of a furious storm. ", "Her eyes flutter heavily as she tries to regain her conscious state. ", "Instead of awakening in her meditative lotus position in front of the altar, she finds herself prone on the stone floor of her dimly lit sacred shrine.", "\n\nPainfully inhaling deep agonizing breaths, Zahara gasps, \"Is it possible? ", "Could he be alive?\"", "\n\n*****\n\nZahara sought out Thunder with urgency as she rushed through the training compound so flustered it never occurred to her to simply trace to her destination. ", "Her only thoughts were to reach her leader to inform him of her latest vision.", "\n\nShe was a tall, willowy beauty with an incandescent glow to her skin. ", "Her long black hair draped down her back over her flowing robes and framed her face with a light silver frost. ", "She served as a visionary and a member of the Freyodin Warriors in the fight against the demon Huldrekall. ", "She was an original member of the three hundred Shieldmaidens, sometimes called Valkyries, the women warriors who fought and died so bravely at the Battle of Bråvalla in the year 750 AD and made immortal by the Goddess Freya. ", "She now used her gifts as a visionary, an empath and a scryer to aid the warriors' efforts in protecting mankind. ", "She was a well-respected member and served as Freya's co-captain for the female warriors, overseeing with an even temper, normally handling crises with patience and love at the forefront.", "\n\nBut this vision was anything other than normal, thus her current anxious state of mind. ", "She located her superior in his office with his nose buried deep in an unsteady pile of paperwork that looked as if it would topple with the slightest nudge or miscalculated touch.", "\n\nThunder, also known as Thor, son of Odin and a God in the immortal realm, was the leader of all earth planed warriors, male or female. ", "He was a demanding, but fair authoritative leader with the massive six-foot eight-inch build of a thousand-year-old Viking, with rippling muscles to spare. ", "He had the power of not only his legendary mighty hammer, but control of thunder, lightning and sonic waves, and a direct connection with the Gods themselves never hurt either.", "\n\nGolden shoulder length blonde hair partially covered his sparkling blue eyes as she tried to greet him casually, but her anxiety showed through the constant fidgeting of her hands. ", "Her normally angelic voice was unusually rushed and high pitched.", "\n\n\"Thunder, I've just had a very disturbing vision. ", "A binding chain has been unearthed. ", "I believe it belongs to Alarr.\" ", "She saw the look of confusion flash across his face before he replaced the mask of control took over once more.", "\n\nAlthough a God, and demanding some modicum of respect, Thunder was usually just one of the guys around the warriors he commanded. ", "With his deep based voice, he replied, \"Good day, Zahara. ", "Please calm yourself. ", "Everything will be alright.\"", "\n\nZahara relaxed somewhat realizing she may have overreacted in the tiniest way. ", "At least, that was all she was willing to admit to herself.", "\n\n\"Where is the chain now?\" ", "he asked.", "\n\n\"In the hands of mortals. ", "We must retrieve it immediately. ", "I don't understand how the chain still exists. ", "It should have perished with Alarr hundreds of years ago. ", "Unless...\"\n\n\"No,\" he stepped in. \"", "I know what you're thinking, but there's no way Alarr is still alive. ", "We can be sure of that. ", "I don't know what this means, but I'll consult with Odin and Freya on the matter. ", "I agree though that we must get that chain back and out of human hands. ", "In the meantime, give me all the details you can from your vision and then summon Danielle for me. ", "I'll need to inform her of what's happened.\"", "\n\nZahara filled him in on every detail she could recall about her vision, including the location of the sighting. ", "Thoughts of their homeland always brought back unhappy memories of a time they could never forget and losses they had all endured. ", "After imparting all she knew, she excused herself and hurried away to call Danielle.", "\n\nHaving no idea where Danielle might be at the moment, she took a few deep breaths to calm herself and reached out to her through a mental link. ", "Danielle, I hope I'm not interrupting something important, but Thunder needs to see you right away in his office, please.", "\n\nNo, you're not interrupting. ", "Just sword practice with Slash. ", "Heading his way now. ", "Thanks, Danielle answered.", "\n\n*****\n\nStraightening gracefully from her attack stance with one arm arched above her head, brandishing her mighty magical sword in a full circular motion in front of her skilled and toned form, Danielle brought the exercise to a sudden halt.", "\n\n\"Sorry to break this up, Slash, but the big guy beckons.\" ", "And big she meant, as they didn't come any bigger than Thunder.", "\n\n\"No problem, love. ", "We'll catch up later. ", "You know...you almost had me there. ", "That sword of yours is one special weapon,\" Slash said with a wink of one of his deep dark eyes.", "\n\n\"Yes, but it only works like that for me. ", "You know that. ", "Maybe you can talk Freya into gifting you with one someday. ", "But, then again, you're uber talented with your monster scimitar. ", "That damn thing scares the crap outta me,\" she laughed easily.", "\n\nShe enjoyed the comfortable relationship she had with Slash. ", "He was one of the warriors she could at least flirt with innocently, knowing he would never cross the line with her. ", "She had a 'thing' about crossing that line and it wasn't good. ", "But she and Slash, they shared a mutual respect between them.", "\n\n\"Alas, I must trace.\" ", "She mockingly said, bowing low.", "\n\nSlash simply laughed, shaking his head and rolling his eyes.", "\n\n\"Later.\" ", "Then she was gone.", "\n\nWith the fading sound of Slash's laughter ringing in her ears, Danielle proceeded to trace from their training ground directly to the outside of Thunder's office at the compound. ", "She could have walked it, but when being summoned by Thunder, it was best to hurry. ", "Besides, she'd gotten enough of a workout in today and felt like being a little lazy. ", "Wondering just how serious this was, she knocked on his closed door and waited patiently for his reply.", "\n\n\"Enter.\"", "\n\nShe opened the door and made her way to the front of his desk suddenly feeling a bit nervous. ", "Although clad in simple jeans and a T-shirt, Thunder sat with a majestic air behind his ordinary office desk and continued with what he was doing, making no move to acknowledge Danielle upon her entrance.", "\n\nClearing her throat, Danielle inquired, \"You asked to see me, sir?\" ", "Her mind raced through countless scenarios. ", "Goddess, I hope I'm not in trouble again. ", "I can't think of anything I've done lately. ", "Shit!", "\n\n\"Yes, Danielle. ", "I've just returned from an impromptu meeting with Odin and Freya.\" ", "He raised his head and met her eyes as they widen in obvious fear.", "\n\nOh shit, shit, shit! ", "I'm really screwed!", "\n\n\"Zahara has had a vision that pertains to your past. ", "Something valuable has been found and this item needs to be recovered before the mortals who found it have time to examine it properly. ", "The Gods feel it is best that you retrieve it. ", "I really hate to have to tell you this, but I must.\" ", "He paused and reached for her hand tenderly.", "\n\nDanielle allowed his comforting touch and swallowed painfully, not being able to begin to know what he was referring to. ", "Her emotions warred between feeling confused, distressed and slightly relieved. ", "Her mind felt as if she was in a hurricane, but had it passed or was this just the calm of the eye before the real shit hit the fan.", "\n\nSeeing the confusion on her face, Thunder continued, \"Alarr's binding chain has been located. ", "There was no mention of remains, just the chain being unearthed.\"", "\n\nA shudder shook her body as Danielle reached her trembling hand up to touch the chain that would forever grace her throat, the twin to the one in question that once belonged to her bondmate. ", "Memories of the past flooded her brain like a rising tidal wave threatening to drown her beneath its weight. ", "She remained silent, staring sightlessly beyond into nothing, having no further reaction or response to Thunder's news.", "\n\n\"I realize this comes as a shock to you, Dani. ", "It's a shock to us all. ", "It has been over eight hundred years since...\" he trailed off, being at a loss for words.", "\n\nShe didn't hear him though, didn't even notice that he called her by her hated nickname, of which he meant no offense. ", "Danielle was swimming in a mindless, unfathomable foggy sea that she couldn't seem to reach the surface of. ", "She was near the point of panic, her breath becoming fast and shallow.", "\n\n\"Danielle, are you alright?\" ", "he asked taking note of her countenance and full of genuine concern. \"", "Here, why don't you sit? ", "I'll call Emeline.\"", "\n\n\"Yes, I...I mean no. ", "I'm all right. ", "Don't call Eme. ", "Please, I just need a minute,\" she barely murmured under the short breaths she managed to draw in. ", "Her chest felt constricted and her lungs were screaming, but she knew it wasn't too serious. ", "There was no need to call their healer for a simple panic attack.", "\n\n\"Okay, I'll just step out for a moment and give you a little time to yourself. ", "Call me if you need me.\" ", "Thunder exited his own office, closing the door behind him and saying a silent prayer to the Goddess for Danielle's wellbeing.", "\n\nThis type of event had never happened before. ", "The binding chain was only received and worn by those who became truly bonded mates and only broken and removable by death. ", "It was a ceremony blessed by Freya, the Goddess of love, war and fertility herself, equivalent to a mortal's marriage but binding for the remainder of their immortal lives together. ", "It was a sacred symbol of that commitment and psychically bonded the lovers allowing the bonded mates to hear the thoughts and feel the emotions of their counterpart. ", "A true connection of mind, body and soul.", "\n\nThe chain in Zahara's vision belonged to Alarr, Danielle's lost love, who died in The Great Battle for the Eye of Odin. ", "It was assumed that he died, although his body was never recovered because Danielle lost her connection with him. ", "Freya and Odin were correct in that Danielle should be the one to retrieve it. ", "It would call to her and obtaining it should help close any remaining old wounds she may harbor. ", "She had never been the same since that day of loss. ", "No one who lived through it had. ", "Such a day of tremendous loss of friends and fellow warriors and such a waste of life, as the Eye of Odin was never retrieved.", "\n\n*****\n\nThe Windjammer was the hottest club within a hundred and fifty miles of their secluded mountain home, supplying alcoholic libations, loud music, local drug dealers and all the sex you could handle by gyrating out on the dance floor to whatever top forty, rap or R & B artist was at the top of charts at the moment. ", "And one night a week they offered karaoke to the faithful patrons who liked that sort of thing.", "\n\nMakayla, Justice and Vex had the night off from assignment and made their way through the smoke-filled atmosphere to their usual table nearest the exit, in case they had to make a hasty departure. ", "No VIP seating in this joint. ", "This was Oregon after all, not New York or California. ", "Still, this place was doable. ", "It offered a great sound system, lighted dance floors on two levels, the drinks weren't watered down and if you ordered that drink at the second level bar, you could ride the twisted slide all the way back down to the first floor. ", "Of course, if you weren't very careful, you'd also be wearing that recently purchased pomegranate martini and would be going back for a replacement.", "\n\nMakayla swept her auburn hair up into a ponytail high on her head. ", "She took in the club with her almond shaped brown eyes flashed fiery green specks when caught by the club lighting that swirled rhythmically around the club's surfaces. ", "She was short for a warrior at a curvy five foot three inches, but made up for being height challenged with her fiery bow and arrow – a gift of Freya, of course, that only performed its extraordinary feats when used by Makayla herself. ", "That was the catch with the females' weapons. ", "The weapon only reacted to its owner, capable of extraordinary feats, otherwise, it was just a normal bow and arrow, spear, etc. ", "Of course, she had her warrior training and superior strength, which certainly didn't hurt either. ", "But tonight Makayla wanted to unwind and have some fun. ", "Sing a little, dance a little, drink a lot, which was afforded her because it took a lot of alcohol to even get a buzz when you had the metabolism of an immortal.", "\n\nShe was accompanied by two of her fellow Freyodin Warriors, her World War Buddies, she liked to call them. ", "First, there was Justice, an eccentric, explosives expert and avid Elvis fan from Memphis, who was 'brought over' from World War II. ", "His career choice would have been to be an Elvis impersonator and he claimed to have personally met The King, but not during his mortal life. ", "That life ended before Elvis' career began. ", "He even sported sideburns with hair just a hint of the early Elvis style and aqua blue eyes, but the huge muscles and fangs brought the similarities all to a crashing halt. ", "Plus, although he had a wonderful voice, he didn't sound enough like Elvis to pull it off successfully.", "\n\nCompleting the WW buds was Vex, who was brought over from World War I. Vex's specialty was knives and daggers. ", "He bore an underlying sadness he refused to talk about, and was sometimes very bitter, but all in all, he acted as the protector of the Shieldmaidens and was a most reliable warrior in battle. ", "The kind you always wanted by your side. ", "He drank way too much, was a master at poker and enjoyed loud music. ", "Mostly current and 80's rock. ", "But the boy could croon like an angel and, because it was karaoke night, the patrons of the Windjammer were in for a real treat.", "\n\nVex raked his slender fingers through his shoulder length wavy brown hair, something that he did frequently when he was preoccupied or nervous, and perused the song list. ", "He had an almost baby face with an irresistible smile that topped a sinewy warrior's body. ", "His eyes could be either blue or green depending on what he wore that set the color in motion. ", "Tonight they were deep green.", "\n\nBeing 'brought over' was the politically correct term for male warriors who died bravely in battle, were delivered to Valhalla and transformed into an immortal vampire via a blood ritual performed by the God Odin. ", "Not all who died were worthy to become warriors and their numbers were not as strong as in the past due to the losses of The Great Battle, but they were rebuilding, slowly and steadily. ", "Along with this transformation, they received powers that assisted them in their fight to protect the mortal realm against the demon Huldrekall. ", "They were not the vampires spoken of in movies and legends. ", "They only partook of bottled or donated blood about once a month unless they were severely injured, but they also required a physic charge taken from a woman during sex to replenish them. ", "And acquiring sex for this bunch of fellows was not a problem. ", "Sunlight could not hurt them and they loved to eat, a lot. ", "They were big muscular warriors, after all. ", "Their transition saw to that.", "\n\nMakayla took a sip of her lime flavored kamikaze and reached across the table brushing Vex's shoulder tenderly. ", "They were not lovers, but they shared a special bond, nonetheless.", "\n\n\"Ve-ex, please sing some Journey for me tonight,\" she begged shamelessly in a sing-song voice, comically batting her eyelashes at him. ", "She loved to hear him sing and hoped she could con him into it tonight.", "\n\n\"You just want to indulge in your Steve Perry fantasies. ", "Don't you get enough of that messing around with Savage? ", "The resemblance between the two hasn't gotten by me, you know,\" he jested back at her. ", "Although he knew he'd do it for her, he really enjoyed making her beg.", "\n\nJustice beckoned a nearby waitress and turned toward his friends. ", "He loved to tease and saw a golden opportunity, so he couldn't help but jump in the fray. \"", "Yea, you should have come back as a groupie, not a warrior.\"", "\n\nThey all shared a big laugh picturing Makayla as an 80's groupie, then placed their orders for more drinks when the waitress approached. ", "Makayla couldn't help secretly agreeing with Justice's assessment. ", "A girl could dream after all.", "\n\nTurning slightly serious, Vex leaned into her and inquired about her dual relationship with Vengeance. ", "There was no use whispering as Justice's hearing was as good as his own and would hear it anyway. \"", "If you're living your fantasy with Savage, why Venge?\"", "\n\nPicturing both of her fierce warrior lovers with a dreamy look in her eyes, she replied, \"Because he's a long, tall drink of sexy Viking. ", "Why not? ", "The boys are cool with it, so am I. And they both have such gorgeous hair.\" ", "She suddenly sobered. ", "Her smile not as bright and the playfulness was gone from her voice. \"", "Besides, I've done the chain bonding thing. ", "I won't do it again.\" ", "Adamancy showed in her eyes and stature as she threw back the shot of Patrón sitting on the table in front of her. ", "It went down a little too smoothly and she needed something stronger, something with more heat to it. ", "She longed to feel the burn scorching the back of her throat.", "\n\nVex felt a similar stabbing in his chest as a near fresh wound but hid any physical reaction. \"", "Yea, I'll never chain bond. ", "That ship passed me by,\" Vex mumbled solemnly, turning away from his friends to check out the club goers and effectually hiding the remorseful look on his somber face that had silently crept up on him.", "\n\nMakayla recognized the pain of loss that etched across his now stern face, how his jaw had tensed and he resumed running his long fingers over the top of his head and through his chestnut hair. ", "She also wondered when/if Vex would open up to her and tell her what his pain was all about. ", "Now was not the time to press the issue.", "\n\nThe ribbing had died down along with the laughter, but this subject brought Danielle to mind. \"", "Did you guys hear about Danielle's new mission?\" ", "Makayla inquired attempting another sip of her drink and remembering she'd drained it already. ", "The others nodded.", "\n\n\"It's so strange finding Alarr's binding chain after eight hundred years. ", "I really can't imagine what she's going through right now,\" she said sympathetically, running her fingers along her own binding chain that was hidden beneath her top.", "\n\n\"Yea, but it's a simple search and retrieval. ", "She ought to be in and out easily enough,\" offered Justice while sucking on his usual drink of choice, a cold-as-ice long necked beer, wrapped in his personal beer koozie that boldly read 'I deliver justice. ", "Want some?'", "\n\n\"Think someone should go with her? ", "I hear she's going out by herself,\" Vex asked, turning back with sudden interest. ", "He always felt the need to protect the ladies even though they were very capable of taking care of themselves.", "\n\nMakayla signaled the waitress over again, still craving the burning sensation. \"", "Nah, she's tough enough to handle it, I think. ", "And since it's so personal, she probably prefers to do it alone. ", "It's just so strange that the thing still exists. ", "Her bondmate has traveled across the Veil and his chain should have accompanied him. ", "Besides, we don't get a night off that often and I'm ready to cut loose a little.\"", "\n\n\"I'm with ya on that one. ", "Hurry up and pick out a song, Vex. ", "It's time to get this party going.\" ", "Justice reached for the song list Vex was hogging but he wasn't quite quick enough.", "\n\nJerking back away from Justice, Vex snarled, \"Hey, wait your turn.\" ", "Then he took on a look of nonchalance and added gruffly, \"Besides, you're just gonna sing some Elvis number anyway and you know them all by heart.\"", "\n\nMakayla shot him a sharp look of disapproval.", "\n\n\"Not that you don't do them well,\" he threw in quickly trying to soften his harsh comment in an unspoken apology. ", "Thoughts of his past had soured his mood.", "\n\nJustice didn't let it bother him, though. ", "He was used to Vex's occasional flights of fury and thought nothing of it. ", "He recognized the bitterness in his friend's life and forgave him his sometimes transgressions.", "\n\nThe three loved to sing and had an unspoken understanding that, although karaoke might not be all that cool for badass warriors to be doing, it was a vice they permitted amongst themselves and ragging on each other about it was not cool. ", "Besides, when you're a badass motherfucking immortal warrior, you could pretty much do whatever the fuck you wanted, as long as you didn't piss off the Gods.", "\n\n\"Hey, Vex. ", "Wanna try that duet again tonight?\" ", "Makayla said trying to change the subject.", "\n\n\"Sure, Mac. ", "Sounds good.\" ", "He flashed a small grateful smile at her realizing that he could really be a dick sometimes. ", "Circumstances had caused his past problems, not his friends, so he shouldn't take it out on them.", "\n\n\"Great. ", "I'm just going to the little ladies. ", "Be right back.\" ", "Makayla left the table noticing eyes watching her. ", "She looked great tonight in her tight jeans, low cut halter top and red fuck me heels. ", "She accented her ensemble with a belt decorated with four-inch spikes that not only gave her a Gothic edge but conveniently fit her mini crossbow that she carried with her on outings. ", "Heading to the second level of the club, she kept an ever watchful eye for any Huldrekall demons that might be lurking around causing trouble and in need of being dispatched. ", "Huldrekall were the demon horde that crossed into the mortal realm in human form who compelled evil or weak-minded humans, their minion, to perpetrate all manner of evil on earth. ", "They were formidable opponents. ", "Strong and fast healing and were ruled by the God Loki who falsely promised them immortality for their service. ", "Loki's demi-god son, Tormond, reigned here in the mortal realm over the horde in his father's stead. ", "He was just as ungodly as his father was.", "\n\nAs Makayla climbed the winding stairway, she felt the familiar vibrations in the air, along with the slight scent of brimstone, warning her of a demon presence. ", "At the far end of the bar sat a Huldra, a female demon disguised as a fair red haired human, wickedly laughing with a group of unsuspecting humans. ", "Within seconds, she spun around on her bar stool and met Makayla's hated glare head on.", "\n\nWonderful. ", "So NOT what I wanted to do tonight, she thought as she returned the hardened hateful look. ", "Looked like she'd have to put her bladder on hold for the moment. ", "Huldrekall always ran in packs, never alone. ", "Somewhere in this establishment were at least two more male demons, otherwise known as Hulders. ", "Confrontation in the presence of mortals was an unspoken rule, but miraculously one they all seemed to abide by.", "\n\nShe could have communicated their presence via a mind link, but chose not to. ", "She wanted to be there when the shit hit the fan. ", "With a quick leap, she landed on the two-story twisted slide and rode it back down to the first floor, then hurried back to their table. \"", "Heads up, guys. ", "We've got company.\"", "\n\n\"Seriously? ", "No night off. ", "Damn!\" ", "Justice complained. \"", "Let's try to get this over with quick 'cuz my song is coming up and I don't wanna miss it. ", "I was gonna sing C'mon Everybody from Viva Las Vegas. ", "Love that Ann Margaret. ", "Elvis was one lucky son of a bitch.\" ", "Then he jumped up from the table and did the ever famous hip wiggle of his legendary idol.", "\n\n\"Let's do this. ", "I'm sooo in the mood to kick some ass,\" Vex chimed in. ", "He knew from experience that a good fight would alleviate the thoughts of the past that haunted him. ", "A little beat down was just what the doctor ordered. \"", "Come on, Justice. ", "This won't take long. ", "You can even sit this one out and watch.\"", "\n\n\"You've been in a mood all night. ", "So yeah, I'll let you have 'em.\"", "\n\nMakayla led the way through the emergency exit door by their table knowing no alarm would sound when it opened, then carefully checked for their enemy and any possible traps that might be waiting for them. ", "Seeing and sensing that the coast was clear, Vex took the lead and they continued towards the back alley. ", "They were assaulted by the stench of the dumpsters occupying its space. ", "Clumps of weeds grew up through the uneven ground and the wind whipped discarded fast food wrappers in a circular pattern as if a mini cyclone were passing through the passageway. ", "The lighting in the alley was almost nonexistent, but Vex and Justice didn't need light with their exceptional eyesight. ", "All of their heightened senses were on alert, and Makayla, not being blessed with the sharper senses, took up position between the male warriors.", "\n\nWhen the Shieldmaidens were transformed by Freya they were made stronger than humans and had the ability of accelerated healing, but they also received the abilities to shadow, trace and speak – the ability to communicate with the other warriors via thought. ", "Odin's transformation of his warriors through a blood ritual changed the males into vampires with additional abilities but also additional needs. ", "Makayla didn't begrudge the men their additional abilities because she didn't want to have the additional needs to go with it. ", "She wanted to have sex purely for enjoyment, not because it was necessary at times.", "\n\nThe air was stifling and the pungent odor that fell around them grew stronger. ", "Makayla armed herself with her mini crossbow and quickly loaded the spikes from her belt. ", "This was a street fight and no place for her gifted weapon, not that she'd carried it with her tonight. ", "She was supposed to be off tonight and was hoping for a little downtime, but was always prepared for battle. ", "Vex motioned for her to hold up as he rounded the corner of the club, spotting their prey. ", "Joining him, Justice whispered, \"Well, there you go, Vex. ", "I promised to sit this one out and let you have 'em. ", "Knock yourself out.\"", "\n\nStanding in the back alley were three large, malevolent looking demons with one of their small minded minions in tow. ", "The warriors had no misgivings about taking out any minions that were foolish enough to confront them, even though they were still technically human. ", "If their minds were evil or weak enough to be controlled by the Huldrekall, they were too far gone to save anyway and posed too great a danger to others.", "\n\nThese motherfuckers are fast. ", "They beat us out here. ", "Must be itching for a fight tonight, like I am, Vex projected silently.", "\n\nJust be careful and don't get too cocky, Makayla chided and pinched the back of his leather jacket. ", "I'm right behind you. ", "Let's do this. ", "The Huldrekall knew they were coming. ", "There was no need for a sneak attack.", "\n\nFull of confidence, Vex rounded the corner, dagger drawn, and taunted, \"Well, well, well. ", "Look what we have here. ", "Who wants to be first?\"", "\n\nThe greasy haired minion who resembled a gang reject was feeling extremely brash, filled with the compulsion of his demon counterparts. ", "He stepped up first wanting to impress everyone present with his boldness, obviously not realizing who he was up against. \"", "Me. ", "I'll kick your ass and send you home screaming to your mama, asshole.\"", "\n\n\"Ahh, come on guys. ", "You gonna let a newbie fight your battles for you? ", "He's so green he doesn't even know who he's dealing with.\" ", "Their only reply was to snicker and grunt their distaste of their opponents. ", "What did they care? ", "Minions were a dime a dozen.", "\n\n\"Okay by me,\" Vex said as he calmly walked up to the unlucky fellow and slit his throat with a quick raise of his arm. ", "With red streaking down the front, the body slumped toward the hard gravel filled ground making strangled bubbling noises. ", "No need to make him suffer too much.", "\n\nAnd just like that, the fight was on. ", "Two demons leapt at Vex, the third charging Makayla, who began firing her four-inch spikes at her targets into the melee, working that crossbow just like a six shooter, spike after spike. ", "The scent of fresh blood filled the air. ", "True to his word, Justice stood back leaning against the brick wall with a confident playful smile on his face, his bulging arms folded across his chest and took in the display, making sure to keep a protective eye on Makayla.", "\n\nVex removed the first unfortunate by grabbing his thick neck and slamming him into that same wall head first, just shy of Justice's inclined body, receiving a look of surprise from Justice. ", "Then Justice threw his hands up in the air and broke out in a howl of laughter. ", "Demons were a little harder to kill than minions but were not immortal. ", "They could perish by a mortal wound, but it had to do enough damage that their quick healing abilities couldn't repair it before their complete termination. ", "That being so, Justice reached down, grabbing the crumpled body and finished the job by plunging his dagger through its still beating heart, instantly turning the demon to ash. ", "He snickered at Vex with a sense of accomplishment.", "\n\nThe red-haired female attacked from behind brandishing a six-inch switchblade and managed a minor injury to his throat before Vex reached back grabbing her shoulders, whipping her over his head and into a full body slam onto the unforgiving terrain. ", "He then fell upon her disarming and dispatching her quickly by gouging her chest and obliterating her heart. ", "Ash floated thick around him as he searched for Makayla's whereabouts, knowing that Justice would look out for her, but needing to know she was okay for himself.", "\n\nAnd she was. ", "Having discharged all of her spikes, she was engaged and holding her own in a tangle with a six foot and muscled looker. ", "Hate to mar that pretty face, but a girl's gotta do what girl's gotta do. ", "She didn't have Vex's and Justice's vampire speed, but she could kick and punch with the best of them. ", "The looker didn't have a chance as she used her shorter status to her advantage quickly nailing him with a right hook and ducking back low thwarting his attempts to grab her. ", "She'd managed previously to injure him with a couple of her piercing spikes that now protruded from his chest and dripped his crimson life force heavily on the surface with a consistent plop, plop, plop. ", "Taking advantage, she grabbed and drove them deeper hoping to hit something vital to weaken him further. ", "But he wasn't slowing down fast enough and managed to wrap his arms around her slender waist, crushing her body to his. ", "Makayla was suddenly trapped and unable to wrench her way free of his embrace.", "\n\nVex and Justice both lunged for the remaining demon at the same time breaking his hold on Makayla and flinging him backward through the air with mighty force. ", "Vex said, \"I've got this,\" and proceeded toward the downed offender ending his existence.", "\n\nMakayla had dropped to the ground but quickly recovered as Justice helped her stand with an inquiring look. ", "Dusting herself off and finger combing her long auburn locks, she said, \"I'm fine, Justice. ", "Thanks, guys. ", "Now, let's get back inside and have some fun.\"", "\n\n\"Sure, I just need to dispose of this,\" Vex said as he lifted the minion's remains and traced off into the deep woods. ", "Within seconds, he returned and joined the others reentering the club.", "\n\n\"Alright!\" ", "Justice yelled. \"", "Let's sing!\" ", "The three friends smiled and nodded to each other in agreement and as they settled themselves back at their table, a fellow crooner was on stage singing Cutting Crew's I Just Died In Your Arms Tonight.\" ", "Makayla put on a mischievous grin and snickered, \"Oh, the irony....\"\n\n*****\n\nAfter overcoming her initial shock of the news, Danielle realized that she'd been chosen to retrieve the binding chain. ", "Freya's orders. ", "Mom, huh. ", "Being a demi-goddess and one of the daughters of Freya wasn't all it was cracked up to be. ", "More of a hindrance, in her opinion.", "\n\nThe second shock came when she discovered she'd be flying back to the shores of the North Sea. ", "She hadn't been back in that area of the world for eons, it seemed. ", "She lived and trained in their little village community, magically hidden in the Blue Mountains of Oregon since its inception over a hundred years ago. ", "It felt like home now. ", "Those long ago memories faded in the past. ", "A feeling of dread came over her like a strong ocean wave that threatened to grab hold and drag her into its icy depths. ", "She was afraid nothing good could come of this mission, even if it was classed as a simple retrieval. ", "She had so many questions that she feared discovering the answers to.", "\n\nIt was a spectacular day for air travel. ", "At least the weather was cooperating. ", "That was one positive aspect. ", "Too bad she couldn't come up with even one more. ", "And it would surely be cold when she reached her destination. ", "Cold and gloomy. ", "She would have preferred an assignment on the coast of California with sun and the sea. ", "She couldn't fool herself, though. ", "Any other assignment would have been preferable.", "\n\nShe made her way out to the private airstrip that was located just outside of their village and boarded the sleek silver Falcon 900LX, the private jet that was owned and utilized by the warriors. ", "Mumbling sarcastically to herself about honor and duty, she brusquely closed the door of the jet, locking it in place, took her seat and signaled for the pilot to commence the flight.", "\n\nLooking back from the cockpit, the pilot ignored her obvious bad mood and greeted her, \"Mornin' ma'am.\"", "\n\n\"Good morning, Taylor. ", "You'll forgive me if I'm not very sociable today. ", "I just want to sit here silently and think.\"", "\n\n\"Of course, ma'am. ", "I'll just close the door and give you some privacy. ", "Have a pleasant trip.\"", "\n\n\"Thank you, Taylor.\"", "\n\nThey were lucky to have Taylor and others like him. ", "He descended from one of the few mortal families that served the warriors through the ages in capacities they would otherwise have to enthrall mortals to perform for them. ", "The trusted families shared their secret and considered it an honor and privilege to be of service.", "\n\nAs the jet leveled off, she took note of the vision surrounding her. ", "The sky was resilient with the splendors of white cottony clouds and golden streams of sunlight weaving through them, laid against an azure backdrop. ", "She longed to lay upon one of those clouds and let it engulf her with its welcoming gentleness.", "\n\nIt would be a long flight and she had already been exhausted both mentally and physically before it began. ", "She'd make the best of it and catch up on some much-needed rest. ", "There, that was positive. ", "And the flight was nonstop, not some commercial flight switching planes in different cities with constant layovers. ", "She was on a roll. ", "Two positives.", "\n\nTry as she might to push them away, the memories of her past kept haunting her. ", "She reached over and pulled the sliding shades down over the windows nearest her blocking out the welcoming clouds beyond. ", "With heavy eyelids, she reclined in the comfortable leather seat and closed her weary eyes. ", "Letting herself mentally drift on a sea of clouds, she began to dream...\n\n*****\n\n# Chapter Two\n\nEight Hundred Years Earlier...\n\n\"Danielle, you must hurry. ", "Alarr will be arriving any moment and we still need to ready you for him,\" Valeria said. ", "Danielle had always loved and respected Valeria, so beautiful and with such a wondrous heart. ", "She always looked upon her as a motherly figure, as did all of their close community. ", "She was someone Danielle could turn to when she needed advice. ", "Valeria could be relied upon to provide her assistance and opinions to all that required them, but with the warning that they shouldn't ask, if they didn't really want to hear it. ", "At times, her advice could be harsh, but it was always given in the spirit of love. ", "Danielle would never have felt comfortable turning to her Goddess mother for such guidance. ", "Freya was completely beyond such things.", "\n\nThe binding chain ceremony had taken place only a few hours earlier in the presence of Freya with everyone of importance in attendance. ", "It seemed no one dared miss the joining of the demi-goddess and a high ranking officer of the Freyodin Warriors. ", "Chain bonding oneself to another was a serious matter indeed. ", "It was a commitment to be bound through mind, body and soul for the rest of your immortal life. ", "It was not a step to be taken lightly, if at all.", "\n\nDanielle had been in love with Alarr Janssen for as long as she could recall and she couldn't believe her dreams were coming to light. ", "She remembered the first time she had met him. ", "Such a mighty brave warrior, he'd caught her eye immediately. ", "He is everything I've ever wanted in a man. ", "He was gorgeous, of course, in every way that a Viking warrior could be, strong with a powerfully built muscular body. ", "He always respected her as a woman, not just a fellow warrior. ", "Daniel had always hated that she was the physically strongest of the female warriors and that all of the males looked upon her as too manly...even going as far as nicknaming her 'Dani', knowing she hated it. ", "I am not a man! ", "I have womanly feelings, too.", "\n\nShe took a deep fortifying breath and straightening her spine with resolve, she said, \"Alright, Valeria, I put myself into your hands. ", "I know you'll make me feminine and beautiful. ", "If you could manage somewhat sexy, too, I'd be forever grateful. ", "I want Alarr to be so beside himself with lust that he will never for a moment regret falling in love with me and becoming my bonded mate.\"", "\n\nValeria stopped brushing the new bride's long blonde hair, sighed and cupped her face with her hands. \"", "Danielle, you are so gorgeous, why would you ever doubt it? ", "Being strong does not reflect all that you are. ", "My dear girl, I hope in time you will come to believe it and see the woman that I see in you.\" ", "She removed her hands and turned her forward again to resume brushing. \"", "Now. ", "We've had this conversation before. ", "Time is fleeting and we must get you ready.\" ", "Valeria wished Danielle had more confidence in herself. ", "Despite her size and strength, she really was a truly beautiful woman. \"", "Here, let's put on the beautiful nightrail that your mother gifted to you, then we will quickly braid your silky hair.\"", "\n\nThankful for the blazing fire that was chasing away some of the chills rippling along her skin, Danielle lifted the nightrail that she would receive her newly bonded mate in. ", "She had to admit, the nightrail was the most beautiful garment she had ever seen, other than her ceremonial gown. ", "She slipped it over her head and admired its beauty. ", "Its sheer flowing panels draped over her sensuous curves in the most alluring way.", "\n\nWith her hair intricately braided in several long blonde locks and settled over one shoulder, Valeria drew Danielle's attention to the reflection in the tall gilded mirror that sat in one corner of the stone-floored room. \"", "There now, look, Danielle. ", "See how beautiful you are. ", "Alarr will see you as you are, truly stunning.\"", "\n\n\"Oh, Valeria, you are so talented. ", "Thank you for assisting me this evening. ", "It means more to me than I can ever say.\" ", "With an excited yelp of a young girl she continued, \"I can't wait for him to see me.\" ", "As she admired the sight of herself, the sound of approaching footsteps invaded the room. ", "Revelry turned to hurried anticipation. \"", "Quickly, I hear him coming up the stairway.\" ", "She gave a quick hug to her warrior sister.", "\n\nAs Valeria opened the door to exit the room, before her stood the quintessential form of a Viking warrior. ", "Standing proud, strong and sure, Alarr inquired, \"May I enter? ", "Is my lady ready for me?\"", "\n\n\"Hello, Alarr, I was just leaving. ", "Yes, Danielle is waiting for you inside,\" Valeria said as she quietly turned towards the stone steps and made her exit. ", "She hoped this night would be everything Danielle wished for and that Alarr would be gentle with her. ", "Danielle may be as strong as a man in battle, but the ways of a woman and love were physically unknown to her.", "\n\n*****\n\nEntering his room, Alarr immediately saw Danielle standing before the hearth. ", "She breathed deeply of the subtle scents of beeswax candles and citrus wreaths that hung in the air attempting to sooth and calm herself, but the sight of him resurrected chills throughout her body. \"", "Danielle, you are so lovely,\" he said as he took the few steps needed to reach her.", "\n\nShe shyly looked into his eyes unable to hide her apprehension. ", "He wrapped his arms around her waist and gently hugged her to him. ", "Slowly, he lifted her chin as he leaned down to give her a sweet kiss. ", "Wetting her own lips with the tip of her pink tongue, she met his kiss with her own tenderness and all trepidation within her melted away.", "\n\nSensing her assent to move forward, he deepened the kiss, invading her mouth more forcefully and slowly backed her towards the bed in the center of the room. ", "Momentarily breaking their kiss, he gently began to lift her nightrail to bear her beautiful body. ", "Her breasts were high and firm. ", "Her skin light and creamy with curves belonging to a woman, not a warrior.", "\n\nOh Goddess, how I love this man, Danielle thought as Alarr lowered her to the bedding.", "\n\nAlthough some rumors amongst the warriors and community speculated otherwise, she believed Alarr had come to love her for herself, not due to her position as the daughter of the Goddess. ", "Oh, how blessed I am!", "\n\nAlarr trailed kisses down her jaw to her throat, kissing, nipping and licking down to where her pulse beat rapidly. ", "He stroked his hands caressingly down around her breasts cupping and lightly pinching her nipples. ", "She gasped taking in the musky scent of his skin and couldn't stop the moan that escaped caused by his ministrations. ", "His sweet touches made her body ache and long for more. ", "Kissing his way down to her breasts he took a nipple into his mouth, lightly suckling one and then the other, bringing them to an almost painful peak.", "\n\nAlarr moved his right hand down to curve around her hip and onto the center of her thighs, the place on her body that she most ached. ", "She was so wet and ready for him, her body felt as if on fire. ", "Danielle's passionate moans turned into whimpers. \"", "All will be well, Danielle, I will be as gentle as I can be,\" Alarr consoled, interpreting her whimpers as hesitation.", "\n\nAlarr leaned back and looked at her hungrily, taking in the vision of her most precious part between her thighs, and quickly divested himself of his clothing. ", "Lids heavy with desire, Danielle forced her eyes open to watch as Alarr began kissing his way up her body. ", "As he rose above her, she admired the wonder of his broad shoulders and sleek blonde hair as it fell to curtain around her face. ", "Lowering himself to take her in another breathless kiss, he gently worked himself into her innocent core. ", "As she felt the sharp sting of him penetrating her barrier, her only thoughts were of her love for him and the future that they would forge together. ", "Their passion grew and peaked, each crying out their pleasure as Alarr bit into the pulsing vein at her throat. ", "As he fed on her blood and drew the physic sexual energy he required, she felt the pull of the chains they had donned during the binding ceremony, cementing their consummation. ", "A feeling of unity came over Danielle as she shuddered in Alarr's strong and steady arms.", "\n\nShe mentally reached out to him to test their newly formed connection. \"", "Oh, Alarr, how long I have waited for this...for you.\"", "\n\n\"So have I, Danielle.\"", "\n\nAs Alarr rolled onto his side tucking Danielle in the crook of his arm, he slowly caressed her back. \"", "Isn't this strange? ", "I can hear what you're thinking and feeling,\" Danielle projected through her thoughts. \"", "Can you hear how happy I am at this very moment, Alarr?\"", "\n\n\"Yes, Danielle. ", "As am I.\"\n\nSated from their shared passion, she sleepily replied, \"Oh, Alarr, we will love each other forever. ", "Goodnight, my love.\"", "\n\n\"Sleep well, Danielle.\"", "\n\nAs Danielle closed her eyes entering her slumber and being dragged deeply down into the oblivion of sleep, she caught a last escaping thought from Alarr, \"I've secured my station...Won't feel guilty...I know I'll come to truly love her in time...\"\n\n*****\n\nAs Danielle awoke the next morning, she realized that she was alone in their bed. ", "Alarr had already left for preparation of the coming battle. ", "Memories of his last thoughts slammed into her, tormenting her. ", "She couldn't believe he had chosen the binding with her for anything less than love. ", "Goddess! ", "This meant forever! ", "Anything less would mean an eternity of misery. ", "She realized binding with her would raise his status in their ranks but believed his intentions to be honorable. ", "She was a fool to think any man could truly love her. ", "Unfortunately, she had no more time to ponder her situation now. ", "She had to ready herself for battle against the demon Huldrekall and join the others. ", "They must retrieve the Eye of Odin at all costs.", "\n\nRising to don her battle gear, Danielle knew that her confrontation with Alarr would have to be delayed until after the battle. ", "She hoped he would reassure her that she was wrong. ", "She clung to that hope and steeled herself for the battle ahead.", "\n\nShe made her way outside the castle searching for a glimpse of Alarr and was unable to mentally connect with him. ", "Finding none, she put up her own mental barrier, marched with her fellow warriors, gathering on the shore of the North Sea.", "\n\nWith the roar of the battle cry rising around her, she put all thoughts of betrayal out of her mind and engaged the enemy demons with the ferocity of the true warrior that she was. ", "Slicing through the fray with her mighty sword. ", "A sword forged for her alone that was spelled to aid her in her efforts as a Freyodin Warrior. ", "A weapon that had been bestowed upon her by the Goddess of war herself. ", "No one else could make the weapon perform as she could.", "\n\nThe battle raged on and on. ", "It seemed almost insurmountable. ", "Danielle watched as many of her fellow Shieldmaidens, friends and warriors lie wounded and dying around her. ", "Blood and death were everywhere. ", "She saw Emeline and other healers racing about attending the wounded. ", "Wand wielders used their magic spells to amplify the strengths of others. ", "Shields threw up their protection spells all around. ", "Even Myste, with her hair flowing black as night, was raining down thunderbolts side by side with Thunder. ", "But there seemed no end in sight and no greater battle had been fought with such cost.", "\n\nRefusing defeat, she battled on with her mighty sword until an unbearable pain racked through her entire body. ", "It felt as though her soul was being ripped from her being. ", "With an agonizing scream, she fell to her knees and knew nothing more...\n\n*****\n\nDanielle started and opened her eyes, waking in a cold clammy sweat. ", "She was still in flight. ", "She tried to push down the bitter memories and wounds of her past that the dream had awakened. ", "Multitudes had died that day, including Alarr, and the Eye of Odin was never recovered. ", "Lost, they said. ", "But at least the demon horde didn't still have possession of it. ", "Better lost than in their hands. ", "The horrors on earth would be endless.", "\n\nBecause of their bonding, she had felt Alarr's death immediately. ", "Although his body was never found, she felt it in her soul that he was no more. ", "She wrapped her fingers around the chain still located around her neck, where it would stay, removable only upon death. ", "A reminder of her bitterness and the resentment she harbors, of who she is and the position of her life that haunts her, keeping her from being the ordinary woman she wishes to be, immortal or not.", "\n\nI never wanted to be a demi-goddess anyway.", "\n\nAll the perks seemed to be on the negative side and she'd gladly give it up any day. ", "But no one offered her the option of picking door number two. ", "Unfortunately, life, or in this case, immortality, just wasn't a game show.", "\n\n*****\nChapter Three\n\nThis was the location in Zahara's vision. ", "As Freya had foretold, she could feel the presence of the binding chain in the area. ", "She was in the right place.", "\n\nShe breathed in the salty sea air and was thankful for the shrouded cover of night. ", "The moon was not shining its brightest as the clouded skies obscured its pathway toward the earth's surface. ", "Very few stars were visible in the smoky tinted heavens. ", "She wouldn't need to utilize her shadowing skills that normally would cloak her from the view of unsuspecting mortals.", "\n\nOr would she? ", "She knew she was alone in the sense that no mortals were about, but something was near. ", "Something not quite ominous or threatening, but a presence none the less. ", "Whatever it was, it masked its existence successfully like an unseen specter, with an almost non-existent manifestation.", "\n\nOr maybe it was just her imagination because Danielle had a great sense...of the paranormal or otherwise, and being paranormal herself assured her of that. ", "She was probably just spooking herself because of this assignment. ", "If you could really call it an assignment. ", "Moreover, it was her duty to retrieve the binding chain. ", "A duty she dreaded more than ever after reliving the horrid past via her nightmare on the plane. ", "Too bad she couldn't get one of the guys to erase that particular memory. ", "But that neat little trick wouldn't work on her.", "\n\nYes, that's what it was. ", "Just her nerves working overtime. ", "Best to get on with it then.", "\n\nAfter a quick reconnaissance of the building and surrounding area, Danielle determined there were no guards or alarms to disarm. ", "That was a promising sign. ", "This mission might play out easier than expected. ", "Goddess, I love a quickie. ", "She snickered quietly to herself, glad that her mood had improved somewhat. ", "Nobody liked a 'Debbie Downer,' or in this case a 'Downer Danielle\".", "\n\nWith a deep breath and a quick shiver to dispel the lack of confidence she felt about this assignment, she grabbed her tool kit from inside her leather coat and proceeded to pick the lock of the solid steel door in front of her. ", "She preferred not to trace into unknown buildings. ", "Safety first. ", "Being immortal is no excuse for carelessness. ", "Running into something hard or sharp in the dark could be a real bitch. ", "Besides, it hurt.", "\n\nEntering the pitch black warehouse with caution, she immediately regretted not having the forethought to bring one of the guys along to be her eyes and ears on this one. ", "She could have used a pair of those wondrous preternatural eyes right now. ", "Why didn't I get that nifty little gift? ", "Because you're not a vampire, dip shit! ", "Alright, this was no time for jealousy. ", "Ahh, but Ghost would have been especially useful with his invisibility skills. ", "Another thing she'd never have. ", "She'd have to give herself a good ass-kicking later, but for now, she had a job to do. ", "She was just too disturbed by the discovery of Alarr's binding chain, and all that it might imply, to think clearly enough to have handled this mission on her own. ", "Berating herself once again, she realized that she really had to get her head in the game. ", "Oh well, she'd just have to enter blindly, or rather with her standard issued flashlight.", "\n\nWith a click, she was able to maneuver around the room enough to see tall, metal shelving lining the walls laden with objects that had been retrieved from the site where the digging was taking place. ", "In the middle of the room, long worktables ran parallel to one another down the length of the room. ", "Archeological tools for examination, along with a few finds in various stages of cleaning cluttered on the surfaces. ", "Knowing the chain was somewhere nearby, she wished she had another nifty little gift like an alien tracking beam would be really nifty about now. ", "She snickered to herself.", "\n\nSupposing this was as good a place to start as any other in her search, she perused the shelves and tables as quickly and quietly as possible but saw nothing remotely resembling what she sought. ", "Albeit, there sure was a lot of dirt and dust. ", "She felt the overwhelming need for a coughing fit but managed to hold it in. ", "Bins full of dirt, covered by what she thought to be straining screens of some sort, sat haphazardly around the room. ", "Obviously used for sifting of smaller objects. ", "Didn't even play in the dirt when I was little, now I have to go through all of this? ", "Yuck!", "\n\nEven as stealthy as she was, she knew she was busted when bright light suddenly flooded the darkened room.", "\n\nOh well, can't win them all, she thought as she turned, armed and ready for confrontation, toward a deep, rich, male voice clearing his throat. ", "When she met his gaze, she got lost in the abyss of his deep blue eyes.", "\n\nWow. ", "He's beautiful. ", "He was unarmed and didn't look threatening. ", "Shirtless and clad only in rumpled pajama pants, she took him in from head to toe. ", "His sandy blonde hair was disheveled with a bad case of bedhead syndrome and a strong, square jaw that needed a shave. ", "Then there was that mouth...that very kissable mouth, whose lips tilted upward in a quirk showing a bit of curiosity. ", "Intrigued she continued her gaze downward admiring the tanned muscular build of his bare chest. ", "Hairless, I like it. ", "She could see the definition of every sinewy muscle, his flat stomach, then the fine arrowing of hair below leading to a pronounced V shape of his hips pointing the way to a nice sized bulge at half-mast that was strategically hidden by his pajama pants - until it twitched slightly under her gaze.", "\n\n\"Are you quite finished?\" ", "he inquired very calmly.", "\n\nSnapping back to reality, she replied, \"Excuse me?\" ", "She realized she had completely forgotten to try and shadow herself or trace out of there. ", "Oops.", "\n\n\"Checking me out. ", "Have you seen enough yet? ", "Or should I turn around and give you the full tour? ", "And while we're at it, who are you and what are you doing in my facility?\" ", "Aaron didn't feel the least bit threatened but was definitely intrigued. ", "What was this black leather clad beauty doing sneaking around here?", "\n\n\"Firstly, I wasn't checking you out,\" she lied unconvincingly. \"", "Secondly, my name is Danielle and I'm looking for something I've lost that belongs to me,\" she confessed, not knowing why she offered so much information. ", "Goddess, she felt so embarrassed, which was kind of pissing her off. ", "She could feel the reddened flames crawling up her neck and onto her face, so wishing he'd turn the lights back off. ", "She should just conk the guy on the head and continue her search unimpeded, but for some reason she was drawn into the conversation, almost compelled. ", "I'm so screwed.", "\n\nWidening his stance, he folded his arms across the front of his chest displaying beautifully defined biceps and raised his eyebrow into an expression of disbelief, staring narrowly at her. \"", "You were so checking me out, Danielle.\" ", "He realized sarcasm wouldn't get them anywhere so he changed his tactics. \"", "What is it that you've lost? ", "Perhaps I can assist you in finding it,\" he offered.", "\n\n\"Believe me, if I was checking you out, you'd know it, buddy,\" she threw back sassily at him placing her hands on her slender hips. ", "This was a distraction she didn't need. ", "A gorgeous distraction, but a distraction none the less. ", "She had to keep her mind on the mission and find the chain.", "\n\nRealizing he was starting to annoy her and enjoying it, he continued the banter in a playful manner. \"", "Oh, I'm absolutely positive, and turnabout's fair play,\" he chuckled slightly then began to move toward her, slowly making his way nearer to his would-be burglar. ", "Obviously, he wasn't the least bit apprehensive of Danielle's unexpected presence, but then he didn't realize he was confronting an immortal warrior with superhuman strength.", "\n\nAgain, she zoned out and stared glassy-eyed at him. ", "All she noticed was the sleek, sexy swagger in the way he moved towards her. ", "Holy Hell, what is wrong with me. ", "Concentrate!", "\n\nWith one hand on her concealed weapon, Danielle braced herself, widened her stance and put up the other hand in front of her signaling him to stop. \"", "Hold it right there. ", "Don't come any closer. ", "I wouldn't want to have to hurt you.\"", "\n\nAlthough she had a veritable arsenal hidden in her leathers, hurting him was the very last thing on her mind at the moment, unless it was in a very good way. ", "This was so not the time to have a John Cougar Mellencamp melody running through her head. ", "She sure didn't want to bruise the merchandise so she'd just have to play it cool and hope to get out of here as quickly as possible. ", "Then she'd get Ghost to come back with her to continue the search. ", "Thunder would just have to understand about the delay, somehow...\n\nAs he walked toward her, he blatantly ogled her body by making a mental account and cataloging ever detail to memory. ", "She was quite tall for a woman. ", "He estimated her to be about five foot ten, with true hourglass curves. ", "Beautiful blond hair streaked with red and brown highlights which was braided and hung down to the small of her back, penetrating hazel eyes that were once more appraising his physical attributes with interest, and she must have had that black leather outfit custom made because it looked like she'd been sewn into it. ", "The black vest revealed a pair of the most beautiful breasts he'd ever seen, or at least they would, if she'd let him remove it. ", "She certainly wasn't one of his crew or workers and she didn't look like she belonged around here in any fashion. ", "Although he wasn't normally the type to consistently peruse the fairer sex, he would have noticed this one for sure.", "\n\n\"No need to get violent, Danielle. ", "I'm not going to hurt you.\" ", "He wondered if the woman had actual training or if she was relying on some community self-defense type course that had been given by her local police or fire department. ", "By looking at her, he guessed it wasn't the latter. ", "He threw his hands up in surrender and continued to come nearer, stopping with only an arm's length between them. ", "He could smell her scent even through the stale dust filled air that surrounded them. ", "Vanilla and spice. ", "Intriguing.", "\n\n\"Not even a concern on my part, Mister. ", "So, what's the verdict?\" ", "Danielle swept her arms out in front of herself as if she was a merchandising model on a game show and her body was the display. ", "She still refused to admit she had started the obvious ogling. ", "Maybe if she just moved on and concentrated on his...\n\n\"I'm afraid I may insult my own intelligence by answering that question and offend you in the process, which I really don't care to do either of. ", "I must insist on reserving judgment at the moment. ", "Further investigation and analysis are required to provide a satisfactory and more accurate report.\"", "\n\nDanielle just stared, unsure of what to say, which was very un-Danielle like. ", "Normally, her smartass comments seemed to be readily available without much thought at all. ", "She couldn't recall ever feeling this disoriented, especially in the presence of a man. ", "And what a delicious man.", "\n\n\"Listen, nothing seems to be disturbed here so I don't believe there's any reason to involve the authorities or anything.\" ", "He paused for a moment trying to judge her reaction to the situation, but she continued her doe-eyed stare. ", "Then he smiled at her. ", "And it was a lovely smile, a genuine smile, not one usually given by such an attractive, confident-looking man. ", "Not one of those Yes-I'm-Gorgeous-And-You-Know-You-Want-Me smiles.", "\n\n\"Let me introduce myself. ", "I'm Dr. Aaron Janson. ", "I'm an archeologist from the University of Oregon, in the United States. ", "And you are currently standing in my storage and research facility.\"", "\n\nDanielle accepted and lightly shook the hand that he offered. \"", "Very nice to meet you, Dr. Janson.\"", "\n\n\"And you, as well, Danielle..?\" ", "Aaron said fishing for a last name.", "\n\n\"Please, just call me Danielle.\" ", "Then with curiosity, she added, \"You're very far from home. ", "What's so important that brings you all this way to dig in the dirt?\"", "\n\n\"I'm here in search of an ancient relic.\"", "\n\n\"Hah! ", "Somehow I knew you'd say that. ", "Isn't that pretty much always the case for archeologists?\" ", "she chuckled but then quickly recovered. \"", "I'm sorry. ", "May I ask what this ancient relic might be?\"", "\n\nHe saw no reason not to tell her. ", "She did look rather tough in her black leather get-up but was surely no threat. ", "And she was oh so sexy, too. ", "Thinking with his other brain, he pressed on with his explanation.", "\n\n\"Sure. ", "It's called the Eye of Odin which is rumored to have been lost somewhere in this vicinity around eight hundred years ago.\"", "\n\nShe immediately jolted back to her senses as if a lightning bolt had zapped her right in the ass. \"", "You're searching for what?\" ", "Danielle asked in a surprised elevated voice, not truly believing what she'd just heard.", "\n\n\"The Eye of Odin. ", "Local folklore and legend tell that there was a mythical battle around 1200 AD in which the Eye of Odin was lost and never recovered. ", "I know it's a long shot, but I've recently uncovered information that leads me to believe that the battle was not so mythical after all and the Eye really exists. ", "Hence, my presence in your fair country.\"", "\n\nHoly shit! ", "This is worse than we thought. ", "He's looking for the EOD. ", "Not to be confused with WMDs, but just as potent. ", "She couldn't let him get his hands on the Eye of Odin. ", "Somehow, he was correct in his knowledge that it had been missing ever since that mythical battle he referred to, which of course wasn't mythical at all. ", "But just how did he know? ", "No mortals knew.", "\n\n\"Okaayyy, Dr. Janson,\" she singsonged whimsically. ", "After a brief pause and further thought she continued, \"Maybe I can be of help to you. ", "I'm sort of from around here, you know, my relatives and all. ", "We go waaaay back.\" ", "Chuckle. ", "Chuckle. \"", "I might be able to provide some insight or information that may be useful in your search. ", "Who better to know the local legends of the area? ", "I'd like it if you'd allow me to hang around a bit and help out.\" ", "She really hoped he bought her feigned interest. ", "She had to locate the chain and didn't believe he had even the slightest chance of finding the EOD.", "\n\n\"Please, just call me Aaron, and I think I'd really enjoy having you around to give me a hand.\" ", "Boy, would he? ", "He wasn't quite sure what this sudden attraction was or why he was speaking in tacky double entendres, but he wasn't getting any more sleep tonight and he sure as hell didn't want Danielle to leave. ", "If he let her go, he may never find her again and he'd like the opportunity to get to know her better. ", "Much better. \"", "You can start first thing in the morning.\"", "\n\n\"Sure, that sounds great. ", "I'll just be going now,\" she said quickly, hoping to escape unscathed and before he came to his senses and had her arrested. ", "Well, tried to have her arrested anyway. ", "She passed by him quickly heading toward the exit she'd broken into earlier to leave.", "\n\n\"Wait, you never told me what you lost and were looking for. ", "I'd still like to return the favor and assist you in your quest.\"", "\n\n\"It's an unusual piece of jewelry.\" ", "Wondering how best to put this to make it sound like a legitimate excuse, she continued, \"A family heirloom, a chain, actually. ", "One that I lost around here a while back.\" ", "Like eight hundred years back. \"", "Figured that if you and your crew were digging around the area, you might have stumbled upon it. ", "I'd sure like to retrieve it, if possible.\" ", "She pasted a semi-sweet smile on her face. ", "She had a feeling this relationship was going to be chocked full of half-truths.", "\n\n\"A chain, huh? ", "Could you be a little more specific?\" ", "he inquired with curiosity.", "\n\n\"Yea, as I said, it's very unusual. ", "Made from a rare metal and it sort of... glows.\" ", "Then she quickly added, \"Well, actually it wouldn't be glowing now.\" ", "She hoped he didn't put too much stock into the 'glowing' remark. ", "Why can't I keep my big mouth shut?", "\n\n\"It must be very meaningful to you to go through all this trouble. ", "You could have simply asked, you know.\" ", "Aaron was full of sincerity and it was obvious that he truly meant his offer.", "\n\nShe shrugged her shoulders, rolled her eyes and replied, \"I'm not the type to do anything simply. ", "I'm the more adventurous type.\" ", "When he didn't respond, she continued, \"So, anything like that happen to be found at your dig site yet?\"", "\n\n\"I'm not sure. ", "My workers brought in some items today that I haven't been able to examine yet. ", "They still need to be cleaned, sorted and cataloged, but we could take a quick look if you'd like.\" ", "This was as good an excuse as any to enjoy even more of her company, and he looked forward to the task ahead. ", "With the closer proximity, he might even get the opportunity to touch her at some point. ", "Accidentally, of course. \"", "They're right over here,\" he shared as he moved to the far end of the worktable closest to him. \"", "Please, join me.\" ", "He crooked his finger in her direction beckoning her to him.", "\n\nDanielle sidled up next to him, feeling the heat his body exuded. ", "She breathed in his scent. ", "Spicy, earthy and all male. ", "Yum. ", "She had the oddest feeling that she'd met him before. ", "He reminded her of someone... She just wasn't quite sure yet though who that might be.", "\n\nAaron lifted several small items and began supplying various facts about each. ", "He obviously loved his work and was apparently very good at it, but most of what he said went right over Danielle's head. ", "Not only because she was ignorant about the subject matter, but because her attraction was definitely getting in the way and making it difficult to focus on what he was actually saying. ", "She did enjoy watching his sensuous mouth, though. ", "Thank Goddess there wouldn't be a test later.", "\n\nUnfortunately, their search was fruitless, but with Aaron's invitation to help out around the dig site, she wouldn't get a better opportunity to continue with her own search. ", "Freya had insisted on its recovery and she didn't want to piss off dear old Mom. ", "With that thought, she realized she needed to retreat and report on all she'd discovered, no matter how much she enjoyed the current view. ", "There was more at stake now than just the binding chain. ", "They had to discover just how close Aaron was and stop him from actually finding the Eye of Odin, or at the very least, retrieve it the moment he located it if it really had ended up at this location. ", "She wondered just where he got his information, but would have to focus on that later. ", "No need to make him too suspicious.", "\n\nBy sensuously stretching with her arms raised and bent behind her head, thereby jutting out her firmly pebbled breasts for his viewing pleasure, Danielle stifled a fake yawn and tried to excuse herself for the evening. ", "No reason not to leave him with something to think about. \"", "Thank you so much for helping me tonight,\" she said. \"", "I apologize for not taking a more practical approach in my quest.\" ", "Not. ", "She ambled toward the door adding a little sexy strut to her movements and, with a last perusal over her shoulder, she threw back, \"I'll see you in the morning.\"", "\n\nRegretting that she was leaving and not knowing quite what to say, he spit out, \"We get started bright and early around here. ", "I, uh, look forward to tomorrow. ", "Do you need a lift home?\"", "\n\n\"No thanks. ", "I've got my own transportation.\" ", "With that she quickly exited the building, shot around the corner and disappeared. ", "Literally.", "\n\nFor Aaron, morning couldn't come soon enough.", "\n\n*****\n\nThis is going rather nicely, she thought to herself.", "\n\nFrom a distance, she watched with muted interest as Danielle traced from the dig site. ", "There was no need to follow her. ", "She'd gathered all the information she could gleam for the moment. ", "No, spying wasn't beneath her. ", "Sometimes it was necessary. ", "She smiled slyly to herself as the scent of arousal skittered through the air and brushed the tip of her nose. ", "The atmosphere wasn't rank with the provocative fragrance, but the scintillating waif was promising of things to come.", "\n\nYes, she'd have to keep watch and hope the plan she'd set into motion played out to her expectations. ", "It may be wrong, but she planned to use this to her advantage.", "\n\nShe'd just have to keep waiting for the right time and watching...\n\n*****\n\nDanielle reappeared on the edge of Reine, a nearby fishing village located on the island of Moskenesøya in the cluster of islands called Lofoten. ", "The Shangri-La-like village with a population of just over 300 people lay just beyond the Reinebringen Mountain. ", "Even in the dark of night, the sprawling village dotted with red and white abodes along its coast called to her like a Whooper Swan's noisy but irresistible honking call echoing through the air. ", "The air was cool and the waters calm as she made her way to the small but charming cottage she currently occupied. ", "She looked forward to waking to a familiar and much-missed dawn where the crystal blue lake surrounded by deeply green covered brush would happily greet her. ", "She'd missed the traditional fare available for consumption here, but most of all the local cuisine, she'd longed for bilberries and cloudberries, used in marmalade, desserts and cakes. ", "With a smile, she recalled a time she had cultivated these same wild berries in her own private garden.", "\n\nKnowing she had to report to Thunder about the unexpected findings of the day, but dreading it all the same, Danielle grabbed her cell and placed the call. ", "She feared what this new discovery might entail, but steeled herself for the conversation ahead while the phone made its connection.", "\n\nChecking the display that announced Danielle as the caller, Thunder answered his cell phone without a needed greeting, \"Yes, Danielle. ", "Report.\" ", "Always straight to the point.", "\n\n\"Thunder, you're not going to like what I have to tell you, I'm afraid. ", "First, there's no sight of the binding chain yet, but I've managed to gain a position to assist with the discoveries of the dig site starting tomorrow morning. ", "The problem lies in what they are actually searching for. ", "It's the Eye. ", "The freakin' Eye of Odin.\"", "\n\nStunned momentarily by her revelation, Thunder sat up ramrod straight in his chair, his voice raised steadily in pitch and volume as he inquired, \"The Eye? ", "But how do they know about the EOD? ", "Their mortals! ", "It's only myth to them.\"", "\n\n\"Not sure, but this archeologist named Aaron Janson, from the University of Oregon, tells me that he's recently uncovered information that leads him to believe that The Great Battle was not so mythical after all and that Eye really exists.\"", "\n\n\"And just what is it he's found that leads him to believe this?\" ", "Absolutely nothing came to mind. ", "Surely, no immortal would communicate such information to a human. ", "Whether on the side of good or bad, the secrecy of their existence must be kept, for all their sakes. ", "Pandemonium would ensue otherwise.", "\n\n\"I haven't been able to get that bit of information yet but, like I said, I'm returning in the morning and will prod him further. ", "I'll report any findings, of course.\"", "\n\n\"Most definitely. ", "Keep me apprised immediately. ", "We may have to intervene depending on what you discover,\" Thunder instructed. ", "Innocent mortals would never be harmed, but they may be in for a major memory wipe that would leave them feeling like they weren't in Kansas anymore. ", "Then they would have to follow all of the rabbit trails to any and everyone that had been privy to the forbidden knowledge.", "\n\n\"I'll call you back as soon as I have something else to report.\" ", "Danielle took the opportunity to disconnect as soon as it was offered. ", "Depending on what she discovered, Dr. Aaron Janson might find his little excursion taken over by unwanted guests in the very near future.", "\n\n*****\n\nTormond felt the tormenting but familiar pain coursing through his brain. ", "It was an unwelcomed agony. ", "A tactic used against him for simultaneous torture and a reminder of who was in complete control. ", "He wanted to clutch his head within his hands and longed for a reprieve of even the smallest of relief.", "\n\nIn his crouched subservient position, he watched the God before him as he drilled into his skull with deceptively piercing eyes, unable to retract from the compulsion governing the unwilling vessel he resided within. ", "His deep punishing voice convulsed through him, consuming his mind and body, even to the depths of his very soul, though there was little of that left to be had.", "\n\n\"What is taking so long, Tormond? ", "I am not pleased! ", "I must have the Eye of Odin, to be able to locate the Spear of Truth and the Heart of Hope. ", "This is a race against time and as of now the Gods are unaware of my actions in seeking the relics. ", "If Freya and Odin discover what's taking place right under their noses and find them first, they will be able to banish me from the mortal realm. ", "I will not allow the Gods to deny me access to my playground that I have enjoyed for centuries. ", "It is bad enough their warriors intercept so often in my musings. ", "You will get me the sacred relics or face the consequences.\"", "\n\n\"I have hired a human and provided him with all of the necessary documents needed to locate the Eye of Odin and soon you will have it in your hands, Father,\" Tormond rasped through ragged breaths, kneeling before Loki's sacred shrine.", "\n\nAlthough fierce, Loki was seductively handsome draped in his royal garments of emerald and gold and appeared before him like the air that seemed to move in shimmering waves above a heated highway. ", "He was known as the Trickster God with evil intentions, called the Originator of Deceits, and the disgrace of all Gods and men, possessing the powers of fire and magic.", "\n\nTormond knew well the punishments that Loki was capable of inflicting when dissatisfied. ", "He had seen and experienced enough of them over his centuries of service. ", "Loki took pleasure in twisting the most pleasant dream or worst nightmares into a reality that no sane person or immortal could bear.", "\n\n\"As soon as I have acquired the first relic, I will decimate the site and destroy all involved. ", "Our continued efforts to locate the remaining relics will be secure from prying eyes. ", "I assure you.\"", "\n\n\"Do not make me wait much longer, Tormond. ", "My patience is limited and if need be, I will replace you with one of my other Earthbound children. ", "Perhaps a little persuasion is needed.\" ", "The anger drained from Loki's face and with an utterly bored effort, he limply flipped his wrist and snapped his fingers.", "\n\nBefore Tormond could plead for leniency or mercy, his worst fears became reality. ", "He instantly found himself writhing and drowning in a river of lava, the flames licking his entire body, the smell of burnt flesh filling his nostrils. ", "He knew that this event was not physically happening to him and was a complete figment of his imagination, but the experience always felt real, as tangible as the screams he emitted. ", "He felt his skin melting away from his bones, his eyes bursting from their sockets, every nerve within his body alert to feel every excruciating torment as it was given in slow increments. ", "The punishment went on and on until finally his body seized and Loki allowed him the sweet relief of darkness.", "\n\nRegaining consciousness, Tormond realized that the candles had completely melted around the altar where he had previously knelt. ", "The smell of burning flesh lingered in his mind and in his nostrils. ", "His throat felt as raw as a wooden plank that had been stripped of it's protective coat of varnish thanks to the uncontrollable screaming he had emitted. ", "Painfully rising to a sitting position, he reached into his pocket for his bottle of aspirins, popping several into his mouth and chewing them like candy, as he examined himself. ", "The immortality granted to him by Loki afforded his body to take all measures of torture and he would never meet his true rest unless his head or heart was removed.", "\n\nDrained, he craved the blood he needed to replenish his strength. ", "He rose slowly on unsteady legs and shuffled his way to the door. ", "He stood still for a moment, taking in deep restorative breaths. ", "I will not show weakness to any of those beneath me. ", "I must feed.", "\n\nHe couldn't begrudge his father. ", "After all, he enjoyed and used torture to serve his own needs, as well. ", "Although, not with the magnitude Loki managed to do so. ", "He also knew that if he did harness that kind of power within himself, he'd do the same without hesitation. ", "Why dish it out if you can't take it?", "\n\nExiting the altar room, Tormond locked the door behind him and immediately became aware of the sounds rising up from downstairs on the casino floor. ", "The pull of the automated arm, the musical clanging of coins dropping, the clinking of glasses and shouts of elation and despair. ", "Then the pungent smell of a patron smoking assaulted him. ", "A reminder he didn't relish, causing him to cringe.", "\n\nWalking down the narrow hallway he spotted one of his elite personal bodyguards. ", "As he approached, he appreciated the strength the human exuded and took in his physical form. ", "He was built like a mountain. ", "Dressed in a black custom fit suit that covered his double shoulder holster, Stan was the perfect specimen to keep all of the other humans in his employment in line. ", "But Stan was more than that. ", "For reasons he didn't quite understand, he had a soft spot for the guy that bordered on protective. ", "Maybe it was because Stan, out of all his other employees and demonic underlings, was genuine in his role as his bodyguard. ", "He performed his duties above and beyond without expectation like it was an honor to serve him. ", "Everyone else wanted something from him whether it be immortality or a bonus check, they all wanted something.", "\n\n\"Stan, how are my profits this evening?\" ", "Tormond did his best to stand tall and reclaim his authoritative voice.", "\n\n\"A great many losers and no issues with security, Mr. T,\" Stan replied respectfully. \"", "The Fire and Dice Casino is always a winner. ", "Everything is so in line that I'm feeling a little bored. ", "I think I need to go out and have a little fun.\"", "\n\nTormond was not only a demi-god, the son of Loki and leader of his demon horde, he was a successful business owner and had his hands wrapped around the organized crime in the Las Vegas area. ", "The Fire and Dice Casino had made him a wealthy and respected businessman.", "\n\n\"Oh, you'll find something fun soon enough. ", "Now, go downstairs and send Holly to my office. ", "I'm feeling a little hungry.\" ", "Tormond commanded Stan with as much strength he could muster as he continued to make his way towards his office.", "\n\n\"Yes, sir. ", "I'll send her up right away,\" Stan said making his way down the hallway towards the elevator leading to the slot machine area below.", "\n\nOpening the door to his office, Tormond made his way across the plush red carpet, towards his mahogany desk. ", "Seating himself in his high-backed executive leather chair, he pulled his cell phone from his jacket pocket. ", "Noting there were no current messages or missed calls, he dialed Holden, one of his most trusted demons. ", "Impatiently waiting for the call to connect, Tormond mumbled to himself. \"", "Damn cell phones. ", "Holden had better be nearby and pick up.\" ", "He popped another couple of aspirins and ground them between his teeth swallowing down the acidic chalky taste.", "\n\nUpon the second ring, he heard Holden grunt and say, \"Yes, my Lord.\"", "\n\n\"Be in my office in thirty minutes. ", "Bring Hanna and Heidi with you,\" Tormond commanded, trying to keep the urgency out of his voice.", "\n\n\"We will be there, my Lord.\"", "\n\nPressing end and putting his cell phone back in his pocket, Tormond heard a quiet knock on his door. ", "Ahh, my nourishment has arrived. ", "And she's one of my favorites. \"", "Come in, Holly,\" he called out, anxiously awaiting this evening's meal.", "\n\nHolly timidly entered his office, the scent of fear wafting around her. ", "He loved intimidating these puny human females. ", "They were really good for only two things, blood and sex. ", "He often wondered if enthralling them multiple times is what caused their fear. ", "Maybe it had less effect in that instance. ", "He knew it couldn't be caused by his personal appearance or his treatment of them in a normal setting. ", "He was known to be quite handsome, especially with his ice blue eyes and charming demeanor. ", "He was tall, tanned and strongly built with a much better-than-average physique. ", "He kept his lightly highlighted brown hair in a neat, professional men's style, not too long, not too short.", "\n\nHis status and wealth aside, he knew that with his tall good looks alone, he could have any of the women down in his casino with the snap of his fingers. ", "They'd fall all over themselves to rub their willing bodies up against him. ", "But he preferred his women on the unwilling side. ", "They were a bit more fun.", "\n\nHell, he'd topped the list of Las Vegas Sexiest Bachelors just last year. ", "The conclusion must be over-enthrallment.", "\n\nHe would not kill this one. ", "She was one of his favorites to feed from. ", "He'd have to keep a close eye on her though for any signs of recognition. ", "Besides, it was always such a bother having to replace employees. ", "Enthralling would do, once again, for this evening.", "\n\n\"Good evening, Mr. Tormond,\" Holly said with a tremor in her voice. \"", "I've brought you your evening meal and your usual Bloody Mary,\" she continued as she came around his desk to place the serving tray in front of him. ", "Once her hands were empty, Tormond grabbed her roughly, causing her to gasp in greater fear.", "\n\n\"Look at me, Holly,\" he ordered. ", "She reluctantly met his gaze, a look of shock still on her face. ", "He immediately enthralled her to a calmer state, relaxing her, as he drew her down onto his already eager lap.", "\n\nHe moved Holly's long blond hair to the side, longingly watching the rapidly pulsing vein that stretched the length of her neck. ", "She smelled of light sweat and something sweet and he breathed her in as he drew her down to his mouth. ", "Baring his fangs, he pierced her slender neck and the blood flowed pleasingly down his throat causing him to groan as he lapped at her fair skin. ", "As great as his need was, he was mindful of controlling his intake and not leave Holly in an unsuitable condition. ", "She would have to return to work, after all.", "\n\nHis hands trembled with anticipation as he ran them along the hem of her short-skirted uniform, up her silken thighs, grabbed her panties and quickly removed them. ", "Lifting her onto the desk, he released his belt and lowered his pants to his knees. ", "He grabbed her waist and brought her closer to him as he adjusted her to straddle him with her center and plunged to the hilt in one satisfying thrust. ", "He had no concern for her comfort as she whimpered in pain. ", "There were no tender caresses to be shared. ", "His needs were all that mattered.", "\n\nHe lifted her by her hips along his length and as he felt his climax approaching, he resentfully willed her to orgasm so he could receive the psychic sexual feed he required along with her blood. ", "This would add to the replenishment of his strength. ", "Completion was quick with grunts and fleeting moans. ", "No shouts of elations were expected or shared. ", "He closed the wound on her neck with a lick of his tongue, lifted her off of his body and instructed her to get dressed.", "\n\nAfter straightening his own clothing, he placed his hand under her chin forcing her to look into his eyes once more, releasing her from his enthrallment and wiping away the remnants of what had just transpired between them.", "\n\n\"Thank you for bringing my dinner and drink to me this evening, Holly. ", "Now, go on downstairs and continue with your work,\" Tormond said returning to a professional demeanor.", "\n\n\"Yes, Mr. Tormond,\" she replied with confusion in her voice as she slightly wobbled on her way to the door. ", "He smirked devilishly as she turned her back to leave. ", "When she opened the door to exit, he saw the demons he had summoned standing in the doorway, preparing to enter. ", "They glared down at the human, and with a snarl, pushed their way past her, closing the door behind them. ", "The smell of sex and blood hung thickly in the air.", "\n\n\"You needed to see us, my Lord?\" ", "Hanna inquired as she, Heidi, and Holden moved as one to stand in front of his desk, their solidarity reminded him of stiffly marching German soldiers from that World War he barely paid attention to. ", "Inheriting the ability to shapeshift from Loki, the demons could change their appearance as they pleased, but Tormond demanded them in human form in his presence. ", "Hanna had chosen today's human form resembling a young college student with long blonde hair and innocent blue eyes, whereas Heidi had selected short black hair and piercing green eyes. ", "As predicted, Holden maintained his black hair and black eyes. ", "He didn't prefer the option to change frequently as the females did. ", "At well over six feet, he lived to look the vicious demon that he was, which stemmed from the fact that in his human life, he had been a very scrawny, weakling of a man.", "\n\n\"Hanna, you will head to the North Sea excursion site and light a fire under that archeologist's ass. ", "I want that damn Eye of Odin now. ", "It's imperative that I get it soon,\" Tormond instructed, noticing his strength had been restored. ", "Showing weakness was not an option, especially before his demons. ", "Looking at Heidi and Holden, he ordered, \"You two hold down the fort while Hanna is away and keep working on the recruiting campaign. ", "Building our army is imperative for our future needs.\"", "\n\n\"Yes, my Lord. ", "As you command,\" all three answered in unison then turned and exited his office.", "\n\nOnce again, Tormond reached into his pocket for his bottle of aspirins.", "\n\n*****\nChapter Four\n\nNorthern Norway is often described as the land of the midnight sun, a natural phenomenon occurring in the summer months at places north of the Arctic Circle and south of the Antarctic Circle where the sun remains visible at midnight. ", "It is also the land of the northern lights, or aurora borealis, a natural light display in the sky caused by the collision of energetic charged particles with atoms in the high altitude atmosphere. ", "Thus named by the French philosopher, priest, scientist, astronomer, and mathematician, Pierre Gassendi, in 1621, after the Roman Goddess of Dawn, Aurora, and the Greek name for the north wind, Boreas.", "\n\nThis occurrence cannot normally be seen by the naked human eye during daylight hours, but Danielle relished the beautiful and majestic marvel as she walked along the cliffs of her homeland in the direction of the archeological site. ", "She could have quickly traced directly to her desired location, but chose instead to take the scenic route along the coastline, reminiscing about the innumerable fjords, skerries and islands that converged together to create the mountainous cliff she currently trod. ", "As she peered over the rugged edge, she watched the thunderous waves crash angrily against the jagged stacks of rocks below. ", "If she had time, she would have loved to dive far off the precipice and into the deep waters below and swim in the wild current letting the icy, chilling liquid envelope her being. ", "She dreamed of taking long, languid strokes until her mind entered a blissful, thoughtless state. ", "But sadly, that was not to be on this glorious morning.", "\n\nAaron was already busy at work when Danielle arrived, still sporting his bed head look. ", "In typical Aaron fashion, he was wearing a pair of nice fitting jeans and a tight black T-shirt that stretched across an impressive looking chest and biceps that read 'Archeologists Do It In The Dirt.' ", "Danielle couldn't help but visualize that scenario which made her skin start tingling again.", "\n\nSeeing her enter, Aaron set aside what he was examining to give Danielle his full attention. \"", "Good morning, Danielle. ", "I'm so glad you could make it. ", "I was wondering if you truly wanted to get down and dirty with me today. ", "At the dig site, I mean.\" ", "Not. ", "He chuckled teasingly adding, \"If you'd like, I can get you a safety mask to avert any possible respiratory problems that might come up caused from the dust,\" he offered. \"", "I hope you don't have any allergies.\"", "\n\nDanielle acquiesced and sauntered over to him, proffering her hand in greeting. \"", "Good morning to you, too, Aaron. ", "And no, I won't be requiring a mask. ", "I've got a great set of lungs. ", "Thanks anyway.\" ", "She puffed out her chest slightly in demonstration drawing his attention directly to her breasts but trying not to be too obvious. ", "She never was very good at subtle.", "\n\nOkay, so the teasing has already begun. ", "I've really got to find that chain and gather the info on the EOD. ", "Have to stick to the plan. ", "I don't get paid to goof around. ", "Wait a minute, I don't get paid!", "\n\nHe pulled his eyes back to her face meeting her at eye level and noticing the additional glorious features thereon. ", "What a beautiful face. ", "Her moist lips, riveting eyes, a pert little nose, the curve of her jaw, leading down her slender throat to her collarbone and then lower to the inviting swells atop her breasts. ", "Wait, I'm back where I started.", "\n\nClearing his throat, he quickly recovered and motioned to the table behind him. \"", "My assistant, Jake, brought in some additional items this morning. ", "We could start there if you'd like. ", "Come on, I'll give you the speedy version of what I teach at the University. ", "Sort of like speed dating...five minutes here, five minutes there...\"\n\n\"That sounds great,\" she chuckled. \"", "While we're doing that, why don't you tell me a little more about this Eye of Odin thingy you're searching for,\" she said hoping to get him on the right topic. ", "She remembered well her inability to withhold much information last night and hoped there wouldn't be a repeat performance today. ", "She needed to be the one retrieving intel now, not giving it.", "\n\n\"Yes, well, as I mentioned last night, I work with the Department of Archeology at the University of Oregon. ", "I was approached by a private benefactor who had access to some unusual documentation he claimed was passed down in his family over the years. ", "I have someone back at the University, a linguist colleague of mine, working on translating it, but we were able to decipher enough information that led me here to begin the search. ", "You could say that I'm a wee bit impatient.\"", "\n\n\"A private benefactor, huh? ", "Wow, he must really want that Eye thing pretty bad,\" she said fishing for more information. ", "Got to figure out who this person is and where those documents are. ", "They must also be retrieved.", "\n\n\"Yes, it's quite the opportunity and I was very fortunate to receive it.\" ", "He picked up a bin and headed to a worktable that contained a laptop and a number of other archeological tools. \"", "Come on, let's get started,\" he prompted. ", "Before she could inquire further, he said with excitement, \"Oh wow, I think I've found a chain here. ", "Let's clean it up and see if it's the one you're missing.\" ", "He held it up for her review. \"", "What do you think? ", "Does it look familiar?\"", "\n\nDanielle gave a noncommittal gesture as her answer then became excited as well and rushed by his side to inspect what he'd found. ", "Immediately, she felt the attraction to the chain and although she was certain it was Alarr's binding chain due to the lure of the object, she allowed Aaron to take his time with the steps he'd normally take with any other object. ", "She didn't want to arouse his suspicion any more than necessary before she had a chance to actually take possession of it. ", "It currently looked like a broken length of dirty chain.", "\n\n\"I'll just give a bit of going over so that I can examine it more closely. ", "I'll do a proper cleaning afterward.\"", "\n\nShe watched as he carefully donned a pair of gloves and began meticulously brushing the earthly clumps from the chain, cleaning it in a manner that wouldn't add further damage to it.", "\n\nDanielle watched and waited patiently, observing the way Aaron treated his find with such care and concern as if it might be made of sand and crumble right within his hands.", "\n\nAfter the initial cleaning was completed, he began to examine the chain carefully when he asked, \"How old did you say this chain was? ", "I can't seem to identify the material.\" ", "He removed his gloves to get a better feel of the object. \"", "It's some kind of metal but almost fluid-like in its consistency. ", "I've never seen anything like it.\" ", "He looked a little closer. \"", "Wow, if I had to guess\", he lowered his voice quizzically, \"and didn't know any better, I'd say we've uncovered some kind of alien artifact here.\"", "\n\nDanielle chuckled and started intoning the Twilight Zone theme song. \"", "Do do do do, do do do do...\"\n\n\"I know, that's completely ridiculous. ", "There's got to be an explanation.\"", "\n\nFeigning interest, Danielle leaned in closer to Aaron's side to get a better look at the chain in his hands, her arm brushing up against his as she did and suddenly there was a stunning jolt of electricity that shot through both of them.", "\n\n\"OW!\" ", "they both yelled simultaneously while blinking the black spots from their vision. ", "She grabbed the edge of the worktable until her vision cleared and a wave of dizziness had passed.", "\n\n\"Are you alright, Danielle?\" ", "Aaron gasped with concern, his breathing rapid and his heart pounding.", "\n\n\"Yes, I think so. ", "How about you?\" ", "She found his concern flattering and tried to play off the connection they had just shared, hoping he wouldn't delve too deeply into it.", "\n\n\"Yes, quite. ", "That was very strange.\" ", "He had a puzzled look on his face that did nothing to detract from his appeal. ", "If anything, it made him more endearing.", "\n\nIf you only knew the half of that statement, she thought. ", "There wasn't much left in the world that was considered weird or strange to her.", "\n\n\"I suppose I'd better put the gloves back on until I figure out what this is. ", "That was quite a shock.\"", "\n\nDanielle was still somewhat breathless as she noticed the chain wasn't in his hands or on the table. \"", "Where'd the chain go?\" ", "she asked as she took a seat on the opposite side of the table. ", "Distance would be a great thing to prevent another possible shock.", "\n\nHe looked around the table, then checked the surrounding floor, bending down to look underneath it. ", "As he stood back upright, he felt something cold brush his neck. ", "He began laughing and tugging on the neckline of his t-shirt.", "\n\n\"Well, somehow it's wound up around my neck.\" ", "For a split-second, he braced himself for a repeat shock, but nothing happened and he sighed with relief.", "\n\nHe had his arms bent with his hands behind his head to the back of his neck searching for the clasp to remove it. ", "Finding no clasp there, he began rotating the chain on his neck continuing the search. \"", "Can you give me a hand? ", "I can't seem to get this thing off.\"", "\n\nShe joined in his laughter thinking it must be hung up on his shirt. \"", "Glad you didn't say it disappeared. ", "Here, let me have a look.\" ", "If she was really careful she could dislodge the snag from his shirt without touching his actual skin. ", "She didn't know why or what caused that previous jolt, but she certainly didn't want another one.", "\n\nDanielle reached out to assist him with the chain and braced herself for another possible shock, actually dreading any contact with him, at the moment. ", "She tentatively reached for the chain brushing up against him lightly with her fingers. ", "Instead of a shock, the sensation was replaced by a delicious tingling that riveted throughout her body from her fingers to her toes. ", "She suddenly felt flush, her nipples hardening and an ache was building low in her stomach. ", "The look on Aaron's face told her that he'd experienced the same sensation, though neither commented on it.", "\n\nMaybe if we ignore it, it will go away.", "\n\nAs she got a good look, her nervous laughter turned to quiet concern. ", "Holy crap! ", "It has attached to Aaron? ", "Why? ", "He is not Alarr. ", "Danielle conceded that there were similarities between Aaron and Alarr which could explain her first impression of thinking that he reminded her of someone. ", "She now understood that 'remembered' someone was Alarr. ", "Aaron had the same height and coloring, and although he was nicely built, he certainly wasn't near the size Alarr had been. ", "But still, she couldn't shake the peculiar feeling she had that ambled somewhere in the back of her consciousness.", "\n\nDanielle knew that once attached, the chains were only removable by death. ", "Oh Goddess, what was she going to do. ", "How can I explain this to him when I don't understand it myself.", "\n\nAttempting to rein in her panic, she quickly removed her hands and said, \"I'm afraid I can't find a clasp either. ", "It's too small to remove over your head. ", "Maybe we can cut it off or something,\" she said while putting the distance back between them.", "\n\nShe knew full well this was not possible, but she needed to tell him something to postpone until she could get some help from the others. ", "She avoided eye contact hoping he couldn't see the lies she was forced to tell him. ", "And forced it was with that almost-compulsion-to-tell-the-truth thing going on, giving her a feeling of dismay and sadness she was sure ran to the depths of her soul.", "\n\n*****\n\nAaron was rather unconcerned with his current dilemma. ", "It was only a chain after all. ", "He was more preoccupied with the beautiful woman in the room. ", "He had resumed working in order to take his mind off of her, but it wasn't working quite as well as he'd hoped. ", "He couldn't explain his reactions when she had touched him earlier. ", "A rush of heat inflamed his body and his cock hardened uncomfortably within his jeans. ", "He fought the impulse to reach down and rearrange himself.", "\n\nHis scientific mind insisted he explore the cause of the initial shock, but his body knew firsthand the reaction to her nearness. ", "When her hands had brushed against him and the tingling sensation began, an overwhelming craving for more of her touch consumed him and now he fought hard against the urge to reach out and drag her across the table that separated them.", "\n\nAt least Danielle's demeanor had improved. ", "Before resuming their work, he had the crushing feeling that she was saddened. ", "Maybe she felt responsible because it was her property. ", "Or at least he thought it was her property. ", "She'd never quite answered his question. ", "And what strange property it was. ", "He had a lot of new questions to find answers for.", "\n\nAaron's eyes drifted toward her. ", "She looked incredibly sexy and inviting in dusty jeans and a red top that stopped just above her navel. ", "She pushed stray loose hairs from her face and shook her head, tossing her long silky braid over her slender shoulder. ", "Looking up, she noticed his attention on her and smiled nervously.", "\n\n\"You have a beautiful smile, Danielle.\" ", "His voice was warm and soft, belying the sudden desire in his stormy eyes.", "\n\n\"Thank you. ", "I like your smile, too,\" she said unable to look away, her heart rate began to soar and her breath shortened. ", "The heat reflected in his deep blue eyes made her yearn for his touch drawing her like a moth to a flame. ", "She felt the result of that heated look as moisture spread between her legs dampening her panties.", "\n\nUnable to resist further, he rose from his seat and stepped closer to her, never losing contact with her beckoning eyes. \"", "Danielle,\" he said in a deep husky voice. \"", "Can I touch you?\"", "\n\n\"Yes. ", "Please...\" Her soft voice mirroring his fervent need.", "\n\nHe slowly lifted his hands cupping her face in them, his thumbs brushing over her cheekbones. ", "Skin soft as satin. \"", "I have to touch you, Danielle. ", "You're so beautiful. ", "I've never seen anything so beautiful, felt anything so exquisite.\"", "\n\nShe felt the tingling jolt return, racing through her body as he touched her. ", "Her skin heated wherever he stroked causing her body to tremble. ", "He ran the pad of his thumb over her lower lip, moving down to her throat, caressing her with intimacy and passion. ", "Her pulse and breath increased and her eyelids became so heavy they closed of their own accord.", "\n\nHe lowered his face to hers and took her willing mouth in a demanding and hungry kiss, licking along the seam of her lips until she opened for him. ", "Eagerly sucking his tongue into the warm recesses of her mouth, Danielle met his kiss greedily, marrying her tongue with his, exploring each other in a sensual dance.", "\n\nHer body readied for his welcomed invasion, tightening, clenching and aching for his touch. ", "He lifted her from her seat, wrapping one arm around her waist and pulled her to him. ", "He pressed his lean hips to hers revealing the hardness of his erection directly against the seam of her jeans.", "\n\n\"Feel what you've done to me. ", "I'm on fire for you,\" he rasped and his panting breath matched her own.", "\n\nTrying to gather her senses, she pushed him away gently. ", "Aaron searched and saw the confusion clearly reflected on her face. ", "The nagging voice of doubt intruded her mind like a thin fog making her unsure this was a wise decision. ", "Unsure of what to say or do and so not used to being this out of control of her emotions.", "\n\nStill, lust permeated the air and the intensity was crushing. ", "He wanted her. ", "Wanted her with a passion and need he'd never felt before. ", "Wanted to feel her soft skin next to his, to suck her heavy, supple breasts in his eager mouth and lap her taut nipples with his tongue. ", "Wanted her under him naked, to fill her everywhere he desired until they were both sated and drained. ", "Although the current place and timing were not convenient to carry out his wishes, he couldn't wait any longer.", "\n\nThe heat that was evident in his eyes was contagious. ", "Her own hazel eyes flared brightly as images flooded her mind of just what he might do to her. ", "She could feel his length jutted against her sex through her jeans, but it wasn't enough. ", "She wondered what his cock would feel like in her hands, how thick, long and hard it was when erect. ", "But she had no chance to find out as the decision was suddenly ripped from her.", "\n\nShe looked at him and when their eyes met the wanton gaze on her face was all the permission he needed to the unasked question between them. ", "He recognized her need was as great as his. ", "With a wild, hungry look in his eyes and growled, \"I have to have you. ", "Now.\"", "\n\nLabored breath escaped her body in a rush as he drove her up against the wall, crushing her inviting mouth with his and grinding his strong hips against hers. ", "Taking her mouth with forceful, deep strokes of his tongue, showing no mercy. ", "Danielle returned his kiss just as aggressively meeting his hips grind for grind. ", "Raising his muscular jean clad leg, he wedged his knee between her already weak thighs and began rubbing against the apex of her legs. ", "She submitted fully, letting go and allowing her body to float away as on a sea of sensations. ", "His swollen cock flexed against his body, aching to be free of confinement. ", "He groaned, needing to be buried deep within her.", "\n\nWithout pause, she reached between their bodies to unfasten his jeans, reaching down to fill her hand with his hard, rigid length. \"", "Yes, please...\" she moaned breathily. \"", "Now.\"", "\n\nForeplay forgotten, neither took the time to explore or revel in the sight of the other, nor was there shared tenderness or fond caresses, but she didn't care. ", "The urgency and heat were explosive, the ache between her legs unbearable, and all she wanted was to ride him until the ache was gone.", "\n\nWith one arm encircling her waist, he hurriedly used the other to push his jeans down just past his lean hips then quickly did the same with hers, only removing one entire leg with her hasty assistance, the rest pooling around her calf. ", "Clumsily, they completed the task of partially disrobing while managing to cling to one another. ", "The fingers of cool air suddenly touched their exposed skin. ", "Hungry lips meeting time and time again between constrained movements. ", "Then, in what seemed one graceful, fluid movement, Aaron grabbed her bare ass, lifted her and entered her, thrusting to the hilt in one stroke. ", "Roughly, he recaptured her swollen, crimson lips stifling the sounds of their cries as they joined.", "\n\nAaron paused reveling in the feeling of being inside her. ", "So tight, so perfect. ", "He felt a fleeting twinge of guilt at the way he was treating her, but she seemed to be a more than willing participant. \"", "Danielle, you're so hot, so wet. ", "I couldn't wait any longer,\" he whispered in her ear as if apologizing.", "\n\n\"Then don't. ", "It's okay,\" she panted. \"", "Take me, Aaron,\" she whispered back, nipping at his earlobe and down the side of his neck. ", "It had been so long since she truly desired someone this much. ", "Too long.", "\n\nThe rough exterior of the cement wall rubbed against her back as he pumped into her hard. ", "Not slow, not easy. ", "Hard, with a feral need that wouldn't be denied. ", "Thrusting to her core. ", "Calloused fingers held her hips with bruising force as he pummeled into her, over and over again and she welcomed his thrusts wrapping her arms around his neck and latching on. ", "Her juices dripped from her scorching, wet pussy, coating his cock and running down his trembling thighs.", "\n\nGasping for breath, she hung on and rode him hard right back, digging her nails into his shoulders, but trying desperately to maintain a modicum of control so as not to injure him with her inhuman strength. ", "He tilted his hips at an angle that caused delicious friction against her clit with each of his strokes, moving her closer to orgasm. ", "She threw her head back moaning and calling his name as she tightened her inner muscles around his rock hard cock. \"", "Aaron... you feel so good... Don't stop.\"", "\n\n\"Yes, baby, that's it... Squeeze me hard. ", "Make me come inside you.\"", "\n\nMoans, grunts and sexy slaps of skin on skin were the only sounds to meet their ears. ", "The smell of shared sex was heavy in the air diminishing the dusty atmosphere. ", "Body heat emanated through the material of their clothing, soaking them to their skin.", "\n\nAaron tightened his jaw, fighting to maintain control. ", "He reached down between them stroking her swollen clit, causing her to arch her back and cry out. \"", "Oh, Aaron, I'm coming...\"\n\n\"Ahh, fuck.\" ", "Aaron threw back his head and with a curse followed her over the edge. ", "She gripped him tight with her inner core and felt every pulse of his cock as he filled her.", "\n\nWith their breaths still ragged and hearts still racing, Aaron held on to Danielle feeling her shudder in his arms.", "\n\n*****\n\nAaron slowly lowered Danielle on her unsteady legs depositing a slow sweet kiss on her lips. ", "They parted somewhat awkwardly and then each corrected their clothing in silence.", "\n\nSummoning her courage, she managed to look towards him but was unable to meet his gaze. \"", "Wow, I think we just gave new meaning to the term 'Wham, bam, thank you, Ma'am',\" she said nervously, trying to lighten the mood and somewhat alleviate the tension-filled room.", "\n\nWhat the fuck just happened? ", "Am I a complete wench, or what? ", "Although she was no angel and had certainly been around the block her fair share over the past millennia, Danielle had never experienced such wanton lust before. ", "Her strange attraction to Aaron was one thing, but to feel so out of control, wanting to surrender in such an unrestrained manner, was completely out of character for her. ", "Giving control in any area of her life to any male of any species was definitely not in her Top Ten. ", "Hell, it wasn't even on her list. ", "She'd fought too many years, figuratively and literally, to get the respect she deserved as a woman. ", "She was not, nor had she ever been, a weaker sex just because she is female. ", "She earned her position within the ranks just as everyone else did, male or female. ", "She saw to it that she received no differential treatment due to her lineage, but it was a constant battle, it seemed. ", "If she could turn back time and be born of someone other than their Goddess, that's exactly what she'd choose to do.", "\n\nCould it be the chain? ", "If so, how and why? ", "Yes, Aaron is now wearing the other half of her bonding chain, but she wasn't bound to him. ", "It didn't work that way. ", "Not without Freya's blessing and they certainly couldn't hear each other's thoughts. ", "Thank the Goddess. ", "Hopefully, Zahara would be able to shed some light on this. ", "But, wow. ", "Who knew a science geek could be so passionate. ", "For surely that's all that was between them. ", "Simply lust.", "\n\n\"Yes, again I must apologize. ", "Not for doing it, but for just jumping you the way I did,\" Aaron offered as he awkwardly crossed the room to get some space between them. ", "He needed to think. ", "He felt bad about basically assaulting her, even if she was willing. ", "It was crude and he wouldn't blame her if she didn't want to have anything else to do with him. ", "But she wasn't running out the door to get away from him and her moans said she hadn't abhorred their joining either. ", "They obviously were both a little embarrassed with the situation. ", "He'd make up for it next time, if there was a next time. ", "And he definitely wanted a next time.", "\n\nWhat was it about her exactly? ", "She was tough, breathtakingly beautiful, but also very cocky in a smartass kind of way. ", "He liked that about her. ", "But he really knew nothing about her, definitely didn't know if he could trust her after the B and E she pulled last night. ", "And what was up with this chain? ", "Why such interest and why couldn't he get it off. ", "She had some serious explaining to do. ", "It was obvious she knew a whole lot more than she was saying.", "\n\nWhen Aaron looked up, Danielle had made her way to the door and was posed to exit. ", "She half turned her body in his direction and looked at him. ", "She couldn't stand the defeat she read in his normally handsome face. ", "His unfocused eyes, the downturn of the corners of his mouth, the sunken shoulders. ", "She met his somber gaze, bringing a small smile to her lips. \"", "I wanted it as much as you did, Aaron. ", "Truly, it's alright.\"", "\n\nAaron sighed heavily, somewhat accepting and returned her sweet smile. \"", "Where are you off to?\" ", "He hoped with all his being she would return and let him make this right.", "\n\n\"I'm just gonna check in with a friend of mine about the chain. ", "See what we can do about it. ", "I'll see you again soon,\" she said soothingly.", "\n\nHe raised his hand slightly to wave her goodbye but his smile brightened, his mood lightened. ", "And she knew he believed her.", "\n\nDanielle took a deep breath once she was outside. ", "She leaned against the side of the building and tried to release the tension that was tightening her entire body. ", "She was alone once again. ", "Not only did she need distance from Aaron, but she couldn't shake the feeling of being watched. ", "Chills had run through her as the hairs on the back of her neck and arms stood rigid with the current of electricity flowing through the air. ", "Electricity generated by something paranormal. ", "She was sure of it. ", "Again, it didn't seem to be dangerous or threatening. ", "At least not yet.", "\n\nIt was that same feeling she'd had when she first arrived here last evening. ", "Maybe it had something to do with the site itself because she sure didn't feel it anywhere else and didn't think it was connected to her in any way. ", "Maybe it was a spirit of some kind and didn't like Aaron digging up the past. ", "Yea, that made sense. ", "Perfect sense.", "\n\nUntil I know otherwise, I'm going with that idea, she told herself. ", "Works for me.", "\n\nAmazingly, in all her years, she'd never met any spirits, personally, but had heard that some could be pretty nasty if provoked. ", "And they'd just have to make sure they didn't provoke it. ", "Or at least try not to.", "\n\n*****\n\nAaron and Danielle never saw the elusive figure lurking nearby and observing the events taking place between them. ", "They didn't suspect that anyone or anything other than coincidence could or would have a hand in the situation they found themselves.", "\n\nShe possessed enough power that even Danielle wouldn't detect her, which was her intent. ", "She metaphorically clapped herself on the back, congratulating herself for her cleverness. ", "The binding chain was working out brilliantly. ", "If events continued to travel in this direction, she'd have what she desired sooner than she anticipated. ", "If it weren't beneath her, she'd hop around giddily like a school girl squealing.", "\n\nShe was terribly pleased that the binding chain had indeed attached to Aaron, just as she'd suspected it would. ", "He was the perfect specimen for what she had planned. ", "But the instant attraction between them had even her blushing. ", "That it happened so quickly shocked and delighted her. ", "She'd of course given them their privacy when things began to steam up. ", "Little doubt could be left as to what the conclusion would be and there was no need to be voyeuristic. ", "That just wouldn't be right, after all.", "\n\nShe smiled to herself knowing that this time she'd accomplish what she'd set out to do and she would get what she desired. ", "Now, she just had to be patient and keep watch.", "\n\n*****\nChapter Five\n\nDanielle needed some help and she needed it fast. ", "Zahara was the only one she could think to go to with this, other than Freya, but that option was definitely a last resort. ", "She got the distinct feeling from Thunder that Freya wanted this handled quickly and quietly without intervention from Freya herself. ", "Nervously, she pulled out her cell phone to call.", "\n\n\"Hey, Danielle. ", "How's the mission going?\" ", "Zahara's melodious voice sang across the phone line.", "\n\n\"Well, that depends on how you look at it. ", "There's some bad news and some good news,\" Danielle offered.", "\n\n\"Yes, I've gotten the intel from Thunder regarding the EOD dilemma. ", "Any more news on that yet?\" ", "Danielle could hear the excited rising pitch in Zahara's voice. ", "Hopeful, she pressed on.", "\n\n\"Actually, nothing to report on that yet, but I have another dilemma that I'm hoping you can help me with.\"", "\n\n\"Anything I can do, you know I will. ", "Tell me about it.\" ", "Good. ", "At least she was willing to listen.", "\n\n\"I've located the binding chain but something unexpected has happened to it. ", "For some reason, the chain has attached itself to the archeologist,\" Danielle informed while recalling the strange event.", "\n\n\"Really? ", "But, why? ", "How could that be?\"", "\n\nOh, great. ", "That means no quick fix. \"", "My questions exactly. ", "What can I do? ", "I've tried everything I can think of to remove it. ", "Please help me, Zahara. ", "Freya ordered the chain brought back and I can't very well chop his head off to do that. ", "Well, I could, but I won't. ", "His head is actually quite nice looking where it is,\" she snorted, trying to find some humor in the situation.", "\n\n\"Oh, for Goddess sake. ", "Don't do that! ", "No chopping!\" ", "Zahara shrieked. ", "Zahara's mind raced with knowledge and the possibilities of the situation and decided some more information gathering was needed. \"", "Okay, I'll tell you what. ", "Start from the very beginning and don't leave even the smallest detail out. ", "Sometimes, the answers to these things are in the details or right in our face and we just can't see it. ", "Sort of like that forest for the trees thing, you know?\"", "\n\nDanielle proceeded to relay the story giving all the information she could recall. ", "When she finished, Zahara tried to console her. \"", "Okay, I need to do some research in our ancient scrolls to see if this situation has ever happened before, but honestly, I don't remember anything similar. ", "I'll just double check and of course, I'll try to find a hidden or forgotten way remove the chain. ", "Every once in while these things happen. ", "Sort of. ", "In the meantime, stay near him and don't let that chain get away.\"", "\n\nDanielle was mind numb at this point and nodded her head in agreement, although Zahara couldn't see it.", "\n\nTrying to comfort her again, Zahara offered, \"Don't worry, Danielle. ", "We'll get to the bottom of this. ", "Why don't you enjoy the merchandise while you wait? ", "You sound more than a little interested in this archeologist. ", "Since you have to babysit him for a while till we figure this mess out, you might as well enjoy yourself.\"", "\n\n\"Zahara! ", "I can't believe you just said that. ", "But, if that's an order...\"\n\n\"Hold on. ", "I'm not Thunder, and while you're on a mission, he's in charge. ", "Remember?\"", "\n\n\"Killjoy,\" she called Zahara, not meaning it at all. ", "But she knew that and there was no need to apologize.", "\n\n\"Let me get started here and we'll touch base again soon. ", "Don't worry. ", "Okay?\" ", "she said trying to sooth.", "\n\n\"Yes, okay. ", "But please don't take too long. ", "This really is driving me nuts.\"", "\n\nDanielle knew Zahara would make every effort to find some answers and solve the puzzle they were now facing. ", "She couldn't fathom what that might be. ", "The one thing she did know. ", "She wanted her life to go back to normal and as painlessly as possible.", "\n\n*****\n\nZahara mentally summoned her sister warriors to assist her and those that were not currently on assignment answered her call. ", "Among them were Nadine, the warrior's protector and shield, Annika, the wand wielder, and Emeline, the healer.", "\n\nAlthough they referred to themselves as sister warriors, only two of them actually were biological sisters and were also present. ", "Makayla, who had once been chain bonded, but lost her mate, and Valeria, who was currently chain bonded to Ghost, or Joseph, as was his given name. ", "Their input could be vital, as none of the others had ever made such a commitment.", "\n\nSurely, together we can find a solution for Danielle, Zahara hoped, but being the visionary she was, she wondered just how much Fate had to do with the dilemma at hand.", "\n\nMakayla and Valeria arrived first, tracing in together. ", "They were as thick as thieves and both had the same thing on their minds.", "\n\n\"Tell us what's going on?\" ", "they both chimed in together.", "\n\n\"Not before everyone arrives. ", "We'll give them a few minutes.\"", "\n\nThe others all arrived promptly and Zahara spent a few minutes explaining Danielle's predicament without giving away too much where it concerned Danielle's sexual exploits. ", "Everyone was perplexed and had no personal knowledge to share regarding the mishap that might lead to its resolution.", "\n\n\"Ladies, I've told you all of the relevant information I have and that will have to be enough to get us started on our research. ", "We need to carefully review the ancient scrolls for anything that might either contribute to this situation or indicate a possible solution. ", "I'm afraid until we figure out what caused the attachment we won't be able to remove it, if at all. ", "If you have any suggestions, I'm open to hearing them. ", "I have to admit, this is completely new to me. ", "I'm rather stumped.\"", "\n\n\"I agree. ", "I've never heard of such a thing in all my years,\" Nadine agreed, her disbelief displayed in her big brown eyes.", "\n\nThe others mumbled their agreement, as well. ", "They were all original Shieldmaidens and had died in the same Earthly battle, therefore shared the same number of years together.", "\n\nNadine continued, \"The chain can only attach to its owner and the archeologist couldn't be Alarr. ", "Too bad we know reincarnation isn't possible, well except for becoming immortal, that is.\" ", "Snickering ensued. \"", "That would help matters along a bit.\" ", "A collective accord traveled around the room again.", "\n\nValeria offered, \"Poor, Danielle. ", "I can't imagine what she's going through. ", "I'd just die if I lost my Joseph. ", "I was there when she and Alarr were mated. ", "I helped her dress on her wedding night. ", "I can't believe she's having to relive all of this after such time has passed.\"", "\n\nThis thought brought the ladies back to a more solemn mood and they all settled back into their seats.", "\n\nZahara had an idea. \"", "Why don't we concentrate on what we do know and maybe it will lead us closer to some kind of solution.\"", "\n\n\"Okay, as Nadine pointed out, the chain can only attach to its owner. ", "Normally anyway. ", "Also, for the binding to be complete, it must be blessed by Freya at the binding ceremony,\" offered Emeline.", "\n\nAnnika jumped in with, \"Yes, and that blessing is what allows us to become fertile and bear our young.\" ", "Everyone was thoughtfully beginning to contribute to the topic now.", "\n\n\"And the binding chain is a never ending circle without a clasp that is magically sealed during the ceremony,\" Annika continued remembering the magical qualities of the chain.", "\n\n\"You must truly love your mate to enter into a chain bonding because once consummation takes place the bonding is complete and the bonded mates cannot only speak through their thoughts, as all warriors can but also gain the ability of knowing their mate's thoughts and feelings. ", "Oh, and the chain can only be removed by death,\" Valeria said, again thinking of her Joseph.", "\n\n\"Yes. ", "I, of course, still wear mine although my beloved is gone,\" Makayla added a bit sadly. ", "Valeria leaned into her sister tenderly offering understanding and support and a silent apology for having broached the subject. ", "She would never hurt her sister intentionally and didn't realize that she still suffered after all this time. ", "She loved her dearly.", "\n\n\"As does Danielle,\" Zahara remembered aloud. \"", "She still wears her chain.\" ", "That definitely gave her something to think on.", "\n\n\"Alright, then. ", "I would appreciate the donation of any spare time that you may have to assist me in searching the ancient scrolls, when you're not out on missions or training, of course.\" ", "Zahara knew they'd all do their part to help a sister warrior in need.", "\n\n*****\n\nGhost anxiously opened the front door of his two-story Tudor style home. ", "After a successful mission or training session, he couldn't wait to get home to his bonded mate. ", "He was as high on adrenaline as the other warriors after training, but his gifted talent of invisibility added a sense of urgency that only Valeria could seem to soothe. ", "Although not painful, the alteration of his chemical make-up during transitions would eventually return to normal, but sexual activity could speed up the recovery process and was his remedy of choice. ", "As if it was a hard choice to make.", "\n\n\"Honey, I'm home,\" he called out. ", "He stopped in the bone colored marble-floored foyer and opened the double doors to the side closet to hang up his weapons, then crossed through the living room, with the oversized maroon sectional set front and center of the fifty-two-inch entertainment theater center and the large stone fireplace. ", "The house smelled wonderful. ", "Meat and roasted potatoes...my favorite! ", "Hearing his stomach growl, he called again, \"Valeria, where are you, Mi Amor?\" ", "Hmm, she's blocking again. ", "Wonder what new surprise is in store...\n\n\"Have a seat in the dining room, sweetheart, and I'll be there in just a few. ", "Dinner is ready, and I knew that you'd come in hungry after your practice with the boys.\"", "\n\nHe noticed that her voice carried a sultry manner that belied the kind of hunger she was implying but decided to wait it out and see what she had in store.", "\n\nAs he entered the dining room, and took a seat at the bench style table that Valeria had talked him into purchasing after explaining all of the many fun things they could do on the benches or with the additional chairs placed along the wall for guests that tended to visit from time to time. ", "Sometimes the visits happened more often than he would have liked. ", "He spent all day with his warrior brothers and sisters and most nights all he wanted was to steal a moment alone with his wife. ", "Those moments were always valued and precious, but also exciting. ", "It was this excitement and the inevitable outcome that released the additional adrenaline and calmed him.", "\n\nHearing her enter from the kitchen through the connected swinging door, he couldn't help but stare in awe. ", "After all the years he'd spent as Valeria's bonded mate, she still took his breath away like the first time he'd seen her. ", "She'd stood proudly on the battlefield with her sleekly defined arms and shoulders posed to deliver a deathly blow, with her gifted spear raised in the air horizontally and aligned to her strong but curvaceous body, her rich brunette hair waving boldly behind her and her captivating brown eyes sparkling with golden flecks reflecting the sun.", "\n\nAnd strangely enough in opposition to his remembered image of her, here she was now, wearing a French maid's costume with fishnet thigh highs and five-inch black stiletto heels. ", "Her hair was pulled into a French twist, exposing that long, beautiful swan neck, her most appetizing spot. ", "He felt the lustful ache in his gums as his fangs extended.", "\n\n\"It's always the best moment of my day to come home to you, my wife. ", "You make me so hungry for you, that I no longer hunger for food. ", "Can we play millionaire warrior and sexy maid now?\" ", "he whispered softly growling in her ear while nibbling her beckoning neck. ", "They both enjoyed role playing, not that their love life needed any additional heat, even after seventy-five years. ", "They could still turn each other on at the drop of a hat.", "\n\n\"Joseph,\" Valeria said with a gasping breath, referring to him by his given name. ", "She'd always loved his Spanish heritage coloring and his beautiful accent sent rivers of shivers throughout her entire body. ", "She was breathless, seeing his broad shoulders and muscular thighs that were now stretching the material of his black jeans, straining the zipper with his mouth-watering bulge.", "\n\n\"Just the response I wanted,\" Joseph said as he reached out to her. ", "But she was too quick for him and jumped out of his reach before he could continue. ", "He raised a questioning brow and gave her a mischievous look with a sly grin etched across his face.", "\n\n\"Now, you know that's not how we play,\" she admonished teasingly. \"", "No rushing. ", "Go upstairs, put on the outfit lying on the bed and I'll be there in a few moments.\" ", "She released the block in her mind that she had raised earlier, anticipating the shared sensations they would feel through their bond while making love.", "\n\nStill wearing that sly grin, Joseph obeyed running up the stairs two at a time to their master bedroom. ", "The spacious suite was cluttered with all manner and size of candles, their radiance casting the room in an ethereal glow. ", "He quickly removed his clothes and redressed in the silk robe lying on the bed. ", "He adjusted the pillows on the headboard and lowered himself to the bed, anxiously awaiting his beloved. ", "Hurry, Mi Amor, I' m so ready.", "\n\n\"I'm right here, Mr. Joseph,\" Valeria purred as she greeted him in his 'play name'. ", "She entered the room and crossed to the side table lighting several candles. ", "Their fragrance filled the room with a wonderful vanilla scent. ", "Approaching the bed with two bowls in her hands, one of fruit and one of whipped cream, she slowly lowered to her knees before the bed. \"", "Sit up on the edge of the bed and put your arms behind you so that I can feed you. ", "And no touching,\" she warned.", "\n\nShe knelt down in front of him and from her subservient position, she brought a ripe strawberry to his mouth, brushing his lips in a teasing manner. ", "As he bit into it, juice ran down his chin and Valeria began to lick the trail of juice, following its path from his chin to the corner of his full bottom lip. ", "Joseph groaned, trying to remember to stay in his role and let her enjoy her part in their game, but it was proving to be difficult. ", "She reached into the bowl again and pulled out another piece of fruit, dipped it into the bowl of cream and brought it to his right nipple. ", "Slowly she circled the fruit, leaving his nipple covered in sweet smelling whipped cream. ", "She repeated the same movement and circled his left nipple.", "\n\n\"Oh, look at the mess I've made, Mr. Joseph. ", "I'll clean that up right away.\" ", "She brought her lips to his right nipple and grasped it lightly between her teeth. ", "She used her tongue with a slight but firm suction and proceeded to clean it.", "\n\n\"Aaahh, Val,\" Joseph moaned before she kissed her way to his other nipple and proceeded to clean it also. \"", "I'm not going to be able to control myself much longer if you keep this up. ", "You know I can't keep my hands off of you.\"", "\n\nYes, this she knew all too well and it thrilled her beyond measure. ", "She secretly was glad that he was on the receiving end this time and not her. ", "She planned to enjoy driving him mad.", "\n\n\"Now, Mr. Joseph, I must do a thorough job so that you feel compelled to call for my services again,\" Valeria said as she kissed and nibbled her way around his ribs. ", "She continued working her way down to his hip, then further down to the place he wanted her the most.", "\n\n\"Oh, I will definitely call for your services again,\" he chuckled. \"", "Ahh, Goddess,\" Joseph gasped as she suddenly took his painfully erect cock into her mouth, almost to the root and sucked until her cheeks caved. ", "Valeria moaned as she enveloped Joseph's engorged cock, the vibrations of her moans adding to his pleasure. ", "He slid his hand into her lacy blouse, grasping her nipple between his forefinger and thumb and gently pinched it with a slight twist causing her to moan once again.", "\n\n\"Ah, ah, ah. ", "No touching,\" she admonished pulling back and shaking her head. ", "Her black thong was already dripping wet, her clit so tight and swollen with need, but she had other fun activities planned for him and refused to give into her need just yet. \"", "Mr. Joseph, please lie back on the bed,\" she panted pulling further from his grasp. \"", "I need to make sure that you are thoroughly clean and I have just the instrument to do just that.\"", "\n\nFollowing her instruction, he adjusted himself on the satiny sheets and rested his back against the headboard with his long muscular legs stretched out in front of him. ", "He watched her as she rose to retrieve her toy from the side table.", "\n\n\"Oh yeah, baby, that will certainly do the job,\" he said as he saw the toy. ", "It was a feather duster she had purchased on-line from a specialty store, advertised for maximum pleasure. ", "So far, she agreed that she'd gotten her money's worth. ", "It had long pink feathers on one end and a vibrating bulbous tip on the other.", "\n\nJoseph's fangs were now extended at full length. ", "She brushed back his chestnut brown hair and met eyes that were so green they glowed like Caribbean waters reflecting a brilliant sun, and his golden skin shone in the candle light that encompassed the room. ", "She turned on the vibrator and, straddling his body, firmly ran it from shoulder to shoulder circling it down and around his pectoral muscles.", "\n\nYou're driving me crazy, Val. ", "He couldn't help but release another moan as she turned the feather duster over and brushed a trail down past his stomach leading down to his cock. ", "She brushed him with quick flicks of the feathers, seductively dusting him as if a piece of fine furniture. ", "The feeling was ecstasy sending shivers throughout his body.", "\n\nHis patience at an end, Joseph reached up and grabbed the shoulders of her blouse, quickly dragging them down her arms to expose her beautiful full breasts. \"", "Enough, I can't take anymore. ", "I'm clean!\" ", "he growled, his voice almost feral. ", "Using his vampire speed, he had her blouse up and over her head but hadn't the patience to properly deal with her skirt. ", "With his mouth devouring her nipples, he ripped the skirt from her body and then proceeded to do the same with her thong. ", "Finally, he could give her body the attention he'd been aching to give it.", "\n\nValeria screamed at the aggressive, passionate waves rolling off of Joseph. ", "His mind was repeating words of lust and love in his native language as he proceeded to move his full, sensuous lips up her chest, around her throat, and finally consuming her lips with his hunger. ", "Her body heated as it went up in flames and she couldn't wait another minute. ", "She lifted herself, reached down to grab his stiff cock in her hand and guided it to her anxiously awaiting core. ", "She slammed down taking him to the hilt within her, barely conscious of Joseph's exclamations and began pumping up and down his full length.", "\n\nJoseph knew he wouldn't last long with all of the 'cleaning' he had received, so he wrapped his mouth around her nipple and reached down to find her engorged clit, knowing just how to touch her to drive her to the edge.", "\n\nValeria leaned back, grabbed his knees and opened herself fully for him, giving him better access to pleasure her. ", "But the view of him entering her with her slick juices dripping from her pussy was too much for him. ", "He quickly sat up, grabbed her by the nape of her neck, pulling her towards him and pierced her throat with his aching fangs. ", "Her climax hit instantly and Joseph felt it with her through their bond. ", "He shuddered as he felt her energy prickle over his skin. ", "She came in hard waves, screaming his name and heard his own triumphant yell as he joined her.", "\n\n\"Goddess, I love you,\" Valeria sighed once she was able to catch her breath.", "\n\n\"As I love you, Mi Amante,\" Joseph whispered kissing her tenderly.", "\n\n\"By the way, where's my tip?\" ", "she asked beguilingly feeling her passions rising again.", "\n\n\"I've got your tip right here,\" he said as he dragged her underneath him, placing her in their position of love.", "\n\n*****\n\nAaron sat behind his metal desk in deep concentration. ", "On his desk lay an encrusted sword unearthed in yesterday's dig. ", "Although he could not determine it's age without research and testing, it was obviously very old and valuable. ", "In his mind, it added credence to the mythical battle theory. ", "As he studied the sword, he was distracted by a beautiful, tall blond woman who entered with a straggly young man in tow. ", "Beautiful or not, he didn't recognize her or the obvious flunky that stood beside her as belonging on his team, but she held an air about her that said I-Go-Wherever-I-Damn-Well-Please. ", "Irritated by the interruption and her rudeness of entering without an invitation, he stared hard at her.", "\n\n\"Who are you and what are you doing in my office?\" ", "What's with all these strangers on my site? ", "We certainly aren't open to the public.", "\n\nAs Danielle neared Aaron's office, she felt the vibrations in the air of a demon presence. ", "The putrid stench of sulfur pervaded her nostrils. ", "Silently approaching the door, she turned the knob slowly and heard mention some familiar names that made her blood run cold as an icy river. ", "She peered undetected through the crack in silent observation.", "\n\n\"Dr. Janson, I'm Hanna.\" ", "She did not offer her hand in greeting, which was fine by him. \"", "I work for Mr. Tormond and he sent me to check on the progress of the search for the Eye of Odin. ", "I'm to collect that information and report back to him.\"", "\n\n\"Mr. Tormond, or you, could have simply picked up the phone if he wanted an update. ", "There was no need to send you barging in here unannounced, as you have.\"", "\n\nHanna barely registered Aaron's ill-mannered response as she suddenly felt the presence of a warrior and steeled herself for the inevitable confrontation. ", "She hadn't been paying attention, thinking this was the last place she'd expected to find a warrior as they weren't aware of this project. ", "She knew Tormond had gone to great lengths to hide this excursion from the warriors. ", "She quickly scanned the room for an exit. ", "The minion was unimportant and on his own as far as she was concerned. ", "She'd just get another to replace him later. ", "Weak and evil minded humans were plentiful and littered very corner, crack and crevice of the earth.", "\n\nForcing the shock of the information to the back of her mind for future examination, Danielle quietly drew her sword from the hidden sheath at her back. ", "She kicked the door open with such force it slammed into the wall behind it with a thunderous bang and rushed into the room immediately dispatching the minion with a precipitous downward swipe of her sword. ", "Crimson blood arched across the room in splattered patterns hitting the ceiling, walls and fixtures as his lifeless body hit the cold cement floor in a crumpled heap. ", "Hearing a shocked gasp, she turned ready to engage the demon but instead discovered Hanna heading toward Aaron. ", "Feeling the overwhelming need to protect him, she quickly grabbed Aaron by the arm and threw him out of the way, not thinking to mask her true strength. ", "With arms flailing, Aaron sailed through the air and hit the wall with a loud crashing thud.", "\n\nAs Danielle leaped forward, preparing to strike the demon with a deadly blow, Hanna ripped her garment from her body and quickly shifted into a gleaming black raven and flew out of the open doorway.", "\n\n\"Damn it! ", "I can't believe I let that demon get away. ", "Shit, shit, shit! ", "I should have had her,\" Danielle yelled while stomping her feet madly. ", "She suddenly stopped realizing she resembled a toddler throwing a tantrum and looked around the room for Aaron. ", "She found him seated against the far wall, his posture slightly slumped. ", "He looked a little goofy, but still alert.", "\n\n\"Oh, Goddess. ", "Are you alright? ", "I'm so sorry.\" ", "She reached for him, but he turned her efforts away using a 'stop' motion with his hand held out between them.", "\n\n\"What the fuck was that?\" ", "Aaron moaned, as he picked himself up from the floor and examined himself. \"", "Damn, that hurt, I feel like I was just hit by a truck.\"", "\n\nTrue realization dawned on Danielle too late. ", "Oh, this is totally FUBAR. ", "Shit, what am I going to tell him?", "\n\n*****\n\nChapter Six\n\n\"Danielle, look at me. ", "What the fuck was that? ", "I've got a dead guy lying on my floor! ", "Holy shit! ", "You just killed this guy!\"", "\n\nAaron was freaking out, ranting and pacing back and forth. ", "No bones were broken, but clearly, he was on the verge of going into shock. ", "His eyes were wide, wild and full of fear. ", "Danielle had to get this situation under control, and fast.", "\n\nAs she attempted to approach him again, he froze in place and stared at her still unsheathed sword in horror. ", "Following his line of vision, she realized she was still holding her blooded sword in a stance that screamed 'ready for battle'. ", "The blood oozed downward to the tip of the blade and pooled on the floor beneath. ", "She relaxed her stance, lowered the sword and laid it on the floor slowly, making sure Aaron watched as she did. ", "She'd have to keep it within reach though in case Hanna returned.", "\n\n\"Aaron, look, the sword is down. ", "I'm not going to hurt you.\" ", "She raised her arms in the universal sign of surrender. \"", "I know you don't understand, but I'm going to try and explain. ", "Are you calm enough? ", "Will you listen to me?\"", "\n\nAaron met her eyes, studied her face, watching for any sign of aggression. ", "Seeing none he allowed her to continue. \"", "Go ahead, explain. ", "Although I can't fathom what you could tell me to justify this. ", "My office looks like some gruesome television crime scene.\" ", "He gasped audibly and his eyes lit up. \"", "I need to call the authorities. ", "Oh God, I can see it now...some guy like Monk is going to come in here with his hands out in front of him like he's looking through a camera and find clues that don't exist that link me to this whole thing and I'll wind up in jail or prison in a foreign country.\" ", "He had his hands out in front of his face forming a frame, mimicking the action. ", "And though his tirade and actions were humorous, Danielle didn't dare laugh. ", "She'd store that up for later when he'd calmed down.", "\n\nAs his paranoia grew, he suddenly tensed, realizing he'd probably made a fatal mistake announcing his intentions to report this to the police. ", "It was one of those obviously stupid moves made by inconsequential actors in the movies that guaranteed you were the next to die. ", "She'd just kill him, too, and stop him. ", "Eliminate the loose ends. ", "After all, what did he really know about her? ", "Sure, they'd shared a maddening fuck earlier, but that certainly didn't make him the love of her life. ", "Nor did he want to be at this point. ", "She'd have nothing to lose by disposing of him, too and more to gain if she did. ", "Stepping lightly, he carefully moved back behind his desk to put something – anything – between them.", "\n\nDanielle saw the sudden panic in his eyes. \"", "Please, Aaron,\" she pled softly. \"", "You look like you're about to freak out on me again. ", "I swear I won't hurt you. ", "I was actually protecting you from them. ", "I would never hurt you.\" ", "Danielle really surprised herself with that confession. ", "Then she realized she had hurt him unintentionally. \"", "I mean, I would never hurt you on purpose. ", "That throwing-you-against-the-wall stuff was an accident. ", "She would have hurt you or worse – killed you. ", "I was simply trying to move you out of the way. ", "I just acted and didn't take my strength into consideration.\" ", "Here she was again, spilling her secrets out to him for some unknown reason. ", "Even secrets that she didn't either realize or want to admit to herself.", "\n\n\"But they weren't threatening me. ", "They were sent by my employer, my benefactor, to check on the progress of the search. ", "That's what Hanna was asking me when you came charging in here. ", "Speaking of Hanna, what the hell was that?\" ", "He turned toward the open doorway pointing in its direction. \"", "Did I really just see her turn into a bird and fly away or did I hit my head harder than I thought? ", "That can't be what I saw...\" Slowly and with a blank stare of defeat, Aaron grabbed the arms of his chair and melted down into it appearing very lost and very distraught.", "\n\nShe wanted to console him and understood his confusion. \"", "I promise everything's going to be alright. ", "Whether you believe it or not, they most certainly would have hurt you. ", "Killed you, most likely, when they were done with you. ", "You don't understand who Tormond is and...shit...now I've got to tell you.\" ", "Damn it all.", "\n\n\"What's Mr. Tormond have to do with all this?\" ", "he asked as he motioned to the dead body in front of his desk.", "\n\nAnd there it was, the direct question that would compel her to tell him a lot more than she knew she should. ", "Damn that chain! ", "It has to be the chain.", "\n\n\"Everything actually.\" ", "Seeing he was still seated but seemed a little more in control of himself, she decided just to spit it out, but as vaguely as possible. ", "She was starting to feel cursed. \"", "You saw Hanna transform into a raven because she's a demon. ", "A demon that belongs to Tormond. ", "He isn't a successful business tycoon in Las Vegas, as you probably believe. ", "Well, he's not just that anyway. ", "He's a demi-god, son of the God Loki. ", "And you're right, the battle wasn't mythical. ", "We call it The Great Battle. ", "He's hired you to find the Eye of Odin which went MIA over eight hundred years ago.\" ", "The compulsion to tell him the truth was unrelenting. ", "What have I got? ", "This stuff just comes gushing out like vomit.", "\n\n\"I knew those documents he gave me looked authentic,\" Aaron suddenly sounded excited with this discovery. ", "He sat up straight in his chair and his eyes and smile were beaming. ", "Amazingly, that seemed to be all he picked up from her spewed confession. ", "Go figure. ", "One tracked mind.", "\n\n\"Yes, and unfortunately, I'm going to have to retrieve them.\" ", "She tried to sound regretful but doubted she'd actually achieved the effect.", "\n\n\"Why is that? ", "What right do you have to them?\" ", "He looked at her sternly and suspiciously. \"", "How do I know that you're not here for the same thing? ", "Just who are you, really?\"", "\n\nKnowing at this point it was probably irrelevant, but still attempting to omit as much as possible, which wasn't much, she continued, \"I'm a warrior of the God Odin. ", "And Freya, but no sense bringing her into this. ", "I was sent to retrieve the chain that you're now wearing and discovered what you were actually looking for. ", "We can't let the others get their hands on the Eye. ", "I really can't tell you much more. ", "You've already seen too much.\" ", "And then she pleaded, \"Please, give me the documents that you got from Tormond.\"", "\n\nAaron seemed to relax and accept her explanation. ", "For a scientific mind that normally required proof and fact, he was taking this fairly well. ", "She attributed his trusting attitude toward his already existing involvement in the search for the EOD.", "\n\n\"I only have copies here. ", "The originals are at the university. ", "Should I be worried that Tormond will be after me now? ", "I'm afraid you may have pissed him off and if Hanna could become a bird at will, I don't want to know what Tormond can do.\"", "\n\n\"You're right again. ", "Let me make a phone call. ", "In the meantime, I'll keep you safe. ", "Don't worry,\" she promised.", "\n\nAaron wasn't sure how he felt about a woman protecting him. ", "Should he be offended and insist on taking care of himself? ", "She wasn't exactly the norm when it came to females, was she? ", "He remembered her strength when she threw him up against the wall. ", "Okay, maybe she could protect him, but it didn't feel very masculine. ", "He also wondered just how dangerous she actually was. ", "He decided to take an analytical approach and reserve judgment until he had additional information on which to base his decision. ", "But even now, as he looked at her across the room taking out her cell phone, he couldn't help but notice how sexy she looked as a tough, self-assured female. ", "Yes, she looked every bit the warrior she claimed to be.", "\n\nHow in the hell can I be thinking about how sexy she is, when I'm surrounded by blood and death?", "\n\n*****\n\nLanding on the porch, Hanna immediately transformed back into her human form and entered her secluded cabin. ", "I can't believe this bullshit! ", "A Freyodin Warrior. ", "At our dig site. ", "She ruined all my fun. ", "I was going to get to scare him, maybe hurt him a little. ", "Tormond is going to be so pissed. ", "Damn it, I'm screwed.", "\n\nGrabbing her cell phone, she hesitantly placed her call to Tormond. ", "Fuck, she hated this!", "\n\n\"Speak,\" Tormond commanded. ", "He'd waited impatiently for this call and the news had better be good.", "\n\n\"My Lord, there was a complication we did not foresee.\" ", "Swallowing hard, feeling the sweat run down her back and her heart rate increasing, Hanna tentatively explained, \"There is a Freyodin Warrior at our dig site.\"", "\n\nTormond jumped to his feet, swiping half the contents off of the desk in front of him in a black rage. \"", "What did you say? ", "What the fuck is a Freyodin Warrior doing at my dig site?\" ", "Tormond was screaming so hard he thought he might just pop a blood vessel. ", "This was definitely an unexpected and unwelcomed turn of events. ", "Where are my aspirins? ", "He patted his pockets unsuccessfully.", "\n\n\"I don't know, my Lord. ", "She attacked when I was speaking with the archeologist. ", "It's possible she sensed me in the area,\" she replied timidly.", "\n\nTormond could hear the fear in her voice oozing through the phone connection like a blistering pus. \"", "I'll have to investigate this new complication,\" he almost muttered to himself. \"", "What did you find out about the Eye of Odin?\" ", "Tormond stormed.", "\n\n\"I didn't have a chance to find out anything, my Lord. ", "I felt that it was more important that I let you know about the warrior, so I left...,\" Hanna tried to explain as Tormond interrupted her.", "\n\n\"You incompetent fool! ", "You couldn't take out one simple warrior? ", "I can't believe I sent you. ", "Keep your butt there out of sight and wait for me to get back to you. ", "I'm sending reinforcements,\" Tormond commanded as he disconnected the call.", "\n\nI am so screwed. ", "I fear I'll be ash soon. ", "If he'd only made me immortal, as he promised, I could have eliminated her. ", "Defeated, Hanna sighed heavily as she headed to her bedroom to put on her clothes.", "\n\nHow the fuck did the Freyodin Warriors find out about my dig? ", "I hired a human to prevent this and to keep that witch, Zahara, from getting into my business. ", "Who's been talking? ", "Tormond angrily wondered as he sat at his office desk reaching into his pocket and coming up empty, again. ", "When I find out who betrayed me, I will boil him alive and have him for dinner. ", "Where are my fuckin' aspirins?", "\n\n*****\n\nDanielle pulled her cell phone out of her pocket and let her fingers hover over the keypad. ", "Goddess, what am I going to tell Thunder? ", "This mission just keeps getting more complicated by the hour. ", "Okay, girl. ", "Suck it up. ", "Make the call. ", "She speed dialed Thunder, wishing none of this had ever happened.", "\n\n\"Yes, Danielle. ", "Update me.\" ", "Thunder never was much for small talk.", "\n\n\"Yea, um... I've got new information on the EOD documents, but we've got bigger, more immediate problems over here now. ", "Not to sound cliché, but do you want the bad news or the really bad news first?\" ", "Oh, fuck me.", "\n\nGiving it some thought, Thunder instructed, \"Hold it right there for a minute. ", "Let me get Vengeance in here first. ", "You can fill us in at the same time.\" ", "There was a muffled sound on her end as Thunder placed his hand over the phone and yelled for his second-in-command to join him in his office.", "\n\nA minute later, Thunder urged Danielle to continue, \"Alright, we're here. ", "Just spill it.\"", "\n\n\"The site has been compromised and attacked. ", "Hanna and one of her minions showed up a little while ago. ", "I dispatched the minion, but Hanna got away. ", "It seems our old friend Tormond is the actual benefactor of the excavation. ", "They know I'm here with the archeologist and I've got a body to dispose of now.\"", "\n\n\"Holy shit! ", "You just went to get a fucking chain!\" ", "bellowed Vengeance throwing his hands into the air in disbelief.", "\n\n\"Ahh, yeah. ", "That's not good news at all,\" Thunder stated obviously. ", "She heard several curse words in the background from her superiors, followed by a heavy sigh of resignation over the speaker phone.", "\n\nDanielle took a cleansing breath of her own and kept going, piling on more bad news. \"", "I'm sorry, Thunder, but there's more,\" she said with even more regret.", "\n\n\"You mean to tell me it gets worse?\" ", "She heard Vengeance say and could just imagine his already towering height hitting the ceiling as he jumped out of his chair. ", "She heard the sound of the chair hitting a wall. \"", "Fan också.\" ", "Damn it.", "\n\n\"Vengeance, cool down. ", "Let's hear the warrior out.\" ", "He paused and addressed Danielle again. \"", "We realize all of this is out of your control, Danielle, and you're certainly not the cause of it. ", "Please, go on. ", "We're listening,\" Thunder uttered lowly and in a slightly more forgiving tone.", "\n\n\"He's right. ", "My apologies, warrior.\"", "\n\nDanielle appreciated their acceptance of the situation and the respect they showed her as a female warrior. ", "It had taken her many years to earn that respect. ", "She felt some respite as she continued to explain their latest plight. \"", "As I'm sure Zahara shared the information about the binding chain, I won't go over that again but...Aaron saw everything. ", "The attack, me slaying the minion, Hanna shapeshifting...and he knows...about me at least. ", "Some, but not all.\" ", "She paused searching her brain for a way to explain the unnatural compulsion she felt toward Aaron, then decided just to go with it. \"", "I don't know why, but I can't seem to hold much back from him when he asks me something. ", "I can only attribute it to the chain. ", "It's like some of the effects of the chain are there but, thankfully, some aren't.\"", "\n\nComplete silence followed with no reply from Thunder and Vengeance as they stared at each other across the desk.", "\n\nShe continued. \"", "You know he's a target now. ", "He can't very well defend himself against them alone and I can't stay here indefinitely. ", "Tormond will send others. ", "I can't just leave him here to die. ", "We have to find out why the chain has attached itself to him, then we can make a decision of what to do.\"", "\n\nThunder thought for a minute. \"", "You're right. ", "It's unprecedented, but I want you two on the jet back here immediately. ", "He'll be safe here and Zahara can work on the chain complication more efficiently if he's accessible. ", "We can even give him a little self-defense training, in the meantime, to help him better protect himself. ", "We can worry about scrubbing his memory later. ", "You two just get here.\"", "\n\nShe felt somewhat relieved that eventually everything would be okay and wondered why the thought of Aaron's future memory wipe bothered her. ", "It was a sad relief and it puzzled her.", "\n\nShaking her head to clear her thoughts, she answered, \"Yes sir. ", "I'll take care of it right away. ", "And sir?\"", "\n\n\"Yes, Danielle.\"", "\n\n\"Thank you,\" she said softly and ended the call. ", "Now she had to figure out a way to get Aaron on the plane and explain everything else to him. ", "When she'd left him to place her call, he'd probably gone back to freaking out again like a cat on too much catnip. ", "Nervous energy permeated the room.", "\n\n\"Alright. ", "Might as well get this over with,\" she mumbled to herself as she headed back to Aaron's office. ", "Her chest felt extremely heavy and she wondered if immortals could hyperventilate. ", "She'd never seen it happen before, but she could dream. ", "Not that blacking out would solve anything right now, but it would be a welcome delay.", "\n\nAs she entered the room, she took in Aaron's appearance. ", "He was paler and seemed eerily calm. ", "As a matter of fact, his eyes seemed a little glazed over. ", "But if you overlooked all of that, he was still gorgeous and hot as hell. ", "Oh, I'll protect you all right. ", "What I could do with that body...after all, I was ordered to get him safely back home. ", "How can you think of sex at a time like this? ", "You're a warrior!", "\n\nClearing away the naughty thoughts and memories of their recent tryst, she cleared her throat loudly to gain his attention. ", "Which didn't work. ", "So, she tried another approach. ", "She crossed the room, stood in front of him and snapped her fingers several times in front of his face.", "\n\n\"Yo, Aaron. ", "You in there? ", "Still with me?\"", "\n\nAaron had been staring out the window on the opposite wall. ", "For how long, he didn't know. ", "Once Danielle had left the room, he realized he was in the room alone with a dead body – demon - whatever it was. ", "Anything not to look at that dead body on the floor in front of his desk. ", "And the blood... that was on the floor...streaking the walls...covering the menacing looking blade... Get it together, man. ", "Shaking his head slightly, he looked up at Danielle, brought himself back to the present.", "\n\n\"Yeah, I'm here. ", "Sorry,\" he managed.", "\n\nDanielle tried for compassionate. \"", "Sorry? ", "No need to be sorry, Aaron. ", "You're the innocent in all of this. ", "You didn't know who was hiring you, especially for what is probably an unbelievable opportunity for someone like you. ", "But now, I've got to get you someplace safe.\"", "\n\nThat did it. ", "Something suddenly snapped in Aaron and his manly pride spoke up and stepped front and center. \"", "I can take care of myself.\" ", "His entire demeanor had changed to one of confidence. ", "Or at least that's what he hoped he was portraying.", "\n\nGreat timing, she thought. ", "If he would have stayed comatose, I could have jetted him away without any more problems. ", "Shit!", "\n\nStroking his macho ego, Danielle tried another avenue. ", "Putting a demure look on her face and the tiniest, flirty little smile, she said, \"Of course, you can. ", "I didn't mean to imply that you couldn't. ", "Do you think I'd be attracted to some wimpy guy? ", "Hell no! ", "I need a man, a strong man, a virile man. ", "Someone who knows how to take care of himself and those around him.\"", "\n\nShe continued, hoping this was working, because although she was certainly attracted to him, the last thing she needed was a man. \"", "It's just that these bad guys are a little different and I've made arrangements to get you some training so that you can learn all about their weaknesses and how best to defeat them. ", "Besides, you've got to admit that the scientist in you really wants to learn all about me, my kind and where we come from. ", "Don't you?\" ", "There, that should grab him.", "\n\nAnd.... It did. ", "Aaron was a goner. ", "Hook, line and sinker. ", "Last minute long distant shot from the three point line. ", "And that's the ball game!", "\n\nThe next thing Aaron knew, he was boarding a magnificent privately owned jet. ", "He was about to find out by whom it was owned and he couldn't wait.", "\n\n*****\n\nVengeance had managed to calm himself and upright his chair bringing it back to Thunder's desk front. ", "Thunder remained his fairly composed self, as he did in most situations.", "\n\n\"Well, Venge. ", "What do you think? ", "Could this be any more of a cluster fuck?\" ", "Thunder leaned back in his plush leather chair and propped his feet up on his desk. ", "Just because everything was going to shit was no reason not to be comfortable.", "\n\n\"Yes, I'd say it's time for us to brainstorm and come up with some kind of preliminary plan.\"", "\n\n\"We can't disregard that Aaron may be a plant by Tormond, whether knowingly or not.\"", "\n\n\"True, but the wards should take care of that. ", "Just in case, I'll speak with Annika about checking him out. ", "She should be able to detect any spells Tormond may have attached to him and dispel them to protect us. ", "Also, I'll ask Ghost to do a background check on him. ", "With his seemingly magical computer skills, if there's anything to find out about him, even the tiniest bit of information, Ghost will find it.\" ", "Vengeance began to chuckle a bit.", "\n\n\"What the hell's so funny? ", "I can't think of a thing that's humorous about this.\"", "\n\n\"I can. ", "Danielle.\" ", "He chuckled some more. \"", "She's probably having a shit fit right about now. ", "Gotta love it.\"", "\n\nThunder caught on to his train of thought then. \"", "Yeah, she prides herself on being tough and independent.\"", "\n\n\"I don't need a man,\" Vengeance mocked in a high pitched voice, repeating the mantra he'd heard Danielle quote in the past. \"", "And now she's saddled with a mortal one. ", "It just keeps getting better and better.\" ", "He was laughing full on now and Thunder had joined him.", "\n\nAfter having their fun, Vengeance said, \"Okay, back to your original question of what do I think. ", "You know I'm always ready to battle, T.\" Which was an understatement for Vengeance. ", "He lived for it both in his mortal life as a Viking and immortal life as a vampire warrior. ", "He never did anything halfway when it pertained to battle, women or sex. ", "He was all confidence and sex on a stick at six foot five with long flowing blond hair that draped down to the middle of his well-honed muscular back, sleepy crystal blue/gray eyes, and a tempting sexy smile surrounded by a barely-there van dyke beard and mustache. ", "And when he smiled, he always loved to show just a hint of fang. ", "He knew what a turn on it was. ", "The rest of him just all fell into place from there following the same design.", "\n\n\"And do you realize she managed to get off the phone without mentioning the status of the EOD search or the documents? ", "We'll have to corner her on that when she lands which should be in about twelve hours,\" Vengeance continued.", "\n\n\"Well, at least we now know why Zahara's vision didn't touch on the EOD. ", "With Tormond secretly financing and outsourcing his search efforts to the archeologist, there would be no godly or demon interaction and no direct threat to mortals. ", "She would have no warning through her visions. ", "He was smart not to send any demons or minions to the dig site previously. ", "We would have been tipped off immediately. ", "Of course, now that he knows, we know....\" Thunder realized this was a whole new ball game.", "\n\n\"Yes, we'll have to send a team out there, at least, maybe more. ", "What about this archeologist anyway? ", "This chain binding situation is really puzzling.\"", "\n\n\"I have to agree. ", "The females are working on it. ", "They're searching the ancient scrolls for any possible answers. ", "Zahara is utilizing her scrying and visionary skills and Annika is looking into any magical solutions, as well. ", "So far we've got zip.\"", "\n\n\"Well, those chains are permanent for a reason,\" Vengeance said and visibly shuddered. ", "His thoughts turned to Makayla. ", "He enjoyed his encounters with her immensely and didn't mind sharing her with Savage. ", "As long as she was okay with it, so was he, and Savage didn't seem to mind the arrangement either. \"", "At least he's human and doesn't have to wear it or be tied for an eternity. ", "He gets to pass away and be done with it. ", "Lucky bastard.\"", "\n\nThunder chuckled, \"You're so morbid. ", "I'd say you're the lucky one. ", "You've got an eternity and no chain. ", "Someday someone will nail your ass and put a chain on it. ", "Just watch.\"", "\n\n\"Not in this loooong lifetime, my friend.\" ", "On that he was adamant.", "\n\n\"Okay, so when the archeologist gets here, we'll gather everyone for a meet and greet and discuss our options and current findings. ", "Let me know the moment Danielle arrives,\" Thunder instructed.", "\n\n\"As you will, my Lord and friend. ", "Later, T.\" Vengeance gave an unceremonious salute and traced out to the training field.", "\n\n*****\n\nChapter Seven\n\n\"Wow, this is some extravagant jet you have.\" ", "Aaron took in the spacious layout of the extended cabin, the rosewood trim, the extra-wide plush leather seating, the fully stocked bar, a hallway that lead off to what looked like a bedroom and private bath. ", "It smelled of a wonderful scent of vanilla and spices. ", "Wait, no. ", "That was Danielle.", "\n\n\"It's not mine personally, Aaron. ", "Let's just say it's a company jet and we have a private airfield.\" ", "So private you can't see it. ", "She hid her smiled with a quick turn and wished she could LOL right now because she could use a really good laugh after the few past days she'd had. ", "But, he'd think she was plain crazy bursting out laughing at what he couldn't hear. ", "She was extremely glad that ridiculous chain that was stuck around his neck hadn't given him access to her innermost thoughts and feelings. ", "Thank Goddess for small favors. ", "She couldn't imagine being tied to a stranger who knew everything about you and you'd have no secrets from. ", "Oh, wait. ", "Been there, done that, eight hundred years ago. ", "That traitorous... Deciding she shouldn't speak ill of the dead, she let that notion go and took a deep breath to cleanse her thoughts and mind.", "\n\nThe ride to the airport had been uneventful. ", "Danielle had phoned Taylor ahead of time to ready the jet. ", "Aaron had remained calm, so far, and had managed to professionally make arrangements to leave his loyal assistant, Jake, to supervise the dig site in his absence. ", "She was actually quite impressed with him at the moment. ", "Now it was time to take the next step. ", "Full disclosure.", "\n\nDanielle was nervous about telling all or most of the warriors' secrets, but it had to be done and Thunder had already given his approval. ", "But where to start? ", "The beginning? ", "That was in 750 AD. ", "He's going to freak on me again. ", "How do I tell him he just screwed a dead woman who is over twelve hundred years old? ", "Oh, Goddess, I am a dead woman that's over twelve hundred years old! ", "No, not dead – immortal.", "\n\nThat fact had never mattered to Danielle before. \"", "So why does it matter now?\" ", "she mumbled to herself in wonder.", "\n\n\"What was that?\" ", "Aaron inquired absently while investigating the contrast of elegance versus high-tech equipment that made up the atmosphere of the jet. \"", "What do these do?\" ", "Aaron had begun darting around the jet examining everything. ", "To say he was highly intrigued by his surroundings would have been an understatement.", "\n\n\"Oh, my Goddess! ", "You're like a kid in a candy store. ", "Should I whip out the toddler safety devices so you don't hurt yourself?\" ", "She finally did laugh out loud. \"", "Would you mind taking your seat, please? ", "We're about to take off and I really need to fill you in on a few things.\" ", "He was seriously getting on her nerves. ", "She couldn't decide if that was a good or bad thing.", "\n\nAs if she'd willed it, the jet was suddenly in motion. ", "They both quickly buckled their seatbelts and braced for takeoff. ", "Then, without further warning, the jet shot rapidly down the runway emitting a roar under its mighty wings and with a lift they were sailing through a celestial pale blue sky.", "\n\n\"Sorry, I'm scholarly. ", "I like to absorb new experiences. ", "My mind is like a sponge,\" he acknowledged her comparison of him to a child's learning mind.", "\n\nFinding that explanation lacking, Danielle was still mildly annoyed with him. ", "She leaned forward, turned his seat to face her and braced her hands on the arms of his seat, ensuring she had his undivided attention.", "\n\n\"Well, soak this up, big boy.\" ", "Here goes nothing. ", "She took a deep breath and let the verbose knowledge fly from her lips rapidly and nonstop. \"", "I'm an immortal warrior in a paranormal army from Valhalla that guards and protects mortals from demons that crossed over into your realm. ", "I died over twelve hundred years ago only to be saved by the Goddess Freya along with my two hundred and ninety-nine other warriors sisters. ", "My sisters and I, in turn, bring over brave, honorable and deserving warriors, that are chosen by the God Odin, from all the wars over the past twelve centuries to join us in our fight. ", "We are the Freyodin Warriors. ", "You've got my binding chain around your neck and we have to find a way to get it off of you and you can't find the EOD for Tormond.\"", "\n\nSilence. ", "Nothing but.", "\n\nDanielle leaned back and took another loud, deep and much-needed breath, breathing in the scent of him as she did so. \"", "I think that about covers it. ", "Do you have any questions?\"", "\n\nAaron just stared at her in awe. ", "Shit, not that glazed look again.", "\n\nThen she thought she'd try something different. ", "She was desperate, really desperate. ", "So, she unbuckled her seatbelt, leaned toward him covering the distance between her extra-wide plush leather seat and his extra-wide plush leather seat and kissed him full on the mouth. ", "Gently at first, so as not to further his shock.", "\n\nIt only took him about twenty seconds to realize what was happening to him and, being the virile man that he was, he took over complete control of the kiss. ", "And she let him. ", "Reaching down and unbuckling himself blindly, he wrapped his arms around her waist and pulled her onto his lap. ", "He licked the seam of her sweet lips and she opened for him, whimpering, allowing his tongue to sweep inside, searching, exploring the cavern of her mouth with a kiss that became demanding and greedy. ", "She tasted like warm honey and smelled of that same wonderful scent of vanilla and spices.", "\n\nAs she wrapped her arms around his neck, she pulled him closer to her body and positioned her legs to straddle his hips, grinding her hips against him in tight circular motions. ", "When he groaned, she did it again. ", "She arched her back pressing her succulent breasts into his chest and returned his seductive kiss with her own. ", "Closing her lips around his tongue, she began seductively sucking in a slow steady rhythm that made him long for her perfect red lips to be wrapped around his rigid cock sucking it in the same way.", "\n\nTheir passion was immediate and wild once again. ", "He slid his roughened hand up under her leather vest, molded his palm to her firm breast and gently squeezed her beaded nipple, causing her to slightly pull away from him and cry out her pleasure. ", "His hungry mouth traveled down her jaw to her swan-like neck and over her collarbone nipping and licking his way downward. ", "She made quick work of the few buttons on her vest and dropped the garment to the floor carelessly.", "\n\nThat's when he noticed the chain emulating his own around her neck.", "\n\n\"What's this? ", "Do you all wear these?\" ", "Aaron asked fingering the article.", "\n\n\"No, not all. ", "It's why I originally came to you. ", "To retrieve the chain. ", "It's not of this earth and you shouldn't have found it,\" she explained, hoping he wouldn't press further. ", "She had no intention of explaining Alarr to him at all, especially not now. ", "What a buzz kill that would be. ", "I'll just entice him with my womanly wiles and change the direction of his thoughts. ", "Shouldn't be too hard. ", "He is a man, after all.", "\n\nAs he held her around the waist, she leaned backward giving him full access to her aching breasts, it took him no time at all to take the bait. ", "He used his teeth and tongue to worship her swollen peaks, sending jolts of pleasure to her very center.", "\n\n\"Oh, yes!\" ", "she cried tunneling her hands into his hair holding him to her.", "\n\n\"Too many clothes,\" he rasped against her skin.", "\n\n\"I so agree,\" she murmured against the top of his head while still holding him in place. ", "At that, she relented and released him while they hurriedly divested themselves of the remaining clothing obstructing them from attaining the skin to skin contact they both craved.", "\n\nAaron pulled a condom out of the pocket of his jeans and dropped them to the floor.", "\n\n\"You won't need that,\" she offered.", "\n\n\"We didn't use anything before. ", "I'm sorry for that. ", "Don't know where my head was. ", "You're on the pill?\"", "\n\n\"No, but I'm safe. ", "From pregnancy and disease. ", "You can't give me either.\"", "\n\nDeciding to take her at her word, he lowered himself back into the chair they'd previously occupied. \"", "Come back here,\" he commanded with heat blazing in his darkened eyes as he took in her now naked form. ", "She burned him to the core and he knew he'd never wanted another woman as much as he did her at this moment.", "\n\nThis was the first time they'd actually seen each other unclothed. ", "Approving of his very imposing manhood, his muscular thighs, and noting once more just how damn much she wanted him, she returned his gaze with a heat all her own. ", "Bodily, he wasn't quite as muscular as the male warriors, but by human standards, he was most impressive. ", "She slowly and seductively repositioned herself on his lap, giving him an up close and personal view of every inch of her. ", "Once settled, she reached between her legs clutching his firm cock in her eager hands. ", "He felt her fingertips gliding across the crown of his cock as she spread the drop of moisture beading at the tip, swirling it around and then moving her fisted hand down to the base of him. ", "He groaned deeply, grabbed the nape of her neck, bringing her to him for more lustful kisses as she steadily stroked him. ", "He knew he had to slow this down or it would be over entirely too fast, like the last time. ", "He swore to himself that if they ever got the chance to do this again, he was taking her slowly and properly – in a bed.", "\n\n\"Danielle, you must stop or I'll never last,\" he begged as he removed her hand from around him and placed his own into her creamy center. ", "She felt hot, wet and ready to take him inside, but he wanted to hold off a little while longer.", "\n\n\"Oh, baby, you're so wet for me.\" ", "He parted her swollen lips and inserted two fingers into her core, circling her clit slowly with his thumb.", "\n\n\"Umm, Aaron!\" ", "she moaned as she allowed her head to fall back and rode his hand. \"", "More,\" she demanded softly. \"", "I need more.\"", "\n\n\"Yes, baby. ", "Whatever you need.\"", "\n\n\"Inside. ", "I want you inside. ", "Now,\" she panted heavily, searching for his lips.", "\n\n\"Don't worry, baby. ", "I will. ", "But I want you to come for me first,\" he said as he watched her beautiful face. ", "The expressions of ecstasy that crossed her face showed him all the pleasure that he was giving her, without speaking the words. \"", "You're so beautiful, Danielle.\" ", "He wanted to always remember her looking just this way.", "\n\nFeeling she was near, he increased the speed and pressure of his ministrations and sent her spiraling into her first orgasm within seconds, still watching her loveliness unfold as the spasms surged through her body. ", "While still shuddering from her climax, he grasped his cock and rubbed it between her wet folds. ", "Lifting her hips, he centered her over his erection and entered her slowly, letting her body drop down onto him as he filled her inch by inch. ", "He growled his approval as her spasms contracted around him. ", "Her pussy felt like nirvana, hot, tight and dripping wet. ", "He reached down to touch her wetness where they joined and brought his fingers up to his mouth savoring the taste of her and inhaling her womanly scent. ", "Danielle watched as he did and groaned her approval in return.", "\n\nShe trailed her fingers down between his pecs, to his taut stomach, then back up to his darkened nipples, caressing him. ", "She then placed her hands solidly on his shoulders and began to ride him slowly and sensuously. ", "She reveled in the way he filled her. ", "It seemed more than just a physical gratification that she didn't understand. ", "But she knew she needed it and knew it felt so right.", "\n\nAaron grasped her hips firmly and began to thrust up into her in earnest, meeting her thrusts with his own, the momentum building. ", "Their movements became frenzied and prodded them both closer to orgasm.", "\n\n\"Oh Goddess, Aaron. ", "I'm so close.\" ", "Her breathing hitched as she spoke and she felt like she couldn't wait one more second to explode.", "\n\n\"I'm right here with you, baby. ", "Come with me. ", "Let me hear you,\" his voice hoarse with passion.", "\n\nDanielle had no trouble giving into his demands when she squeezed his cock deep inside her as she came, screaming his name, milking every drop from him as he joined her falling over the edge. ", "As the spasms subsided, she fell forward collapsing against his chest.", "\n\nWhen their breathing finally resembled something close to normal, Aaron held on to her tightly, reclined the seat they occupied back and sighed, \"Woman, you're going to kill me. ", "But what a way to go.\" ", "He chuckled, kissing her temple and added, \"Thank you. ", "You are amazing.\"", "\n\nNeither moved to leave the seat or redress. ", "They simply laid together comfortably, Danielle's body molded to his in his arms with her hand resting on his chest lightly making lazy circular patterns.", "\n\n\"Well, I do aim to please.\" ", "She raised her head from his shoulder and tilted it upward to look into his eyes. \"", "But seriously, thank you back. ", "You're not so bad yourself, you know. ", "And by the way, I really don't want you to think that I do this kind of thing all the time. ", "I mean I'm not a nun or anything, but I don't usually jump a guy I've known less than a couple of days. ", "I'm obviously really attracted to you and I don't understand it at all.\"", "\n\n\"It's alright. ", "I feel it, too,\" he confessed as he worked her hair out of the braid she usually wore it in and ran his hand through the silky strands of her hair. \"", "It's strange and difficult to describe. ", "I'm just drawn to you and I want to touch you all the time. ", "Does it have anything to do with this chain? ", "I caught most of what you told me earlier, but can you tell me a little more about what I've stumbled into?\" ", "He knew he needed to hear this, but was afraid of his own reaction to it. ", "If he'd heard her correctly, what she'd said previously was just too fantastical, and he certainly wouldn't believe a bit of it if it weren't for what he witnessed earlier. ", "That demon shape-shifted right before his eyes.", "\n\n\"Think you can listen to me without freaking or zoning out on me this time?\" ", "She was half joking and half serious at the same time, trying to make light of the situation. ", "She hoped he could be receptive and have an open mind. ", "She knew she was about to blow a lot of his scientific beliefs sky high and she really did feel regret for having to do that and even involve him in any of this. ", "She didn't like being the one to destroy some of his beliefs. ", "He'd spent years of study and practice on those beliefs to become the archeologist that he was today.", "\n\nBut circumstances hadn't been in his favor once he met up with Tormond. ", "Then again, maybe finding the binding chain was a good thing for him. ", "It had gotten the warriors involved with his excavation and shown him the truth of what was happening. ", "Probably saved his life. ", "If he'd located the EOD before they had a chance to intervene, it's certain Tormond would have done away with him when he was no longer necessary.", "\n\n\"Yes, I believe I can. ", "I've got several questions, but I think I'll have a million more by the time you finish explaining. ", "Why don't you start and I'll try not to interrupt or at least attempt to keep my questions to a minimum until you're through. ", "But first, can you tell me where we're going?\"", "\n\n\"I can work with that. ", "We're actually going back to Oregon. ", "I'll try not to repeat myself too much, but as I told you before, I'm an immortal warrior that was saved by the Goddess Freya. ", "Have you ever heard of the three hundred Shieldmaidens who fought and died in battle on the Danish side at the Battle of Bråvalla in the year 750 AD? ", "Some call us Valkyries. ", "I'm one of the original Shieldmaidens.\"", "\n\nAaron nodded but remained silent and motioned for her to continue. ", "He knew the Norse history that she spoke of and their mythology.", "\n\n\"I also happen to be the daughter of Freya herself and a mortal man.\"", "\n\n\"Wait, doesn't that make you a demi-goddess?\" ", "he asked, a little on the stunned side.", "\n\n\"Unfortunately, yes. ", "But let's save that little ditty for another time.\"", "\n\nOh God, I've just had sex with a demi-goddess. ", "Oh, I hope her mother doesn't kill me.", "\n\nShe knew she had thrown him for a loop by the look of puzzlement with just a touch of panic etched across his face, but she chose to ignore it for now.", "\n\n\"Freya has her chosen and Odin has his and together we are called the Freyodin Warriors. ", "We are given the chance of immortality and take an oath to serve and protect mankind, to fight against Loki's demons and minions, a couple of which you've already met. ", "Tormond, your benefactor, is Loki's demi-god son and controls the western portion of the country's demons, wreaking havoc across the seaboard and adjoining states. ", "He's just one such tormentor and of course, we have communities all over the world to combat them. ", "I currently live and serve in a hidden village located in Bridge Creek Wilderness. ", "It's not on any map and it doesn't exist to mortals. ", "It's magically warded against detection from humans and demons alike. ", "That's where I'm taking you now for your protection and training. ", "You can't just say 'bang, bang, you're dead' to a demon and I can't, in good conscience, leave you to fend for yourself. ", "At least not until you learn a few ways to protect yourself and know your enemies weaknesses.\"", "\n\nAaron didn't repeat his mistake of earlier, of feeling too macho to let her help him. ", "He respected her as a woman and a warrior, now that he understood where she was coming from and her purpose. ", "He held his comment and let her continue once more.", "\n\nShe noticed that he seemed to be taking this rather well, considering their rough beginning, and this pleased her. \"", "I need to give you fair warning, though. ", "As immortals, we have abilities that have been granted to us by the Gods. ", "Some of the abilities differ from men to women and some of the other abilities are individually based.\"", "\n\n\"What abilities do you have?\" ", "he finally asked listening intently.", "\n\n\"Well, I am stronger and heal faster than a human. ", "I can shadow, trace, speak, and block. ", "Oh, and Freya blessed me with my sword.\"", "\n\n\"Can you explain what some of those terms mean?\"", "\n\n\"Okay. ", "Shadowing allows me to blend into the shadows and be pretty much undetected. ", "Tracing allows me to transport myself via thought to another place.\"", "\n\nAaron raised his eyebrows and looked extremely intrigued at that prospect.", "\n\n\"Speak allows me to project thoughts to my fellow warriors either collectively or individually and blocking lets me block others from hearing anything I deem private in my life. ", "My sword is magically enhanced to aid me in battle. ", "It will seem just like a standard sword to anyone else, but me.\"", "\n\nThere was a pause and then she concluded, \"I think that about does it. ", "If I've forgotten anything of importance, we'll cover it later. ", "Any questions?\"", "\n\n\"Yes, many. ", "But let me process what you've told me thus far and get back to you.\" ", "He snuggled down more comfortably against her and produced a small yawn. \"", "I'm actually exhausted from all the excitement today,\" he drowsily confessed. ", "With his finger, he lifted her chin up to face him and placed an innocent kiss on her nose.", "\n\nLater sounded fabulous to Danielle. ", "She could use a rest herself. ", "I'll just close my eyes for a few moments, she thought to herself as her body became limp as noodles.", "\n\nThey were both comfortable in their nudity and eventually drifted into a deep sleep, still wrapped together, arms and legs entwined, in the reclined extra-wide plush leather seat.", "\n\n*****\n\nFearing for her existence, Hanna knew she had to try something to get back in Tormond's good graces. ", "He had ordered her to stay hidden until the arrival of reinforcements, but she knew that was a definite death sentence. ", "She felt she couldn't make the situation worse, so she decided she would infiltrate the dig site and retrieve the Eye of Odin herself. ", "With such a success, surely then Tormond would forgive her failure.", "\n\nA quick mental scan of the facility told her there were no warriors present, so she hid in one of the buildings waiting for the right opportunity. ", "As she stood unobserved between one of the tall metal shelves lining the back wall, she watched as the human stood at one of the far tables, sifting dirt into a bin. ", "Sensing he was weak and susceptible to her will, she delved into his mind, searching for the one weakness that would give her the power she required.", "\n\nHanna manifested into a young college aged, curvaceous female, with long dark brunette hair and emerald green eyes. ", "His dream woman. ", "Taking on a demure but sensual appearance, she stepped out from between the shelves and slowly approached him.", "\n\n\"Hello. ", "Can you help me? ", "I'm looking for Dr. Aaron Janson,\" Hanna inquired innocently.", "\n\nStartled, Jake looked up from his work and took notice of the young beauty that was approaching. ", "Her legs were long and led up to a trim waist and ample breasts, but her angelic looking face was framed by long, luscious dark locks and her emerald colored eyes were mesmerizing, almost hypnotic. ", "He could get lost in the deep pools of green. ", "In the back of his mind, Jake knew he should have been wondering not only who she was, but where had she come from. ", "But his southern brain was currently doing all if his thinking for him and his northern one didn't have the capability to override any such decisions.", "\n\n\"I'm afraid he's not here. ", "He returned to the University and I'm not sure when he will be returning,\" Jake answered with unconcealed interest written across his face and intrigue in his voice. \"", "May I help you in some way?\"", "\n\n\"Sure, my name is Hanley Smith and I'm a student from the University of Oregon. ", "Professor Johnson received approval from Dr. Janson to have me join your team in the search for the Eye of Odin since my thesis is on Norse mythology,\" Hanna said reaching out her hand in a greeting while throwing a compulsion for Jake to believe everything she was saying. ", "She knew her story was unbelievable, but as long as she told him to believe it, he would and by the look on the human's face, he was putty in her hands.", "\n\n\"Oh, well, he didn't say anything to me, but I'm sure that will be fine. ", "Glad to have you on our team.\" ", "Jake said with total acceptance. \"", "My name is Jake Thomas and I'm Dr. Janson's assistant. ", "I can tell you everything you need to know about the Eye of Odin. ", "I know all of the ins and outs of what's going on here at the dig site,\" he bragged, slightly shaking her hand and lingering to hold it a little longer than necessary.", "\n\nWith his knowledge, about Aaron Janson and the site, he will be the perfect tool. \"", "Very nice to meet you, Jake. ", "I'm so glad to be here,\" Hanna said as she pulled him in closer to her body and strengthened her compulsion. \"", "I need for you to tell me everything that you know. ", "And I mean everything.\"", "\n\nHanna wasn't the slightest disappointed with Jake. ", "He was a lovely mortal specimen and would suit her needs perfectly. ", "The female warrior had messed up her plans of fun and games with the doctor, but Jake would make a very nice substitution. ", "She was feeling a little more optimistic about the future ash party she was sure Tormond was going to throw. ", "Maybe she could turn this thing around, after all. ", "Who knows? ", "Maybe even Loki would take notice if she did it well enough. ", "Other than her goal of staying alive and surviving Tormond's wrath for her previous blunder, her number one goal was to convince Loki to fulfill his promise of immortality. ", "This just might be the opportunity she'd been waiting for. ", "A girl could dream...\n\n*****\n\nTaylor's voice over the com-system startled them awake, \"Excuse me, Miss. We will be arriving at our destination in approximately fifteen minutes. ", "Please take your seats and prepare for landing.\"", "\n\nAaron and Danielle disentangled themselves from the reclined seat where they had drifted to sleep wrapped in each other's arms. ", "They'd slept through the night and the remaining flight. ", "The atmosphere between them was suddenly thick with awkwardness and Danielle gave Aaron a polite tight smile when she realized they had actually shared such an intimacy. ", "Sex was one thing, cuddling another altogether and was reserved for lovers, which they were not. ", "Their coupling had only been hot and heavy, spur of the moment events. ", "An attraction she hoped to have gotten out of her system. \"", "We'd better hurry and dress.\"", "\n\nWithout saying a word, Aaron nodded in agreement, gathering up his clothing and peering out the small window next to him. ", "The view was a familiar one of the scenic Blue Mountain Range. ", "There were tree covered mountains and valleys all around as far as he could see. ", "As they drew nearer to their destination, a cloudiness seemed to lift from his view and he spotted a private airstrip that hadn't been there previously and moments later they glided safely to the ground.", "\n\nThe hatch opened and the whine of the aircraft's motorized stairway filled the air as it lowered to the ground. ", "Aaron disembarked the jet and took in his surroundings. ", "Around them was a surreal open meadow covered in bunchgrass and a wide variety of wildflowers, all in the shades of the rainbow, and the air was rich with their fragrance. ", "In the forest beyond were tall fir and pine trees, sagebrush and yellow mountain mahogany. ", "He could hear a pileated woodpecker in the distance picturing its red topped head as it carved out its nest high in the cavity of a lifeless tree.", "\n\nHe knew where they were, in the Bridge Creek Wilderness of the Ochoco Mountains in central Oregon, which are located at the western end of the Blue Mountains province. ", "His university was located approximately one hundred and sixty miles away in Eugene, Oregon. ", "He recognized the sights, sounds and smells of his home.", "\n\nTurning back, he offered his hand to Danielle for assistance in descending the aircraft's stairway. ", "When she smiled but refused his hand, he realized that she could take care of herself and was used to that being the case, probably since before he was ever born. ", "Twelve hundred years. ", "Wow. ", "The things she must have seen in her lifetime. ", "The historian in him held a new found appreciation for her and the wealth of knowledge she could share with him, should she choose to. ", "He noticed that she had withdrawn since they arrived though and that might not be the case.", "\n\n\"Welcome to my world,\" Danielle stated with a bit of dramatic flair, drawing him back to the present. ", "She knew she had come off sounding somewhat sarcastic, but in reality, she truly did love this place. ", "It was her home.", "\n\nDaniele motioned for Aaron to follow her and ambled toward a well-trodden trail. ", "The wooded area was alive with forest life and sounds. ", "They ventured on a minor trek through the woods and came upon a small but functional village. ", "There were different styled and sized homes, some rustic, some modern, but all well maintained. ", "In the center of the village was an elaborate Nordic altar, or _horgr_ _,_ built of heaped stones and surrounded by a park full of various colors and types of flora. ", "At the far end of the village was what appeared to be a compound of military style buildings.", "\n\n\"This,\" Danielle said with a sweeping motion of her arm in front of her, \"is Bridge Creek. ", "My home is located on the opposite end near the compound. ", "Why don't we go there and freshen up, change our clothes and get something to eat. ", "It was a long flight and I could use a nice, hot shower. ", "Then I'll introduce you to Thunder, our leader.\" ", "She had mentally alerted Thunder to their presence and made arrangements to meet with him after they had settled in and rested.", "\n\n\"Food, shower and clean clothes sound wonderful,\" he said in anticipation with a smile.", "\n\n\"Alright, then. ", "Let's go. ", "It's not far and we can easily walk there. ", "We're a small community,\" she said using her head to nod in the direction they should go.", "\n\n\"After you.\"", "\n\nAaron walked beside Danielle silently through the quaint little village. ", "All was quiet and there didn't seem to be anyone outside or on the street at the moment. ", "But it really was quite lovely, homey even, surrounded by tall pines and various fir trees. ", "He noted that, even if this place weren't magically warded, you'd have to stumble upon it to locate it. ", "The trees masked the village in such a way as to make it virtually undetected. ", "Maybe you'd spot it from the air if you flew right over it. ", "He'd add that to his growing list of questions. ", "Was it possible they'd somehow managed to make this area a no-fly zone? ", "And what of wild animals? ", "Then again, they were immortal warriors, so he imagined they weren't too concerned with a few black bears and cougars.", "\n\nBridge Creek Wilderness was a very remote part of Oregon predominantly made up of steep forested slopes and barren plateaus with some mountain meadows, like the one they'd arrived in. ", "He wasn't aware of any trails in the area, so chances of curious hikers stumbling upon the village were extremely low. ", "This harsher rural area was for the more experienced outdoorsmen, who probably hunted elk and deer in the fall hunting season.", "\n\nDanielle headed up the walkway of a simple, but well cared for ranch style house, the front surrounded by a railed wooden porch. ", "The landscaping was beautifully trimmed to conform with the flow of the house making it inviting and welcoming. ", "There was even a rope swing hanging from a tree in the center of the yard perfect for a child to swing on. ", "Aaron hadn't seen any children or anyone else for that matter as yet.", "\n\n\"This is me.\" ", "She motioned towards the house. \"", "Come on in. ", "I haven't spoken with Thunder yet about where you will be staying, but you're welcome to stay here if you'd like. ", "I have a spare bedroom. ", "Or, I'm sure one of the guys would be willing to let you stay with them if you'd prefer that.\" ", "This is a little awkward. ", "She honestly hadn't given any thought to whether he'd stay with her or not and wondered what his expectations might be.", "\n\n\"No, this is great. ", "Thanks.\" ", "He knew they weren't actually an item per se, but he hoped he'd be able to persuade her to carry on with what they had started. ", "He didn't know where it was leading to and doubted whether they could even have a future, but he enjoyed what had happened between them so far and wanted it to continue. ", "At least for the time being.", "\n\nAaron followed Danielle inside her home. ", "It was typically feminine and homey. ", "Just what you'd expect from any normal female, not a tough battling warrior, and it smelled of her scent. ", "One he couldn't seem to get enough of.", "\n\nShe showed him to her guest room and told him to make himself comfortable. ", "It also showed a woman's touch and her scent permeated the air around him. ", "Aaron inhaled deeply to take it in. ", "God, she smells wonderful. ", "He wasn't sure what he expected her tastes in decorating to be but was a little surprised that she seemed so normal. ", "Maybe a little leather and chainmail to go with the typical warrior persona. ", "But not Danielle. ", "She seemed to be a normal twenty-first-century woman.", "\n\nAfter showering and changing, they met again in her kitchen for a simple and relaxing meal. ", "They made small talk, refraining from talking about their current situation, instead sharing modest impersonal things about their lives, like and dislikes, etc., ", "then Danielle suggested that they go to the compound, where Thunder was waiting to meet Aaron.", "\n\nDanielle could sense Aaron's nervousness and assured him there was nothing to be concerned about. ", "As they were strolling through the village on the way to the compound, she pointed out various aspects of the village. ", "It seemed they were self-sustaining for the most part due to their abilities and thanks to the magic provided by Annika, the Wand Wielder, and Nadine, their Protector, who helped to shield them. ", "The outside world was easily accessible for anything else they required and they had the help of the loyal mortal families that had been with them through the generations.", "\n\nThe compound was a combination training facility, meeting rooms, recreational amenities and other areas that were needed to train and care for the warriors. ", "As they were walking through the halls, Aaron saw a few of the warriors and asked Danielle about them. ", "They looked like very fierce and intimidating men.", "\n\n\"Who is that over there?\" ", "he inquired somewhat uncertain. ", "Aaron was looking across the large room at the back of a very muscular male who was six foot four with shoulder length wavy black hair. ", "He carried the bulk of years from swinging a broadsword very much like the one strapped to his back. ", "It was an aiming sword, or otherwise called a knight's sword, with a straight double edged blade that appeared razor sharp. ", "As he turned, Aaron noticed the wide expanse of the warrior's chest, his tree trunk legs and his bulging biceps that all screamed power.", "\n\n\"Oh, you mean the dude with the sword?\" ", "Danielle replied. ", "She was enjoying his intimidation a little too much and knew she should feel some measure of guilt.", "\n\n\"Yeah. ", "That's one big man and one mean looking sword.\"", "\n\n\"Oh, that's just Steele, sometimes known as DWAS. ", "Get it? ", "Dude With A Sword?\" ", "she laughed out loud. \"", "It's a running joke around here. ", "He's an impressive warrior with an impressive sword. ", "Wait till you see him in action. ", "Oh, and he has a tattoo on his arm of himself.\" ", "She laughed some more, but was proud of her fellow warrior brothers and sisters and it showed.", "\n\nAaron joined in her laughter and was thankful that she had lightened his anxiety somewhat. ", "Maybe this wouldn't be so bad after all. ", "Though they were obviously tough and dangerous, they seemed to have a sense of humor about themselves.", "\n\n\"Come on. ", "Let me introduce you. ", "You'll love him. ", "He's a real sweetie.\" ", "Danielle really cared for Steele. ", "He was charming, funny, reliable and provided a great source of comic relief. ", "Most importantly, he acted as a brother/father figure to all in need and he was a Master of the sword.", "\n\nSweetie, my ass. ", "Aaron didn't feel so at ease anymore but followed her anyway. ", "There was nothing about this huge intimidating hunk of male that even remotely brought to mind the word sweet. ", "He decided if he didn't show any fear, maybe he'd survive this ordeal.", "\n\nDanielle called out to the mighty warrior as they approached. \"", "Steele, I'd like you to meet someone.\"", "\n\nSteele turned around to greet them with a huge smile on his handsome face, instead of the gruff scowl that Aaron expected. ", "He had a pair of deep-set blue/black eyes that his infectious smile had spread to lighting them up, haloed by high arching eyebrows. ", "He sported a van dyke, and the mustache/goatee combo suited him with his high cheek bones.", "\n\n\"This is Aaron Janson. ", "He's an archeologist from the University of Oregon that Thunder has invited to stay with us for a while,\" she said, suddenly realizing that she had no idea what Thunder had said to the others. \"", "Aaron, this is Steel. ", "My good friend and fellow warrior.\"", "\n\nSteele held out his hand in greeting and Aaron shook it, trying to add a bit of extra strength in his grip, but not too much so he'd look ridiculous like he was overcompensating. ", "It was a man thing he felt compelled to do.", "\n\n\"Glad to meet you, Aaron,\" Steele offered in his deep based voice. ", "He widened his smile, unintentionally flashing a little fang in the process.", "\n\n\"Holy shit!\" ", "Aaron yelled ripping his hand out of Steele's grip and jumping back in alarm. \"", "Fangs? ", "You're fucking vampires?\"", "\n\nOh shit! ", "He's gonna freak on me again. \"", "Oops, sorry. ", "I forgot to mention that.\" ", "She snickered and hid her smile by biting her nails. ", "As soon as she met Steele's eyes and noticed he was having trouble fighting off a fit of laughter, too, she couldn't help it when it came bursting out of her. ", "Steele joined her in her revelry. ", "Before she was finished, she was holding her stomach and wiping tears from her eyes. ", "She looked over at Aaron and took pity on him as he stood there staring at her like she'd lost her mind. \"", "Whew! ", "Goddess, I needed a good laugh.\"", "\n\nShe turned to Aaron, placing a comforting hand on his arm. \"", "I'm so sorry, Aaron. ", "Really. ", "I told you that if I forgot anything important, I'd tell you later. ", "Guess, what? ", "It's later.\" ", "She really wanted to laugh again but thought better of it, so she attempted to calm him instead, noticing this time the shock wasn't as bad as before. ", "Alright, looks like he's coming around.", "\n\nWith the unusual commotion of Aaron's outburst, others came rushing into the room wearing curious faces and murmuring their concern. ", "Steele motioned to them that everything was under control.", "\n\n\"You're a vampire, Danielle?\" ", "His face had lost all color and searched hers with false hope in his eyes. ", "He had the sudden urge to feel for bite marks on his neck but didn't.", "\n\n\"Oh, no. ", "Not me. ", "Just the guys. ", "I'm just a dead girl.\" ", "she blurted. ", "This was just too funny. ", "She should feel bad that he was freaked but she just couldn't manage it.", "\n\nA laughing Steele continued to watch their exchange, not insulted by Aaron's reaction. ", "He'd certainly seen humans scream and yell at the sight of him before, but he was able to simply enthrall them and remove their memories. ", "A convenient little trick.", "\n\nDanielle stifled her laughter once again and cautiously approached Aaron, putting an arm around his back. \"", "Hey, it's okay, Aaron. ", "Really. ", "I'm sorry. ", "I should have told you but I honestly forgot. ", "I had so much to tell you at once. ", "I promise no one here will hurt you. ", "We're your guardians, remember?\"", "\n\nAaron heard the sincerity in her voice and took in a few much needed, but shaky, deep breaths. ", "He bent over resting his hands on his knees trying to calm himself. ", "Holy bejesus! ", "This is too much... Just breathe... When he felt he'd regained a modicum of control, he stood back up and looked around him, hoping he hadn't drawn too big of a crowd. ", "Then he noticed the additions in the room.", "\n\n\"It's okay, buddy. ", "Sure didn't mean to scare you like that. ", "We're just not used to having mortals around here. ", "As a matter of fact, I believe you're the first human guest we've had,\" Steele offered in consolation. \"", "I've got some other friends I'd like you to meet when you're ready.\"", "\n\nAaron nodded his consent and held his hand out cautiously to greet the warriors who stood at Steele's side.", "\n\n\"This is Nadine, our Protector, Emeline, our Healer, Justice, our explosives expert, and Turbo, our mechanic and mixed martial arts expert.\"", "\n\nSalutations were passed all around. ", "The warriors made a collective effort to make Aaron feel welcomed over the next few minutes and he was able to begin relaxing again. ", "I just might survive this, if I don't piss any of them off.", "\n\nDanielle leaned into Aaron and whispered softly in his ear, \"Doing better now?\"", "\n\n\"Yes, thanks. ", "Sorry, I freaked out on you – again.\"", "\n\n\"As you can see, it's no big thing.\" ", "He watched as she swept her eyes around the room to encompass the others and their easy demeanor. ", "He nodded in agreement.", "\n\n\"I think it's time you meet Thunder. ", "Let's go.\" ", "She grabbed his hand in hers, offering further comfort and made her way in the direction of Thunder's office. ", "Danielle sent her thoughts out to Thunder. ", "Thunder, I'm bringing the mortal with me now. ", "He's very on edge. ", "Please be kind to him.", "\n\nAnd just why do you think I'd do otherwise? ", "I agreed to him being brought here, did I not? ", "Don't worry. ", "All will be well, was the reply she received.", "\n\n\"Aaron, there's one more thing I think you should know.\"", "\n\n\"Don't tell me that Thunder is actually Dracula.\"", "\n\n\"No... He's actually Thor.\"", "\n\n*****\n\nChapter Eight\n\nStill reeling from Danielle's latest news flash, Aaron braced himself to meet the God of Thunder. ", "Unbelievable. ", "Someone should slap me now so I can wake the fuck up. ", "You'd think I'd be used to it by now and she wouldn't be able to continue surprising me.", "\n\nWith Thunder's open door policy, there was no need to knock and request an audience, but Danielle knew she was probably walking a fine line at the moment and didn't want to push her luck. ", "So she knocked on the doorjamb to get her leader's attention. ", "As they entered his office, Thunder stood and gave Danielle a frustrated look.", "\n\n\"I know, I know. ", "Just call me Vomitus,\" she said warily. \"", "I told you I can't help it.\" ", "Aaron gave her a strange sideways look.", "\n\nThunder ignored her then and turned to Aaron. \"", "Mr. Janson, pleased to meet you. ", "I trust you were comfortable on your flight here and that everything Danielle has told you hasn't been too much of a shock.\" ", "He already knew from Ghost's extensive background check on Aaron Janson that he was merely what he portrayed – an Archeologist from the University of Oregon who was orphaned and raised in the state foster system with no family connections and his hard work and intelligence had gotten him to the status he held today. ", "Other than scholarships, Aaron had never been given anything free in his life and those he rightfully earned.", "\n\nShould I bow or kneel? ", "In the end, Aaron simply shook the proffered hand in front of him. ", "Wow, what a grip. ", "He did his best not to stutter as he looked at the God standing in front of him, who didn't look anything like he thought a God should look like. ", "Not that he'd ever had need or opportunity to have given it much thought. ", "All Aaron had to work with were either early comic book drawings from when he was a child or the occasional superhero movie, so in his mind, he'd conjured up a picture of Chris Hemsworth, all deck out in battle gear. ", "Sure, the man was massive both in height and build, standing upwards of six foot eight, but with his shoulder length blond hair and sparkling blue eyes, dressed in well-worn jeans and a T-shirt, he looked rather normal. ", "And no fangs, that he could see. ", "Other than the battle gear, Chris Hemsworth was not too far off the mark. ", "Go figure. ", "I mean, really. ", "Who knew?", "\n\n\"It's an honor to meet you, uh... sir,\" he said not knowing what a God should be addressed as. \"", "She's been most informative and supportive, I might add. ", "I'm afraid I'm still trying to take it all in.\"", "\n\n\"I understand. ", "Just call me Thunder like everyone else around here.\" ", "Then to Danielle, he added, \"So, 'Vomitus'... I get the feeling that it would be much simpler and faster to ask you what you haven't told Aaron about thus far.\" ", "Danielle chose not to say a word but stood frozen in place with a strangely comical look etched across her face, her eyes cast downward.", "\n\n\"Well, she failed to warn me that you guys are vampires,\" Aaron proffered rather innocently in an attempt to actually aid Danielle in her dilemma. ", "Danielle noted it was a sweet attempt and appreciated it.", "\n\n\"Actually, I'm not a vampire. ", "Only those men who died and then are brought over by my father, Odin, are vampires. ", "I'm very much still a God,\" Thunder said calmly. \"", "But you needn't fear any of us. ", "None would dare harm you on my orders unless forced to do so under the guise that you're a threat to us and our way of life.\"", "\n\nAaron understood the subtle warning that had been issued in his communication. ", "In other words, 'Don't fuck with us.'", "\n\n\"No, sir,\" he dragged out thoughtfully. \"", "I mean, Thunder. ", "I swear I would never give you a reason to hurt me. ", "Ever.\"", "\n\n\"Alright...\" Thunder said as he seriously eyeballed Aaron up and down. \"", "I'll have to trust you, for now.\" ", "Thunder was forced to accept this unusual situation and had decided to do so with an open mind. ", "It was either that or smite him where he stood. ", "He chuckled to himself at the thought. ", "It had been quite a while since any smiting had taken place, especially regarding humans. \"", "Please take a seat, both of you.\"", "\n\nThey did as instructed and Aaron audibly sighed while Danielle took a deep breath and attempted to gather her wits. ", "She spent the next few minutes bringing Thunder up to date.", "\n\n\"As for the binding chain, I was hoping we could appeal to Freya to intervene in removing it,\" she inquired. ", "Her expression reflected the plea she was delicately trying to make.", "\n\n\"Absolutely not,\" Thunder adamantly replied. \"", "The chain is secondary to the EOD's retrieval. ", "You know what's at stake if we don't find it. ", "Especially now that we know Loki is actively searching for it.\"", "\n\n\"Yes, sir. ", "I'll keep working with Zahara on finding a solution for Aaron then.\"", "\n\nThunder turned his attention back to their guest. \"", "Aaron, I hope you've gotten all settled in and are comfortable. ", "If there's anything that you require, please let us know. ", "I ask that you be patient with us. ", "We have a meeting scheduled to bring everyone else up to date in just a few minutes. ", "I'm requiring both of you to attend. ", "If there's nothing else, you're dismissed.\"", "\n\nAlthough he had a multitude of questions, Aaron nodded his assent, hoping to gain additional information from Danielle at the nearest opportunity.", "\n\n\"We'll be there,\" Danielle agreed while grabbing Aaron's arm and guiding him away from Thunder's office.", "\n\nOnce they'd made their way down the hall a safe distance, Aaron stopped her abruptly, placing his hands on her shoulders and turning her to face him. \"", "I think it's time you answered some of those questions I have.\"", "\n\n\"Actually, I think it would be best to wait until after this meeting. ", "You should learn quite a bit more there. ", "Then we will talk. ", "I promise.\"", "\n\n\"You may be right. ", "We'll talk later and you can fill in what I'm unable to piece together. ", "But can I just say, 'Wow!' ", "I never...I mean, wow!\" ", "Aaron's eyes were alight like a child's shone at Christmas time. ", "He looked ready to jump around and do cartwheels down the hallway like a member of the US Olympics gymnastics team going for the gold medal prize.", "\n\n\"You know, for such an intelligent man, you sure have a way with words,\" she chortled sarcastically, reflecting the excitement in his eyes. ", "I like this bubbly side of him. ", "Not bad. ", "Not bad at all.", "\n\n\"This is all so phenomenal. ", "Gods, vampires, Shieldmaidens... All these things that I've been taught were myths,\" he said bewilderedly with a goofy grin on his face. \"", "I can't wait to research all of this and document everything...\"\n\nDanielle threw her hands up in a stop motion. \"", "Whoa, whoa, whoa. ", "Hang on, now. ", "Hold up. ", "Not gonna happen, Einstein.\" ", "After getting his attention, she continued, \"Why do you think you believe that all of these things are myths in the first place? ", "We planted all of those rumors, made them seem unbelievable so that mortals wouldn't know and couldn't interfere.\"", "\n\nAaron's face went immediately from surprised to crest-fallen. ", "The corners of his usually tempting mouth drooping downward and the corners of his eyes to match. ", "The sight gave Danielle a slight pain in her chest, puzzling her.", "\n\nTo think I'll never get to share my findings. ", "I'm a scientist. ", "I'm not good at keeping secrets. ", "I find them out and shout them to the world.", "\n\n\"I'm sorry, Aaron, but you have to understand. ", "If all of this was common knowledge, we wouldn't be able to stop the horrid events that could demolish your world. ", "If you'd just stop and think, you'd realized that,\" she pled with genuine concern while rubbing the heel of her hand over the top of her chest to ease the twinge still located there. ", "She wasn't sure why this bothered her so when she knew they would enthrall Aaron as soon as he was out of danger. ", "He'd never remember any of it anyway, but she didn't want him to know that now.", "\n\n\"You're right. ", "I wasn't thinking clearly,\" he conceded. \"", "Humans couldn't handle this without somehow destroying themselves in an all-out struggle for power. ", "This is all so much to assimilate at once. ", "And I can't help wondering what else is out there that I don't know about yet. ", "I'm looking forward to learning everything I can, even if it's only for my own knowledge.\" ", "Danielle could live with that for now.", "\n\nIf you only knew just what all was really out there, she thought to herself.", "\n\n*****\n\nDanielle wanted to introduce Aaron to Zahara before the meeting began and reached out to her through her thoughts. ", "Zahara, can I speak with you a minute before the meeting?", "\n\nCertainly. ", "I understand the mortal is with you. ", "I look forward to meeting him.", "\n\nThey hurried through the corridors, the sound of their booted feet echoing off the walls and saw Zahara standing just outside the doors to the conference room.", "\n\n\"You must be Aaron,\" she greeted him, holding out her hand.", "\n\nAaron returned the gesture, taking her hand in his, smiling. \"", "Yes, I am. ", "Aaron Janson. ", "Glad to meet you.\"", "\n\n\"Aaron, this is Zahara, our visionary. ", "She's the one assisting us in finding a way to remove the chain.\"", "\n\nZahara may be a visionary for the warriors, but she was also certainly a vision. ", "Aaron couldn't help thinking that she should be a high fashion New York model. ", "Tall and lithe in Grecian style robes with long flowing black hair and a silver frost framing her face. ", "Her skin so radiant it almost glowed and her voice was reminiscent of angels singing. ", "Is she an angel?", "\n\nDanielle elbowed him in the side to stop the stupor he'd fallen into. ", "She felt another twinge and began rubbing her chest again with the heel of her hand. ", "Strange. ", "Maybe I should visit Emeline for a healing.", "\n\n\"Well, we appreciate your efforts, of course. ", "Any progress in that area?\" ", "he inquired still with a slightly glazed look, appearing somewhat mesmerized.", "\n\nZahara took no note of Aaron's attention. ", "She seemed to have that effect on mortals. ", "There were times she would have loved to yell 'Snap out of it! ", "I get that I'm ethereally beautiful,' accompanied by the vigorous snapping of her fingers right in front of their faces. ", "Alas, that was not her nature, but she could dream...\n\nIn answer to Aaron's question, she shook her head. \"", "No, I'm afraid not yet, but I do have some theories that I'm investigating and hope to have a solution soon. ", "I assure you we're doing our best. ", "You must understand that this is a first. ", "We've never had it happen before, but we're diligent in our efforts.\"", "\n\n\"Thank you. ", "That's all I can ask,\" Aaron replied humbly with obvious admiration on his face.", "\n\nTime to break this up, Danielle thought. \"", "Come on, Aaron. ", "I want to introduce you to some of the others you haven't met yet.\"", "\n\nWith a nod to Zahara, she guided Aaron inside of a typical large conference room with an oversized oval table in the center surrounded by accompanying leather seats. ", "Other than comfortably luxurious, he didn't see anything special about it and wondered why he felt just a little disappointed. ", "Maybe he was expecting these immortals to live like kings and this room would resemble a more upscale executive suite. ", "So far, he'd seen nothing that would remotely point out that these people were anything other than normal, except the fangs on Steele, of course. ", "And the size of the male warriors. ", "There was that.", "\n\nHe watched as the males greeted each other by embracing in manly one-armed bear hugs, slapping each other on the back and spouting, \"Brother,\" in unison. ", "Then everyone in the room settled around in for the meeting.", "\n\nDanielle called for the others attention. \"", "Hey, everyone. ", "I'd like you to meet Aaron Janson. ", "I'm sure by now you all know why he's here, so I won't go into that right now.\"", "\n\nShe paused for everyone to look their way and started the introductions from one side of the room to the other. \"", "Aaron, you've already met Steel, Turbo, Nadine and Emeline. ", "This is Ghost, Vex, Valeria, Blaze, Savage, Raven, Makayla, Annika, Slash and over there is Myste,\" she said pointing to the other side of the room at a lovely red haired beauty who seemed to have isolated herself. ", "One and all greeted Aaron with a friendly welcome except Myste, who simply nodded her head once with a blank, unaffected stare. ", "He noticed that Myste maintained her distance from the others, speaking and making eye contact with no one.", "\n\nAaron leaned into Danielle and whispered, \"What's up with Myste? ", "Does she not like humans or something?\"", "\n\n\"Oh no, she's actually really great,\" Danielle spoke softly. \"", "Don't take it personally. ", "You see, she's really flighty and moody and her hair color changes with her moods, kind of like that mood ring you guys had back in the 70's. ", "Currently, her hair is red, so what do you think that means?\"", "\n\nAaron took a guess. \"", "She's pissed off?\"", "\n\n\"You got it. ", "So we keep our distance. ", "She can also control the weather and we don't want to get on her bad side right now. ", "You could wind up all wet with a lightning bolt up your ass.\"", "\n\nAmazed at this new knowledge, Aaron looked up to see several of the men exchanging knowing smiles, not realizing they heard the entire exchange with their enhanced senses. ", "He silently continued to observe the others in the room, wondering what gifts they each possessed. ", "He'd already figured out the correlation between the male's names and their talents or gifts. ", "He just wasn't sure what all of them were yet. ", "There was something else to add to his list of questions.", "\n\nAcross the room, a silent exchange was happening between the bonded warriors. ", "Valeria squirmed in her seat as Ghost reached below the table and teased the inside of her thigh with his forefinger. ", "She lightly grabbed his hand and shoved it off her leg. ", "Without delay, he replaced his hand on her leg and once again teased the inside of her thigh. ", "She again removed his hand and crossed her legs in the opposite direction, distancing herself from him. ", "Knock it off, Joseph, she warned through their shared link.", "\n\nI can smell your arousal, babe. ", "You like it.", "\n\nYea, you and every other male in this room! ", "Cut it out!", "\n\nBut Ghost was not to be deterred that easily. ", "He loved to tease her whenever he got the chance and now was as good a time as any. ", "Truth be told, she loved it, too. ", "He hooked his foot in a bottom rung of her chair and slowly turned her back to his direction.", "\n\nSo help me, Joseph, if you don't stop I'll break it off. ", "Wait till we get out of here. ", "Please, she pleaded.", "\n\nShe was saved when Thunder and Vengeance entered the room commanding everyone's attention. ", "Simply the presence of the God and his second was more than enough to dominate a room and everyone in it. ", "Pure might and strength revolved around them like a whirling dense London fog.", "\n\nOkay, you win. ", "For now, Joseph acquiesced, leaving Valeria to sigh with relief.", "\n\n\"Thank you all for coming on such short notice. ", "I believe everyone's present and no one is currently out on assignment,\" Vengeance began. \"", "We'll get to new assignments shortly, but first I believe we need to address the immediate matter regarding the EOD.\" ", "He turned to Thunder for his input.", "\n\n\"Yes, as I'm sure you've all heard at least something about it by now, there have been new documents regarding the EOD discovered by Dr. Aaron Janson, Danielle's, uh... new acquaintance.\" ", "He motioned to Aaron acknowledging his presence. \"", "I wish to extend a welcome to him and want you all to do the same. ", "This is an unusual circumstance for all of us but I believe we'll get through it with minimal disturbance to our regular routines. ", "On that note, I'd like Dr. Janson to explain a little about the documents and current excavation taking place at the North Sea. ", "Doctor, if you don't mind...\"\n\n\"Ah...Yes, I'd be glad to tell you what I know.\" ", "Aaron was put on the spot but quickly gathered his wits about him and imagined himself to be in an ordinary college campus staff meeting addressing his peers. ", "I can do this. \"", "I understand after the fact that I've been duped by Mr. Tormond into working for him to acquire the Eye of Odin. ", "He provided me with some documents he claimed were passed down through his family lines. ", "I've brought copies of the documents with me, but the originals are currently at the University of Oregon in the custody of our linguist. ", "She's attempting to translate the documents to determine clues to the actual location of the EOD. ", "So far, we've currently been led to the North Sea location site but have not as yet found it or any sign that leads me to believe it's actually there. ", "I'm still hopeful it will eventually come to light.\"", "\n\n\"Thanks, Doctor. ", "Some of you may not be aware that Danielle and the doctor were attacked at the dig site recently, which is why he has been brought here for our protection until we can determine Tormond's full involvement and possible next moves. ", "We do know that he was able to keep Zahara from discovering his plans through her visions by hiring through a third party human, the doctor, and keeping both himself and his demons physically uninvolved. ", "This is a new concern for us as we depend on Zahara's visions in directing us where we are needed, especially for something as important as the EOD. ", "Fortunately, the binding chain was located and triggered the necessity of our involvement.\"", "\n\n\"Is there any word on the recovery of the Spear of Truth and the Heart of Hope?\" ", "Steele asked.", "\n\nConcerned murmurs spread throughout the room and Aaron listened attentively, unaware of what these items were or their impact on the current situation.", "\n\n\"No, not at this time. ", "There's been no mention of their whereabouts or any recovery attempts. ", "But keep your eyes and ears open. ", "Since Loki is diligently searching for the EOD, it won't be long before he'll be searching for the remaining relics, if not already through the same type of efforts he's using now. ", "We must keep him from acquiring even one of these sacred relics. ", "In the wrong hands, all three combined would mean the destruction of us all.\" ", "Thunder turned his attention to his visionary. \"", "Zahara, I'm afraid you'll need to be more vigilant in conducting your vision quests now.\"", "\n\n\"Yes, of course. ", "I'll do my best, My Lord,\" Zahara replied with respect to her commander.", "\n\n\"Looks like we can expect things to escalate in a much nastier way than usual,\" another said.", "\n\n\"Yes,\" agreed Vengeance. \"", "I've also received intel that Tormond's recruiting efforts have escalated. ", "We'd best do the same. ", "I smell another great battle on the horizon.\" ", "Vengeance loved battle most of all and the thought excited him on some level. ", "Certainly not the death and destruction of his comrades, but he secretly thrilled to the thought of giving a great battle cry and slaying his enemies.", "\n\n\"I will speak with Odin about increasing our numbers in preparation,\" Thunder offered. \"", "Further recruitment and training should be implemented in force right away. ", "At the least, I'll start making arrangements for a temporary transfer of warriors from other settlements. ", "As for our current situation, I'm going to ask some of you to assist Dr. Janson in acquiring both combat and weaponry training. ", "It would be best if he could assist in his own defense, as much as possible. ", "I realize time will not allow for extensive training, but do what you can in the time we have. ", "Turbo, please get him started with some hand-to-hand and then pass him off to Slash and Blaze for the weapons training. ", "You guys know what to do.\"", "\n\nThunder received a combined \"Yes, My Lord\" response from the warriors. ", "He sat back in his chair with his hands steepled in front of him.", "\n\nVengeance took over the meeting. \"", "On to other business...Zahara has shared her latest visions and these are the newest assignments. ", "Since Turbo, Slash and Blaze will be otherwise occupied here at the compound, I need Vex and Ghost to head over to Las Vegas and get a handle on the recruitment scene happening there. ", "Ghost, if you can use your gifts to get close to Tormond's men undetected, do it. ", "His bodyguards should have plenty of intel to unwittingly share. ", "Keep it low keyed and don't start anything if you can prevent it. ", "This is a fact-finding mission, at this point, but report anything suspicious immediately. ", "Justice, I need you and Raven to head out to California. ", "There's some trouble about to take place there that needs attending to. ", "Get with Zahara for further instructions.\"", "\n\nVisibly gritting his teeth and tightening his jaw, Thunder rose and added, \"Finally, Zahara has asked that those ladies who can, please meet her for a quick discussion regarding the binding chain issue. ", "I think that's it for now. ", "Everyone stay alert and be safe.\"", "\n\nWith the meeting dismissed, they all filed out of the room. ", "Most seemed to be murmuring to each other and sharing concerns. ", "Some left through the door while others traced off without notice.", "\n\nDanielle took Aaron by the arm and reintroduced him to Turbo. \"", "Turbo is our mixed martial arts expert. ", "He'll be a great teacher for you, Aaron.\" ", "Aaron looked at her with saucer-wide eyes when he realized she was leaving him behind. ", "He wasn't sure if it was the immortal warrior part, the vampire part, or just the fact that this guy was six foot two with endless muscles covered in tattoos and looked like a consummate soldier-for-hire part that had him on edge. ", "Turbo was dressed in jeans and a leather jacket, had a blond military buzz cut, commanding blue eyes, mustache/goatee combo, and piercings in his ears, nose and lip, not to mention the fangs Aaron knew were also there, even if not currently visible. ", "This guy looked like he could go off at any minute.", "\n\n\"I'm leaving him in your hands, Turbo. ", "Be easy on him,\" she said as she trailed off laughing. \"", "Don't worry, Aaron. ", "You'll be fine and I'll catch up with you later,\" she yelled from down the hall, disappearing around a corner.", "\n\nAaron swallowed hard and Turbo's first thought was to play it up and scare the shit outta this newbie. ", "But his second thoughts prevailed. ", "He figured the guy had been through quite a lot in the past twenty-four hours and he might as well give him a break. ", "There'd be plenty of time for harmless antics later. ", "So he pocketed his tough exterior and donned an amiable face, motioning for Aaron to follow.", "\n\n\"Alright, Doc. ", "Let's go. ", "It's okay if I call you Doc, right?\"", "\n\n\"Sure, or just Aaron would be fine.\"", "\n\n\"Great, Doc it is.\"", "\n\nAaron followed along wondering what he'd gotten himself into and how the hell he was going to get out of it. ", "Preferably alive.", "\n\n*****\nChapter Nine\n\nThe corner of Fifth and Main at five p.m. was about as busy as a one-armed taxi driver with crabs. ", "Traffic puttered along a little faster than a snail's pace. ", "It was rush hour in downtown Whiting, California. ", "Not exactly a big city, but they had their fair share of automobiles, minus the thick clouds of suffocating smog.", "\n\nJustice and Raven stood in the nearby alley shadowing their presence from possible onlookers. ", "Luckily they weren't surrounded by smelly dumpsters that contained a week's worth of local garbage from the surrounding businesses. ", "For an alley in the middle of a prosperous business district, it wasn't too bad. ", "The sun was still shining as it descended into the western horizon and the temperature was cool enough to allow for their leather jackets.", "\n\nAccording to Zahara's vision, they were on the lookout for two school buses full of high schoolers heading Northbound on their way to an out of town football game. ", "Her vision had revealed a hostage situation with an outcome of several deaths. ", "Unnecessary deaths. ", "Of course, this was only one possible outcome, thus the pre-warning of the vision Zahara received that involved the Huldrekall and their human minions wreaking havoc in the mortal realm. ", "If they could thwart the demons and their horde of miscreants before they caused any damage, none would be the wiser and the mortals could go on about their lives, business as usual, in complete ignorance of the malevolent forces surrounding them. ", "Blissfully unaware of the evil that breathed down their necks like a bill collector, or worse, a telemarketer.", "\n\nThe warriors couldn't prevent all bad occurrences and only received warnings, through their visionary, of those that included direct involvement of the Huldrekall. ", "If they were out and about and happen to see a problem not demon related, they would certainly sneak in and assist the human authorities however they could, without revealing their existence. ", "As they referred to it – an unseen event – which was both unseen by Zahara beforehand and the hero's sight unseen by the mortals.", "\n\nSo far, Justice and Raven hadn't felt any of the usual vibes or detected that sulfuric scent of brimstone that accompanied the demons, but they stayed on high alert knowing whatever was going to go down would happen fast and without much warning. ", "Justice just hoped they could stop the event with minimal detection. ", "It was definitely rush hour out there and he didn't want to have to corral a large mass of people to enthrall. ", "Raven didn't share the gift of enthrallment and he certainly didn't have one of those flashy thingies that they used in the Men In Black movies. ", "Nope, he had to do it the old fashion way, one by one, reaching into their minds, removing and replacing each memory separately. ", "He really wanted one of those flashy thingies right now. ", "Ah, fantasy. ", "Isn't it ironic? ", "In the words of the immortal Rolling Stones, You Can't Always Get What You Want.", "\n\nRaven had the ability to control animals, but in the middle of the busy city, a bunch of stray dogs and cats, rats or pigeons weren't going to do a whole lot of good. ", "And shapeshifting would really call attention to them. ", "They were going to have to rely on good old superhuman strength and fighting skills to carry this one through. ", "Plus, there was always Justice's speed to assist in gaining the upper hand.", "\n\nBefore he saw them round the corner a few blocks away, Justice heard the excited rallying, cheering and the raspy shake of pom-poms headed their way. \"", "Be ready, Raven. ", "Our buses are about to make an appearance.\"", "\n\n\"Ready and waiting to ash their asses.\" ", "And she was. ", "Nothing would make her feel better right now. ", "Raven knew that the demon horde was growing in size and she didn't mind the extra time they all seemed to be spending lately to cull the herd, so to speak, of the bad guys, but it really just pissed her off when they chose children as targets. ", "Why not two tour buses full of adults vacationing nearby? ", "Not that she wished them ill, of course. ", "But these were just kids. ", "She even accepted the fact that this fight could continue forever. ", "Or at least until all of Odin's symbols could be located and the power of the realms was restored to the rightful Gods.", "\n\n\"Ah, and right on cue...there's the lovely bouquet of brimstone. ", "I just love the stench of brimstone in the morning. ", "Don't you darling?\" ", "Justice said in his best Cary Grant imitation. ", "He quickly did a three-sixty scan of the area and spotted the culprits on the roof of the three-story building across the busy street. \"", "Demons. ", "Two of them. ", "Up high, three o'clock. ", "I guess I don't need to tell you that if we know they're here, they know we are, too.\"", "\n\n\"Got them. ", "And I think their lowly peons just rounded the corner behind the school buses.\" ", "She reached into her leathers for one of her daggers and throwing stars, whereas Justice preferred to carry a sword strapped to his back as his weapon of choice. ", "They also had their holstered Glocks, but they would be a last resort due to the vast number of mortals in the current vicinity.", "\n\nSix Hells Angels wannabes cruised slowly behind the buses about two car lengths back. ", "Obviously, they were going to have to overtake the buses to create a hostage situation, but thanks to the snail crawling traffic, the demons were forced to wait until they had an appropriate opening to do so. ", "It wouldn't do to be caught in traffic while making demands. ", "They would need an escape route.", "\n\nThey watched the buses pass the alley they were currently concealed in. ", "At least a hundred extremely loud teenagers occupied them, half of which were hanging out the rows of small double paned windows with painted faces, blowing horns, waving pom-poms of red and black, and chanting 'We're number one!' ", "with the accompanying hand gesture. ", "Being the teenagers that they were, some of those 'number one' hand gestures looked more like birds.", "\n\nJustice and Raven continued to move down the street in pursuit of the buses, maintaining their positions by shadowing along the way. ", "The borders of town housed the warehouse district of Whiting approximately five miles North and Justice presumed the confrontation and attempted takeover would happen in that vicinity. ", "If the demons didn't make their move at that time, they'd have to wait until nearing the next city on the map. ", "It wouldn't do to get caught out in the middle of nowhere with not even a mountain to use for cover.", "\n\nThe rooftop demons across the busy street were leaping from the top of one building to the next following the procession of buses to the edge of the city. ", "Their final leap from the last accessible building took them to the tops of the buses themselves. ", "One on each of the nomadic yellow repositories that were unwittingly transporting a number of America's youth directly into the jaws of destruction.", "\n\nRaven and Justice had no choice but to follow until the vehicles came to a stop. ", "With all the noise coming from the buses, they'd probably never notice a commotion happening right above them, but confrontation now could result in indirectly harming the driver, risking the lives of the occupants they carried. ", "Besides the two demons, there were the six motorcycle flunkies to deal with. ", "Holding out a few more minutes would make a world of difference when it came to saving innocent lives and it gave Raven time to call for the assistance of a few furry friends.", "\n\nAs Raven made her way toward the warehouse district still shadowing down the street in secrecy, she opened her mind up to the various animals around the industrial area, her powers calling out to them. ", "Come, my friends. ", "Heed my call. ", "I need your help.", "\n\nThe buses came to a halt at a stoplight near the edge of the warehouse district, one behind the other. ", "Justice felt now was the best time to thwart any further plans the Huldrekall had to take over the vehicles and their passengers.", "\n\n\"Raven, I'll disengage the demon on the first bus. ", "You grab the second one. ", "Let's stop this before anyone gets hurt or the situation worsens.\"", "\n\n\"My pleasure,\" she replied with a sly, slightly devilish smile.", "\n\nJustice watched as Raven ran and leaped to the top of her assigned bus, her short blue/black mane whipping around her face and her long leather coat winging behind her.", "\n\nShe looks like Kate Beckinsale in Underworld. ", "Minus the fangs, he thought.", "\n\nEven though the demon knew warriors were present, they still had no idea where they located. ", "They also had a really bad habit of being too sure of themselves and never fearing the warriors, as much as they should. ", "It was easy for Raven to sneak up on this unsuspecting demon, which she did in a movement reminiscent of a cannonball. ", "Leaping up on top of the bus in a nonstop running fashion and barreling the demon off on the other side so fast it wasn't sure what had hit it. ", "They hit the ground rolling and tumbling across the hard asphalt stopping a few yards away near the dry cement gutter's edge.", "\n\nAh, I've seen this Huldra before. ", "She won't get away this time.", "\n\nThe female demon apparently recognized Raven, also. ", "When she finished rolling to her knees, she swiftly jumped into a running stance and headed off into the nearest warehouse building, breaking through its locked oversized doors with ease. ", "And Raven was right on her ass just twenty feet away already retrieving two throwing stars and hurling them in her direction.", "\n\nAfter seeing that Raven had successfully forestalled the capture of the second bus, Justice managed to duplicate her hit and run the procedure with his own style and flare thrown in. ", "There was always room for improvement in his book. ", "After taking down his own demon, they followed suit into the same warehouse Raven and her foe had disappeared into. ", "Before entering, Justice stopped to check on the whereabouts of the motorcycle gang and was pleased to see that they were joining the party already in progress and had abandoned the two school buses that were now safely driving away in the opposite direction.", "\n\nDisaster averted, he was pleased to report to Raven.", "\n\nAwesome.", "\n\nMinions coming this way to join us.", "\n\nThanks for the heads up. ", "I'm fine and I've called some friends to help us out.", "\n\nYour friends are always welcome. ", "Call if you need me. ", "I'm just heading inside the warehouse now.", "\n\nJustice had lost the visual on the second demon and the smell of brimstone was permeating the air in the building now. ", "He took in the scene of the warehouse before him. ", "There were rows and rows of crates creating mazes throughout the warehouse that were stacked taller than anyone could see over. ", "He unsheathed his sword and decided to perch on top of one such row discerning it might be easier to locate his enemies this way. ", "The bikers hadn't made it inside yet and there was no one else in sight, but he chuckled as he took in a spectacular view of an army of rats that seemed to be congregating on the second level at the top of the stairs. ", "Someone was in for a surprise attack. ", "All they awaited was the Pied Piper to toot his flute.", "\n\nRaven followed a trail of dribbling blood spots on the ground in front of her. ", "Obviously, at least one star had made its target. ", "She caught up with her nemesis trying to exit on the other side of the warehouse.", "\n\n\"I wouldn't do that, if I were you,\" Raven warned, but the demon didn't heed that warning.", "\n\nThe Huldra just hadn't been expecting the pack of mean and snarling stray dogs to be waiting for her and impeding her departure to what it had hoped was relative safety. ", "Raven directed the pack to simply stand guard around the demon to prevent her escape. ", "They formed a circle around the demon, snarling, snapping and growling low in their throats, gnashing their wickedly pointed teeth as saliva seeped from the corners of their muzzles. ", "The strays parted allowing Raven to enter their savage circle.", "\n\n\"Must you have your dogs do your fighting for you, warrior?\" ", "the she-demon asked.", "\n\n\"Of course not. ", "They won't harm you unless you keep trying to run away. ", "We've apparently met before and you're scared of me, aren't you? ", "I don't recall what I did to you last time, but it was enough for you to remember me anyway. ", "Just not enough to get rid of you. ", "I'll remedy that this time,\" Raven taunted and blew through the demon's false sense of bravery.", "\n\n\"Aaarrgghh!\" ", "the demon screamed in frustration as it readied for attack.", "\n\nDagger in hand, Raven braced as the demon lunged toward her with a dagger of its own. ", "She effectively blocked by throwing her left arm out and up against the offending attacker's outward thrust. ", "Then followed through with her right, planting the dagger deep into the demon's chest cavity. ", "As the demon doubled over she ripped its own dagger from its grip and returned it to its owner, plunging it into the demon's back straight into the heart. ", "Without wasting a breath, she tore her blade from its chest and swiped it underneath the folded form across its throat, then placed her booted foot on its back shoving it prone to the ground.", "\n\n\"Recover from that, bitch,\" she spat as ash began to float around her. ", "She cleaned her weapon and assessed herself noticing a cut in her leather sleeve where she'd blocked her attacker. \"", "Shit, I liked this coat. ", "You got off easy,\" she snarled at empty air. ", "Motioning for her pack of strays to follow, she headed back into the warehouse.", "\n\nJustice had lost his sword and was going hand to hand with his demon. ", "This one was twice the size of Raven's opponent and bigger even than Justice. ", "Loki sure did know how to pick them. ", "Justice was one of the shorter male warriors at six foot two inches, but the muscular shape he'd acquired from his transformation made up for any lack of height. ", "Not that Raven could really call Justice short. ", "Her five foot five stature wasn't exactly commanding. ", "She watched Justice battle as she approached cautiously from the opposing end of the building knowing there might still be minions amongst the maze of crates that surrounded her.", "\n\nJustice froze. ", "A biker clad minion had successfully snuck up on him from behind and there was the cold steel of the barrel of a gun digging into his back. ", "But the inevitable bullet never expelled, for Justice used his supernatural speed to step sideways, turn and kick the gun out of minion's hand, breaking it's wrist in the process. ", "Then he jammed his fist up into the ugly mug staring daggers at him and connected with an already crooked and obviously-previously-broken-several-times-over-nose, driving the broken fossil upward into its brain. ", "The sound of cartilage disintegrating reverberated off the spacious warehouse walls. ", "As the battered body crumpled to the ground, another came at him with massive, meaty fists that reminded him of some overstuffed toy boxing gloves, but Justice still had a demon at his back to contend with. ", "Justice took two running steps toward the Mr. Meaty Fist, jumped and planted his feet mid-chest, using the flunky as a springboard to propel him up and over the demon at his back. ", "He tucked and flipped mid-air in his best aerobatic-gymnastics move, landing several feet back, putting him now at the demon's back.", "\n\nRaven picked up the pace and stormed into the fray, recovering Justice's sword in the process. \"", "Justice...catch!\" ", "she yelled as she tossed the weapon through the air in his direction.", "\n\nThe rapier flew arching through the air with perfect precision and Justice snatched its hilt in a graceful fluid movement, following through with its momentum already on course, slicing through and taking the head clean from the demon in front of him. ", "Mr. Meaty Fists had second thoughts and began backing away.", "\n\n\"Impressive,\" Raven praised, \"But watch this...\" She placed two fingers in her mouth and gave a loud, eardrum splitting whistle.", "\n\nThere was a low rumble that began on the upper floor and grew louder by the second. ", "The remaining five bikers looked at each other and searched around them for the cause of the disturbance. ", "One of them pointed toward the stairway and shrieked, \"Rats! ", "Thousands of them!\"", "\n\nA waving carpet of rats was scurrying down the stairs, hundreds scampering in their direction, appearing like crazed rabies infested rodents. ", "The bikers ran for the exit and met Raven's mongrel pack waiting for them, thick saliva still dripping from their hungry snouts. ", "Looking back over their shoulders at the advancing mass of beady-eyed muroidea rolling toward them, they decided to take their chances with the growling and snarling pack of dogs, tearing off toward their motorcycles with canines snapping at their heels and ripping their pants legs to shreds.", "\n\n\"Now, I'm impressed,\" Justice offered with a mock bow and sweep of his arm.", "\n\nRaven raised her Glock, but Justice placed his hand on it, lowering it back toward the ground and shook his head.", "\n\n\"I don't think we'll see them again. ", "Tormond doesn't like surviving minions unless they have a dead warrior to show for it,\" he offered.", "\n\n\"Yea, you're right. ", "They're toast for sure. ", "They'll wish they'd stuck around to let us finish them off by the time he's through with them.\"", "\n\n\"Let me get rid of this guy and we can head home,\" he said pointing to the nose-less corpse.", "\n\n\"I suppose you want his bike,\" she said motioning to the lone motorcycle still standing in the empty lot.", "\n\n\"You suppose right. ", "But it's not a bike. ", "It's a hog.\"", "\n\n\"Right...,\" she said rolling her eyes. \"", "I'll just drive the SUV then.\"", "\n\nWhen Justice didn't move, she shoved his shoulder playfully. \"", "Do your speedy thing already and let's go. ", "I'm hungry.\"", "\n\n\"I'm not doing my speedy thing. ", "I'm tracing him out of here to someplace woodsy. ", "You could do it just as well.\"", "\n\n\"Oh, no. ", "You offered first. ", "And besides, you whacked him. ", "He's your mess to clean up.\"", "\n\n\"You know, I liked you better when you were impressed.\"", "\n\n*****\n\nAs Danielle entered Zahara's home, she took in a deep breath of the calming scents surrounding her. ", "A nice blend of lavender and chamomile filled the air, but what interested her most was the aroma of freshly ground and brewed coffee. ", "Ah good, Emeline is here. ", "Emeline may use her dried herbs and potions for healing, but she also made the best damn cup of coffee around and that was the type of healing Danielle currently required. ", "Who needed a famous national coffee chain when you had Emeline's freshly brewed goodness?", "\n\nValeria, Makayla, Nadine and Annika were also in attendance and everyone greeted Danielle with warm but guarded smiles. ", "She had the feeling that the news regarding the binding chain must not be good. ", "Valeria usually kept her in the 'know', but they hadn't seen or communicated with each other recently due to Danielle's current assignment and distraction.", "\n\nIf she didn't know any better, Danielle would have looked upon the scene before her as just a neighborhood committee meeting of local ladies in the community. ", "Everything and everyone looked so normal relaxing and chatting amongst themselves in Zahara's spacious and decadently decorated living room. ", "Nothing about the scene conveyed the realization of who gathered here and what their topics of discussion were. ", "No one was dressed for battle, no weapons were present and no battle plan was laid out before them. ", "There was no need for all of the battlement couture they donned on assignment as the outside world was completely ignorant of their presence on the earthly plain and they were well guarded against any otherworldly creatures and beings that could pose a threat to them.", "\n\nZahara served tasty finger sandwiches and coffee to the others in the room, while Emeline brought a cup of coffee especially to Danielle. \"", "Here, have a seat. ", "I put a small shot of whiskey in there for you. ", "Thought you could use it. ", "Healer's orders,\" she chuckled smiling sweetly. ", "All she needed was a little Irish Cream to top it off.", "\n\nDanielle thanked her and then addressed the group of women she knew as both warrior sisters and friends, \"Thanks for being here to help me brainstorm and hopefully find some kind of solution. ", "I understand you've all been conducting research in your spare time. ", "I really do appreciate it.\"", "\n\nZahara stepped up to begin the discussion. \"", "Yes, and so far, we haven't discovered any useful information in the ancient scrolls. ", "Actually, we didn't know specifically where to begin, so we've been working backward, starting with what we do know about the chain and its ceremony.\"", "\n\n\"Yes,\" Nadine said. \"", "We were able to rule out a few things, such as reincarnation and the removal only by death, that obviously have no bearing – well, that we know of.\"", "\n\n\"And then there are the magical qualities,\" Annika offered. \"", "I'd like to go over exactly what took place when the chain attached and possibly examine Aaron. ", "Emeline could assist me with this. ", "There may be something learned through the examination that will give me some insight as to why it happened.\" ", "Emeline nodded her assent.", "\n\n\"Sure,\" Danielle agreed. \"", "Anything you need us to do, we will.\"", "\n\nMakayla spoke up. \"", "I pointed out that, even though my bondmate has passed, my chain is still attached, which prompted us to realize that the situation is the same with you.\"", "\n\nDanielle absently brought her hand to her chest and felt the chain through her clothing, nodding in agreement.", "\n\n\"And don't forget about the ceremony, the blessing received by Freya, how you must truly love your mate to enter into a chain bonding,\" Valeria added.", "\n\nDanielle gasped audibly and her gaze seemed to glass over, barely keeping the wetness at bay and gaining the curious and concerned stares of everyone present. ", "She so did not want to cry. ", "Yes, Alarr had hurt and deceived her, but it was such an embarrassment to have to tell these women the truth of their belief. ", "The chain was certainly not a 'true love' guarantee.", "\n\nEmeline rushed to her side. \"", "What is it, Danielle?\"", "\n\n\"I'm afraid that's not exactly true,\" she barely whispered, unsure if anyone even heard her.", "\n\n\"What's not true?\" ", "Emeline pressed further gently, placing her arm around Danielle's shoulders.", "\n\nDanielle's face flushed and silent tears trailed down her cheeks. ", "Her shame consumed her, but she knew they needed to know the truth. \"", "It's possible to bond without loving. ", "Alarr didn't love me. ", "Not truly.\" ", "Several comments of exasperation filled the room, but she continued. ", "She had to get it out once and for all. ", "She'd been hiding the truth for eight hundred years and realized it was eating her alive, preventing her from opening herself to any form of love or meaningful relationship. ", "It was easier to push it all to the back of her mind until Alarr's chain resurfaced. ", "All of the hurt and betrayal was fresh and new once again.", "\n\nSuddenly frustrated, she wiped the tears roughly from her eyes with the backs of her hands, physically shook her head to clear all thoughts of her humiliation and straightened her shoulders taking in a much needed deep breath and expelling it slowly with resignation. ", "Having fortified and gathered herself together, she continued. \"", "When Alarr thought I was sleeping, I discovered he bonded with me to further secure his military station. ", "He must have thought that he would be exalted because of my parentage. ", "He told himself that he wouldn't feel guilty about what he'd done and he hoped to come to love me in time. ", "I know, or at least I believed, that he cared for me, but I discovered quickly that it wasn't love. ", "Not true love.\"", "\n\nHorrified gasps filled the room.", "\n\n\"Oh, Goddess! ", "You would have been trapped forever. ", "How could he have done something like that to you?\" ", "Makayla said feeling so grateful for the time and love she had shared with her bonded mate. ", "It had been a long time since she'd allowed herself to feel that way because after all this time, losing him still hurt.", "\n\nThe revelation was quite a shock to everyone and they did their best to console Danielle.", "\n\n\"I never thought I'd say this about one of our fellow brothers, especially one that has fallen in battle, but – what a selfish asshole!\" ", "Emeline cried causing everyone, including Danielle, to laugh out loud. ", "And it felt good. ", "Real good.", "\n\nNadine joined in with her. \"", "I so have to agree with you on that! ", "Danielle, this is certainly not your fault and you shouldn't blame yourself in any way. ", "You should not have carried that burden by yourself for so long. ", "We are your sisters and we love you.\"", "\n\n\"You must promise never to do something like that again,\" Emeline added.", "\n\nDanielle looked around the room once more and saw the incredible bond that she shared with her warrior sisters. ", "It showed in each face and pair of eyes that affirmed Nadine and Emeline's statements and she knew she'd been a fool to bear this alone all of those years and her burden lifted.", "\n\nNodding she pledged, \"I promise.\"", "\n\nThe laughter and camaraderie had lightened the mood and there were several contented sighs throughout the room.", "\n\n\"So, where does this leave us? ", "It rules out the love connection, for sure,\" Annika asked, trying to get the conversation back on track. \"", "I'm going to really focus on the magical aspects for you, Danielle. ", "Please bring Aaron to my place and I'll get the examination underway. ", "As I mentioned, Emeline will assist, also. ", "And it wouldn't hurt to give you a good examination while we're at it.\" ", "Danielle was reminded of the chest pains she'd been suffering and agreed with their judgment.", "\n\n\"I agree,\" Zahara chimed in. \"", "But before we finish up here, I think we need to consider some of the strange things that have been happening to Danielle since the chain attached itself to Aaron. ", "They may have some barring on finding our solution.\"", "\n\n\"Well,\" Danielle began, \"I'm overwhelmingly attracted to him, uh...sexually. ", "And I can't seem to hold anything back. ", "I can't lie or even fudge the truth a little. ", "Whenever he asks me something, it just comes blurting out. ", "Which is why he's here in the first place. ", "Needless to say, Thunder is not too happy with me right now and it's going to take a veritable brain surgeon to enthrall him and remove all the information he's gained from me at this point.\"", "\n\n\"Wow, those sound like characteristics of being bonded. ", "Are you sure you don't have actual feelings for his guy?\" ", "Valeria asked while screwing her mouth in a quizzical shape and raising one eyebrow.", "\n\n\"No! ", "No way, he's mortal!\" ", "screeched Danielle. \"", "It's not even allowed.\" ", "She chewed on her nearest fingernail lost in her thoughts. \"", "Sure, he's great looking. ", "He's smart...and funny. ", "He's definitely got his good points and some even better points...\"\n\n\"Sounds like definite chemistry to me, mortal or not,\" Zahara deliberated. ", "I'll need to give this some more thought. ", "May need to look at it from a different angle, she contemplated silently.", "\n\nAs the meeting began to break up, Danielle pulled one of her friends to the side. \"", "May I speak with you a minute, Makayla?\"", "\n\n\"You betcha. ", "What's up?\" ", "Makayla took in her sudden serious face and continued, \"Do you want to go someplace a little more private? ", "We could head to my house if you'd like.\"", "\n\n\"Yea, let's do that. ", "Thank you.\"", "\n\nDanielle traced outside Makayla's front door. ", "Makayla was famous for her welcome mats with their original sayings, and sure enough, there was a new one in place reading 'If the House is a Rockin', Don't Bother Knockin'. ", "Nice Stevie Ray reference.", "\n\nBefore she could knock, the door opened instantaneously.", "\n\n\"What the hell you doin' out here, girl? ", "Come on, get in here.\"", "\n\n\"I didn't want to just invade your space.\"", "\n\nAnd a nice space it was.", "\n\n\"Invade away. ", "I invited you over, you know.\"", "\n\n\"I really like your new doormat.\"", "\n\n\"Yea, can you believe you can't buy a doormat with that on it? ", "I scoured the internet. ", "I was jamming to that song and thought what a great doormat that would make. ", "I had to have it custom made. ", "Just watch. ", "Now that I've done it, someone will copy my idea and make a fortune. ", "Thank you very much.\"", "\n\nDanielle let her ramble and laughed.", "\n\n\"So, what can I do for you, sweetie?\" ", "Makayla inquired.", "\n\n\"Well, you're the only one I know well enough that has been where I am. ", "You know, a chainmate survivor, for lack of a better term.\"", "\n\n\"Yes, I see. ", "You want to compare our situations because you're completely confused, aren't you?\"", "\n\n\"How'd you know?\" ", "Danielle asked, a little shocked at Makayla's understanding.", "\n\n\"Sweetie, after the bomb you laid earlier, it would be lucky if you weren't all kinds of messed up. ", "Especially after all this time. ", "I don't know how you internalized that for so long, if at all. ", "I'm waaaaay too impatient and would have been screaming from the rafters within a week.\"", "\n\n\"At first I was shocked and didn't think about it because of Alarr's death. ", "It didn't seem right to speak ill of him like it didn't matter anymore. ", "Then there was never a right time. ", "Everyone was grieving their own losses. ", "I guess I just kept pushing it down until I got used to acting like it was just life, something I, myself, had to get over.\"", "\n\n\"So, you tucked away the hurt and pain and learned to manage on your own, vowing never to love anyone like that again...\" Makayla said trailing off and looking into the beyond of misplaced thoughts.", "\n\n\"Yea. ", "That's why I wanted to talk to you. ", "I felt you might understand it and could maybe help shed some light on my current situation.\"", "\n\nMakayla gathered herself and smiled, giving her full attention back to her friend. \"", "Of course. ", "I'll do whatever I can to help.\" ", "She grabbed Danielle by the hand and led her over to the oversized couch to sit.", "\n\n\"Okay, tell me all about it.\"", "\n\n\"It's just that I'm so confused. ", "Now that you know you don't have to be in love to chain bond...\"\n\nMakayla cut her off. \"", "Whoa, stop right there. ", "You may not have to be in love, but you'd damn well better be. ", "Deeply, hopelessly and beyond all reason...ly... Or whatever. ", "You get my meaning. ", "Anyway, Alarr was an idiot and I can't believe he actually doomed you along with himself.\"", "\n\n\"It's just that I don't trust myself. ", "I thought I loved him, but now I'm not so sure. ", "It's totally possible that, if he would have survived the battle, I would have woken up one morning and realized I didn't love him after all. ", "Thank the Goddess I was spared that fate.\"", "\n\nMakayla let her continue without comment. ", "She seemed to be doing a pretty good job of reasoning on her own.", "\n\n\"But when I think like that, I feel guilty for it, like I'm glad he's dead.\" ", "Danielle put her head down, covering her face with her hands. ", "I'm not going to cry one more tear for that jerk!", "\n\n\"None of what he did, or didn't do, is your fault, Danielle. ", "That includes dying. ", "He died bravely in battle protecting our cause. ", "But you deserve to be free of him. ", "Unlike you, my mate did love me, and I, him. ", "I don't want to enter into another relationship like that because I've had my true love.\" ", "She lifted Danielle's face gently. \"", "You haven't. ", "You still have your heart to give away to some deserving man who will love you back.\"", "\n\n\"But I've closed myself off for so long, I really don't think I know how to. ", "Maybe I don't even really know what love is. ", "Not that kind of love, anyway.\"", "\n\n\"All I can say to that is, you'll know. ", "When the time is right, you'll know with every fiber of your being. ", "Trust me on this. ", "You're a beautiful, wonderful woman - worthy to be loved.\"", "\n\nMakayla had given Danielle much to think on. ", "The one thing she was sure of, though – whatever her future held – she wasn't hiding anymore.", "\n\n*****\n\nChapter Ten\n\nTurbo led Aaron through the compound and into the training sector, giving him a tour of the facility as they progressed through the corridors. ", "It was all very impressive, complete with offices, conferences rooms, medical facilities, a gymnasium with a full basketball court and boxing ring, a swimming pool and whirlpool spa, a team room, a weight room with all the latest exercise equipment, changing rooms with private multi-jet showers and a shooting range. ", "The tour ended in the gym at the boxing ring which Aaron viewed with trepidation.", "\n\nTurbo was watching Aaron's reactions carefully and needed to size up his trainee before they began. ", "He certainly didn't look helpless, which was to his advantage. ", "Aaron held a healthy amount of muscle and bulk for a mortal.", "\n\n\"Okay, Doc. ", "Why don't you tell me a little about yourself and any training you may have already had. ", "You're not a small guy and you're in great shape, so I assume you've got some type of physical regiment that you do to keep in shape.\"", "\n\n\"I'm obviously more of a scholar than a fighter, but I have had some self-defense training before, although I imagine it needs to be perfected somewhat, especially since it appears I may be up against demons. ", "I've only seen one that shifted into a raven and flew away, so I'm not well versed on the harm they can cause me or what their weaknesses are. ", "I also used to box at my neighborhood gym on occasion and know enough basics to get around the ring fairly well. ", "I'm no stranger to adversity. ", "I grew up on the streets and did my share of fighting there, too.\"", "\n\nTurbo was impressed and relieved he wouldn't have to deal with a beginner. ", "That made his task so much easier and Aaron was going to need every ounce of strength and cunning he could muster if he had a chance in defending himself against the Huldrekall. ", "But he silently vowed to help the guy out as best he could. ", "Then again, being immortal didn't make you a miracle worker.", "\n\n\"Great. ", "You've got a really good basis to build on then. ", "Why don't we get suited up and go a couple of rounds in the ring to start off. ", "I'll help you perfect any moves that may need improvement and show you how to protect yourself against our enemies, plus give you pointers on how to eliminate them. ", "I'll even teach you a few mixed martial arts moves that may come in handy.\"", "\n\nAaron was relieved to hear Turbo's positive response and decided to give it everything he had. ", "There were no rules here, no right or wrong. ", "The situation with the demons was serious. ", "You either lived or you died, or in his case still being mortal, he could be maimed for the remainder of his life. ", "He intended to learn all he could to increase his chances of survival. ", "The warriors wouldn't be around to protect him forever. ", "And neither will Danielle. ", "He didn't like that thought so much.", "\n\n\"Alright, let's do this. ", "Although, I've got to admit I'm not looking forward to facing you in the ring. ", "We're the same height, but you've got muscles to spare on you.\"", "\n\n\"Comes with the territory and the transition when you're brought over.\" ", "Turbo flexed his powerful arm for emphasis.", "\n\n\"You haven't been with this group for very long, have you?\"", "\n\n\"Actually, no. ", "I'm the newbie here, Doc. ", "Lost my mortal life in Afghanistan in 2007.\"", "\n\n\"Real sorry to hear that. ", "But I'm sure you know your countrymen appreciate what you've done for us.\"", "\n\n\"It's cool. ", "I've got no regrets. ", "I was proud to serve my country then and now.\" ", "The conviction with which Turbo spoke left no room for doubt about his sincerity.", "\n\nThey began walking back towards the changing rooms when another thought crossed Aaron's mind. \"", "This may be too personal, and you can certainly tell me to mind my own business, but what about family members? ", "Did you leave any behind? ", "I suppose you can't visit them.\"", "\n\n\"Lucky for me, there was no one. ", "But, you're correct in that, if there were, there wouldn't be any contact allowed. ", "Too much to explain and too much at risk. ", "This is my home and now I finally have a family, a place where I belong,\" Turbo said thoughtfully.", "\n\nAaron nodded his head in understanding. \"", "One more question. ", "Why do they call you Turbo?\"", "\n\n\"Because I like fast cars, fast bikes and I can repair or modify anything on wheels to hit turbo speeds. ", "It beats Speedy Gonzalez,\" he laughed heartily flashing his elongated canines.", "\n\nAaron decided he liked Turbo. ", "Tattoos, piercings and all. ", "Even with fangs.", "\n\nAfter donning their protective boxing gear, both men entered the ring, circling and sizing up their opponent. ", "Turbo knew Aaron was nervous. ", "Couldn't blame him, being a mere mortal with all of the vulnerabilities that entailed. ", "Other than minions, who deserved the trouble they brought onto themselves, he hadn't laid a harmful hand on a mortal since his transformation and this was a different situation entirely. ", "Even training or roughhousing with his brother warriors didn't require him to hold back his preternatural strength and speed. ", "Good thing he wasn't a hothead. ", "He'd be able to keep his wits about him and wouldn't worry about losing his temper. ", "But he did have to be extra careful and mindful not to unintentionally harm Aaron. ", "Danielle would have his hide for sure if that happened, unintentional or not. ", "It was obvious to everyone that she had some kind of attachment to this mortal, but what exactly that attachment was, he couldn't say.", "\n\n\"Why don't you come at me and show me what you've got and we'll take it from there? ", "Just treat this like a sparring match back at your local gym and I'm an everyday guy.\"", "\n\n\"Wow, that's the understatement of the year,\" Aaron laughed, the nervousness in his voice belying his attempt at appearing calm.", "\n\n\"Don't worry, Doc. ", "You can't hurt me and I won't hurt you. ", "It's all good.\"", "\n\nAaron moved into Turbo and gave it his best shot, delivering jabs, hooks, a few right crosses and uppercuts. ", "Turbo successfully block them all but was impressed with Aaron's power. ", "He packed quite a punch. ", "After several skirmishes, Turbo switched it up and taught Aaron some very useful kickboxing moves. ", "Moves that, if delivered correctly, would cause quite a bit of damage and incapacitate his opponent. ", "From there, he taught him improved ways to protect his own body and what he needed to know to take out not only the minions but the dreaded demons themselves.", "\n\n\"Okay, Doc. ", "Let's try that round house one more time. ", "Don't focus on how much air you can get, but how much force you can put into this one.\"", "\n\nAaron did as instructed but overestimated his landing a bit causing him to come down on his foot at a bad angle. \"", "Ahh... Shit that hurts!\"", "\n\nTurbo was by his side instantly. ", "Aaron never saw him coming. \"", "Let me look it.\"", "\n\n\"Man, you're fast. ", "I mean really fast,\" Aaron sputtered with fascination in his eyes.", "\n\n\"Also comes with the territory,\" Turbo explained while examining his ankle. \"", "Looks like a slight sprain. ", "Nothing broken. ", "Hang tight and Emeline will be here to take care of that shortly.\" ", "Eme, you're needed in the gym, please. ", "Our visitor has a slight injury.", "\n\nSure, I'll be right there.", "\n\nSuddenly, Emeline was standing next to Aaron and startled him. \"", "Hey Aaron, I'm Emeline. ", "We met earlier when you met Steele.\"", "\n\n\"Yes, the big dude with the sword and fangs. ", "Sorry about my freaking out back there.\"", "\n\n\"No need. ", "Forget about it. ", "Everyone else has,\" she smiled sweetly. ", "There was something about her that just seemed pure and kind. \"", "I'm a healer. ", "Kind of like you're human equivalent of a doctor and physical therapist all in one. ", "Can I take a look at your foot?\"", "\n\n\"Yea, but I figure some ice and a little rest off of it is all that's necessary.\"", "\n\nTurbo stepped back to let her do her thing, knowing Aaron was in good hands.", "\n\nEmeline knelt down beside him and began carefully examining his foot and ankle. \"", "Nothing's broken, so this will just take a second. ", "You're going to feel some heat along with a needle sensation.\" ", "Then she wrapped both her hands around the injured surface.", "\n\nAaron felt the comforting heat and the prickling sensation she spoke of for about thirty seconds. ", "Then she replaced his foot on the floor and stood. \"", "Okay, that should do it. ", "Move it around and tell me how you feel.\"", "\n\nAaron flexed his ankle and felt nothing. ", "No pain at all. ", "He leaped to his feet, walked around in circles, jumping and testing the strength of his foot and ankle. ", "Emeline just smiled knowingly.", "\n\n\"Wow, I believe it's better than before the injury,\" he said in amazement. \"", "How'd you do that?\" ", "Before she could answer, he put up his hand in a stop motion to silence her. \"", "Actually, don't tell me. ", "I shouldn't be surprised by all the things I continue to learn about you guys. ", "It's just my inquisitive nature and I know you can't give me a scientific explanation. ", "I promise to learn to accept some things at face value from here on out and stop asking unanswerable questions.\"", "\n\nEmeline graciously replied, \"We don't mind, really. ", "This is all new to us, as well. ", "I'm sure it's been mentioned to you that no mortal has ever been to our village. ", "Except those that help us out periodically. ", "You're the first. ", "We expect lots of things to be confusing to you.\"", "\n\n\"Even so, thank you – for the healing.\" ", "Aaron took her hand and placed a gentle kiss on the back of it.", "\n\nEmeline blushed. \"", "It was my pleasure.\" ", "She turned to Turbo and said, \"If there's nothing else, I've got some things to get back to.\" ", "Then added silently to Turbo, No wonder Danielle likes him. ", "So charming. ", "And then she traced away. ", "Turbo's only reply was to chuckle quietly, shaking his head.", "\n\nReturning his attention to Aaron, he said, \"Okay, now that you're all fixed up, we'll wrap this session up.\" ", "Then he looked Aaron in the eye with all seriousness. \"", "Just remember, demons are hard to kill, but they can be killed. ", "They heal fast, just as we do, but if you inflict enough mortal damage, they will expire before their body can heal itself. ", "Massive blood loss to your opponent from a main artery is always a good thing.\" ", "He paused noting that, even though this was all a lot to take in in such a short time, Aaron looked as though he could handle it, physically and mentally.", "\n\n\"You did very well,\" Turbo praised enthusiastically. \"", "You know Danielle is a lot stronger than normal, too, right? ", "She'd also make a great sparring partner. ", "I've gone a few rounds with her myself.\"", "\n\nAaron's first reaction was arousal, imagining his previous physical contact with Danielle, but when Turbo mentioned his own association with her, he didn't like the rush of images of them together that flooded his mind. ", "He didn't like the feeling that somewhat tightened his chest and lower jaw, either. ", "What the hell was that all about? ", "Oh, crap! ", "Am I jealous?", "\n\nTurbo didn't need to scan Aaron's mind to know what he was thinking. ", "He'd noticed the change in his demeanor, but didn't take it personally. ", "Laughing aloud he said, \"Go hit the showers, lover boy. ", "Tomorrow you can tackle weapons.\"", "\n\nWith a flushed face, Aaron thanked him and headed off towards the showers. ", "He was tired and a little confused about this new revelation but pumped full of endorphins and he felt strong, ready to take on the world. ", "Bring it on, demons.", "\n\n*****\n\nAs Aaron made his way out of the gym, several male warriors appeared behind him on the basketball court obviously ready to start a game. ", "Curiosity caused him to pause by the door to observe them. ", "He noted the raw masculinity that engulfed the atmosphere and envied the familiar camaraderie that they all seemed to share. ", "As he continued on his way, their playful banter trailed down the corridor behind him, bringing a smile to his lips.", "\n\n\"Alright. ", "We're playing this one like normal mortals.\"", "\n\n\"Yea, the rules are no tracing, no speed and no nonverbal communication to your teammates. ", "And Blaze, no getting pissed off and biting the ball this time. ", "Everyone agreed?\"", "\n\nA chorus of deep voices responded, \"Agreed,\" followed by the familiar sounds of dribbling and screeching shoes that echoed in the large open space.", "\n\nLocating the changing rooms, Aaron appropriated one for his use. ", "He quickly stripped and turned toward the oversized private shower searching for the mechanism to start the water flow. ", "Seeing nothing obvious he stepped inside to further his search, only to immediately be blasted by the multi-jet system. ", "Perfect temperature. ", "Perfect water pressure. ", "Perfect fix to his aching muscles. ", "There was no need to adjust a thing. ", "Every jet seemed to seek out his underused and overworked muscles. ", "Sensored, he thought. ", "What genius.", "\n\nHe groaned sensuously and murmured to himself, \"This is definitely my new favorite place on Earth.\" ", "Being in his own little world, he never thought to take into account the acoustics of large tiled bathing rooms and his groans of ecstasy carried outside his current domain.", "\n\nHe closed his eyes reveling in the sensations as the multi-jets pulsed and massaged his taut muscles, languidly relaxing his entire body. ", "Suddenly a softer, naked form pressed against his back, wrapping its arms around his hardened chest, compressing its bared breasts against him. ", "Remarkably, he wasn't surprised. ", "He immediately knew her scent – vanilla and spice. ", "Heaven. ", "Truth be told, he could sense her nearness, although he wasn't sure how. ", "He decided to stick to his new motto concerning his newly acquired associates and not press to understand or rack his brain for a solution. ", "Some things just were, and that was a huge exception and step for him to take.", "\n\n\"Hey there,\" Danielle whispered softly into his ear and placing light teasing kisses against the nape of his neck. \"", "You don't seem surprised to see me.\"", "\n\n\"Maybe a little, but certainly not as much as I should be,\" he replied with a sexy smile that had turned up the corners of his mouth.", "\n\n\"I heard you were injured and wanted to make sure you were okay, although Emeline assured me you were. ", "Then I heard you here in the shower.\" ", "She continued pressing small kisses and nips along his neckline and shoulders, slowly turning him to face her. \"", "The sounds you were making were too inviting to ignore.\" ", "She placed more slow, deliberate kisses and nips up the front of his throat and onto his jawline. \"", "Couldn't help myself,\" she almost purred.", "\n\nStill luxuriating in the feel of her tantalizing lips, he tilted his head downward to complete her journey and brought his mouth to meet hers with a kiss that was more tender than they'd ever shared thus far. ", "She opened for him, welcoming the invasion of his tongue and the taste of him heightened her desire. ", "Her hands traveled up his chest, wrapping her arms around his neck and ending with her fingers deftly entwined in his drenched hair. ", "She felt his instant arousal brush against her body.", "\n\n\"I was supposed to be showering,\" Aaron said against her lips unconvincingly.", "\n\n\"Later,\" she muttered and pulled him back to her waiting lips.", "\n\nThe water forgotten, he gently pushed her flush against the cool tile wall, running his hands down her arms and back up again, his fingers trailing along the outside of her breasts. ", "He pulled slightly away and cupped her face in his hand searching her hungry hazel eyes, but for what exactly he couldn't say. ", "He tried to identify the unfamiliar emotions that flooded him as he touched her. ", "Affection, wonder, admiration, the need to protect, and overwhelming lust. ", "The culmination of these made him feel whole. ", "There was something about being in her arms that felt right. ", "Whatever was between them was so real it was almost tangible, although he could not give that something a name. ", "He could only hope she felt it, too.", "\n\nDanielle studied his face as he did hers seeing the multitude of emotions that seemed to pass before her eyes. ", "Unsure of what to do or what to say. ", "Confusion clouded her mind, but she tried to hide it. ", "Both were breathing heavily, their lips scantly brushing together, mingling their breaths as one. ", "She brought her hand to the nape of his neck and closed the distance once again, matching his hunger with her own. ", "Then she let all thought go and allowed herself to succumb to the passion hovering between them, surrounded by a swirling fog, cocooned in their own private world. ", "Tasting him, feeling him, the hard length of his cock surging against her belly.", "\n\n\"I need to taste you. ", "I've wanted to taste you for so long,\" he said as he knelt slowly in front of her. ", "He nuzzled her belly, swirling his tongue around her navel and dipped inside before trailing his tongue lower. \"", "Open for me, baby.\"", "\n\nDanielle groaned at his words and allowed him to lift her leg over his shoulder, opening her wide for his perusal. ", "His fingers crept along the silky skin of her outer thigh moving back to caress her perfectly formed ass and sliding down the crevice between her cheeks until they came to stroke the swollen lips between her thighs. ", "He spread the slick moisture he found there from her opening to her engorged clit, encircling it over and over again leisurely.", "\n\nShe gasped, inhaling her breath sharply at his tantalizing touch, canting her hips forward for more of his ministrations. ", "Moving his fingers downward, he entered her, slowly and deeply thrusting two digits within her core. ", "Then he parted her with his other hand and slid his tongue along her dampened folds.", "\n\n\"Oh baby, you taste so sweet. ", "I knew you would.\" ", "The feel of his hot breath against her swollen flesh added to her pleasure. \"", "Just like honey.\"", "\n\n\"Oh Goddess...don't stop, Aaron,\" she begged grabbing his head in her hands and holding him to her. ", "Her pleas and the calling of his name sent jolts of longing straight to his cock. ", "He throbbed painfully with his need but refused to enter her before she reached her peak.", "\n\n\"Never baby,\" he assured her and continued his unhurried barrage, tonguing her clit and sucking her silken flesh as his unrelenting fingers kept up their teasing, slowly driving in and out of her sex.", "\n\n\"So good...,\" she mewed tossing her head from side to side. \"", "So good...\"\n\nWhen he felt she was close to coming, Aaron set his mouth directly to her clit, nipped her lightly, then locked his lips around it and suckled, sending her over the edge. ", "She bucked against his face and her clenching pussy tightened around the fingers buried deep within her.", "\n\nHe lifted his eyes to watch her as she came. ", "Her eyes were closed, her sensuous mouth open as if waiting just for him to enter it and as she cried out. ", "The wondrous rapture that encompassed her face was beautiful. ", "Absolutely beautiful, he thought.", "\n\nAs the clenching subsided and her shudders ceased, Aaron removed his fingers and rose up slowly caressing her body and stopping to worship her breasts with his tongue, teeth and lips. ", "Sucking and nipping, bringing her quickly back to a state of need. ", "He worked his way from her breasts, up her collarbone and throat, finally joining their lips once again.", "\n\nDanielle let her hands glide over his strong shoulders to his muscled chest, relishing in the smoothness she found. ", "Dipping lower she ran the backs of her fingers across his abdomen, feeling the rippling muscles jump at her heated touch. ", "She brushed against his silken cockhead, taking him fully in her hands, causing him to groan loudly.", "\n\n\"I want you so badly.\"", "\n\n\"Then come inside me, please. ", "I need you,\" she said with half closed eyes.", "\n\nAaron ran his hand down her side, over her hip and lifted her leg, opening her to him. ", "Bending his knees slightly, he entered her in one forceful thrust, causing them both to gasp. ", "He stilled, allowing her to adjust to him before continuing to move within her. ", "Danielle lifted her other leg rising up to straddle his waist, clinging to him with her arms around his neck. ", "She began lifting herself to rise and fall on his hot throbbing cock, her body arching against his as he joined her, pulling out and surging back inside her tight channel.", "\n\nAaron grabbed her hair with one hand, pulling back to expose her neck. ", "He ravenously attacked her throat with nipping, sucking and kissing, making his way back to her supple breasts. ", "He bit down on her stiffened nipple then laved it with his rough tongue to sooth the sting. ", "She loved his forcefulness and delighted in the knowledge that he wanted her so badly. ", "She reciprocated her pleasure, she tightening her vaginal muscles, contracting around his rock hard length, forcing a deep groan from him against her breast. ", "He rotated his hips, grinding his pelvis against her distended clit while she milked him within her. ", "Reaching their peak, they cried out together, riding out their mutual orgasm, clinging and shuddering in each other's arms.", "\n\nOnce he could speak again, Aaron ran his tongue around the shell of her ear and whispered, \"Sometime I'd like to actually take you in bed.\"", "\n\nDanielle smiled slyly. \"", "If we hurry and finish our shower, you can take me there right now.\"", "\n\nAnd that's just what they did – a few times.", "\n\n*****\n\n\"Tell me something about yourself,\" Danielle prompted as she lay boneless in Aaron's arms.", "\n\nHe rolled onto his side facing her as she rested her head on the crook of his arm. \"", "Ladies first.\"", "\n\n\"Really? ", "You're really going to try and derail me with chivalry? ", "I mean it's not like you don't already know tons of stuff about me already.\"", "\n\n\"Correction. ", "I know tons of stuff about the warriors. ", "Not so much specifically about you.\"", "\n\n\"Okay, fair enough. ", "What do you want to know?\"", "\n\n\"How did become a demi-goddess?\"", "\n\n\"What? ", "Are you telling me you don't know how babies are made?\" ", "she laughed teasingly.", "\n\n\"Of course, I know how babies are made,\" Aaron said rolling his eyes. \"", "You know that's not what I meant. ", "You're just averting the question. ", "I take it you don't get along very well with your mother.\"", "\n\n\"That's an understatement if I ever heard one.\" ", "She decided it was no big deal. ", "It didn't bother her as much anymore, if at all. ", "Well, as far as she was willing to admit to herself or anyone else. ", "She certainly didn't let it influence her life and, the fact that she came from Freya, certainly didn't dictate who she really was.", "\n\n\"Well?\" ", "he encouraged.", "\n\n\"Okay, my mother and father had a 'thing,' I guess you'd call it. ", "I don't know if they loved each other or not. ", "I was too young when he died and she would never talk about it. ", "I was actually raised by my father's parents and they were the kindest people I've ever known. ", "I still miss them terribly. ", "Even after all this time. ", "But I do remember my father – and that he loved me.\"", "\n\nAaron guessed her grandparents had something to do with keeping her memory alive regarding her father. ", "In that she was lucky.", "\n\n\"Your mother wasn't in your life?\" ", "He could certainly identify with that, but didn't share that thought with her.", "\n\n\"Not like a mother should be, at least. ", "Suffice to say, she is a goddess and had 'godly duties' to attend to. ", "No time for a child, I suppose.\"", "\n\n\"I'm sorry to hear that.\" ", "And he truly was. ", "He understood the loss she must have felt growing up that even the love of her grandparents couldn't quite fill.", "\n\n\"Yes, well it is what it is. ", "At least, I was loved. ", "I learned that I could never rely on my mother and actually resented even having to refer to her as such.\" ", "She frowned deeply. \"", "Sorry if I sound bitter, but I really hate being associated with her at all. ", "I wish I wasn't a demi-goddess. ", "It's not like I get any perks from the title and sometimes others seem to look at me as if expecting extraordinary things from me because of my link to her. ", "I simply don't have anything else to give – to them or her. ", "Especially her.\"", "\n\nAaron pulled her closer into him, not surprised that she shed no tears with her revelation. ", "He wasn't sure whether it was because she was strong or embittered to her circumstances, but he suspected a bit of both.", "\n\n\"So, what else do you want to know? ", "My sorted family history aside, there should be other curiosities spiraling in that brain of yours.\"", "\n\n\"Well, having been alive for more than twelve hundred years, I imagine you've seen so many great things in your life. ", "All of the things that have happened in those years throughout the world.\"", "\n\n\"Not so much as you'd think. ", "Sure I've heard of things, but technology didn't evolve to the information sharing state that it's in until the most recent years. ", "I've only been in the communities I was assigned to and protected those areas. ", "Nothing major happened that would interest you, I'd imagine. ", "Not the type of things you're referring to. ", "I only knew what was happening in and around my community or region.\"", "\n\n\"I guess you're right. ", "People do tend to live in their own little worlds.\"", "\n\n\"I did get to witness some wonderful inventions, like cars, telephones, airplanes, computers...\"\n\n\"Yes, I don't know what we did before them,\" he laughed. ", "Changing the subject he asked, \"I was wondering...if Tormond and his demons are the main problem, why haven't you gone straight to the source and taken him out?\"", "\n\n\"We can't. ", "He's protected by Loki. ", "Even the Gods have their hands tied to some extent. ", "We've rarely come in contact with Tormond himself and he's only one of many.\"", "\n\n\"I see. ", "So, if I understand correctly, your specific group wasn't responsible for stopping the 9/11 terrorist attacks. ", "There's another community of warriors on that coast covering that territory.\"", "\n\n\"Yes, there are others for different territories, although we'd assist wherever needed at any time. ", "But Loki and his demons had nothing to do with the 9/11 incidents, therefore Zahara had no insight or forewarning of what took place. ", "It's what we call an unseen event. ", "Unfortunately, those evil men acted of their own accord. ", "There was no way we could have thwarted what they did.\"", "\n\n\"In other words, you can protect us from otherworldly demons, but not from ourselves.\"", "\n\n\"That about sums it up, I'm afraid.\"", "\n\nSilence followed and Danielle felt it was time to change the subject. \"", "So, now. ", "Your turn. ", "Tell me about you.\"", "\n\n\"What would you like to hear?\" ", "he queried. ", "He knew turnabout was fair, but he was normally a quiet and private person.", "\n\n\"Just about you. ", "Something about your life. ", "Like, what you were like as a child and what made you want to become an archeologist?\"", "\n\n\"May I ask why you'd like to know? ", "Other than the fact that since you shared, I should, too.\"", "\n\nShe gave this some thought and really wasn't sure she knew why herself. ", "She chalked it up to curiosity and the fact that she loved to talk. ", "Lying in bed was great, but lying in bed and talking was even better. ", "Something she didn't normally do with a partner. ", "She'd never kept one around long enough to get that comfortable. ", "So, she gave him the first decent reason that came to mind. \"", "I don't get the chance to get that close to mortals. ", "My own mortal existence is from such a different time. ", "I suppose I just want to understand you. ", "Where you come from, you know?\"", "\n\n\"Well, don't make me sound so alien,\" he jested, his chest shaking slightly with his laughter. \"", "I'm not really all that interesting or complicated.\"", "\n\nShe looked at him, whimpered and made a silly pouty face. ", "A pouty face he thought was more sexy than sad. ", "But he gave in anyway. ", "She was just too cute to ignore.", "\n\n\"Alright. ", "You win.\" ", "He thought for a moment then said, \"I've never had anyone I could rely on. ", "I'm where I am through my own efforts, my own blood and sweat. ", "When I was four, my mother died and I was raised by my grandmother until she passed away two years later. ", "I never knew my father. ", "He's dead for all I know or care.\"", "\n\n\"Continue,\" she encouraged. ", "His reveal was proving to be much sadder than she initially expected, but she didn't want to discourage him so she listened quietly and attentively.", "\n\n\"I was sent to the state orphanage at the age of six, but by then I was too old to be adopted and no one was interested. ", "I guess I was somewhat fortunate, though, because by the time I turned eight, the teachers at the public school that I attended noticed that my learning capabilities far exceeded that of my fellow students. ", "The other children would either ignore me or single me out because of my intelligence. ", "I much preferred being ignored. ", "I couldn't tolerate having stupid or childish conversations with them anyway. ", "My curiosity for knowledge and intelligence singled me out. ", "At times, I felt like I had this huge flashing neon target strapped to my back. ", "Needless to say, I had to learn to defend myself very quickly and at an early age.\"", "\n\nShe held her tongue and motioned for him to carry on with a circular wave of her hand, assuring him that she was listening.", "\n\n\"As I grew older, I was encouraged to take honor classes, join academic clubs, and later completed all of the applications necessary to acquire a full scholarship to the University of Oregon.\" ", "These memories seemed to excite him. \"", "My passion is history, thus the archeology. ", "I love to touch something that has been in the earth for hundreds or thousands of years.\"", "\n\n\"Ah ha!\" ", "she squealed comically, plastering a knowing look on her beautiful face. \"", "I knew there was a reason you were attracted to me. ", "It's because I've been on this earth for hundreds of years.\"", "\n\nHe couldn't help but laugh heartily and noted that she had a way of making him laugh often, and he liked it.", "\n\n\"Maybe you're right,\" he said reaching for her again with a feral grin. \"", "Because I do love to touch you.\"", "\n\n*****\n\nChapter Eleven\n\n\"Oh, real funny,\" Steele scoffed turning away from his computer screen. ", "He leaned back in his chair, raking the fingers of both hands through his wavy black hair. ", "His normally smiling eyes and easy going manner were nowhere to be found. \"", "Ha. ", "Ha. ", "Ha,\" he added sarcastically.", "\n\n\"What are you moaning about? ", "Can't get past another level on your latest RPG game?\" ", "Turbo asked as he whirled his chair around and gave his best friend his full attention. ", "The two had become fast friends and confidants ever since Turbo's transformation when Steele had taken him under his wing. \"", "It can't be all that bad.\" ", "Then he held up his hand. \"", "Wait, I've got it! ", "You're online companion from Timbuktu just lost his last life and now you're stuck fighting all by your lonesome against an alien foe, forcing you to utilize most of your stored resources to even have a slight chance of defeating them. ", "No, never mind. ", "That you'd look forward to and just jump into the fray all gung-ho, balls to the wall.\"", "\n\n\"No dude, you're way off. ", "I'm not even playing a game right now,\" Steele replied defensively.", "\n\n\"Will miracles never cease?\" ", "Turbo laughed. \"", "Okay, what's up?\"", "\n\n\"Look at this.\" ", "He pointed to his oversized flat screen monitor. \"", "I just got this anonymous e-mail. ", "Someone thinks they're real cute sending me this.\" ", "He wasn't furious, but he felt like venting all the same. ", "He really did have a sense of humor most of the time.", "\n\n\"You should really let Ghost take a look at your e-mail if you're getting bombarded by junk. ", "He fixed mine up in nothing flat.\"", "\n\nSteele gave him a stern look that told him where he could put his advice.", "\n\n\"Alright, I'll look,\" Turbo said with exasperation. \"", "Slide over and let me take a peak.\"", "\n\nSteele vacated his seat and Turbo plopped into it grabbing the mouse to click on the offending e-mail in question. ", "To Steele's dismay, he began laughing as he read it. ", "He was staring at a Certificate of Knighthood obtained from a local visiting Renaissance festival that bore Steele's name which stated: 'We the Kings and Queens of Bridge Creek, by Royal Decree, do hereby Knight you Sir Steele of Bridge Creek in honor of your bravery and faith, chivalry and swordsmanship, and do recognize your loyalty to King and Country, for all of your good and generous deeds.'", "\n\nAs Turbo finished reading it, he looked up at Steele and started laughing even harder. \"", "Oh, come on, big guy. ", "No offense, but it is funny,\" he sputtered. ", "He stood and lightly whacked Steele on the back. \"", "Lighten up already.\"", "\n\nThe former medieval knight watched his friend continue to laugh at his expense and decided to join him. \"", "Okay, I guess you're right. ", "It's funny,\" he chuckled with a little less conviction.", "\n\nWithout warning, Myste came cantering into the room. ", "Today, or at least this morning, her hair was golden blonde and she chose to be light and airy, wearing one of her favorite Bohemian ensembles. ", "She sported a billowing rainbow colored skirt with a bright yellow top and matching sandals that laced up her calves. ", "Her exotic violet eyes were wide and sparkling with excitement. ", "But all that could change, even before lunch, depending on her mood. ", "Myste was very versatile, with styles ranging from Goth to Bohemian to Grunge and her hair color changed to match. ", "Or vice versa. ", "It all depended on her mood at the moment.", "\n\nYou definitely wanted to keep your distance when her hair turned red. ", "It had the potential of being worse than throwing two cats in a bathtub full of icy water. ", "But when in battle, her mane streamed strong and true in the purest black and she was a force to be reckoned with and definitely a warrior you wanted fighting by your side.", "\n\n\"Hey, bros, what's so funny? ", "I heard you laughing all the way out in the hall.\"", "\n\nThe male warriors took one look at her and mentally transmitted to one another the same message. ", "She's in a good mood.", "\n\nSmiling, Turbo engaged her before Steele could deny what was happening. \"", "It's an e-mail that Steele just got. ", "Check it out,\" he said as he waved her over, knowing Steele wouldn't mind him sharing this with Myste.", "\n\nAmong the warriors, Steele was respected and considered a big brother/father figure to all, but none so much as Myste. ", "Although not lovers, their relationship was special and he cared for her deeply. ", "She was the little sister he never had in his mortal existence. ", "The feeling was mutual on her part and she believed no one tolerated or understood her like Steele did.", "\n\nMyste's moods were flighty and each consumed her with complete fervor. ", "She never did anything small. ", "It was 'go big or go home' where she was concerned. ", "Most enjoyable was her laughter. ", "She had an infectious hysterical giggling problem. ", "One so unruly, that if the switch got tripped, or the box got turned on, it was almost impossible to turn off before she and everyone around her were agonizingly holding their heads and/or stomachs from laughing so much. ", "It might be a painful destination, but the voyage was fun and memorable.", "\n\nSteele's e-mail happened to trigger just such an incident. ", "Before Myste could say a word, she began hee-hee-heeing with heart, so hard and so long that she could scarcely catch her breath. ", "Watching Myste herself was hilarious enough to have Steele and Turbo joining in full force. ", "The effect was similar to a yawn. ", "Once you see someone do it, you can't stop yourself from doing it, too.", "\n\n\"Oh, that's awesome!\" ", "she blurted sincerely when she was able to speak and the keening laughter had subsided to mere snickers. \"", "I know it's supposed to be a joke, but I think you should embrace it, Steele. ", "Print it out, frame it and put it on your wall. ", "This would be a great spot right here,\" she said pointing at a particular place on the wall that would be in view of everyone entering the room. \"", "I'll even buy the frame.\" ", "It would only be the right thing to do since I'm the one who sent it to you, she thought to herself, chortling. ", "Turbo gave her a knowing smile. ", "He'd figured out the mystery sender.", "\n\n\"Thanks for the offer. ", "I'll think about it and get back to you. ", "Not.\" ", "Steele threw her a look of disbelief.", "\n\n\"Oh come on! ", "You'd really turn down my idea? ", "I mean, look at you two.\" ", "She over-exaggeratedly motioned toward them. \"", "You're both wearing Zombie Apocalypse T-shirts, for Goddess' sake. ", "And you,\" she jabbed a finger in Steele's rock hard chest, \"You love the Renaissance festivals. ", "You never miss them. ", "I should know because you drag me to most of them.\"", "\n\n\"Okay, I'll give you that. ", "I do love getting a little taste of home,\" Steele said reminiscing. \"", "But the Zombie Apocalypse is legit. ", "Several of us are participating in an upcoming 5K charity event where we will be running for our lives while chased by zombies and maneuvering through an obstacle course. ", "I know it won't be much of a challenge for us, but it's different and we thought it would be fun. ", "Besides, it's really cool. ", "Want to join us?\" ", "Steele smiled, full of excitement about the upcoming event.", "\n\nTurbo proudly stuck out his chest flashing his tightly stretched T-shirt at her that said, 'When The Inevitable Zombie Apocalypse Comes, I Will Trip You And Save Myself.' ", "Snickering, she glanced over at Steele's T-shirt and found, 'Zombie Apocalypse Preparedness Team, We Help The Dead Stay Dead.'", "\n\n\"Thanks for the invite, but I'm afraid not, boys. ", "I may trace over during it and trip you up, though. ", "Just for fun,\" she teased. \"", "Who knows? ", "I may even look and feel like a zombie that day.\" ", "She snorted, poking fun at herself.", "\n\n\"Actually,\" Turbo added only half serious, \"We could consider this a run practice. ", "If we were to ever lose the battle against the Huldrekall, their numbers would increase so fast, it would seem like an apocalypse.\"", "\n\n\"Yes, if the mortals only knew,\" Steele agreed solemnly.", "\n\nMyste had heard enough and could physically feel the mood in the room flexing and changing. ", "The roots of her hair were beginning to tingle, signaling a possible color change that would go with the mood change. ", "But she didn't want it to change. ", "It was a good day and today she wanted to be golden blonde. ", "And then she knew...It was time for a change of venue.", "\n\nShe hopped up lively from the edge of the desk she'd be sitting on and walked over to where Steele was standing. ", "Placing one hand on his shoulder and hooking the other into the crook of his arm, she suggested, \"I've got a brilliant idea. ", "Let's go out to lunch at the medieval restaurant you like so much.\" ", "Excitedly she added, \"We'll eat chicken with our bare hands and you can get in a little jousting. ", "Turbo and I will sit in the stands and cheer for you. ", "Our Champion! ", "Whatcha say?\"", "\n\n\"I'm in!\" ", "Turbo cried encouragingly, siding up to Myste so she could take one of his arms, as well. \"", "Steele? ", "It's up to you.\"", "\n\n\"Yea. ", "That really does sound great. ", "Let's go drink ale and get foxed. ", "I may even be in the mood for a little swordplay when we get back.\"", "\n\nWith a warrior on each arm, Myste lead the way jabbering nonstop. \"", "Hey, you guys know I like you, right? ", "People say I don't have any taste, but I like you. ", "We driving or tracing...\"\n\n*****\n\nVex entered the oversized underground garage that housed the various vehicles utilized by the warriors, some personally owned, namely the sportier, expensive lot, others used for mission or community needs. ", "The official vehicles were top of the line SUV's, sleekly black with illegally dark tinted bulletproof windows, equipped computer and surveillance apparatus, stock weapons and emergency gear that might be needed in a pinch. ", "All additional special weaponry was kept separate in the protected weapons locker and added as needed.", "\n\nHe pulled his keys out of his pocket, hit the key fob unlocking the doors with the obligatory chirp and dropped down into his gleaming jet black ZR1 Corvette. ", "His license plate said it all – GR8 BITE. ", "He depressed the automatic start button and his dream machine roared to life. ", "His seat did its automatic adjustment to his preferred settings which puzzled him for a moment. ", "Ah, yes. ", "He'd forgotten that he'd let Makayla drive back from their recent visit to the bar. ", "That had turned out to be a great night, indeed, until Makayla drove like a bat of hell all the way home. ", "He wasn't worried about them being injured if she screwed up, but his 'baby' could be permanently damaged in the process. ", "He hung on best he could since he didn't have an 'Oh Shit' handle to grab on to. ", "Luckily, they made it home in one piece and he silently cursed to himself, swearing she'd never drive his 'baby' again. ", "She'd just have to get her own.", "\n\nHe lowered the convertible top that almost soundlessly slid back into place at the rear of the vehicle under its protective shelf. ", "Goddess, he loved this machine and the speeds at which it could take him. ", "That feeling gave him a sense of carefree freedom that he didn't get very often these days. ", "He'd do pretty much anything to escape the sense of loss and guilt he'd felt the past ten years because of her. ", "He said a silent prayer to the Goddess that she was safe...and happy. ", "He could check up on her to be sure, but that would only drag out and intensify the inevitable pain and agonizing grief and his heart couldn't take it. ", "Best left alone. ", "Yea, he had to think of her that way or he wouldn't be able to carry on himself.", "\n\nHe switched on the stereo system choosing something appropriate and classic for the trip ahead, jacked up the volume to a screaming cruise setting, then followed the ramp upward, hitting the control that raised the garage door and punched down on the accelerator headed in the direction of the compound front to pick up his assigned partner for this mission.", "\n\nGhost heard the roar of Vex's Corvette as he came sliding to an undetermined stop on the unpaved and uncharted road of their magically warded community. ", "With ACDC's Highway To Hell blazing on one of his favorite satellite radio stations, Vex donned his designer sunglasses to shade his blue/green eyes and tied his shoulder length wavy brown hair in a leather thong at his nape. \"", "Yo, Ghost. ", "Hop in and let's hit the road.\"", "\n\n\"Let's do this. ", "Road trip!\" ", "Ghost shouted, joining in the revelry and jumping in the passenger seat without opening the door.", "\n\nThe choice to drive, rather than trace, to Las Vegas was an easy one. ", "Las Vegas was simply too populated to easily trace in and out of inconspicuously and too large to cover any other way than by vehicle. ", "It certainly didn't hurt that they loved their fast cars and looked forward to opportunities when they could to drive them. ", "The vehicle was warded by Annika, the Warriors' wand wielder, against detection enabling them to travel at higher speeds than normal and Turbo was a remarkable mechanic who customized their vehicles, making them ultra-fast and efficient.", "\n\nVex turned to Ghost as they made their way out onto Ochoco Highway No. ", "26. \"", "Hey, one request. ", "When I say vanish, you immediately do your disappearing act - literally. ", "I might just get me some on this trip and I don't want you ruining my fun. ", "You've already got your permanent piece.\"", "\n\nSlightly offended, but knowing Vex meant no harm, Ghost replied, \"Sure thing, but after the job is done. ", "And don't call Valeria a piece. ", "She's my bonded mate.\"", "\n\n\"Sorry, I didn't mean any disrespect. ", "You know I care about her, too,\" Vex said sincerely.", "\n\n\"Yea, someday you'll find yours.\"", "\n\n\"Not in the last or this lifetime,\" Vex answered with conviction.", "\n\nVex leaned back in his seat, turned up the volume on the radio and pressed his foot down on the accelerator. ", "With the wind whipping through their hair, the glorious sun on their faces and the clean woodsy smell of the Christmas tree covered mountains surrounding them, Vex and Ghost journeyed down the highway to their destination.", "\n\nIt seemed very little time had passed when they were cruising down the famous Vegas Strip heading to the Fire and Dice Casino.", "\n\n\"There's Tormond's casino over there. ", "If Zahara's visions are correct, he's actively recruiting to gear up for battle,\" Ghost stated, pointing ahead of them to the mammoth multi-light covered flashing sign. ", "As with everything in Vegas, the structure was over-the-top and shone so bright you could see it from miles away. ", "Especially the giant pitchfork and animated rolling dice with the searing flames that rose up behind them that graced the entrance. \"", "I didn't get a chance to speak with Zahara about her visions before we left. ", "Did you?\"", "\n\n\"No,\" Vex answered while pulling into the circular drive of the valet parking zone. \"", "Thunder was clear enough on his instructions at the meeting. ", "This is a recon mission. ", "But with the business in the North Sea now coming to light, he doesn't want to take any chances. ", "I'm sure everyone is staying on full alert.\"", "\n\nEntering the casino, they couldn't help but notice how it would certainly draw in the decadent and some of the more savory types of clients. ", "The walls were painted blood red with the illusion of live golden flames actively shooting up from floor to ceiling. ", "The ceiling itself was soot black as if it had actually burned. ", "The air was cool and thick with refreshing oxygen being pumped in from the many vents disguised along the floorboards and outer walls. ", "They strolled down the main center aisle between the numerous discordant slot machines, noticing the waitresses wearing short black spandex skirts and red bikini tops accented with flames who were actively serving drinks to anyone in the casino, whether they were gambling or not. ", "Their vampiric sense of smell confirmed that the drinks being served were not watered down, but were intended to ensure that everyone became so inebriated they wouldn't notice that mechanisms within the casino were designed to cheat, con and swindle its customers right under their very own noses.", "\n\nAs owner, Tormond trusted that his staff, led by his personal bodyguard Stan, could handle any security issues, should anyone attempt to cause any trouble in his casino. ", "Stan was merely human and ignorant of all that Tormond was and Tormond never involved him in his demonistic and hedonistic dealings. ", "He thought the Warriors were just some gang related group, or mafia types trying to horn in on Tormond's business. ", "Tormond preferred to keep it that way. ", "At least for now.", "\n\nStan was a born protector and his career selection as a bodyguard fit him like a glove. ", "He revered Tormond. ", "The two shared an understanding and respect that he'd never had for a former client, making it seem they were almost like family. ", "Stan knew that he would do whatever it took to protect his employer without regret.", "\n\nStan was on the floor of the casino by the blackjack tables, watching over the crowd and checking for any security breaches, when he heard the familiar beep initiating a call coming over his ear piece. ", "He answered immediately with, \"Yes, Mr. T.\"\n\n\"Stan, I got a vibe a few minutes ago and after checking the monitors, my suspicions were confirmed. ", "The two big guys at two o'clock are Warriors. ", "Keep an eye on them and make sure they aren't going to cause me any trouble in the casino. ", "Don't let them out of your sight while they're on the property and call me immediately if there's a problem.\"", "\n\n\"Of course, Mr. T.\" Stan looked around zooming in on the targets in question. ", "Yeah, they were big alright, but so was he. ", "If they were looking for trouble, he'd be glad to oblige them.", "\n\nVex and Ghost sat down at the green felt covered table joining three other players and motioned for the dealer to break each of their two hundred dollars into chips. ", "They settled in to enjoy a few hands of blackjack while they scanned the area for any vibrations or sulfuric smells, watched over the crowd for possible trouble and listened around them for any hints of recruitment activities. ", "The only offensive smells filling the air were coming from the blonde at the next table with too much sickly-sweet perfume on and her partner who was smoking like a chimney.", "\n\nThe petite female dealer made their requested exchange and greeted them with, \"Welcome, gentlemen. ", "Good luck.\"", "\n\nHave you picked up anything yet? ", "Ghost communicated via their link.", "\n\nNo, nothing unusual, Vex replied. ", "I always expect to feel some vibrations when we enter this joint, but I can't get a handle on the number or the distance. ", "It could just be coming from Tormond sitting in his office. ", "I don't feel anything close by, but stay alert.", "\n\nIf this recruiting thing is true and they are increasing, they're probably all out in the worst parts of town adding to their numbers, while we're sitting in here. ", "Maybe we should head out, too.", "\n\nNot yet, I'm on a roll here. ", "No hurry anyway. ", "They have to come back this way at some point. ", "Vex's current first love was poker, anyway, anyhow.", "\n\nSuddenly, there was a disturbance next to Vex as one of the drunken college boys, who was sitting to his left, pounced out of his seat, sending it toppling to the multi-colored carpeted floor and shouted threateningly at the dealer, \"Hey, hold up. ", "I stayed on two split hands with kings and jacks each. ", "You had to take a draw having only a queen and a six of clubs. ", "I'm tired of raising my bet so high and then watching you draw the perfect card needed to beat my hands every time. ", "That fucking deck is fixed.\"", "\n\n\"Sir, I assure you, this is a random draw machine. ", "I can't control what card I choose. ", "The shuffles are completely automated,\" the dealer pled in a shaky voice. \"", "Please, sir, calm down and take your seat. ", "It's random luck and I'm sure you'll win again,\" she said with a hopeful voice.", "\n\n\"I will not calm down! ", "It's amazing how when I first sat down I seemed to have quite a few winning hands and just when I started to get a nice stack of chips, you keep teasing us into the perfect bids and then coming up with the perfect cards needed for the house to win,\" he bellowed.", "\n\nHaving heard enough, Vex couldn't stand by and watch the abuse of the obviously terrified dealer who stood wide eyed, her hands visibly trembling. ", "He decided to take control of the situation, his natural protective instincts kicking in. ", "This guy should pick on someone his own size. ", "Don't ya think?", "\n\nAbsolutely, but do it calmly. ", "We can't start something here and draw too much attention to ourselves.", "\n\nNo worries. ", "I'll keep it cool.", "\n\nVex calmly turned his attention to College Boy. \"", "Sir, you know everyone wins and everyone loses in casinos. ", "You didn't honestly think that you would come to Vegas and go home a millionaire, did you? ", "That's why it's called gambling - there's a possibility that you will lose. ", "There's certainly no reason to verbally abuse this nice young woman. ", "She's just doing her job.\" ", "Vex turned to smile at the dealer who, while still trembling, nodded her head in thanks.", "\n\n\"What business is it of yours? ", "I'm not gonna listen to your crap advice. ", "I'm so pissed, I just want to hit something, and I figure you might just do,\" College Boy said, standing to his full towering height. ", "He was built like a linebacker so Vex had no problem with obliging him.", "\n\nOh, this could be so much fun, Ghost.", "\n\nNo can do, Vex. ", "You know that's not our mission. ", "We have to bow out of this one. ", "You know that we can't fight innocents, even if they are the biggest jerks.", "\n\nYeah, you're right. ", "Come on, let's make a subtle exit. ", "Shit, he's going to think I'm a coward...\n\nVex reigned in his temper and plastered a sarcastic smile on his face. \"", "Sir, I hope you have a nice night,\" Vex said. \"", "Cheer up. ", "Maybe you'll win the next one.\" ", "Turning toward the table once more, he placed a hundred dollar chip in front of the dealer this time with a genuine smile. ", "She returned his smile mouthing 'Thank you' as she looked at him with wary eyes.", "\n\nI'm heading to the men's room. ", "I need a secure place to disappear then I'm going back over to the table to see what I can find out. ", "I noticed that bodyguard eyeballing the confrontation. ", "Wait for me at the front entrance.", "\n\nWill do, Ghost. ", "Be careful and yell if you need me.", "\n\nAs Vex headed for the front entrance, Ghost entered the nearest men's room and checked to see if anyone had a visual on him. ", "He wasn't worried about cameras as they weren't allowed in restrooms, but he didn't want to have to take the time to enthrall anyone either. ", "Confirming he was alone, he mentally called on his gift, instantly transforming with no need to disrobe beforehand, then he snuck back out onto the casino floor.", "\n\nHe carefully made his way back over to the blackjack table he and Vex had occupied previously, making sure not to collide with anyone in the process. ", "He had been correct in his assumption regarding the bodyguard's curiosity. ", "He hovered in the background observing the scene that was unfolding before him.", "\n\nSpeaking into his headset, Stan motioned for another guard to follow the Warriors as they left the card game, then headed toward the table himself. ", "He became very interested once he heard College Boy confront the Warrior, but when he stood at his full height, Stan couldn't help but be impressed. ", "And his friend was no slouch either. ", "He knew he needed to introduce these gentlemen to Mr. T. for possible recruitment. ", "He could decide whether he wanted them to join in their cause.", "\n\nApproaching the two drunks, he tapped the verbal one on the shoulder and said cordially, \"Excuse me, sir. ", "My name is Stan. ", "I'm with the casino's management and I couldn't help but hear your concerns earlier. ", "I would like to apologize for any misunderstanding and invite you to meet with the owner, Mr. Tormond.\" ", "Glancing at the dealer, he noticed a look of trepidation flash through her eyes, before she quickly lowered them. \"", "I think he would really like to make your acquaintance,\" he encouraged.", "\n\n\"Yea? ", "Really? ", "Wow, the owner. ", "How cool is that, Bart?\" ", "the drunk addressed his companion. ", "He was beaming with so much self-pride he gave the impression of someone puffing out his chest and banging on it with his fists like Tarzan in the jungle, minus the trademark yell.", "\n\n\"Yea, that's really cool, Larry. ", "Wow, we come to Vegas, have a few drinks, win a few bucks, and now we get to meet the owner of one of the top casinos,\" Bart said excitedly.", "\n\n\"Lead the way, my man,\" Larry said with enthusiasm.", "\n\nGhost was frustrated that he wouldn't be able to follow them to their meeting with Tormond. ", "Even with his ghostly appearance, his presence would still be detected. ", "He had no doubt that Tormond was aware of their presence, but there was no way he could get away with being in the same room. ", "Having quickly scanned their minds, he had no doubt these boys were recruitment material. ", "They were definitely corruptible and perfect specimens for doing Tormond's bidding. ", "He made note of their physical features because he knew they would be meeting again. ", "Only next time, they wouldn't be walking away.", "\n\n*****\n\nStan was getting really tired of listening to the college boys going on and on about getting to meet the owner as he lead them through the casino and further into the office area. ", "Sheesh, these boys just won't shut up! ", "As he neared Tormond's door, he instructed, \"All right, boys. ", "You're about to meet Mr. T. You will only speak when spoken to.\" ", "Stan's commanding voice left no room for argument.", "\n\n\"Mr. T?\" ", "Bart asked.", "\n\n\"You don't need to worry about his name, just feel privileged that you're getting this introduction,\" Stan replied as he quietly knocked on the office door.", "\n\nSitting behind his desk observing the security monitors, Tormond watched as the last of the two warriors exited his casino. ", "Good, they've gone with no incident. ", "Guess they didn't find what they were looking for.", "\n\n\"Enter\" Tormond commanded, viewing the monitor reflecting Stan along with the same two college boys he had seen in a confrontation at the blackjack table earlier.", "\n\nTormond sat casually behind his desk with his typical air of authority. ", "He emanated the presence of a true leader and Stan was proud to have been invited at such a young and troubled time in his life to be included in Mr. T's justice for a free life. ", "He was proud to bring him new recruits for their cause and hoped that Mr. T would see that both Larry and Bart would be an added benefit. ", "Even with their incessant talking, their physical size alone was impressive. ", "They'd have to learn some discipline, but that came with the territory.", "\n\nTormond's first impression of the new recruits revealed that their minds were completely corruptible. ", "They certainly conveyed more than half of the so-called Deadly Sins, sloth not being one of them, considering their muscle-bound physiques.", "\n\nRising from his chair, he addressed the larger of the two. \"", "Welcome to the Fire and Dice Casino. ", "I'm Mr. Tormond. ", "And you are...?\"", "\n\nStan stepped up and introduced Larry and Bart who offered handshakes to Tormond.", "\n\n\"I don't know if Stan has fully explained what this meeting is all about, but I'm sure that you will fit right in.\"", "\n\n\"Fit in?\" ", "Larry asked.", "\n\n\"Stan, please return to the floor and make sure that all security issues have been handled,\" Tormond cordially instructed, ignoring Larry's question.", "\n\n\"Certainly, Mr. T,\" he replied, understanding that he needed to make sure that the warriors had truly left the building and if not, continue monitoring them.", "\n\nAfter watching the door close, Tormond turned his attention back to the two men. \"", "Now, where were we?\"", "\n\n\"Well, sir, we were...,\" Larry began.", "\n\nTormond immediately silenced Larry's response, really not caring what he had to say, and got right down to business. ", "Connecting with both of their minds, he took immediate control. ", "Oh, my favorite part. ", "The fear - it's euphoric.", "\n\nHe knew they felt the strength behind the hold he had over their minds and bodies and he felt their meager struggles. ", "He also heard their thoughts. ", "Like all mortal males that were built like linebackers, Larry and Bart thought they would never have anything to fear.", "\n\nOh, my God! ", "I can't move. ", "What the hell's going on? ", "Bart screamed silently. ", "He could only move his eyes and really wished he hadn't as he observed the casino owner standing in front of Larry in a commanding stance. ", "Tormond was menacing with his lips curved into an evil sneer and his eyes gleaming wholly black like the darkest marbles. ", "Larry!", "\n\nLarry's face was filled with pure terror and unbearable pain. ", "His eyes were huge and bulging out of his skull. ", "His ashen face was contorted in a horrible scream filled with agony, but the sound... Oh, God...the sound...\n\nAlong with Larry's screams, Bart swore he heard hundreds of screeching voices as if devils or demons surrounding them with their hellish cries of torment. ", "It was the sound of absolute death.", "\n\nBart couldn't move to cover his ears. ", "The sound alone was so painful he thought his ears would begin bleeding at any moment. ", "He needed help. ", "Why was no one coming to help? ", "Surely they heard the horrific screams and wails. ", "Please God, help me! ", "But no one came as he watched Larry's body surrender and crumple to the floor.", "\n\nThen the casino owner turned toward him and he heard his own screams as he felt his mind and soul being ripped from his body.", "\n\nAs Bart's screams eventually turned to whimpers, Tormond stepped back and addressed both men. \"", "Now, you are mine and you will do everything that I command.\"", "\n\n\"Yes, my Lord,\" they responded in unison.", "\n\nTormond was pleased. ", "These two would make a great addition to his minion ranks. ", "But they needed more, many more. ", "And the search would continue. ", "They had an army to build.", "\n\n*****\n\nChapter Twelve\n\nThe languid feeling of lying in Aaron's arms had vanished. ", "Danielle was fraught with too much tension. ", "Her chest felt strung so tight it just might spring like an overused string of a violin. ", "She made her way to the weight room, hoping to work off the tension or at least relieve it somewhat. ", "She was pleased to find the room empty and grabbed a towel from the shelf as she entered. ", "She stepped up onto an elliptical exercise machine, chose her preferred course on the control panel and began the hour long trek of pushing, pulling, stepping and climbing. ", "Instead of inserting the available ear buds and immersing herself in music, she lost sight of everything around her. ", "Closing her eyes and allowed her thoughts to wash over her.", "\n\nBut allowing this all at once was too much and caused the pain within her chest to increase. ", "She mentally chastised herself as her pulse and breath quickly increased at an abnormal pace with her thoughts and the problems revolving around Aaron took hold of her. ", "She realized she must take control of her thoughts, organize them into smaller pockets that she could handle without them overwhelming her. ", "She'd tackle one concern at a time, analyzing it rationally. ", "Not allow her thoughts to engulf her, sweeping her out to sea like an insurmountable undertow and swallowing her whole, never to resurface. ", "She was a disciplined warrior – she could do this. ", "She took deep even cleansing breaths until her heart rate lessened. ", "Once this task was achieved, she was ready to begin again.", "\n\nWith her eyes still closed, Danielle pictured Aaron in her mind. ", "He was so beautiful to look at and delightful to touch, so very sexy. ", "And when he touched her...\n\nWait...stop. ", "That thought would have her pulse racing again. ", "But, that in itself, was definitely not a problem as far as her vision and body were concerned. ", "Although she certainly wanted him sexually now, just how long would that last? ", "Her past had taught her that men weren't reliable or trustworthy. ", "Alarr had unwittingly taught her that. ", "As did the other men in her past that refused to respect her as a woman and a warrior.", "\n\nThe real question was her strange and instant attraction, the pull she felt towards him and not only on a physical level. ", "Almost as if she knew him, not as a person, but deeper, as in his soul. ", "Yes, he shared the same coloring as her former mate, but so did millions of others and they didn't make her do and say the things she was drawn to do with Aaron. ", "She'd unbelievably outed her entire race with little thought of the consequences. ", "It must be the binding chain. ", "Had to be. ", "There just was no other explanation. ", "So predictably, once it was removed, the attraction would go with it. ", "Wouldn't it? ", "She trusted Zahara and the other's to find a solution.", "\n\n\"The sooner the better,\" she mumbled somewhat unconvincingly.", "\n\nPlaying devil's advocate, another thought took form. ", "What if they didn't find a solution? ", "She admired him. ", "His occupation, his character, his intelligence, his bravery. ", "His willingness to put aside his scientific beliefs and not only believe, but trust her here in her existence. ", "She wanted to be treated like a normal woman, not a warrior or demi-goddess, and he did all that without being asked to. ", "He also seemed to respect her as an equal. ", "Mentally as well as physically. ", "Although in reality, she was not only physically stronger, but they didn't share the same life expectancy. ", "She still appreciated his efforts. ", "For eight hundred years, she'd longed to be seen as a normal woman and she wanted to be loved as one, as well.", "\n\nHe also annoyed her. ", "He was too dedicated to his work and narrow-minded at times. ", "Especially regarding the EOD. ", "Knowing all that he did about the dangers involved, he didn't have the sense to walk away. ", "He was still determined to continue his quest. ", "Just what was his problem? ", "Didn't he get it? ", "You'd think with that brain he would. ", "One thing he didn't realize was that, should he actually locate the EOD, he wouldn't just have Tormond and his crew to contend with, but the Gods would never allow him to keep it and study it. ", "They'd not only take it away from him, but they might not leave him alive long enough to attest to having found it. ", "Too much memory scrubbing could be seriously dangerous. ", "The Gods would probably see it as a mercy to end his existence.", "\n\nBut what was she thinking anyway? ", "She couldn't possibly have a future with this mortal. ", "And he was just that – mortal. ", "He was not a warrior and could never fit into her world, and wishing it was so wouldn't make it right. ", "Those thoughts were foolish. ", "It was forbidden. ", "Having sex with mortals was commonplace amongst their kind, but never could they hope to keep them for themselves. ", "She knew of only one before her that had been reckless enough to allow such an attachment to come to fruition – Vex. ", "And his was a very sad tale.", "\n\nNo, she could never allow herself to fall in love with a mortal. ", "Thunder would never allow it. ", "She knew Aaron was only welcome here for a short while. ", "Thunder would only allow him to stay until he wasn't useful anymore. ", "They could have no future.", "\n\nFall in love? ", "A future? ", "Why would she want a future with him anyway? ", "What crazy thoughts? ", "It's not like she was in love with him. ", "No how, no way. ", "She'd learned over the past eight hundred years not to allow such feelings.", "\n\n\"Been there, done that, have the scars to prove it,\" she murmured to herself again.", "\n\nWell, if you could call what she had with Alarr love. ", "Since having to face her past again of late, she wasn't so sure. ", "At least it wasn't the kind of love she craved at the time. ", "She'd allowed herself to be tricked into an illusion. ", "One mistake she would never repeat again.", "\n\nBut she felt such contentment when she was lying in Aaron's arms this morning. ", "So satisfied. ", "So serene. ", "So warm. ", "So...safe.", "\n\nShe visibly shook her head, as if she could vanquish the thoughts and remembered feelings by her movements. ", "No, that's all it was – contentment. ", "She was simply pleasantly sated at the time from his masterful lovemaking. ", "Nothing more.", "\n\nAnd she had to ensure it stayed that way.", "\n\n*****\n\nAaron stood with a large sword in his hand facing off his opponent. ", "A huge warrior who carried a confident look in his dark deep-set eyes. ", "He had full sleek black hair that fell just past his shoulders and the top portion was pulled back into a leather thong held at the back of his head. ", "His broadly muscled chest was shirtless and his darkly tanned skin sported a tattoo of three interlocking triangles directly over his heart. ", "He bore many other tattoos. ", "Egyptian symbols adorned the center of his forehead and cheeks and accented the van dyke beard and full lips on his exotically sun-bronzed face. ", "He wore black silken pants that were secured around his trim waist by a wide matching sash that reminded Aaron of a tuxedo cummerbund. ", "He was shoeless and moved around nimbly on the balls of his feet with the grace befitting an adept dancer in a wide arc circling his opponent. ", "Then he took a stance that was battle ready with a lethal scimitar held out in front of his formidable body.", "\n\n\"So, Slash,\" Aaron began, trying to control the trembling in his voice. ", "He knew he was no match, but he refused to come off appearing cowardly. \"", "This is a first for me, but you obviously know what you're doing.\" ", "Aaron assumed ignorance trumped cowardice in this instance.", "\n\nThis was the beginning of his weapons training. ", "Without consulting him, they'd decided he would most benefit from training in daggers, swords and guns. ", "Gee, thanks, guys. ", "The guns he could deal with and Turbo had given him some constructive instruction regarding daggers, using his Egyptian jambiyah, during yesterday's hand-to-hand training. ", "But facing off with a largely ripped Egyptian who smiled incessantly didn't make that same list. ", "The smiles looked genuinely friendly, which made it feel that much more wrong.", "\n\n\"Yes, my friend. ", "I've been around for a very long time. ", "Since the fourteenth century actually.\" ", "Aaron's eyes went wide. ", "He didn't think anything else could shock him, but once again, he was wrong.", "\n\n\"There's no need to be nervous. ", "I just want to see what you've got,\" Slash said with a slight Middle Eastern inflection that flowed from his lips in a low sexy drawl. \"", "But I can see that you've never held a sword before. ", "Correct?\" ", "The genuinely friendly smile never left his face, although he wasn't striving to be condescending.", "\n\n\"That's right. ", "And I think I could've happily gotten through the rest of my life without ever having done so. ", "I'm obviously not too fond of this choice of weapon,\" Aaron said sheepishly while pointing the sword out and away from his body. ", "He tried his best not to appear geeky, but sometimes it was beyond his control, which was one reason he kept his own body fit and toned. \"", "And yours looks even more intimidating,\" he admitted evenly.", "\n\n\"That's perfectly understandable. ", "But don't worry. ", "We'll start from the beginning with how to properly hold it.\"", "\n\nSlash had relaxed his warring posture and closed the distance between them. ", "With his right arm, he held his sword out straight in front of him at shoulder lever and turned his grip inward, demonstrating the proper positioning of his hand on the hilt of his sword. ", "The strength of his grasp was apparent, as well as the sinewy muscles that draped his limb and continued up into his shoulders.", "\n\nAaron mimicked the hold on his own weapon noting the view of his own grip and silently praised himself. ", "It wasn't best in show, but it was still impressive.", "\n\n\"Are you really from the fourteenth century? ", "Forgive my curiosity, but my passion is history – of all kinds.\"", "\n\n\"Yes, from Egypt. ", "I was brought over in the year 1312. ", "I was the ruler of my Wuhadept tribe. ", "My given name is Ammon, an honor my parents bestowed on me after the King of the Egyptian Gods, whom some also call Amun.\" ", "Slash held a fond faraway look in his eyes and stared over Aaron's shoulder into the unseen.", "\n\nAaron couldn't help but picture a masterful Slash sitting steadfastly upon a strong black steed atop a mountainous sandy peak with his black hair and robes whipping behind him.", "\n\nThen Slash blinked, his sight refocusing on Aaron. \"", "But I'm afraid you won't find me in any history books.\"", "\n\n\"Wow, your tribe may have been part of the early desert-dwelling Bedouins,\" he queried.", "\n\n\"Of that, I have no idea. ", "Shall we continue with your training?\"", "\n\n\"Yes, of course.\" ", "Aaron also let go of the past and refocused his attention to the task at hand.", "\n\n\"Okay, first you should know that the foible, the top third of the blade, is the weakest part of your sword and the forte, the bottom third of the blade, is the strongest part. ", "I want you to thrust your sword at me. ", "Just extend your sword arm straight out to its fullest length without lunging.\"", "\n\nAaron did as instructed and Slash met his thrust by capturing his sword near the hilt, performing a circling motion around it and ripping it from his grasp. ", "Aaron marveled at the speed and accuracy Slash demonstrated in his moves.", "\n\n\"That,\" Slash said motioning to Aaron's sword lying on the ground, \"is not what you want to happen. ", "Whatever you do, never let your opponent disarm you.\"", "\n\nThey practiced lunging, thrusts, parries, cuts, attacking, advancing, even when to retreat and Aaron felt somewhat adept when they had finished. ", "He wouldn't ever look forward to fighting in this manner, but at least he had the basics down and could hold his own if need be.", "\n\n\"Well done, my friend,\" Slash acclaimed. \"", "We'll make a warrior of you yet.\"", "\n\n\"Oh, no.\" ", "Aaron shook his head adamantly. \"", "I have no intention of becoming a warrior. ", "At least not anytime soon. ", "Although, I guess it could be something to aspire toward once I've lived a full and fruitful life.\"", "\n\n\"My friend, we never know what life, or the possibly of another thereafter, has destined for us. ", "Always aspire to live the one you have now, fully and fruitfully, every day.\"", "\n\nAaron could see, through Slash's words and actions, he had been a wise and gracious ruler then because he was a wise and gracious warrior now. ", "He was glad to know Slash was on the side of good now, too, because he'd much rather fight with him than against him. ", "Any of the warriors actually. ", "They were a formidable bunch. ", "This thought led him to ponder just how bad the 'bad guys' really were and whether he'd be able to protect Danielle when and if the time came. ", "He wasn't sure how effectual he would be, but he did know one thing – he'd sacrifice his life trying. ", "After all, she'd already saved his.", "\n\nAaron's next stop was the shooting range. ", "While Slash escorted him there, his love of history and knowledge got the better of him once more.", "\n\n\"Can you tell me about the tattoos you have?\"", "\n\n\"Gladly. ", "This one,\" he said as he pointed to his chest, \"You will see a lot of. ", "It is the symbol for the Eye of Odin. ", "All of the male warriors carry this mark. ", "It symbolizes the Valknut or slain warriors knot\"\n\n\"I thought I recognized it, but I wasn't sure.\"", "\n\n\"As for my facial markings, this one symbolizes honor,\" he instructed pointing to his forehead. \"", "These on my cheeks symbolize loyalty and strength.\" ", "These were obviously qualities that he lived his life by and it showed.", "\n\n\"Nice. ", "Anymore?\"", "\n\nHe laughed heartily. \"", "If you mean do I have a big heart-shape with a lady's name in it tattooed on my ass, I'm afraid not.\"", "\n\nAaron laughed along and then asked, \"Speaking of ladies... How does that work around here between all of you?\"", "\n\n\"Are you referring to the relationships between the male and female warriors?\"", "\n\n\"Yes. ", "For reasons I'll refrain from mentioning, I know you can have sex with mortals, but how does that work between all of you being immortal?\"", "\n\nThere was a sudden blur in Aaron's peripheral vision.", "\n\n\"Well, there certainly aren't any mass orgies going on around here. ", "Not that I haven't tried to organize it,\" Blaze interrupted playfully with a sly smile spread across his face. ", "They'd entered the shooting range where Blaze had picked up on the conversation from across the range with his preternatural hearing and decided he'd like to participate.", "\n\nAaron had met Blaze previously in the meeting but now was unprepared for the intimidating man that stood before him. ", "This vampire could scare the skirts off a schoolgirl. ", "He was at least six foot six, if an inch, with a wrestler's build, wearing a body-hugging cotton shirt that wrapped his impressive abs and bulged around his biceps. ", "He must have possessed some fashion sense as he was dressed in style from his crown to his Italian loafer wearing toes. ", "He sported a nice sized diamond earring in one ear and designer sunglasses perched on the edge of his slightly crooked nose that had seen its share of fists. ", "His head was smooth as a baby's butt and the whole package was covered in mocha colored skin. ", "He projected a stunningly dangerous aura that Aaron imagined many women would be irresistibly drawn to.", "\n\n\"Dream on,\" Slash laughed. \"", "The ladies may be liberated, but they certainly aren't that liberated.\"", "\n\n\"I don't know...,\" Blaze sing-songed. \"", "Mac's getting real close.\" ", "He and Slash embraced in a manly bear hug accompanied with the appropriate slap on the back and the greeting, \"Brother,\" in unison.", "\n\nHe stuck out his hand in greeting to Aaron. \"", "Blaze. ", "Nice ta meet cha. ", "We sorta met earlier.\"", "\n\nAaron returned the salutation chuckling along with the warriors. \"", "You, too. ", "I'm Aaron.\"", "\n\n\"Actually,\" Slash continued with his explanation, \"Some are bonded, but many aren't. ", "It's not a very popular choice.\"", "\n\n\"Really? ", "Why's that? ", "Isn't it like getting married for mortals?\" ", "Aaron asked. ", "He didn't notice the two men glancing at the chain around his neck with interest.", "\n\n\"Oh, no. ", "Getting married by promising vows that can be easily broken at a later date is nothing like being chain bonded. ", "Mortals promise to love and cherish for life and, as we all know by a divorce rate of over fifty percent, that usually isn't what happens. ", "It's much easier to make that type of commitment when you know you have an 'out' if things aren't all sunshine and roses.\" ", "Slash pointed to the chain around Aaron's neck. \"", "Chain binding is much more serious and should never be entered into unless you're one hundred percent positive that no matter how much you may want to hate her right now, you still love her, no matter what.\"", "\n\nBlaze added, \"There is no divorce for us. ", "And because we're immortal, there is no end. ", "You'll never see me putting one of those things around my neck. ", "I mean, I love the ladies, and I do it very well and often. ", "But then I just want them to go home. ", "Case closed.\"", "\n\nAaron looked stricken as his hand glided up to touch the chain. ", "Panic was evident in his eyes. \"", "Of course, that doesn't mean you're bound to Danielle. ", "We really don't know yet what this means, but definitely not that,\" Slash assured him. \"", "I'm sure we'll figure it out soon.\"", "\n\n\"Bound to Danielle?\" ", "Aaron asked wide eyed.", "\n\n\"You know she was bound before, years ago, right?\" ", "Blaze asked. \"", "That chain you're currently wearing belonged to her mate who was killed in The Great Battle.\"", "\n\nStunned, Aaron shook his head slowly back and forth. \"", "N- no,\" he stuttered. \"", "I knew it belonged to her, but no one's really told me much else.\"", "\n\nSlash gave Blaze a hard look. ", "Way to go, brother. ", "Danielle should have been the one to spill the beans.", "\n\nOh, man. ", "I'd have thought she'd told him by now, Blaze responded.", "\n\n\"I'm sure Danielle will tell you. ", "Maybe she just hasn't had the time yet.\" ", "Slash tried to make a recovery of the mess they'd just created. \"", "You haven't been here very long.\"", "\n\nAaron appreciated Slash's efforts but recognized them for what they were. ", "He suddenly felt the need for a change of topic and turned his attention to Blaze. \"", "You ready to get started here? ", "I feel like I could shoot something right now.\" ", "No explanation necessary.", "\n\n\"Sure, buddy,\" he chuckled. \"", "Come with me and we'll get to it.\"", "\n\nAaron thanked Slash for his time and training and headed in the direction Blaze indicated. ", "He spent the next couple of hours with Blaze and was glad to do something constructive. ", "He shot the hell out of every target that was thrown at him with a variety of weapons. ", "He discovered that aggressively firing at inanimate objects was great stress relief. ", "Who knew?", "\n\nBy the end, he hadn't figured out how to approached Danielle about this latest bit of news. ", "Then again, maybe he wouldn't approach her at all. ", "He wasn't exactly pissed off at her, just disappointed. ", "But why am I disappointed? ", "It really had nothing to do with him and once this chain was off, they'd go their separate ways. ", "Right? ", "Like Slash said, he wasn't bonded to Danielle. ", "This was just a fluke, so he'd enjoy what they had together now, while he could. ", "There was no reason to stir things up. ", "They weren't in love and they never could be. ", "So why do I still feel disappointed?", "\n\nBlaze pulled him out of his thoughts and suggested they join some of the others in the rec room. ", "There was a soccer game he wanted to catch. ", "Agreeing, they made their way to an area where several others had gathered.", "\n\nThe room was furnished like a first class recreational zone completed in an elegant-posh-sports-bar style. ", "One wall housed the largest flat-screen TV he'd ever seen, where there was sure to be all the latest video games available and the entire room was wired for surround sound. ", "There were a couple of oversized couches and several more oversized chairs stationed around the vicinity of the flat screen. ", "Oversized was the theme run rampant here. ", "He deduced it was to accommodate the bevy of bulky men who lived and worked here.", "\n\nThe opposite side of the room housed a full mirrored bar and professional pool table, rounding out with an authentic fully functional 1950's Wurlitzer Jukebox complete with rainbow colored bubble lights. ", "An elaborate door to the side of the bar exhibited a stylishly lit sign above it that read 'Theater.'", "\n\nThey made their way in and settled onto one of the couches to join the soccer game already in progress. ", "Low-toned male grunted greetings were passed all around, including the obligatory \"Brother\" greeting, then Blaze got up to journey towards the bar.", "\n\n\"What can I get you to drink, Aaron?\"", "\n\nLooking around him, he noticed each had a beer in hand. \"", "A beer would be great, thanks. ", "Whatever you've got will be fine.\"", "\n\n\"Hey, bro, grab me another while you're at it,\" Savage ordered while spread lazily lounging in his seat with one leg draped over the side dangling.", "\n\n\"Sure,\" he replied. \"", "Anything else you require, Sire?\" ", "Blaze said mockingly with his eyebrow raised.", "\n\n\"A woman,\" he replied.", "\n\n\"You don't need no woman. ", "You've had so many blind dates, you should get a free dog.\"", "\n\n\"Actually, it was Homer Simpson that said 'A woman is like a beer,'\" Vengeance spoke up. ", "He had his hands behind his neck and leaned back against the overstuffed chair he occupied.", "\n\n\"Okay, I'll bite. ", "How so?\" ", "Savage asked.", "\n\n\"They look good, they taste good and you'd step over your own mother just to get one.\"", "\n\nAaron enjoyed the teasing camaraderie they shared and laughed along with the group of friends. ", "Not knowing what to say or how to act, he sat back and simply observed, hoping to fade into the background.", "\n\n\"Hey, we heard that!\" ", "Makayla said bursting into the room with several of the other females. ", "They crowded around the couches getting comfortable themselves. \"", "And since we're quoting analogies about the sexes, you know what Mae West said...'A hard man is good to find.'", "\n\n\"No, no, no. ", "My favorite is...the best way to get over one man is to get under another,\" Raven offered.", "\n\n\"Works for me,\" Savage threw in, his dark brown eyes hungrily devouring Makayla.", "\n\n\"Careful now, Savage. ", "Don't let your brains go to your head,\" Vengeance chortled with quiet challenge.", "\n\nThat shut him up and the ladies loved it, laughing it up the way only a rowdy group of ladies can. ", "They could dish it out and take it just like they were one of the guys. ", "The closeness and teasing cemented their bond like an anchor through a storm as they fought and faced death side by side on a regular basis.", "\n\n\"Sorry, ladies,\" Blaze said, returning with an armload of bottles and began passing them around. \"", "We're not watching Lifetime today.\" ", "Soon there was the 'fzt' sound of beer being opened throughout the room.", "\n\n\"What?\" ", "Nadine said flipping her brunette mane over her shoulder. \"", "Do you think all we do is sit around romanticizing to Lifetime Movie Network?\"", "\n\nA puzzled Blaze simply shrugged and rubbed his massive hand back and forth on his smooth-shaven head.", "\n\nShe placed her arms akimbo and persisted. \"", "Really, we'd like nothing more than to sit around watching gorgeous international soccer players and fantasizing about what we'd like to do to them...and vice versa. ", "Not so different from you guys.\" ", "She thought for a moment realizing what she'd inferred. \"", "With women, I mean,\" she tried to recover. \"", "I certainly wasn't insinuating that...\"\n\n\"Yeah, yeah, yeah,\" Justice cut in. \"", "You have no interest in this game. ", "We all know you really want moonlight and roses.\"", "\n\n\"Wrong. ", "We just want to put our hands all over their gorgeous bodies and ride them,\" Makayla said in a somewhat husky tone with her eyes burrowing in on two particular men. ", "Savage and Vengeance smiled greedily back.", "\n\n\"Well, that brings us back to Mae West,\" Raven laughed.", "\n\n\"Right. ", "Like that's ever going to happen with famous international sports stars.\" ", "Justice rolled his eyes.", "\n\n\"Well, that's why it's called fantasizing, dummy. ", "Unlike some people I know, we don't have the ability to enthrall every good looking, young thing that we want,\" Nadine said accusingly with a slight trill in her voice. ", "She knew she'd pushed the wrong button that time.", "\n\nA chorus of oooos and ahhhs filled the room.", "\n\n\"Oh no, you don't. ", "You didn't just go there,\" Slash sat up straight, finally joining in with something other than laughter. ", "He watched the silent exchange Mykayla was embedded in.", "\n\n\"Sorry, boys. ", "No offense.\" ", "Nadine brought her palms together in front of her and bent at the waist in a mock bow. \"", "You know I love you all.\"", "\n\n\"And we love you, too,\" Justice roared as he jumped up from his seat, grabbed her, tucking her head under his arm and commenced to rubbing his knuckles gruffly on her crown, torturing her like a little sister. ", "She squealed until he released her.", "\n\n\"Well, I think I've had enough fun for the night,\" Vengeance said rising and making his way to the door. ", "He looked back over his shoulder. \"", "You coming, Mac?\"", "\n\n\"Not yet...\" Makayla sing-songed lowly with a suggestive smirk as she followed him to the door. \"", "But my hopes are high.\"", "\n\nNo one said a word when Savage quietly got up and crept out of the room in pursuit.", "\n\n*****\n\nChapter Thirteen\n\nHey, wait up, Mac.", "\n\nMakayla touched Vengeance's arm halting him and turned to acknowledge Savage as he jogged to catch up with her. ", "They hadn't even heard him draw near. ", "He had the uncanny ability to be extra quiet and not make his presence known when he chose and could sneak up on anyone without them being aware. ", "Luckily, this time, he didn't surprise the crap out of her, making her jump, like he sometimes did. ", "She supposed it had to do with his Lakota Indian nature or all that meditating and the rituals he did. ", "Either way, he was great for recon missions and the things he could do with a bow and arrow rivaled her own talents, and she'd been gifted the same weapon by Freya.", "\n\nShe noticed he was looking exceptionally attractive tonight. ", "He never liked to wear very many clothes so she knew he was commando in those jeans that snuggly fit his well-toned and tanned ass and rode low on his sculpted hips. ", "Above the waist, he filled out a shirtless black leather vest perfectly with his beautifully sleek and athletically muscled body. ", "She admired his dark olive complexion and the deep V at his neck that emphasized the intricately displayed tribal tattoos on his chest. ", "They matched the sexy spherical ones that wrapped his biceps, giving him an almost Inca vibe. ", "Vex had teased her that Savage was her Steve Perry look-a-like. ", "With the same tanned skin and his long silky black hair that hung straight down to the middle of his back, she supposed he could be right. ", "And that may be what first attracted her, but it wasn't the only reason she cared for Savage. ", "Sure she loved him, but she wasn't in love with him. ", "They'd been lovers now for a couple of years, even before she hooked up with Vengeance.", "\n\nLuckily, Venge wasn't the jealous or selfish type. ", "Both she and Venge had been around for over a thousand years. ", "They knew the score well and simply enjoyed each other's company. ", "What they shared was comforting and satisfying, yet exciting. ", "And it would last until it was over. ", "No regrets. ", "He wasn't the bonded mate type and neither was she – anymore. ", "She'd had her true love and lost him many years ago. ", "It had nearly killed her and she swore never to allow herself to be that vulnerable again, never to open herself or give that much of herself ever again. ", "Her sister just didn't understand, having never sustained such loss. ", "Hopefully, she and Joseph would never have to endure such pain.", "\n\nBoth men were phenomenal lovers and she refused to choose between them, which didn't seem to be a problem for them, either. ", "If she weren't immortal, she wouldn't be able to handle both their blood and physic sexual needs. ", "But it was a fair trade-off for being held and caressed occasionally.", "\n\nBy the scowl on his face, Vengeance didn't like being interrupted by Savage. ", "She'd noticed the low-lying competition between them during the soccer game and wasn't in any mood to break up a skirmish now. ", "Not that she actually could.", "\n\n\"What's up, gorgeous?\" ", "she asked.", "\n\n\"I thought maybe you'd like to hang with me for a while tonight.\"", "\n\nUh oh. ", "She heard the low rumbling of a growl vibrating Vengeance's chest. ", "The simmering challenge continued. ", "The tension surrounding them was palpable and was escalating like a tea kettle on the verge of whistling. ", "Loud.", "\n\n\"Well, as you can see, I've already left with Venge.\" ", "Diffuse, diffuse, diffuse. ", "She touched Savage's arm briefly in apology.", "\n\nVengeance didn't like seeing her so puppy-dog-eyed. ", "He blew out a huge heavy lungful of air, stuck his hands in his jean pockets and directed his attention to Savage. \"", "I don't mind sharing if you don't.\"", "\n\nMakayla's head snapped way up to meet his six and a half foot frame, her face a mask of confusion and shock. \"", "Did I just hear you right?\"", "\n\n\"Yea, you did. ", "You're sleeping with both of us anyway. ", "So, what's the big deal?\"", "\n\nShe lowered her gaze and bit the inside of her bottom lip, pondering. \"", "Well...yea...but not together.\"", "\n\n\"Look, I wouldn't have suggested it, but knowing you the way I do...I think you'll like it...a lot.\" ", "He stepped back a little to search her face and folded his bulging arms across the span of his magnificent chest. \"", "Well, what do you say?\"", "\n\nSavage hadn't said a word, which wasn't unusual for his normally quiet demeanor, except this involved his participation and no one had consulted him. ", "There were no tale-tale signs on his face. ", "I bet he's great at poker, she thought.", "\n\n\"Aren't you going to ask Savage how he feels about it?\" ", "she inquired, avoiding answering his question. ", "Obviously, Vengeance had no qualms about it. ", "The sparkle in his eyes reflected the glee of a six-year-old boy who couldn't wait to share his favorite toy.", "\n\n\"Nah, he's a red-blooded male. ", "There's your answer right there.\"", "\n\nSavage said nothing, just smiled and raised his eyebrows comically. ", "But his gums tingled imagining the possibilities.", "\n\n\"Well, hell,\" she said unsuccessfully trying to convey a small portion of defeatism. \"", "Let's go then. ", "But we're going to your place, cuz I'm not cleaning up afterward.\" ", "Oh, Goddess. ", "Can I do this? ", "I guess we'll find out very shortly.", "\n\n\"Well, alright then.\" ", "Before she could stop him, Vengeance bent down and scooped her up, tossing her over his shoulder head down and whacked her on the butt. ", "She squealed, which pissed her off somewhat because she hated to squeal. ", "She was definitely not a squealer. ", "Intending to thwart any further embarrassment, she silenced herself and tamped down on her irritation, taking in her situation to counter his attack. ", "Just have to wait for the right moment. ", "She closed her eyes and took a deep, cleansing breath, reaching for a tranquil state of mind, so she could plot her good-humored revenge, then opened them and had a sudden change of heart.", "\n\nA slow, sultry smile formed, though none could see it with her face practically buried in Vengeance's backside. ", "There, right before her eyes was a familiar, but worthy specimen, a true work of art – his ass. ", "Maybe it wasn't all so bad after all. ", "Guess I'll forgive him – this time.", "\n\nSavage followed close on Vengeance's heels, anticipation growing at the view of his lover in a state of helplessness before him. ", "He was extremely grateful to Vengeance for the invite and looked forward to sharing some true wickedness between them. ", "It had been a while since he'd delved into a threesome and never before with Makayla. ", "This was new to her, but they'd make it good. ", "The excitement of what was to come had put a twinkle in his eye, a little bounce in his step and an impressive erection in his jeans.", "\n\nVengeance opened the door of his home which screamed bachelor like a complete battalion of men had virtually thrown up their male essences throughout the entire floor plan. ", "Instead of sports memorabilia, every corner showcased Viking relics that reminded him of home and the good old days of battles long past. ", "He loved to escape and visit the Viking Ship Museum in Oslo, Norway, whenever possible, dreaming of standing on the bow of his former ancient ship near the huge ornately carved dragon's head that protruded from it with the winds of the European Coast whipping through his long blond hair and the massive billowing sails. ", "Then, he was a mighty warrior known as Erik to his people and he ruled the seas commanding his dragon ship, a symbol of great strength and power to drive his enemies away.", "\n\nContinuing down the hallway, they entered the master suite that boasted an equally impressive king sized platform bed, the headboard ornamented with expertly crafted battling dragons. ", "Makayla's fireman carry came to an abrupt end as she was unceremoniously flung down to the center of the bed. ", "Managing to withhold the squeal this time around, she abruptly found herself being overpowered once again by two very impressive hot male bodies. ", "Two very impressive hot naked male bodies, as evidenced by the hardness she felt prodding against her lower half.", "\n\n\"Not fair, you two. ", "Speed stripping, huh? ", "I was so looking forward to watching you take it all off for me...slowly.\" ", "Her attempt at disappointment fell short. ", "And yes, unlike Savage, her poker face sucked. ", "She wasn't very adept at hiding her true feelings, lying, or any of that devious, sneaky and sometimes devilishly fun stuff.", "\n\n\"I guess we'll have to make up for it,\" Savage rumbled lowly.", "\n\n\"Yes, you won't be disappointed,\" Vengeance promised teasingly, his lips brushing against her neck and shoulders.", "\n\nShe couldn't help but admire them on either side of her, their beauty and coloring in such contrast. ", "Savage, with his long silky black hair flowing around his olive, tanned muscular torso. ", "His beautiful sleek lithe body bearing his tribal tattoos on his chest and biceps and his dark chocolate eyes alight with lust and need. ", "Vengeance, with his equally long blond hair tied with a thong at his nape, sexy sleepy crystal blue/gray eyes, fairer skinned broad shoulders and rippling abs. ", "He smiled down at her with his trademark smile – beautiful and sinfully suggestive, showing a hint of fang. ", "She delighted in the desire displayed on both their faces as she realized it was all for her and her alone.", "\n\nMakayla reached up to dislodge the thong holding Vengeance's hair and met his kissable lips in a hungry embrace. ", "His kiss was contradictive, soft and sweet, yet demanding at the same time. ", "She relished in the feel of the whiskers of his barely-there beard and mustache abrading her sensitive skin. ", "Using her clever little tongue, she explored his mouth hungrily, sliding along the tips of his partially extended fangs, causing him to moan into her mouth. ", "She pushed back slightly on his chest withdrawing for a moment.", "\n\n\"Don't either one of you laugh or I swear this will be over before it starts,\" she said with a heated warning burning in her eyes, \"but I'm not sure what to do.\" ", "Hoping to save herself a bit of embarrassment, she continued, \"I mean I know what to do, but not exactly where to start.\" ", "Her eyebrows furrowed, her face showing a look of pleading and uncertainty. \"", "Know what I mean?\"", "\n\n\"Min Älskare,\" Vengeance began, his arousal thickening his accent. \"", "You need not worry about a thing. ", "Savage and I will let you know when you're participation is required. ", "Otherwise, just lay back and enjoy. ", "I promise you won't regret it.\" ", "He stroked the fingertips of one hand lightly down her cheek to her throat and onward between the valley of her breasts as he spoke softly, lulling her to relax with his touch and soothing voice. ", "She loved when he called her his lover. ", "Just the way it rolled off his tongue. ", "Like any other girl, she was a sucker for hot guys speaking foreign languages.", "\n\nShe looked to Savage, searching his face for confirmation. ", "The man of few words simply growled deeply in his chest, the flash of fire growing more intensely in his eyes, his nostrils flaring as he detected her heightened scent. ", "She found it amazing that a man of so few words could speak volumes with his eyes and expressions. ", "Feeling no further verbal response necessary, Savage covered her lips with his, consuming her with his teeth and tongue in a kiss that affirmed his descriptive name – savage. ", "He was no easy lover and she'd have him no other way.", "\n\nAfter they quickly divested her of her clothing, Vengeance moved to sit with his back against the headboard in a sea of feather-filled pillows, sliding behind Makayla, nestling her against his chest and extending his long muscular legs to either side of hers. \"", "Raise your arms up around my neck and don't let go.\" ", "He grasped her hair in his hand and tilted her head back, capturing her lips in open-mouthed kisses, sucking on her tongue and nibbling her swollen lips between his teeth. ", "His other hand skimmed down her neck, over her shoulder, moving downward to cup and squeeze her full breasts succinctly, his thumbs strumming the tips to hardened peaks.", "\n\nShe arched into his touch pressing her breasts firmly in his strong hands. ", "He captured her moan, smothering it with his mouth as he kissed her. ", "His tongue met hers, stroking deeper and deeper, taking her breath away. ", "She could feel his body harden against her, his cock twitching against her back.", "\n\nSavage slowly kissed his way down her trembling body, settling himself between her legs, nudging them wider apart, but meeting with some resistance. ", "He looked up the length of her body searching her eyes.", "\n\nShe battled the onslaught of sensations caused by multiple hands, tongues, teeth and mouths showering attention to several areas of her body at once. ", "Bites, licks, sucking, firm squeezes and soft caresses assailed her senses with no reprieve in sight. ", "Her responses both confused and excited her, raising her passion to heights she'd never before experienced. ", "It was all so overwhelming, she struggled to maintain control of herself or she feared she might be completely lost.", "\n\nVengeance skimmed a hand down her belly and below, combing his fingers through the soft curls covering her mound. \"", "It's okay, Min Älskare. ", "Open your legs for us. ", "Just let go...and feel,\" he whispered lowly in her ear, nipping at her earlobe. \"", "You're safe. ", "We'll take good care of you.\" ", "His husky, sensual voice alone could bring her almost to the brink of climax and she felt the warm wetness between her legs begin to trickle down her inner thigh.", "\n\nHugging her closer, he continued his sensual caresses on her upper body, while Savage moved lower to run slow-moving hands up her calves, the backs of her knees, her thighs and underneath to the curve of her bottom. ", "She let the tension and inhibitions drain from her body, released her apprehension and relaxed into their wonderful ministrations, which was steadily replaced by her growing arousal and need. ", "Her thighs parted and she arched her pelvis slightly, offering it up to him.", "\n\nSavage dipped his tongue into the folds of her sex, running it from bottom to top, giving her clit a teasing lap. \"", "Ah, Makayla, you're so wet already and you taste so sweet.\" ", "He began to slowly, thoroughly feast on her core, flicking, licking and nibbling her tender flesh. ", "She moaned and writhed beneath his tormenting mouth as he brought her closer and closer to glorious release. ", "He felt her body tighten and quiver as it prepared to plunge over the edge and he suddenly stopped and pulled away. \"", "Not so fast.\"", "\n\n\"Please, don't stop,\" she begged.", "\n\n\"Not stopping, sweet. ", "Just prolonging. ", "The longer I make you wait, the better it will be. ", "I promise.\"", "\n\n\"Noooo,\" she whined. \"", "I need to come.\"", "\n\n\"Patience,\" Vengeance commanded gently as he pinched her nipple. ", "He bit the sensitive spot between her shoulder and neck, laving over the slight sting it caused. ", "Working his way upward, he blew a heated breath along her throat that sent delicious shivers throughout her body, then bit again on the delicate spot right behind her ear.", "\n\nSavage began to build her passion once more, slowly thrusting two fingers in and out of her dripping pussy, curling them inside to graze along her sensitive G-spot. ", "He began to spread her cream back towards her anal star, massaging and prodding her tight little hole. ", "He withdrew his fingers, replacing them with his thumb inside her core, then inserted the two fingers into her now slick dark passage. ", "She accepted the delicious invasion, clamping around his thick digits as he pumped within her, her desire steadily rising. ", "He lowered his mouth, swirling his tongue on and around her swollen clit.", "\n\nAs Makayla reached her pinnacle, Savage caught her nub between his lips and sucked hard sending her over the edge. ", "Her back arched and she let out a strangled scream as light exploded behind her eyes and her entire body convulsed with spasms.", "\n\nVengeance hissed with pleasure as her nails dug and scraped along his neck and shoulders. ", "Before her pleasure ebbed completely, the vampires prolonged her ecstasy causing more spasms to race through her by feeding. ", "Vengeance bared his fangs and sank into her slender throat; Savage turned his head and latched onto her trembling inner thigh, while both fed from the intense sexual charge she generated. ", "Deep guttural moans and groans filled the room.", "\n\nVengeance retracted his teeth from her throat, licking the puncture wounds to seal them. ", "He lowered Makayla's arms from his neck and raised her into his lap, rearranging his legs to bend at the knee underneath him. ", "With her back still resting against his chest, he grasped his cock and instructed, \"Slide down on me, Makayla.\"", "\n\nWith his assistance, she spread her knees on either side of his and lowered herself onto his thick length. ", "She gasped in pure pleasure as he filled her completely. ", "He raised her arms around his neck once more. \"", "Hang on, baby.\" ", "Gripping her hips he forced her down snuggly on his shaft and he began thrusting into her wet, slippery center as she raised and lowered her body, meeting his thrusts. ", "She clung to his neck, turning and tilting her head upward, searching for his lips. ", "They met in a fiery kiss as their lips were sliding and sucking, tongues whirling and mating.", "\n\nSavage moved closer, taking one of Makayla's lush breasts into his mouth, nipping and suckling, while his hand squeezed and pinched the other to a hard peak, spiking her desire even higher. ", "With her pussy stretched tight around Vengeance's cock, Savage dipped his other hand down sliding his palm along her belly until his fingers came to the top of her folds and circled her distended clit.", "\n\n\"More. ", "Fuck me deeper, harder, Venge.\"", "\n\n\"It would be my pleasure, babe.\"", "\n\nAs Savage backed away slightly, Vengeance brought her arms down and bent her forward on her hands and knees sustaining his connection deep within her. ", "Digging his fingers into her hips for purchase, he gradually withdrew all but the head of his thick staff, then forcefully slammed back into her channel causing Makayla to throw her head back and cry out.", "\n\n\"Oh, yes. ", "Goddess, that feels so good.\" ", "She could feel him all the way to her womb, his magnificent rod stretching her with painful pleasure and rubbing all the right places.", "\n\n\"Better, my lover?\"", "\n\n\"Yes, yes. ", "Do it again. ", "Don't stop.\"", "\n\nWith measured control, he repeated withdrawing slowly and ramming hard back into her to the hilt as her body rocked with his forceful thrusts. ", "She cried out with each masterful thrust. ", "Though he was pleased that he could bring Mykayla such pleasure, he feared continuing would hurt her and he relented to a steadier, milder pace. ", "Her cries became whimpers and she mewled as she ground back into him, meeting his thrusts.", "\n\nSavage reached out, cupping her chin in both hands and raised her head. ", "He smiled wickedly at her and placed his smooth, satiny head against her mouth, coating her lips with its fluid. \"", "Open.\"", "\n\nMakayla looked up through lust filled eyes and observed the long, thickly veined shaft before her with its swollen plum tinted crown, jutting out from a nest of crisp, black curls. ", "His cock was an object of beauty and no matter how many times she took it into her mouth, she never could get enough. ", "She knew exactly what he wanted and how he wanted it from previous experience. ", "Although she wasn't into intense pain, she loved when he commanded and controlled her the way he did. ", "His forcefulness was an extreme turn on for them both.", "\n\nOpening her mouth, she licked the pre-cum from his slit and continued running her tongue longingly around the head. ", "Then she greedily closed her lips around him, sliding him deeper into her wet cavern, over her tongue until she'd engulfed his entire length. ", "As he bumped the back of her throat, she swallowed causing him to groan. ", "He lightly grabbed onto the sides of her head and began guiding the movements in and out of her mouth. ", "Acquiescing, she gave over control to him, allowing him to fill her mouth as he pleased while Vengeance filled her from behind.", "\n\nAn electric current surged through her body, a burning need demanding to be filled. ", "Surrendering herself over to her lovers, putting her needs completely in their capable hands, gave her a sense of relief and a conscious freedom she'd never experienced before. ", "In her mind, she floated in a haze and felt only pleasure.", "\n\nVengeance felt it when Makayla wholly let go. ", "Smiling, he silently recommitted himself to fulfilling all of her needs and making this encounter unforgettable for her. ", "Although it wasn't love exactly, at least not the kind of true love that bondmates shared, what he felt for Makayla went far beyond the normal compassion he usually felt for his lovers. ", "She was definitely special, but also reserved, which he understood from her past loss. ", "She'd built walls around her heart and he realized a long time ago he'd never be able to penetrate them. ", "So, he resigned himself to share with her whatever she was willing to share. ", "He gave her sexual satisfaction in exchange for the feedings he required. ", "And that was enough, for both of them. ", "At least for now. ", "He had no idea what was actually between Savage and herself but knew it wasn't any more serious than what they shared between themselves. ", "In fact, he doubted very much that Savage felt as deeply for her as he himself did, as Savage was even more emotionally reserved than Makayla. ", "The relationship they shared didn't bother him in the slightest, it was just sex, and since this was the first time they'd actually shared Makayla, he wasn't sure where it would go from here. ", "That would entirely be up to her.", "\n\nMakayla looked up meeting Savage's chocolate brown eyes as he continued to glide over her tongue and thrust to the back of her throat. ", "She watched his face while she sucked him, never lowering her gaze, while at the same time, meeting Vengeance's hard steel plowing her from behind, his strokes slow and controlled.", "\n\nAs if on cue, Vengeance and Savage both picked up the pace, their breathing became more ragged. ", "Obviously, someone in the room was communicating mentally and left her out of the loop, but she wasn't complaining. ", "She was about to come apart herself and hoped she could hold out long enough.", "\n\nBut Vengeance knew her too well and reached around beneath her, circled the tips of his fingers over her distended clit, bringing her higher toward climax. ", "With a low authoritative tone, he commanded her, \"Come for us, Makayla. ", "Do it now.\"", "\n\nAs if her body had no mind of its own, Vengeance's demand took complete control of her, like a puppet on a string. ", "Her release caused a chain reaction as she screamed against Savage's thickness. ", "He broke eye contact with her, threw his head back and let out a deep masculine groan, filling her mouth in hot spurts of musky saltiness that she swallowed again and again. ", "Vengeance followed with his own grunts and groans of satisfaction and collapsed over her back, supporting himself enough that he didn't crush her with his massive size. ", "Savage joined them prone on the bed, the sounds of their heavy breathing echoing off the walls.", "\n\nVengeance stood up from the bed, picked Makayla up and rearranged her comfortably in the middle with her head resting on heavenly soft pillows. ", "He tenderly brushed her hair back from her face and placed a kiss on her forehead. \"", "Rest,\" he said as her eyelids floated downward.", "\n\nShe awoke responding to Savage's scorching kisses, his large callused hand sinfully massaging her breast, stimulating her nipple between his finger and thumb. ", "He moved his hand down to cup her bottom and rolled them both to lie on their sides continuing his wondrous attention up and down the roundness of her hips, to the dip of her waist and up again to her full breasts made sensitive by his fiery touches. ", "She felt his long thick hardness twitch against her belly. ", "He reached down, guided her thigh over his hip and nudged between her folds, shoving upwards to enter her already moist core. ", "As he moved slowly in and out of her, she moaned with pleasure.", "\n\nA hard male body eased up against her back. ", "She knew that body intimately. ", "Vengeance. ", "He nuzzled her neck and nibbled her ear while stroking her hips. ", "She felt his cock nestled between her buttocks and begin to rub between her cheeks. ", "A slick finger then circled her anus, massaging, teasing, prodding, until it slipped past the tight muscles entering her. ", "She enjoyed the anal play and pushed back to meet the invasion as the digit moved in and out inviting the delicious pleasure pain. ", "Vengeance added a second finger, stretching and preparing her muscles to accept him.", "\n\nMakayla felt the burn and pressure increase. ", "She was not an anal virgin, but she'd never taken two cocks inside her at once before and wasn't quite sure she could do it. ", "The doubt caused her to tense up slightly.", "\n\nSavage stilled within her and Vengeance replaced his fingers with his hard staff and pushed against her tight ring. \"", "Let me in, Min Älskare. ", "Relax and let me in.\"", "\n\nTrusting his soothing yet commanding voice, she breathed out and let her body slacken. ", "He entered her slowly allowing her muscles to adjust to his thickness. ", "Makayla whimpered but allowed his complete penetration, panting heavily. ", "Both men groaned loud and long.", "\n\n\"Ah, fuck...So tight.\"", "\n\n\"Not going to last long...too good.\"", "\n\nThen her lovers began to move in tandem, each slowly moving in and out. ", "She was lost between the pushing and pulling, the utter sensation of fullness and burning friction that caused her entire body to throb and brought her arousal to new heights, igniting nerves endings she never knew she had. ", "They murmured continued words of praise encouraging her on as their rocking motions increased.", "\n\nSavage recaptured her lips and Vengeance bit into the soft spot between her neck and shoulder sending her over the edge and unleashing a huge explosion within her. ", "She barely heard herself scream as her body shook with a release the likes she'd never known, light exploding behind her eyes until everything went momentarily dark.", "\n\nSuddenly Makayla was lying loosely atop Vengeance. ", "She opened her eyes to soft kisses covering her face and soothing strokes and kisses down her back. \"", "Oh, Goddess. ", "I think the entire village heard me scream.\" ", "She was exhausted and sweat covered with her hair molded in a hot mess to her face and neck, but she was sated beyond belief. ", "She wanted nothing more than a cool refreshing shower as soon after she got some feeling back into her limp, boneless body.", "\n\n\"I knew you'd like it.\" ", "Vengeance wore a confident, self-satisfied grin. ", "If he could have moved his arms, he would have slapped himself on the back, but Makayla's dead weight was occupying them, at the moment and he didn't want to disturb her. ", "They were all tangled together with Savage inhabiting the space opposite her and he was also pinned down. ", "His arms were numbing with tingling sensations and he just couldn't be sure who was on what.", "\n\nWith considerable effort, Makayla lifted her arms from her sides and placed one each on her lovers' chests. \"", "I believe that's an understatement.\"", "\n\nVengeance raised his head enough to see her turned face. ", "Her eyes were closed with her lush lashes spread out against her cheeks beneath them and her kissed, passion-swollen lips were upturned in a dreamy satisfied smile. ", "Savage shared a similar smile on his face but said nothing.", "\n\nWhen their breathing once again neared normal, but they still hadn't moved, Makayla's mind roved to similar activities. \"", "Although I think we just took the prize for the best sex ever...did you guys hear the sounds that were coming out the showers yesterday? ", "Goddess, I was so turned on.\"", "\n\nFinally, Savage spoke. \"", "Yes, we were in the gym. ", "Couldn't miss it if we tried.\"", "\n\n\"I know Danielle thinks this is temporary, how much you want to bet they stay together for a while? ", "Even after this little mystery is solved.\"", "\n\n\"Seriously? ", "I can't see her making that kind of mistake. ", "No need to get attached when nothing can become of it,\" Vengeance opined. \"", "She'd only be hurting herself.\"", "\n\n\"No, she'd be hurting him, too,\" Savage said. \"", "It's not worth it. ", "Best to let it go and move on. ", "Thunder would never encourage such a coupling.\"", "\n\n\"If she wants a relationship, she should stick to her own kind. ", "She's a worthy female and there are plenty warriors who would consider at least a monogamous relationship with her,\" Vengeance offered.", "\n\n\"Wow, I never thought you guys had such deep thoughts. ", "Especially about relationships,\" Makayla mused. \"", "I'm impressed and I see where you're coming from. ", "But from what I've seen and heard, I think she might give it a shot, for a little while anyway.\"", "\n\n\"Okay, so what's this bet you mentioned?\"", "\n\n\"Let's see...If I'm right, I get a favor of my choosing from each of you in the future.\" ", "She looked at both of them and they seemed to be onboard so far. ", "Why she didn't know. ", "She'd never agree to such terms. ", "Maybe they didn't think she was devious enough to come up with something they would really regret. ", "Normally, she wasn't. ", "But this was a challenge she was going to give some thought to.", "\n\n\"Well, that's very vague,\" he commented thoughtfully. \"", "And if we win...\" Vengeance paused looking at Savage, obviously linking with him. ", "Savage grinned devilishly and nodded.", "\n\nHer eyes shifted nervously between their devious visages, afraid of what she might have just gotten herself into, but determined not to show it. ", "No matter what they tried, she wouldn't show it bothered her. ", "Yea, act like it's no big deal.", "\n\n\"If we win, we get to do this all over again.\"", "\n\nRelief washed over her quickly, like a balloon deflated by a puncture wound the size of a roman candle. ", "Instantaneous. \"", "You've got yourselves a deal, fellas,\" she giggled excitedly. \"", "I can't lose!\"", "\n\nSavage took that opportunity to quickly roll her over and sink his teeth into her backside.", "\n\n\"Ow! ", "What did you do that for?\" ", "She reached back and rubbed her sore butt cheek.", "\n\nSavage just raised his eyebrows and smiled wickedly, showing off his red tinged fangs.", "\n\n\"You give new meaning to 'tap that ass'. ", "You know that?\" ", "Vengeance laughed. \"", "Here, let me join you.\"", "\n\n*****\n\nVal, I'm back.", "\n\nOh, Joseph. ", "Wonderful. ", "Glad you're safe. ", "Was the mission successful?", "\n\nOur intel was correct. ", "Tormond's increasing his army. ", "There's something big on the horizon.", "\n\nThat's what I was afraid of, my love.", "\n\nDon't worry, we'll be fine and I'll protect you with my life. ", "You know that.", "\n\nI know. ", "As would I.\n\nSomething else is bothering you. ", "I can feel it.", "\n\nI'm so worried about Mac. ", "She just seems so lost. ", "I believe this chain binding issue has opened up fresh wounds. ", "I wish she'd find someone to heal her and open her heart again. ", "She actually told me today to remember that 'love' spelled backward is 'evol.'", "\n\nPatience, Valeria. ", "It will come in time. ", "When her heart is once again ready.", "\n\nYes, I suppose you're right about Makayla. ", "I have a report to give to Thunder, myself. ", "Can't wait to see you, too.", "\n\nValeria promised Danielle she would join them for the examinations Annika and Emeline were giving her and Aaron. ", "The healer and wand wielder worked well together and the exams were already in progress when she arrived. ", "The scene before her would have seemed odd to an outsider or anyone in the current medical field. ", "It was a typical hospital-styled examination room filled with the norm – needles, vials of blood samples, exam table and a plethora of rubber gloves. ", "Then there was the not so norm – homeopathic salves, potions, dried herbs, scented candles, and magic so thick in the air you could almost inhale it. ", "Annika was entranced, murmuring in a low monotonic intonation while Emeline was slowly, but methodically, passing her hands a half inch above an almost completely nude Aaron.", "\n\nAaron felt strange sensations flowing throughout his body, including a calmness that didn't feel quite natural. ", "He suspected it was someone's gift or power or whatever they called them that was the cause. ", "He didn't think, that under normal circumstances, he'd be able to lie here, practically naked, with an attractive female's hands all over him and not show it physically. ", "He'd had massages before under similar circumstances and always had to hide the effects the intimacy had on his manhood. ", "These type of situations just caused a normal healthy male to respond. ", "Maybe they had something to do with that also. ", "Nice trick. ", "Wonder if it works both ways? ", "Wonder if Danielle can make me feel passionate.", "\n\nKeeping her suspicions to herself, Annika let her magical powers flow over and through Aaron, determining whether he'd been sent by Tormond as a spy or trap of some kind to catch the warriors off guard. ", "It would be a perfect set up. ", "To her relief, she discovered he was not a threat and they were safe. ", "He was just an ordinary mortal. ", "Her examination did reveal that the chain had bonded to Aaron purposely. ", "Aaron held a strong, but unknowing, power over the chain as if it was a natural part of him. ", "This discovery would have to be investigated further. ", "She planned to speak with Zahara and Emeline before disclosing this information to anyone else. ", "Perhaps including more pieces of the puzzle would make more sense at that time.", "\n\n\"Hi. ", "Sorry, I'm a little late,\" Valeria whispered to Danielle. \"", "Anything yet?\"", "\n\n\"Nothing unusual about me, but they've just begun with Aaron.\"", "\n\nThey observed the proceedings for a while in silence. ", "Danielle watched as Emeline moved her fingers gracefully flowing over Aaron's body. ", "That strange pain was building in her chest again. ", "Instinctively her hand went to her chest to relieve the ache. ", "She'd forgotten to mention it earlier, but Emeline peered suspiciously over her shoulder at her, her face reflecting perplexity. ", "She said nothing and turned back to continue the examination in progress.", "\n\nValeria also noticed her rubbing her chest with the heel of her hand. \"", "Are you okay?\" ", "She motioned with her eyes to Danielle's hand.", "\n\nKeeping her voice equally low she answered, \"I'm not sure. ", "I've been getting this tightness sometimes.\"", "\n\n\"Well, you're certainly in the right place to have it checked out.\"", "\n\n\"Yes,\" she agreed. \"", "When they're finished with him, I'll let them know.\"", "\n\nAlong with tissue, hair and blood samples, the sisters had swabbed the binding chain for any residue it might contain and planned to compare and analyze all the samples further.", "\n\n\"Okay, I think we're done here. ", "Aaron, you can get dressed,\" Emeline said. ", "Then she addressed Danielle. \"", "You want to tell me how long you've been getting those chest pains?\" ", "She observed her kindly, but suspiciously.", "\n\n\"Just a couple of days. ", "I meant to ask you about them. ", "I know we're not supposed to get sick, so I thought it's possible I just pulled a muscle or something. ", "It's not bad. ", "Really. ", "It just gets tight at times.\"", "\n\n\"Hmmm. ", "Could be stress, I suppose. ", "Although, that's not really common around here,\" she said with a sarcastic gleam in her eyes. \"", "I didn't notice any physical injuries when I examined you, so it's not a pulled muscle. ", "If I had, I could have healed it very easily.\"", "\n\n\"I'll keep an eye on it and let you know if it continues,\" Danielle offered. ", "She wasn't too concerned. ", "It wasn't really painful. ", "More annoying than anything. \"", "Can you tell us what you've learned through the exams so far?\"", "\n\nAnnika looked at Emeline for a moment. ", "After their shared thoughts, she said, \"I think we need to confer and do a little more analysis before we give you a report on our findings. ", "Just to be sure. ", "We wouldn't feel comfortable speculating right now. ", "We just don't have enough information yet. ", "Please know that there's nothing physically wrong with either of you. ", "Aaron, you're as healthy as a horse. ", "I believe that's one of your mortal idioms.\"", "\n\nStill feeling the tingling effects of the full body inspection, Aaron thanked Annika and Emeline and finished redressing.", "\n\n\"Danielle, I want you to let me know if the pain happens again. ", "Be mindful of your surroundings and what is taking place at the time. ", "This information could be useful in finding the cause or trigger. ", "Now, if you will excuse us, we'll get to work on the samples we've gathered. ", "Maybe we'll have an answer and solution for you very soon.\" ", "Emeline escorted them to the door with promises to share what they discovered.", "\n\nThe late afternoon sun was bright and the forest fragrances greet them as they exited the compound.", "\n\n\"I need to take off. ", "I've got lots of things to attend to before the day's end,\" Valeria explained.", "\n\n\"Of course. ", "I'll see you later.\" ", "Danielle conveyed her unspoken thanks to Valeria for her friendship and support. ", "Valeria knew how nervous Danielle was about the examinations and the situation at large.", "\n\nAs Valeria took her leave, Aaron looked out to the forest line surrounding the village. ", "The atmosphere was blanketed with undefined tension and he kept his gaze averted. \"", "I think I'll take a walk in the woods...to clear my head. ", "If you don't mind.\"", "\n\nHe wanted to be alone. ", "She got that. ", "She had some more thinking of her own to do.", "\n\n\"No, of course not.\"", "\n\nAs Aaron stuffed his hands in his front pockets and turned to leave, Danielle called out to him. \"", "Be careful and don't go too far, please. ", "You won't be able to find your way back due to the wards.\"", "\n\nStopping to look back he responded, \"Don't worry. ", "I'll be fine.\" ", "After a few additional steps, he turned once again, noticing she still watched him. \"", "Danielle.\"", "\n\n\"Yes?\" ", "He met questioning eyes.", "\n\nWanting to say something but uncertain as to what, he sighed and simply said, \"I'll see you soon.\"", "\n\nNodding, she turned away. ", "Her steps lacked the assured confident structure usually held within her frame. ", "Uncertainty and confusion reigned supreme.", "\n\n*****\n\nThe tire swing hanging from the old tree drifted lazily back and forth with the soft fragrant breeze blowing through the yard. ", "The sun was setting low in the sky and Danielle was beginning to worry as she smoothly rocked back and forth, the action belying the turmoil building within her. ", "What would normally be a relaxing and recharging time wasn't, because Aaron had yet to return from his walk in the woods. ", "Wondering if he's gotten lost, she decided to search for him. ", "There were no trails in the Bridge Creek Wilderness and the terrain of the forest was full of steep slopes, not to mention black bears and cougars. ", "That pain in her chest was back once again. ", "Pulling herself from the swing, she set out for the surrounding tree line to search for Aaron. ", "Vex caught her attention as she entered the edge of the wooded area.", "\n\n\"Hey, Danielle. ", "Can we talk for a minute?\" ", "Vex approached swiping his hand across the crown of his shoulder length, caramel colored hair a couple of times. ", "He appeared agitated and uncertain.", "\n\nDanielle halted. \"", "Sure. ", "What's up?\" ", "She looked at him, but he wouldn't meet her eyes. ", "He mumbled something unintelligible under his breath.", "\n\n\"I'm sorry. ", "What was that?\"", "\n\n\"I said, I saw you with him,\" he repeated slightly louder with his head still tilted downward.", "\n\n\"Saw me with who, Vex?\" ", "She was curious now. ", "His manner was off, just not quite right. ", "He could be shy at times, but never this timid.", "\n\n\"With the mortal,\" he said.", "\n\nHe wasn't very forthcoming and she didn't have time for twenty questions just now. ", "So, she gave him a quizzical look and motioned for him to continue. ", "She knew she seemed impatient, but tried not to reflect too much rudeness in her actions.", "\n\n\"In the shower,\" he finished.", "\n\nNow, that brought some fine memories to mind and put a mischievous grin on her face. ", "Trying to lighten the mood, she jested, \"Oh, so you're a voyeur, huh?\"", "\n\n\"No, not at all.\"", "\n\nHe didn't seem shy or embarrassed about that subject. ", "That he was adamant about. ", "But something was not quite right in the Kingdom of Vex. ", "She let him continue without interruption.", "\n\n\"Look, this isn't easy,\" he persisted, finally looking her in the eye. \"", "But we all heard you and I'm sorry. ", "I just couldn't help myself.\" ", "Vex looked more pissed than sorry to her, although there was that, too. ", "And strangely, there was a hint of concern in the mix that shown on his face.", "\n\nVex was a constant in her and her sisters' lives. ", "Always caring and reliable, like an unobtrusive brother forever watching over them silently but never interfering unless needed. ", "They all valued him highly.", "\n\n\"And? ", "Is there a problem?\" ", "she added, still not sure where this was going. ", "Even more puzzled now. ", "She certainly wasn't embarrassed that everyone knew of her little tryst with Aaron in the shower.", "\n\nVex felt like his mouth was filled with thick sludge that rested at the bottom of a muddy river and he had to literally force the words from his lips. \"", "You can't fall in love with him. ", "You can't.\"", "\n\nHis pleading voice confused her even more. ", "All sincerity showed in his face, his eyes.", "\n\nWhat is he talking about? \"", "Well,\" she said gathering her thoughts that were now running a marathon through her brain at lightning speed. \"", "I never planned to do that.\" ", "She wondered just what he saw, what he perceived. ", "What did she and Aaron actually look like?", "\n\n\"That's the problem. ", "You won't plan to, but it can happen. ", "Trust me.\" ", "He reached out and gently touched her arm. \"", "You know I care for you. ", "I'm just trying to save you from the pain.\"", "\n\nRegret had taken the forefront in his aqua colored eyes. ", "Danielle thought she could almost see down into his soul and it was marred with deep hurt and sadness. ", "She had the urge to comfort him and make all the pain she saw there go away. ", "And she suddenly felt very ashamed. ", "Had they all gotten so used to Vex's underlying despondency? ", "Yes, he refused to share his problems or accept help from them, but they shouldn't have just given up on him.", "\n\n\"Vex, are you okay? ", "What happened to you?\" ", "They both knew she was referring to his unshared past.", "\n\nHis entire countenance visually changed as he let go of her arm, straightened his stance, pushed his shoulders back and lifted his head, plastering a hard mask on his face. \"", "Nothing. ", "Forget about it. ", "Sorry to bother you.\" ", "Uh oh. ", "Guess I hit a nerve. ", "He turned on his heel and started to move away.", "\n\n\"Vex,\" Danielle called out lightly, this time resting a hand on his arm to halt him. ", "She couldn't let him go like this. \"", "I'm sorry. ", "I didn't mean to pry, but what you're saying isn't really making any sense. ", "Help me to understand. ", "Please.\"", "\n\nVex stopped but didn't turn back around, just stood there staring at nothing in front of him, remembering. \"", "Your face. ", "It was written on your face when you were in his arms. ", "Don't fall, Danielle. ", "It can't be. ", "They won't allow it. ", "Don't fall.\" ", "He took two steps forward and traced away.", "\n\nMy face? ", "Oh Goddess, he seemed so haunted. ", "I'm not falling in love with Aaron. ", "It's forbidden. ", "I'm not falling in love with Aaron.", "\n\nDanielle wasn't sure how long she stood there rooted to that same spot when she heard someone frantically yelling her name and knew he was in trouble. ", "Aaron.", "\n\n*****\n\n# Chapter Fourteen\n\nThe light was beginning to fade from the sky. ", "It's brilliant hues melding together to glow in golden red as it made its descent into the horizon below. ", "Surrounded by the heavy coverage of towering pines, he hadn't paid much attention to the dimming daylight as bursts of bright sunlight patched through periodically but weren't as brilliant now. ", "He'd been too deep in thought to notice.", "\n\nCountless thoughts. ", "Countless complications. ", "Countless contemplations. ", "So numerous were the discoveries his brain was on overload threatening to spiral out of control. ", "He felt like he was sitting behind the wheel of a speeding car on the verge of spinning out, facing imminent doom with no hope of gaining control. ", "There was insufficient logic in this new world of discoveries. ", "His brain was scientifically wired and trained to ferret out fact from fiction and logic played no part in this newly revealed fantastical world.", "\n\nHe'd remembered his first impression of his beautiful 'would be' criminal instigating and failing miserably at breaking and entering. ", "Well, okay. ", "She got in but got caught. ", "She was tall, attractive, cocky with a smart, but a kissable mouth, all tough in her form-fitting black leather, and mysterious. ", "She intrigued him and solving mysteries were right up his alley. ", "He didn't find the warrior trait a turn-off either. ", "He wasn't intimidated. ", "He liked that she was physically strong. ", "Of course, that wasn't going to keep him from protecting her, if need be. ", "He was a man, after all, and not a weakling himself. ", "He may be a geek, but he was a strong, capable geek. ", "All brains, no brawn, did not describe Aaron. ", "Danielle was stubborn, though, and he knew she'd never accept his help willingly. ", "He was sure it would probably piss her off.", "\n\nMost importantly, she was immortal and that's where it all ended. ", "He'd grow old. ", "She wouldn't. ", "He didn't know if she could give it all up if that was even an option, but he wouldn't expect her to. ", "Hell, he wouldn't let her do it. ", "Not for him. ", "Besides, he could never measure up. ", "He wasn't a warrior and sure wasn't going to die just to become one, even if that were possible.", "\n\nNo, they didn't fit in each other's worlds at all. ", "They'd get this chain off from around his neck and he'd go home and try to solve this dilemma with Tormond. ", "That was best and the way it should be. ", "For now, he'd just have to reign in his feelings. ", "Not overthink it or make it into something it wasn't or something it could never be. ", "He sure hoped he was right. ", "He had to be. ", "It would solve everything and make everyone happy – mostly. ", "They'd all go on with their lives, picking up where they left off. ", "So, why didn't he feel good about that?", "\n\nAaron was torn from his thoughts when he noticed movement up ahead through the dense thickness of the trees. ", "Among the copse stood a woman with blue/black hair swirling in the breeze behind her. ", "He recognized her as Raven, one of the female warriors. ", "She was walking slowly toward a sizeable tan cougar that had leaped onto a large rock surface protruding from the ground. ", "It was a majestic animal with a strong muscular form, the muscles rippling under its sleek coat. ", "Aaron halted his step and his breathing as he hid behind the nearest thick tree trunk, peering around to watch the cougar's progress. ", "He was close enough to see its magnificent steel blue eyes, the black and white whiskers extending from its pale fur covered snout and the pink fleshy portion that topped it.", "\n\nRaven showed no fear or threat toward the cougar, simply walked up to it and stroked its enticing fur as if it were an everyday domesticated house cat. ", "Aaron watched as she further bent down by the wild animal and scuffed it behind its ears, laughing sweetly as it purred. ", "As if some communication had been exchanged between them and all arrangements had been made, Raven stood up, letting the loose flowing garment she wore float to the ground and began to run through the forest and the cougar followed. ", "Within fifteen feet Raven gracefully leaped into the air as if she were diving off of the tip of a tropical waterfall and instantly transformed midair into a cougar herself, disappearing into the opaque green forest with her beastly companion.", "\n\nStunned, Aaron stared off into the wooded area unmoving. ", "As reality took hold, Danielle's name tore from his lips as he whirled around trying to decipher which way led back to the village. ", "Demons. ", "Unable to navigate in his present mind state, he concluded that any direction away from the animals was better than nothing. ", "He was unarmed and certainly not prepared to face off with one, let alone two demons. ", "He didn't think all the training in the world could prepare him for that.", "\n\nTurning back in the direction he hoped he'd come from, a sense that Danielle was nearby added to his confusion. ", "With his arms pumping hard, his heart thump, thump, thumping nearly out of his chest and his legs tearing through the forest floor as fast as they would carry him, he chose to follow that instinct. ", "He didn't have the mind to care where the instinct originated from, he just knew he needed to get to her. ", "To warn her and protect her.", "\n\nDanielle rushed across the woodland terrain. ", "She knew Aaron was near and ran in the direction her senses led her. ", "She spotted him in the distance and traced the remainder of the way to him, surprising him and causing him to stumble into her, sending them both crashing to the forest floor. ", "He quickly wrapped her safely in his arms as they rolled to a stop near the base of a towering pine attempting to take the brunt of the fall.", "\n\n\"Are you okay? ", "Are you hurt?\" ", "Danielle blurted as she frantically ran her hands up and down his face and torso searching for possible injuries.", "\n\nHis heart was thundering in his chest and he held her a little tighter to him wildly looking around them in every direction that he could see hoping they were well away from the demons he'd come upon earlier.", "\n\n\"Yes, yes, I'm fine. ", "But we have to get out of here now. ", "There are demons in the woods,\" he breathily replied.", "\n\nShe looked quizzically at him. \"", "No way. ", "That's just not possible, Aaron. ", "These woods are impeccably warded. ", "All manner of alarms and mayhem would be happening right now. ", "Listen,\" she paused. \"", "See, nothing other than normal forest sounds. ", "Little animals scampering...birds doing their thing...\"\n\nShe pushed at his chest slightly, making a move to separate and stand, but he held her firm.", "\n\n\"No, I swear. ", "I saw them. ", "Two...back that way,\" he motioned with his head. \"", "Cougars. ", "She changed into a cougar right in front of me. ", "One of those female warriors I met earlier. ", "You've got a spy in your camp.\"", "\n\n\"Sweetie, it's okay,\" she soothed, trying in vain not to laugh at his panicked state. \"", "Was it Raven?\"", "\n\nHe nodded, suddenly feeling like a first class idiot. ", "She obviously knew something he didn't – again.", "\n\n\"Oh hell, don't tell me. ", "You guys can shapeshift, too.\"", "\n\n\"No, only she can. ", "At least in our community. ", "There are others of my sisters, of course, elsewhere that acquired the same power. ", "It's her gift from Freya.\"", "\n\n\"What about the other cougar she was with?\"", "\n\n\"Just another cougar. ", "She has the gift of communicating with animals, too.\"", "\n\nHe let out a heavy, calming breath, blowing the stray hairs that had fallen from her usual braid and curtained around her now grinning face and let his head fall back to the ground resting among the dirt, piles of leaves, wild grass and twigs scattered there. ", "She regarded him carefully to ensure that his fears had been alleviated. ", "When she was satisfied, she began to gently pull stray leaves and twigs that were embedded in his hair from their recent tumble.", "\n\nWith Danielle still lying atop him, Aaron loosened his hold on her, wrapping one arm around her waist and trailing his other hand up the ridge of her back in a tender circling motion. ", "Danielle relaxed into his ministrations moaning lowly. ", "Her eyes fluttered closed as she enjoyed the blissful touch of his hand. ", "Aaron watched the pleasurable emotions cross her face, her full darkened lashes fanned out over the rise of her slightly rosy cheeks, her perfectly proportioned nose and smooth chin framing her erotically enticing mouth while she gently bit into the lower lip. ", "The look portrayed ecstasy and he wanted to share that feeling with her.", "\n\nHe brought his other hand up to lightly brush the side of her face with the backs of his fingers. ", "She slowly opened her eyes and met his gaze full of wonderment and longing and brought her own hand down from his hair to cup his face. ", "Unable to stop herself, Danielle leaned the few remaining inches left between them and caressed his lips with her own, unhurriedly drawing them gently between each other's. ", "The kiss was soft, soothing and somehow fulfilling. ", "Filled with a wholeness that felt complete and right.", "\n\nAs Aaron began to languidly roll her onto her back, she gave up control of the kiss and opened to him, allowing the lazy sweep of his tongue to explore the recesses of her mouth, joining him in his exploration and softly dueling and teasing her tongue with his. ", "She felt the evidence of his erection against her thigh and her passion began to climb higher, but not with the frenzied fire they'd previously shared. ", "This need felt different. ", "Not hurried, but an extension of the kiss they were sharing accompanied by the necessity to be closer to Aaron. ", "As close as she could possibly be. ", "She clung to him with everything she possessed.", "\n\nWith the wild grasses beneath them as their bed, their clothing fell away bit by bit while they continued to thoroughly touch, stroke, nip and embrace each other. ", "Hands, fingers, lips, teeth and tongues worshipfully caressed, leaving no surface of their bodies uncharted.", "\n\nAaron had never felt anything like it before. ", "Had never wanted any woman the way he wanted her now. ", "He was consumed with needing to touch her, hold her and feel her body against his – naked and unfettered, skin to skin. ", "The surface of his skin tingled everywhere and ached for her touch in return. ", "Her writhing, moans and responses to his touch made it evident she fully shared and returned his desire.", "\n\n\"Danielle, look at me. ", "I want to watch you as I take you.\" ", "Aaron settled between Danielle's opened legs and held her gaze as he entered her. \"", "So beautiful...\" His voice trailed off into a low growl as he gave into the pleasure of her tight sheath surrounding his shaft. ", "So perfect. ", "So right.", "\n\n\"Oh, yes. ", "Perfect,\" she moaned. \"", "You fill me so full,\" she gasped as she raised her hips to meet his solid molten thrusts, her nails digging almost painfully into his strong shoulders. ", "Please don't let this end. ", "I want to feel this forever.", "\n\n\"Forever,\" Aaron murmured as he softly bit the sensuous skin between her neck and shoulder.", "\n\nAs Aaron and Danielle moved sinuously together in the world's oldest dance, time and the world with all its thoughts and sounds melted away. ", "They were surrounded by only the sensation of each other, their mingling breaths and the reverberation of their thundering heartbeats. ", "Together they elevated the desire between them. ", "They reached for their ultimate pleasure, for fulfillment, bringing each other over the edge in perfect synchronicity. ", "Their sensuous cries jointly intermingled, roaring through the electrically charged air that encompassed them.", "\n\nAaron remained atop Danielle as he rested his forehead against hers, their breaths comingling, neither wanting to break the embrace they shared as their hearts continued to race.", "\n\nNeither realizing the unspoken communication they'd shared in the height of their passion.", "\n\nHis lips sought hers in the same tender kiss they'd shared at the beginning of their lovemaking. ", "Dawning revelation hit Aaron causing a tightness in the center of his chest. ", "This isn't just sex. ", "Not anymore. ", "Sure there was still the uncontrollable urge that drew them together from the start. ", "So hot and demanding. ", "Almost unquenchable. ", "But it had evolved. ", "It had become so much more.", "\n\nHave I fallen in love with her?", "\n\nWaking with her in his arms this morning and holding her now just felt so right.", "\n\n\"Danielle. ", "I...\"\n\n\"Shh, Aaron.\" ", "She placed a finger to his lips. \"", "Just lie with me. ", "Just like this.\" ", "She closed her eyes and, although she smiled outwardly, inwardly she felt the unease of Vex's warning and her heart broke just a little bit. ", "Oh Goddess, help me. ", "This can't be.", "\n\n*****\n\nHolden stretched his long limbs out languidly in the faux leather covered booth in a dark corner of the Goth-themed bar located at the older, lonelier part of the Las Vegas Strip. ", "He felt the familiar vibration of his cell phone within his front shirt pocket. ", "Reaching into his pocket he checked the caller ID and noted that it was Stan, Tormond's flunky human, as he liked to refer to him. ", "He'd never understand why Tormond thought this human was so special. ", "The flunky was, after all, only human. ", "Holden himself, being a demon, was much higher on the food chain and felt he deserved a bit more respect and admiration from his boss than the flunky. ", "Hell, Stan wasn't even at minion status. ", "And minions were considered lowly piss ants who were always expendable. ", "The thought of taking this call sickened him.", "\n\nWith unconcealed disgust, he answered, \"What do you want? ", "I'm busy.\"", "\n\n\"Mr. T wants to see you and Heidi. ", "He told me to tell you that he wants you now. ", "His words, not mine. ", "All right? ", "So don't show me any attitude. ", "The boss needs the both of you in his office.\"", "\n\nDisconnecting the call, Holden had no idea where Heidi was within the club. ", "Probably in some obscure corner fucking the latest catch of the night, as was her habit of late. ", "He sent a mental link out to her. ", "Let's trace, the boss wants us in his office. ", "Like now.", "\n\nUh oh. ", "This can't be good, she replied.", "\n\nThe she-demon was standing at the end of the bar scouting a tall, mean looking bloke with some of the largest muscles she'd ever seen on a human male. ", "His body resembled a young Arnold Schwarzenegger with bulging muscle on top of muscle. ", "The black leather vest he was sparsely wearing was stretched taunt across his tattooed chest and back. ", "He was surrounded by several overheated, fake-breasted females that stroked, squeezed and fondled his shoulders, chest and biceps while giggling like a pack of hyenas in a wild desert night. ", "Eww, she thought as she cringed both inwardly and outwardly. ", "So not her type. ", "But that was beside the point because he looked like he could give those warriors a good run for their money.", "\n\nWith a grunt of frustration, Heidi replied, Great timing. ", "I just had my line of sight on an ideal candidate. ", "Wouldn't you know it? ", "He would have been perfect. ", "Just give me a minute to connect with him so that I can get back to him after we're done.", "\n\nHer face took on a blank expression as she entered the unsuspecting fool's mind to get the information that she needed for future contact. ", "She was impressed with what she found rummaging around inside his brain. ", "The boy actually had some – brains, that is. ", "She gathered what she'd came for and backed out, him none the wiser. ", "Be seeing you soon, Butch.", "\n\nShe quickly made her way over to the booth that Holden was occupying.", "\n\n\"All right. ", "That should do it. ", "Let's go.\"", "\n\nHolden rose and Heidi joined him as they made their way through the crowd to the exit at the back of the club that led into the dark, damp alley behind the building. ", "Pushing through the door, they scanned the immediate area to ensure the alley was empty from prying eyes, then visualized the location that they needed to trace to and vanished.", "\n\nRematerializing within the hallway outside of Tormond's office, Holden raised his fisted hand and knocked on the door.", "\n\n\"Come,\" came the command to enter from within.", "\n\nOpening the door, Holden noted that his boss looked none too happy. ", "His eyes were hard and black as the deepest night. ", "That was a very bad sign.", "\n\nI hope I didn't do anything to give him that look. ", "Maybe it's Heidi, he thought with a smirk and a spark of hopefulness.", "\n\n\"Sit!\" ", "Tormond took a calming breath as the demons complied. \"", "I've heard some very disturbing news regarding the dig site and I want you two to get down there and clean it up. ", "You will eliminate any warrior on the premises and get me that worthless human, Dr. Janson. ", "I don't care if he's harmed, but I want him alive and able to communicate. ", "Hanna is waiting for your arrival. ", "Her I'll also deal with upon your return.\"", "\n\n\"We'll leave immediately, my Lord,\" Holden replied as he stood. ", "He knew a dismissal when he heard it and, with the mood Tormond was in, he wouldn't be any more damned than he already was and give Tormond any excuse to bring down his wrath upon him. ", "He saw Heidi rise also and received the thoughts she projected.", "\n\nKiss ass. ", "This is such a man's club. ", "He didn't even acknowledge me.", "\n\nAnd why should he? ", "Look how he sent a woman to do a man's job and she failed. ", "You should be glad you're not Hanna. ", "I sure am. ", "I wonder how he'll release his wrath on her. ", "Besides, if he's not acknowledging you, you don't have to fear any backlash from his temperamental moods. ", "It's best to be invisible right now.", "\n\nYeah, you're right. ", "At least about the invisible part. ", "Although, I refuse to be compared to Hanna just because I'm a female. ", "I don't know how she fucked up, but I can guarantee I'd have done a better job.", "\n\nMaybe you'll get your chance to prove it before this is all over.", "\n\nYea, looking forward to it. ", "Let's go kick some warrior butt.", "\n\n*****\n\nFeeling some relief at the quiet that currently surrounded his office, Tormond popped the cap on his latest bottle of aspirins and confiscated four of the little white chalky tablets, downing them without the aid of any liquid to wash them down his parched throat. ", "The bitter taste and gritty, grimy texture was almost a welcome respite to thwart the constant debilitating headaches that plagued him, an unwelcome complication to the almost unwelcome link he shared with his father. ", "He needed to feed, and soon. ", "A generous portion of warm healing blood would do wonders for his present physical state and peace of mind. ", "He'd have to call for one of the girls.", "\n\nHmmm. ", "Rosa maybe. ", "A little Spanish spice would be nice and he looked forward to sinking his teeth in - literally. ", "The thought caused his gums to ache, his fangs to descend slightly and tingle with anticipation. ", "It did wonders for his fifth appendage, too.", "\n\nAs Tormond leaned comfortably in his throne-sized executive office chair and leisurely delved in his thoughts, his hand drifted to his crotch and began massaging his now hardening member. ", "Suddenly, he tensed and felt that familiar unwelcome fatherly link amplify as though a red hot poker had been speared directly into his brain.", "\n\n\"Oh, God,\" Tormond moaned painfully, instantly dropping to the floor into a fetal position as he squeezed his eyes shut tightly and clutched his head with both hands.", "\n\n\"Yes! ", "That is correct. ", "It is me.\" ", "Loki's voice boomed and echoed through his conscious mind. \"", "My patience is wearing thin. ", "You are completely useless to me.\"", "\n\n\"Father, please!\"", "\n\nNormally, nothing could make Tormond beg. ", "It was the weakest of traits and an act that he even abhorred watching his own victims do. ", "Weakness was unacceptable in any form. ", "But, as much as he hated to beg, the pain was too great. ", "The mind fuck that Loki chose to play this time proved to be too much. ", "Knowing it wasn't actually reality, didn't stop him from feeling the torture as if it were real, just as Loki intended. ", "He only hoped that he would survive. ", "He suspected one day he would not and prayed that day was not today.", "\n\n\"I have solid reasons that explain this delay,\" Tormond hurried to explain as he started to feel the skin on his back being peeled from his body, strip by agonizing strip. \"", "The warriors have discovered the dig and I have already sent my top demons to take care of this matter,\" he cried painfully again as he felt the skin on his torso pulling from his chest muscles.", "\n\n\"Do you think this will appease me? ", "Why did you send your demons? ", "You should be there handling my business yourself, not some slackers. ", "Go and get me the \"Eye of Odin! ", "And do not fail me again!\"", "\n\nLoki let his fury unfurl with the greatest of roars, tearing the remaining skin from Tormond's body all at once. ", "Tormond writhed in unbearable agony as he screamed with his last breath before darkness finally took him, \"Thy will be done!\"", "\n\nWith the passage of time unknown to him, Tormond slowly gained consciousness and hated the feeling of fear that washed over him. ", "He still felt remnants of pain and suffering from the torture he had endured but knew that there would be no physical evidence.", "\n\nI am a demi-god! ", "An immortal! ", "This is Hanna's fault. ", "Her weakness has caused me to suffer for the last time. ", "If she hadn't failed to eliminate that warrior, none of this would have happened. ", "I would have the Eye of Odin and be rightfully placed in the highest ranks with my father, as is my due. ", "I will make her pay for her incompetence and for the pain and humiliation she has caused.", "\n\nDragging his legs underneath himself, Tormond slowly crawled towards his desk. ", "He placed his right hand on the desktop and his left on the chair seat enabling him to slowly pull himself into his chair. ", "Grunting through his pain, he pulled himself into a sitting position. ", "It took excruciating effort to reach for his intercom, as his muscles stretched and burned with each movement. ", "He pressed the speak button and called for his loyal associate.", "\n\n\"Stan, contact Holden and tell him to hold the plane. ", "You and I, along with a few others of my staff will be accompanying them.\" ", "His voice sounded forced and breathless.", "\n\n\"Sir, are you all right?\" ", "Stan's concerned voice came over the intercom.", "\n\n\"Yes, just do this for me...and prepare to leave immediately,\" he replied as he disconnected.", "\n\nTormond knew this was only the beginning. ", "A first step. ", "After they retrieved the Eye of Odin, they would be able to move forward in the search for the other two artifacts needed to banish the other Gods from the mortal realm. ", "He realized that with the discovery of his secret dig operation, the others now knew about the lost documents that had been located and it would just be a matter of time before they had their hands on them and interpreted their hidden secrets. ", "It was a race to the finish and the winner would win big. ", "The thought of what he could do ruling by Loki's side was what kept him going most days. ", "He wanted – no needed – his reward as ruler in this realm. ", "And if anyone deserved it, he did.", "\n\nA light knock at his office door broke his train of thought.", "\n\n\"Come.\"", "\n\n\"Sir,\" Stan said as he entered. ", "His concern was evident on his face. \"", "Forgive my intrusion, but I was concerned. ", "Are you sure you're all right? ", "It is my job to guard and keep you safe. ", "I would be remiss to not confirm your welfare myself.\"", "\n\n\"Yes, Stan. ", "Thank you. ", "Just having one of my moments.\"", "\n\nStan was aware that his employer suffered from chronic migraines and interpreted that was what Tormond alluded to.", "\n\nLuckily, there were no physical marks on his person, although his hair and clothes were disheveled and his face, paler than normal, hosted a sheen of perspiration. ", "He began straightening the garments and sat a little stiffer and taller in the chair, forcing a sense of confidence he didn't feel at the moment. ", "His father's visit had shaken him to the core. ", "If the damage had been physical, his body would have healed it with a little time and blood. ", "But Loki's mental attacks seemed to take more of a toll on him.", "\n\n\"See...\" he said popping the cap off his pocketed aspirin bottle once again. \"", "A few of these and I'll be good as new.\" ", "He palmed a few tablets and tossed them into his mouth.", "\n\n\"Yes, sir. ", "If you say so,\" Stan acquiesced, still a little disbelieving. \"", "Holden is holding the flight per your instructions.\"", "\n\n\"Thank you, Stan. ", "Please tell my driver to be out front in thirty minutes.\"", "\n\n\"I'll take care of that right away.\"", "\n\nStan headed for the door to leave but then turned back for a moment.", "\n\n\"Was there something else?\" ", "Tormond asked with as much pleasantry as he could muster.", "\n\n\"Can I get you anything before I head downstairs? ", "I want to do a quick security check before we leave.\"", "\n\n\"Yes, actually. ", "Please send Rosa up with my dinner. ", "I'm especially ravenous tonight. ", "In fact, send up that new red-headed masseuse from the salon, also. ", "I need her to work this kink out of my neck. ", "And make sure no one else disturbs us until I'm ready to leave. ", "I need a few minutes of recuperative time.\"", "\n\nTormond was starting to feel a bit more energetic. ", "Rosa would be an appetizer to the newly acquired main course. ", "He loved to expand his horizons and try new things and he especially needed the extra pick-me-up tonight. ", "Stan picked up on his enthusiasm and smiled.", "\n\n\"There. ", "You're starting to look like your old self. ", "I'm glad, sir. ", "Had me worried there for a minute.\"", "\n\n\"No need to worry, but it's always comforting to know that I can count on you, Stan. ", "You're my most loyal employee.\"", "\n\n\"Thank you, sir. ", "You can count on me.\"", "\n\nStan exited the office and hurried downstairs to make arrangements for the women as Tormond requested.", "\n\nTormond wondered if Stan would be as loyal if he knew what he was sending those women to him for. ", "He wanted Stan to stick around. ", "He was the best mortal, the loyalist – mortal or otherwise – that he had working for him. ", "He'd need to keep him in the dark for a little while longer. ", "Then maybe, when he was ready, Tormond would reward him. ", "Move him up the food chain. ", "Make him immortal, too.", "\n\nI definitely need more demons, but he's too valuable to me where he's at for now. ", "But someday. ", "Yes, someday...\n\n*****\n\nChapter Fifteen\n\nAaron's training had been completed. ", "Slash, Blaze and Turbo had done exceptionally well. ", "The warriors had taught him all that they could given his earthly limitations and the time constraints. ", "They were surprised and pleased at his innovation in using everyday items one might find on a desk, such as a pencil or a letter opener, wielding it as a makeshift weapon to wound and incapacitate his opponent. ", "Where he lacked in strength and preternatural powers, they were confident he would make up for in cunning.", "\n\nThunder assigned several warriors to accompany Aaron back to the dig site at the North Sea. ", "Their job was to provide protection and aid in the search for the EOD. ", "Thoughts were somber as they boarded the plane for the long journey ahead.", "\n\n\"I haven't been back there in many, many years,\" Steele said solemnly reflecting on the losses the warriors had sustained in The Great Battle. ", "He made his way to the back of the plane to take his seat.", "\n\n\"Yes, I had the same thoughts when I returned last week,\" Danielle offered as she followed behind, motioning for Aaron to sit beside her.", "\n\nThey each settled in and buckled for takeoff. ", "The brilliant sun sat midway toward the horizon. ", "There were only a few hours of daylight left and they would fly through the night arriving early the next morning.", "\n\n\"Vex, I think your idea of a memorial ceremony is wonderful. ", "We owe them so much that we'll never be able to repay.\"", "\n\n\"Thanks, Makayla. ", "What we've prepared may be simple, but it's meaningful...and healing, I hope.\"", "\n\nKnowing Aaron was somewhat clueless, Danielle turned to him, offering an explanation of the current conversation. \"", "After The Great Battle, we resurrected a Memorial Stone to our fallen warriors. ", "It's been a long time since the most of us have returned there to pay our respects.\"", "\n\n\"I've been all over that area, but I've never seen the stone you speak of. ", "Is it far from the site?\"", "\n\n\"Well, you wouldn't have seen it,\" Steele explained. \"", "It's warded just as our village is.\"", "\n\n\"Yes, it's located just a short way from your dig site. ", "Nearer the cliffs with a lovely view of the sea,\" Myste added.", "\n\n\"Well, maybe I'll get a chance now that I'm with you guys.\"", "\n\n\"Get a chance to do what?\" ", "Vengeance inquired, walking up take a seat across from Aaron and Danielle, joining the conversation late.", "\n\nDanielle leaned forward. \"", "To see the Memorial Stone.\"", "\n\n\"Oh, yes. ", "It's quite impressive and meaningful to us, as I'm sure you've gathered.\"", "\n\n\"Yes,\" Aaron added. \"", "I'm looking forward to it.\"", "\n\nThe last warriors to board were Nadine and Justice, bringing up the rear and securing the door behind them.", "\n\n\"You almost made us late. ", "I can't believe you almost made us miss the flight.\" ", "Nadine scolded Justice as they took the remaining seats near the front of the plane. ", "He ignored her, refusing to give into her OCD about rigid schedules and such. ", "Everyone knew you couldn't throw a wrench into Nadine's day or she'd freak out on you in an instant.", "\n\n\"Pilot says strap in. ", "We take off in two minutes. ", "Anyone needing a stewardess is SOL,\" Justice laughed. \"", "But I'm sure Nadine here would love to demonstrate the use of your air masks and the nearest exits for us.\" ", "He accompanied his quips with flaunty little pointing motions at the side and rear exit doors, mixed in with a signature Elvis hip move. ", "The move was a bit awkward, but he made it work.", "\n\n\"I believe they like to be called flight attendants. ", "And no, I will not be demonstrating anything except maybe sticking my foot up your ass,\" she teasingly replied with a sickeningly sweet smile.", "\n\n\"Now that demonstration I'd like to see,\" added Myste.", "\n\nThe engines that had been previously humming lowly began to rev up to the timbre of a mild roar as the plane began to taxi forward at a crawl. ", "Speed gathered at a rapid pace and without further warning the craft jolted forward, the front rising toward the heavens. ", "In no time, they'd reached their cruising altitude and leveled off for the long flight to the North Sea.", "\n\n\"You guys are lucky I'm on this flight. ", "I can guarantee no turbulence. ", "Mother Nature and I had a chat and we've got smooth sailing all the way to the North Shore. ", "You can all thank me later. ", "Ha ha,\" Myste mockingly laughed. ", "The currently blonde haired warrior had obviously utilized her powers of manipulating the weather to her advantage.", "\n\nYes, we are lucky. ", "But not so much due to the weather as to the good mood you're currently in, Vengeance thought to himself. ", "Thank the Gods.", "\n\nHe stood, stretched slightly and addressed the others as he made his way down the aisle to the back of the plane. \"", "I'm retiring to private quarters. ", "You'll let me know if I'm needed.\" ", "With a suave motion and smoothness of the best playboys in the universe, he effortlessly snagged Makayla's hand as he passed her chair and pulled her along with him.", "\n\nMakayla raised an eyebrow and looked at him. ", "I thought this was going to be a smooth flight. ", "Seems you plan to cause a little turbulence yourself.", "\n\nOh, no. ", "It will be smooth. ", "I promise. ", "Nice, slow and smooth, he added as he closed them in the small bedroom suite with a click of the door lock.", "\n\nAaron leaned toward Danielle and whispered in her ear seductively while trailing a finger teasingly downward from the tender spot behind her ear to the center of her cleavage. \"", "We didn't get to use the bedroom on our last trip.\"", "\n\nShe batted his hand away as inconspicuously as possible and returned his whisper. \"", "That's because: a) we didn't make it that far, and b) we didn't have an audience.\" ", "Then she slid her finger lightly from his knee up to his groin. \"", "Now, keep your hands to yourself or it's going to be a really long flight.\" ", "She paused then said, \"Oh, and c) No, I won't meet you in the bathroom.\" ", "She giggled and grinned mischievously.", "\n\n\"Don't be cruel,\" Aaron responded with a playful pout, not realizing that every vampire on the plane had heard this entire conversation.", "\n\nOne of whom was Justice, the Elvis enthusiast, who felt that was his cue to break out into a chorus of 'Don't Be Cruel.' ", "The women even had an idea what was being said in such close quarters so everyone laughed. ", "Even Aaron had a sense of humor.", "\n\nAs he settled back in his seat for the flight, his thoughts turned to Danielle. ", "The intelligent, strong and amazing Danielle. ", "Although reflecting a state of calm on the outside, deep down Aaron felt somewhat apprehensive about his relationship with her. ", "He was getting so used to being around her, with her. ", "He realized how relieved he was that she was accompanying him back to the dig site. ", "Relieved that he hadn't had to tell her goodbye, just yet. ", "He knew it was inevitable, but he was glad for the reprieve. ", "No matter how short it turned out to be. ", "He'd take the time granted to him.", "\n\nThe remainder of the flight was uneventful. ", "Everyone had rested comfortably and were alert and ready for their mission. ", "Scanning of the small private airstrip they used for arrival proved secure and safe. ", "No demons detected or in sight. ", "They were greeted by hired SUV's and all equipment and bags were easily loaded for their first stop at the Memorial Stone before going on to the dig site.", "\n\nThey parked the vehicles and walked the short distance to the area at the cliffs surrounding the Memorial Stone. ", "The sun had yet to make an appearance and it seemed they would be able to accomplish their task as it rose across the horizon where the ocean's surface kissed the sky. ", "The female warriors prepared the site draping the consecrated stone with flowers, garland and candles. ", "Nadine, as the Shield of the warriors, widened the magical circle of protection to include the area they encompassed.", "\n\nThe stone, itself, was magnificent in size and stature. ", "Made from highly polished black granite with the rough edges glittering in dots of silver, white, blacks and grays. ", "Upon the stone was the Valknut, Odin's symbol of the slain warriors knot. ", "It was inscribed in an old Norse language that he recognized but could not actually read, although inexplicably the translation came to him at once. ", "We will remember you always. ", "Our friends, our loved ones, our brothers and sisters, our protectors. ", "Freyodin Warriors forever.", "\n\nAaron was awestruck at the reverent atmosphere the location held. ", "The cliffs bordering the site with the mighty rocks and waves crashing beneath seemed to add a sense of belonging that enveloped everything within the cove above and below. ", "At first, he thought he'd feel unwelcome, intrusive in some way. ", "After all, these were their warrior brothers and sisters that they had lost. ", "Although he recognized the sacrifice they had made for humanity, he had no personal connection to them. ", "But the feeling that wove in and out of everyone and everything was undeniable and all consuming. ", "Without understanding it, something within him felt a loss, too.", "\n\nAs the sun began its low ascent on the horizon, sending sparkling streams of gold across the ocean stretched out below it, Vengeance stepped forward and everyone gathered silently in a semi-circle facing the stone. ", "His booming voice a timbre of command and reverence at once.", "\n\n\"We are here to pay homage to our fallen sisters and brothers. ", "Not only those lost to us in The Great Battle but to all those that have lost their lives in upholding the pledge and beliefs of the Freyodin Warriors; bravery, honor, loyalty and strength. ", "The task given to us by Odin and Freya in protecting the mortal realm is not an easy one, but it is a noble one. ", "A fight we will continue, and win so that our brothers and sisters did not die in vain. ", "Join me in a moment of remembrance to those we hail today.\"", "\n\nVengeance stepped back in line with the other warriors and in unison they lowered to their left knees, drew their daggers in their right hands and crossed them over their hearts. ", "Thrusting the fisted daggers into the molten sky, they raised their voices and chanted as one, \"For the good of all!\", ", "then solemnly bowed their heads. ", "A bright glowing light burst from the heavens and shown down upon the Memorial Stone that could only have been sent by Odin and Freya.", "\n\nVex rose from his kneeling posture and began to sing. ", "Aaron recognized the moving tribute as the song Overcome by Live that became so popular after 9/11. ", "With his arms outstretched to his sides and his head looking skyward, Vex reverently sang the verses while Makayla and Justice rose to join in for the choruses in a beautiful a cappella rendition that touched everyone and sent chills racing through them all. ", "Their voices rose magnificently in the solemn air, blending perfectly in homage to their fallen brothers and sisters.", "\n\nMyste, sporting blue hair to reflect her sadness, made her own contribution during the performance by surrounding the blessed place and all those within it with a blanket of light, swirling iridescent fog that provided a wondrous ethereal effect. ", "It was a moment that brought a sense of awe and remembrance for the sacrifice the fallen had made, leaving not a dry eye or ungrateful heart among them.", "\n\nAaron was moved by the devotion and sense of family and closeness that all of the warriors shared. ", "He wondered at how it must feel to belong to such a group. ", "Being an orphan, he'd never had the chance to share in such a feeling or be a part of such a family. ", "He was envious of Danielle at that moment and secretly wished he could share that feeling with her.", "\n\nAs if she'd read his mind, Danielle reached to her side for Aaron's hand and held it until the song concluded. ", "How could she know I needed this? ", "She couldn't, could she? ", "She probably needed comforting herself and reached out for me. ", "I'm glad she did, for whatever the reason.", "\n\n*****\n\nThe remaining drive to the dig site was quiet and uneventful. ", "Once they arrived, Danielle paid special attention to any spectral presence that might be lurking nearby, expecting a visit from their previous unseen observer, but felt nothing for the moment. ", "Others did visual and mental scanning of the area that proved to be clear of any demon presence. ", "Vengeance suspected it was the lull before the storm and called the warriors together to give instructions and assignments.", "\n\n\"It goes without saying that everyone should be on high alert and have your weapons at the ready at all times. ", "Tormond knows we're here by now and will not be pleased that we've invaded what he considers his territory. ", "We'll work in three shifts – assisting in the search for the EOD, standing guard and downtime. ", "Everyone pair off, one male to one female, and rotate shifts on an eight-hour basis. ", "Danielle, you'll be with me guarding Aaron fulltime. ", "We'll keep his schedule and alternate resting periods. ", "No blocking on this assignment. ", "Communication is key, so stay open and be ready for anything. ", "There are only eight of us to cover the entire site and with two down that leaves only six of us awake and alert at any given time. ", "I'm counting on the men to pay special attention and utilize your abilities to their fullest extent. ", "We'll be working amongst mortals so try to shield your abilities as much as possible and be mindful of what you discuss in public. ", "I don't want to waste a lot of time enthralling Aaron's workers unless it's unavoidable. ", "Any questions?\"", "\n\n\"I'll be working with my assistant, Jake Thomas, so we need to have some type of cover story for everyone's presence around the site,\" Aaron inquired.", "\n\n\"That's not a problem. ", "I can suggest something believable to him and he'll buy it.\"", "\n\nWhen no one else responded, Vengeance added, \"Okay. ", "Be ready for anything. ", "Let's do it.\"", "\n\nMyste grabbed Steele by the arm. \"", "I've got my man,\" she said jokingly and batted her eyes.", "\n\nThe remaining warriors laughed and paired off as instructed then they all headed out for their respective assignments.", "\n\n\"Let's go to my office and I'll introduce you to my assistant.\"", "\n\nVengeance and Danielle followed Aaron through the dreary corridor with its channeled gray metal walls and cold cement flooring. ", "The office's only occupant was Jake who sat working behind Aaron's desk.", "\n\n\"Hey, Aaron. ", "So glad you're back with us and I hope your trip was successful.\"", "\n\n\"Yes, it's good to be back. ", "I appreciate you taking the extra time and effort to cover for me in my absence.\" ", "Turning to his guests, he added, \"I'd like you to meet some friends of mine. ", "This is Danielle and Vengeance. ", "They're going to be on site for a while along with their team.\"", "\n\n\"Jake Thomas. ", "It's nice to meet you both. ", "What kind of team are you?\"", "\n\nVengeance stuck out his hand to shake Jake's proffered one. \"", "We are a security team and Dr. Janson has hired us for some extra security for the time being due to a recent break that occurred on the property.\"", "\n\nDanielle winced slightly at the jab Vengeance made of her prior pitiable attempt at breaking and entering. ", "Vengeance grinned innocently while Aaron raised his eyebrow in surprise but quickly recovered.", "\n\n\"A burglary? ", "Here?\" ", "Jake asked.", "\n\n\"Oh yes, I failed to mention that to you, Jake. ", "It was minor, really, but I'd also received a threat and thought I'd feel safer taking it seriously. ", "You know the old adage – better safe than sorry, right?\"", "\n\n\"Well, I guess I should make you aware of what happened recently then. ", "I wouldn't think anything of it except I've been unable to verify her story.\"", "\n\n\"Her who?\" ", "Aaron probed with interest.", "\n\n\"She just popped out of nowhere a few days ago. ", "Said her name was Hanley Smith and she was a student from the University. ", "She said that Professor Johnson received approval from you to have her join your team in the search for the Eye of Odin because her thesis was on Norse mythology. ", "I answered all her questions. ", "Quite a lot of questions actually, and got her started on some simple assignments. ", "But she hasn't shown up the last couple of days. ", "I was getting concerned, but like I said, I can't verify her story through the University. ", "And you were incommunicado. ", "No one knows who she is unless you do.\" ", "Quite a looker, too.", "\n\n\"No, I'm afraid not. ", "I haven't spoken with Professor Johnson or anyone else from the University lately.\"", "\n\nVengeance cut in. \"", "Jake, where was she working?\"", "\n\n\"She was over in the secured building where we clean and store our findings.\"", "\n\nThey left Jake in the office and made their way to the building in question. ", "Danielle knew this building intimately. ", "It and her B&E building were one in the same. ", "The last time she'd been in here, she and Aaron were getting to know each other intimately, too.", "\n\nVengeance's keen sense of smell picked up on the faint residue of demon in the air.", "\n\nListen up, everyone. ", "We've had a Huldra on the premises within the last forty-eight hours. ", "Stay alert. ", "She'll probably bring some friends with her on her return.", "\n\nDanielle spoke up, \"My guess is it was the ever popular Hanna. ", "She probably returned after our last run in.\"", "\n\n\"Do you mean the demon that flew off as a raven? ", "Maybe Jake would recognize her by a description,\" Aaron asked.", "\n\n\"Yes, that's exactly who I mean, but they can change their appearance, so that's irrelevant. ", "Let's hope her search was unsuccessful since she hasn't been around the last couple of days. ", "She probably didn't get the information she was looking for out of Jake. ", "He's one lucky SOB to still be standing.\"", "\n\n\"We'll need to keep a special eye on him, just in case,\" Vengeance said.", "\n\nAaron looked at them concerned. \"", "Why, is he in danger? ", "I mean more so than the rest of us?\"", "\n\n\"Not exactly, but he could be a danger that we're not aware of if Hanna had her way with him.\" ", "Vengeance notified the team of the possible threat within their midst.", "\n\n*****\n\n\"We've completed all the tests we can think of with the samples we obtained from both Danielle and Aaron. ", "Nothing stands out as unusual or abnormal. ", "But, we also took a swab of the chain that Aaron is wearing which showed some interesting results.\" ", "Excitement flashed in Annika's eyes as she shared the findings of the tests ran by her and Emeline. ", "Emeline reflected a similar look across the table.", "\n\n\"Really?\" ", "Zahara questioned. \"", "Please continue.\"", "\n\n\"Yes,\" Annika began. \"", "Aaron is mortal, of course. ", "But we found dried blood residue still embedded between the links of the chain, which we assume belonged to Alarr since Aaron hasn't been injured and no one else has worn the chain. ", "Again, an assumption, due to the nature of the chain, but one we're pretty sure of.\"", "\n\nEmeline nodded enthusiastically. \"", "The thing is...they, Aaron and Alarr...they match. ", "It's like their brothers or something. ", "I even had a couple of the guys examine both samples without giving them any additional information. ", "I figured with their extra vamp senses, they'd be able to decipher between the two, but they said the samples were very similar also. ", "Just that one was quite older than the other. ", "I know it's impossible, but it would at least give us a reason why the chain attached.\"", "\n\n\"Danielle said that they were both touching the chain when the explosion of light burst and suddenly, the chain was on Aaron. ", "It must think Aaron is Alarr.\"", "\n\n\"Wow,\" Zahara stared blankly ahead. \"", "That would explain it. ", "It could all boil down to chemistry, after all. ", "I'll go back to the scrolls and research Alarr specifically. ", "I've been searching for anomalies regarding the binding chain. ", "I'll just change the parameters of my search and see what I can find.\"", "\n\nAnnika sighed and continued. \"", "Unfortunately, it doesn't solve how we're going to remove it. ", "This just brings up more questions.\"", "\n\nEveryone nodded, sighing in agreement. ", "Then Annika had an idea.", "\n\n\"Hey, what if I assist you in the search? ", "I can enforce and enhance the powers and gifts of the others. ", "Why can't I help you enhance your search?\"", "\n\n\"I don't know. ", "I've never had anyone join me in my visions before. ", "I've been searching the scrolls through my visions instead of traveling back and forth to Valhalla.\" ", "Giving the idea some thought, she bit the tip of her index finger and turned to Emeline.", "\n\n\"You could help us, too.\"", "\n\n\"How do you mean?\" ", "Emeline replied.", "\n\n\"Just for safety's sake. ", "You'd be here in case anything happened to Annika. ", "Your healing powers could be useful. ", "I seriously don't know what, if anything, could go wrong, assuming it works at all.\"", "\n\n\"Sure. ", "Of course, I'll help.\"", "\n\nAnnika was looking forward to this endeavor. ", "She could trace as well as everyone else, but traveling through a vision was simply...exciting. ", "Impatiently she said, \"Well, what are we waiting for? ", "Let's get to it.\"", "\n\nFollowing Zahara through her home, they entered the room that she had deemed her vision room. ", "She kept this sacred room separate from everything else in her life. ", "As she opened the double doors, they were met with a serene forest scene that gave the impression of walking outside into the forest itself. ", "It was much more than an indoor garden. ", "Dozens of white candles lit a path and provided low lighting giving the room a serene atmosphere. ", "Sheer drapes flowed around the outer edges of the copious room and the ceiling portrayed a life-like view of a blue sky dotted with cottony white clouds. ", "A trickling waterfall could be heard in one corner and living plants and other greenery surrounded the remainder of the room. ", "They followed the lit path across a small raised bridge that crossed a tiny moving stream.", "\n\nThe other side of the bridge housed an altar that was adorned with dozens of burning white candles of varied shapes and sizes. ", "Zahara motioned for the others to stand to the side and lowered to her knees on the large satin pillow in front of the altar.", "\n\n\"Annika, if you will simply add your magic to mine once I enter my trance, I believe that will be sufficient. ", "If you start to feel uncomfortable in any way, please pull back and sever the tie between us. ", "I don't want you to get caught up and transcend anywhere but this room. ", "I wouldn't know how to bring you back into your body if that happened. ", "Emeline, just watch out for her and do what you can to aid her should she need it, please. ", "Whatever happens, don't let her go into a trance herself.\"", "\n\nWhen both women had nodded their acquiescence, Zahara began by getting into a meditative yoga position. ", "She closed her eyes, resting her hands palm up on her knees and took deep breaths, clearing her mind completely. ", "Her body became weightless and lifted, floating just a few inches above the pillow she'd previously occupied. ", "A tingling feeling engulfed her form as she reached a mindless thoughtless state. ", "She felt her essence leave her body as her mind entered an astral plane and floated along a stream of consciousness, crossing through the veil of the mortal realm and entering the realm of Asgard. ", "She glided atop Glasir, the most beautiful tree among gods and men, bearing red-golden leaves, that stood vigil outside the doors of Valhalla, and finally projected into the hall that held the ancient records she sought.", "\n\nZahara felt Annika's magic flowing through her enhancing the clarity as she conducted her search of the archived records, mentally projecting her inquiries. ", "In her vision, several volumes and pages floated around her and various bits of information gathered together from the pages and flowed like a swirling stream of energy into her mind, filling her with the answers she sought. ", "When the flow of energy ebbed slowly to a halt, Zahara returned to her body and reentered her physical state of being.", "\n\nBlinking her eyes, Zahara happily proclaimed, \"I think I've got it. ", "Thanks so much for the help, Annika. ", "Searching the scrolls was never so clear. ", "I may utilize your assistance again in the future.\"", "\n\n\"It was my pleasure. ", "But tell us what you found.\" ", "Annika joined in her excitement and jumped giddily like a child, clapping her hands.", "\n\n\"It seems that Alarr had a human family before he came to join us. ", "He left a wife and two sons behind when he was brought over. ", "It's very possible that Aaron may be his descendant.\"", "\n\n\"Well, that might explain the blood similarities. ", "Although, it's been hundreds of years and I don't know how reliable that solution would be.\"", "\n\n\"The records also provided a ritual that can be performed to verify their ancestry. ", "It's fairly simple and I think we should try it. ", "At the very least, it will out rule the theory,\" Zahara suggested.", "\n\n\"I agree,\" Emeline offered. \"", "It's not like we can go to Ancestry.com.\"", "\n\nAs the women laughed, Zahara added, \"Yea, wouldn't that be something. ", "I sure wish they'd put our scrolls on-line.\"", "\n\n*****\n\nChapter Sixteen\n\nThe quiet in Aaron's office was disturbed by Marvin Gaye singing a muffled version of 'Let's Get It On.\" ", "A startled Danielle grabbed her backpack and shyly said, \"Oh, that's me,\" while she dug out her cell phone.", "\n\nThe others within the room snickered. ", "Danielle felt the heat of embarrassment creeping up her face. ", "Arrg! ", "I haven't blushed in years.", "\n\n\"Hello,\" she said answering and stepping out into the hall.", "\n\n\"Danielle, it's Zahara. ", "I've got some news.\"", "\n\n\"Good news, I hope. ", "What's up?\"", "\n\n\"Actually, it just might be good news. ", "Annika, Emeline and I did some additional checking and examination of the samples they took from you and Aaron. ", "There seems to be a strange anomaly with the blood samples taken. ", "Also, I've discovered that Alarr had a human family before he died. ", "With Aaron's permission, I want to conduct a ritual that will conclude whether he is a descendant of Alarr's or not.\"", "\n\n\"Wow.\" ", "She slumped a little harder against the wall she'd been leaning on. \"", "That's a stunner. ", "Sure wasn't expecting you to tell me that.\" ", "She paused and then in a slightly panicked voice asked, \"How can that be?\"", "\n\n\"Calm down. ", "It's going to be okay. ", "I don't know how these things happen and we don't know anything for sure yet.\"", "\n\nDanielle sighed heavily and tried to slow her rapid breathing. ", "Her mind swarmed with abstract thoughts. ", "What's going on? ", "How can they be related? ", "Why is this happening? ", "Is this fate or just some weird coincident? ", "This is a joke, right? ", "Mommy Dearest is playing a cruel joke on me. ", "Does this mean I'm bonded to him because we've had sex? ", "Is that even possible? ", "Would that be so bad? ", "Oh Goddess, what am I going to do?", "\n\n\"Please don't fall apart on me yet, Danielle. ", "Even from here, I can tell your brain is in overdrive. ", "Let us figure out what's going on first. ", "I'm sorry to have to tell you like this, but I need you to bring Aaron up to speed and get his permission to do the ritual. ", "He has to be a part of it. ", "Can you do that for me?\"", "\n\n\"I'm okay. ", "I'm okay. ", "Yea, sure, I can do that,\" she mumbled unconvincingly.", "\n\n\"Alright. ", "Call me back if you need to. ", "I'm worried about you, sweetie.\"", "\n\n\"Don't worry. ", "I'm fine. ", "I'm sure he'll agree. ", "He wants this over with as much as I do.\" ", "Yea, keep telling yourself that. \"", "We'll see you as soon as this assignment is completed.\"", "\n\nDanielle disconnected the call, walked back into the office and zoned in on Aaron like a tractor beam.", "\n\n\"Aaron, we need to talk.\"", "\n\n*****\n\nAaron stood up from his chair and walked around his desk. ", "Once he reached Danielle's side, he lifted her chin with his index finger and looked into her eyes. \"", "You sure look serious.\"", "\n\nIgnoring his questioning look, she cast her eyes downward and said, \"Come on. ", "Let's find a place with a little more privacy.\"", "\n\nAaron swept his hand out in front of him toward the direction of the door. \"", "After you.\" ", "They walked in silence down the corridor and out of the building.", "\n\nDanielle wanted as much space as possible between her and Aaron and the others for this conversation. ", "She never meant to keep the knowledge of her past from him. ", "It just never seemed the right moment for the discussion. ", "The more she thought about it, now didn't feel right either. ", "Actually, on second thought, she needed to lighten the subject up a bit. ", "Yea, that would do the trick. ", "If she didn't make such a big deal out of it, maybe he wouldn't. ", "She didn't want him to get the wrong idea anyway, right? ", "Why should he care about her past with Alarr? ", "For that matter, why should she care what he thought? ", "Oh crap, she was probably making a mountain out of a molehill. ", "She knew she had to tell him about Alarr because of the ritual Zahara wanted to perform, but it was time to loosen up. ", "To not be so serious.", "\n\n\"Okay, what's up? ", "Are you all right, Danielle? ", "You're scaring me a little here.\" ", "His concern was obvious.", "\n\nShe visibly changed her entire demeanor and put a little smile on her face. \"", "No need for alarm. ", "I'm fine. ", "Really I am. ", "Sorry to worry you back there. ", "I really just needed some air.\"", "\n\n\"Are you sure that's all?\"", "\n\n\"Well, I do need to ask you something, but it's not such a big deal as you might think.\" ", "She reached behind her back and drew her sword from its sheath. \"", "Here, take this.\" ", "She motioned toward her sword, holding it out to him by the hilt. \"", "Let's have a little practice while we talk. ", "I've been hearing all about what the guys taught you, but haven't seen you in action yet.\"", "\n\nWhen Aaron didn't move to take the sword, she lifted her chin and donned a sexy, sly smile, taunting him. \"", "Come on. ", "Show me whatcha got.\"", "\n\nAaron was relieved to see the worried look had left her face and was willing to go along with her new plan of action if it made her happy. ", "He walked toward her and accepted the sword she offered.", "\n\n\"And what will you use now that I've got your sword?\"", "\n\nDanielle reached down into her boot and retrieved a lengthy dagger. \"", "Oh, I'll use this little ole' thing.\" ", "She brandished the dagger, letting the light gleam off the menacing and deadly looking blade.", "\n\n\"That doesn't seem quite fair. ", "Mines much longer than yours.\"", "\n\n\"Oh, you're longer, all right,\" she laughed naughtily. \"", "Don't you worry about me. ", "Just bring it.\" ", "She gave him a daring look to go along with her daring words and motioned with her free hand for him to come toward her.", "\n\n\"Okay, if you really want to do this...\"\n\nAaron brought the sword up settling into a fighting stance. ", "He figured he'd need all of the advantages he could get anyway against a warrior, female or not, so without further warning, he lunged toward her in a playful manner. ", "Danielle met his advance and blocked it easily with her dagger.", "\n\n\"Okay, what did you want to ask me?\" ", "he inquired as they continued the lighthearted duel. ", "His curiosity hadn't been side-tracked by her obvious diversion.", "\n\n\"Well, I really haven't told you a lot about myself and especially about that chain that's currently locked around your neck.\" ", "She circled around him threateningly in a sideways foot sliding motion.", "\n\n\"Danielle, if you're trying to tell me that you were once mated, I already know.\"", "\n\nShe stopped in her tracks, stood up straight from her battle stance and her weapon went slack in her grip. \"", "What? ", "How could you?\"", "\n\nHe advanced on her again continuing their contest. ", "Her instincts brought her back to the skirmish without thought.", "\n\n\"Other's talk, you know. ", "It doesn't matter who told me. ", "They certainly didn't do it to hurt you in any way. ", "It just came out in conversation.\"", "\n\nAccepting his explanation, she said, \"Then you know about Alarr.\"", "\n\n\"No, not really. ", "All I know for sure is that you were previously chain bonded. ", "Why don't you start from the beginning and fill me in on what I'm missing.\"", "\n\nShe lowered her weapon. \"", "Okay, but let's sit and talk. ", "You know, you're actually very good with my sword. ", "I'm impressed considering the time constraints we've been under.\"", "\n\n\"Thanks, but I'm afraid I'll never be as good as all of you.\"", "\n\n\"No need to be. ", "That's why we're here,\" she laughed feeling a little relieved that he at least had some knowledge of her past and she wouldn't be hitting him out of left field.", "\n\nAaron relinquished her sword, took her hand and led her toward a nearby tented area used for meals and gathering. ", "It was currently dark and empty but would serve for their purposes. ", "He continued to hold her hand as they sat.", "\n\n\"Where to start?\" ", "she mused.", "\n\n\"The beginning,\" he answered, meeting her eyes.", "\n\n\"All right. ", "It's true. ", "I was once chain bonded for one whole night a long, long time ago. ", "His name was Alarr.\"", "\n\n\"There's been no one since him?\"", "\n\n\"Not many. ", "And not anyone serious, no. ", "And I found out the hard way that he was a mistake. ", "We should never have made that commitment either.\"", "\n\nShe told Aaron everything. ", "From how she believed their relationship had grown to love, only to discover the reality of the situation and then, how she'd lost him. ", "Aaron listened patiently for her to finish her tale of betrayal.", "\n\n\"I'm so sorry that you were hurt that way,\" he said stroking her hand softly with his thumb.", "\n\nShe searched his eyes and saw only sincerity in them. \"", "Thank you. ", "But there is more, I'm afraid.\" ", "She sighed and continued. \"", "You know that Zahara has been searching our ancient scrolls for a way to remove the chain you're currently wearing.\"", "\n\nHe nodded.", "\n\n\"She's discovered that when Alarr was brought over, he left a family behind. ", "A wife and two sons. ", "We don't know why, but your blood sample is very similar to the dried sample that remained encrusted on the chain, which we believe belonged to Alarr.\"", "\n\n\"You mean like we're both A positive or something?\"", "\n\n\"No, I mean like your DNA is almost identical.\"", "\n\nAaron released her hand and sat back. \"", "How can that be? ", "What exactly does that mean? ", "I'm an archeologist, not a hematologist.\" ", "His expression showed his total disbelief and puzzlement. ", "He stood and began pacing.", "\n\n\"We're not sure without some further testing. ", "As unbelievable as it may seem, it's possible that you're his descendant.\"", "\n\nHe stopped and faced Danielle. \"", "So, what? ", "You're telling me that Alarr could be my...great times...six or eight...grandfather?\"", "\n\nNow it was her turn to nod.", "\n\n\"Incredible! ", "Really, it can't be. ", "I mean seriously...what are the odds?\" ", "He began pacing again.", "\n\nDanielle said nothing, let it all soak in. ", "She found this possibility incredulous herself and her life revolved around crazy, unexplainable phenomenon on a constant basis.", "\n\n\"How do I deal with this? ", "How am I supposed to feel? ", "I don't even know where to begin.\"", "\n\n\"Well, if you think about it, your last name is Janson, which could be an American form of the old Norse Janssen, which was Alarr's last name.\" ", "She mumbled that last bit of information slightly under her breath. ", "She wondered why she felt the slightest twinge of guilt about not having made this connection before, but seriously, she had no real reason to think that Aaron had anything to do with Alarr. ", "Really? ", "What were the chances?", "\n\nShe paused to let him absorb the information she'd given him before dropping the next bomb.", "\n\n\"With your permission, Zahara would like to perform a ritual that will determine any connection between the two of you.\"", "\n\nWithout voicing it aloud, he thought, Could this really be happening? ", "If it's true, is this fate or something? ", "The odds are astronomical.", "\n\nShe stood and reached for him, stopping him in his stride to face her. \"", "After all of the fantastical things you've seen and learned recently, one more shouldn't be too much of a stretch, right? ", "Besides, it's only a theory at this point. ", "The ritual will tell us more and I'm sure you want to get this thing removed.\" ", "She traced a finger over the chain lying under his shirt resting against his chest. \"", "At this point, it seems you have three choices. ", "Either do the ritual and possibly discover a solution to removing the chain or wear the thing for the rest of your life.\"", "\n\n\"Three. ", "You said three. ", "What's the third choice?\" ", "He looked at her expectantly.", "\n\nShe grimaced. \"", "Chop your head off.\" ", "Well...he did ask.", "\n\n\"Right,\" he said somewhat unconvincingly as he stared blindly into the night over her shoulder. ", "He seemed to take that in stride.", "\n\nDanielle wondered for a moment if his response meant he really didn't want to remove it. ", "No, he's just distracted.", "\n\n*****\n\nThe hour was late when Aaron and Danielle returned to the office. ", "Vengeance had been briefed of the latest news by Zahara and he could feel the tension in the air like a taunt wire about to spring. ", "A little rest would do them all good and maybe alleviate some of the strain, so he sent them off for a few hours, instructing Danielle to stay close to Aaron. ", "Aaron led Danielle to a room that contained a few blanketed cots and she lied down in one next to his.", "\n\n\"Sleep well, Aaron.\"", "\n\n\"You, too,\" he replied but knew sleep would not come quickly for him tonight.", "\n\nHe settled on his back and braced his arms under his head with his fingers linked together. ", "He thought of all Danielle had told him which led to even more unanswered questions. ", "Usually, he loved the quest to find the answers hidden by time, but this pursuit was a little too close to home. ", "Hell, it was home, as it was all about him. ", "That was damned uncomfortable. ", "He really shouldn't be surprised or stunned by anything he discovered now. ", "He really should have reached his limit at being shocked, but the hits just kept on coming.", "\n\nHe silently chuckled to himself, astounded that he wasn't in the slightest upset, but mostly amused. ", "My great 'whatever' grandfather! ", "Oh God, I've been sleeping with his wife! ", "Okay, a wife of one day. ", "Well, I guess there are a totally different set of rules regarding the afterlife and immortality. ", "I mean, it's not like I'm related to her at all. ", "She didn't further my mortal bloodline. ", "God, what a mess.", "\n\nAaron turned to his side. ", "He watched Danielle sleeping on her side, looking innocent with her knees drawn up and her hands under the side of her beautiful face, pressed together as if in prayer. ", "He thought of the pain and betrayal she spoke so reluctantly of. ", "How must she feel? ", "I was so taken aback that I didn't even consider how she was taking this epiphany.", "\n\nAs he watched her, her eyes fluttered open and she met his gaze. ", "She hadn't been asleep after all. ", "Neither moved as they held each other's attention, but Aaron saw the hopelessness conveyed in her face and realized that he wanted to share her pain, past and present. ", "He wanted to bring her more of the joy they've shared these past few days together. ", "His realization dawns.", "\n\nOh, my God. ", "I love her. ", "I really love her.", "\n\nWhen did that happen? ", "Was it when that sassy-mouthed sexy woman broke into his warehouse and tried to con him? ", "Was it the first time he couldn't keep his hands off of her and took her roughly against the wall? ", "Was it when he discovered the wonderful, independent being that she really was? ", "Or when she shared her world with him? ", "Maybe it was simply when he held her and didn't want to let go. ", "He didn't know when he started to love her, but now he was sure he did.", "\n\n\"Why are you watching me?\" ", "she murmured softly. \"", "You should really get some sleep.\"", "\n\n\"Can't sleep. ", "I was just observing you...thinking about...everything.\"", "\n\n\"I'm really sorry, Aaron. ", "I never meant to drag you into all of this...endanger your life...your project. ", "Goddess, I've made such a mess of everything.\" ", "Her voice was thick with remorse.", "\n\n\"No, Danielle. ", "Please don't be sorry.\" ", "He slid off his cot and knelt next to her still prone body, running his strong hand across the side of her face and softly into her hair.", "\n\n\"I don't regret a thing. ", "Yes, I'll admit to freaking out occasionally, but this has been an adventure beyond my wildest dreams. ", "I may not be able to share any of these discoveries with my colleagues, but I'll know. ", "I'll know there are phenomena out there around us that can't be explained, some good and some bad. ", "I'll know that you're out there watching me and protecting me. ", "Not just me, but all of us, because you're good, noble and strong you've been called to a higher existence to become so much more than the majority of humanity can ever aspire to. ", "My life will be so much better just having known you. ", "If the chain can't be removed then I'll wear it with pride, remembering our time together.\"", "\n\nDanielle's eyes were brimming with tears, but she refused to let them bleed over. ", "She didn't want him to see her cry. ", "She couldn't share the extent of her feelings now. ", "Nothing lasting could be acted upon and nothing could become of it. ", "The weight of hopelessness sat on her heart like a crushing vise.", "\n\n\"I just wish...,\" Aaron began. ", "He glanced downward, breaking eye contact with her.", "\n\nShe sat up suddenly and framed his face with her hands. ", "Though she knew his answer would pain her, her fear couldn't stop her from asking, \"What? ", "What do you wish, Aaron?\"", "\n\n\"That I could keep you, Danielle. ", "You've given me a new outlook on life...and love. ", "It's as if I haven't really lived until now. ", "Until you. ", "You're so much more than that jackass, Alarr, ever knew. ", "Great grandfather or not, what he did to you was wrong and I want to spend the rest of my life proving it to you. ", "I'll do the stupid ritual to satisfy everyone's curiosity and fears, but it doesn't really matter to me anymore. ", "If this chain is all I'll have left of you, I'll wear it till the day I die, remembering you. ", "Loving you.\"", "\n\nAaron softly brushed the tears from her face that she was unable to hold back. ", "There was no need to search his face for his sincerity. ", "She felt the truthfulness of his words deep within her being like something she'd never felt before, breaking down and crumbling the unbreachable walls she had built around her heart.", "\n\n\"I don't want to end this, to lose you,\" he continued. \"", "I never thought I'd find someone like you. ", "Never thought I'd ever feel this way.\"", "\n\nShe threw her arms around his neck and drew him close. \"", "Oh, Aaron. ", "I feel the same. ", "Please know I do. ", "But we both know that it can't be. ", "I'm bound by my world as you are yours.\"", "\n\n\"With all of the strange and wondrous things I've discovered out there recently, can't we find one that will let you stay with me. ", "They've got plenty of warriors. ", "Surely they wouldn't miss just one.\"", "\n\nShe pulled back to look at him. ", "The sadness in her eyes rivaled the hope in his. \"", "I'm so sorry, my love, but it's forbidden. ", "If I could do anything to change it, I would. ", "Please believe me.\"", "\n\n\"I do. ", "But I don't have to like it.\" ", "Aaron closed his eyes and took a deep breath. ", "He was determined to be the optimist tonight. \"", "All right. ", "It's not over yet. ", "Maybe we'll think of something or discover something. ", "Maybe I can bargain with Zahara in exchange for letting her do her little ritual on me. ", "I'll ask her help in finding a solution. ", "Just don't give up hope yet.\"", "\n\nDanielle smiled weakly and nodded her agreement while pulling his lips to meet hers. ", "She knew it was hopeless. ", "Had seen it happen once before. ", "But she kept up the pretense for his sake. ", "He'd be okay once his memory was wiped. ", "Of that she was glad. ", "He wouldn't suffer. ", "His memory would be wiped clean and he'd forget all about her. ", "But she wouldn't forget. ", "She'd carry these wonderful memories to the end of her days.", "\n\nBut she'd worry about her suffering another day. ", "She wanted to enjoy the happiness she'd finally found, if only for a short time. ", "Their kiss quickly turned to an insatiable hunger.", "\n\nAaron pulled back slightly and whispered against her lips. \"", "Let me show you what love can really be. ", "That a man can love a woman unselfishly and not betray her. ", "Let me love you, Danielle.\"", "\n\n\"Oh, Aaron. ", "Yes.\"", "\n\nDanielle pulled Aaron up from the floor and onto her cot. ", "Her body immediately melted into the contours of his and she felt cradled in his warmth. ", "Comforted. ", "Contented. ", "Loved. ", "For the first time in her long, long life.", "\n\n*****\n\n# Chapter Seventeen\n\nDanielle understood that these feelings couldn't last, but she pushed all of those thoughts to the back of her mind, insistent that she would exist in the present, not the future or the past. ", "For just a little while. ", "She'd charge it to that credit card of fate and pay for it later.", "\n\nBut fate had other ideas and their lovemaking was suddenly brought to a halt as Vengeance broke through her euphoric state of mind.", "\n\nWe have a breach. ", "I repeat, we have a breach. ", "The North side. ", "I need everyone in full battle mode. ", "Now.", "\n\nSteel was on watch duty positioned on the opposite side of the site. ", "We've also got a breach on the South side. ", "Looks like Tormond himself has graced us with his presence.", "\n\nUnexpected fear gripped Danielle. ", "Not for herself, but for Aaron, and he noticed her body suddenly stiffen and grow cold like ice spreading through her veins.", "\n\n\"What is it? ", "What's happened?\" ", "he demanded with concern.", "\n\n\"They're here. ", "Tormond and his demons are here.\" ", "She pushed back from the warmth of his body. \"", "I have to go.\"", "\n\nAs she hurriedly pushed to her feet, he stood and began following her to the door. ", "She turned to face him stopping his pursuit.", "\n\n\"No. ", "You stay here where it's safe. ", "I won't let them get to you.\"", "\n\n\"In what universe do you think I would actually sit here and cower while my woman goes into battle? ", "And to protect me, no less.\" ", "He threw his hands up in wonder.", "\n\n\"You don't know what you're up against. ", "They aren't human. ", "Even his lowly minions are mindless killing machines. ", "Promise me you'll stay here where it's safe.\"", "\n\nAaron saw the pleading in her eyes, felt her fear as it coursed through his body like a physical entity. ", "He met her gaze with resolution, adding as much tenderness and understanding as he could muster. ", "He knew full well the anxiety she was dealing with at the moment at the thought of losing him. ", "He was filled with the same and was determined to either live or die with her by his side. ", "He may be only human, but his determination and protectiveness of her at that moment amped his blood to a boiling point of indestructible euphoria.", "\n\n\"No, I can't do that. ", "The warriors have trained me. ", "I can help. ", "Besides, they'd find me here anyway. ", "I'd rather be out there in the thick of it with all of you fighting then stuck here hoping not to be caught alone. ", "I have to be with you.\"", "\n\nAaron reached down into his boot and produced a long lethal looking blade. ", "He smiled wickedly, brandishing the knife with a stern iron grip.", "\n\n\"A gift from Vex,\" he answered the questioning look on her face.", "\n\nDanielle eyed him up and down in strict consideration, concluding he was right. ", "He looked strong and mentally ready. ", "She clenched her hands at her side, closed her eyes and prayed it was enough.", "\n\nGrabbing two fistfuls of the front of his T-shirt, she brought him roughly up against her body, stretching upward on her toes to meet him face to face, and breathily whispered, \"Okay. ", "But don't get yourself killed. ", "We have unfinished business.\" ", "Then she kissed him hard, pouring her whole being into the hurried embrace, withdrawing with an auspicious smile.", "\n\nShe drew her magical sword from its sheath, put on her combat-ready game face and moved cautiously but purposely down the hall. \"", "Let's go. ", "Stay with me and don't leave my side,\" she ordered rather fiercely.", "\n\n\"Yes, Dear,\" he mocked, following closely on her heels. ", "He rather liked this strong forceful side of her.", "\n\nDanielle sensed the demons in the area, feeling the creepy vibrations they emanated and the smell of brimstone, but they were visually nowhere within range. ", "As they exited the building and rounded the nearest corner, they joined the warriors already engaging the demon horde. ", "Her senses informed her that the horde was a mix of demons, minions and...was that...yes, a human. ", "She sensed no evil within the human, which made him no threat. ", "She wondered what would merit Tormond bringing a human to a fight. ", "Not that he cared about mortals in the least, but a human wouldn't stand a chance against the warriors.", "\n\nSteele wielded his medieval thirty-inch double edged sword with strength and ease, with a fang-filled smile on his handsome face and his stance resembling a child dueling with wooden sticks. ", "Obviously enjoying himself. ", "Myste was by his side, complete in gothly robes, her crown of flowing hair pitch as the darkest night as she battled the demon before her. ", "Aaron watched as she raised her hands causing the terrain to erupt around the vile creature, utterly swallowing it into an earthly prison of dirt, rocks and sand.", "\n\nAlthough the healer of the warrior tribe, Emeline was also a trained warrior, sharing the strength of her sisters-in-arms. ", "She fought side by side with Steele and Myste, brandishing a blade similar to the one that Aaron was gifted with, swinging it in wide arcs and inducing damage to her foe with stunning success. ", "He only hoped he could rival Emeline's efforts.", "\n\nAaron watched as Danielle leaped into the fray before them. ", "She was fierce, powerful and absolutely beautiful, clearly in her element. ", "Her movements were stunning as she masterfully grasped the sword, sweeping it before her as if it were an extension of herself. ", "This is who she was, he realized. ", "A warrior. ", "A protector. ", "A savior of mankind. ", "Pride filled him as he contemplated his assault tactics, having never been in this kind of situation before. ", "He would never have thought that he would be in the midst of a battle. ", "A medieval style battle, at that.", "\n\nHe looked at the blade in his hands and didn't know if he could actually maim someone or not. ", "At least not without provocation.", "\n\nDanielle easily dispatched the minion who dared to attack her and looked back over her shoulder searching for Aaron's whereabouts. ", "She saw him and the minion approaching him at a fast pace. ", "Fear gripped her as she yelled, \"Behind you, Aaron!\"", "\n\nAaron turned, braced for the attack, but was still contemplating what action to take. ", "She could actually see the wheels turning over and over in his mind calculating and searching for the best course of action.", "\n\nRecognizing the habit he had to overthink things, Danielle shouted, \"Just hit the motherfucker already!\"", "\n\nAaron met her eyes for a split second, but it was enough. ", "She'd understood and given him an alternative. ", "Resolved, he tossed the blade into his left hand and pulled his right arm back just in time to plow a solid fist into the surprised face of his enemy. ", "The blow landed him out cold on the ground at his feet. ", "He heard a hearty 'Whoo-hoo!' ", "coming from Danielle's general direction and smiled knowing the yell of encouragement accompanied the usual arm pump into the air.", "\n\nHe turned toward her and she stood just as he imagined. ", "Sudden fear gripped him as he looked beyond her only to see an advancing demon bringing down a sword that plunged deeply into her lower back. ", "As he screamed out her name in warning, he knew it was too late.", "\n\nIt was his fault. ", "She'd been distracted by him instead of protecting herself. ", "He felt his whole world darken as he filled with an all-consuming feral rage, the likes of which he had never known.", "\n\nRushing to her side, he tossed the blade back into his right hand and thrust into the exposed throat of the demon with all his might. ", "He knew he was no match for this demon, but didn't care what happened to him. ", "He had to keep the evil creature from harming her further.", "\n\nThe demon fell backward with the force of Aaron's weight slamming into it. ", "He pulled the knife free and raised it once again plunging into the flesh of the murdering demon again and again. ", "All thought left him except protecting Danielle. ", "Steele grabbed Aaron's arm in mid-swing, stopping his maddening thrusting motion.", "\n\n\"She's gone.\"", "\n\nStunned for a moment, Aaron came back to himself, his face contorted with pain while his mind screamed with the realization of Steele's words. ", "NOOOO!!!", "\n\n*****\n\n\"Aaron!\" ", "Steele yelled in a commanding voice and grabbing him forcefully. \"", "Not Danielle. ", "Hanna. ", "The demon, Hanna. ", "You killed her.\"", "\n\nAaron looked down at the ground expecting to see the lifeless body of the woman...no demon...he had bludgeoned and mutilated in his frenzied fury, but there was nothing there but a large smattering of ash. ", "What? ", "Where's the blood? ", "The body? ", "He checked himself envisioning his blood-soaked clothing but found no evidence there either.", "\n\n\"Where'd she go?\"", "\n\n\"Where all dead little demons go.\" ", "With a nod of his head, Steele added, \"Take care of her,\" while turning around to rejoin the fight.", "\n\nAaron collected himself, remembering the cause of his madness and knelt down reaching for Danielle, finding the evidence of blood he'd been searching for. ", "He immediately yanked off his shirt and pressed the wadded fabric to her back encompassing the wound, applying pressure to stem the flow. ", "Once his rage had subsided, he sensed the pain that Danielle was in, not physically, but he just knew the anguish she was feeling.", "\n\n\"Oh God, Danielle. ", "I'm so sorry. ", "I'm sooo sorry. ", "It's all my fault.\" ", "The panic in his eyes shown like a beacon in the night, but couldn't cover the wetness that glazed his vision. ", "He held her head in his lap, smoothing the hair from her eyes.", "\n\n\"No,\" she said weakly. \"", "It's not your fault. ", "I should have been paying attention. ", "I know better.\"", "\n\n\"No, I distracted you.\"", "\n\n\"Let's argue later, after I've healed a bit.\" ", "Danielle attempted a hollow laugh and a tight smile that quickly turned into a grimace of pain.", "\n\nAlong with a heavy dose of concern, Aaron felt a small amount of relief fill him. ", "That this wonderful woman could joke at a time like this, was a good indication.", "\n\n\"How bad is it? ", "What else can I do?\"", "\n\n\"You're the doctor,\" she chided weakly.", "\n\n\"Wrong kind of doctor, babe. ", "And now is not the time to joke about it.\"", "\n\nSuddenly, Emeline was right by their side breathing heavily. \"", "Hey, girl. ", "Hang in there. ", "I'll do everything I can to alleviate the pain and help you heal.\" ", "Switching her attention to Aaron, she commanded seriously, \"Protect us. ", "Keep them off me while I help her. ", "She'll be fine. ", "I promise.\"", "\n\nAaron nodded to Emeline and with a last look at his lover's face, he turned back to the melee that was happening around them. ", "With his knife in one hand and Danielle's sword in the other, he was determined to take on anyone or anything that threatened his charges. ", "He prayed Danielle would be all right because he didn't know what he would ever do without her now. ", " \nShe had become a part of him, as important as the air he breathed.", "\n\nEmeline lifted Danielle's shirt, removed Aaron's makeshift bandage and pressed one hand to her wound at her back and the other to her stomach. ", "Aaron stole glances as Emeline attempted to heal Danielle, remembering the heat and the prickling sensation he'd felt when she'd healed his ankle. ", "This time, her hands seemed to glow somewhat and Danielle stirred, wincing in pain.", "\n\n\"I'm sorry for the discomfort, Danielle, but the puncture is deep. ", "You've got quite a bit of internal damage that I must attend to.\"", "\n\n\"It's okay. ", "I understand. ", "Do what you need to...and, thank you.\"", "\n\nEmeline smiled then returned her concentration back to the required healing.", "\n\nDanielle closed her eyes and let her thoughts wonder, trying not to focus on the pain. ", "She thought of her sister warriors, the ages they had endured and shared together. ", "She thought of Emeline's smile and the kindness that seemed to always be evident in her azure eyes. ", "She not only healed through her herbs, potions and touch but through the interaction, she shared with the other warriors. ", "Her very nature was calming and healing. ", "Freya had gotten the gift spot on with this one.", "\n\nA loud roar filled the air, drawing Danielle back to the present conflict around her. ", "Vengeance and the others had apparently wreaked havoc on their throng of undesirables and traced across the site to join in on the remaining cleanup. ", "Once again Vengeance let out a mighty battle cry.", "\n\nVex looked out into the melee seeing a familiar face that he remembered from his latest casino visit. \"", "Hey, College Boy! ", "Looks like we're gonna get to dance after all.\" ", "He charged into the fight looking ready to rip someone's head off with his bare hands and Danielle lost sight of him.", "\n\nYou go, Vex, she thought silently.", "\n\nThe roar emanated from Tormond, his displeasure unmistakable. \"", "Vengeance!\" ", "he bellowed. ", "His voice dripped with disdain and his eyes radiated hatred. ", "The malice oozing from his pores was thick like a black oily sludge.", "\n\n\"Face me. ", "Leader to leader,\" Tormond demanded. \"", "Let us end this battle between us. ", "The winner takes control of this place.\"", "\n\nTormond knew he hadn't much chance left to come out on top of this confrontation. ", "He decided to take his chances, demi-god against ancient immortal. ", "The odds were in his favor.", "\n\nVengeance was thrumming with the thrill of battle. ", "He lived for it and missed his kingly conquering Viking days. ", "His entire body vibrated with an electric energy and his blood boiled and rolled through his veins rushing like a roaring river wild. ", "Arrogance ruled and refused to let him back down from the challenge Tormond had issued, even though the warriors already had the upper hand and control of the dig site. ", "Their victory at this point was assured.", "\n\nHe stood proudly in his formidable stance. ", "His long blonde hair flying over his broad shoulders, brilliant crystal blue/gray eyes shining like diamonds in the dark, fangs extended in his confident poised smile, covered in the blood of others and his broad sword resting downward in his powerful grip. ", "Vengeance was a sight to be awed and revered.", "\n\nStan stood beside Tormond ready to defend his employer. ", "He wasn't quite sure what all of this was about, but he'd seen things tonight that curled his toes and would give him nightmares for ages to come. ", "People turning to ash, disappearing from one place to the other in the blink of an eye, eyes glowing demon red and torturous weapons that he thought only existed in museums. ", "People. ", "That was a loose term. ", "He wasn't exactly sure what some of them were and was afraid to ask. ", "The overly large man Tormond had confronted was anything but human. ", "And those fangs... My God, what is he? ", "A vampire or something?", "\n\nStan looked inquisitively at Tormond, fearing for his employer's safety. ", "He had no idea how to protect him against the threat at hand. ", "Even with his many years of experience, his bodyguard skills did not prepare him for anything like this.", "\n\nWithout looking at Stan, Tormond kept his voice low and instructed, \"You stay here. ", "No matter what happens. ", "You're no good to me dead.\"", "\n\nStan had his eyes transfixed on the enemy and failed to notice Tormond's own set of pointy dental work protruding from under his upper lip.", "\n\n\"Aw. ", "Now you're speaking my language, demi-god. ", "I'll be happy to end your miserable existence and that of your father, as well.\"", "\n\nTormond masked his secret relief that Vengeance had accepted his challenge. ", "He'd lost most of his crew, including that worthless Hanna, and it was his last chance to turn this conflict around to his advantage and please his father. ", "He didn't want to think about what Loki would do to him if he failed this time. ", "Even though he was disappointed that he wouldn't get to flay Hanna alive as he was looking forward to doing, since that traitorous human had managed to do a decent job of it for him, he just might let the archeologist live. ", "Maybe.", "\n\n\"It's agreed then.", "\"Tormond attempted to take advantage by immediately tracing directly in front of Vengeance, weapon at the ready to take his head. ", "But a vampire as old as Vengeance couldn't be tricked so easily. ", "Demi-god or not, Vengeance was not intimidated and had learned a few ruses over the centuries. ", "He was ready for anything Tormond intended to throw his way.", "\n\nIn the split second, it took for Tormond to rematerialized in front of him, Vengeance traced back behind Tormond, wrapping his arm around his neck in a crushing manner that would have instantly killed a normal male and placing the tip of his sword at his throat. ", "A rivulet of blood trickled downward. ", "Tormond countered the attack with a menacing blow to his solar plexus causing Vengeance to stumble backward several yards, releasing his hold. ", "Tormond turned to face his foe, swiping a finger at the blood slowly seeping from his neck and viciously licking it from his appendage, while bringing his own sword up into play and lunging.", "\n\nVengeance recovered quickly and met Tormond's advances, defensively parrying his strikes. ", "He then moved evasively by dropping his agile body beneath Tormond's stealthy weapon, bracing himself on the ground with his free hand and plunging his sword arm forward, angling for his enemies ribs. ", "Tormond thwarted his attack but not without severe injury.", "\n\nStan watched as Tormond slouched over and touched his stomach, his hand came away covered in crimson blood. ", "Without thought for his own safety, Stan rushed toward his boss, his friend, the man who he respected as the father he'd never had. ", "He had to save him at all costs. ", "But as he drew closer, Tormond waved him off.", "\n\nVengeance observed the exchange between Tormond and his bodyguard. \"", "I think it's time to throw in the towel, Tormond. ", "You're damaged goods. ", "Give up and change your ways before I have to put an end to you. ", "I'm sure the Gods will be forgiving after the proper punishment has been meted out.\"", "\n\n\"I won't give up so easily, warrior. ", "I happen to like my life the way it is and intend to keep it that way. ", "You will not take my head.\" ", "Tormond managed to stand fully erect and raise his sword. ", "His arm containing a slight tremor at the effort. \"", "Ready when you are,\" he taunted with more conviction in his voice than he felt. ", "He was determined that if he died this day, it would be bravely.", "\n\n\"As you wish,\" Vengeance responded and advanced on him once again.", "\n\nThey continued to spar once more with brutal, vicious blow after blow. ", "Tormond's strength draining away as the blood flowed freely from his wound. ", "His failure to feed before the battle was taking its toll on his body, weakening him and slowing his ability to heal. ", "Like a vicious cycle, he needed blood to heal and to stop the blood that was currently steadily coursing down his body.", "\n\nTormond stumbled, falling to one knee, unable to muster the strength required to bring himself back to his feet. ", "His heaving chest and labored breathing now more painful than not. ", "He'd fought a good fight and knew his time had finally come. ", "Accepting his fate, he sighed with relief that he would not have to face Loki, ever again.", "\n\n\"Finish it then, warrior.\"", "\n\n\"As you wish,\" Vengeance replied gravely, and raising his arm back at chest level, he made ready to thrust his sword directly through Tormond's heart.", "\n\n\"No!\" ", "Stan roared and propelled himself between the beaconing sword and Tormond's withering body.", "\n\n*****\n\nLoki didn't understand why he had done it. ", "Tormond certainly didn't deserve the gift he'd bestowed. ", "He wasn't pure evil after all. ", "Being the god of mischief and malice didn't mean he was completely heartless, although cruelty did occupy a large part of his existence. ", "Mirth often filled the corners of his life at someone else's expense.", "\n\nMaybe it was the unusual human-like torment that he saw on Tormond's face or the un-god-like beseeching clearly demonstrated in his crystal ice blue eyes. ", "Or maybe it was the begging and imploring verbiage spewing from his anguished lips. ", "And for someone other than himself. ", "Strange that. ", "A human-esque sight Loki never thought to behold from his half human son. ", "Well, there wasn't much of that human part left, which suited Loki just fine. ", "What did he care? ", "The better to do his bidding.", "\n\nHe was aware of the loyalty and fondness Tormond's human servant had portrayed for his son. ", "He had watched Stan's devotion and allegiance on more than one occasion. ", "Such commitment would even serve him well, should his son fail, as he expected. ", "So, when Tormond had suddenly appeared and pleaded with Loki to save the human and reward the sacrifice of his life for his son's with immortality, it wasn't such a hard decision to make, as Loki himself would benefit from such a resolution. ", "But Tormond need not know the truth of it.", "\n\nHe watched now as Tormond sat very near his newly transformed underling's prone body, still shuddering from the violent alteration that had taken hold of his body. ", "Loki had never mastered the ritual created by Odin for his warriors and their secret brotherhood. ", "He cared not for the pain it caused when completed hastily. ", "It wasn't his pain to deal with, so he chose the simplest path and plowed through the process as quickly as possible. ", "To him, it was a simple procedure of reciting the required ritualistic words in a hurried mechanical manner, draining a portion of their essence, or soul, and depositing a small part of his own within them. ", "Odin was too soft, making a big deal of the transformation with his warriors by dragging the process out over a matter of hours. ", "Maybe it even had something to do with which God you shared your essence with, but again, Loki didn't care.", "\n\nAt least the seizing has stopped, Tormond thought. ", "I'll never live this down with my father. ", "He'll hold the begging over my head for eternity. ", "But I don't regret it. ", "Stan is almost like a son to me. ", "He's certainly the son I'll never have. ", "Unless you were a God, chain bonding and a blessing from the Goddess of Fertility, herself, was the only way to conceive once becoming immortal. ", "Did he consider ever taking such a step? ", "Would he ever find that one true mate to satisfy him for the rest of his days? ", "Would Freya give her blessing for him to bring forth a child?", "\n\nNo, no and hell no!", "\n\nHe imagined the only thing Freya would be granting him ever would be the size of the stick she impaled his swollen bodiless head on. ", "No, he'd chosen his path long ago and banished all thoughts of love and family from his life in exchange for his immortality and power. ", "Power was the only constant in his existence, along with the need for more and more.", "\n\nStan was the closest thing to family he had. ", "He'd had plans to reward Stan's loyalty with this gift of immortality, petitioning Loki to make the change, but just not so soon. ", "He would have preferred to ease him into the idea, but circumstances and time were not on his side and he'd had to beg his father to transform him. ", "He had never begged his father for anything. ", "Stupid, stupid, Stan. ", "You shouldn't have run in front of me. ", "Although, I am grateful. ", "His thoughts continued to flutter and buzz around his brain frantically like a lightning bug caught in a mason jar. ", "How will Stan take the news? ", "He will be completely blindsided with what he's about to learn.", "\n\n\"What news? ", "Did you say I'm blind? ", "I'm not blind...\"\n\nTormond turned his already healed body to face his friend and realized that he'd have to block his thoughts from him now. ", "Stan didn't notice that Tormond hadn't spoken the words aloud.", "\n\n\"How do you feel? ", "And no, you're not blind. ", "As a matter of fact, you're better than ever now and will feel more than one hundred percent within a few more hours.\"", "\n\nStan remained lying in the makeshift bed but cautiously patted himself down and glanced down his own body. \"", "I'm not sure. ", "I feel strange. ", "Strong, yet like I'm burned on the inside.\"", "\n\n\"That will pass soon and you'll feel like a new man,\" Tormond assured, the irony not lost on him.", "\n\nStan remembered his injury but felt nothing. ", "He ran his hands along his chest, surprised and confused that there was no pain or even a wound. \"", "But I was wounded. ", "I'm sure of it. ", "That thing...whatever it was...stabbed me with his sword. ", "I know I'm not imagining it.\" ", "He shuddered recalling the sight of the large man/vampire standing menacingly with pink tinged fangs and murderous piercing eyes. ", "His gaze rose to meet Tormond's. \"", "How can this be?\"", "\n\nLoki's mischievous laughter assaulted them from across the room. \"", "I'll leave this mess for you to clean up. ", "Good luck with that,\" he said sarcastically and then vanished into thin air.", "\n\nThe expression Stan wore on his face was beginning to look somewhat terrified, his eyes widening ever further as Tormond leaped into his explanation. ", "He couldn't avoid it any longer.", "\n\nUsing his usual dramatic flair, Tormond looked directly at Stan and projected his thoughts. ", "You died saving me, Stan, but you're not dead now. ", "I asked my father to save you, to make you like me...like those people we were fighting today...immortal.", "\n\nSlowly, realization enlightened Stan and the reactions showed clearly on his pale, strained face. ", "Shock replaced the terror that had previously ruled. ", "Then wonder, as thoughts whirled through his overloaded mind.", "\n\nWhat is he talking about? ", "This can't be. ", "It's impossible. ", "But Mr. T wouldn't tell me something like this unless it was true. ", "And I have no reason to doubt him. ", "He's always been good to me.", "\n\nAnd finally, acceptance.", "\n\nWow, immortal. ", "I can't die. ", "I'll live forever. ", "Oh, my God. ", "I'll live forever...\n\nTormond patiently listened in while Stan worked through his thoughts of what was happening to him. ", "He knew there would be a million endless questions to answer soon enough.", "\n\n\"Being transformed doesn't mean you can't die, Stan. ", "But you have a better chance at beating the odds. ", "You'll heal faster if wounded and injuries or illnesses that would end the life of a human won't affect you any longer. ", "But, should you sustain major injuries that you are too weak or can't heal fast enough from, or if your heart is punctured or your head removed, you will cease to exist and turn into a pile of gray ash to float away on the wind.\"", "\n\nAshes to ashes.", "\n\nAs Tormond watched his reaction, he could see the rage transforming on his face. ", "His normally serious sky blue eyes turned to hardened crystal daggers that Tormond felt straight through the walls of his chest as if they'd physically made contact with his skin. ", "He knew he had to be cautious with Stan and try to maintain some level of calmness. ", "Stan did not realize how strong he was now and even though Tormond was stronger and more powerful, he didn't want to cause Stan further pain in trying to contain him.", "\n\nStan quickly sat up. \"", "Wait, wait, wait...you said like them. ", "I saw their fangs. ", "Are you telling me that I'm a vampire? ", "That you're a vampire?!\"", "\n\n\"Yes, Stan. ", "That's exactly what I'm saying. ", "But you're not only a vampire. ", "You're stronger and possess powers that you've never dreamed of.\"", "\n\n\"What about blood? ", "I won't drink blood.\" ", "He seemed adamant on that point.", "\n\n\"Actually, you will.\" ", "There was no cruelty or sarcasm in his tone. ", "Tormond simply wanted to impart the truth. ", "He hoped Stan would accept his fate and even come to be grateful for it one day.", "\n\n\"You won't be able to help yourself. ", "You can fight it, but the craving will eventually win. ", "And you will enjoy it.\" ", "Tormond paused, trying to find another approach but coming up blank. \"", "There's a lot to learn and adapt to. ", "Just take it slowly. ", "I promise everything will be all right.\"", "\n\nStan continued to sit. ", "His shoulders slumped in defeat, looking very dejected. ", "Hopeless.", "\n\n\"I'm sorry, Stan, if I've given you something that you didn't want. ", "There was no time and I couldn't let you die in my place like that. ", "Even though you may hate me now for what I've done to you, please know that I am grateful and will forever be in your debt.\"", "\n\n\"I understand, Mr. T, and I don't hate you or blame you. ", "I know you did what you thought was right and for the right reasons, even if it may not have been right for me. ", "Just give me some time to get used to all this.\" ", "Then with disgust, \"I'm still not drinking blood from...humans. ", "Can I use animals instead?\"", "\n\n\"You can, but it's not as nourishing and tastes disgusting.\" ", "Tormond made a tortured face while chills and shivers raced throughout his body like someone had dragged their nails across a blackboard.", "\n\n\"I saw a movie once where they drank bagged blood. ", "Can I do that?\"", "\n\n\"Yes, you can, but you'll be missing out on the euphoria of taking a young woman in your arms and quenching yourself fully in all her body has to offer. ", "Plus, you'll need to have sex regularly to feed off the woman's aura.\"", "\n\nStan couldn't miss the dreamy, faraway look in Tormond's eyes as if he was reliving a specific memorable experience. ", "Still, he didn't think he'd be able to harm a person in such a way. ", "He was strong and had faced adversity throughout his life. ", "This would just be one more challenge to overcome. ", "He refused to become the monster that he now imagined Tormond to be.", "\n\nYea, he thought to himself. ", "Just another hurdle...\n\n*****\n\nPost battle cleanup was somewhat extensive. ", "Dead demons may turn to ash and drift away into the salty sea air, but the minions had to be disposed of. ", "Vengeance, Steele and Vex traced in and out of the ghastly scene depositing the mutilated remains deep into the nearby frost covered forest. ", "If they were ever found, it would appear that a wild brown bear or polar bear had attacked and mauled them. ", "Humans out that far into the wilderness could only be up to no good and probably were illegally poaching. ", "Myste lent a hand with a small rainstorm, her mane no longer jet black, now a mélange of blonde and purple, twirling like a mini tornado. ", "She cackled with glee as the wind and rain washed away the residue, leaving no evidence that a battle had ever transpired in this peaceful little place by the sea.", "\n\nThe few crew members currently on staff at the dig site were easily compelled to forget anything they may have seen, including the warriors' presence and even Aaron's short term return. ", "His assistant, Jake, now believed Aaron to still be back in Oregon and nothing out of the ordinary had ever transpired. ", "Unfortunately, in the short time they were at the site, there was still no evidence of the EOD.", "\n\nThe victory was bittersweet with Tormond's unforeseen escape. ", "When he looked like he had reached the end of his rope, the sacrifice of his bodyguard seemed to rejuvenate his strength and tied a preverbal knot into it. ", "He found some reserved power deep down inside his cursed existence. ", "The battleground had grown silent as Tormond grasped the human in his arms and roared with mighty hatred at the warriors. ", "He silently commanded Heidi and Holden to join him, then without warning, he traced the group, along with the dead human, away to safety.", "\n\nVengeance hadn't meant to kill the human male. ", "He had sensed no evil or threat in the man. ", "His blow was intended for the malicious demi-god that had challenged him. ", "His only regret was that the man had prevented him from delivering the deadly blow. ", "The man, himself, got what he deserved by his own actions. ", "He must have been mad. ", "No one in their right mind would have sacrificed themselves for such a vile monster as Tormond, not even his own demons. ", "He lured them all into his service with the promise of immortality, which they unknowingly would never achieve. ", "He wondered just what it would take for Tormond to actually allow another to be transformed.", "\n\nAs soon as they boarded the jet, Vengeance contacted Thunder about sending out a team to Vegas for recon purposes. ", "He should also check with Zahara, in case she had any visions or wisdom to throw in the mix. ", "The warriors needed to stay on top of this and in control of the situation, least it somehow backfire on them. ", "It was certainly no time to not keep their guard up.", "\n\nLuckily, the human in their care had come away unscathed. ", "He had to once again return with them to their base of operation. ", "That had not been the original plan. ", "They had hoped to locate the EOD or some evidence leading to its whereabouts then intended to wipe his memory and let him carry on as before once they made sure he was safe. ", "Vengeance knew this attraction between Aaron and Danielle couldn't go on much longer. ", "He was afraid that she was already going to pay a heavy price and he didn't want to see her suffer such a loss. ", "Not much could be done about it right now, though. ", "With a sigh, he sat back in his oversized seat and closed his weary eyes.", "\n\nEmeline peaked into the bed chamber of the jet where Aaron held Danielle while she rested and continued healing. ", "She'd done all she could in healing Danielle, but her serious injuries still needed some time to completely mend. ", "Resting on the flight home should do it. ", "With their fast healing abilities, the remaining warriors were able to mend their abrasions without intervention. ", "Seeing that Danielle was resting comfortably with her head on Aaron's chest, Emeline softly reclosed the door to the chamber, giving them privacy.", "\n\nDanielle stirred and tilted up her face to look at Aaron. ", "His sense of remorse coursed through her so strongly she couldn't ignore it. ", "Along with that seemed to be a feeling of resolve, which made her uneasy.", "\n\n\"Please stop blaming yourself,\" she pleaded.", "\n\n\"I can't. ", "Every time I think of how close I came to losing you...\"\n\n\"But you didn't. ", "It's over now. ", "I'm still here. ", "You're still here.\" ", "Little did he know all she meant by that statement. ", "Her next flight home should have been without him, leaving him behind with no memory left of her. ", "But fate had given her a reprieve, at least for now.", "\n\n\"Yes, thank God for that,\" he sighed. \"", "I've come to a decision and I need to know what you think, Danielle.\"", "\n\nHis statement made her very apprehensive. ", "Here was the resolution she'd been dreading. ", "How could he make such a decision when he didn't have all the facts to work with? ", "Of course, he didn't know that he was missing a huge piece of the pie that he was partaking of. ", "But she was bound by her oath for all eternity. ", "He knew too much already for his own good.", "\n\nShe pasted on a slight smile, bit the loaded bullet and responded as lightly as she could bear, \"What decision might that be?\"", "\n\n\"I'm going to quit my job. ", "Yes, I am,\" he said with conviction, nodding to himself.", "\n\nAs she sat up to look him square in the face, he continued, \"I'm going to quit my job and stay with you.\"", "\n\n\"But Aaron, you can't! ", "You love your job. ", "It is your dream and you worked so hard to get where you are. ", "You love what you do.\"", "\n\n\"Yes, I do. ", "But I don't have to do it for the university. ", "I can research and commit myself to helping your people find the relics you need to put Loki out of business.\"", "\n\nAs she stared dumbstruck at him, she thought, Oh, Goddess. ", "If only.", "\n\n\"Marry me, Danielle. ", "Be my wife. ", "Let me stay with you and love you. ", "I know it won't be forever. ", "I know that if I'm lucky enough to have this time with you, I'll grow old and die someday, but I want whatever time I can get with you. ", "I've been alone all my life and I know now it was because I was waiting for you.\"", "\n\nHe tenderly cupped her face in his hands, kissing away the salty tears that escaped down the sides of her face.", "\n\n\"I feel it so surely...like it's the answer I've been searching for and didn't even know the question until you came into my life. ", "I'm so attuned to you. ", "I even feel you wanting this, too, but it's clouded by reservation. ", "How is it that I can feel and know these things if we're not meant to be?\"", "\n\n\"Oh Aaron, I don't know what to say.\" ", "For surely, she did feel those things and her mind was filled with conflict and confusion.", "\n\n\"Then just say 'Yes'.\" ", "His eyes implored her.", "\n\nShe had to make him understand somehow that this was impossible, but she didn't have the strength left within her to do it, so she decided to compromise for the moment.", "\n\n\"Aaron, please listen...and know that I want the same things you do. ", "It's just not that simple, love. ", "I wish it were, but it's not. ", "I have to ask you to give me a little time. ", "I have an idea, but I don't know...,\" her voice trailed off, without finishing her thought aloud.", "\n\nAaron sought her eyes, seeing the truth of her words in them, he acquiesced.", "\n\n\"Okay, I understand. ", "I really shouldn't have put you through this now. ", "You're still recovering and I wasn't thinking clearly. ", "Forgive me. ", "I guess I just panicked at the thought of almost losing you. ", "As long as I know you'll consider it, I can wait a while longer.\" ", "He paused, placing light teasing kisses from one corner of her mouth to the other. \"", "I love you, Danielle.\"", "\n\n\"I promise not to make you wait too much longer. ", "I love you, too, Aaron. ", "More than you know.\"", "\n\nShe did have an idea in mind. ", "It was a long shot, but being a demi-goddess and the daughter of Freya should have some kind of perk to go along with it. ", "She'd never used her clout for anything – ever. ", "It was time to see just what her lineage was actually worth. ", "She was going to do something she'd never done before – pay an unexpected visit to mom.", "\n\n*****\n\n# Chapter Eighteen\n\nShe was summoned to Loki's Temple. ", "Contact with her father was not unusual as they had a fairly comfortable relationship, but normally he preferred to mind link with her. ", "There they would enjoy the pretense of a peaceful meal and she would share the latest happenings of her life; how ruthless she was in her recent business dealings, whom she was corrupting, and whom she was able to blackmail and practically enslave to do her bidding. ", "The more powerful the person, the better for her to be able to use for her own desires and gain.", "\n\nShe entered his private quarters as requested. ", "She liked to dress for her father, wearing the traditional long, flowing robes that accented her perfect curves in all the right places and leaving very little to the imagination where her generous breasts were concerned. ", "Her long jet black hair flowed over her slender shoulders of soft, flawless alabaster skin, dropping in brilliant waves that stretched down to her full hips, brushing against them seductively. ", "She kicked off the sandals she wore near the arched entrance and glided across the spacious room, her smile fully radiating the excitement she felt in being called to her father's presence. ", "She adored and aspired to be just like him.", "\n\nShe found Loki sitting in his majestic chair that was a close match, but slightly smaller, to his actual throne which stood in his ornate throne room. ", "He sat behind an equally impressive desk and smiled brightly when she came upon him.", "\n\n\"Lustra, my dear, dear daughter.\"", "\n\n\"Hello, Father. ", "I've come as you bid of me. ", "Thank you for allowing me to visit.\" ", "Her voice was silky smooth and sweet, like a melody on the wind. ", "So unlike her usual demeanor, but seeing her father also put her in a good mood.", "\n\n\"Now, now, Lustra. ", "You know you are always welcome here. ", "I'm so happy you came.\"", "\n\nShe bowed her head in reverence. ", "He may be her father, but he was still the God of Deceit and worthy of her worship and admiration.", "\n\n\"Come, I have a gift for you,\" he said as he stood and took her arm, leading her through a small anteroom and into a lushly decorated lounge.", "\n\nThere, resting on a red velvet settee with gold gilded edges was one of the most beautiful men she'd ever seen. ", "Dressed merely in a loin cloth that left little to the imagination, barely concealing his manly bits, his perfectly proportioned body was draped leisurely across the extravagant divan. ", "His well-defined chest moved up and down in a steady rhythm as he reposed comfortably. ", "He had hair of golden sunshine to match the tone of his skin that had been kissed by the sun. ", "His muscular arms were stretched above his head and held magically secured, as she was sure the rest of him was, leaving him in a tranquil, although helpless, position and at her mercy to do with as she pleased. ", "Perfect in every way. ", "Perfect for her. ", "Lustra's eyes, the color of the deepest ocean depths, flashed brightly with her approval.", "\n\n\"Oh, Father. ", "How wonderful. ", "You've brought me a blood slave.\" ", "She clapped her hands together and did a quick little skipping dance like a small child might do when delighted. \"", "And a quite handsome one, at that,\" she added as she got closer and felt her hunger rising.", "\n\nShe threw her arms around his neck and pressed a soft kiss to his cheek. ", "Loki reciprocated by hugging her back around her waist. ", "He loved seeing and making her happy. ", "Of all of his children over the many, many years, she was his favorite child, after all. ", "Only the favored few were worthy of his gift of immortality and not all of those were able to remain in his good graces and keep the status.", "\n\n\"What did I ever do to deserve such a gift?\" ", "she inquired. ", "Lustra was never suspicious of Loki's motives. ", "She'd seen him interact with some of his other offspring and he could be malicious and cruel at times, but never with her. ", "And she agreed with him on his choice of punishments. ", "They always deserved whatever he bestowed on them.", "\n\nHe pulled back from her and grasped her smaller hands in his. \"", "It's not what you've done, but what you are going to do, my love.\"", "\n\n\"Anything for you, Father. ", "What will you have of me?\"", "\n\nLoki saw the sincerity in her face, how she hung on his every word. ", "Why hadn't he given this important responsibility to her in the first place? ", "He should have never trusted it to Tormond. ", "Normally, Tormond pleased him, even if he had to coax it out of him at times via painful mind links. ", "But Lustra never disappointed. ", "She was definitely her father's daughter.", "\n\n\"Thank you, Daughter. ", "I knew I could count on you most of all. ", "Your earthly sibling, Tormond, has fallen short too often of late. ", "I'm afraid his immortality may be coming to an end very soon.\"", "\n\nOh shit! ", "Lustra knew how to read between the Loki-lines. ", "The look on his face told all. ", "Tormond had pissed Loki off one too many times and he was toast - literally. ", "Oh well, she mentally shrugged. ", "His tough luck. ", "So long, brother mine. ", "Ashes to ashes and all that.", "\n\n\"I love how you think, daughter,\" he chortled loudly. \"", "You're so witty!\"", "\n\nOops.", "\n\n\"It's great to see you laugh, Father. ", "So glad I could be the cause,\" she laughed in return, then added more seriously, \"Of course, you know I will do whatever you need me to do.\"", "\n\n\"Yes, you will,\" he said confidently. \"", "Now, let me explain what I need and how we shall go about getting it...\"\n\nSometime later, as Lustra stroked and feasted on her scrumptious delicacy, courtesy of her father, she began plotting and planning, not only taking over Tormond's Las Vegas operation, but in retrieving the three lost relics so Loki could take his much-desired place of power among the Gods, and wiping those pesky warriors off the face of the earth. ", "All she needed to do was find the Eye of Odin, the Heart of Hope and Spear of Truth before they did. ", "She relished the challenge before her and would pay her brother a visit very soon.", "\n\n*****\n\n\"I hope you don't mind that I invited a few of the others to join us tonight.\"", "\n\nZahara leaned into where Danielle and Aaron were seated, patiently waiting for the details of what tonight's ritual would consist of. ", "Aaron hoped it wasn't anything too painful, if painful at all. ", "He really didn't care whether they discovered the cause, or the solution for that matter, of the mystery surrounding the binding chain that he still wore about his neck. ", "It suited him just fine. ", "Especially if it meant that he'd be able to keep his connection with Danielle, which was all he currently cared about.", "\n\n\"No, it's fine with me,\" Danielle answered sedately as she watched several of her fellow warriors file into the conference room they presently occupied.", "\n\nAaron nodded in agreement.", "\n\nAs he looked around the room, he noted the table and some surrounding surfaces were meticulously cluttered with varying styles, sizes and colors of candles. ", "To his untrained eye, they seemed haphazardly gathered and strewn about, but he suspected their disbursement was purposeful and each was placed to enhance the ritual about to commence. ", "There was no additional lighting in the midsized chamber and images of spooky séances from horror movies past slipped through his befuddled mind. ", "He'd never admit it, but he was a little spooked himself. ", "Of course, he loved solving puzzles, learning about the past and uncovering historical relics and facts. ", "As an archeologist, it was his nature. ", "But this hit too close to home. ", "This was about him and he was pretty sure that whatever was about to take place was going to happen to him.", "\n\nGreetings were exchanged and everyone seated themselves around the table. ", "The mood seemed to be one of reverence and silence, so much so that it was almost stifling until their last two guests arrived.", "\n\nWithout noticing the quiet disposition of the room, Steele spouted, \"And that's when I told him, 'Any similarity between you and a human is purely coincidental.'\"", "\n\n\"And of course, he thought you were just insulting him,\" Turbo responded.", "\n\nBoth warriors guffawed loudly until they looked around them, suddenly clamping down on their private party.", "\n\n\"Oh shit. ", "Sorry everyone. ", "Didn't mean to interrupt.\"", "\n\n\"No problem. ", "We were just about to start,\" Zahara offered. \"", "Please come in and have a seat. ", "I want to explain a little of what we're going to try to accomplish tonight. ", "I'm not sure exactly what will happen, if anything, but with your support, I'm sure we can handle it. ", "Not that it's dangerous.\" ", "She paused as a look of thoughtfulness flashed across her face. \"", "At least I don't believe it isn't,\" she said in a lower, slightly murmured tone.", "\n\nThunder was among the observers, deciding this experiment was too important to not warrant his personal attention. \"", "What kind of danger do you expect?\"", "\n\n\"I don't expect any. ", "Really. ", "Let me explain and then I can answer any questions you all may have.\"", "\n\nWith murmurs of consent and nods around the room, she continued, \"There is unsubstantiated evidence that Aaron may be the descendant of Alarr Janssen, Danielle's former chain bonded mate.\"", "\n\n\"I know of what evidence you speak, Zahara, but I believe it would be best if you explained it to the group,\" Thunder stated.", "\n\n\"Simply put, an old and very dated blood sample that was taken from the chain, one we assume is Alarr's blood, matches Aaron's blood sample, almost identically.\"", "\n\n\"Yes,\" Steele added. \"", "Along with the tests that Emeline and Annika ran, Turbo and I both sampled the blood via taste and smell, and we agree with the females' assessment.\"", "\n\nTurbo nodded, adding his agreement to Steele's. \"", "Yes, surprisingly similar.\"", "\n\nZahara continued, \"Because of this possibility, we're trying to attempt something called a Descendants Ritual. ", "It has also been called Ancestry Worship or Ancestry Veneration. ", "It is believed that departed ancestors have the ability to communicate with the living through dreams and by possessing their descendants. ", "This ritual is usually used by many Earthly religions to guide the descendant's path in life and even stems from some of our own Nordic roots. ", "We're not assured of any success because this ritual usually only reaches a more recent ancestor. ", "On average, a departed ancestor will take about one to three generations to lose attachment to his previous life on Earth before he is unreachable. ", "One generation can be taken as roughly thirty years. ", "In other words, people are most affected by the generations that pertain from their parents to great-grandparents. ", "Of course, we're way off course for such a time period here, but we're hoping that because Alarr was brought over and made immortal at one time, that we might have better odds of reaching him. ", "Hope is all we have at this point.\"", "\n\n\"Excuse me, but just how exactly do you plan to do this?\" ", "Aaron asked, swallowing audibly and looking a bit peaked.", "\n\n\"Don't worry, Aaron. ", "I promise you'll be safe and there should be no pain involved. ", "Not from the research I've conducted. ", "You will simply enter a dream state and should wake feeling rested and well. ", "Kind of like hypnosis,\" she said with a flourished wave of her hand in the air.", "\n\nKind of like a test subject, Aaron thought.", "\n\n\"And besides, I'm here to make sure it all goes well,\" Emeline added.", "\n\n\"And me,\" said Annika.", "\n\nHaving seen them in action, Aaron acknowledged that Emeline and Annika's attributes of healing and magic could be helpful. ", "He relaxed a bit as Danielle encircled his hand in hers under the table. ", "She'd been quiet until now, but he could almost hear her mentally convincing herself that everything would be all right. ", "Strange that.", "\n\nHe gave her a knowing smile whispering, \"It will be fine.\"", "\n\nDanielle had that watched feeling again. ", "But I shouldn't have it. ", "That only happens at the dig site. ", "No spectral being could enter here without all hell breaking loose. ", "It's got to be the eeriness of this whole ritual thing. ", "I must be imagining it due to the stress of the situation. ", "Yea, that's it.", "\n\n\"If there are no more questions, let's begin. ", "Everyone please gather closer to the table and join hands.\" ", "Turning toward the test subject she said, \"Aaron, I need you to lie up on the table on your back, please.\"", "\n\nDanielle gave his hand one last squeeze and, as gracefully as possible, Aaron climbed on top of the conference table, taking his position between the circle of candles placed there.", "\n\nZahara noticed Aaron's awkwardness as she placed a silk pillow underneath his head. \"", "Good,\" she whispered to him. \"", "Just place your hands wherever you're most comfortable and try to relax. ", "This shouldn't take long.\"", "\n\n\"Is it okay if I stand here?\" ", "Danielle asked, taking up a position near Aaron's head.", "\n\n\"Yes, that would great.\" ", "Then she added for her ears only, In case we need you, too.", "\n\nDanielle silently let Zahara know she understood.", "\n\nAs everyone settled into their positions, Aaron thought the scene resembled a séance from childhood and wondered when they would all stick their digits underneath the edge of his prone body and start chanting 'Light as a feather, stiff as a board.' ", "Only this wasn't spooky fun and certainly nothing to laugh about.", "\n\nInstead of the juvenile game, Zahara began to chant in earnest, \"We remember. ", "We remember. ", "Nothing is ever lost. ", "Nothing is ever forgotten. ", "Ancestors, draw near and bless this gathering. ", "Hear us, Old Ones, our ancestors and kin. ", "You whose blood flows in our veins. ", "From far beyond this mortal plane, mothers and fathers of old, we ask that you return again, to share with us the mysteries and secrets long untold. ", "Be with us here tonight.\"", "\n\nA mystic wind swept through the room, flickering the flames of the many candles, but strangely not extinguishing them. ", "The wind wasn't chilling cold as one might expect, but oddly comforting and soothing as it flowed through the air, swirling around all present. ", "Everyone turned their heads in Myste's direction with looks of accusation.", "\n\n\"Wasn't me,\" she sing-songed with conviction. \"", "I swear.\"", "\n\nBut Aaron didn't hear Myste. ", "He no longer saw the warriors and candles that bordered him. ", "He was lost in the atmosphere that shrouded him, drifting into a soundless, sightless state that resembled a deeper sleep than he'd ever experienced. ", "With no thought, no feeling. ", "Only absolute rest.", "\n\nZahara peered at Aaron and, pleased with his state of being, continued the chant. \"", "We gather here this night to ask the father of Aaron, Alarr, to make yourself known. ", "Alarr, if you be the father we seek, speak to us now.\"", "\n\nTo everyone's surprise, Aaron calmly and gracefully rose from his prone form into a sitting position with his legs crossed yoga style in front of him, hands resting palm upward on his knees as if he were meditating. ", "His face showed no lingering of the trance-like guise he previously wore, but his features did seem to waver slightly, giving the illusion of melding or transitioning slightly into another face altogether, then fading, never quite setting in stone. ", "He said nothing but searched the faces that encircled him.", "\n\nZahara caught his attention with a look and spoke directly to him. \"", "Who are you?\"", "\n\n\"I am Alarr, an Officer in the service of the Freyodin Warriors. ", "I know not you, but I see my Danielle is here to greet me.\"", "\n\nHis voice held the same gruffness Danielle remembered, but he looked like Aaron, mostly. ", "The entity seemed to have taken possession of this vessel that was offered to him. ", "Except for his eyes. ", "They were still blue but lacked the deep drowning blue quality that Aaron's held. ", "She found it unnerving to address Aaron in this manner. ", "Confusion as to whom she actually spoke played havoc in her head flashing old and new memories alike. ", "She didn't quite know who, what or how to address the presence before her.", "\n\n\"Yes, I am here,\" she said weakly. ", "That was all she could manage. ", "As she realized just who it was she was really talking to, hurtful memories crowded the corners of her mind. ", "Her facial features and heart hardened to a degree she never thought possible.", "\n\nHow dare he call me 'his Danielle.'", "\n\nStill, she knew it wouldn't be prudent to piss off Alarr now. ", "There would be nothing gained from alienating him, so she metaphorically bit her tongue, although she wasn't sure just where the initiative came from to perform such a feat. ", "Her entire being wanted to give him the tongue lashing he so righteously desired. ", "She so hoped that he didn't share a mind link with her now that he'd reentered the mortal plane or her thoughts would surely send him right back to the grave. ", "Where he belongs.", "\n\nAlarr didn't react to her well-hidden hostility. ", "He looked at her with the same innocence he did years before, but with a slight variation.", "\n\n\"You hide it well, Danielle, but I can see the hurt you hold within you. ", "My coming here has two purposes. ", "First, to tell you that I was wrong and what I did to you was unforgivable, although my actions were driven by more ignorance than greed. ", "I never meant you harm and never meant to cause you so many years of suffering. ", "I beseech you to forgive me, but will hold you blameless if you cannot.\" ", "He held out the hand he embodied to her.", "\n\nFury and hurt warred within her, eventually turning to acceptance. ", "She'd been mad far too long. ", "It was time to let it go. ", "She could never move forward until she let go of the past and to let go, she had to forgive. ", "Danielle softened and accepted his peace offering, expecting to feel Aaron's hand within her own, and astonished to recognize Alarr's touch through the vessel. ", "She gasped at the realization which caused Alarr to smile. ", "A smile she knew from a past long ago. ", "She had no doubt of who was before her at that moment.", "\n\nAlarr looked her in the eyes, placed a light kiss in the palm of her hand and bowed his head in supplication. ", "Satisfied, he then turned back to Zahara.", "\n\n\"My second purpose in answering your call tonight is to confirm that Aaron is my son of many generations.\" ", "He looked around the circle of warriors. \"", "Some of your faces I remember. ", "Others are new to me. ", "Know this about my son, Aaron: I feel the affection he has for my Danielle within him. ", "Know that he is true, faithful and good of spirit. ", "A noble warrior he would make.\"", "\n\nHe turned once again to Danielle, his countenance beginning to waver and his eyes began to darken to a hue of deep cerulean. \"", "I haven't much time left. ", "Be good to each other. ", "Tell him he has my blessing,\" he whispered to her as his eyes closed and Aaron's body slouched back to the table beneath him. ", "Turbo and Steele both reached out to soften the impact of Aaron hitting the table.", "\n\n\"Thank you, Alarr, Forefather of Aaron,\" Zahara intoned. \"", "The winds of time have carried you to this place. ", "We have been honored by your company. ", "Depart now in peace until we meet again.\"", "\n\nThat same mystic wind returned, sweeping through the room, this time extinguishing the flickering flames of the candles scattered about and the room was pitched into darkness.", "\n\n\"I've got the lights,\" someone said and the room brightened around them.", "\n\n\"Well, that clinches it. ", "We've got our answer now.\"", "\n\n\"Not hardly, Myste,\" Makayla said. \"", "The only thing we know for sure now is that this is definitely Alarr's chain and Aaron is definitely his descendant.\"", "\n\n\"Close, but not quite,\" Zahara cut in. \"", "My best educated guess it that the chain simply acknowledges Aaron is Alarr due to their relation. ", "I'm starting to think we may never get it off of his neck – for that reason alone.\" ", "She turned to her friend, \"I'm really sorry, Danielle.\"", "\n\nDanielle thought for a moment and looked down at Aaron still snoozing peacefully on the conference table. ", "Annika had kindly conjured up a soft surface for him and replaced the pillow beneath his head.", "\n\n\"No, it's okay.\" ", "Then she addressed the remaining group. \"", "Thank you, everyone, for supporting us in our time of need.\"", "\n\nDanielle sighed as she sat back into her chair pondering how she felt. ", "Was she defeated? ", "What did she really want to come out of all of this? ", "She reeled as the realization that she had in fact been hiding her true feelings smacked her in the face. ", "Deep down, she had known she was fooling herself, but to finally admit it was somehow freeing in a major way, as if something that was closed off inside her for too long had opened wide, letting in a life-giving breath of fresh air.", "\n\n\"Aaron doesn't look to being awake anytime soon,\" she said as she rose from her chair and started for the door, \"and, if you'll excuse me...I've got an errand to run.\"", "\n\nThunder noted that she said the last with definitive conviction and a look of determination on her face.", "\n\nEmeline gently grabbed her arm. \"", "You're not doing what I think you're doing...are you?\"", "\n\n\"Yea, I think maybe I am.\"", "\n\n*****\n\nShe knew her mind was made up as she raced into the woods toward her destination. ", "There was no turning back now. ", "She was willing to do whatever it took, take whatever time she could take, give up whatever she had to give up. ", "To be with Aaron. ", "Forever now meant nothing if she had to spend it alone. ", "Eight hundred years was enough. ", "She wouldn't settle for being content. ", "She couldn't go on and on without love like she had before. ", "She knew what she was giving up and it didn't matter. ", "Not one little bit.", "\n\nAaron would, of course, be livid if he knew what she planned to do, but what he didn't know now, wouldn't hurt him. ", "Sometimes it's better to ask forgiveness than permission. ", "Nice motto, that one. ", "She'd have to incorporate more of that within her new life. ", "If Freya would give it to her, that is.", "\n\nShe located the portal hidden within the woods, visible only to her kind. ", "It was at the base of an old Ponderosa pine tree. ", "Sometimes she loved to sit and lean against the trunk among the deep-seated roots and fallen needles to relax after a stressful mission, allowing her mind to wander and be free. ", "This time, as she knelt at the base of her comfortable old friend, she prepared her mind for a different kind of journey. ", "And if all went well, it would be her last time to make this particular trip.", "\n\nShe closed her eyes and envisioned her destination – Valhalla – and more specifically, her mother's domain that she occupied when staying in Asgard. ", "Tracing short distances from place to place on the mortal realm was much easier than transporting to another world, making the portal necessary, and this was one trip she hadn't made in quite some time. ", "Her lack of a relationship with Freya was not a secret and didn't even register as a blip on her radar nowadays. ", "But this visit was vital. ", "She would demand an audience with Freya if she tried to put her off.", "\n\nArriving in the desired hall within milliseconds, she grabbed the nearest marble pillar, bracing herself so as not to fall down from the dizzying effects that followed. ", "She swallowed the wave of nausea that sometimes accompanied such effects, breathing deeply to dispel the sickness until it passed.", "\n\nGathering her courage and her wits, she approached the guards stationed at the entry to Freya's domain.", "\n\n\"I wish to speak with my mother. ", "Please inform her that I am here,\" she said with as much authority as she could muster, while still trying to remain civil and somewhat respectful. ", "No use making any enemies. ", "At least not yet. ", "Catching bees with honey and all that.", "\n\nTo her surprise, the guards immediately open the oversized gilded doors allowing her admittance. \"", "You are expected, Danielle, daughter of Freya.\"", "\n\nHot damn! ", "I should try using authority more often. ", "Wait a minute...expected? ", "Oh shit.", "\n\nBut she refused to let her confusion and suspicion show. ", "Re-gathering her courage up around her like an invisible barricade, she forged through the open doors with what she hoped looked like confidence.", "\n\nAlthough it had been many years since she'd graced her mother with her presence, Freya's throne room was just as she remembered it, over-the-top and richly ornate. ", "Danielle expected to look across the vast room with its vaulted ceilings dripping with cherub carvings donning gold tipped wings and see the Queen of the Valkyries herself, perched on her also over-the-top golden throne that screamed 'Look at me! ", "Look at me!' ", "But she was sadly mistaken. ", "Instead, she was ushered through the room to the entrance of the queen's private quarters. ", "This was hugely uncommon and out of character. ", "She couldn't remember the last time she had been in her mother's private quarters. ", "Surely, something must be afoot.", "\n\nWas Freya ill or injured and too weak to greet visitors in the usual fashion? ", "Or was Danielle, herself, in some kind of trouble or dilemma that required privacy to discuss. ", "This trouble had to do with the chain. ", "That's all she could fathom. ", "Freya had instructed her to retrieve it and so far, that had been impossible. ", "Oh, this was going to be bad indeed. ", "She felt it to her bones.", "\n\nWell, whatever it was, she would just deal with it. ", "Or not. ", "Depending on what impact it would have on her newly chosen future life – or at least what she hoped would be her newly chosen future life. ", "That remained to be seen. ", "Strengthening her resolve, she slowly, but boldly, opened the door, immediately feeling the presence of a woman seated across the room. ", "There in all her majestic glory, looking very beautiful and healthy indeed, sat the Ruler of Shieldmaidens, the Goddess of love, beauty, fertility, war and witchcraft, and by far the most glorious of all the goddesses in existence.", "\n\nFreya stood to approach Danielle, adjusting her flowing royal blue robes about her curvaceous body as she virtually glided across the polished stone floor. ", "Her strawberry blonde locks gathered in intricate braids and artfully arranged around the crown of her head ended just at the slender cinched waist of her regal gown. ", "Strangely, Danielle noted she wore no slippers and her unpainted cream colored toes peeked out from under the hem of her dress as she strode closer.", "\n\nNo shoes? ", "Miss prim and proper, royalty and all that, blah, blah, blah... Not the time. ", "She'd ponder that later. ", "Much later, if at all.", "\n\n\"Danielle,\" she said with a true fondness in her voice. \"", "It's about time you came to see me.\" ", "Surprisingly, Freya had management to admonish Danielle while at the same time keeping a welcoming motherly tone.", "\n\nChecking to see if she needed to pick her jaw up off the floor, Danielle lost her determined demeanor for a moment. \"", "What?\" ", "she replied with a staunch look of puzzlement she couldn't hide to save her soul and knowing that her reply was extremely inappropriate. ", "A thwacking sound filled the room as she immediately slapped her hand over her own mouth to restrict any further garbage from spewing forth.", "\n\n\"Oh, my! ", "You should see your face,\" Freya laughed heartily. \"", "Your eyes are big as teacups! ", "Put your tongue back in your mouth, dear. ", "That's not a good look for you,\" she teased further.", "\n\nDanielle was at a complete loss – of words, thoughts and actions. ", "She was completely stunned by the circumstances at hand. ", "She scarcely remembered why she was here in the first place. ", "Oh yeah...that. ", "Mustn't blunder this entirely before I've even begun.", "\n\nFreya gently reached out and removed the hand that was covering Danielle's mouth. \"", "It's quite all right, dear. ", "I know you've come to speak with me about some very important matters. ", "I've been waiting for you. ", "It took a little longer than I originally thought, though...\" Her musings strayed as she spoke tapping her index finger against her bottom lip.", "\n\nDon't be intimidated...Don't be intimidated, Danielle chanted internally.", "\n\n\"What do you mean; you've been waiting for me?\" ", "Danielle demanded with as much respect as she could muster. ", "Freya was a Goddess, after all. ", "And her mother. ", "Let's not forget that little tidbit. ", "Whoopee!", "\n\nEven if Danielle was a little put out and confused. ", "Make that a lot. ", "But no matter how confused she was, she was determined and silently vowed she wouldn't be put off her course of action. ", "She had to achieve her goal...or she would be lost for all eternity...\n\nSensing the saddening grief in her daughter, Freya decided Danielle had suffered enough. ", "Not that her suffering was Freya's doing, by any means. ", "Time and circumstance deemed the follies of Danielle's life. ", "Not all things could or should be controlled by the gods. ", "It's not as if she could see the future or weave a fabric of time that pleased her and those she cared for. ", "No, she only had a spark of intuition at times, not exactly like a vision or anything such as Zahara experienced regularly. ", "She just knew things. ", "Sometimes all at once, sometimes a little here or there over a period of time. ", "The curse of it all was never knowing if her involvement would change the direction of the outcome or not. ", "But when it came to one of her own, especially this time with Danielle, she had to try to monitor and manipulate with what little control or resources she had for a favorable conclusion. ", "Danielle had attempted to follow her heart once before, only to be burned. ", "Which is why Freya had tried to intervene or push events along this time. ", "And it was time to come clean with her daughter.", "\n\n\"We'll get to that...but first, why don't you tell me why you've come to visit me?\" ", "Before she spilled the beans, so to speak, she needed to know which side of the fence Danielle was inclined to fall, from the precarious perch she now sat.", "\n\nDanielle looked at her questioningly with distrust in her hazel tinted eyes.", "\n\n\"Daughter,\" Freya said, cringing inwardly from the flinch Danielle was unable to hide at her use of what should be a familiar term of endearment between them. \"", "I promise I will reveal all. ", "Please, just this once...trust me. ", "Tell me why you've come.\"", "\n\n\"I don't know if what I need is possible, but if it is, you can make it happen,\" she began. \"", "I've done something that I know I shouldn't have done, but I couldn't help it. ", "Really, I couldn't. ", "It was like I was drawn to do it without a will of my own.\" ", "She took a steadying breath and dropped the bomb she was sure would have all of Asgard in an uproar. \"", "I've fallen in love with a mortal man.\" ", "She held her head up higher meeting Freya's gaze straight on to prove she felt no shame in her actions.", "\n\nFreya stood stock still and said nothing, but secretly smiled to herself. ", "She was giddy as a tornado in a trailer park and couldn't wait to share it with her daughter. ", "Only Danielle hadn't finished her oration.", "\n\n\"I want you to make me mortal again. ", "I want to give up my immortality to be with him until my dying day.\"", "\n\nAnd there it was. ", "The bomb of all bombs that Freya had not been expecting.", "\n\n\"Whoa, whoa, whoa. ", "Wait. ", "What are you thinking? ", "There's no 'giving up your immortality' unless you really want to meet Alarr in the afterlife. ", "I can do no such thing for you, nor would I want to even if I could.\"", "\n\nHer patience and wits at end, Danielle snapped rather loudly, resembling the spoiled child she'd never even once been in her childhood. \"", "I should have known you wouldn't help me!\" ", "Her accusation was filled with old wounds, sufferings and disappointments that she'd kept within herself, squashing them down, down deep until they seemed to burst forth on a fiery flume of condemnation. ", "All hope was lost. ", "If Freya wouldn't help her, no one would - even if they could. ", "They wouldn't dare cross Freya. ", "God or no.", "\n\nWith stinging salty tears spilling down her face, she sank limply onto the oversized couch at her back. ", "One word crept through her mind – Hopeless.", "\n\nFreya dropped down right beside her minus her usual poise and grace. \"", "Oh my dear, dear girl. ", "I never meant for this to hurt you. ", "You've already been through much more than your share of heartache. ", "That was never my intention. ", "I wanted so much for you to find happiness.\"", "\n\nBlinded by bitterness, all Danielle perceived from Freya's confession was that she had interfered, turning her hopelessness to unbridled anger. \"", "How could you do this to me! ", "And just what is it that you did? ", "Did you make me fall in love with him just to see me writhe in pain once again?\" ", "she demanded. \"", "Was I that entertaining to watch?\"", "\n\n\"No! ", "I'd never do that to anyone. ", "Especially you. ", "You're my daughter, my own flesh and blood.\" ", "Freya was horrified that her daughter could believe these things of her.", "\n\n\"Could have fooled me,\" Danielle spat with disgust.", "\n\nInsolence toward the gods was never permitted. ", "Had it been anyone else that had spoken to Freya like that, they would have been jettisoned straight to the bowels of Helheim, or Hel as some called it, the lowest level of the Norse universe. ", "The grim, cold, dark and misty abode of the undeserving dead. ", "An icy Norse Underworld, ruled by Hel, daughter of Loki, that is inhabited by a growing population of ghastly spirits - the souls of cowards, losers, profligates, slothful bums and liars - who must suffer in the mind-numbing cold with nothing for the punished soul to do accept shiver out their miserable existence for eternity.", "\n\nBut Freya took no offense at Danielle's cruel, disrespectful words. ", "It was no secret that mother and daughter had never shared the relationship they could have had. ", "Freya regretted this more deeply than Danielle could ever know, so she'd set about taking steps to change all of that. ", "Starting with helping her daughter find the love she so richly deserved.", "\n\nFreya thought luck had brought about the binding chain, until her intuition kicked in, giving her insight – just a glimpse of possibilities to come - and with it, she discovered the connecting bloodline between the two males. ", "She knew then what she had to do, so she'd sent Danielle to retrieve the binding chain personally and watched and waited to see if her suspicions were correct. ", "And thank her fellow gods, they were. ", "Now, she just had to make Danielle understand by filling in blanks.", "\n\n\"I've had knowledge of the chain for quite some time now, but I had to bide my time, waiting for the correct circumstances to reveal themselves. ", "I've been watching you very carefully lately.\"", "\n\nThat caught Danielle's attention. \"", "What circumstances are you talking about? ", "And that presence I've been feeling...that was you?\"", "\n\nFreya nodded. \"", "I didn't realize you noticed me. ", "I thought I did a pretty good job of shielding myself.\"", "\n\nA light bulb flickered on in Danielle's reeling mind. \"", "Wait, you set me up, didn't you? ", "I didn't have to go get the chain back myself. ", "Did I?\"", "\n\n\"No, you didn't,\" Freya admitted. \"", "But I wanted you to have an opportunity, however, slight that opportunity might have been, to find another connection. ", "Your first was all wrong and I knew there was a chance that this could be the right one.\"", "\n\nDanielle's anger had suddenly dissipated and she bore a dazed, glassy-eyed look of disbelief, practically mumbling to herself. \"", "I can't believe you set me up.\"", "\n\nSeeing that Danielle had passed the hysterical I'm-really-fucking-pissed-off-at-you-and-am-going-to-scream stage, Freya gathered her dignity and continued, \"Well, you certainly weren't doing anything to changed your circumstances, were you? ", "I saw a chance and I took it for you.\"", "\n\nWithout repeating the tirade she'd just been through, Danielle kept her tone and attitude in check. ", "She needed information and knew she wouldn't get what she needed showing disrespect. ", "And she needed much more than just information. ", "Most of all, she needed her mother's help.", "\n\n\"What right do you have taking chances for me, for my life?\" ", "she inquired.", "\n\n\"I'm your mother. ", "That gives me every right to try and help you find happiness.\"", "\n\nShe raised her hand to ward off Danielle's expected protest. \"", "I don't care how old you are, I will always be your mother. ", "Even if you do hate me. ", "That fact won't change,\" Freya said determinedly.", "\n\n\"I don't hate you. ", "I've missed you. ", "Since father died, you seemed to never have time for me. ", "You gave up on me and I was still a child.\"", "\n\n\"I know. ", "What I've done is unforgivable. ", "You must understand. ", "I couldn't look at you without missing him. ", "It hurt too badly. ", "I knew I'd lose him someday and didn't handle that very well. ", "And then there was you. ", "Because of your mortality at the time, I realized I'd lose you, too. ", "I couldn't take any more of the pain. ", "It was selfish, I know, but it was easier to stay away. ", "I didn't want you to know my pain. ", "I allowed it to overshadow my love when you were a child, and then when you became a Shieldmaiden, I thought it was simply too late. ", "I was a coward and I'm sorry, Daughter. ", "Please find it in your heart to forgive me – someday.\"", "\n\nFreya spoke the truth. ", "There was no doubting it. ", "Danielle realized there was no malice, no trickery to be expected. ", "Her mother wasn't cruel, didn't harm intentionally. ", "She was just absent. ", "Knowing now how she, herself, felt about Aaron, she could completely understand how Freya must have felt then. ", "If she stayed with Aaron and Freya couldn't make her mortal again, then she would have to someday watch him die, too. ", "Just as Freya had watched her father die. ", "But even with this knowledge, she would choose whatever time they could have together and the suspended pain of losing him in the future over not loving him at all. ", "This much she knew.", "\n\n\"I understand and I promise to try. ", "You must give me time.\"", "\n\n\"Since we have plenty of that, take all you need.\" ", "Freya seemed satisfied with that answer, as proven with the lightened attitude and tone of her voice.", "\n\nAs Danielle met her gaze, Freya actually smiled with watery eyes but refused to let them spill over.", "\n\n\"Now,\" she cleared her throat, \"How to help you with your dilemma?\"", "\n\nShe had Danielle's full attention now. ", "The hopefulness bubbled up in her like a fountain that was uncontainable and on the verge of eruption.", "\n\n\"There's no hope. ", "He's human.\"", "\n\n\"All right. ", "Let me first start by explaining then. ", "You must know that I could not intervene, but I knew the chain was meant for another, that Alarr was not your intended true love. ", "I was forced to let you make your own decisions and mistakes. ", "I could not inform you of the future as it is against our laws and the consequences could be devastating. ", "I don't know all anyway and only receive what knowledge I do have in indistinct, imprecise details that are never set in stone. ", "They are only possibilities. ", "Which is why I hoped this was a possibility that would come to fruition. ", "You deserve to be happy and appreciated for all you are and I believe Aaron can give that to you. ", "Obviously, the magic of the binding chain agrees with me.\"", "\n\n\"But how? ", "You just told me you can't make me mortal again.\" ", "Danielle waved her hand dismissively in front of her. \"", "And honestly, it doesn't matter. ", "I will stay with him anyway for as long as I can.\"", "\n\nAnd Freya believed her. ", "At that moment she saw Danielle's heart, frantically clinging to whatever crumbs she could gather as if a fragile crumbling wafer was falling through the cracks of her fingers.", "\n\n\"Would your life span be enough? ", "For the two of you, I mean,\" Freya asked.", "\n\nDanielle's eyes scrunched in disbelief. ", "Surely, she'd misheard her mother. \"", "What do you mean - my life span? ", "I'm immortal, failing I die in battle or something.\"", "\n\n\"Exactly.\" ", "Short and succinct.", "\n\n\"You can do that?\" ", "Danielle almost shouted her inquiry. ", "She couldn't believe her ears, thinking surely she'd misheard her mother.", "\n\n\"No, you can do that. ", "Together with your young man.\" ", "Freya beamed. ", "She loved knowing a secret that others did not. ", "It was totally exhilarating. ", "But now was not the time to tease.", "\n\nThis couldn't be. ", "Danielle had never heard of such a thing. ", "If her mother was playing with her, she'd...she'd...oh, she didn't know what she'd do to her, but it would be bad. ", "Very bad indeed.", "\n\n\"I know I'm repeating myself - but how?\" ", "she stammered.", "\n\n\"There are levels to the chain. ", "You already have a small connection with him, yes?\"", "\n\n\"At times, yes, I do believe I know what he's thinking. ", "But it's not often and I can't be sure. ", "I feel and hear something when emotions are high or in extreme situations, but I thought it was just my imagination. ", "I thought that I was being overly sensitive.\"", "\n\n\"That's because you already have a connection. ", "It's slight, but there is a definite link there.\" ", "Instant excitement leaped onto her face. \"", "He's the one. ", "I knew it!\" ", "Freya jumped with glee and clapped her hands.", "\n\nDanielle was shocked. ", "She's completely lost her marbles! ", "She'd never seen this side of her mother. ", "Not even close. ", "Except maybe... Then it hit her. ", "Not since her father had passed.", "\n\n\"But the chain hasn't glowed or sparked or anything likes it's supposed to,\" Danielle argued. ", "She didn't mean to argue, didn't want to even. ", "But she refused to get her hopes up too high fearing this had to be a mistake. \"", "It's impossible. ", "He's mortal, not even a demi-god.\"", "\n\n\"And?\" ", "Freya knew Danielle wasn't finished with her argument. ", "This situation was unique, to say the least.", "\n\n\"It's not allowed!\" ", "She knew she had her mother there. ", "The only way around that little obstacle would take a divine decree and she didn't think the Gods were all going to get together and change the game plan for little ole' her.", "\n\n\"That's true...sort of.\"", "\n\n\"What do you mean – sort of?\" ", "Now she was really losing her patience.", "\n\n\"Well...,\" Freya's voice took on a higher pitch, sing-songing her response and refusing to meet Danielle's eyes.", "\n\nBut Danielle kept watch, noticing the purse of Freya's lips and the scrunch of her eyebrows. \"", "What aren't you telling me?\" ", "she demanded.", "\n\n\"It's not exactly forbidden. ", "I mean you warriors carry on with mortals all the time. ", "It's just that we don't encourage deeper relationships. ", "It's so tragic having to watch someone you love grow old before your eyes and fade away, knowing there's nothing you can do for them. ", "Chain bonding is the only way to keep them forever. ", "And I do mean forever, with their lives literally bound and tied to yours. ", "Of course, the forever part is still the same with immortals, but as you know personally, the end of their existence doesn't end your own. ", "And look how rarely we immortals actually take those vows.\"", "\n\nFreya looked at Danielle's silent shocked expression. ", "She was slack-mouthed with almost bulging eyes, with a mix of confusion and silent rage rolling off her in indiscernible waves.", "\n\n\"Close your mouth, daughter, or you'll catch flies.\"", "\n\nDanielle complied and blinked her eyes a few times as Freya continued. \"", "We discourage a union with a mortal because firstly, bondings are so rare even between our own kind, and mortals don't seem to understand the meaning of forever. ", "Everything with them is so...temporary – like instead of Mr. Right, it's Mr. Right Now. ", "And I'm not picking on the females, as the males are just as culpable,\" she clarified. \"", "It's just less complicated to leave the bonding out of the equation where mortals are concerned, as I did with your father. ", "Secondly, it is our goal to keep our existence hidden, after all.\"", "\n\n\"I don't understand. ", "Are you telling me this has happened before?\"", "\n\n\"Yes, but only twice before. ", "It's rather hush-hush, you see. ", "Practically top secret,\" she admitted. \"", "Man, I'm going to catch some Hel for this one,\" she said worriedly. ", "Freya sighed, shrugged her shoulders and let a bright smile return to her face. \"", "But not today...\"\n\n\"Who? ", "Who are the others?\" ", "Danielle demanded. ", "She felt she need something tangible, some proof of what her mother was explaining to her – rather vaguely.", "\n\n\"Oh no. ", "Not going to happen, dear. ", "I've said too much already. ", "But you're my daughter. ", "Daughter of Freya.\" ", "She spun in an extensive circle, arcing her arms wide out to her sides as her long splendid strawberry blonde hair swirled about her intertwining with her lengthy billowing royal robes. ", "Her azure eyes sparkled with mischief. \"", "Am I not the Goddess of love, beauty, fertility, war and witchcraft? ", "The most glorious of the Goddesses? ", "Queen of the Shieldmaidens?\"", "\n\nFreya didn't wait for an answer. ", "It was a rhetorical question anyway. ", "Of course, she was – all of that and more. \"", "So why should my daughter continue to suffer, I ask?\"", "\n\n\"Mother,\" Danielle began demurely, \"My suffering was not unbearable, nor your fault.\"", "\n\n\"True, it was not my fault, but the only way you could bear it was to hide your heart, wearing an invisible cloak of protection around you at all times.\"", "\n\nFreya knelt at her daughter's feet and tenderly took her hand. ", "Danielle couldn't remember the last time her mother had touched her in such a way. ", "She wasn't sure how to respond, so she simply didn't move even the tiniest muscle, afraid she would disrupt this most unusual moment.", "\n\n\"That is no way to live, Danielle, whether immortal or not. ", "You can't go on simply existing. ", "Now is your time and I intend to give it to you.\"", "\n\nDanielle was still feeling quite shocked and meek, filled with crumbs of disbelief. \"", "How? ", "How do I keep him?\"", "\n\nThat question seemed to perk Freya up. \"", "That's the simple part. ", "A chain binding ceremony, of course. ", "Performed by moi.\" ", "She batted her glistening eyelashes with false modesty.", "\n\n\"But Aaron and I already wear the chains.\"", "\n\n\"Semantics, my dear. ", "If you want to keep him, you must complete the bonding and then all will be as it should be.\" ", "She paused and then explained the steps in the simplest form. \"", "I will bless the union. ", "You stay immortal. ", "And although Aaron will not become immortal, the chain will recognize him fully as your mate and he will live as long as you do, never aging. ", "You can even give me grandchildren to spoil. ", "The way you two have been acting, that shouldn't take too long to accomplish.\"", "\n\nA river of red spread across Danielle's cheeks. ", "This was soooo not happening. ", "She refused to discuss anything to do with sex around her mother. ", "And right then she realized she was actually thinking of her as her mother. ", "Not some vacant Goddess, void of all feeling and without an ounce of empathy or compassion.", "\n\n\"Who are you and what have you done with my mother?\"", "\n\n\"You're very comical, my dear. ", "But I need to make amends for my derelict ways towards you. ", "And even if I'm not successful in this mission I've set for myself, at least I will have tried and you will once again be happy.\" ", "Freya's sincerity was obvious. ", "There was no sign or reason to doubt her. \"", "Besides, Aaron will be very useful in our quest to rid the mortal plane of Loki and his horde. ", "His ability to locate artifacts is quite impressive. ", "I believe the Gods will be pleased to add him to our numbers.\"", "\n\nDanielle rose from her seat, unsure of what to do or say. ", "She was still apprehensive about the entire situation, but Freya had given her so much more than she could have dreamed of. ", "She'd been ready to forfeit her immortality but instead had been given a solution that could possibly mean she and Aaron would have lifetimes ahead to spend together. ", "The possibility of a family – of her own. ", "That was a dream she'd not entertained in...she couldn't remember when.", "\n\nSeeing her uncertainty, Freya came to stand in front of Danielle. ", "She took her hand once more between her own. \"", "All will be well. ", "I promise. ", "This time, we will make it right for you. ", "Go now, daughter, and share the good tidings with your intended mate.\"", "\n\nAs Danielle descended into a slight curtsey and lowered her head to show respect, Freya placed a small kiss on the top of her head, then stood back and waved her arm dramatically with a flourish, watching as Danielle faded away.", "\n\n*****\n\nDanielle blinked to clear her vision and found herself standing outside of her home in the warriors' village. ", "Wow, that was quick. ", "She's never done that before either. ", "It was a day of surprises. ", "Many of which she had to share with Aaron immediately.", "\n\nShe was curious about the connection that Freya claimed she and Aaron already shared, so she decided to test their tentative link as she purposely reached out to him with her mind. ", "She couldn't hear him, but she could sense him - and the worry that held like a heavy weight upon his shoulders. ", "If she knew where he was at this exact moment, she would trace there immediately and begin their new lives together.", "\n\nOh Goddess, she suddenly thought as doubt came crashing down around her. ", "What if he doesn't want to spend eternity with me?", "\n\nShe remembered his declarations of love. ", "How he professed he would give up his career to aid the warriors in their quest for humanity. ", "How he wanted to spend his life with her. ", "But if he knew that he would live as long as she did, that his life would be irrevocably tied to hers, would he still want those things? ", "She could be killed in battle tomorrow. ", "There were no guarantees, just possibilities. ", "If she let Aaron go, he could live a long and perfectly normal life with a perfectly normal wife, not this crazy mixed up bizarre world that she lived in that was constantly threatened and thrown off balance at a whim. ", "She could have one of the guys completely erase her out of his mind and he would go on as if nothing had ever happened. ", "She would have to stick around in the shadows to make sure he was safe, hoping he wouldn't remain a target of Tormond's for too much longer. ", "Maybe they could plant a suggestion that he leave the area completely to go and work at another archeological program across the country. ", "That would keep him safe and away from Tormond for good.", "\n\nBut there was one problem with all of those solutions. ", "She was selfish. ", "And thoughts of Aaron being in some other female's arms brought out the ugliest green-eyed monster tripped up on a massive amount of steroids she could muster. ", "She pictured the fictional comic book character, the Hulk. ", "No, the picture in her mind's eye was the Freyodin vampire warrior equivalent of the already bulking green fictional comic book character. ", "There's a new character for you, Stan Lee.", "\n\nSwallowing the bile that had risen in her throat from fear and pushing the green-eyed monster away, she knew, that no matter what she wanted, she had to give Aaron the chance to make an informed decision for himself. ", "It was his life to control and not hers to toy with.", "\n\nLost in thought as she dealt with the turmoil in her head and heart, she'd instinctively made her way to her front door. ", "Upon entering, she knew where she'd find Aaron and wasted no time in tracing outside her bedroom door. ", "She was at peace with her decision to be completely honest with Aaron. ", "Sure, the pain would be insurmountable should he choose to leave her, but she was strong. ", "Stronger than she'd been previously, and she would carry on, knowing he was happy and safe.", "\n\nAaron was resting comfortably in an overstuffed chair located in the raised portion of her split-level bedroom, looking out of the large bay window at the foliage of the forest. ", "He turned in her direction as she entered the room.", "\n\n\"Hey there. ", "I've been waiting for you. ", "Emeline said you had an errand to take care of.\" ", "He rose from his chair and met her halfway across the room. ", "The smile on his face dictated he was at ease, seemingly unfettered by the crisis they faced. ", "His countenance was completely calm and unassuming as he leaned into her and kissed her sweetly on her forehead.", "\n\nShe melted just as sweetly into his embrace, allowing him to wholly enfold and surround her, resting her head on his chest with her arms tucked up between them.", "\n\n\"An errand? ", "Oh, yes,\" she said as she began to clear the cobwebs that had instantly clouded her mind in his embrace. \"", "I went to see my mother.\"", "\n\nHe pulled back a little to look at her face. ", "His eyes questioning, well aware of Danielle's and Freya's...differences.", "\n\n\"I had this crazy idea that I could be human again...completely forgetting that I already have been once before and lost that privilege when I lost my life.\"", "\n\nHe sighed heavily and pulled her back in his arms. \"", "No, Danielle. ", "I won't have you giving up your immortality. ", "Not for me. ", "It's your selflessness that earned you this life and your status as a warrior and protector of humankind. ", "It's who you are and part of the reason that I love you. ", "You don't need to worry. ", "If they will let me stay, then I will take whatever time I can with you. ", "I've already told you that and I meant it. ", "I just hope the assistance I can give them in the searches is enough of an incentive.\"", "\n\n\"I don't think you have to worry about that. ", "I have it on the highest authority that you are vital to our fight against Loki and his horde.\"", "\n\n\"Great! ", "Then there's no problem at all. ", "Especially since Alarr gave us his blessing.\" ", "Aaron pulled back once more and cupped her face in his calloused hands. ", "Hands that worked in the roughened earth but tenderly caressed, soothed and ignited her body with pleasures she'd never felt before.", "\n\n\"You remember what happened with Alarr?\" ", "she said, her eyes going wide.", "\n\n\"It's an experience I'll never forget. ", "Felt like I was dreaming or something, just observing. ", "I couldn't participate, only watch,\" he chuckled, still observing her face.", "\n\n\"Well...you're right. ", "There's no problem really...but you have a decision to make.\"", "\n\n\"And what would that be? ", "Honestly, I really don't want to become a vampire and a warrior, but I'd do it for you.\"", "\n\n\"Oh no, nothing that drastic. ", "You don't even have to die,\" she chided. ", "Danielle felt the relief flood his body when she informed him of that portion of the decision.", "\n\n\"Then what do I have to do?\"", "\n\n\"If you want to, you can choose to go back to your life before we met and carry on never knowing of our existence. ", "We can fix it where you can't remember me or any of this at all. ", "Quick and painless. ", "You can go forward with your dream of archeology, none the wiser. ", "Unfortunately, we can't remove the chain, so we'll have to come up with some excuse for that.\"", "\n\nTry as she might, it was extremely hard to put a positive spin on this idea. ", "She didn't want to sway him one way or the other, but the sickly looking smile she had plastered on her face, almost made him laugh. ", "He still had her locked in his arms with his hands clasped behind her lower back.", "\n\nHe bit his lower lip to squelch his amusement and shook his head adamantly. \"", "Not acceptable. ", "What's my other option?\" ", "At this point, it didn't matter to Aaron what the other option was. ", "He figured if it didn't include making him leave and forget her, it simply included conditions on how he could stay, which is what he had hoped for all along.", "\n\n\"You can become my chain bonded mate,\" she said but added quickly, \"But before you make that decision there are things you need to know – pros and cons, if you will.\"", "\n\nYes! ", "This was sounding very promising to Aaron and he encouraged her to continue with a quizzical lift of his brow, doing his best to hide his excitement. \"", "Is this where you ask whether I want the bad news first or the good news first?\"", "\n\nShe swatted his shoulder. \"", "You're not taking this very seriously and believe me – it's serious.\"", "\n\n\"I'm sorry. ", "I didn't mean to make light of the situation. ", "I mean I did, but not in the way you probably thought I did.\" ", "He became a little flustered then. \"", "Oh forget it. ", "Just tell me what the pros and cons are. ", "Please?\"", "\n\n\"Begging doesn't suit you.\" ", "She smiled, deciding he was right and she could lighten up a bit now. ", "She knew now that he didn't want to leave her and she had to trust that they'd work all the other kinks out of their predicament. \"", "Alright. ", "You would remain human, of course.\"", "\n\nTension was mounting again as they both examined their inner thoughts and feelings.", "\n\nAfter a moment he said, \"Okay, I can accept that. ", "I don't have to like it, but I actually expected it. ", "I only regret that I won't have your strength and that I'll grow old. ", "How will I protect you? ", "Are you sure you can deal with that?\" ", "His fears of her not wanting him as he grew older terrified him to his very core.", "\n\n\"I don't need your protection, I need your love. ", "And you won't grow old. ", "Your life will be tied to mine. ", "As long as I live, you live, just as we are now. ", "But,\" she paused, \"if ever I die, you'll die, too. ", "I want you so badly, but I don't want to do that to you.\"", "\n\nAaron said nothing. ", "He simply stared into her eyes as if searching for something. ", "His thoughts churning like a whirlwind as he continued to listen to her.", "\n\n\"You realize this is no guarantee of forever together. ", "I could die in battle tomorrow and then so would you. ", "That's not fair to you, Aaron. ", "You deserve to have a normal life and this life will be far from normal.\" ", "Danielle sighed then, laying her head on his shoulder and letting the weight of her tormented feelings drift away. ", "Instead of waiting for his decision, she'd made her own. ", "She mentally straightened her backbone and locked her gaze with his once more. \"", "Goddess, how I love you. ", "But I can't do this to you, Aaron. ", "I won't.\"", "\n\nThat's when he found it. ", "The something he'd been searching for in both her and himself. ", "Her altruistic strength, determination and bravery had returned, radiating out around her like a protective shield. ", "He loved these qualities about her. ", "Qualities that defined the warrior woman he fell in love with. ", "Her courage, in turn, fed his own.", "\n\nAaron knew it was now or never. ", "With one arm holding her tightly to him, he cupped her face to gain her complete attention. ", "He had to make her understand.", "\n\n\"For me, there is no life without you, chain bond or not.\"", "\n\n*****\n\n# Chapter Nineteen\n\nWord spread like wildfire throughout the village. ", "This news that a mortal would be chain bonded to a warrior was unprecedented. ", "A chain bonding itself was a rarity, but to a mortal, unheard of. ", "Most were accepting and excited, especially the females. ", "Some were uncertain and weary of this pairing and there was one who was confused and fighting to control his fury about the decision handed down from the Gods. ", "Although Vex and Danielle had been close friends for the almost one hundred years since he had been brought over, he envied her to no end and jealousy ate at his gut, abating some of the elation surrounding the preparations for the upcoming bonding ceremony. ", "No one knew the cause of Vex's obvious aversion, or if they did, they weren't telling. ", "His secrets were his to keep.", "\n\nNadine took the lead and called an impromptu meeting in the rec room to discuss the preparations for the ceremony that was to take place the following evening. ", "If they couldn't pull this together tonight, the ceremony would have to wait until the following week and Nadine didn't want to put it off. ", "All weddings and chain binding ceremonies alike were held on Fridays in honor of the Goddess of Marriage, Frigga.", "\n\nNadine's anal tendencies made her perfect to ensure a successful celebration, except when everyone else didn't cooperate with her plans. ", "She, of course, wanted this event to go off without a hitch, but when several warriors, both male and female, took it upon themselves to straggle late into the meeting, Nadine was beside herself.", "\n\nZahara leaned into Makayla whispering, \"I swear, if I didn't know for a fact that we cannot have mortal illnesses and other medical conditions, I'd think that girl has OCD.\"", "\n\nTo which Makayla laughed heartily and countered, \"Yea, we'd better go save her and be quick about it before she blows a gasket.\"", "\n\nWithin a short time, plans were made, Nadine's worries were soothed and everyone pitched in to ensure that the ceremony would rival the grandest of ceremonies they had ever witnessed among them. ", "Danielle beamed brightly and both she and Aaron expressed their gratitude to their fellow warriors and friends.", "\n\nBefore anyone could depart, Thunder and his second-in-command, Vengeance, marched into the room carrying champagne and trays of delicious looking food, followed by the human staff with more of the same.", "\n\nThunder's voice boomed through the doorway, grabbing everyone's attention. \"", "All right, everyone. ", "Since we've got the business portion of this meeting out of the way, I believe it's time for the mandatory bachelor and bachelorette party to commence. ", "And let me be the first to kiss the bride.\"", "\n\nShouts and cheers went up throughout the room and several warriors headed toward the bar area to start the celebration with their favorite beverage. ", "Thunder unloaded his cargo of party goods and headed in Danielle's direction. ", "After surveying the room, he smiled to himself. ", "It was nice to see everyone enjoying this blessed occasion. ", "Too soon he knew that events in their lives could take a sharp turn for the worse. ", "But tonight was for celebrating and he intended to join them in it.", "\n\n\"Warrior Danielle,\" Thunder recited formally, placing his hands on her upper arms and beginning his skål, a traditional Scandinavian toast of friendship and goodwill. \"", "May you have walls for the wind and a roof for the rain, and drinks beside the fire; laughter to cheer you and those you love near you, and all that your heart may desire.\" ", "Then Thunder pulled Danielle into his arms and kissed her sound and proper on the lips. ", "Pulling away he yelled, \"Someone hand me a drink, so I may conclude my toast to our sister warrior.\"", "\n\nInstantly there was a mug of cold beer thrust into Thunder's hand. ", "He turned with his glass held high, addressed the group and, with an old Gaelic salute, wished Danielle and Aaron great health and good blessings. \"", "Slàinte mhòr agus a h-uile beannachd duibh.\"", "\n\n\"Slàinte,\" everyone echoed.", "\n\nImmediately, Danielle was surrounded by every male in the room taking turns kissing the new bride. ", "She knew what to expect but laughed whole-heartedly at Aaron's discomfort as he was mobbed by the females. ", "After a moment, she noticed he'd decided to be a good sport about this new turn of events and even seemed to be enjoying himself, although she knew he'd never admit it in a million years. ", "A million years... I wonder just how much time we will actually have together... Eternity wouldn't be enough for her.", "\n\nA series of individual toasts began in which everyone toasted the bride and groom, then each other, taking a drink with each toast.", "\n\n\"I think I've had quite enough.\" ", "Aaron excused himself before the conclusion of the toasts. ", "He didn't have the stamina the warriors did in holding their drink, although it seemed everyone would be rather intoxicated by the end of the evening.", "\n\nDanielle laughed in agreement. \"", "Yes, I think that would be best for me, also. ", "We're lucky we've got such a short time restraint. ", "Normally, they'd spend an entire day feasting and toasting us.\"", "\n\nAaron pulled her up into his lap and she instantly felt his arousal beneath her. \"", "I know what I'd like to spend an entire day feasting on,\" Aaron growled lowly in her ear. \"", "Let's get out of here.\"", "\n\nDanielle melted against him burying her nose in the crook of his neck. ", "He growled. ", "He actually growled. ", "Goddess, what a turn on! \"", "I think I like this side of you. ", "I should get you snockered more often,\" she said as she lightly ran her tongue up the side of his neck and nibbled his ear lobe.", "\n\n\"Alright, that's enough of that,\" Steele's large powerful hand gripped Aaron's shoulder and his deep-based voice sent unwelcome vibrations all the way up Aaron's spine. \"", "Looks like its time to call it a night, folks,\" he announced to the room. ", "The reply of several downtrodden 'ahs' reverberated around him.", "\n\n\"Ladies, please escort Princess Buttercup away and we gents will put the Dread Pirate Roberts here,\" he gestured to Aaron, \"out of his misery for the evening.\"", "\n\n\"What? ", "We're being separated? ", "Really?\" ", "He looked at the others. \"", "Isn't that a little old fashioned? ", "I thought you guys were a bit more progressive than that.\"", "\n\n\"Nice try, Doc,\" Turbo cut in, \"But your cutoff for the night – from everything!\" ", "Several of the men who had gathered around them laughed, high-fived and fist-bumped, all while removing Danielle from Aaron's lap and assisting him up from his chair.", "\n\n\"Don't worry, love. ", "You're in good hands. ", "I'll see you tomorrow night,\" Danielle said while being gently torn from his arms and passed in the opposite direction. ", "The last he saw of her, she was throwing him a kiss as the women began to shuffle her from the room. ", "Then suddenly he was hoisted high and carried away on the shoulders of several very large warriors. ", "White Wedding was blazing from a nearby speaker and Aaron felt as if he was body surfing the crowd at a Billy Idol concert.", "\n\n\"Wait, wait!\" ", "Nadine cried out. \"", "Please, please, please. ", "I'm reminding you all now. ", "Don't be late tomorrow evening. ", "The ceremony begins at promptly at eight o'clock.\" ", "She received assurances from those around her and allowed herself to relax a bit. ", "Well, as much as she could anyway.", "\n\nBeing the pranksters that they were, Turbo and Steele exchanged a look. ", "You know that means we'll have to be at least ten minutes late, right?", "\n\nWhy, of course. ", "It will drive her bonkers. ", "I'll spread the word.", "\n\nAaron must have drunk more than he realized because he was ready to pass out. ", "Guess the guys did him a favor. ", "It would have been embarrassing if he'd passed out on Danielle- or worse – couldn't get it up. ", "His last thoughts were about tomorrow. ", "He didn't know exactly what to expect at the ceremony and was surprised that he felt not one shred of nervousness. ", "But that could have just been the booze talking.", "\n\n*****\n\nVoices. ", "Too many voices. ", "And way too loud. ", "But she couldn't open her eyes to make out who the intruders were. ", "They definitely put the 'rude' in 'intrude'. ", "She just wanted them to go away.", "\n\n\"Get up sleepy head. ", "Time to make you beautiful for that luscious man of yours!\"", "\n\n\"Yea, and by the looks of it, she's going to need a lot of help.\"", "\n\n\"By the Gods! ", "What an awful thing to say! ", "She obviously isn't sleeping beauty in the morning, but neither are you. ", "You shouldn't throw stones like that.\"", "\n\nOh Goddess, please make them stop. ", "Please make them go away and leave me alone. ", "Obviously, the Goddess wasn't listening.", "\n\n\"Oh come off it. ", "I was only kidding. ", "She knows I was just joking around. ", "Right, Danielle?\"", "\n\nThe only reply she could manage was a very unladylike grunt. ", "Danielle wanted to pull a pillow over her head to shut them out, but she didn't have the strength. ", "Someone sat on the side of the bed jostling her and causing the pain already in her head to intensify, rolling around from side to side and base to tip, throbbing like a beating drum in a Hawaiian festival.", "\n\n\"Oh no, sweetie. ", "You had way too much to drink last night, didn't you?\"", "\n\nSomeone snickered. \"", "Of course she did. ", "We carried on the celebration after separating from the men last night. ", "It was wild! ", "We danced the night away. ", "The only thing missing was a male stripper.\" ", "The voice lowered slightly. \"", "You should have heard her going on about her mother. ", "It was the strangest thing I've ever heard and must have been wishful thinking, the poor dear. ", "Something about them being 'best buds\". ", "I believe that's what she called it anyway.\"", "\n\n\"She must have been hallucinating as everyone knows that will never happen. ", "Oh well, no matter. ", "She probably won't remember any of it this morning.\"", "\n\nDanielle turned over slightly from her stomach prone position and groaned deep, low and sickly, like something out of a horror movie that was dying.", "\n\nThe women got their first real glimpse of the victim before them.", "\n\n\"Wow, she really is a mess. ", "Looks like this calls for desperate measures. ", "Ladies, grab a limb. ", "We'll have to trace over to the spa. ", "She'll never make it any other way.\"", "\n\nArms and legs were braced and before Danielle could protest, she was whisked away from her safe haven of a bed. ", "She must have passed back out because the next thing she knew there was a flood of cold water rushing up her nasal passages.", "\n\n\"Holy shit!\" ", "she sputtered, trying to expel the water and fill her lungs with oxygen. ", "She sat up so fast her world spun around and her stomach dive bombed then threatened to rocket out of her throat in a fiery spewing mess.", "\n\n\"Well, now. ", "That's an improvement. ", "We got a response. ", "If she would just open her eyes now, we could verify she's still among the living,\" someone jested.", "\n\nDanielle knew these voices. ", "Of course, she did. ", "So why couldn't she place them?", "\n\n\"Anybody got any toothpicks?\"", "\n\n\"Okay!\" ", "Danielle shouted, then lowered her voice, clutching her head. \"", "Ha ha, very funny. ", "I'm awake.\"", "\n\n\"Yes, but are you alive?\"", "\n\nDanielle finally recognized a voice. ", "She was sure that was Makayla. ", "She turned her head in the direction of the voice, causing sharp shooting pains to spear through her and her eyes shut tightly to block out the bolts of too bright light penetrating through them. ", "Another agonizing groan escaped.", "\n\n\"Emeline,\" the wiser Valeria said, \"I'm afraid we are in need of an intervention of the healing kind.\"", "\n\nEmeline inched closer to Danielle. ", "The closeness of her five-foot-nine-inch willowy frame seemed to somewhat lessen Danielle's agony already and she hadn't even touched her yet. ", "Being a healer sure had its pluses.", "\n\nFortunately, Emeline had been present for most of the after party last night and had anticipated this. ", "She pulled out a small vial containing her premade potion and held it up to Danielle's lips. \"", "Drink this, honey. ", "We'll get you soaking in the spa and you'll feel like your old self in no time.\"", "\n\nDanielle gladly downed the vile tasting potion quickly and took a few deep breaths to keep it from returning on her. ", "Emeline then laid a hand each on Danielle's forehead and stomach. ", "Danielle felt the energy flow from Emeline's body into hers. ", "A warm, soothing relief that her body craved and drank in greedily.", "\n\n\"Thank you, Emy,\" she said, resting her head on the healer's shoulder.", "\n\n\"My pleasure, my friend,\" Emeline replied. \"", "Now, let's get you prepared for the binding ceremony,\" she added excitedly with a lift in her voice. ", "The excitement grew throughout the circle of women surrounding her and Danielle as they looked forward to carrying out the tradition of readying the bride.", "\n\nThe tradition consisted of a magical day equivalent to visiting a Finnish sauna, featuring a lengthy and relaxing soak in a spa filled with herbs, flowers and scented oils meant to act as an aphrodisiac and enhance fertility. ", "The female warriors all participated in applying the oils and massaging the bride's body to a dreamlike and relaxing state. ", "She'd recovered quite nicely from her previous hangover ailment thanks to the efforts of all of her sisters. ", "Once Danielle was taken care of and laid out to rest, the others jumped into the spa to indulge a bit themselves.", "\n\nThe final preparations involved dressing the bride for her ceremony. ", "They fussed over the smallest details and Danielle let them.", "\n\n\"We've got a little something for you,\" Zahara said approaching with a beautifully adorned pink box. ", "She thought she recognized the box from a popular women's boutique but wasn't sure.", "\n\nDanielle took the gift and opened it revealing a skimpy but beautiful red negligée with barely there matching panties.", "\n\nAnnika chimed in chuckling, \"We got it at Victoria's Don't Tell Anybody. ", "As soon as we saw it, we knew it would go great with your skin tone and hair. ", "Is it me, or do all of their bras look the same on every commercial?\"", "\n\n\"Oh my Goddess,\" Nadine added. \"", "I've always thought the same thing! ", "I honestly can't tell them apart.\"", "\n\nDanielle blushed. ", "Not so much from the gift, but from thoughts of events to come later that evening.", "\n\nValeria walked up to Danielle and pulled her into a tight hug. \"", "I'm having a sense of déjà vu,\" she said referring to a similar night like this eight hundred years earlier. \"", "But I seem to remember your nightrail was virginal white, very, very differently styled and not quite so revealing.\"", "\n\nDanielle blushed deeper and laughed with everyone else. \"", "Yes, I'll never forget your kindness that night and all the times thereafter.\" ", "She hugged her back even tighter.", "\n\nValeria pulled back and smiled. \"", "Well, something else is very similar, as well.\" ", "She turned toward the doorway and called out, \"Girls, you can bring it in now.\"", "\n\nRaven and Myste had previously slipped from the room unnoticed by Danielle. ", "When they came through the doorway, they graciously carried the most beautiful Grecian style gown she'd ever seen. ", "Yards of white chiffon draped across their arms topped by a wide slightly gathered silk shantung waist that sat high, just below the bust. ", "They assisted Danielle and held it up in front of her in the full-length mirror. ", "The sweetheart neckline was also gathered vertically and topped by a V-shaped strap on the right side that cut across the chest and wound to the back completing the Greek look worn by Goddesses.", "\n\n\"Oh, I don't know what to say...\" Danielle began with tears shimmering in her eyes.", "\n\n\"Now don't go crying on us. ", "You'll ruin that perfect makeup job, even if you wouldn't let me put as much as I wanted to,\" Nadine spouted tenderly. \"", "Besides, it's not from us.\"", "\n\n\"It's not? ", "Then who is it from?\"", "\n\nEveryone turned to Valeria, leaving it to her to explain. ", "Of course, she rose to the challenge. \"", "No, sweetie. ", "It's from Freya.\" ", "Valeria donned a comical sickly smile, not knowing what reaction she would receive.", "\n\n\"Oh, wow,\" Danielle replied as if it was no big deal. \"", "That explains the Grecian style then.\"", "\n\nEveryone had been holding their breath and were virtually stunned by Danielle's retort – or lack thereof.", "\n\n\"What? ", "I told you guys last night that we sort of made up and were going to give this whole mother/daughter thing another try.\"", "\n\nThey all burst out laughing.", "\n\n\"We thought you were just drunk. ", "We had no idea you were serious,\" Zahara laughed and Danielle laughed with her.", "\n\n\"Oh wait!\" ", "Myste yelled. \"", "There's a note with the dress. ", "I'm sorry. ", "I forgot.\"", "\n\n\"Thanks,\" Danielle said taking and opening the note that was still affixed with Freya's seal. ", "It read:\n\nDaughter,\n\nI'm filled with more pride than you could ever know. ", "Thank you for allowing me to preside over tonight's ceremony. ", "The only thing that could have made this moment more perfect would have been watching your father deliver you to the altar.", "\n\nWear this gown with the certainty that you are the Goddess you were meant to be.", "\n\nDanielle lowered herself down on the edge of her bed and slowly folded the note, resting it in her lap. ", "She closed her misty eyes and reverently bowed her head. ", "Thank you, mother. ", "For everything. ", "Then she smiled brightly and leaped from the bed. \"", "All right, let's get that thing on me and get the show on the road!\"", "\n\nOnce Danielle had the garment on, she felt every bit a Goddess and ready to start the next phase of her life with Aaron. ", "Her thoughts were interrupted by Thunder's arrival.", "\n\n\"He's coming up the walk,\" she heard shouted down the hallway.", "\n\nThunder had stepped in and requested to deliver her to the altar. ", "Who was she to say 'No'. ", "He was her leader and a God in his own right. ", "She felt privileged and wondered if her mother had anything to do with it.", "\n\n\"I heard that,\" Thunder said.", "\n\n\"Oh, crap. ", "I wasn't aware I was broadcasting,\" she replied sheepishly.", "\n\n\"And no, Freya didn't ask me to escort you. ", "It was all my idea.\" ", "He pulled back and looked at her. \"", "My Gods, Danielle. ", "You look ravishing.\" ", "He smiled that dreamy smile of his and stuck out his arm for her to latch onto. \"", "Shall we go forth?\"", "\n\nShe returned his smile just as brightly and placed her arm in his. \"", "We shall.\"", "\n\n\"All right, then. ", "But we'll go slow as I've been given instructions to be at least ten minutes late for some reason.\"", "\n\n*****\n\nTrue to her nature, Nadine paced back and forth, wearing a dull path in the grass at her feet. \"", "I knew some of them would be late...but all of them? ", "Even the bride? ", "That's just unacceptable!\"", "\n\nZahara did her best to rein in her mirth. \"", "You brought this on yourself, you know. ", "You shouldn't have said anything last night. ", "You simply gave them the ammunition to torment you with.\"", "\n\n\"You're right. ", "And I know just who the instigators are.\"", "\n\nIf she didn't know better, Zahara would have thought Nadine's eyes were glowing. ", "Lots of things were possible, but that wasn't one of them. \"", "Nevertheless, they'll be here soon, so try to relax. ", "You've done a fantastic job in such a short time. ", "It will all go off without a hitch, I'm sure.\"", "\n\n\"From your mouth to the Gods' ears,\" Nadine prayed aloud.", "\n\nNadine suddenly felt a heavy sudden wave of presence. ", "She turned, knowing full well what she would find. \"", "Oh you...,\" she expelled on a heavy breath as she looked out over the sea of her friends all smiling brightly and innocently at her. ", "A couple of those smiles were also somewhat apologetic. ", "She should have guessed they would choose to trace in at the same time. ", "At least they'd all dressed appropriately – the men were all stylish and the ladies were adorned with their flower-strewn wreaths. \"", "Ha ha. ", "Jokes on me,\" she said yet unfazed.", "\n\n\"They obviously love you or they wouldn't care to tease you so,\" Zahara offered as she tenderly laid a hand on Nadine's shoulder.", "\n\n\"All right, fine.\" ", "She spoke to her friends, \"If I weren't your protector, I'd tear each of you a new one.\" ", "She was only half jesting...and they knew it. \"", "Luckily, your presence tells me Danielle should be here any moment.\"", "\n\n*****\n\nAaron stood in front of the horgr, or altar, that was built of heaped stones from their homeland and rested in a blossoming garden at the center of the village. ", "The ceremony would be held outside in the open at this place that was considered sacred and used to invoke the Gods and Goddesses. ", "Myste assured him the weather would be perfect today as she'd seen to it personally. ", "He took a deep relaxing breath and noticed he felt eerily calm, which he attributed to the events the morning had brought.", "\n\nHe'd been woken that morning and put to the task of working side by side with the other males in building a Gate of Honor for Danielle. ", "Because she was originally from Denmark, it was a traditional wedding custom to build and place this ornate gate in front of the bride's home. ", "After being given instructions, he caught on quickly, assembling the arch of pine branches for his bride-to-be.", "\n\nOnce the arch was complete, he was ushered to a full spa treatment including sauna and massage, then measured and fitted for an elegant tuxedo which he would wear for the ceremony. ", "The males joined him in the spa treatment and he enjoyed the camaraderie and playful bantering they shared among themselves. ", "They even made a point to include him which eased his mind about not fitting in. ", "Brains and brawn didn't always mesh well together and, even though he had a little brawn of his own, it could never match up to the bulk and physical strength these men had achieved. ", "But they seemed to welcome him as a member of the team anyway with no apparent discrimination.", "\n\nThunder made an appearance and he recalled the privileged feeling he had knowing that an actual God was attending his ceremony. ", "Never in a million years or in my wildest dreams, he thought as the deity approached him.", "\n\n\"Aaron, I have something for you,\" Thunder said reaching behind his back to produce a long sword from the sheath strapped across his broad shoulders. ", "It looked substantially heavy and razor-sharp.", "\n\n\"Thank you, but you didn't need to get me a gift.\"", "\n\nThunder poised the sword blade first across his out-stretched left arm laying it horizontally in a formal presentation and smiled with pride. \"", "Son, this isn't a gift. ", "It's your birthright.\"", "\n\n\"I'm sorry, my what?\" ", "Aaron said completely confused.", "\n\n\"Your birthright,\" he repeated. \"", "This sword has been in safekeeping for a very long time and was given to me by Odin this very morn. ", "I've been given the charge of presenting it to you. ", "It is yours by right of your birth as it once belonged to your ancestor and a former Freyodin Warrior, Alarr.\"", "\n\nStunned was a misnomer in describing Aaron's then state of mind. ", "He thought he mumbled something in disbelief like, \"Alarr's sword...my sword.\"", "\n\nThunder never acknowledged Aaron's astonishment. ", "He simply held his stance and instructed him further. \"", "You are to give this sword to Danielle during the ceremony tonight where she will then hold it in trust for her future son, just as was done by her ancestors, signifying the traditions of the family and the continuation of the bloodline.\"", "\n\nAaron accepted the sword with as much grace as he could muster. ", "Grasping the sword with both hands firmly on the hilt, he lifted it out in front of him, testing its weight and admiring the beauty of the embedded rubies that flanked the hilt on either side. ", "He fought hard not to let out the response of 'Wow, this is really cool' slip past his lips, knowing it contained no dignity whatsoever. ", "Instead, he offered a humble, \"Thank you. ", "I am honored.\"", "\n\n\"And there's one more thing...Freya asked me to give you this.\" ", "Thunder held out an official looking sealed envelope. ", "Aaron broke the waxy seal and opened the envelope and read the note it contained. ", "A smile crept across his face.", "\n\n\"Well, what does it say?\" ", "Steele blurted out his curiosity. \"", "I mean, if you don't mind sharing, that is.\"", "\n\n\"You are worthy,\" Aaron answered and a wide smile slowly spread across his handsome face.", "\n\nVengeance stepped forward and gave Aaron a manly slap on the back. \"", "Of course, you are. ", "Which is why you must now come with us.\"", "\n\n\"To where?\"", "\n\n\"To the portal of Valhalla,\" Thunder answered. \"", "Being mortal, you can't enter the portal, but being near it will be the next best thing and very acceptable for our purposes.\" ", "He turned to the group, \"Come, we're running short of time, so we're tracing to our destination.\"", "\n\n\"I've got the newbie.\" ", "Steele grabbed Aaron's arm and said, \"Hang tight. ", "We're going for a ride.\"", "\n\nBefore Aaron knew what had happened he suddenly found himself in a clearing beside a base of an old Ponderosa pine tree, feeling a bit woozy.", "\n\n\"Don't worry. ", "You'll get used to that,\" Steele offered after he made sure Aaron had his bearings.", "\n\nThunder and Vengeance stood next to the ancient looking tree while the others gathered in a half-circle formation in front of them.", "\n\n\"Aaron Janson, come forward,\" Thunder called out in his deep booming voice.", "\n\n\"It's okay,\" Steele whispered, sensing Aaron's hesitancy. \"", "This is all formality and we all go through it. ", "You'll be fine.\"", "\n\nAaron did as he was commanded and made his way to stand in the center of the circle where Vengeance joined him. ", "It was quite unnerving to be surrounded by such strength but he held his intimidation in check and refused to show any fear. ", "Thunder nodded for Vengeance to proceed. ", "He unsheathed a heavily jeweled dagger and instructed Aaron to hold out his right arm.", "\n\n\"This is the Dagger of Destiny given to us by Odin. ", "Its purpose is to make us one with each other, of the same blood. ", "Freyodin Warriors, come forth and welcome our newest warrior,\" Thunder instructed.", "\n\nBefore Aaron realized what was happening, Vengeance had made shallow cuts in both Aaron's palm and his forearm. ", "Then he took the dagger and did the same to himself and clasp his forearm to Aaron's firmly linking their forearms from elbow to elbow, and causing the blood from their palms to mingle with the blood from the other's forearm. \"", "You are now a part of me, as I am of you. ", "Welcome, brother mine.\"", "\n\nSteele was next to approach him from the outer lying circle. ", "Accepting the dagger from Vengeance, he repeated the same cuts on himself, then held his muscular arm arced in front of his large body.", "\n\nAaron clasped Steele's offering with his own and met him eye to eye as Steele repeated the oath. \"", "You are now a part of me, as I am of you. ", "Welcome, brother mine.\"", "\n\nOne by one, each of the warriors joined him in the circle to apply the same cuts to their sinewy arms and clasp Aaron's forearm, mingling their blood with his and repeating the sacred oath. ", "Thunder was the last to approach him and complete the ritual.", "\n\n\"You are now a part of me, as I am of you. ", "You are now our brother warrior, joining us in our fight against the evil forces and protection of mankind. ", "Welcome, brother mine.\"", "\n\nAaron's lack of confidence welled to the forefront. \"", "But I don't possess your strength and cannot wield a weapon like each of you. ", "How can I be a brother warrior?\"", "\n\n\"You wield your own weapon...that of knowledge that can lead us all to the end of this war. ", "That type of weapon makes you no less important.\"", "\n\n\"Should I say something? ", "Are there vows or an oath of some kind that I should make?\" ", "Aaron wondered what pledge he would now have to make. ", "He was still uncertain that he could live up to the commitment that the other warriors had made. ", "Then Thunder smiled at him with assurance and placed his hands firmly on Aaron's shoulders.", "\n\n\"You already have or you wouldn't be here now. ", "The Gods know what is in your heart and judge you by your actions and deeds. ", "No spoken words could be more sincere than the light your own soul reflect to the heavens for all to see. ", "The honor bestowed on you now is a rare gift that many will never aspire to. ", "Accept it and use it wisely for the good of your people.\"", "\n\nAaron nodded because there was no other choice for him but to accept it and do the best he could with what he'd been given. \"", "Thank you for this honor. ", "I hope to live up to the Gods expectation of me.", "\n\nHe wasn't sure, but he felt different. ", "A little stronger, surer and more confident of his body and how it moved. ", "Surely, the blood exchange didn't cause some change in him. ", "He was still concerned about the warrior title that had been bestowed on him. ", "He didn't believe he was worthy. ", "Maybe someday, but not today.", "\n\nAaron looked down at his hand and noticed the cut was completely healed, then check his forearm for the wound that should have been there, but wasn't. ", "He saw the smearing of blood but nothing more and the sting of the gash was also now absent. \"", "All right, the weapon aside. ", "I'm not going to turn into a vampire, I am?\" ", "Yea, he was a little freaked out all of a sudden. ", "He hadn't had a chance to think about mixing vampire blood with his own until now - which was too late, no matter the cost.", "\n\nEveryone laughed.", "\n\n\"Absolutely not. ", "You are still human, Aaron. ", "Just enhanced a bit with a few upgrades.\"", "\n\n\"Yes, you'll heal a little faster, run a little faster, be a little stronger. ", "Oh, and have a little more stamina, too. ", "If you know what I mean...,\" Turbo explained with a wicked grin.", "\n\n\"Not quite as well as we do, but it's still an upgrade,\" Steele offered.", "\n\n\"I do feel a little different. ", "Can I trace and speak and all that?\"", "\n\nGive it a try, Thunder suggested mentally.", "\n\n\"Hey! ", "I heard that!\" ", "Aaron shouted. ", "Oh shit. ", "Maybe I should have said that in my thoughts.", "\n\n\"You just did. ", "We all heard you,\" Turbo laughed.", "\n\n\"Guess I'll have to work on that.\"", "\n\n\"Don't worry,\" Steele injected. \"", "We'll show you how.\"", "\n\n\"Can I talk to Danielle, too?\"", "\n\n\"Of course, she's a warrior,\" Thunder answered. \"", "But you'll have a much deeper connection with her after tonight. ", "Just wait and see.\"", "\n\nThe stirring of the gathered crowd brought Aaron back to the present, reminding him of where he stood. ", "All eyes watched as a woman of pure ethereal beauty approached and strode gracefully behind the altar, her cerulean robes and long blonde hair seemed to magically swirl around her. ", "She caught and held his gaze with her electric blue eyes as she nodded to him, acknowledging his presence, and Aaron returned the gesture. ", "He knew this must be Freya and wondered if he should bow or something.", "\n\nThank you, but no. ", "You needn't bow. ", "She continued her perusal. ", "You'll be good for my daughter, I'm sure.", "\n\nI'm certainly going to try.", "\n\nI have it on good authority that you will succeed...in many things.", "\n\n*****\n\nVengeance preceded Danielle down the pathway to the horgr that was ornamented with flowering vines and candles. ", "He bore a dazzling sword that would be Danielle's wedding gift to her new husband and strode confidently to the altar. ", "Reverently, he acknowledged Freya, then carefully placed the sword on the altar, smiled at Aaron and took his place among the small gathering beside Makayla.", "\n\nLooks like you boys owe me a little something, Makayla projected to Savage and Vengeance.", "\n\nAnd what might that be? ", "Vengeance asked.", "\n\nHave you forgotten so easily? ", "It went a little something like 'a favor of my choosing from each of you' should these two hook up for any extended amount of time. ", "And you can't get more 'hooked' than this.", "\n\nSavage, who was standing by her other side, simply gave a non-committing grunt, but his eyes flashed daringly.", "\n\nYep. ", "Someday in the near future, I will come collecting on those favors. ", "Not sure when or what they will be, but be prepared, lovers. ", "No sense cashing in her chips early. ", "She'd just hang on to these chips until she needed them.", "\n\nThe two men shared a look of uncertainty, the daring gone from Savage's eyes, replaced with a bit of unease. ", "At least that's what it looked like to Makayla. ", "It was good to keep them a little off balance. ", "Her attention was brought back to the ceremony as Thunder arrived on the pathway, regally escorting Danielle.", "\n\nAaron watched as Danielle made her way toward him. ", "She was resplendent in her beauty. ", "The red and brown highlights in her long blonde hair shimmered around the crown of flowers resting on her head, intermingling with the ribbons that loosely braided throughout and draped down over her graceful shoulders. ", "She looked like a true Goddess and was, in his eyes. ", "He couldn't wait to peel those lovely layers of white chiffon off of her delectable body to worship her the way she should be worshiped. ", "As his eyes traveled back to her face, she met and held his gaze until she came to stand beside him. ", "Thunder placed her trembling hand in his, kissed her sweetly on the cheek and bowed with a nod to Freya before joining the other witnesses.", "\n\nFreya took a moment to look at her beautiful daughter and smile before her melodic voice rose summoning the attention of the Gods and Goddesses with an ancient invocation, invoking the deities of fertility and marriage, inviting them to join her in blessing the bonding between Aaron and Danielle.", "\n\nKeeping with tradition, Danielle took the sword from the altar and, with slightly trembling hands, presented Aaron with her gift, symbolizing her willingness to trust he would guard and protect her body and soul. \"", "I give you all of myself,\" she said, her voice low and quivering.", "\n\nAaron then pulled his ancestor's sword from its sheath at his back and, kneeling down on one knee, presented the blade to her. \"", "This is my ancestor's sword, from my bloodline. ", "Please keep this always, for our future son or daughter.\" ", "He smiled up at her, knowing she'd appreciate that he'd broken the traditional vow by mentioning a female offspring.", "\n\nWhen Danielle saw what he held, she flinched in recognition. \"", "But where did you...,\" she whispered.", "\n\n\"It seems the Gods have their ways,\" he answered her softly. ", "He stood when she smiled, assuring him that all was right with the world.", "\n\nFreya cleared her throat lowly to gain their attention. \"", "Normally, at this point of the ceremony, I would bless the bonding chains upon the altar, to strengthen the link between them, the unbroken circle and the unbreakable and sacred vows, but it seems these two are in a hurry and ahead of schedule.\" ", "The audience of friends laughed at Freya's jest. \"", "So instead, they will receive my blessing directly unto themselves.\"", "\n\nLooking at Aaron, she said, \"Don't worry. ", "It's painless. ", "Or so I've heard...\" More laughter followed, but Aaron wore a less than confident look on his face. \"", "Before we continue, Aaron, I need to know that you understand the commitment you are making, how your life will change from now until forever, the secrets you must keep to protect our kind and the sacrifices you must make in order to live a life with Danielle. ", "This choice can never be unmade, never broken and your lifespan will now be joined with hers. ", "Should she live a thousand years or only a day more, you will share her fate from this day forward. ", "No one here would think less of you if you walked away right now. ", "Not even Danielle. ", "The commitment you are making is beyond the bravery of even most of us here today, so we would not fault you for choosing to leave.\"", "\n\nWith a confidence his hadn't quite felt before, Aaron stood his ground physically straighter and firmer as he answered, \"No, this is what I want. ", "I choose to bond with Danielle.\"", "\n\nDanielle let out a breath she hadn't known she held, closing her eyes as she tried to calm her suddenly rapid beating heart. ", "With that breath, she also let go of the last doubts that had plagued her heart and mind. ", "All of the previous hurt she'd harbored within her flowed out into the atmosphere and disappeared on the sweet forest scented breeze.", "\n\nFreya was pleased and convinced that now they were both truly ready. ", "She plunged Aaron's sword into the ground between them. \"", "Please join hands upon the sword and we'll do the expedited version.\"", "\n\nThey did. ", "She blessed. ", "Aaron felt no pain whatsoever. ", "Just relief...until he noticed that Danielle's chain began to lightly glow. ", "He looked down and discovered his did the same.", "\n\n\"Almost done,\" Freya assured him as she made her way around the altar. \"", "Danielle, step forward and give me your hand.\" ", "Freya took her offered hand and reached out with her other one, twinning it around Danielle's binding chain. ", "When her hand came away, she held a dainty ring made of the same unearthly material and placed it on Danielle's finger. \"", "This is a ring for motherhood, which I have blessed with fertility and bestow to you, my daughter.\" ", "Danielle thanked her and kissed her lightly on the cheek.", "\n\nWith the ring upon her hand, the chains around their necks, and their hands joined once again upon the hilt of Aaron's sword, the couple then spoke their vows.", "\n\n\"Aaron, you are mine, the other half of my soul. ", "You were meant for me and this time destiny got it right. ", "It took twelve hundred years to find you. ", "The binding chain knew that you were my true soulmate all along. ", "No one else can fill the empty void my life would have been without you and no one else will love you like I will. ", "This I swear.\"", "\n\nUpon hearing Danielle's vows, Makayla and a few of the other females began to softly cry. ", "Most for happy reasons, but Makayla felt torn between sadness and hope. ", "Sadness shadowed her soul for the loss of her mate and what they had shared. ", "Hope for Danielle's future happiness, and possibly someday, even her own. ", "She was flanked on either side by her sister, Valeria, and her friend, Zahara, who both understood her turmoil and draped their arms around her, drawing her near.", "\n\nMakayla's discomfort wasn't the only feeling that Zahara was picking up on in the assembly of warriors and friends. ", "She glanced behind her to see Vex quietly leaving the gathering. ", "It would take a blind man to miss the sorrow and bitterness that consumed him. ", "She sent a prayer to the Gods for his safe keeping and well-being before returning her attention to the ceremony.", "\n\n\"Danielle, you are my friend, my lover and now my mate. **", "I promise to love you unconditionally, to support you in your goals, to honor and respect you, to laugh with you and cry with you, and to cherish you.** ", "I look forward to sharing life's journey with you, however long that may be. ", "Whether we have forever together or only a day, the time will have been worth it, because I have you to share it with.\"", "\n\nA small tear spilled over and slid down Danielle's cheek, catching at the corner of her bright smile. ", "Aarons own eyes glowed with adoration as Freya's voice whispered on the wind for their ears alone. \"", "Good show, you two. ", "Now, go forth and make me proud of your union.\" ", "Then she raised her arms and her voice and addressed the assembly, \"All who are gathered here, gods, warriors or immortals be, whether in body or spirit, bear witness this eve to the eternal bonding of Danielle, daughter of the Goddess Freya, and Aaron Jansen, descendant of Freyodin Warrior Alarr. ", "All of Valhalla rejoices this blessed union.\"", "\n\nA mighty cheer went up around them that echoed through the forest. ", "A smattering of light brilliant white snowflakes descended on and mystically swirled around them. ", "Danielle looked out toward their guests searching for one in particular.", "\n\nMyste winked and smiled brightly, speaking to Danielle's mind alone, Just a little magical wedding present for you...\n\nDanielle inclined her head in thanks then returned her adoring gaze to Aaron.", "\n\nFreya leaned into Aaron. \"", "You may kiss her now.\"", "\n\nAnd so he did. ", "Aaron wasted no time, taking her in his arms and none-too-shyly ravishing her mouth, which she returned with equal fervor. ", "It was an emboldened kiss. ", "One Danielle would remember for her long lifetime to come. ", "But before they could bring their connection to a mutual end, Danielle was surrounded by a gaggle of women dragging her away. ", "She quickly blew a kiss to Aaron and joined them at a full run without a single word.", "\n\n\"Move your ass, man, or we'll be serving those wenches all night long!\" ", "Steele yelled from behind him. ", "He was instantly caught up in a horde of running male warriors being practically dragged between them.", "\n\n\"What? ", "Where are we going?\" ", "Aaron was completely lost as to what was happening at the moment. ", "All he knew was that he had been separated again from his new bride. ", "Definitely, something he was not okay with this time.", "\n\n\"Move, move, move!\" ", "Steele roared, hanging on to Aaron's jacket with one hand, his other arm pumping fast at his side as he flew across the field before them.", "\n\nTurbo interjected through huffs of breath, \"It's an old Scandinavian custom of ours called the bride-running or bride-grooms ride. ", "If we don't beat the females to the feasting hall, we'll be serving them ale all night long instead of the other way around. ", "No tracing aloud. ", "So move your ass!\"", "\n\nOkay...This sounded like fun. ", "Aaron picked up speed. ", "Although the earlier blood exchange had made him stronger and faster, he still wasn't as fast as the others, but with their help he sort of ran like he was semi-floating above the ground, touching about every other footfall. ", "Soon the males were gaining on the females, working their way through the throng and leaving them behind in their wake. ", "Aaron felt Danielle's nearness and searched for the sight of her but couldn't locate her.", "\n\nOnce they reached the feasting hall, Aaron was placed at the doorway to await his bride. ", "Another custom called for him to lead her into the hall so she would not stumble over the threshold. ", "Unlike modern day homes, medieval homes had a raised lip at the bottom of the doorway in order to stop the cold winter drafts and had to be stepped over in order to pass through. ", "Stepping over the threshold represented the bride's transformation from maiden to wife. ", "It was very similar to carrying a bride over the threshold of her new home, which was the custom Aaron chose to adhere to.", "\n\nAs soon as Danielle approached the door, Aaron whipped her up into his arms and brought his lips down to hers in a rousing kiss that sent heated flames through Danielle and a rosy glow spread up her cheeks and down to her breasts.", "\n\n\"There you are,\" he murmured softly against her mouth.", "\n\n\"Yes, and I'm all yours now,\" she answered before pulling back slightly. \"", "We'd better get inside before they come looking for us.\"", "\n\n\"If we must,\" he teased and laughed as he held her close and entered the hall.", "\n\nThe night was filled with dancing, laughter, love and food galore. ", "The women accepted their loss and kept the ale flowing freely all evening. ", "As the festivities came to a close, Thunder approached the table where the newly bonded couple sat. ", "He knelt at the feet of Danielle and placed his famous weapon, the Hammer of Mjolnir, onto her lap as a blessing of fertility.", "\n\n\"Please accept this token as a blessing on you both for a fruitful marriage,\" Thunder offered. ", "He placed another chaste kiss on Danielle's cheek. ", "The couple thanked him in turn.", "\n\n\"Another custom?\" ", "Aaron asked.", "\n\n\"I'm afraid so.\" ", "Danielle turned to look at Aaron. \"", "Thank you for being such a good sport about all of this. ", "We don't get to practice these traditions very often around here.\"", "\n\n\"Anything for you, love. ", "Anything.\"", "\n\nHis words came back to bite him in the ass as a roaring cheer filled the room and the women gathered around to claim Danielle once more.", "\n\n\"Oh, no. ", "Not again,\" Aaron complained.", "\n\n\"It's only for a short while, love. ", "I'll see you soon. ", "Promise.\"", "\n\nAnd then she was gone.", "\n\n\"Damn! ", "This is the third time over the last twenty-four hours that she's been taken away from me,\" Aaron grumbled, but with humor. ", "If he didn't know any better, he'd think these customs were simply a way to make him suffer. ", "He'd been sporting a semi since last night and couldn't take much more.", "\n\n\"Not to worry. ", "We'll take you to her soon enough,\" Blaze offered, draping his arm around Aaron's shoulders.", "\n\n\"Yea, don't worry, Doc,\" Turbo interrupted. \"", "After tonight, you won't ever be able to get rid of her. ", "Literally. ", "Forever.\" ", "Laughter erupted all around Aaron.", "\n\nForever. ", "He smiled. ", "It was a forever he couldn't wait to begin.", "\n\n*****\n\n\"I wondered when you'd get around to paying me a visit. ", "I actually expected you sooner.\" ", "Thunder looked pointedly at the warrior across the room whose entire demeanor appeared emotionally battered. \"", "You've shown exceptional restraint throughout this entire ordeal, Vex, and I'm very pleased with you.\"", "\n\nBarely holding his rage in check, Vex requested, \"Permission to speak freely, sir.\"", "\n\n\"Yes, of course. ", "You know we hold no ceremony here. ", "Say what you will, warrior.\"", "\n\n\"I am not pleased with you! ", "How can this be?\" ", "he spat through tight lips, knowing full well that he was raging at an actual god, but caring naught at the moment.", "\n\nThunder watched as the rage physically drained away from Vex's body to be replaced by unmistakable defeat. \"", "Why?\" ", "his comrade asked. \"", "Why him? ", "Why not her?\"", "\n\nThunder wished he could console his warrior, his friend, but he knew his answer would be inadequate. \"", "I'm sorry, Vex, but it's not for me to speculate the reasons or choices of the gods.\"", "\n\n\"But you are one...\"\n\n\"Yes, you're right, I am. ", "This decision, as well as the decision made ten years ago, was not mine to make. ", "I was only charged with carrying it out, just as you were. ", "I know you blame me, and if that makes you feel better, I'll gladly bear the culpability. ", "Yet, in my defense, in my capacity as a warrior, I am not unlike you. ", "I follow the rulings and orders passed down by those above me with the belief that they have the knowledge necessary to make a more informed decision. ", "It's the way it has always been since the creation of the Freyodin Warriors and I trust them to do what has to be done for the betterment of us and mankind alike. ", "The warriors' vow and duty is selfless. ", "This life is a second chance to save humanity from the immortal threats our kind has brought upon them. ", "Without us, they would be annihilated, or worse, enslaved. ", "God or not, this is also my vow. ", "But I'm not telling you anything you don't already know.\" ", "He paused a moment then continued, his tone low and filled with sincerity, \"Tell me. ", "How can I help you, my friend?\"", "\n\n\"Help me to understand. ", "Please,\" Vex pleaded. \"", "I hear what you're saying and my brain accepts and agrees with you, but my soul...it still cries out for her.\"", "\n\n\"I can tell you this...although mortal, Aaron was needed. ", "He holds a place in this battle, just as you do. ", "If not for this reason alone, he would not have been permitted to join us. ", "Your female was not only mortal but was so young. ", "There are things happening around us that we don't understand and are not meant to, whether now or ever. ", "It's not up to us to question. ", "Only accept.\"", "\n\nVex steadied himself and stood taller, pulling his back ramrod straight in military fashion. ", "His youthful face hardened and his normally blue/green eyes turned dark and cold. \"", "You're right. ", "I apologize for my emotional outburst.\"", "\n\n\"No apology necessary, warrior,\" Thunder conveyed with respect. \"", "Now, if you're ready, you've been selected for a special assignment.\"", "\n\n\"Always ready, sir.\" ", "Vex maintained his rigid stance.", "\n\n\"Then will you relax, please? ", "Sit down and I'll fill you in on the details. ", "You're going to the University of Oregon to check out the linguist that works with Aaron. ", "We need to find out what she knows and get our hands on the original and all copies of the documents that Aaron discovered. ", "This mission is vital. ", "Select a female to go with you undercover...\"\n\n*****\n\n# Chapter Twenty\n\nValeria placed the nightrail of creamy silk over Danielle's head. ", "Déjà vu. ", "I think we've been here once before.", "\n\nDanielle heard the shared thoughts. ", "Yes, and once again, you are assisting me for my wedding night, my friend. ", "Thank you.", "\n\n\"No need to thank me and you know it. ", "I wouldn't have missed this for the world. ", "At least this nightrail, I mean negligee, is of this century. ", "Not like the first one. ", "Quite sexy, I'd say. ", "And beautiful to boot. ", "Freya did really well this time,\" she said, referring to another of Freya's gifts to her daughter.", "\n\nDanielle thought back to her first wedding night, that first nightrail and her tragedy with Alarr. ", "She felt more and more blessed as this day had progressed. \"", "Yes, things are looking up in that part of my life, too.\" ", "Danielle smiled as she thought of her renewed relationship with her mother. ", "She watched as the other women scurried around, fluffing pillows and placing fragrant flowers and candles around the room, setting a romantic atmosphere.", "\n\n\"It's all so lovely. ", "Thank you, everyone.\"", "\n\n\"You're very welcome, sister,\" Makayla answered as she hugged her. \"", "But we need to hurry. ", "With the looks Aaron was giving you, we don't have much time before...\"\n\nA thunderous interrupting knock sounded at the door. ", "The ladies listened as demands of entry were made with peals of laughter and lewd suggestive advice. \"", "It's time, woman. ", "Your man awaits and by the looks of it, is very impatient, I might add.\"", "\n\n\"What did I tell you?\" ", "Makayla laughed loudly and then shivered with thoughts of her own prospective night at Vengeance's authoritative voice. ", "The excitement was quite contagious.", "\n\nBy torchlight, the men had led Aaron to Danielle's house and to her bedroom door. ", "Tradition dictated that they put the groom to bed with his wife before they left them alone.", "\n\n\"Hurry, Danielle,\" Valeria instructed. \"", "Climb up in the bed before they bust that door completely down.\"", "\n\nShe jumped onto the bed, trying to feign a casual appearance that wasn't anywhere near convincing, when the door came swinging open wide and large, hulking male bodies streamed through and tossed an exuberant groom onto the bed beside her. ", "Danielle bounced high, nearly flying off the bed completely on the other side. ", "Cheers and laughter filled the room.", "\n\nAaron immediately reached out and steadied her in his arms. \"", "I've got you. ", "Come here.\" ", "He took in the sight of her from head to toe, then looked into her eyes smiling. \"", "Now, this Scandinavian tradition I actually like!\"", "\n\nDanielle's own laughter died on her lips as he pulled her in closer for a kiss.", "\n\n\"That's our cue,\" Vengeance bellowed while herding everyone toward the door. \"", "Everyone out. ", "The party will continue back at the hall.\"", "\n\nAlong with much ribaldry and hilarity, someone heralded the obligatory, \"Don't do anything I wouldn't do...\" Shortly after, the house fell silent as their friends all traced away.", "\n\n\"Are they gone?\" ", "Aaron whispered against her lips.", "\n\n\"Yes,\" she laughed and teasingly added, \"Oh, what shall we do now?\" ", "in her best Scarlet O'Hara voice, the back of her hand resting on her forehead in a feigning fashion.", "\n\nAaron pulled back and sat up on the bed with his legs stretched out in front of him. ", "She lovingly admired his well-developed chest and stomach muscles through the unbuttoned tuxedo shirt he wore. ", "The scent of his maleness filled the air around her. ", "Thrilled at the thought that he was now hers, only hers.", "\n\n\"Frankly, I have no idea, darlin',\" he replied mockingly while see-sawing his eyebrows in an up and down gesture. \"", "Why don't you climb up here on my lap and we'll figure something out.\" ", "As Danielle moved to do as he asked, Aaron halted her for a moment, cupping her chin gently in his hand. \"", "God, do you have any idea how beautiful you are? ", "How amazing you looked in your gown? ", "Like an angel. ", "When you walked toward me, it took everything I had not to say the hell with it all and drag you into my arms tonight.\"", "\n\nAs Danielle gracefully continued her descent onto his lap, he guided her legs around his waist, virtually wrapping her around him, she noticed the serious look in his startling eyes. \"", "You don't have to tell me I'm beautiful, silly. ", "We're already bonded. ", "I'm a sure thing.\" ", "She meant it playfully, of course, but he remained sincere.", "\n\n\"I mean it, Danielle. ", "I love you. ", "I love touching you and holding you and...\"\n\n\"Shhh,\" she said, effectively cutting him off with a finger on his lips. \"", "I know. ", "And I love you, too. ", "Just hold me for a sec, will you?\"", "\n\n\"For the rest of my life,\" he vowed as he pulled her head down to rest on his shoulder.", "\n\nGently, they began to rock together. ", "Danielle felt so safe in his arms, and there was something else she'd never felt before...complete. ", "She knew to the depths of her soul that wherever they were from now on, as long as they were together, it would feel like home.", "\n\nAaron pressed feather light kisses along the top of her head, slowly moving downward, his tongue darting around the shell of her ear and continuing into the tender bend where her neck met her shoulder. ", "The ministrations of his sensual mouth, teeth and tongue stirred her desire and she moaned as her hips began a subtle grinding movement against the hardening length between them.", "\n\nThe hem of her sleek nightgown was inched upward, tugged slowly over her head and tossed carelessly to the floor beside the bed, baring her completely to him. ", "She shivered as he cupped her breasts in his hands, her silky soft skin against his callused palms, strumming his thumbs over her dusky nipples until they formed tight rigid peaks that beckoned his mouth to savor them. ", "His head lowered, taking her into the warm cavern of his mouth and groaning at the sweet taste of her skin.", "\n\nMine, he thought.", "\n\nYes, she answered.", "\n\nDanielle clutched his head to her breast, delighting in the feel of him as she ran her fingers through his short sandy hair. \"", "Help me,\" she said, eagerly pulling his shirt off partially over one shoulder.", "\n\n\"Hold on to my shoulders,\" he instructed. ", "Then Aaron reached back, pulling off the remnants of his shirt and lifted Danielle upward with one arm high enough to push his pants and briefs down over his hips with the other, kicking the remainder down and off with his out-stretched legs. ", "As he brought her back into his lap, he aligned his cock to her center and slowly lowered her onto his steely length. ", "Danielle closed her eyes, consumed by the feel of Aaron entering her so intimately in a single slow glide.", "\n\n\"No, love.\" ", "He tenderly cupped her cheek with his hand. \"", "Open your eyes. ", "I want to watch your beautiful face while I make love to you.\"", "\n\nDanielle complied and he saw as well as felt the profoundness of her love flowing through her. ", "Aaron reached behind her, gripping her bottom in his hands with barely controlled restraint and rocked solidly into her. ", "He was torn between tenderly ravishing her and madly thrusting into her, but contained his near feral urges. ", "They had plenty of time for the latter. ", "Danielle's hazel eyes blazed brighter with each thrust Aaron made into her tight slick sheath.", "\n\nAs they began to move together, the sensations emitted became almost a physical presence surrounding them and melding into their very beings, lifting them higher to a plane of existence all their own. ", "This position limited Aaron's movement, preventing him from pulling his hardened length completely out of Danielle, locking them in a constant intimate connection as they unhurriedly explored each other.", "\n\nAaron took her mouth in a rapturous kiss, moving his tongue against hers, building the intensity of their coupling. ", "He torturously dragged his mouth down her neck and shoulders with tender kisses and teasing nips of his teeth, across the dimly glowing chain encasing her throat, slowly reaching the destination he sought at the hollow cleft between her breasts. ", "The same supple breasts that were peaked to full arousal, their hardened nipples rubbing sensuously against his chest and beckoning him to taste them again. ", "Danielle moaned as he took her in his mouth, continuing his torment of little nips, laving his roughened tongue on one breast and then the other.", "\n\nDanielle continued her exploration of his hard lean body, unable to get her fill of touching him. ", "Her senses heightened to the sights and sounds around her. ", "The scratching of her nails on his tight muscular torso, running up and down his sides toward the straining glistening shoulders at his back. ", "His hot panting breaths against her skin as he nuzzled her neck and lightly kissed her hairline up to her temple. ", "The friction and heat of their joining as they rocked together, the ease turning to more frantic needs and movements as their passion built higher and higher.", "\n\nAs their lips sought out and met, Aaron kissed her with an urgency that spread like fluid fire throughout her body, burning her so deep that she could feel his soul mingling with hers. ", "He cupped her bottom with both hands, lifting her completely off his iron cock and plunged fully and profoundly into her slick heated cavern, grinding his pelvis with hers. ", "Then again and again.", "\n\nSo close. ", "So close. ", "The waves of pleasure crescendoed until they peaked together at the same moment in ecstasy. ", "Danielle arched backward, screaming out as he filled her with his hot seed. ", "Aaron's animalistic roar pierced the air as he claimed his new mate, throbbing and pulsing within her, feeling the completion of their joining. ", "They clung tightly together without a word until their rapid breathing began to slow.", "\n\n\"Oh, my God.\" ", "Aaron looked down at Danielle's throat, his eyes wide.", "\n\n\"What? ", "What is it?\" ", "She began to panic, running her hand up her chest.", "\n\n\"Everything,\" he said a little more calmly then added a small smile. ", "Finally, the smile moved upward and his eyes began to twinkle somewhat.", "\n\n\"Everything?\" ", "she asked, attempting to match his calm.", "\n\nYes. ", "I not only hear your thoughts, but I can feel what you're feeling. ", "Not physically, but intuitively. ", "And the bonding chain...it's glowing...I mean really glowing now.", "\n\nOf course, it is, silly. ", "What did you think was going to happen?", "\n\nI don't know. ", "We never got around to talking about that.", "\n\n\"Yea, I guess you're right.\" ", "she laughed aloud. ", "She examined and fingered the chain draped across his collarbone. \"", "Come to think of it, I've never seen them glow this brightly either.\" ", "Hmmm..., she pondered for a moment then pushed it away for tomorrow. ", "Tomorrow her dreams would be noted, for they were held to be prophetic of the number of children she would bear, the fortune of her marriage, and the destiny of her descendants.", "\n\n\"Let's let the mystery lie for now and chalk it up to how very much I love you.\" ", "Aaron cupped her face with his hand, tilting it upward and looked soulfully into her shining eyes. \"", "Thank you, Danielle.\"", "\n\nDanielle didn't need to ask for what. ", "For the first time in her long life, she felt whole and content. ", "No longer would she be haunted by doubts or regrets from the past. ", "No longer would she be alone. ", "She completely understood Aaron's thought and feelings. ", "For they were also her own.", "\n\n\"Thank you back, my love.\"", "\n\n*****\n\nDear Reader:\n\nIf you liked Love's Betrayal, we would appreciate it if you would help others enjoy this book, too, by recommending it to your friends on Goodreads, lending it on your e-Reader or by writing a positive review at your favorite retailer or other media that you acquired it from. ", "Look for Vex's story, Timeless Love, now available, with more in the Freyodin Warrior Series to follow close behind. ", "Drop us an email to let us know which characters are your favorites and who or what you'd like to see a story on. ", "We're always interested in meeting new friends.", "\n\nPlease send your feedback via email at http://elizabetteremon.com.", "\n\nThank you.", "\n\nElizabeth & Jeanette\n\nABOUT THE AUTHOR\n\nElizabette Remon is actually a team of two best friends doing one of the many things they enjoy doing together – creating and writing. ", "They are both native Texans and have been friends for more years than they're willing to admit.", "\n\nElizabeth is a lover of mystery, paranormal and romance of all kinds. ", "Her passions are laughing, reading, writing, singing, 80's music, travel, family and romantic comedies – not necessarily in that order. ", "Between her family and life's necessities, she gets her creative writing juices flowing bringing her experiences and over-active imagination to life, creating worlds of passion and fantasy.", "\n\nHer biggest personal fantasy is to find and fall into that Hot Tub Time Machine which would throw her back into the 1980's where she would devote her life to being an avid groupie of Steve Perry, Jon Bon Jovi, Sammy Hagar and Eddy Van Halen – preferably in that order.", "\n\nJeanette cares for family and friends and loves traveling and experiencing life to the fullest, which provides great opportunities to expand on her creative imagination. ", "She fell in love with reading romance novels when she was a teenager. ", "Now her dream is to write her own. ", "Her motto is 'I live reality. ", "I want to write fantasy.'", "\n\nBut most of all, they are avid believers in the HEA – Happily Ever After – filled with fun and feisty heroines and alluring muscled men, cowboys, pirates, highlanders, vampires, werewolves, or anatomically correct aliens, draped in leather, denim, kilts or nothing at all. ", "Their goals in writing are to take you away to another world, place or time - an alternate reality where they hope you will discover love, desire, laughter, excitement and maybe an occasional tear. ", "Come join them and escape...\n\nTo learn more about Elizabeth and Jeanette and for upcoming releases, giveaways and free books, please visit:\n\nOur webpage at: http://elizabetteremon.com\n\nEmail us at: mailto:elizabetteremon@yahoo.com\n\nOr at: elizabeth.emmons_author@yahoo.com\n\nVisit us on Facebook at: https://www.facebook.com/Elizabetteremon\n\nUPCOMING RELEASE\n\nTIMELESS LOVE\n\nBy\n\nELIZABETTE REMON\n\nAvailable Now\n\nImmortality is never ending and unforgiving when you're all alone...\n\nVex is a Freyodin Warrior sworn to protect mortals from the evils of the world. ", "He's bitter and angry since he lost his love several years ago, but pushes through to do the job he pledged to do when he became immortal. ", "With his deadly daggers, he duals out punishment as fierce as the pain that slices his own heart.", "\n\nRebecca is a linguist at the nearby university working on translating an ancient scroll and solving a riddle that could change the course of history as well as the future as we know it. ", "She stumbles into trouble that requires someone rescue and protect her. ", "Hiding her away from the danger that seeks to destroy her. ", "And she is Vex's lost love. ", "Lost because of her humanity.", "\n\nIt's an assignment he doesn't want, but can't trust to anyone else. ", "Will Vex be able to save her from their enemies and from himself or will she be lost to him once again?", "\n\nTimeless Love is about 100,000 words, and the second book in a series of paranormal romance novels, following the Freyodin Warriors and the mortals that love them. ", "If you're looking for stories that contain love, lust, epic battles, fierce warriors and the enemies who taunt them, you've found the right read! ", "These books can be read standalone or in the series order. ", "No cliffhangers and every book contains a guaranteed HEA!", "\n\nRead on for an excerpt -\n\nCHAPTER ONE\n\nIt was the hardest goddamn thing he'd ever had to do.", "\n\nHis gut clenched and he felt as if someone was ripping out his heart from his chest cavity with a million red hot pokers as he softly closed the door for the final time and began to force his feet to trudge down the cement walkway. ", "The pressure encompassing his head would surely explode at any moment and his vision blurred, making it impossible to decipher the jagged cracks on the pavement below. ", "The brilliant early morning sky above him resembled a kaleidoscope bursting upon the horizon, but all he could see was the gloomy grays burrowing his feet. ", "Oh Goddess, why did it have to hurt so much? ", "Why did he have to feel so much? ", "He hadn't intended for this to happen, hadn't planned it. ", "But it did. ", "Like it was preordained, predestined or something utterly unavoidable. ", "He wished he'd had Zahara's gifts of sight and visions to forewarn him of this insufferable mistake. ", "He'd gladly go back and undo it all to stop this torture he alone must bear.", "\n\nWait! ", "No! ", "That's not right. ", "Never.", "\n\nNever would he forget, nor would he regret. ", "This was his path to travel and it had been so blessedly sweet while it lasted. ", "Somehow, he'd try to remember the happier moments when it became too hard to deal. ", "Like now. ", "He'd have to find a way to separate the pain from the memories. ", "Somehow.", "\n\nHe attempted that now as his thoughts drifted to last night...\n\n*****\n\nIt took everything he had within him to hold his emotions in check. ", "This was their last night together and she couldn't know it. ", "If all went well, he'd keep it together long enough to use his gift of enthrallment to carefully extract all memory of him and their time together from her mind. ", "He had to do it. ", "It was the only way he could think to spare her the pain. ", "She deserved a better life. ", "Although letting her go would hurt worse than the pain of a thousand scorpion strikes upon his flesh, he knew it was the right thing to do. ", "For her sake.", "\n\nThunder was right. ", "His leader had commanded him to end the relationship. ", "The relationship that should not have gotten as far as it did, especially in such a short time span. ", "The warriors could dabble in sexual adventure with mortals but lasting relationships were forbidden. ", "It was too great a threat to their secret existence.", "\n\nEven though she was incredibly mature for her age, in reality, she was only eighteen years of age. ", "She was finishing her first year at college and her life had just begun. ", "He was no match for her. ", "Only through the grace of the gods was he living out his second existence as a Freyodin Warrior. ", "A life she knew naught and could never be a part of.", "\n\nBut knowing this hadn't kept him from falling in love with her. ", "Falling hard and fast. ", "And now he must end it. ", "But he would make love to her...one last time. ", "That is what he must think on for now.", "\n\n\"Rebecca,\" he murmured against the soft shell of her ear while running his strong hands up and down the length of her long, slender legs. ", "He continued his slow exploration of her body as they lay naked together, memorizing every curve, bend and dip of her. ", "Just as he would take her memories away, he wanted his memories to last until his last breath.", "\n\nRebecca's passion heightened almost to the point of madness. \"", "Ben, stop teasing me,\" she begged. ", "She was the only person he allowed to call him by his given name. ", "The name he answered to when he was mortal. \"", "Please.\" ", "Her plea was a warm rasping whisper across his skin as she nuzzled into the crook of his neck.", "\n\n\"In due time, my love. ", "We have all night.\"", "\n\n\"No, Ben. ", "I need you now.\" ", "She writhed against him trying to find purchase and force him to cease his gentle ministrations, to touch her where she needed him most. ", "She wanted his rough hands on her, in her. ", "His mouth doing all the things she so loved that sent her soaring to the clouds.", "\n\n\"And you have me now,\" he teased with a slight laugh, refusing her request. ", "He continued with his light strokes up and down the sides of her ribs, barely brushing the underside of her breasts.", "\n\n\"Stop mocking me.\" ", "She playfully swatted on his powerfully muscular chest then ran her hand down his perfect stomach. ", "His torso was hard as granite and she bit her bottom lip to stop from moaning as she let that hand fall lower, taking a firm grasp of his cock. ", "Also granite hard.", "\n\nVex growled against her throat as he involuntarily thrust up into her hand. ", "Only she could ring such intense reactions out of him so easily. \"", "You're not playing fair, love. ", "But two can play that game,\" he warned. ", "Then he bit down on her tender flesh where her neck and shoulder met with just the right amount of teeth and pressure. ", "Just enough pleasure and pain that he knew would make her squirm with need even more. ", "He knew all of her erogenous zones intimately and planned to draw them out.", "\n\nTonight, he would explore, savor and commit to memory every part of her, every sound, sigh, cry or pant that emitted from her lips, the way she moved above and beneath him, how she felt as her silky core surrounded him, the feel of her hands and lips on his eager body, the look of rapture on her face as she came apart in his arms. ", "He wanted everything emblazoned in his mind so that he might recall it on the long lonely nights ahead of him.", "\n\nHe gave her what she wanted, entering her core in maddeningly measured increments. ", "He made love to her languidly, tenderly, passionately. ", "Long lingering kisses, slow deliberate strokes inside of her, building her desire unhurriedly to a fever pitch that caused her to beg for relief. ", "When she could finally take no more, he plunged harder, faster, and rose himself above her to view her beautiful face as she reached her peak, crying out his name. ", "The feel of her inner muscles contracting around him forced him to relinquish his own control. ", "He joined her in his own release, filling her with his seed, his heart and his soul with a gut wrenching cry.", "\n\nVex immediately gathered her to him, holding on so tightly, his body refused to let her go. ", "It was too hard and he was too emotionally raw, but he knew he had no choice, so he quickly pulled himself together and fixed a false smile on his face. ", "Fortunately, she still floated in her bliss and his blunder hadn't given him away.", "\n\nThey laughed, talked and made love several more times before dawn. ", "As Rebecca drifted off to sleep wrapped tightly in Vex's arms, she murmured, \"Thank you, Ben. ", "It was a wonderful, unforgettable night. ", "You know I love you, right?\" ", "Her long tawny eyelashes fluttered slowly down to rest on her cheeks.", "\n\n\"Yes, Rebecca. ", "I know. ", "I love you, too, and I shall never forget,\" he answered her though he doubted she was cognizant enough to hear it.", "\n\nHe would hold her while she slept this one last time, as he began the agonizing task of making her forget...\n\n*****\n\nAt least she wouldn't suffer. ", "He took solace in that. ", "She'd never recall the times he held her in his arms. ", "Kissing her sweet lips until they were swollen with desire. ", "Molding her supple curves perfectly into his hard yearning body. ", "Bringing her to completion again and again as she cried out his name. ", "A cry that would haunt him for eternity.", "\n\nThe godsdamn eternity he had to face...alone...without her.", "\n\nNo, there was no going back. ", "Even if he could. ", "Why had he finally found love as he'd never known before just to have it viciously wrenched away? ", "Fate had played a cruel, cruel joke on this poor excuse of a man. ", "But he wasn't just a man any longer. ", "Hadn't been for well over one hundred years. ", "He'd bravely died a man on that World War I battlefield in 1918, protecting all that he loved and treasured at the time. ", "Then they had saved him. ", "Gave him a choice to go on. ", "To fight for all mankind and not just those that he cared for in his small portion of the world. ", "They offered him life...immortal life...and brought him over, training and turning him into a warrior.", "\n\nWould he still make that same choice today? ", "Knowing all that he would lose and all that he would yet have to endure? ", "Every fiery nerve, strained tendon and cramping, clenching muscle in his body, especially his traitorous heart, screamed No! ", "But his soul admitted defeat. ", "Yes, yes...always yes. ", "Odin informed him that there was no shame in rejecting the offer, no shame in choosing to take his well-earned rest in the eternity hereafter. ", "He had already proven his exceptional bravery and honor and those qualities made him a candidate for serving humanity as a Freyodin Warrior.", "\n\nRealization dawned as he stared blindly at the ground with no care as to where his footfalls were taking him. ", "Fate had not determined the course of what was to be his long life. ", "He himself had and he knew he couldn't blame fate or anyone else for his own mistakes. ", "No, she wasn't a mistake. ", "Never that. ", "He had chosen to break the rules and fall in love with a mortal. ", "Not intentionally, of course, but it had happened none the less. ", "And he would have to bear the consequences...alone.", "\n\n\"Hey, there you are, man.\" ", "The deep Southern Mississippi drawl brought him out of the depth of his momentary sorrows.", "\n\nVex's head whipped up to meet the aqua blue gaze of his fellow warrior leaning against his car at the curb, but he said nothing. ", "Justice had been his closest friend for more than twenty-five years now and wouldn't expect a reply after seeing the sorry state he was sure he reflected. ", "At six foot four, Vex's frame should have stood proudly two full inches over his friend's, but in his current solemnly stature, he was anything but.", "\n\n\"I thought I might find you here,\" he continued as he uncrossed his arms from his broad chest and pushed himself away from his resting spot. \"", "Thought you might need a ride after...uh...\" His voice slowed and trailed away without finishing the thought as he looked first downward and then off into the distance. ", "Anywhere but Vex's tormented eyes.", "\n\n\"Thanks,\" he mumbled raking his fingers over his scalp through his long flaxen hair. ", "It was a nervous habit and an instant tell that all wasn't right in Vex's little world. ", "A habit he could never break himself of whenever he was preoccupied or stressed that left the shorter hair surrounding his face standing up on end in a spiked, bedhead fashion.", "\n\nWithout another word, Justice skirted around the front of the car and sat down in the driver's seat, placing his hand on the key in the ignition. ", "Vex follow suit and took his place in the passenger's seat, not bothering to buckle up. ", "There wasn't much that could end his miserable existence, but a beheading through a car windshield would certainly do the trick well enough.", "\n\nJustice stared straight ahead at the row of houses that banked either side of the street, a hardness claiming his jaw as he clamped his teeth tightly together trying to bite back the words. \"", "Are you okay?\"", "\n\nVex's gaze matched the direction of his friend's, but the fog centered in his mind left him blindly staring at nothing but a white haze. \"", "I guess. ", "I mean, I don't have a choice, do I? ", "I didn't have a choice in any of this.\"", "\n\nTogether, Justice and Vex were known as the World War Buddies, as Justice had been brought over during World War II. ", "They seemed to be naturally drawn to each other and had become and remained fast friends since that time. ", "Justice wanted to reassure his friend, to be there to help alleviate his pain in some way. ", "He wasn't quite sure how he would do that, as he'd never really felt that strongly for a female, but for his friend, he wanted to try.", "\n\n\"No, I don't believe you did. ", "We don't have much choice who we fall in love with, I suppose.\" ", "He paused and silence followed like a heavyweight within the confines of the vehicle. \"", "For what it's worth, I'm sorry...and I'm here for you, brother...\"\n\nThrough his peripheral vision, Justice watched Vex nod his head silently.", "\n\n\"Where would you like to go now?\" ", "Oddly, his fingers were still wrapped around the key in the ignition as if frozen in time.", "\n\n\"Anywhere. ", "Just drive,\" he managed. ", "As his sorrow turned to a simmering rage he hoped they'd run into the Huldrekall. ", "Beating a demon or two viciously to death sounded like something he needed right about now.", "\n\nJustice turned the car's engine over and slowly pulled away from the curb leaving behind Vex's crushed heart and dreams of a love unfulfilled, tattered among the debris of dead fallen leaves on the street below.", "\n\n*****\n\nCHAPTER TWO\n\nTen Years Later...\n\n\"Yes, Rebecca. ", "I know. ", "I love you, too, and I shall never forget.\"", "\n\n\"Wait! ", "No! ", "Don't go. ", "Please. ", "Please, come back.\"", "\n\nBecca Forrester's own sobbing screams woke her as she shot suddenly upright in her bed, fighting amongst the twisted cotton sheets she found herself tangled within. ", "Her heart beat erratically against her aching chest, pulse racing as if she'd just completed a marathon, sweat running in rivulets down her brow and between her breasts and the remnants of salty tears at the corners of her mouth. ", "She stared sightlessly at the outstretched arm in front of her, the hand reaching for some unseen thing that her mind just could not grasp. ", "Whatever it was, it was just out of reach, just beyond her ability to touch or visualize it, as though trapped behind a veil. ", "She screwed her eyes back half-shut, hoping she could still see a glimpse of it. ", "But it was gone. ", "Again.", "\n\nNot it. ", "Him. ", "The man of her dreams that she could never fully remember. ", "She only knew that he was there one moment and then cruelly gone the next. ", "Every time. ", "It was the same thing every time. ", "That faceless man that made such wonderful love to her in her slumber. ", "So wonderful she never wanted to wake up. ", "But she always did and he always said the same thing before he disappeared. ", "Foggily fading out like some Hollywood movie magic illusion.", "\n\n\"Yes, Rebecca. ", "I know. ", "I love you, too, and I shall never forget.\"", "\n\nIt was always the last thing she could remember before gaining complete consciousness.", "\n\nShe snorted to herself with derision. ", "And it seems I'm destined never to remember, she ruefully thought.", "\n\nShe'd been haunted incessantly by these dreams again the past few nights. ", "Years ago, they'd plague her regularly, but the passing of time had lessened them to only the occasional occurrence. ", "Why now? ", "Why was the dream coming back to haunt her?", "\n\n" ]

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[ "Check out our new site Makeup Addiction\n\nadd your own caption\n\nadd your own caption\n\nadd your own caption\n\nadd your own caption\n\nadd your own caption\n\nadd your own caption\n\nadd your own caption\n\nadd your own caption\n\nadd your own caption\n\nadd your own caption\n\nadd your own caption\n\nBullets? ", "More like lead based freedom." ]

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[ "A hungry beggar showing hungry beggars where I'm finding food\n\nConsistent Character that Confesses\n\nTitus was commissioned to appoint elders of every local church. ", "These men were to demonstrate character, courage, consistency, and intellect (vs. 5-9) that could stand in the face of false teaching and ill-motives (vs. 10) that are destructive to the churches (vs. 11 & 14).", "\n\nI find it interesting (and sobering) that a person can “profess” and yet prove their profession to be false by their works. (", "vs. 15-16). ", "This is not a works-based salvation. ", "For, the same author wrote Romans 10:9. ", "Rather, Paul is saying that confession and profession (lip-service) are not the same things. ", "God will not be fooled!", "\n\nHoly Spirit, test my heart and show me my waywardness. ", "Let me see false and selfish motives and know how to repent of them. ", "Help me serve Your Church and the Gospel, that You may be seen as beautiful by many." ]

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[ "Elsey\n\nElsey may refer to:\n\nPlaces\n\nAustralia\n\nNorthern Territory\nElsey, Northern Territory, a locality\nElsey National Park, a protected area\nElsey Station, a former pastoral lease\nElectoral division of Elsey, a former electorate\n\nGermany\nElsey Abbey, a former women's religious house\n\nUnited States\nElsey, California\nElsey, Missouri\n\nPeople\nBill Elsey (1921–2019), British racehorse trainer\nCharles Elsey (1882–1966), British racehorse trainer\n\nSee also\nElseya" ]

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[ "Introduction {#Sec1}\n============\n\nLoss of blood-brain barrier (BBB) functional integrity is a major pathological component of age and disease-associated dementia (Zlokovic [@CR52]; Daneman [@CR9]), and the severity of barrier dysfunction is often associated with worsened cognitive function (Montagne et al. [", "@CR24]; Janelidze et al. [", "@CR17]). ", "Attenuation or rescue of BBB dysfunction is therefore a promising target for treatment of a variety of neurodegenerative diseases disproportionately affecting older adults. ", "The BBB is a specialized system of endothelial cell junctions and glial associations that are dynamically regulated by a signaling network composed of discrete regulatory points (for review see Daneman and Prat [@CR10]). ", "For example, myosin light chain kinase (MLCK) is a signaling protein involved in regulation of barrier integrity that has been identified as a potential therapeutic target in disease-associated tissue barrier dysfunction. ", "There are multiple MLCK proteins, but the focus of the present study is a 210-kDa MLCK protein encoded by the *mylk1* genetic locus, referred to as MLCK210 (for review see Khapchaev and Shirinsky [@CR18]). ", "Prior studies on the role of MLCK210 in tissue barrier dysfunction and the potential of selective inhibitors have largely focused on non-CNS disorders (for recent reviews see Cunningham and Turner [@CR8]; Rigor et al. [", "@CR32]; Khapchaev and Shirinsky [@CR18]; Xiong et al. [", "@CR47]), including acute lung injury models (Wainwright et al. [", "@CR41]; Rossi et al. [", "@CR34]; Mirzapoiazova et al. [", "@CR23]; Usatyuk et al. [", "@CR39]; Fazal et al. [", "@CR11]; Wang et al. [", "@CR43]; Wang et al. [", "@CR42]; Zhou et al. [", "@CR51]), burn injury (Reynoso et al. [", "@CR31]; Guo et al. [", "@CR14]; Zahs et al. [", "@CR49]), acute diarrhea (Clayburgh et al. [", "@CR6]; Clayburgh et al. [", "@CR7]), endotoxic shock (Ralay Ranaivo et al. [", "@CR28]; Gaceb et al. [", "@CR12]), cardiovascular shear stress (Ohlmann et al. [", "@CR26]), atherosclerosis (Sun et al. [", "@CR38]), hypoxia (Arnaud et al. [", "@CR3]), and intestinal injury models (Al-Sadi et al. [", "@CR1]; Gilbert et al. [", "@CR13]; Wu et al. [", "@CR46]; Lorentz et al. [", "@CR20]; Nighot et al. [", "@CR25]; Al-Sadi et al. [", "@CR2]). ", "Additionally, there exists a smaller literature exploring the benefit of inhibition of MLCK in the context of BBB dysfunction. ", "This includes in vivo models of traumatic brain injury (Luh et al. [", "@CR22]; Rossi et al. [", "@CR33]), cerebral ischemia (Zhang et al. [", "@CR50]), subarachnoid hemorrhage (Luh et al. [", "@CR21]), and in vitro experiments modeling cerebral hypoxia (Kuhlmann et al. [", "@CR19]; Hicks et al. [", "@CR15]) and cytokine elevation (Huppert et al. [", "@CR16]; Beard et al. [", "@CR4]). ", "The in vivo data show MLCK suppression can ameliorate acute cerebrovascular injury, while the in vitro data suggest a link to chronic stressors commonly underlying cerebrovascular dysfunction. ", "To extend these findings, we performed comparative studies of the MLCK210 KO mouse response to a diet-induced hyperhomocysteinemia (HHcy) model of chronic VCID. ", "This model uses a B vitamin-deficient diet to induce elevated levels of plasma homocysteine, which leads to progressive BBB dysfunction and reproducible and quantitative cerebrovascular changes that mimic many of those found in clinical VCID (for review see Price et al. [", "@CR27]). ", "Thus, subjecting the MLCK210 KO model to the diet-induced HHcy model of chronic VCID allows a direct test of the hypothesis that MLCK210 is a viable target for progressive CNS diseases such as VCID. ", "We report here that MLCK210 KO mice are protected from HHcy-induced microhemorrhage formation and pro-inflammatory biomarker changes, justifying further exploration of MLCK210 inhibition as a therapeutic strategy for chronic neurological diseases involving a BBB dysfunction mechanism.", "\n\nMethods {#Sec2}\n=======\n\nAnimals and experimental diet {#Sec3}\n-----------------------------\n\nThe experiment was carried out in a 2 × 2 diet by genotype design. ", "All animals received 6 weeks of the HHcy diet (Envigo, \\#TD.97345)---deficient in vitamins B~6~, B~9~, and B~12~ with excess methionine---or nutritionally matched control diet with normal methionine and vitamin levels (Envigo, \\#TD.01636) (Sudduth et al. [", "@CR35]; Sudduth et al. [", "@CR36]; Sudduth et al. [", "@CR37]). ", "C57BL/6J mice (The Jackson Laboratory strain \\#664) were used as wild-type (WT) controls for the MLCK210 KO mice that were generated as previously reported (Wainwright et al. [", "@CR41]). ", "Eight MLCK210 KO mice (4 male/4 female) received control diet, and 8 (4M/4F) received HHcy diet. ", "Eight WT mice (3M/5F) received control diet, and 10 (3M/7F) received HHcy diet. ", "Animals were housed 1--4 per cage (503.22 usable cm^2^) in a room at 23 °C ± 2 °C, under a 14/10-h light/dark cycle beginning at 6:00 AM. ", "All mice were administered experimental diet between 2 and 3 months of age and were sacrificed at 3.5--4.5 months of age after 6 weeks on diet. ", "Mice had ad libitum access to water and chow.", "\n\nTissue collection {#Sec4}\n-----------------\n\nMice were deeply anesthetized with 5% isoflurane and arterial blood collected from the left ventricle for measurement of homocysteine levels by the University of Kentucky Hospital clinical laboratory. ", "Mice subsequently underwent transcardial perfusion with 50 ml ice-cold phosphate-buffered saline (PBS) at a flow rate of 10 ml/min before decapitation and brain removal and dissection. ", "The left hemisphere was post-fixed in 4% paraformaldehyde for 24 h at 4 °C and cryo-protected in 30% sucrose for 48 h at 4 °C before sectioning. ", "A portion of frontal cortex from the right hemisphere was dissected, flash frozen in liquid nitrogen, and stored at − 80 °C until processing for biochemistry.", "\n\nImmunohistochemistry for Prussian blue {#Sec5}\n--------------------------------------\n\nThe left hemisphere was cut coronally into 30 μm sections, with every 24th section collected for staining. ", "A total of 5--7 sections per hemibrain were mounted and stained for hemosiderin using Prussian blue as described previously (Wilcock et al. [", "@CR45]). ", "Slides were incubated in a 2% potassium ferrocyanide in 2% hydrochloric acid solution for 15 min, followed by a counterstain in a 1% neutral red solution for 10 min. ", "The number of Prussian blue positive profiles were counted across each section, and an average per-section value was generated for analysis.", "\n\nQuantitative reverse-transcriptase polymerase chain reaction {#Sec6}\n------------------------------------------------------------\n\nQuantitative reverse-transcriptase polymerase chain reaction (qRT-PCR) was performed as previously reported (Sudduth et al. [", "@CR35]), with all reagents acquired from Thermo Scientific (Rockford, IL, USA). ", "Briefly, RNA was extracted from the right frontal cortex using the Trizol plus RNA purification system according to the manufacturer's instructions. ", "Total RNA was quantified with a nanodrop spectrophotometer, and cDNA made using the cDNA High Capacity kit according to instructions. ", "Real-time PCR was performed using the TaqMan Gene Expression assay kit, and genes normalized to 18s rRNA. ", "TaqMan probes were used to measure transcript levels of Arg1 (Mm00475988_m1), IL-1β (Mm00434228_m1), IL-10 (Mm00439616_m1), IL-12A (Mm00434165_m1), IL-1Ra (Mm00446186_m1), IL-6 (Mm00446190_m1), MMP2 (Mm00439506_m1), MMP3 (Mm00440295_m1), MMP9 (Mm00600163_m1), MMP14 (Mm00485054_m1), TIMP1 (Mm00441818_m1), TIMP2 (Mm00441825_m1), TNF-α (Mm00443258_m1), and YM1 (Mm00657889_mH). ", "Fold change values were determined for mice receiving experimental diet relative to mice receiving control diet within the same genotype. ", "For comparisons between WT and MLCK210 KO mice on control diet, fold change values were determined for the KO mice relative to WT. ", "All fold change values were calculated using the 2^(−ΔΔCt)^ method, and log2 normalized.", "\n\nStatistical analyses {#Sec7}\n--------------------\n\nStatistical analyses and figure generation were performed using GraphPad Prism 7 (GraphPad Software, La Jolla, CA, USA). ", "Two-way analysis of variance (ANOVA) with Sidak's post hoc testing was performed for most comparisons, with a statistical significance level set to *α* = .05. ", "For comparison of gene expression between WT and MLCK210 KO mice on control diet, *t* tests were performed for each gene, followed by the two-stage step-up method (Benjamini et al. [", "@CR5]) to control false discovery rate, with *Q* = 10%. ", "All graphs show means with error bars representing the standard error of the mean (SEM). ", "Where reported in the text, data are described with M = mean, SD = standard deviation, and CI = 95% confidence interval.", "\n\nResults {#Sec8}\n=======\n\nExperimental diet induces HHcy in both MLCK210 KO and WT mice, but MLCK210 KO mice are protected from HHcy-induced microhemorrhages {#Sec9}\n-----------------------------------------------------------------------------------------------------------------------------------\n\nPlasma homocysteine concentration was measured in a subset of 3 mice per group, and levels on control diet were not significantly different between WT (M = 5.89 μM, SD = 0.67, CI = 4.23--7.55) and MLCK210 KO mice (M = 6.34 μM, SD = 0.74, CI = 4.50--8.18) (Fig.", " [1a](#Fig1){ref-type=\"fig\"}). ", "The HHcy diet significantly increased plasma homocysteine levels in both the WT (M = 82.93 μM, SD = 6.17, CI = 67.61--98.25) and KO mice (M = 84.67 μM, SD = 26.57, CI = 18.65--150.7), with no significant difference between the strains. ", "The HHcy model has been reported to induce cerebrovascular pathology such as cerebral microhemorrhages (Sudduth et al. [", "@CR35]). ", "Therefore, we measured microhemorrhages by Prussian blue staining. ", "The average number of Prussian blue positive profiles per section was significantly elevated in the WT mice on HHcy diet (M = 3.124, SD = 0.760, CI = 2.580--3.667) versus control diet (M = 0.421, SD = 0.297, CI = 0.173--0.669) (Fig. [", "1b](#Fig1){ref-type=\"fig\"}). ", "In contrast, the MLCK210 KO mice were completely protected from HHcy-induced microhemorrhages, with no difference found between those mice on HHcy diet (M = 0.175, SD = 0.155, CI = .045--0.305) or control diet (M = 0.175, SD = .208, CI = 0.001--0.349).Fig. ", "1HHcy diet induces hyperhomocysteinemia in both strains but MLCK210 KO mice are protected from microhemorrhages. **", "a** Plasma homocysteine was measured in a subset of mice (*n* = 3) from each group. ", "After 6 weeks of HHcy diet, plasma homocysteine was significantly elevated in both strains relative to control diet. ", "There were no differences between WT and MLCK210 KO mice at baseline. **", "b** Average Prussian blue positive microhemorrhages per section were elevated in WT mice in response to HHcy diet, but unchanged in MLCK210 KO mice. ", "\\*\\*\\**p* \\< .001, \\*\\*\\*\\**p* \\< .0001 vs. within-strain control, two-way ANOVA with Sidak's post hoc tests\n\nA gene expression panel related to neuroinflammation and BBB disruption, previously shown to change in response to HHcy, was screened for differences between WT and MLCK210 KO mice. ", "The panel contained the inflammation-associated genes Arg1, IL-1β, IL-10, IL-12A, IL-1Ra, IL-6, TNF-α, and YM1, and the hemorrhage-implicated matrix remodeling genes MMP2, MMP3, MMP9, MMP14, TIMP1, and TIMP2 (Sudduth et al. [", "@CR35]; Weekman et al. [", "@CR44]). ", "We first compared gene expression levels between the two genotypes at baseline, with values of the MLCK210 KO mice on control diet normalized to WT mice on control diet (Fig.", " [2](#Fig2){ref-type=\"fig\"}). ", "Unexpectedly, 6 genes were differentially expressed between the strains on control diet at baseline: MMP14, MMP3, MMP9, IL-1β, IL-10, and YM1. ", "The basal mRNA levels of these 6 genes were significantly lower in MLCK210 KO compared to WT mice. ", "Because baseline levels were different between strains, we normalized expression levels from mice on HHcy diet to within-genotype controls for characterization of diet-associated changes. ", "Interestingly, levels of MMP14, MMP2, MMP3, and MMP9 were all significantly upregulated in the MLCK210 KO mice on the HHcy diet, in contrast to the WT mice on HHcy diet that showed no changes in MMP levels (Fig.", " [3a](#Fig3){ref-type=\"fig\"}). ", "No HHcy-induced changes were detected in either the TIMP1 or TIMP2 mRNA levels (Fig. [", "3b](#Fig3){ref-type=\"fig\"}).Fig. ", "2Differences in baseline gene expression levels between WT and MLCK210 KO mice on control diet. ", "Cortical expression levels in MLCK210 KO mice relative to WT mice on control diet are shown. ", "The basal mRNA levels of six genes (IL-10, IL-1β, MMP14, MMP3, MMP9, YM1) were significantly lower in MLCK210 KO mice compared to WT mice. ", "\\**p* \\< .05, \\*\\**p* \\< .01 vs. WT mice on control diet, multiple independent sample *t* tests, followed by two-stage step-up analyses (Benjamini et al. [", "@CR5]) with *Q* = 10%Fig. ", "3MMP transcript levels are unchanged in WT and upregulated in MLCK210 KO mice on HHcy diet, with no changes in TIMP transcript levels. **", "a** Cortical MMP expression levels show that in WT mice, there were no HHcy-induced increases in any of the MMP transcripts quantified. ", "In MLCK210 KO mice, all of the MMPs were significantly upregulated as a result of HHcy diet. **", "b** Transcript levels of tissue inhibitor of metalloproteinases (TIMP)-1 and TIMP-2 were unchanged by HHcy in either strain. ", "\\**p* \\< .05, \\*\\**p* \\< .01 vs. within-strain control, two-way ANOVA with Sidak's post hoc tests\n\nMLCK210 KO reduces HHcy-induced pro-inflammatory changes {#Sec10}\n--------------------------------------------------------\n\nIncreased levels of pro-inflammatory cytokines have been implicated as both a driver and consequence of BBB hyperpermeability, and MLCK210 specifically plays a role in BBB dysfunction induced by IL-1β (Beard et al. [", "@CR4]) and pro-inflammatory processes mediated via NFκB signaling (Recoquillon et al. [", "@CR29]). ", "To determine whether the rescue of BBB integrity in this model corresponds with an overall shift from pro- to anti-neuroinflammatory responses, we measured mRNA levels of pro-inflammatory cytokines IL-1β, TNF-α, IL-6, and IL-12A, and the generally anti-inflammatory immune modulators Arg1, IL-10, IL-1Ra, and YM1. ", "In line with previous studies (Sudduth et al. [", "@CR35]; Sudduth et al. [", "@CR37]), mRNA levels of IL-1β, TNF-α, and IL-6 were significantly upregulated in response to HHcy diet in the WT mice (Fig.", " [4a](#Fig4){ref-type=\"fig\"}). ", "This effect was reduced in the MLCK210 KO mice, in which no significant HHcy-induced changes in these cytokines were detected. ", "Interestingly, we found IL-12A mRNA significantly downregulated in the WT mice after HHcy, an effect reversed in the MLCK210 KO mice (Fig. [", "4a](#Fig4){ref-type=\"fig\"}). ", "In line with the attenuated pro-inflammatory response to HHcy diet in the MLCK210 KO mice, there was a concomitant increase in the anti-inflammatory factors IL-10, IL-1Ra, and YM1, an effect not observed in WT mice (Fig. [", "4b](#Fig4){ref-type=\"fig\"}). ", "Arg1 levels were unchanged in either strain in response to HHcy diet (Fig. [", "4b](#Fig4){ref-type=\"fig\"}).Fig. ", "4MLCK210 KO mice are protected from HHcy-induced neuroinflammation. **", "a** Cortical levels of pro-inflammatory cytokines IL-1β, TNF-α, and IL-6 were upregulated in WT mice on HHcy diet, and IL-12A was downregulated. ", "There was no significant change in these cytokines in the MLCK210 KO mice on HHcy diet. **", "b** Anti-inflammatory mediators IL-10, IL-1Ra, and YM1 were significantly upregulated in the MLCK210 KO mice with HHcy, but not in the WT mice. ", "Arg1 was unchanged with HHcy in either strain. ", "\\**p* \\< .05, \\*\\**p* \\< .01 vs. within-strain control, two-way ANOVA with Sidak's post hoc tests\n\nDiscussion {#Sec11}\n==========\n\nBlood-brain barrier dysfunction is a critical factor in neurological dysfunction and neurodegeneration, contributing to multiple causes of cognitive impairment and dementia primarily affecting older populations. ", "MLCK210 is an established regulator of tissue barrier permeability, the suppression of which is related to its potential as a therapeutic target in diverse preclinical models. ", "The present study was designed to address whether such an approach might also be useful in some of the chronic stressors contributing to cerebrovascular damage. ", "For this purpose, we subjected the MLCK210 KO mice to the dietary HHcy model of VCID that recapitulates many core pathophysiological features of cerebrovascular damage, including neuroinflammation and BBB disruption. ", "We found that knockout of MLCK210 abrogated HHcy-induced microhemorrhage formation. ", "In addition, MLCK210 KO mice showed a reduced neuroinflammatory profile after HHcy, as reflected in decreased transcript levels of pro-inflammatory cytokines (IL-1β, IL-6, TNF-α) and increased levels of anti-inflammatory modulators (IL-10, IL-1Ra, YM1). ", "Analysis of baseline expression levels of these genes between WT and MLCK210 KO mice indicated that these results were not likely due to a generally immunosuppressed phenotype in the KO animals. ", "Overall, our findings using the MLCK210 KO mice extend the preponderance of data across diverse tissue barrier injury models that there is a potential for therapeutic benefit by targeting MLCK210 in future drug discovery efforts.", "\n\nThere were two interesting observations during the course of this study that remain to be addressed in future investigations. ", "First, the finding that MMP levels were unchanged in the WT mice on HHcy diet despite significant microhemorrhage pathology and, conversely, MMP levels were elevated in the MLCK210 KO mice on HHcy diet without significant microhemorrhages was unexpected. ", "Caution needs to be taken in the interpretation, however, as mRNA levels of the MMPs do not necessarily reflect the levels of the protein or protein activity (for review see Rempe et al. [", "@CR30]). ", "Therefore, it is not known if MMP enzyme activity differs between WT and MLCK210 KO mice on HHcy diet. ", "To address whether MLCK210 might play a role in the homeostatic maintenance of brain extracellular matrix as mediated via the MMP system, future studies should directly measure MMP enzyme activity at baseline and in response to HHcy in MLCK210 KO mice. ", "Second, IL-12A was an exception to the trend where most of the immunomodulatory gene expressions were altered. ", "We previously found an increase in IL-12A transcript levels in hippocampus after 6 weeks on HHcy diet (Sudduth et al. [", "@CR37]) compared to the decrease in cortical levels observed here (Fig. [", "3d](#Fig3){ref-type=\"fig\"}). ", "The main difference might simply reflect the anatomical region of measurement. ", "This raises the potential of regional variability in brain neuroinflammatory responses to HHcy. ", "IL-12A is also interesting in that it encodes a protein that can function as part of two different heterodimer cytokines: the pro-inflammatory IL-12 and the anti-inflammatory IL-35 (for review see Vignali and Kuchroo [@CR40]). ", "While not widely studied in the brain, IL-35 has recently been shown to have neuroprotective effects in a cerebral ischemia mouse model (Xu et al. [", "@CR48]). ", "Therefore, whether this HHcy-induced cortical decrease in IL-12A in the WT mice is reflective of pro- or anti-inflammatory processes remains to be determined.", "\n\nIn summary, the present study demonstrates that suppression of MLCK210 can provide protection in a model of chronic cerebrovascular dysfunction, and supports the hypothesis that MLCK210 is a viable target for progressive CNS diseases such as VCID. ", "Future studies should explore MLCK210 inhibition as a therapeutic strategy for chronic neurological diseases involving cerebrovascular pathology and BBB dysfunction mechanisms.", "\n\n**Publisher's note**\n\nSpringer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.", "\n\nThis work was supported in part by a NIH postdoctoral fellowship F32 AG058456 (DJB).", "\n" ]

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[ "Charles E. Hoffman\n\nCharles \"Charlie\" E. Hoffman (born January 27, 1949) is an American business executive, having served two publicly traded companies as CEO for over 10 years. ", "As of September 2013, he is the dean of the College of Business Administration at the University of Missouri–St. Louis, his alma mater.", "\n\nEarly life \nHoffman grew up in St. Louis County, Missouri. ", "He served in the Air Force during the Vietnam War era. ", "Hoffman received a bachelor of science, in 1974, and a masters of business administration, 1976, from University of Missouri–St. Louis (UMSL).", "\n\nCareer \nBefore Rogers, Hoffman served as President, Northeast region, for Sprint PCS. ", "He was responsible for operations in the largest region in the U.S. and successfully launched PCS wireless service in nine markets. ", "Hoffman also spent 16 years at SBC Communications (now AT&T) in various senior management positions, including Director General (President) of Telcel, the national wireless carrier in Mexico. ", "During this time, he also served as Managing Director-Wireless for SBC International. ", "Preceding this, Hoffman was President and General Manager of SBC's Cellular One operations, during which he turned around the second and fourth largest SBC markets, Washington/Baltimore and Boston, from underperformers to market leaders in record time.", "\n\nHoffman was President and Chief Executive Officer (CEO) of Rogers Wireless, Inc., at the time Canada's largest wireless service provider. ", "He held this position from January 1998 to June 2001. ", "Under his leadership, the company grew from fourth to first place in a market of four national wireless providers. ", "He also successfully negotiated the sale of one-third interest in this publicly traded company (NYSE and TSE) to a partnership of AT&T and British Telecom.", "\n\nIn June 2001, Hoffman became President and CEO of Covad. ", " He served in the position from June 2001 to April 2008. ", "Hoffman took Covad through bankruptcy and negotiated the sale of the company to Platinum Equity in late 2007, and stepped down from Covad when the acquisition was completed.", "\n\nHe is currently a member of the board of directors of Synchronoss Technologies. ", "He previously served on the boards of Chordiant Software, Softlayer Technologies and Tollgrade Communications. ", "All three companies were profitably sold while Hoffman served on the board of directors. ", "He attended the Directors College at Stanford University in 2006 and the Corporate Governance program at Northwestern University's Kellogg School in 2009.", "\n\nPersonal life \nHe and his wife Maureen have four children and eight grandchildren.", "\n\nReferences\n\nExternal links\nProfile of Charles E. Hoffman at UMSL\n\nCategory:1949 births\nCategory:Living people\nCategory:21st-century American businesspeople\nCategory:20th-century American businesspeople\nCategory:University of Missouri alumni\nCategory:University of Missouri faculty" ]

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[ "A meeting moderator is typically placed in charge of planning and executing a meeting. ", "For example, the meeting moderator may be required to obtain space for the meeting, schedule presenters for the various presentation slots of the meeting and invite attendees to the meeting. ", "Unfortunately, it often becomes difficult to schedule the various presenters into the available presentation slots. ", "It is not uncommon for one or more presenters to pressure the meeting moderator into scheduling them into a presentation slot that may be already reserved by another presenter.", "\nDespite numerous attempts to help facilitate meeting scheduling, it remains difficult to gather groups of people, especially when some of the presenters are high-profile members of an organization, typically with very full schedules." ]

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[ "Si alguien duda todavía del poder de los libros ningún ejemplo es mejor que el de Yuval Noah Harari (Haifa, Israel, 1976), que pasó del anonimato a la fama con la publicación de Sapiens. ", "De hombres a dioses, un texto que además de situarlo en primera plana lo convirtió en un hombre rico. ", "Su éxito terminó de consolidarse con la salida de Homo Deus. ", "Breve historia del mañana, donde marcaba el final de muchas cosas y anunciaba el advenimiento de una era glacial basada en fríos algoritmos.", "\n\nSus ideas, que más que revolucionarias son desapasionadas y se alejan de toda ideología, tienen el aval de gente como Mark Zuckerberg o Barack Obama, personas a las que, curiosamente, ha cuestionado en más de una ocasión. ", "Su mayor aporte al debate mundial es señalar que el momento es ahora o nunca. ", "Que llegó el tiempo de tomar decisiones antes de que las máquinas y las matemáticas dominen por completo al ser humano.", "\n\nSi algo tiene claro este profesor historia de 42 años, doctorado por la Universidad de Oxford y catedrático en la Universidad Hebrea de Jerusalén, es que la humanidad se encuentra en un punto crítico, en un momento donde una o dos decisiones pueden llevar al hombre al desastre o a la salvación definitiva. ", "Según Harari, los grandes problemas como la guerra o las hambrunas están en vías de extinción y lo que de verdad empieza a preocupar es el control cada vez más férreo de la Inteligencia Artificial sobre todas las conductas humanas.", "\n\nMáquinas que aprenden a aprender, que saben más de nosotros que nosotros mismos, que reúnen datos constantemente y sin fatigarse en absoluto, que ya superan al hombre en casi todo. ", "Y que, según advierte en su último libro 21 lecciones para el siglo XXI (Debate), tienen la capacidad de manipularnos y dirigirnos como ninguna ideología pudo. ", "En otras palabras: Hal 9000, Skynet y The Matrix, combinados.", "\n\nPuesto así, no resulta raro que el cineasta Ridley Scott tenga pensado adaptar sus libros a la gran pantalla. ", "Pero para Harari no es cine o ciencia ficción, el peligro es real y está a la vuelta de la esquina. ", "Pone como ejemplos del poder de las nuevas tecnologías la campaña presidencial de Estados Unidos que terminó con Donald Trump en la Casa Blanca o el Brexit inglés, donde herramientas como Twiter o Facebook, manipularon a la opinión pública de forma descarada.", "\n\nPorque cada clic en la web es una seña de identidad, un dato a codificar, un aspecto más de la personalidad de ese potencial votante que queda al descubierto. ", "En una entrevista reciente afirma que Google nos conocerá mejor que nosotros mismos y que terminará eligiendo a la pareja que más nos conviene. ", "Para 2050 anticipa que el cuerpo humano será monitoreado en tiempo real las 24 horas del día y que esa será la nueva medicina. ", "Como protegerse o detener esta suerte de apocalipsis digital es algo que no tiene muy claro Harari, que dice no sentirse un Gurú porque no tiene las respuestas, tiene solo las preguntas.", "\n\nDe todas formas es difícil no aplicarle ese mote gracias a su estética y a su carisma, a lo que se suma que decidió hacerse vegano hace poco tiempo, que se casó en Canadá con su pareja masculina, que no usa teléfonos inteligentes, que es ateo y que medita dos horas por día escuchando el flujo de su respiración para centrase y percibir la verdadera realidad del mundo.", "\n\nTambién es políticamente incorrecto y no se corta a la hora de marcar diferencias. ", "Aunque es reconocido en Israel, ha protagonizado diversos altercados con el gobierno de Benjamín Netanyahu. ", "Se ha declarado, por ejemplo, en contra de la Ley del Estado–Nación, por considerar que segrega a las minorías no judías que habitan Israel. ", "Y no hace mucho se negó a participar en una actividad del consulado israelí en Los Ángeles, Estados Unidos, por estar en contra de la ley de maternidad subrogada que permite a madres solteras y parejas heterosexuales que no pueden tener hijos utilizar los servicios de una madre sustituta, pero no le da ese derecho a los homosexuales.", "\n\nEstá convencido del fin de la globalización tras la crisis económica de 2008 y augura un rebrote de los nacionalismos a los que considera, en esencia, fascistas. ", "Por otra parte minimiza el poder del terrorismo, al que recomienda ignorar y vivir sin miedo para derrotar, pero se cubre la espalda al decir que si consiguen armas nucleares o biológicas el tema será distinto. ", "También le preocupan el cambio climático y la desaparición de especies animales.", "\n\nPero lo que más lo inquieta es la pérdida del libre albedrío, que se decida por nosotros. ", "Harari opina que el Big Data o el dataísmo, amenazan con convertirnos a todos, sino en una pila, en un simple dato, en un bit codificable. ", "Primero las máquinas nos dejarán sin trabajo y después asumirán el control dictándole a los que manden lo que hay que hacer según las probabilidades matemáticas. ", "Y donde acierten una o dos veces, predice, ya no habrá vuelta atrás.", "\n\nÚltimamente, en sus charlas virtuales y en entrevistas, está dejando caer el concepto de que lo peor está por venir ya que lo que se está intentando es hackear a las personas, no a las instituciones bancarias o las cuentas de email. ", "Algo similar a lo que planteaba en su momento la serie japonesa de animación Ghost in the Shell.", "\n\nSe nutre también de esa imagen popular de zombis con teléfono, de los que no pueden desconectarse nunca ni prescindir de un like. ", "De esa dependencia extrema hacia lo tecnológico y en cierta forma hacia lo inhumano que tienen todo el mundo.", "\n\nEscritor de prosa amena y muy bien documentado, sus tres libros publicados son una buena invitación para pensar el presente. ", "Porque para Yuval Noah Harari, el futuro ya llegó." ]

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[ "Boeing Company (NYSE: BA) makes passengers safer?", "\n\nTwo essential economists have written the primary analysis of the Boeing 737 Max disaster. ", "Is it referred to as a safer passenger? ", "Boeing has simply made the shareholders richer, ”and has been made by a young French economist, Mustafa Erdem Sakinç, who teaches on the University of Bordeaux and specializes within the aerospace, pharmaceutical and ICT industries. ", "and American Canadian economist William Lazonick, who taught in Columbia for years and targeted on enterprise innovation. ", "After analyzing the evidence, two economists got here to this conclusion: Boeing execs ought to be shot and the cash they took from the longer term sale of Boeing 737 returned. ", "This aircraft's future is at present unknown as a result of it seems to have elementary design errors that execs determined to repair with software program somewhat than design modifications. ", "And what should Boeing be paid to the aircraft without these faults? ", "$ 7 billion. ", "Apparently, execs in Chicago decided to switch this money to their shareholders (and finally themselves) as an alternative of with the ability to fly safely.", "\n\nSakinç and Lazonick write:\n\nCompensation for the newest know-how in clear disk was estimated to be $ 7 billion greater than reused 737. ", "This is roughly the same quantity that Boeing has spent on common yearly since 2013. ", "By 2008, when the need for a new medium-sized slender niche was clear, Boeing had thrown $ 11.zero billion into repurchases and on the similar time granted shareholders a large dividend of $ 4.8 billion. ", "If Boeing, the only competitor to Airbus, had financed a well-planned and estimated funding on a totally new aircraft, the company might have generated substantial income and income far into the longer term.", "\n\nAs I doubted in March, inventory repurchases (which improve the worth of the shares) come to the middle of this disaster, just as they’re discovered within the midst of the subsequent massive stock market fall (coming to the neighborhood). ", "In the 2008 accident, Epicenter was in residential development; The subsequent one might be within the corporate sector, which has turn into the stream of giant loans. ", "And a huge amount of this borrowed cash, in response to Washington Submit's enterprise author Steven Pearlstein, is accustomed to doing what Boeing did just a few months ago: \"buy their very own shares, pay special dividends to enterprise capitalists, and acquire different corporations that each one have an impact on inventory worth increases. “", "And the way dangerous is the state of affairs?", "\n\nThis dangerous: “In the first three months of this year, Treppen said that only loans – loans that do not require repayment of capital before the loan matures – accounted for three quarters of all new commercial real estate loans. “", "This means that we are about to enter Hyman Minsk's“ Classic Ponzi Phase of the Economic Instability ”[FIH]. ”", "\n\nMinsky has died almost 1 / 4 of a century. ", "And in the 1992's hypothesis, the detailed Market Critiques, which have been virtually ignored by the mainstream, until the 2008 merger, now referred to as the basic Minsky second. ", "Making use of FIH to current occasions in US funding is obvious that we left the first moment of Minsk, the Hedge second, around 2016. ", "Then the borrower can \"fill all his contractual payment obligations from his cash flows.\" ", "We at the moment are at the end of the speculative moment (when the borrower can solely pay interest on money flows) and it involves the Ponzi part, during which the borrower borrows to pay solely his interest on debts (hence solely \"interest-only loans\")\n\nAgain to Boeing and all the issues which are at the root of the transition described by Gérard Duménil and Dominique Lévy within the Neoliberal crisis. ", "It goes like this: in the 1970s, the union between staff and management, which in the USA was an instance of what is referred to as the Mid-Century Detroit Settlement, was subjected to a robust assault on the financial sector, which needed corporations to concentrate on worth creation, however on the transfer of income (present and future) to Wall Road [19659003] Duménil and Lévy:\n\nThe dramatic social change that occurred throughout neoliberalism would have been inconceivable if the covenant had not been made between capitalists and management teams, particularly their higher fractions. ", "This transformation of alliances may be labeled a \"neoliberal compromise\". ", "Depending on the nation, the adherence of the management groups to the neoliberal challenge was kind of straightforward to realize, given the precise energy configurations and the characteristics of the post-war compromise in each country. ", "In america it was simpler than in Europe. ", "There have been additionally vital differences between operations, finance, know-how and so forth. ", "However in the absence of such a compromise a radical alignment of leadership and policies with neoliberal objectives would have been unimaginable\n\nSimply put: post-war management capitalism weakened within the 1970s (the interval that gave delivery to neoliberalism) and eventually stabbed within the coronary heart when Jimmy Carter appointed Paul Volcker to the Fed's chief in 1979. ", "In accordance with Ronald Reagan, Volcker founded what’s now referred to as the Volcker Shock Company, which dramatically raised high rates of interest dramatically in 3 ways: killing inflation, introducing financial policy as a central instrument of financial governance, and bringing a post-war alliance between corporate management and staff. ", "The director stated that they’re now in keeping with the key situation of financing, shareholders. ", "These speculators (who’re certainly not buyers in entrepreneurship) can by no means be convinced that their \"investments\" aren’t rewarded sufficient.", "\n\nThe hypothesis of maximizing shareholders truly achieved financial respect (referred to as the \"agency theory\"). . ", "After the execs occasions that happened in Boeing in Chicago in 2001, it was understood that the shareholders (beneath this new system) have been as an alternative of decreasing and distributing their key interfaces. ", "And to ensure that there was no misunderstanding about this example, the management's wage was tied to the worth of the shares\n\nAnd what do we find in Boeing? ", "Here is:\n\nBoeing CEO Muilenburg has benefited enormously from the corporate's rising share worth (see Determine three). ", "From 2015 to 2018, like Boeing's President and CEO, Muilenburg supported a gross salary of $ 95.9 million, although his annual salary by no means exceeded $ 1.7 million. ", "Of this complete, 51 per cent consisted of the train of inventory options and the earning of share rewards. ", "34 per cent was based mostly on Boeing's profitability in 2013–2016, and in 2017–2018 it was a extra complicated monetary measure.", "\n\nBut why did Muilenburg not shoot and deprive all of the forces in entrance of all these details? ", "Because we stay in an age the place there isn’t any different good than \"shoot a gun\", John Maynard uses the expression of Keynes. ", "Disgrace is lifeless. ", "If the cash you make by suspicious means is already in your checking account, the game is over, the person, the sport is over. ", "You gained.", "\n\nAll in all, the autumn in costs is: Down.", "\n\nWord: This chart exhibits distinctive worth reductions.", "\n\nThe projected upper restrict is: 357.32\n\nThe planned lower limit is: 319.11\n\nThe deliberate closing worth is: 338.21.", "\n\nCandlestick\n\nThe white frame occurred (as a result of the costs have been closed larger than they have been opened) Over the past 10 bars there have been three white candles and seven black candles for 4 black candles. ", "There have been 24 white candles and 26 black candles on the network of two black candles during the last 50 bars.", "\n\nA falling window occurred (where the bottom of the earlier shadow is above the present shadow). ", "This often signifies that the downward development continues. ", "The final 50 candles have fallen by eight, making the present falling window much more tough. ", "The two candles that preceded the falling window have been black, which makes this pattern even rougher\n\n. ", "This is sometimes a rising sign (especially when it occurs close to a low worth degree, at a help degree, or when protection is additional)\n\nMomentum Indicators\n\nMomentum is a generic term used to describe the rate at which prices rise over a given time period. ", "Normally, modifications in the pace usually result in worth modifications. ", "This professional exhibits the present values ​​of the 4 beneficial torques\n\nStochastic oscillator\n\nOne approach to interpret a stochastic oscillator is to seek for over-bought areas (over 80) and additional areas (under 20). ", "The stochastic oscillator is 24.7630. ", "This is not overbought or over bought. ", "The final sign was to purchase 12 episode (s) then\n\nRelative Power Index (RSI)\n\nRSI exhibits over-bought (over 70) and over-sold (underneath 30) areas. ", "The present worth of RSI is 34.29. ", "This is not a filler or base. ", "A purchase order or gross sales sign is generated when RSI strikes from the overbought space. ", "The last signal was to buy 13 durations in the past\n\nCommodity Channel Index (CCI)\n\nThe CCI has overdelivered (over 100) and over bought (less than 100) ranges. ", "The current worth of CCI is -172. ", "Nevertheless, the sign won’t be generated until the indicator exceeds -100. ", "The final sign was to buy 12 episode (s) then\n\nMACD\n\nThe Shifting Average Convergence / Divergence Indicator (MACD) offers alerts when it exceeds its 9-line sign line. ", "The last signal was bought in section 0 (s) then\n\nRex Rear Latch – TD Profile\n\nBOEING CO closed at -2,720,338.890. ", "The quantity was 25% under common (impartial) and Bollinger's tapes have been 48% narrower than standard.", "\n\nBrief-term retailers ought to pay extra attention to purchasing / promoting arrows, when intermediate / long run traders should pay more consideration to the Bullish or Bearish development reflected on the decrease band\n\nSummary\n\nt A chance for Runaway Hole, which often means a continuation of the development. ", "There are 4 totally different worth gaps: widespread, handicap, runaway and exhaustion. ", "BOEING CO is presently 6.8% under the 200-cycle shifting average and is down. ", "Volatility is relatively normal in comparison with the typical volatility of the last ten episodes. ", "Our quantity indicators mirror the quantity getting into and exiting the BA.N relatively steadily (impartial). ", "Development predictor oscillators are at present falling on BA.N and have had views over the previous 16 durations. ", "The safety worth has set a new 14-cycle low, whereas our velocity oscillator isn’t. ", "That is the rising difference." ]

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[ "ADSC NEWS\n\nADSC researchers are working on a project that looks at developing a device to improve the power grid’s situational awareness and minimize the impact of cyber-attacks, especially as the number of intelligent devices connect to the grid continues to grow.", "\n\nAs cybersecurity continues to be a worldwide concern, ADSC researchers are working to improve upon and apply a technology that has been proven to be reliable in identifying and analyzing security attacks" ]

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[ "/*!", "\r\n@file\r\n@author Verox (verox.averre@gmail.com)\r\n@author Nou (korewananda@gmail.com)\r\n@author Glowbal (thomasskooi@live.nl)\r\n@author Dedmen (dedmen@dedmen.de)\r\n@author Senfo (lpsenfo@gmail.com)\r\n\r\n@brief Debug/Diagnose commands\r\n\r\nhttps://github.com/NouberNou/intercept\r\n*/\r\n#pragma once\r\n#include \"shared/client_types.hpp\"\r\n\r\nusing namespace intercept::types;\r\n\r\nnamespace intercept {\r\n namespace sqf {\r\n float diag_fps();\r\n float diag_fpsmin();\r\n float diag_frameno();\r\n float diag_ticktime();\r\n\r\n std::vector<script> diag_active_mission_fsms();\r\n std::vector<script> diag_active_sqf_scripts();\r\n std::vector<script> diag_active_sqs_scripts();\r\n std::vector<script> diag_active_scripts();\r\n\r\n //diag\r\n void diag_capture_frame(float frame_);\r\n void diag_capture_frame_to_file(float frame_);\r\n void diag_capture_slow_frame(sqf_string_const_ref section_, float threshold_);\r\n void diag_code_performance(const code &code_, const game_value &arguments_, float cycles_);\r\n void diag_log(game_value text_);\r\n void diag_log_slow_frame(sqf_string_const_ref section_, float threshold_);\r\n\r\n void enable_diag_legend(bool value_);\r\n void halt(); //only in dev version - at least wiki says so\r\n void throw_exception(game_value exception_);\r\n } // namespace sqf\r\n} // namespace intercept\r\n" ]

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[ "REBEL AGAINST POLICE BRUTALITY IN US: 2nd Night of Worst Riot in Baltimore Near Half Century\n\nA line of police behind riot shields hurled smoke grenades and fired pepper balls at dozens of protesters on Tuesday night to enforce a citywide curfew, imposed after the worst outbreak of rioting in Baltimore since 1968.", "\nDemonstrators threw bottles at police, and picked up the smoke grenades and hurled them back at officers.", "\n\nNo immediate arrests or serious injuries were reported. ", "The clash came after a day of high tension but relative peace in Baltimore, as thousands of police officers and National Guardsmen poured into the city to prevent another round of rioting like the one that rocked the city on Monday.", "\n\nIt was the first time since the assassination of the Reverend Martin Luther King Jr. in 1968 that the National Guard was called out in Baltimore to prevent civil unrest.", "\n\nMaryland’s governor said 2,000 Guardsmen and 1,000 law officers would be in place overnight.", "\nThe racially charged violence on Monday by set off by the case of Freddie Gray, a 25-year-old black man who died of a spinal-cord injury under mysterious circumstances while in police custody." ]

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[ "A Rugby Canada deadline for disgruntled sevens players to sign contracts and report to training has come and gone with no apparent movement.", "\n\n\"The players are unanimously united in their stated position to keep the men's 15s and men's 7s (teams) separate like the other top 11 rugby-playing nations in the world,\" said Melvin Reeves, the lawyer representing the sevens players.", "\n\nThirteen members of the national sevens program are in the second week of boycotting training by a centralized player pool that features players from both the 15s and sevens teams.", "\n\nRugby Canada announced plans in August to centralize a group of 40 to 50 men under contract \"to maximize the development of Canada's men's national team players.\"", "\n\nBut it has clearly failed to sell the idea to the sevens players.", "\n\nIn the past, the two teams essentially have trained apart in Langford, B.C., with separate coaches — with some 17 carded athletes in the sevens squad and up to 30 non-carded players in the 15s — although there has been some movement between the two. ", "Canada's top 15s talent plays professionally overseas.", "\n\nIn essence, the reorganization was an admission that Canada does not have the depth to run the two programs separately — and also that Rugby Canada has to focus more on the 15s program to maintain badly needed World Rugby funding.", "\n\nIn spreading funding over a larger pool or talent, some players are getting more money and some — in the sevens group — getting less.", "\n\nParticularly galling to the sevens players is Rugby Canada's move to cut the appearance fee for the Vancouver Sevens tournament to $500 from $5,000. ", "Reeves calls the cut \"outrageous given Rugby Canada's profit of around $1.5 million from the tournament.\"", "\n\nThe sevens players, many of whom have put careers on hold to play for Canada, are also upset at their Olympic sport being described as a development tool.", "\n\n\"It's not about 7s vs 15s. ", "It's about the future, and there being a men's 7s team in it,\" tweeted co-captain Nate Hirayama.", "\n\nThe sevens players have said little openly. ", "But veteran Harry Jones and Hirayama have used social media selectively to make their point.", "\n\n\"I can say with confidence that most people in Canada with any sort of real investment in rugby are concerned about the way things are going in this country from an organizational standpoint,\" Hirayama tweeted.", "\n\nAs for Rugby Canada, CEO Allen Vansen said the governing body is hopeful of settling the matter.", "\n\n\"Right now we are keeping the dialogue going with a view to reaching an outcome that works for everyone,\" Vansen said in a email to The Canadian Press. \"", "It's a high priority for us, and we hope to have a resolution soon.", "\n\nThe Canadian 15s men are gearing up for a November repechage tournament that serves as a last-chance qualifier for the 2019 Rugby World Cup. ", "Canada, which has never missed a World Cup, will likely face a significant shortfall in World Rugby funding if it fails to qualify.", "\n\nThe sevens team, which finished ninth on the World Series last season, is slated to begin play in Dubai in November." ]

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[ "#!", "/bin/sh\nset -e\nset -u\nset -o pipefail\n\nif [ -z ${UNLOCALIZED_RESOURCES_FOLDER_PATH+x} ]; then\n # If UNLOCALIZED_RESOURCES_FOLDER_PATH is not set, then there's nowhere for us to copy\n # resources to, so exit 0 (signalling the script phase was successful).", "\n exit 0\nfi\n\nmkdir -p \"${TARGET_BUILD_DIR}/${UNLOCALIZED_RESOURCES_FOLDER_PATH}\"\n\nRESOURCES_TO_COPY=${PODS_ROOT}/resources-to-copy-${TARGETNAME}.txt\n> \"$RESOURCES_TO_COPY\"\n\nXCASSET_FILES=()\n\n# This protects against multiple targets copying the same framework dependency at the same time. ", "The solution\n# was originally proposed here: https://lists.samba.org/archive/rsync/2008-February/020158.html\nRSYNC_PROTECT_TMP_FILES=(--filter \"P .*.??????\")", "\n\ncase \"${TARGETED_DEVICE_FAMILY:-}\" in\n 1,2)\n TARGET_DEVICE_ARGS=\"--target-device ipad --target-device iphone\"\n ;;\n 1)\n TARGET_DEVICE_ARGS=\"--target-device iphone\"\n ;;\n 2)\n TARGET_DEVICE_ARGS=\"--target-device ipad\"\n ;;\n 3)\n TARGET_DEVICE_ARGS=\"--target-device tv\"\n ;;\n 4)\n TARGET_DEVICE_ARGS=\"--target-device watch\"\n ;;\n *)\n TARGET_DEVICE_ARGS=\"--target-device mac\"\n ;;\nesac\n\ninstall_resource()\n{\n if [[ \"$1\" = /* ]] ; then\n RESOURCE_PATH=\"$1\"\n else\n RESOURCE_PATH=\"${PODS_ROOT}/$1\"\n fi\n if [[ ! ", "-e \"$RESOURCE_PATH\" ]] ; then\n cat << EOM\nerror: Resource \"$RESOURCE_PATH\" not found. ", "Run 'pod install' to update the copy resources script.", "\nEOM\n exit 1\n fi\n case $RESOURCE_PATH in\n *.storyboard)\n echo \"ibtool --reference-external-strings-file --errors --warnings --notices --minimum-deployment-target ${!", "DEPLOYMENT_TARGET_SETTING_NAME} --output-format human-readable-text --compile ${TARGET_BUILD_DIR}/${UNLOCALIZED_RESOURCES_FOLDER_PATH}/`basename \\\"$RESOURCE_PATH\\\" .storyboard`.storyboardc $RESOURCE_PATH --sdk ${SDKROOT} ${TARGET_DEVICE_ARGS}\" || true\n ibtool --reference-external-strings-file --errors --warnings --notices --minimum-deployment-target ${!", "DEPLOYMENT_TARGET_SETTING_NAME} --output-format human-readable-text --compile \"${TARGET_BUILD_DIR}/${UNLOCALIZED_RESOURCES_FOLDER_PATH}/`basename \\\"$RESOURCE_PATH\\\" .storyboard`.storyboardc\" \"$RESOURCE_PATH\" --sdk \"${SDKROOT}\" ${TARGET_DEVICE_ARGS}\n ;;\n *.xib)\n echo \"ibtool --reference-external-strings-file --errors --warnings --notices --minimum-deployment-target ${!", "DEPLOYMENT_TARGET_SETTING_NAME} --output-format human-readable-text --compile ${TARGET_BUILD_DIR}/${UNLOCALIZED_RESOURCES_FOLDER_PATH}/`basename \\\"$RESOURCE_PATH\\\" .xib`.nib $RESOURCE_PATH --sdk ${SDKROOT} ${TARGET_DEVICE_ARGS}\" || true\n ibtool --reference-external-strings-file --errors --warnings --notices --minimum-deployment-target ${!", "DEPLOYMENT_TARGET_SETTING_NAME} --output-format human-readable-text --compile \"${TARGET_BUILD_DIR}/${UNLOCALIZED_RESOURCES_FOLDER_PATH}/`basename \\\"$RESOURCE_PATH\\\" .xib`.nib\" \"$RESOURCE_PATH\" --sdk \"${SDKROOT}\" ${TARGET_DEVICE_ARGS}\n ;;\n *.framework)\n echo \"mkdir -p ${TARGET_BUILD_DIR}/${FRAMEWORKS_FOLDER_PATH}\" || true\n mkdir -p \"${TARGET_BUILD_DIR}/${FRAMEWORKS_FOLDER_PATH}\"\n echo \"rsync --delete -av \"${RSYNC_PROTECT_TMP_FILES[@]}\" $RESOURCE_PATH ${TARGET_BUILD_DIR}/${FRAMEWORKS_FOLDER_PATH}\" || true\n rsync --delete -av \"${RSYNC_PROTECT_TMP_FILES[@]}\" \"$RESOURCE_PATH\" \"${TARGET_BUILD_DIR}/${FRAMEWORKS_FOLDER_PATH}\"\n ;;\n *.xcdatamodel)\n echo \"xcrun momc \\\"$RESOURCE_PATH\\\" \\\"${TARGET_BUILD_DIR}/${UNLOCALIZED_RESOURCES_FOLDER_PATH}/`basename \"$RESOURCE_PATH\"`.mom\\\"\" || true\n xcrun momc \"$RESOURCE_PATH\" \"${TARGET_BUILD_DIR}/${UNLOCALIZED_RESOURCES_FOLDER_PATH}/`basename \"$RESOURCE_PATH\" .xcdatamodel`.mom\"\n ;;\n *.xcdatamodeld)\n echo \"xcrun momc \\\"$RESOURCE_PATH\\\" \\\"${TARGET_BUILD_DIR}/${UNLOCALIZED_RESOURCES_FOLDER_PATH}/`basename \"$RESOURCE_PATH\" .xcdatamodeld`.momd\\\"\" || true\n xcrun momc \"$RESOURCE_PATH\" \"${TARGET_BUILD_DIR}/${UNLOCALIZED_RESOURCES_FOLDER_PATH}/`basename \"$RESOURCE_PATH\" .xcdatamodeld`.momd\"\n ;;\n *.xcmappingmodel)\n echo \"xcrun mapc \\\"$RESOURCE_PATH\\\" \\\"${TARGET_BUILD_DIR}/${UNLOCALIZED_RESOURCES_FOLDER_PATH}/`basename \"$RESOURCE_PATH\" .xcmappingmodel`.cdm\\\"\" || true\n xcrun mapc \"$RESOURCE_PATH\" \"${TARGET_BUILD_DIR}/${UNLOCALIZED_RESOURCES_FOLDER_PATH}/`basename \"$RESOURCE_PATH\" .xcmappingmodel`.cdm\"\n ;;\n *.xcassets)\n ABSOLUTE_XCASSET_FILE=\"$RESOURCE_PATH\"\n XCASSET_FILES+=(\"$ABSOLUTE_XCASSET_FILE\")\n ;;\n *)\n echo \"$RESOURCE_PATH\" || true\n echo \"$RESOURCE_PATH\" >> \"$RESOURCES_TO_COPY\"\n ;;\n esac\n}\n\nmkdir -p \"${TARGET_BUILD_DIR}/${UNLOCALIZED_RESOURCES_FOLDER_PATH}\"\nrsync -avr --copy-links --no-relative --exclude '*/.svn/*' --files-from=\"$RESOURCES_TO_COPY\" / \"${TARGET_BUILD_DIR}/${UNLOCALIZED_RESOURCES_FOLDER_PATH}\"\nif [[ \"${ACTION}\" == \"install\" ]] && [[ \"${SKIP_INSTALL}\" == \"NO\" ]]; then\n mkdir -p \"${INSTALL_DIR}/${UNLOCALIZED_RESOURCES_FOLDER_PATH}\"\n rsync -avr --copy-links --no-relative --exclude '*/.svn/*' --files-from=\"$RESOURCES_TO_COPY\" / \"${INSTALL_DIR}/${UNLOCALIZED_RESOURCES_FOLDER_PATH}\"\nfi\nrm -f \"$RESOURCES_TO_COPY\"\n\nif [[ -n \"${WRAPPER_EXTENSION}\" ]] && [ \"`xcrun --find actool`\" ] && [ -n \"${XCASSET_FILES:-}\" ]\nthen\n # Find all other xcassets (this unfortunately includes those of path pods and other targets).", "\n OTHER_XCASSETS=$(find \"$PWD\" -iname \"*.xcassets\" -type d)\n while read line; do\n if [[ $line !", "= \"${PODS_ROOT}*\" ]]; then\n XCASSET_FILES+=(\"$line\")\n fi\n done <<<\"$OTHER_XCASSETS\"\n\n if [ -z ${ASSETCATALOG_COMPILER_APPICON_NAME+x} ]; then\n printf \"%s\\0\" \"${XCASSET_FILES[@]}\" | xargs -0 xcrun actool --output-format human-readable-text --notices --warnings --platform \"${PLATFORM_NAME}\" --minimum-deployment-target \"${!", "DEPLOYMENT_TARGET_SETTING_NAME}\" ${TARGET_DEVICE_ARGS} --compress-pngs --compile \"${BUILT_PRODUCTS_DIR}/${UNLOCALIZED_RESOURCES_FOLDER_PATH}\"\n else\n printf \"%s\\0\" \"${XCASSET_FILES[@]}\" | xargs -0 xcrun actool --output-format human-readable-text --notices --warnings --platform \"${PLATFORM_NAME}\" --minimum-deployment-target \"${!", "DEPLOYMENT_TARGET_SETTING_NAME}\" ${TARGET_DEVICE_ARGS} --compress-pngs --compile \"${BUILT_PRODUCTS_DIR}/${UNLOCALIZED_RESOURCES_FOLDER_PATH}\" --app-icon \"${ASSETCATALOG_COMPILER_APPICON_NAME}\" --output-partial-info-plist \"${TARGET_TEMP_DIR}/assetcatalog_generated_info_cocoapods.plist\"\n fi\nfi\n" ]

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[ "Q:\n\nSAPUI5 Using XML-File as View with \"data-sap-ui-resourceroots\"?", "\n\nI'm doing the SAPUI5 Walkthrough and stuck at step 4. (", "Walkthrough Step 4)\nI'm working with Eclipse and don't know how to change this code-line so it works for my project and is going to find my view.", "\n data-sap-ui-resourceroots='{\n \"sap.ui.demo.wt\": \"./\"\n }' \n\nI need to know what to insert for \"sap.ui.demo.wt\" when using an Eclipse project.", "\nThanks for any hints :)\nEDIT:\nNow I got a working page with a button which triggers a pop-up.", "\nFolder structure: \nSAPUI5_Test\n - WebContent\n - controller\n -> NewView.controller.js\n - view\n -> NewView.view.xml\n - index.html\n\nindex.html:\n <!", "DOCTYPE html>\n<html>\n<head>\n <meta http-equiv=\"X-UA-Compatible\" content=\"IE=edge\"/>\n <meta charset=\"UTF-8\">\n <title>SAPUI5 Walkthrough</title>\n <script\n id=\"sap-ui-bootstrap\"\n src=\"https://openui5.hana.ondemand.com/resources/sap-ui-core.js\"\n data-sap-ui-theme=\"sap_bluecrystal\"\n data-sap-ui-libs=\"sap.m\"\n data-sap-ui-compatVersion=\"edge\"\n data-sap-ui-preload=\"async\"\n data-sap-ui-resourceroots='{\n \"SAPUI5_Test\": \"./\"\n }'>\n </script>\n <script>\n sap.ui.getCore().attachInit(function () {\n sap.ui.xmlview({\n viewName: \"SAPUI5_Test.view.", "NewView\"\n }).placeAt(\"content\");\n });\n </script>\n</head>\n<body class=\"sapUiBody\" id=\"content\">\n</body>\n</html>\n\nNewView.view.xml:\n<mvc:View\ncontrollerName=\"SAPUI5_Test.controller.", "NewView\"\nxmlns=\"sap.m\"\nxmlns:mvc=\"sap.ui.core.mvc\">\n<Button \ntext=\"Say hello\"\npress=\"onShowHello\"/>\n</mvc:View>\n\nNewView.controller.js\nsap.ui.controller(\"SAPUI5_Test.controller.", "NewView\", {\n onShowHello : function() {\n alert(\"Hello SAPUI5_Controller\");\n }\n});\n\nSo thanks for the help! ", "And maybe this could help someone in the future :)\n\nA:\n\nSAPUI5 is searching for resources like views, controllers or other classes by their full names.", "\nIt is assuming that every namespace part is a folder and the class/view name is the filename. ", "If its a view the filename has to be xxx.view.xml. ", "if its a controller the filename has to be xxx.controller.js.", "\nThe root folder where it starts its search is by default the folder of the sap-ui-core.js.", "\nYou can change the root folder by defining a data-sap-ui-resourceroots mapping. ", "Its a javascript object that maps a namespace to a path (relative to the index.html).", "\nWith the following bootstrap tag company.myProject.view.", "View1 is searched for at /resources/company/myProject/view/View1.view.xml:\n<script id=\"sap-ui-bootstrap\" \n src=\"resources/sap-ui-core.js\"></script>\n\nWith this bootstrap tag company.myProject.", "View1 is searched for at /view/View1.view.xml:\n<script id=\"sap-ui-bootstrap\" \n src=\"resources/sap-ui-core.js\"\n data-sap-ui-resourceroots='{\n \"company.myProject\": \"./\" }'></script>\n\nAnd with this bootstrap tag company.myProject.", "View1 is searched for at ddd/myProject/view/View1.view.xml:\n<script id=\"sap-ui-bootstrap\" \n src=\"resources/sap-ui-core.js\"\n data-sap-ui-resourceroots='{\n \"company\": \"./ddd\" }'></script>\n\nEdit: Please beware that you have to use \" inside of the map. ' ", "will not work.", "\n\nEdit: Clarification of folder structure\nI would recommend that you put everything in a project namespace. ", "Use this folder structure:\nWebContent\n- controller\n - NewView.controller.js\n- view\n - NewView.view.xml\n- index.html\n\nRename View folder to view (namespaces are camelCase by convention).", "\nRename newView.view.xml to NewView.view.xml (Classes/Views are PascalCase by convention)\nUse data-sap-ui-resourceroots='{ \"myproject\": \"./\" }'. ", "\nChange your Controller name to myproject.controller.", "NewView: Controller.extend(\"myproject.controller.", "NewView\", {...}); or sap.ui.controller(\"myproject.controller.", "NewView\",{...});.", "\nIn the xmlview use controllerName=\"myproject.controller.", "NewView\".", "\nInstantiate the view with sap.ui.xmlview({ viewName: \"myproject.view.", "NewView\"}).placeAt(\"content\");. ", "\n\nWith that you don't have to add a mapping for every subfolder in your project.", "\n\n" ]

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[ "A widely reported new study claims that people -- especially women -- who have multiple sexual parters before tying the knot, report unhappier marriages down the line.", "\n\nThe study comes to us from The National Marriage Project, based off research from two University of Denver professors, Galena K. Rhoades and Scott M. Stanley, who looked at relationship data collected from 2007 to 2008 of 1,000 unmarried Americans ages 18 to 34. ", "During the following five years, 418 of the participants got married.", "\n\nRhoades and Stanley took a closer look at those marriages to see if factors, including participants' sexual past, played a role in current marital quality.", "\n\nCouples' relationship quality was measured using a four-item version of the Dyadic Adjustment Scale, focusing on relationship happiness, thoughts about separation, frequency of confiding in one another, and a general item about how well things are going (the full scale, however, contains 32 items).", "\n\nAccording to researchers, the 23 percent of participants who only had sex with their spouse prior to getting hitched reported higher quality marriages versus those who had other past sexual partners as well.", "\n\nThey claim this finding is especially true for women, writing in the report, \"We further found that the more sexual partners a woman had had before marriage, the less happy she reported her marriage to be.\"", "\n\nOn top of that, researchers say that participants who lived with an S.O. -- who did not become their future spouse -- also reported unhappier marriages (graph below).", "\n\n\n\nCredit: National Marriage Project\n\nSo why would more sexual or relationship experience be associated with worse outcomes later on?", "\n\nRhoades and Stanley hypothesize in the report that \"more experience may increase one’s awareness of alternative partners.\" ", "In other words, people who have a number of prior relationships may become dissatisfied more easily.", "\n\nBut isn't that another way to say they might be more aware of a bad relationship? ", "Isn't that a good thing?", "\n\nIndeed, while the data presented in The Marriage Project's 418-person study is legitimate, experts say that the conclusions drawn from it -- especially those which cast judgement on one's sexual history and incite sentiments of slut-shaming -- may not be entirely accurate.", "\n\nResearchers in this field, who were not involved with this particular study, told The Huffington Post that these findings should be taken with a grain of salt.", "\n\n\"There are a wide variety of reasons that may lead people to have multiple partners before marriage and, independent of how many partners they have, also be less satisfied in marriage,\" Dr. Jim McNulty, a social psychology professor from Florida State University who has published a plethora of research on the topic, wrote in an email.", "\n\n\"For example, people who tend to avoid commitment in general may have more sexual partners and be less happy when they settle down. ", "It’s not the fact that they have more sexual partners that leads them to be less happy, it’s the fact that they don’t really like commitment. ", "I would be very surprised if having multiple sexual partners before marriage, independent of any other factor, has a direct causal influence.\"", "\n\nIn other words, correlation should never be confused with causation.", "\n\n\"We cannot make any conclusions about cause-and-effect,\" says Justin Lehmiller, PhD, sex educator and researcher at Purdue University, adding, \"Could it be that multiple premarital partners impacts marital happiness? ", "Maybe. ", "But it could also be that people who have more partners have different personalities or different attitudes toward marriage or relationships.\"", "\n\nBeyond that, Lehmiller says there may be flaws in the way data was analyzed -- the way in which good marriages were separated from bad marriages was \"rather odd\" he says. \"", "Even the authors admit that they were 'arbitrary' in their report. ", "They defined 'higher quality marriages' as those in which individuals scored in the top 40 percent ... Why the top 40 percent?\"", "\n\nMcNulty also points out that though the authors are respected researchers, the study was not reported by an academic journal nor was it peer-reviewed.", "\n\nWhat do you think: could having more relationship experience prior to meeting \"the one\" actually result in unhappier marriages down the line? ", "Sound off below!" ]

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[ "/*\n * Copyright (c) 1997 - 2008 Kungliga Tekniska Högskolan\n * (Royal Institute of Technology, Stockholm, Sweden).", "\n * All rights reserved.", "\n *\n * Redistribution and use in source and binary forms, with or without\n * modification, are permitted provided that the following conditions\n * are met:\n *\n * 1. ", "Redistributions of source code must retain the above copyright\n * notice, this list of conditions and the following disclaimer.", "\n *\n * 2. ", "Redistributions in binary form must reproduce the above copyright\n * notice, this list of conditions and the following disclaimer in the\n * documentation and/or other materials provided with the distribution.", "\n *\n * 3. ", "Neither the name of the Institute nor the names of its contributors\n * may be used to endorse or promote products derived from this software\n * without specific prior written permission.", "\n *\n * THIS SOFTWARE IS PROVIDED BY THE INSTITUTE AND CONTRIBUTORS ``AS IS'' AND\n * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE\n * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE\n * ARE DISCLAIMED. ", " IN NO EVENT SHALL THE INSTITUTE OR CONTRIBUTORS BE LIABLE\n * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL\n * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS\n * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)\n * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT\n * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY\n * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF\n * SUCH DAMAGE.", "\n */\n\n/*\n * ARCFOUR\n */\n\n#include \"krb5_locl.h\"\n\nstatic struct _krb5_key_type keytype_arcfour = {\n KRB5_ENCTYPE_ARCFOUR_HMAC_MD5,\n \"arcfour\",\n 128,\n 16,\n sizeof(struct _krb5_evp_schedule),\n NULL,\n _krb5_evp_schedule,\n _krb5_arcfour_salt,\n NULL,\n _krb5_evp_cleanup,\n EVP_rc4\n};\n\n/*\n * checksum according to section 5. ", "of draft-brezak-win2k-krb-rc4-hmac-03.txt\n */\n\nkrb5_error_code\n_krb5_HMAC_MD5_checksum(krb5_context context,\n\t\t\tstruct _krb5_key_data *key,\n\t\t\tconst void *data,\n\t\t\tsize_t len,\n\t\t\tunsigned usage,\n\t\t\tChecksum *result)\n{\n EVP_MD_CTX *m;\n struct _krb5_checksum_type *c = _krb5_find_checksum (CKSUMTYPE_RSA_MD5);\n const char signature[] = \"signaturekey\";\n Checksum ksign_c;\n struct _krb5_key_data ksign;\n krb5_keyblock kb;\n unsigned char t[4];\n unsigned char tmp[16];\n unsigned char ksign_c_data[16];\n krb5_error_code ret;\n\n m = EVP_MD_CTX_create();\n if (m == NULL) {\n\tkrb5_set_error_message(context, ENOMEM, N_(\"malloc: out of memory\", \"\"));\n\treturn ENOMEM;\n }\n ksign_c.checksum.length = sizeof(ksign_c_data);\n ksign_c.checksum.data = ksign_c_data;\n ret = _krb5_internal_hmac(context, c, signature, sizeof(signature),\n\t\t\t 0, key, &ksign_c);\n if (ret) {\n\tEVP_MD_CTX_destroy(m);\n\treturn ret;\n }\n ksign.key = &kb;\n kb.keyvalue = ksign_c.checksum;\n EVP_DigestInit_ex(m, EVP_md5(), NULL);\n t[0] = (usage >> 0) & 0xFF;\n t[1] = (usage >> 8) & 0xFF;\n t[2] = (usage >> 16) & 0xFF;\n t[3] = (usage >> 24) & 0xFF;\n EVP_DigestUpdate(m, t, 4);\n EVP_DigestUpdate(m, data, len);\n EVP_DigestFinal_ex (m, tmp, NULL);\n EVP_MD_CTX_destroy(m);\n\n ret = _krb5_internal_hmac(context, c, tmp, sizeof(tmp), 0, &ksign, result);\n if (ret)\n\treturn ret;\n return 0;\n}\n\nstruct _krb5_checksum_type _krb5_checksum_hmac_md5 = {\n CKSUMTYPE_HMAC_MD5,\n \"hmac-md5\",\n 64,\n 16,\n F_KEYED | F_CPROOF,\n _krb5_HMAC_MD5_checksum,\n NULL\n};\n\n/*\n * section 6 of draft-brezak-win2k-krb-rc4-hmac-03\n *\n * warning: not for small children\n */\n\nstatic krb5_error_code\nARCFOUR_subencrypt(krb5_context context,\n\t\t struct _krb5_key_data *key,\n\t\t void *data,\n\t\t size_t len,\n\t\t unsigned usage,\n\t\t void *ivec)\n{\n EVP_CIPHER_CTX ctx;\n struct _krb5_checksum_type *c = _krb5_find_checksum (CKSUMTYPE_RSA_MD5);\n Checksum k1_c, k2_c, k3_c, cksum;\n struct _krb5_key_data ke;\n krb5_keyblock kb;\n unsigned char t[4];\n unsigned char *cdata = data;\n unsigned char k1_c_data[16], k2_c_data[16], k3_c_data[16];\n krb5_error_code ret;\n\n t[0] = (usage >> 0) & 0xFF;\n t[1] = (usage >> 8) & 0xFF;\n t[2] = (usage >> 16) & 0xFF;\n t[3] = (usage >> 24) & 0xFF;\n\n k1_c.checksum.length = sizeof(k1_c_data);\n k1_c.checksum.data = k1_c_data;\n\n ret = _krb5_internal_hmac(context, c, t, sizeof(t), 0, key, &k1_c);\n if (ret)\n\tkrb5_abortx(context, \"hmac failed\");\n\n memcpy (k2_c_data, k1_c_data, sizeof(k1_c_data));\n\n k2_c.checksum.length = sizeof(k2_c_data);\n k2_c.checksum.data = k2_c_data;\n\n ke.key = &kb;\n kb.keyvalue = k2_c.checksum;\n\n cksum.checksum.length = 16;\n cksum.checksum.data = data;\n\n ret = _krb5_internal_hmac(context, c, cdata + 16, len - 16, 0, &ke, &cksum);\n if (ret)\n\tkrb5_abortx(context, \"hmac failed\");\n\n ke.key = &kb;\n kb.keyvalue = k1_c.checksum;\n\n k3_c.checksum.length = sizeof(k3_c_data);\n k3_c.checksum.data = k3_c_data;\n\n ret = _krb5_internal_hmac(context, c, data, 16, 0, &ke, &k3_c);\n if (ret)\n\tkrb5_abortx(context, \"hmac failed\");\n\n EVP_CIPHER_CTX_init(&ctx);\n\n EVP_CipherInit_ex(&ctx, EVP_rc4(), NULL, k3_c.checksum.data, NULL, 1);\n EVP_Cipher(&ctx, cdata + 16, cdata + 16, len - 16);\n EVP_CIPHER_CTX_cleanup(&ctx);\n\n memset (k1_c_data, 0, sizeof(k1_c_data));\n memset (k2_c_data, 0, sizeof(k2_c_data));\n memset (k3_c_data, 0, sizeof(k3_c_data));\n return 0;\n}\n\nstatic krb5_error_code\nARCFOUR_subdecrypt(krb5_context context,\n\t\t struct _krb5_key_data *key,\n\t\t void *data,\n\t\t size_t len,\n\t\t unsigned usage,\n\t\t void *ivec)\n{\n EVP_CIPHER_CTX ctx;\n struct _krb5_checksum_type *c = _krb5_find_checksum (CKSUMTYPE_RSA_MD5);\n Checksum k1_c, k2_c, k3_c, cksum;\n struct _krb5_key_data ke;\n krb5_keyblock kb;\n unsigned char t[4];\n unsigned char *cdata = data;\n unsigned char k1_c_data[16], k2_c_data[16], k3_c_data[16];\n unsigned char cksum_data[16];\n krb5_error_code ret;\n\n t[0] = (usage >> 0) & 0xFF;\n t[1] = (usage >> 8) & 0xFF;\n t[2] = (usage >> 16) & 0xFF;\n t[3] = (usage >> 24) & 0xFF;\n\n k1_c.checksum.length = sizeof(k1_c_data);\n k1_c.checksum.data = k1_c_data;\n\n ret = _krb5_internal_hmac(context, c, t, sizeof(t), 0, key, &k1_c);\n if (ret)\n\tkrb5_abortx(context, \"hmac failed\");\n\n memcpy (k2_c_data, k1_c_data, sizeof(k1_c_data));\n\n k2_c.checksum.length = sizeof(k2_c_data);\n k2_c.checksum.data = k2_c_data;\n\n ke.key = &kb;\n kb.keyvalue = k1_c.checksum;\n\n k3_c.checksum.length = sizeof(k3_c_data);\n k3_c.checksum.data = k3_c_data;\n\n ret = _krb5_internal_hmac(context, c, cdata, 16, 0, &ke, &k3_c);\n if (ret)\n\tkrb5_abortx(context, \"hmac failed\");\n\n EVP_CIPHER_CTX_init(&ctx);\n EVP_CipherInit_ex(&ctx, EVP_rc4(), NULL, k3_c.checksum.data, NULL, 0);\n EVP_Cipher(&ctx, cdata + 16, cdata + 16, len - 16);\n EVP_CIPHER_CTX_cleanup(&ctx);\n\n ke.key = &kb;\n kb.keyvalue = k2_c.checksum;\n\n cksum.checksum.length = 16;\n cksum.checksum.data = cksum_data;\n\n ret = _krb5_internal_hmac(context, c, cdata + 16, len - 16, 0, &ke, &cksum);\n if (ret)\n\tkrb5_abortx(context, \"hmac failed\");\n\n memset (k1_c_data, 0, sizeof(k1_c_data));\n memset (k2_c_data, 0, sizeof(k2_c_data));\n memset (k3_c_data, 0, sizeof(k3_c_data));\n\n if (ct_memcmp (cksum.checksum.data, data, 16) !", "= 0) {\n\tkrb5_clear_error_message (context);\n\treturn KRB5KRB_AP_ERR_BAD_INTEGRITY;\n } else {\n\treturn 0;\n }\n}\n\n/*\n * convert the usage numbers used in\n * draft-ietf-cat-kerb-key-derivation-00.txt to the ones in\n * draft-brezak-win2k-krb-rc4-hmac-04.txt\n */\n\nkrb5_error_code\n_krb5_usage2arcfour(krb5_context context, unsigned *usage)\n{\n switch (*usage) {\n case KRB5_KU_AS_REP_ENC_PART : /* 3 */\n\t*usage = 8;\n\treturn 0;\n case KRB5_KU_USAGE_SEAL : /* 22 */\n\t*usage = 13;\n\treturn 0;\n case KRB5_KU_USAGE_SIGN : /* 23 */\n *usage = 15;\n return 0;\n case KRB5_KU_USAGE_SEQ: /* 24 */\n\t*usage = 0;\n\treturn 0;\n default :\n\treturn 0;\n }\n}\n\nstatic krb5_error_code\nARCFOUR_encrypt(krb5_context context,\n\t\tstruct _krb5_key_data *key,\n\t\tvoid *data,\n\t\tsize_t len,\n\t\tkrb5_boolean encryptp,\n\t\tint usage,\n\t\tvoid *ivec)\n{\n krb5_error_code ret;\n unsigned keyusage = usage;\n\n if((ret = _krb5_usage2arcfour (context, &keyusage)) !", "= 0)\n\treturn ret;\n\n if (encryptp)\n\treturn ARCFOUR_subencrypt (context, key, data, len, keyusage, ivec);\n else\n\treturn ARCFOUR_subdecrypt (context, key, data, len, keyusage, ivec);\n}\n\nstruct _krb5_encryption_type _krb5_enctype_arcfour_hmac_md5 = {\n ETYPE_ARCFOUR_HMAC_MD5,\n \"arcfour-hmac-md5\",\n 1,\n 1,\n 8,\n &keytype_arcfour,\n &_krb5_checksum_hmac_md5,\n &_krb5_checksum_hmac_md5,\n F_SPECIAL,\n ARCFOUR_encrypt,\n 0,\n NULL\n};\n" ]

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[ "Post navigation\n\n2 thoughts on “Your isolated incident of the day”\n\nCouldn’t agree more. ", "You focus on one aspect of the use of deadly force, the aspect of harm an individual may do with a firearm, but are obvious to the lives saved by them. ", "According to who’s research you believe anywhere from 100,000 to 2,500,00 times a year an American uses a firearm in self-defense.", "\n\nAnd depending upon whose statistics you accept, there were about 2.5 million crimes that involved a gun during that same period. ", "And I could also mention the far higher likelihood of a successful suicide attempt for those living in a home with a gun.", "\n\nMisuse of firearms are not isolated incidents. ", "They occur with regular frequency and there are measures that can be taken that could work towards reducing those statistics.", "\n\nBut we live in a denial of reality in which each mass shooting is treated as an isolated incident, something that could never be avoided, because we would rather sacrifice 30,000 or so lives a year than inconvenience a would-be gun purchaser." ]

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[ "\n762 N.W.2d 160 (2009)\nRobert ADAIR, Plaintiff-Appellee,\nv.\nUTICA COMMUNITY SCHOOLS, Defendant, and\nUtica Skilled Trades Association, Defendant-Appellant.", "\nDocket No. ", "138115. ", "COA No. ", "288286.", "\nSupreme Court of Michigan.", "\nMarch 18, 2009.", "\n\nOrder\nOn order of the Court, the motion for immediate consideration is GRANTED. *", "161 The application for leave to appeal the December 11, 2008 order of the Court of Appeals is considered, and it is DENIED, because we are not persuaded that the questions presented should be reviewed by this Court. ", "This denial is without prejudice to the defendant's ability to file a motion requesting that the Macomb Circuit Court set the dollar amount of a stay bond in an amount adequate to protect the opposite party, pursuant to MCR 7.209(B)(1).", "\n" ]

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[ "Emily Pollifax\n\nMrs. Emily Pollifax is the heroine of a series of spy-mystery novels by Dorothy Gilman. ", "Mrs. Pollifax is a widow and senior citizen who decides one day to leave her comfortable apartment in New Brunswick, New Jersey and join the CIA. ", "Through an initial misunderstanding, Mrs. Pollifax is given what is supposed to be a simple courier assignment by Operations Chief, Mr. Carstairs, and her ensuing adventure leads her to a career in espionage.", "\n\nThe Emily Pollifax novels frequently employ comic relief and suspense. ", " A consistent theme throughout the series is Mrs. Pollifax's tendency to take an interest in people who seem disconnected with her mission, but who either become part of the investigation and/or who prove to be of invaluable assistance to resolving the case.", "\n\nRecurring characters include Bishop, Carstairs' assistant; John Sebastian Farrell, an agent turned art dealer; and in later books, Cyrus Reed, a man with whom Mrs. Pollifax finds romance in the book Mrs. Pollifax on Safari.", "\n\nMost of the novels take place in existing countries and include authentic details; however, characters in the stories sometimes originate from fictional places that resemble groups of real-life countries. ", "An example of this trait is evidenced by a character in A Palm for Mrs. Pollifax who is from Zabya, a fictional Middle Eastern monarchy described as one of \"those Arabian oil-producing countries.\" ", "In addition, as is common in the spy fiction genre, many of the stories taking place in the Cold War era are set in Iron Curtain countries or include rival spies from communist countries.", "\n\nBooks in the Mrs. Pollifax series\n\nThe Unexpected Mrs. Pollifax (1966)\n\nMrs. Pollifax is an elderly widow who has come to find life dull and is almost ready to end it all out of sheer boredom. ", "Inspired by a newspaper profile of an actress who began her career in later life, she decides to fulfill a childhood ambition and apply for a job as a spy at the CIA. ", "Meanwhile, Carstairs at the CIA is looking for an agent who can pass as a tourist in order to pick up an important microchip in Mexico. ", "Due to a slight confusion, he thinks Mrs. Pollifax is one of the candidates and decides that Mrs. Pollifax is ideal; Carstairs decided this assignment carries so little danger that even one who is relatively untrained may be sent. ", "So with minimum explanation, Pollifax is ushered off to Mexico City to meet a bookstore owner/secret agent, exchange code phrases, and leave with a book containing the microfilm. ", "Of course, the courier mission does not go as planned, and Mrs. Pollifax finds herself in a prison in Iron Curtain-era Albania, facing harsh questioning and possible torture. ", "But she proves to be unusually resourceful, and with her companion's assistance, manages to outwit the enemy and save the day.", "\n\nThe Amazing Mrs. Pollifax (1970)\nFor this novel, Mrs. Pollifax is tasked by Mr. Carstairs, her CIA superior, to go to Turkey and contact Magda Ferenci-Sabo, a known Russian spy and secret double agent who is defecting to the Free World. ", "Emily Pollifax is to give Magda money and a passport which will enable the former spy to leave Turkey. ", "Although Carstairs gives Mrs. Pollifax only 30 minutes to get ready, the plucky widow is ready for another adventure. ", "She flies to Turkey and sees Magda, but is unable to make personal contact before Magda flees. ", "In pursuing her mission, Mrs. Pollifax embarks on a wild ride, matching wits with a diabolical double agent, traveling with Gypsies, and again surviving imprisonment. ", "However, characteristically, she befriends unlikely allies along her way.", "\n\nThe Elusive Mrs. Pollifax (1971)\n \nMrs. Pollifax is sent, as a tourist, on a routine assignment, to deliver the eight forged passports she is carrying, concealed in her hat, to the Bulgarian Underground. ", "Unbeknownst to her, her boss, Carstairs, has been strong-armed into having her take other items along, sewn into her coat. ", "On the way, she meets a group of back-packing college students at an airport, and offers to help when one of them is arrested by the secret police, upon arriving in Sofia. ", "Mrs. Pollifax then leads both friends and foes on a merry chase, as she travels around Bulgaria, on a series of absorbing, and interwoven, adventures, including helping to rescue the student and several political prisoners from the seemingly impregnable Panchevsky Institute.", "\n\nA Palm for Mrs. Pollifax (1973)\nMrs. Pollifax is dispatched to Switzerland to find some missing plutonium: Mr. Carstairs of the CIA suspects the contraband has been hidden in an upscale clinic in Switzerland. ", " Mrs. Pollifax begins a careful investigation of the guests at the clinic and rapidly befriends a young British man, a Belgian woman, and a young boy and his grandmother from an Arab nation. ", "She soon discovers that very few of the clinic patients are who they claim to be, and she becomes involved in intrigue with men who plan to overthrow the government of a small country. ", " She, of course, displays the courage and ingenuity which Mr. Carstairs has learned to depend on, and she leads her outnumbered friends into the adventure of their lives.", "\n\nMrs. Pollifax on Safari (1976)\nMrs. Pollifax is called upon by the CIA to undertake another mission, this time to photograph members of a safari in Zambia, one of whom is an international assassin nicknamed Aristotle. ", "She innocently posts an ad in the local newspaper trying to contact her old friend Farrell from the first book. ", "This leads to major complications, as Farrell is involved with the freedom fighters across the border and has made some enemies. ", "Another entertaining outing and with a bit of romance as a fellow traveler takes a fancy to Mrs. Pollifax.", "\n\nMrs. Pollifax on the China Station (1983)\nMrs. Pollifax is thrilled when Mr. Carstairs, her boss at the CIA, gives her an assignment in China to help rescue a prisoner from a labor camp. ", "As luck would have it, she has recently completed a course in Chinese history, so she is primed and ready to go. ", "She joins a tour group and is told that one of the other group members is actually a CIA agent who will become her partner later on. ", "She tries unsuccessfully to detect her future partner and is very surprised when the agent's identity is revealed. ", "As the action speeds up she finds the labor camp, rides a runaway horse, and encounters some rough stuff from a Russian spy. ", " But she always comes through in the end.", "\n\nMrs. Pollifax and the Hong Kong Buddha (1985)\nMrs. Pollifax flies on a moment's notice to Hong Kong, to contact Sheng Ti, whom she met in an earlier book, and find out what is going on at Feng Imports where Sheng Ti is working for an agent named Detwiler. ", "Detwiler's reports to the CIA have proved to be false, so he is suspected of being a counterspy and giving evidence to the enemy. ", "Mrs. Pollifax meets some other interesting characters, including a psychic and another old friend, who is a reformed cat burglar, while in pursuit of the truth about Feng Imports. ", "She is captured and tortured, but prevails as always.", "\n\nMrs. Pollifax and the Golden Triangle (1988)\nThis time Mrs. Pollifax's assignment seems simple: while she and her husband Cyrus Reed are vacationing in Thailand, she is to pick up some valuable information on drug smuggling from an informant called Ruamsak. ", "Everything goes awry immediately: Ruamsak is murdered, Cyrus is kidnapped, and Emily joins forces with Bonchoo, an intriguing stranger with complex reasons of his own for wanting to find Cyrus. ", "They meet the Akha people in the jungle. ", "The usual phalanx of muddled but supportive CIA agents try to follow Emily through the jungles of Thailand and are seriously rattled when one of their directors abruptly vanishes, only to reappear in the Golden Triangle as the head of all illicit drug trafficking. ", "Pollifax needs all her wiles and her considerable skills in the martial arts, not only to track her husband but also to put a serious dent in the heroin trade. ", "She accomplishes everything with vigor and charm.", "\n\nMrs. Pollifax and the Whirling Dervish (1990)\nMrs. Pollifax is dispatched to Morocco to provide a cover for another of their agents, Max Janko. ", "She will pose as Max's aunt to make the pair look like tourists, while in reality they will be trying to identify all seven Moroccan CIA operatives in order to ferret out the mole who has recently infiltrated the Atlas network, a secret branch of the CIA. ", "Anticipating a relatively serene journey through picturesque Moroccan villages with an agreeable companion, Mrs. Pollifax is dismayed to find Janko insufferably hostile. ", "Worse, he intends to kill her. ", "By the time the real Janko shows up, a murder has occurred, and Mrs. Pollifax and her inexperienced companion are running for their lives from one dusty hamlet to the next, desperately trying to find the informer and save the rest of the network.", "\n\nMrs. Pollifax and the Second Thief (1993)\nMrs. Pollifax travels to Sicily in this adventure. ", "Former colleague John Farrell, hired to crack a safe and lift a document signed by Julius Caesar sends an SOS while dodging a professional assassin whom he and Mrs. Pollifax jailed some years ago. ", "Soon she too is ducking bullets and the old pals are forced to hole up in the Villa Franca—part farm, part medieval fortress and full-time residence of young CIA agent Kate Rossiter's eccentric aunt. ", "Ancient artifacts, hair-raising chases, art forgery, arms traffic, a nighttime assault on the villa, mysterious millionaires, spectacular scenery and unexpected romance are some of the ingredients simmering in the plot.", "\n\nMrs. Pollifax Pursued (1995)\nThe observant and unflappable Mrs. Pollifax discovers a young woman hiding in a closet of her Connecticut home on the same day that she observes a suspicious white van patrolling the neighborhood. ", "Kadi Hopkirk says the men in the van have been following her ever since she met Sammy, a childhood friend from the African country of Ubangiba. ", "Mrs. Pollifax hides Kadi in the car and takes to the highway but is unable to shake the van until she calls on her colleagues at the CIA, who send a helicopter to whisk them away to a traveling carnival in rural Maine. ", "Mrs. Pollifax poses as a journalist, and Kadi becomes the lower half of the woman who is sawed in two, while the CIA pals find out who Sammy is and why he is being so heavily guarded. ", "Mrs. Pollifax adroitly solves several mysteries, including a stabbing at the carnival, Kadi and Sammy's story and the abduction of a wealthy executive.", "\n\nMrs. Pollifax and the Lion Killer (1996)\nThe sequel to Mrs. Pollifax Pursued, in which we meet Kadi Hopkirk, the daughter of Ubangiba missionaries. ", " Kadi's college friend Sammy is now trying to rule Ubangiba after many years of dictatorship. ", "Sammy calls upon Kadi for help and Mrs. Pollifax decides to accompany her to Africa. ", "There have been a series of violent deaths at the hands of a \"lion killer\", one who dons a lion costume, and Sammy's enemies have accused him of being behind the murders. ", "When Kadi arrives in Ubangiba, she becomes the target of an old enemy, and Mrs. Pollifax does her best to protect the young girl. ", "A potential archaeological dig and the hint of romance for Kadi combine with political intrigue and murder to create another satisfying story of Mrs. Pollifax.", "\n\nMrs. Pollifax, Innocent Tourist (1997)\nMrs. Pollifax travels to Jordan with former Company agent John Sebastian Farrell to receive a manuscript smuggled from Iraq, written by an executed dissident Iraqi novelist. ", "As Farrell's cover, Mrs. Pollifax poses as his tourist cousin but immediately is up to her flowered straw hat in intrigue. ", "Farrell's contact doesn't show up for their scheduled meeting at the Crusader castle at Karak, although Emily does find a dead body there. ", "When their guide, Youseff, and his sister, Hanan, invite them to visit their grandfather, a desert sheik, they're trailed by Jordanian terrorists, the Iraqi secret police and Jordanian police. ", "The climax occurs at an ancient desert fort after a whirlwind of brisk action and seductive scenery.", "\n\nMrs. Pollifax Unveiled (2000)\nMrs. Pollifax teams up with freelance CIA agent John Farrell on an investigation into the disappearance of Amanda Pym in Syria. ", "Ms. Pym was a fifteen-minute media superstar when she allegedly stopped an airplane hijacking from succeeding. ", "Witnesses last saw Amanda enter a vehicle that waited for her at the Damascus Airport. ", "Farrell and Mrs. Pollifax land in Syria where the government places a tail on the duo. ", "However, they quickly elude their shadow in order to obtain information that provides them with the first clue in their hunt. ", "They soon enter the Syrian Desert where they meet American archeologist Joe Fleming. ", "Joining the two operatives on their quest, Joe and the two spies seek an elusive individual who seems to be undergoing a rigorous training for a mission that has world implications.", "\n\nMrs. Pollifax in film\nMrs. Pollifax—Spy (1971), a theatrical film based on the book The Unexpected Mrs. Pollifax, stars Rosalind Russell in the title role, Darren McGavin as John Sebastian Farrell, and Dana Elcar as Carstairs. ", "Russell was also credited as contributing to the story idea under a pseudonym.", "\n\nThe Unexpected Mrs. Pollifax (1999), a CBS television movie adaptation of the eponymous book, stars Angela Lansbury in the title role, Thomas Ian Griffith as Farrell, and Ed Bishop as Carstairs.", "\n\nReferences\n\nExternal links\n\n MrsPollifax.com fan website\n\nCategory:Characters in American novels of the 20th century\nCategory:Literary characters introduced in 1966\nCategory:Fictional secret agents and spies\nCategory:Series of books" ]

{ "pile_set_name": "Wikipedia (en)" }

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[ "Spa Pools\n\nSwimming Pools\n\nThe Pool Centre - Palmerston North\n\nThe Pool Centre, Palmerston North, is NZ's premiere site for Trueform outdoor spa pools, Narellan inground fibreglass swimming pools and pool accessories. ", "If you have any questions please feel free to contact us" ]

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[ "The SitePoint Forums have moved.", "\n\nYou can now find them here.", "\nThis forum is now closed to new posts, but you can browse existing content.", "\nYou can find out more information about the move and how to open a new account (if necessary) here.", "\nIf you get stuck you can get support by emailing forums@sitepoint.com\n\nIf this is your first visit, be sure to\ncheck out the FAQ by clicking the\nlink above. ", "You may have to register\nbefore you can post: click the register link above to proceed. ", "To start viewing messages,\nselect the forum that you want to visit from the selection below.", "\n\nWhat I'd like to know is how I can retrieve the path where the script file is located in the server.", "\nEg: /wwwroot/blahblahblah/myphpfile.php. ", "I know this can be done in ASP using Server.", "MapPath() but I don't know how to do it in PHP.", "\n\nYes, outputs itself very neatly too, probably one of the most useful features I've found since I started playing with PHP. ", "Great when you want to set up your own box for development, and make sure the environment matches the one you're going to publish to on the web. ", "Makes it very easy to see just how PHP is set up on the server even if you don't have any way to access the actual configuration files." ]

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[ "Items identified as Quick Ship will ship within 2 business days from our warehouse in Babylon, New York. ", "Actual delivery times will vary based on your location. ", "If you are ordering multiple items and not all items qualify for Quick Ship, the order will ship when all items are available to ship. ", "Quick Ship may not apply to multiple quantities of the same product.", "\n\nWhen it comes to premium refrigeration, look no further than Liebherr Appliances. ", "Liebherr has over 50 years of refrigeration experience and continually defines the industry with its inspired German engineering and its proactive approach to responsible manufacturing.", "\n\nWine Storage and Optimal Temperature\nImproperly storing your wine is the most common mistake made by wine enthusiasts. ", "Temperature is usually the most neglected factor. ", "Most of us don't have the room for a proper wine cellar in our homes. ", "Thanks to Liebherr, storing and serving wine at the proper temperature can be easily achieved.", "\n\nStoring wine and useful tips:\nMany great wine collections have been devastated by unstable temperature and humidity. ", "When stored in an environment that is too hot, it causes the wine to age prematurely, causing it to lose its delicate flavor and balance. ", "When chilled too cold the crystallization breaks down the molecular structure, also causing to to lose its balance and flavor. ", "Wide fluctuations will also cause the cork to expand and shrink, allowing air to seep in and contaminate the delicate balance. ", "The ideal range to store red wine is between 50-55° f, White wines around 45°. ", "Humidity is another important factor. ", "Too much moisture will allow mold to grow, too little and the cork will dry out. ", "The ideal humidity level is between 60-75% RH.", "\n\nFortunately Liebherr Appliances has a wide range of single and multi zone Wine Storage Cabinets to keep your collection at the peak of its bouquet and vibrancy. ", "They are available in 24\" or 26\" widths and up to three temperature zones, to keep your red and whites each at their optimal temperature. ", "Each can be adjusted separately and independently from the others. ", "With units that can hold up to 143 bottles, your entire collection can be safely stored, and the convenient safety lock will keep it secure.", "\n\nA humidor keeps your cigars at their best by storing them in conditions akin to which they were grown, fermented and rolled. ", "Improper storage or leaving them out in the open air can dry them out in less than an hour. ", "In a humidor, the interior conditions simulate the temperature and humidity of a tropical island, you can keep your cigars fresh for years.", "The best humidors are lined with nonaromatic Spanish Cedar. ", "Spanish Cedar absorbs and re-emits moisture in a way that helps the tobaccos that are blended into a fine cigar to age and mature. ", "If you are a certified cigar aficionado or have just started to indulge, proper storage of your cigars the key to keeping them in prime condition.", "\n\nThe same dedication and commitment Liebherr uses for its Refrigeration and Wine Coolers has been duplicated in its approach to designing the ultimate humidor. ", "The ultra precise Magic Eye control system maintains the perfect balance of temperature and humidity. ", "The humidor can be set from 60° to 68° and the humidity can be set from 68% to 75%." ]

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[ "Category: Fraud\n\nThe mobile tech industry is now seeing fraud costs reaching $1.3 Billion a year. ", "Multiple fraud prevention companies now exist solely to combat this type of behavior and app developers should prepare themselves for the future of rapidly evolving fraud techniques, especially when it comes to app install based campaigns. ", "Fraud ranges from warehouses filled…READ MORE" ]

{ "pile_set_name": "Pile-CC" }

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[ "using System.", "IO;\nusing System.", "IO.Compression;\nusing JT808.Protocol.", "Interfaces;\n\nnamespace JT808.Protocol.", "Internal\n{\n internal class JT808GZipCompressImpl : IJT808Compress\n {\n public byte[] Compress(byte[] data)\n {\n using (var outStream = new MemoryStream())\n {\n using (var gZipStream = new GZipStream(outStream, CompressionMode.", "Compress))\n using (var mStream = new MemoryStream(data))\n mStream.", "CopyTo(gZipStream);\n return outStream.", "ToArray();\n }\n }\n\n public byte[] Decompress(byte[] compressData)\n {\n using (var inStream = new MemoryStream(compressData))\n using (var gZipStream = new GZipStream(inStream, CompressionMode.", "Decompress))\n using (var outStream = new MemoryStream())\n {\n gZipStream.", "CopyTo(outStream);\n return outStream.", "ToArray();\n }\n }\n }\n}\n" ]

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[ "Q:\n\n¿Puede alguien decirme donde tengo el error?", "\n\ndef asignacion_paquetes(U,m,v):\n P={}\n for u in range(U+1):\n P[0,u] =0\n for i in range(1,len(m)+1):\n P[i,0]=0\n for u in range(1,U+1):\n P[i,u] = max(P[i-1, u-x]+v[i,x] for x in range(0,min(u,m[i])+1))\n\n return P[len(m),U]\n\nMe gustaria saber donde esta el error porque me dice IndexError: list index out of range en la linea en la que pongo la flecha ->\nEste codigo representa a un problema de optimizacion de asignacion optima de recursos resuelto por programacion dinamica U representa los recursos totales y m es una lista que representa el limite de recursos que se puede asignar a una actividad i y v es un diccionario que tiene como clave una tupla i,u que representa el beneficio de asignar un recurso u a una actividad i.\nTodo esto con el objetivo de obtener el mayor beneficio.", "\nDe ahi la formula P[i,u]= max(P[i-1,u-x] + v[i,x].", "\n¿Alguien me puede ayudar?", "\nU = 12\n\nm = [2,4,2,4,2]\n\nv=dict(((i,u),randrange(100)) for i in range(1,len(m)+1) for u in range(0, U+1))\n\nEsos son los valores de los parámetros \n\nA:\n\nTienes un problema con él uso de range(), no sé si tienes claro que en Python los índices de cualquier colección de datos comienzan en 0 y el límite superior de range() no es inclusivo. ", "Puntualmente el error lo tienes en el for más profundo:\nfor i in range(1,len(m)+1):\n P[i,0]=0\n for u in range(1,U+1):\n P[i,u] = max(P[i-1, u-x]+v[i,x] for x in range(0,min(u,m[i])+1))\n\nEl primer for iterará desde i=1 hasta la longitud de m, con los diccionarios no tienes problema, el problema lo tienes cuando haces m[i], como m es una lista cuyos índices comienzan en 0, y tu desplazas el mismo 1 valor más el último índice de la iteración no existe de ahí el error. ", "Debieras en todo caso hacer m[i-1]. ", "\nAlgunos comentarios extra:\n\nYo manejaría las claves de los diccionarios con el mismo esquema de los índices de las listas dónde 0 es el primer elemento, esto haría más consistente el código\nTambién para que sea más claro, al definir las claves de los diccionarios usaría los parentesis para cerrar las tuplas, por ejemplo: P[(i,0)]=0 para no confundir a nadie con algún manejo especial de índices.", "\n\n" ]

{ "pile_set_name": "StackExchange" }

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[ "In a recent presentation to the Premier’s Task Force on Improving Education Outcomes, the Newfoundland and Labrador Teachers’ Association presented compelling scientific and anecdotal data showing that the working conditions for classroom teachers are not good.", "\n\nClasses include many students with severe behavioural problems, significant cognitive disabilities and diverse academic skills. ", "With only limited support, teachers find it difficult to provide adequate instruction. ", "They’re pressured to develop multiple lesson plans for each class to accommodate the variety of individual needs.", "\n\nFrankly, this expectation is unrealistic and sets teachers up for failure.", "\n\nOver the last 30 years, Newfoundland and Labrador, like other provinces, has moved to an inclusive education model. ", "In principle, this makes sense. ", "Students deserve to be educated with their peers. ", "While some students require specialized support, there are good reasons to include all students in regular classrooms to the greatest degree possible.", "\n\nHowever, problems arise when faulty educational theories are pushed on teachers who have little choice but to comply. ", "The worst, without a doubt, is that teachers should replace structured, whole-class teaching with project-based discovery learning. ", "Even though a wealth of evidence supports traditional teaching techniques, school administrators, provincial officials and education professors often push an ideological agenda against traditional methods.", "\n\nInterestingly, traditional classrooms are exactly what many students with learning disabilities benefit from the most. ", "A structured classroom with desks facing the front, with a clear and focused lesson delivered by a competent teacher, create an excellent environment in which to learn.", "\n\nInstead, however, teachers are told to seat their students in groups, facing each other, and let them learn together at their own pace.", "\n\nThis is a recipe for disaster, particularly in classrooms with students who have behavioural challenges.", "\n\nDifferentiated instruction is a fad often pushed on teachers. ", "Based largely on the work of Carol Ann Tomlinson, an American educator, differentiated instruction tells teachers to adapt their lessons to the learning styles of each student. ", "While this sounds good in theory, it falls apart in practice since it’s impossible for teachers to design multiple effective lessons for each course they teach every day.", "\n\nTeachers end up dividing their classes into groups and trying to give mini-lessons to each small groups, while hoping that the remaining students remain focused enough on their independent assignments to not cause too much distraction. ", "It’s a horrendously inefficient way to teach and creates an impossible workload for teachers. ", "Teachers burn out in short order.", "\n\nTo make matters worse, there’s no empirical evidence that differentiated instruction works.", "\n\nFor example, Bryan Goodwin of Mid-Continent Research for Education and Learning stated in his 2010 report Changing the Odds for Student Success: What Matters Most that there is a “dearth of evidence supporting differentiated instruction” and that “the extent to which teachers differentiate instruction in their classrooms is not a key variable in student success.”", "\n\nUnfortunately, teachers rarely hear about this evidence.", "\n\nOne of the key faults of differentiated instruction is that it’s based on the even faultier notion of individual learning styles. ", "While many teachers accept the gospel that some students are visual learners, some are auditory learnings and others are tactile-kinesthetic learners, there’s not a shred of evidence supporting this theory.", "\n\nProf. John Hattie, director of the Melbourne Education Research Institute at the University of Melbourne, reviewed thousands of studies about student achievement. ", "In his book Visible Learning for Teachers, Hattie bluntly states there’s “zero supporting evidence” for learning styles.", "\n\nThe damage caused by this failed theory is substantial. ", "Instead of providing well-designed whole class lessons, teachers waste hours trying to adapt to the learning styles of each student. ", "As a result, teachers end up working harder, getting worse results and burning themselves out.", "\n\nThings need to change in Newfoundland and Labrador. ", "Instead of forcing teachers to adopt failed theories and foolish fads, teachers should be empowered to use the most effective methods.", "\n\nDumping bad ideas and bad practices would go a long way to improving the effectiveness of teachers in the province.", "\n\nThe views, opinions and positions expressed by all Troy Media columnists and contributors are the author’s alone. ", "They do not inherently or expressly reflect the views, opinions and/or positions of Troy Media.", "\n\n[popup url=”https://www.troymedia.com/submit-your-letter-to-the-editor/” height=”1000″ width=”1000″ scrollbars=”1″]Submit a letter to the editor[/popup]" ]

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[ "Apologies for the downtime during the Climax Set cardlist drops. ", "We have upgraded our servers to avoid this in the future.", "\nAlso, if you are interested in the Bakugan reboot, check out our sister site, Brawler Cafe, and join its discord too.", "\n\nIllusion the Shade\n\nWorlds\n\nCard Type:\n\nAttributes\n\nCard Ability\n\n■ [Set]\n■ All souls of «Shadow Shade» on your field cannot be dropped by your opponent's card effects.", "\n■ At the beginning of your attack phase, choose a «Shadow Shade» monster on your field, and put the top card of your deck into its soul. ", "Then, put up to one soul from the chosen card into your hand." ]

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[ "INTRODUCTION\n============\n\nAge-related macular degeneration (AMD) is a major cause of irreversible blindness in developed and developing countries, particularly in people older than 60 years.^[@R1]--[@R3]^ There are currently several AMD classification schemes that include the terms nonexudative and exudative AMD,^[@R4],[@R5]^ which correlate with visual acuity. ", "Several histological changes can be useful to make the clinical diagnosis, but some of them have different progression characteristic associated with their dissimilar causes and risk factors (genetic and phenotypic). ", "In 2013, the Beckman Initiative for Macular Research Classification Committee provided a consensus recommendation clinical classification system of the AMD phenotype for either clinical or research purposes. ", "The committee was in agreement that the terms wet and dry AMD were problematic because dry can include simple drusen to geographical atrophy (GA) or even old disciform scars formation. ", "Therefore, a new AMD classification was suggested: those with no visible drusen or pigmentary abnormalities are considered to have no signs of AMD; those with drusen \\<63 μm are considered to have normal aging changes; drusens between 63 and 125 μm without pigmentary abnormalities are early AMDs; drusen \\>125 μm or with pigmentary abnormalities associated with at least medium drusen is intermediate AMD, whereas those with neovascular AMD or GA are late AMD. ", "In this new classification, they limited the term dry to GA and did not refer to earlier stages of AMD as dry. ", "The proposed basic clinical classification scale seems to be of value in predicting the AMD risk.^[@R6]^ The choroid requires high blood flow to satisfy the normal metabolic demands of oxygen supply to the outer retina. ", "In nonexudative and exudative AMD patients, an intimate relationship has been identified between retinal pigment epithelial atrophy and choroidal circulation defects, especially of the choriocapillaris.^[@R7],[@R8]^ In AMD, histological evidence of a loss of the choriocapillaris has also been demonstrated.^[@R9]^ Thus, choroidal structural changes seem to be inevitable in AMD pathogenesis. ", "Significant advances of enhanced depth imaging spectral-domain optical coherence tomography (SD-OCT) and recent use of \"en face\" OCT allow a cross-sectional, noninvasive, layer-by-layer visualized reconstructed image of the involved retina and choroid in vivo. ", "Using SD-OCT, studies have shown choroidal changes in different diseases, such as central serous chorioretinopathy (CSCR),^[@R10]--[@R12]^ high myopia,^[@R13]^ and pseudoxanthomaelasticum (PXE).^[@R14]^ Changes in the choroid, in different types of AMD patients, have also been documented,^[@R15]--[@R17]^ suggesting that reduced choroidal thickness may play an indirect role as an indicator of the natural history of AMD. ", "However, the associations between the choriocapillaris changes and pathogenesis of the progression of AMD remain controversial.^[@R18],[@R19]^\n\nIn this study, we investigated a consecutive series of patients with different stages of AMD based on the 2013 consensus of The Beckman Initiative for Macular Research Classification Committee, to elucidate the choroidal microstructural changes.", "\n\nMETHODS\n=======\n\nThis was a single-center, retrospective, cross-sectional case series, performed at the Department of Ophthalmology, Ninth People\\'s Hospital, Shanghai JiaoTong University School of Medicine, between January 14, 2014 and July 15, 2014. ", "Approval was obtained from the Institute\\'s ethics committee, the study was conducted in accordance with the tenets of the Declaration of Helsinki, and patient consent was obtained.^[@R20]^\n\nSubjects\n--------\n\nAll individuals included were \\>55 years old and underwent a comprehensive ophthalmologic examination and routine diagnostic evaluation consisting of best-corrected visual acuity, color fundus photography, fundus fluorescence angiography (FFA), and optical coherence tomography (OCT). ", "Fellow uninvolved eyes of intermediate and late AMD patients have been found to have predictive risk factors for progressive late AMD. ", "Subjects with additional retinal pathologies known to affect choroidal thickness, other than AMD, or with previous intraocular surgeries including cataract surgery, vitrectomy, or having undergone antivascular endothelial growth factor (VEGF) therapy within the previous 3 months, or eyes with histories of ocular diseases, such as glaucoma, ocular inflammation, retinal detachment, refractive errors \\>3.0 diopters, ocular diseases associated with systemic diseases such as diabetic retinopathy, arteriosclerotic retinopathy, and diseases that obstruct the images of the choroid, such as cataract or subfoveal hemorrhage, were excluded. ", "GA patients were excluded because of its different mechanism and treatment from wet AMD. ", "Polypoidal choroidal vasculopathy (PCV) eyes were also excluded because of the different pathophysiological features when compared with general wet AMD.", "\n\nAccording to the consensus made in 2013,^[@R6]^ individuals with no visible drusen and small drusen (\\<63 μm) should be considered without clinically relevant increased risk of late AMD development, so we put these individuals under the category of age-matched normal eyes serving as controls. ", "Furthermore, the fellow eye of individuals who already have late AMD should be estimated separately because the other eye was affected significantly by the status of the fellow eye. ", "Early and intermediate AMDs which have different relevance to risk of disease progression also need to be discussed. ", "We divided the patients into 5 groups after examinations of color fundus photography, OCT, and FFA images. ", "Group 1 (G1) included eyes with no clinically relevant increased risk of late AMD developing; group 2 (G2) included fellow uninvolved eyes of AMD patients; group 3 (G3), as the early AMD eyes, was characterized by early AMD (medium drusen \\>63 μm and ≤125 μm; group 4 (G4), as intermediate AMD, was characterized with large drusen ≥125 μm; and group 5 (G5) included late AMD eyes, characterized by neovascular AMD.^[@R21],[@R22]^\n\nOCT Scanning and Measurement Protocols\n--------------------------------------\n\nThe choroidal images were obtained using the Zeiss Cirrus SD-OCT (Carl Zeiss Meditec, Inc.) with version 4000 software included. ", "All measurements were performed by 2 independent masked trained examiners (LL, SX). ", "Areas of conflict were discussed, and discrepancies were resolved by consultation with a third masked investigator. ", "Subfoveal choroidal thickness (SFCT) was measured on the OCT screen, by using the contained Zeiss Cirrus SD-OCT Eye Explorer software (version 6.5). ", "Thickness was measured vertically from the outer surface of the hyper-reflective line of the (retinal pigment epithelial) RPE/Bruch membrane band to the sclera-choroidal junction. ", "The choroidal area (CA) was defined as the region between the outer RPE and inner scleral borders. ", "Because of the limitations in identifying the choriocapillaris, the choroid was further subdivided into 2 layers. ", "The Haller layer area (HA) was defined as the larger outer oval vascular profile, whereas the Sattler layer area (SA) was defined as a region between the outer RPE/Bruch membrane band and the inner line of the hypointense space, representing HA (Figure [1](#F1){ref-type=\"fig\"}).^[@R23]--[@R25]^\n\n{#F1}\n\nThe CA and SA were analyzed by 2 independent masked investigators (LL, SX), using the unit pixels Image Pro Plus 6.0 software.^[@R25]^ We performed enhanced-depth imaging (EDI)-OCT to improve the visualization of the hyper-reflective line between the HA and the sclera.^[@R26]^ Choroidal en face images were used to reconstruct en face views at 60 μm below the RPE/Bruch membrane, with a depth of 20 μm, where the inner choroid was well visualized in most healthy control eyes.^[@R27]^\n\nVolume scans were calibrated to scan a square, 6 × 6 mm region of the posterior pole. ", "The scan protocol for the macula region was a 512 × 128 raster scan, acquired in approximately 2.5 seconds.", "\n\nStatistical Analysis\n--------------------\n\nStatistics were calculated using SPSS software (IBM SPSS, Version 20.0, IBM Corporation, Armonk, NY). *", "P* \\< 0.05 was considered statistically significant in this study. ", "Continuous variables, such as age or SFCT, were described as mean ± SD. ", "One-way analysis of variance (ANOVA) was used to compare age, choroidal thickness, and the percentage of area of the SA.", "\n\nRESULTS\n=======\n\nSubject Characteristics\n-----------------------\n\nThe 154 eyes of 96 individuals, with a mean age of 67.1 ± 9.2 years (range 55--85 years), were included in this study, among which 32 eyes of 16 individuals were age-matched normal eyes included as controls. ", "Twenty-six eyes of 20 individuals were fellow uninvolved eyes with intermediate/late AMD, 29 eyes of 20 individuals were early AMD, 28 of 18 individuals were intermediate AMD, and 39 of 22 individuals were late AMD. ", "The age differences between the 5 groups showed no significant difference (*F* = 1.12, *P* = 0.35). ", "Among 96 individuals included, 58.3% (56/96) were males and 41.7% (40/96) were females, 51.9% (80/154) were right-sided, and 48.1% (74/154) were left-sided. ", "Fourteen fellow eyes underwent cataract surgeries, 15 eyes had a \\>3.0 diopters refractive error, and 9 eyes with histories of retinal detachment and vitrectomy were excluded (Table [1](#T1){ref-type=\"table\"}).", "\n\n###### \n\nClinical Characteristics of Included Patients\n\n![](", "medi-95-e02967-g002)\n\nChoroidal Findings\n------------------\n\nAll subjects underwent measurement with SFCT, whereas 110 eyes underwent measurements of percentage of SA, among which 32 were in G1, 24 in G2, 28 in G3, and 26 in G4. ", "Measurements of areas of SA in the eyes from the exudative AMD group were not able to be obtained, because the choroidal neovascular vessels (CNVs) showed hyper-reflection, and thus sheltered the signal from the SA and HA.", "\n\nSubfoveal Choroidal Thickness Changes\n-------------------------------------\n\nThe mean SFCT was 295.4 ± 56.8 μm in age-matched normal eyes, 306.7 ± 68.4 μm in fellow uninvolved eyes of AMD patients, 293.8 ± 80.4 μm in early AMD patients, 215.6 ± 66.2 μm in G4, and 200.4 ± 66.6 μm in G5 (*F* = 14.2, *P* \\< 0.001). ", "Though the thicknesses of SFCT measurements decreased from G1 to G3, no significance was found between these 3 groups (G1 vs G2, *P* = 0.55; G1 vs G3, *P* = 0.93; G2 vs G3, *P* = 0.53), or between intermediate AMD and late AMD groups (*P* = 0.93). ", "However, choroidal thicknesses in the early AMD group (G3) were significantly greater than in the intermediate AMD group eyes (G4), and in the late AMD eyes (G5) (*P* \\< 0.001). ", "Representative images are shown in Figure [2](#F2){ref-type=\"fig\"}.", "\n\n{#F2}\n\nPercentage of SA Area Changes\n-----------------------------\n\nThe mean percentage of SA of affected eyes in each group were 47.2% in G1, 45.8% in G2, 47.6% in G3, and 41.1% in G4 (*F* = 5.53, all *P* \\< 0.001). ", "The mean percentage of SA in normal eyes (G1), fellow eyes of AMD patients (G2), and fellow eyes from early AMD patients (G3) were significantly higher than eyes of intermediate AMD patients (G4) (G3 vs G4, *P* \\< 0.001). ", "There was no significant difference between G1, G2, and G3 fellow eyes (G1 vs G2; *P* = 0.15; G2 vs G3, *P* = 0.27; and G1 vs G3, *P* = 0.26, respectively) (Figures [3](#F3){ref-type=\"fig\"} and [4](#F4){ref-type=\"fig\"}). ", "The morphological features of choroidal findings in the 4 groups are summarized in Table [2](#T2){ref-type=\"table\"}.", "\n\n{#F3}\n\n{#F4}\n\n###### \n\nMorphological Features of Choroid in Patients\n\n![](", "medi-95-e02967-g006)\n\nEn Face Enhanced Depth Imaging OCT changes\n------------------------------------------\n\nEn face views were used to analyze the pattern, density, and size of choroidal vessels at 60 μm below the RPE/Bruch membrane band, with a 20 μm depth. ", "Figure [5](#F5){ref-type=\"fig\"} illustrates the choroidal vascular patterns of the 5 groups. ", "The en face image shows the dense distribution of dark regions, with small bright spots between them, in the age-matched normal eye group, representing small to medium-sized vessels and normal vascular network of the SA. ", "Visibility of the vascular density in G2 and G3 was reduced and substituted by more bright spots, due to the hyper-reflection of melanocytes in the SA. ", "The increased bright regions between the vessels, together with the absence of small vessels in the intermediate AMD group, showed thinning of the SA. ", "While in the late AMD group, the SA was almost completely absent, and straight, large lumen vessels of HA were seen, indicating the atrophy of capillaries and medium-sized vessels of the choroid.", "\n\n{#F5}\n\nDISCUSSION\n==========\n\nThe study measured the choroidal thickness and microstructural changes during the progression of AMD, including age-matched normal eyes, fellow uninvolved eyes of late/immediate AMD, and early, intermediate, and late AMD patient eyes, classified according to the consensus for clinical classification of AMD.^[@R28]^ The retina has a high metabolic demand for oxygen supplied by the underlying choroid.^[@R29]^ The blood flow of the choroid decreases during aging, mainly due to a decrease of blood volume, rather than velocity.^[@R30]^ With the development of SD-OCT for assessment of the choroid, the cross-sectional structure and segmentation of subvascular layers can be quantified with good reliability.^[@R31]^ Age-related changes in choroidal thicknesses have been documented in normal eyes and in various macular diseases.^[@R32],[@R33]^ Some studies have confirmed that both the dry and exudative AMD patients had thinner than average choroids, compared with age-matched normal eyes.^[@R34]^ Some studies also reported reduced choroidal thickness in early AMD eyes,^[@R35],[@R36]^ whereas others reported highly variable or no changes of choroidal thickness with early AMD.^[@R16]^ In our study, choroidal thickness was measured using SD-OCT and screening software for images at different stages of AMD, representing the progression of AMD. ", "The SFCT measurements revealed decreases between age-matched normal eyes and early AMD eyes. ", "Although no significant differences were found between these 3 groups, the mean SFCT was significantly thinner in intermediate AMD eyes and late AMD eyes, when compared with eyes before early-stage AMD. ", "These results were in agreement with recent studies,^[@R16],[@R37]^ indicating that the measurements of choroidal thickness, using OCT, might be good diagnostic criteria for AMD.", "\n\nThe SA is made up of medium-sized choroidal vessels, defined as thick, round, or oval-shaped hyper-reflective cores in the mid-choroid, also including the choriocapillaris, which is not easily distinguished from SA on OCT images.^[@R23]^ It was reported that the choroidal blood flow reduction was mediated by the underlying choriocapillaris supplied by SA as a \"feeder vessel\" layer,^[@R38]^ and choroidal thickness decreased during AMD progression, such as in the eyes with subretinal deposits or GA.^[@R39]^ The loss and/or decrease of the choriocapillaris and the medium-sized choroidal blood vessels were shown histologically in AMD patients.^[@R17]^ However, the relevance of SA changes to the pathogenesis of thinning of the choroid in AMD is poorly understood.", "\n\nIn our study, the percentage of SA changes were measured and significant decreases were found in the intermediate and late AMD patients, compared with AMD in early stages, whereas there was no significant difference between age-matched normal eyes, fellow uninvolved eyes of late/immediate AMD, and early AMD eyes. ", "According to the evidence-based investigation in 2013, there was low risk of 5-year progression to late AMD for normal aging changes (0.5%) and early AMD (1.3%), whereas there was a 50% risk for the highest intermediate AMD risk group.^[@R6]^ The results in our study that there is differences between G1∼G3 and G4∼G5 is in line with the rate of progression to advanced AMD.", "\n\nThough the percentage of SA and SFCT showed no significant changes, the microstructure of the choroid, using en face technology, showed reduced vascular density of the SA, and was substituted by bright spots of melanocytes from normal eyes to late AMD eyes. ", "These results suggested that atrophy of the capillaries and medium-sized vessels may enable an earlier diagnosis, and could distinguish the changes in the perfusion of the sublayer blood flow of the choroid during the 5 stages of AMD.", "\n\nThe pathophysiological factors in AMD not only include changes in vascular components of the choroid, but also in lipofuscin accumulation in the RPE/Bruch membrane.^[@R40]^ There are 2 suggested mechanisms of AMD development, based on clinical and histologic studies. ", "One is that the decrease in the ability of the choroid to deliver oxygen to the RPE and retina causes the damage, and the other is that the deposit of retinal tissues leads to choroidal neovascularization, owing to tissue accumulation in the RPE/Bruch membrane, and subsequent interference with the components that maintain the stability of the RPE-choriocapillaris, eventually resulting in choriocapillaris atrophy.^[@R17],[@R41]^ It was showed that with extensive small drusen, pigment abnormalities, there is only a 1.3% probability of progression to advanced AMD by year 5, whereas the 5-year estimated probability of progression to advanced AMD with extensive intermediate drusen, large drusen was 18%.^[@R42]^ The results of this study demonstrated a relationship between the increasing size of drusen and decreasing thickness of the subfoveal choroid. ", "The diffuse deposits of RPE/Bruch membrane, and the reduced density of the SA could eventually cause atrophy of the choroid.", "\n\nLimitations of the study included the relatively small number of patients. ", "Choroidal thicknesses and the dense vascular network of the inner choroidal in all SD-OCT images were evaluated manually, because of the lack of software for automated measurement, using the OCT equipment. ", "Eyes presenting with GA were not included in this study because of the difficulty of patient recruitment. ", "PCV eyes were also excluded because of the different pathophysiological features when compared with general wet AMD. ", "Moreover, though no significant differences were shown in age and refractive errors between the 5 groups, eyes with refractive errors \\>3.0 diopters were excluded, because it was still a potential factor that could have influenced the choroid measurements.", "\n\nIn summary, our study revealed associated choroidal microstructural changes in AMD eyes. ", "SFCT was reduced, mainly due to the reduced percentage of SA during progression of the disease. ", "The microstructural changes in the capillaries and in medium-sized vessels of AMD eyes, when shown in en face images, occurred earlier than what was observed in SFCT. ", "Our study provided a better understanding of AMD progression, using SD-OCT and the en face technology. ", "Further studies are necessary to fully establish our findings as a diagnostic procedure.", "\n\nAbbreviations: AMD = age-related macular degeneration, CA = choroidal area, CNV = choroidal neovascular vessel, CSCR = central serous chorioretinopathy, EDI = enhanced-depth imaging, FFA = fundus fluorescence angiography, GA = geographical atrophy, HA = Haller layer area, OCT = optical coherence tomography, PCV = polypoidal choroidal vasculopathy, PXE = pseudoxanthomaelasticum, SA = Sattler layer area, SD-OCT = spectral-domain optical coherence tomography, SFCT = subfoveal choroidal thickness, VEGF = vascular endothelial growth factor\n\nLinna Lu and Shiqiong Xu contributed equally to this work.", "\n\nAuthors' contributions: Design and conduct of the study---LL, SX; collection and management---LL, FH, YL, YZ, and JW; preparation and review---SX and LL; decision to submit the manuscript for publication---ZW and XF.", "\n\nFunding/financial disclosure(s): This work was supported by the National Natural Science Foundation of China grant (81170876, 31271029, 81320108010) and the Science and Technology Commission of Shanghai (13ZR1423600, 12ZR1417300). ", "This study has no proprietary or commercial interest in any materials discussed. ", "All authors have no financial disclosures relevant to this article.", "\n\nThe authors have no conflicts of interest to disclose.", "\n" ]

{ "pile_set_name": "PubMed Central" }

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[ "Established in 2009, the APHA Breeders’ Futurity program was created to complement the APHA Breeders’ Trust program by increasing opportunities and financial rewards for Breeders’ Trust-nominated foals. ", "The Breeders’ Futurity is a prestigious competition featuring the finest American Paint Horses and exhibitors in the world competing in a select slate of classes designed to showcase the offspring of APHA Breeders’ Trust-subscribed stallions and the mares bred to them.", "\n\nFoals of 2009 were the first crop eligible to compete in the Futurity. ", "The slate of classes in subsequent years grew right along with them; in 2010, yearling halter, longe line and in-hand trail were added and the performance classes began in 2011.", "\n\nCompetition is offered in two divisions:\n\nGold – for the Regular Registry offspring and all SPB offspring regardless of stud fee.", "In these divisions, the mare owner must nominate the mare to the program.", "\n\nPlatinum – A program unto itself, the Platinum division Breeders’ Futurity is an elite weanling halter futurity. ", "Foals are made eligible for this division by the stallion owner, paying a minimum of $5,000 nomination fee and the Mare owner paying a $200 nomination fee (late fees apply). ", "These foals are also eligible to enter the Gold division, provided all requirements, fees and payments are met accordingly.", "\n\n2018 Classes*\n\nPlatinum Non-Pro Weanling Stallions (Regular Registry and the SPB offspring that have been genetically tested and confirmed to carry at least one approved Paint pattern marker)\n\nPlatinum Non-Pro Weanling Mares (Regular Registry and the SPB offspring that have been genetically tested and confirmed to carry at least one approved Paint pattern marker)\n\nPlatinum Non-Pro Weanling Geldings (Regular Registry and the SPB offspring that have been genetically tested and confirmed to carry at least one approved Paint pattern marker)\n\nPlatinum Non-Pro Weanling Solid Paint-Bred Stallions & Geldings (SPB’s that have not been genetically tested or do not carry at least one approved Paint pattern marker)\n\nPlatinum Non-Pro Weanling Solid Paint-Bred Mares (SPB’s that have not been genetically tested or do not carry at least one approved Paint pattern marker)\n\n*APHA reserves the right to add, cancel or combine classes or hold a “class within a class” as entries warrant.", "\n\nOnce the foals are made eligible, the appropriate Futurity payments must be made for the year(s) the foal is shown only. ", "No futurity payments are made in a year the horse is not shown in Breeders’ Futurity classes at the APHA World Championship Show." ]

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[ "Q:\n\nUsing Mixed mode authentication to authenticate Active Directory users to an application\n\nI have a vendor supplied application that I have very limited access to change. ", " The application controls a machine, and cannot easily be logged off between users (expect up to 5 user changes per hour). ", " I also have to deal with Part 11, and Corporate rules.", "\nThe plan is to have a shared login to the PC (AD user), then the application which has to connect to a MS SQL database anyways, will prompt for the user name and password, which it will use for the database connection. ", " (previous user's DB connection will be closed between users). ", " If the user/password does not authenticate, they will not be able to use the application.", "\nI have AD authentication working, and I can connect with Server Management Studio using either a SQL user, or an AD user. ", " The application can also connect using a SQL user. ", " But the application always fails to connect when I attempt to use an AD user (I am only substituting the user/password, I have also tried to prepend the \"Domain\\\" to the user). ", " The application is using the default MS SQL drivers that are loaded when Server Management Studio is installed.", "\nIs this even workable?", "\n\nA:\n\nHaving an application connect would be very different than an end user on SSMS. ", " Applications tend to use connection strings. ", " Your applications connection string or config might need to be modified to connect to the SQL Server as an AD user as opposed to putting in a username/password for a SQL user. ", " \nYou will want that user to have the same rights as the SQL User and probably want it to own the database. ", " Contacting the vendor might be a good case. ", " Going with AD users gives you more auditing visibility anyways which should please auditors.", "\nSome connection string examples:\nhttps://www.connectionstrings.com/sql-server-2012/\n\n" ]

{ "pile_set_name": "StackExchange" }

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[ "Q:\n\nUnityScript error in Visual Studio\n\nSo I´ve been working with unity this days for school and I have the coding for a spaceship to move only in certain space with the variables hori and vert like this: \nvar vert: float = 0\n\nand\nvar hori: float = 0\n\nbut the program tells me its a semicolon instead of the colon i dont know why and also i use && and it says syntax error... someone please help me\n\nA:\n\nThe problem with the && is improper parenthesis. ", "You have:\nif(Input.", "GetKey(KeyCode.", "UpArrow)) && vert < 3) {\n\nand I think it should be something like:\nif(Input.", "GetKey(KeyCode.", "UpArrow) && vert < 3) {\n\n" ]

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[ "Low molecular weight, sequence based, collagenase inhibitors selectively block the interaction between collagenase and TIMP (tissue inhibitor of metalloproteinases).", "\nSequence-based inhibitors of collagenase bearing an hydroxamate group capable of chelating the active site zinc atom were synthesized and tested. ", "The effect of one of these molecules (RP 59794; Ki about 10(-8) M) on the formation of the TIMP: collagenase complex was also tested. ", "RP 59794 blocks complex formation and can partially dissociate established TIMP: collagenase complexes. ", "It exhibits the same stereospecificity in this activity as in its inhibition of collagenase suggesting that TIMP and RP 59794 both interact with the active site region of collagenase." ]

{ "pile_set_name": "PubMed Abstracts" }

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[ "Q:\n\nOrder of evaluation of if statement in Python\n\nSo I thought I found a typo in code I was working on. ", "I thought 'not' would operate on string \"eta\" and make it False and False is not in the List,so nothing should print - however in both the below case \"Eta not found\" is printed. ", "I guess this has something to do with order of evaluation that both statements are equal, right?", "\nif not \"eta\" in [\"alpha\", \"beta\", \"gamma\"]:\n print (\"Eta not found\")\n\nif \"eta\" not in [\"alpha\", \"beta\", \"gamma\"]:\n print (\"Eta not found\")\n\nA:\n\nThe result is the same in both cases because slightly different syntax for the same statement should result in equal results, right? ", "And\nif not \"eta\" in [\"alpha\", \"beta\", \"gamma\"]:\nis the same as:\nif not (\"eta\" in [\"alpha\", \"beta\", \"gamma\"]):\nwhich is equivalent to:\nif (\"eta\" not in [\"alpha\", \"beta\", \"gamma\"]):\n\nA:\n\nin has a higher precedence than not, so not x in a means not (x in a). ", "Keep in mind two things though.", "\n\nnot in is a new operator by itself, not just a conjuction of not and in. ", "Actually, it couldn't be: the not operator has to be followed by an expression, not by another operator.", "\nthe python interpreter seems to convert not x in a to x not in a\n\n" ]

{ "pile_set_name": "StackExchange" }

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[ "In a rare touch of humour in the dour world of Spanish politics, the anti-austerity party Podemos has published its manifesto in the style of the Ikea catalogue.", "\n\nAs in the Swedish furniture catalogue, the manifesto is organised on a room-by-room basis, with candidates pictured at home in the kitchen, on the sofa, in the garden or working at their desks looking homely and approachable.", "\n\n\n\nThe party leader, Pablo Iglesias, is featured looking pensive on his balcony, working at a table in a sparsely furnished room and watering a solitary ivy plant. ", "His second-in-command, Íñigo Errejón, is pictured busy with documents and relaxing with a book.", "\n\nThe cover of the Podemos manifesto. ", "Photograph: Podemos\n\nWhere possible, the photos correspond with policies. ", "So the policy on social land use is illustrated by party organiser, Pablo Echenique, sitting among pot plants on his terrace.", "\n\nOther party members are depicted feeding their fish, hanging out washing, making the bed and brushing their teeth.", "\n\nThe photographs serve as a reminder of how young Podemos members are. ", "There is little evidence of either children or grey hair.", "\n\nThe party chose the format because “we want it be the most-read manifesto ever produced” said Podemos co-founder Carolina Bescansa at its launch. ", "The manifesto, which includes a detailed breakdown of policies at the end, is available in paper form for €1.80 (£1.40) including postage.", "\n\nThe policies – easier to follow than the instructions inside an Ikea flat pack – boil down to higher taxes at the top end of the scale and more public spending on health and education.", "\n\nPablo Iglesias waters a solitary plant while the manifesto promises an end to austerity. ", "Photograph: Podemos\n\nThe party pledges to bring unemployment down to 11% by the end of the next parliament. ", "Unemployment is currently at 21%, with 4.8 million out of work. ", "Podemos plans to raise taxes on incomes above €60,000, rising to 55% on incomes over €300,000.", "\n\nCorporation tax will go up and there will be a tax on wealth and inheritance. ", "Public spending is to increase by €15bn in each of the next four years and there will be some cuts to the military budget.", "\n\nPodemos’s policies include an increase in the minimum wage. ", "Photograph: Podemos\n\nSpain returns to the polls on 26 June after elections last December failed to produce a clear winner and the parties were unable to agree on a formula for coalition government. ", "Polls show the Unidos Podemos joint slate running second, having overtaken the mainstream PSOE socialist party.", "\n\nThe ruling conservative People’s party continues to lead but is predicted to fall well short of the 176 seats needed for a majority.", "\n\n" ]

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[ "Benchmark: So You're Ready to Go Public?", "\n\nA recent survey of 386 fast-growing companies found that although one in 5 hoped to go public within three to five years, many had not taken the vital steps that pave the way for a successful public offering.", "\n\nPercentage of companies surveyed that had failed to -- document the fair value of recent stock options awarded to investors or employees 53%" ]

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[ "The Climb (song)\n\n\"The Climb\" is a song performed by American singer Miley Cyrus, for the 2009 film Hannah Montana: The Movie. ", "The song was written by Jessi Alexander and Jon Mabe, and produced by John Shanks. ", "It was released on March 5, 2009, as the lead single of the film's soundtrack by Walt Disney Records, and is also included as a bonus track on the international release of The Time of Our Lives. ", "The song is a power ballad with lyrics that describe life as a difficult but rewarding journey. ", "It is styled as a country pop ballad, and was Cyrus' first solo song to be released to country radio. ", "The instrumentation includes piano, guitar, and violins.", "\n\nThe song received a nomination for the Best Song Written for a Motion Picture, Television, or Other Visual Media at the 52nd Annual Grammy Awards. ", "However, the song was withdrawn from consideration by Walt Disney Records because it had not been written specifically for a movie as the category's eligibility rules required. ", "The song became a top-10 single on charts in Australia, Canada, Norway, and the United States. ", "In the United States, it peaked at number four on the Billboard Hot 100 and became the eighth-best selling digital single of 2009. ", "Five months after its release, the single was certified triple platinum by the Recording Industry Association of America.", "\n\nThe song's accompanying music video was directed by Matthew Rolston, and depicts scenes of Cyrus climbing a mountain or singing, intercut with clips of Hannah Montana: The Movie. ", "Cyrus promoted the song with several live performances. ", "Cyrus performed the song as the closing number of her Wonder World Tour. ", "The song was also performed during the Gypsy Heart Tour. \"", "The Climb\" has been covered by several artists and was the most popular choice of song among auditioners for the ninth season of the American singing contest, American Idol, with Hollie Cavanagh performing it in the top six of the 11th season. ", "Simon Cowell, creator of the British television talent show The X Factor, chose \"The Climb\" to be the debut single of the winner of the competition's sixth series. ", "Winner Joe McElderry's cover, released on December 14, 2009 by Syco Music, was produced by Quiz & Larossi and topped the Irish Singles Chart and the UK Singles Chart.", "\n\nBefore its official release, the song was premiered at Kids Inaugural: \"We Are the Future\" event on January 19, 2009.", "\n\nBackground \n\"The Climb\" was not intentionally written for the 2009 musical film Hannah Montana: The Movie. ", "Co-writer Jessi Alexander conceived the song's melody while driving to the home of songwriting partner Jon Mabe. ", "Once she arrived, Mabe and she developed a song about overcoming life's obstacles inspired by their personal struggles in the music industry. ", "Alexander referred to the process as a form of \"therapy\" and recalled, \nThe song they created was titled \"It's the Climb\" and was written in the third person. ", "Alexander described the original song as \"more spiritual\" than the version that was released, and said it contained lines about prayer. ", "However, she claimed she knew it was pop and suitable for the Walt Disney Company.", "\n\nBefore reaching Cyrus, the song had been rejected by several country artists. ", "It was eventually picked up by Peter Chelsom, director of Hannah Montana: The Movie, who gave it to Cyrus to record for the film. ", "Chelsom found what would become \"The Climb\" while visiting Nashville, Tennessee, during a quest to find 11 new songs for the movie. ", "After hearing Alexander's music, Chelsom asked her to submit songs for consideration. ", "Alexander recorded \"It's the Climb\" on a CD and gave it to him. ", "Several weeks later, Chelsom called to say, \"the song was gonna be an integral part of the movie\". ", "However, he wanted Mabe and Alexander to rework some of the song's content and to change the song from third person to first person. ", "Alexander felt the changes amounted to a \"substantial amount of the song\" and commented, \"For me, when you change something from third person to first person, it can change the whole meaning of a line.\" ", " Mabe and she \"wrestl[ed] over taking words out\" and how much they could change while maintaining the song's integrity. ", "After a number of drafts, Mabe and Alexander finally created a version they felt was \"perfect for the movie\".", "\n\nUpon receiving the final draft, filmmakers told the songwriters, \"This is perfect for Miley, it’s gonna change her life, gonna change your life.\" ", "Chelsom commented that the song \"turned up\" the film's music level by tapping into Cyrus's newfound vocal range. ", "As with the other songs featured in Hannah Montana: The Movie, the song is \"tightly woven into the fabric of the story and the characters\". ", "In the film, Cyrus plays Miley Stewart, a character with a secret double life as superstar Hannah Montana. ", "Keeping this secret causes trouble between Miley and many of the other characters in the film, and leaves Miley confused and contrite. ", "She expresses her emotions by writing \"The Climb\". ", "According to film producer Alfred Gough, \"The song is her journey, the lessons she's learned in the movie. ", "It's an epic [...] power ballad that encapsulates Miley's journey and the message of the film.\"", "\n\n\"The Climb\" was chosen as the lead single from the soundtrack due to its country elements, which introduced Cyrus to listeners beyond her usual pop audience. ", "The song is Cyrus's first solo effort marketed directly to country radio, though she had previously recorded and released a country duet with her father, Billy Ray Cyrus, which was titled \"Ready, Set, Don't Go\", in 2007. ", "Warren Truitt of About.com referred to the song as \"Miley's serious attempt to break into the contemporary country world.\" ", "In October 2009, it was re-released to countries outside the United States in the international version of Cyrus' extended play, The Time of Our Lives.", "\n\nComposition \n\n\"The Climb\" is a country pop power ballad that incorporates soft rock and pop rock styles and lasts 3 minutes and 55 seconds. ", "However, at two minutes and forty-five seconds, a \"sudden, spiky burst of violins\" enters the song, and the song switches to full power. ", "Todd Martens, co-editor of the Los Angeles Times music column, says Cyrus uses \"a raspy voice [that] brings a bit of country grit\" to the song. \"", "The Climb\" is set in common time at a moderate tempo of 80 beats per minute. ", "The song is sung in the key of E major and Cyrus's vocals span one and a half octaves, from E3 to C#5. ", "The song uses a standard-issue ballad arrangement with the chord progression, E5—Asus2—F♯7sus.", "\n\nAccording to music reviewer Fraser McAlpine of the BBC, the song's lyrics assert that life should be viewed as \"a journey which is difficult but rewarding\". ", "Both Martens and McAlpine took special interest in the line \"It's always gonna be an uphill battle/Sometimes I'm gonna have to lose\". ", "Martens interpreted the line as an acknowledgment by the singer of her own mistakes in life, while McAlpine wrote, \"In this song which is about plugging away at things, the writers have slipped in [...] that the occasional setback isn't the end of the world.\"", "\n\nCritical reception \n\nCritical reception for the song was generally positive. ", "Fraser McAlpine of the BBC felt the song's lyrics were generic, but complimented Cyrus vocals: \"Miley acquits herself well vocally — there are moments where her voice sounds a tad strained, but it's good to hear her on a track that's a little more subdued and with less frantic production than the uptempo, sassy pop songs we're used to.\" ", "Michael Menachem of Billboard magazine called the song \"one of the year's strongest ballads\". ", "Wesley Morris of The Boston Globe praised \"The Climb\" for being a \"pretty liberation anthem\". ", "Leah Greenblatt of Entertainment Weekly said, \"On tunes like [...] 'The Climb', the 16-year-old Tennessee native turns up her homegrown inflections, but a few elongated r's won't exactly shut out her huge pop audience.\" ", "Todd Martens of The Los Angeles Times believed that \"The Climb\" was \"buried in cheese\" and described it as \"pre-Valentine's Day gooeyness\". ", "However, Martens said, \"'The Climb' is the rare Miley ballad that's on par with some of her more spunky teen pop.\"", "\n\nHeather Phares of Allmusic said, \"the best songs that Cyrus sings on the soundtrack have her own name on them\". ", "She also made musical comparisons to Shania Twain and described the song as \"natural, [...] down to earth and grown-up\". ", "While reviewing The Time of Our Lives, Michael Hann of The Guardian called \"The Climb\" a \"one rather superior ballad\", compared to \"When I Look at You\" and \"Obsessed\". ", "Hann said the song was added to the extended play to \"add some ballast since this collection's US release.\" ", "Jon Caraminica of The New York Times described \"The Climb\" as an \"appealing new single [that] is just the sort of demure, inspirational country-rock that could easily be mistaken for self-reckoning.\" ", "While reviewing a concert performance, James Reed of The Boston Globe called the song \"bland but inspirational fare\".", "\n\nAwards and nominations \n\"The Climb\" won \"Best Song from a Movie\" at the 2009 MTV Movie Awards and \"Music Choice: Single\" at the 2009 Teen Choice Awards. ", "At the 52nd Grammy Awards, \"The Climb\" received a nomination for the Best Song Written for a Motion Picture, Television or Other Visual Media, a songwriter's award. ", "However, Walt Disney Records withdrew the song from consideration because the song was not \"written specifically for a motion picture, television or other visual media\", as the Grammy eligibility rules dictated. ", "According to Rolling Stone, \"The Climb\" was submitted for consideration by mistake. ", "The National Academy of Recording Arts and Sciences (NARAS), the presenters of the Grammy Awards, released a statement stating, \"Walt Disney Records was proactive and forthcoming to our awards department and verified that the song was not written specifically for the film Hannah Montana: The Movie. ", "Based on this information, the Academy has complied with the label's request.\" ", "NARAS replaced the nomination with the song with the next highest initial vote count, \"All is Love\", which was written by Karen O and Nick Zinner for the film Where the Wild Things Are. ", "Dan Milliken of Country Universe gave the song a D+. ", "His review consisted solely of two motivational posters: one reading \"Life: Its not about the destination, but the journey\" to describe the song's content, and a mock poster reading \"Success: Everything is easy when you're cute\" for his actual review. ", "He later expanded his review, calling it \"a soulless rephrasing of an extremely famous philosophical message (so famous it borders on cliche) that doesn’t provide an emotionally coherent context or justification\". ", "Milliken gave the song a higher grade because \"she’s a pretty good singer for someone her age\".", "\n\nCommercial performance \n\nOn the week ending March 7, 2009, \"The Climb\" debuted at number 48 on Billboards Hot Country Songs. ", "It was, incidentally, the same week that \"Back to Tennessee\", by Cyrus's father, Billy Ray Cyrus, debuted at number 59, the first time a father and daughter had separate charting songs on the chart since Johnny and Rosanne Cash charted in 1990 with \"Silver Stallion\" and \"One Step Over the Line\", respectively. \"", "The Climb\" eventually peaked at number 25 on the country-genre chart. ", "For the week ending March 21, 2009, the song debuted at number six on the Billboard Hot 100 due to sales of 166,000 digital downloads, thus making \"The Climb\" Cyrus's highest-charting effort at the time, surpassing her previous best-charting effort \"7 Things\", which peaked at number nine in July 2008. ", "For the week ending May 2, 2009, the song reached its peak at number four on the Hot 100. \"", "The Climb\" also peaked at number seven on the Pop 100 chart, 42 on Hot Christian Songs, and at number one for 15 consecutive weeks on Hot Adult Contemporary Tracks. ", "Cyrus became the youngest artist to top Adult Contemporary since LeAnn Rimes entered the chart in 1997 with \"How Do I Live\". ", "According to Billboard, \"The Climb\" was the eighth best selling digital single of 2009. ", "The single was certified triple platinum by the Recording Industry Association of America (RIAA) for the sales of over two million copies. ", "As of January 2014, \"The Climb\" has sold 3,709,000 copies in the United States. ", "In Canada, \"The Climb\" entered at number 17 and eventually peaked at number five. ", "The single was certified triple platinum by Music Canada for the sales of 240,000 digital downloads.", "\n\n\"The Climb\" was also a success in Australia and New Zealand. ", "The song made its debut on the Australian Singles Chart at number 46 on April 19, 2009. ", "After 10 weeks on the chart, \"The Climb\" reached number five on the chart, where it stayed for two consecutive weeks. \"", "The Climb\" was placed at number 84 on the decade-end Australian Singles Chart. ", "The song has been certified platinum by the Australian Recording Industry Association for sales above 70,000. \"", "The Climb\" debuted in the New Zealand Singles Chart at number 25 on April 13, 2009, and reached its peak at number 12 on June 15, 2009. ", "On September 4, 2009, it was certified gold by the Recording Industry Association of New Zealand for sales exceeding 7,500 copies.", "\n\nIn the UK Singles Chart, \"The Climb\" made its entry at number 82 on March 28, 2009, and reached its peak at number 11 on June 16, 2009. ", "With its peak at number 11, it tied for Cyrus's best-charting effort on the chart with \"See You Again\" from October 2008. ", "The single was certified silver by the British Phonographic Industry (BPI) for the shipment of over 200,000 copies. ", "In Ireland, the song also peaked at number 11. ", "In mainland Europe, the song peaked at number 23 on Eurochart Hot 100 Singles, number 11 on Belgian Tip Singles Chart (Flanders), and number five on Norwegian Singles Chart. ", "The song experienced similar commercial outcomes throughout the rest of Europe; it appeared within the top 30 of charts in Austria, Belgium (Wallonia), and France.", "\n\n Music video \n\nMatthew Rolston directed the music video for \"The Climb\", which premiered on Cyrus's Myspace page on February 11, 2009. ", "The video commences with a shot of Cyrus holding a guitar and a suitcase as she begins to walk down a long path extending through a valley. ", "At the end of the valley, the sun breaks out over a distant mountain. ", "The entire scene is enhanced with computer-generated imagery. ", "Cyrus has her hair tied in a bun and wears a traveling jacket, a gray tank top, and cowboy boots. ", "In a separate setting, Cyrus, wearing a gray short-sleeved shirt and her hair loose, begins to sing \"The Climb\" beneath a blue spotlight in a purple room. ", "The two settings alternate throughout the video. ", "A vignetted scene from Hannah Montana: The Movie appears in front of Cyrus as she walks on the path. ", "The video zooms into the scene and a montage of film clips plays, featuring Cyrus's character and her love interest, Travis Brody (played by Lucas Till) horseback riding. ", "The video returns to Cyrus walking; she picks up a rose fallen on the path, then throws it behind her. ", "As the video progresses, she also sees things such as a herd of horses and a shooting star cross her path. ", "A new setting enters the video in which Cyrus dances in a purple room with a countdown, or occasionally, film clips projected on the wall behind her. ", "Rain begins to pour in the path setting. ", "Cyrus puts down her jacket, guitar case, suitcase, and boots, and continues onwards with only her guitar strapped to her shoulder. ", "More film clip montages play in the same manner as the first. ", "As the last montage ends, Cyrus finally reaches the summit of a reddish, CGI mountain and triumphantly looks over the cliff's edge to watch the sun shining over a shimmering lake. ", "An alternate version of the music video excluding the Hannah Montana: The Movie clips exists and was sent to several channels, including VH1.", "\n\nTodd Martens of the Los Angeles Times wrote that while he enjoyed the song, he was unsure about the video. ", "He commented that while the video was an improvement since Cyrus's video for \"7 Things\" (2008), the settings in \"The Climb\" music video looked as though they had been painted by Thomas Kinkade and Cyrus's dancing appeared off-beat. ", "Travis of MTV described the video as \"beautifully shot (although heavily digitized)\". ", "Lyndsey Parker of Yahoo! ", "Music remarked that the summit setting was similar to that of the music video for Britney Spears' \"I'm Not a Girl, Not Yet a Woman\". ", "Parker also felt the scene in which Cyrus looks out over the cliff, shot using large sweeps with an aerial camera, had been \"lifted straight out of an '80s Bon Jovi video\". ", "In 2009, the video received a MuchMusic Video nomination for Best International Artist Video, but lost to Lady Gaga's music video for \"Poker Face\".", "\n\n Live performances \n\nCyrus opened the Kids' Inaugural: \"We Are the Future\" event with the premiere of \"The Climb\". ", "The event was held on January 19, 2009, in Washington DC, at the Verizon Center to celebrate the inauguration of Barack Obama as President of the United States. ", "Cyrus, dressed in an embroidered red ball gown made by Reem Acra, dedicated the song to Obama's daughters, Sasha and Malia Obama. ", "Following the song's official release in March 2009, Cyrus resumed promotion for \"The Climb\", performing live for shows including American Idol, The Tonight Show with Jay Leno, the 44th annual Academy of Country Music Awards, Good Morning America, and Live with Regis and Kelly throughout April. ", "On April 13, Cyrus performed \"The Climb\" as part of her set for the Sessions@AOL. ", "On April 24, Cyrus sang \"The Climb\" and other songs in a London Apple Store. ", "The performances were recorded and sold exclusively by the United Kingdom iTunes Store as a live extended play titled iTunes Live from London. ", "On June 7, 2009, Cyrus performed the song at the 20th annual A Time for Heroes Celebrity Carnival, an outdoor carnival supporting the Elizabeth Glaser Pediatric AIDS Foundation. ", "Cyrus also sang \"The Climb\" on The Today Show on August 28 and at the first D23 Expo on September 11, 2009.", "\n\nTo promote the Hannah Montana: The Movie soundtrack, Cyrus performed \"The Climb\" on a six-day, five-city acoustic radio promotional tour that reached over 250 radio shows. ", "The song was also used as the closing number of Cyrus' 2009 Wonder World Tour, her first world tour. ", "During the tour performances, Cyrus performed in a white tank top and shorts, boots, and a metallic vest, while giant overhead video screens displayed sunsets. ", "After finishing, Cyrus exited through a passageway in the stage while the images of shooting stars and the earth in space appeared on the screen. ", "Melinda M. Thompson of the Oregonian described the performance as \"really a moment to remember — Miley's soulful and touching rendition of 'The Climb'\", while Jim Harrington of The Oakland Tribune said the performance was a \"tender closer\" that drew a large response at the September 18 concert in Oakland, California, at the Oracle Arena. ", "Cyrus later performed the song at the Rock in Rio concert in Lisbon, Portugal and the London, England nightclubs Heaven and G-A-Y.\n\nCyrus performed the song during the Gypsy Heart Tour. ", "She also performed this song on CNN Heroes on December 11, 2011. ", "Six years later, in 2017, she performed the song on The Tonight Show Starring Jimmy Fallon, followed by an acoustic version on The Howard Stern Show, and on March 24, 2018, Cyrus performed it before a massive outdoor crowd protesting gun violence at the March For Our Lives in Washington, DC.", "\n\nRelease history\n\n Charts and certifications \n\n Weekly charts \n\n Certifications \n\n Year-end charts \n\nDecade-end charts\n\n Cover versions \n\"The Climb\" has been covered several times. ", "Mirror Image Records' indie rock group HelenaMaria covered the song and released it as a digital single in March 2009. ", "At auditions for the ninth season of the television singing competition American Idol, \"The Climb\" was the most popular choice of song amongst contestants. ", "Alan Cumming covered the song in his cabaret tour and included it on the audio CD Alan Cumming Sings Sappy Songs: Live at the Cafe Carlyle. ", "Australian Judah Kelly covered the song on his debut album, Count On Me (2017).", "\n\n Joe McElderry version \n\n Background and composition \nIn the same year of \"The Climb's\" original release, British executive Simon Cowell chose for Joe McElderry, Olly Murs, and Stacey Solomon, the three finalists of the sixth series of the British television talent contest The X Factor, to record the song in preparation for a single release as soon as the winner was announced. ", "After Solomon's elimination, Murs and McElderry sang the song on December 13, 2009, as their final performance in the competition. ", "Upon winning the competition, McElderry's version of \"The Climb\", produced by Quiz & Larossi, was released on December 14, 2009 by Syco Music as the first single from his debut studio album Wide Awake (2010).", "\n\nMcElderry said that the lyrics to \"The Climb\" meant a lot to him: \"It's an emotional song because it's what's been happening in the last few months. ", "It all feels very, very surreal.\" ", "According to Peter Robinson of The Guardian, the cover has a \"plinky\" piano in its introduction. ", "In regards to lyrics, Robinson interpreted, \"lines about 'uphill battles' and 'having to lose' do seem to talk of Joe's probable future.\"", "\n\n Reception \nPeter Robinson of The Guardian described \"The Climb\" as a \"controversially uncontroversial choice\" for a cover and continued, \"While 'The Climb' might be a suitable choice for a winner's single, the fact that it's a cover of such a recent song means that it's still slightly odd.\"", "\n\nOn the week ending 26 December 2009, \"The Climb\" debuted at number two on the UK Singles Chart; its debut position was influenced by a campaign composed of Facebook group members, aimed at getting Rage Against the Machine's 1992 single \"Killing in the Name\" to the top position during Christmas week. ", "In the following week, the song reached number one, becoming the final number one of the 2000s decade, where it maintained for a week. ", "The single was certified Platinum by the British Phonographic Industry (BPI) for shipments exceeding 600,000 copies. ", "The song has sold 810,000 copies in the UK as of January 2015.", "\n\n\"The Climb\" debuted at number one on the Irish Singles Chart on the week ending December 17, 2009, where it maintained in the top position for four consecutive weeks. ", "In mainland Europe, the song charted in the Eurochart Hot 100 Singles at number four on the week ending January 9, 2010.", "\n\n Music video \n\nThe video was shot on 16 December 2009, in London, England. ", "The video begins with footage from The X Factor and then transitions to a close-up shot of McElderry in the main setting, a flooded cityscape — the scene was shot in a flooded set with a cityscape backdrop.", "> McElderry is clothed by a grey vest and a grey shirt, as he stands in the setting and performs. ", "Throughout the entire video, scenes alternate between the flooded cityscape setting and recycled footage from The X Factor, which are in black and white until it shows him in the live shows in colour. ", "The video concludes with McElderry being informed he won the competition, hugging his peers.", "\n\n Track listings \n Digital download \"The Climb\" – 3:36\n\n CD single'\n \"The Climb\" – 3:36\n \"Somebody to Love\" – 2:38\n \"Don't Let the Sun Go Down on Me\" – 2:27\n\nCharts and certifications\n\nWeekly charts\n\nYear-end charts\n\nCertifications\n\nSee also\nList of number-one adult contemporary singles of 2009 (U.S.)\nList of number-one singles of 2009 (Ireland)\nList of UK Singles Chart number ones of the 2000s\n\nReferences\n\nExternal links \n\n \n\nCategory:2009 singles\nCategory:Billboard Adult Contemporary number-one singles\nCategory:Country ballads\nCategory:Number-one singles in Scotland\nCategory:UK Singles Chart number-one singles\nCategory:Irish Singles Chart number-one singles\nCategory:Miley Cyrus songs\nCategory:Music videos directed by Matthew Rolston\nCategory:Joe McElderry songs\nCategory:Pop ballads\nCategory:2000s ballads\nCategory:Song recordings produced by John Shanks\nCategory:Songs written by Jessi Alexander\nCategory:Songs written for films\nCategory:The X Factor (British TV series)\nCategory:Walt Disney Records singles\nCategory:Hollywood Records singles\nCategory:Syco Music singles\nCategory:2009 songs\nCategory:Debut singles" ]

{ "pile_set_name": "Wikipedia (en)" }

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[ "Indigenous All Stars (rugby league)\n\nThe Indigenous Australian rugby league team (also known as the Indigenous All Stars or Indigenous Dreamtime team) is a rugby league football team that represents Aboriginal Australians and Torres Strait Islanders. ", " The team was first formed in 1973 and currently plays in an annual All Stars Match against a National Rugby League NRL All Stars team.", "\n\nHistory\nAn Aboriginal v White Australian rugby league game was held in Barcaldine in Western Queensland in 1963. ", "These 'Blacks v Whites' games continued annually until 1984.", "\n\nThe first Australian Aboriginal rugby league team was assembled in 1973 The Aboriginal team managed to win seven of its nine matches in just 10 days, The team consisted of 34 players – 19 from NSW, 13 from Queensland and two from the Northern Territory. ", "They went on to win games against Kiwi premiers Wellington Petone, the only all-Maori team & Auckland club & Te Atatu, which the Aboriginal side won 17–13.", "\n\nThe side competed in the Pacific Cup in 1990, 1992 and 1994. ", " During this period the team contained New South Wales Rugby League first grade players such as Ricky Walford, Graham Lyons, Ron Gibbs, Darrell Trindall, Paul Davis, Wayne Alberts, George Longbottom and Will Robinson.", "\n\nIn the post-1999 NRL season an Aboriginal side managed by Arthur Beetson defeated the Papua New Guinea Kumuls and the future rugby league Immortal was pushing for an Australia Day match against the Australian national team.", "\n\nIn 2008 World Cup curtain raiser to the Australia vs. New Zealand match included an Indigenous Australian squad playing against New Zealand Māori which featured several prominent NRL players and rising stars, including Chris Sandow, Wairangi Koopu, Preston Campbell, Sam Thaiday, Shaun Kenny-Dowall and Carl Webb.", "\n\nPreston Campbell, a highly respected aboriginal rugby league player, was a driving force behind the setup, in 2010, of a curtain raising match between the Indigenous All Stars, and the NRL All Stars. ", "The Indigenous All Stars played what seems likely become an annual match against the National Rugby League All Stars on 13 February 2010. ", "The squad was chosen in part by public vote. ", "Aboriginal NRL player Sid Domic's artistic ability led him to be selected from a field of six artists to design the Indigenous side's jersey, as well as Johnathan Thurston's and Jamie Soward's custom headgear, for the annual All Stars matches.", "\n\n2019 will see a new format of the Australian Indigenous All-Stars play the New Zealand Māori at AAMI Park in Melbourne on 15 February. ", "It will be part of an All-Stars double header with the women's teams to play the curtain-raiser Māori and indigenous teams to the men's game. ", "With no All-Stars game in 2017 due to the World Cup, the NRL will be hoping the inclusion of the New Zealand Māori side will spark popularity in the fixture. ", "With three Indigenous players also eligible for both teams Dane Gagai, Reimis Smith, Josh Hoffman and Javid Bowen.", "\n\nTeams\n\nFirst Australian Aboriginal Rugby League Team 1973 Tour\n William Widders\n Tom Briggs\n Marshall Brown\n Kenneth Brown\n Max Edwards\n Wally Tallis\n Phil Hall\n John Brady\n Carl Wyles\n\n1990-92-1994 Australian Aboriginies Pacific Cup Team\n Ricky Walford \n Paul Davis \n George Longbottom \n Will Robinson \n Wayne Alberts \n Darrell Trindall\n Ron Gibbs \n Graham Lyons\n Jason Wilson (Walgett Rugby League)\n\n2008 Indigenous Team of the Century (1908–2007)\n\n2008 Indigenous Dreamtime\n\n2010 Indigenous All Stars\n\n2011 Indigenous All Stars\n\n2012 Indigenous All Stars\n\n2013 Indigenous All Stars\n\n2014 Festival of Indigenous Rugby League\nThe NRL launched a Festival of Indigenous Rugby League program to take the place of the prestigious pre-season Rugby League All Stars game following every World Cup year. ", "The 2014 Festival of Indigenous Rugby League featured a trial match between the Knights and a non-elite Indigenous team, drawn from the immensely popular NSW Koori Rugby League Knockout and Murri Carnivals in Queensland, as well as the NRL Indigenous Player Cultural Camp, Murri vs Koori women's and Under 16s representative games, a Murri v Koori match, a jobs expo and community visits.", "\n\n2015 Indigenous All Stars\n\n2016 Indigenous All Stars\n\nIndigenous Team of the Decade (2010–2019)\n\nResults\n\nSee also\n\n Australian national rugby league team\n List of Indigenous All Stars players\n\nReferences\n\nExternal links\n rleague.com\n\n \nCategory:Rugby league representative teams in Australia" ]

{ "pile_set_name": "Wikipedia (en)" }

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[ "The pneumatic tires currently used on automobiles and trucks have stiff, inelastic beads that are not readily forced over a wheel rim during installation or removal. ", "In consequence, tires are usually changed using large, power operated changers. ", "There is a need, however, for a small portable changer that can be carried in a vehicle as part of a repair kit. ", "Such a device would be very useful in situations where there was little or no access to a fully equipped repair shop. ", "It would also be used for field repairs, for example in agricultural operations such as seeding or harvest where considerable down time for trucks and equipment is unacceptable.", "\nIt is therefore the objective of the present invention to provide a portable tire changer." ]

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[ "\"\"Esteemed mortal:\" \"\"they have never caught me,\" \"\"and they never will.\" \"\"", "they have never seen me,\" \"\"for I am invisible,\" \"\"even as the ether which surrounds your earth.\" \"\"", "I am not a human being,\" \"\"but a spirit and fell demon from hottest hell.\"\" \"\"", "I am what you Orleanians call theAxeman.\"\" \"\"", "When I see fit,\" \"I shall come again and claim other victims.\"\" \"\"", "I alone know who they shall be.\"\" \"\"", "I shall leave no clue except my bloody axe.\"\" \"\"", "Undoubtedly, you Orleanians think of me as a most horrible murderer, which I am.\"\" \"", "Charles?\" \"\"", "But I could be much worse if I wanted to.\"\" \"", "No!\" \"\"", "At will, I could slay thousands of your best citizens, for I am in close relationship with the Angel of Death.\"\" \"", "Oh!\" \"\"", "Now, to be exact, at 12:15 o'clock earthly time, on next Tuesday night,\" \"I'm going to pass over New Orleans.\"\" \"\"", "In my infinite mercy,\" \"I am going to make a little proposition to the people.\"\" \"", "Here it is.\" \"\"", "I am very fond of jazz music, and I swear by all the devils in the nether regions that every person shall be spared in whose house a jazz band is in full swing at the time I have just mentioned.\"\" \"", "This is an outrage.\" \"", "This madman is holding our city hostage to his twisted whim.\" \"", "Millie, do you think playing the Victrola will suffice?\" \"", "Come Tuesday evening, a jazz ensemble in New Orleans will be more precious than the hope diamond.\" \"", "We can choose jazz songs from my collection of phonographs.\" \"", "Why should we do anything to appease this Axeman?\" \"", "Because he kills women with an axe.\" \"", "Do I have to remind you?\" \"", "He says, \"one thing is certain and that is some of those persons who do not jazz it on Tuesday night will get the axe.\"\" \"", "His prose could use refinement but we get the point.\" \"", "If we don't play jazz music Tuesday night...\" \"We're inviting an attack...\" \"it could not be more clear, sister.\" \"", "The real question is, what are we to do?\" \"", "Ladies, we have been docile too long.\" \"", "We are powerful, even though none of you have yet to believe it.\" \"", "Not only are we descendents of Salem but we are suffragettes.\" \"", "We're on the verge of our greatest victory, giving us the equal right to vote.\" \"", "If we embody our feminine might, intelligence with grace, strength with an iron will, no man can make us cower in our home.\" \"", "I'm off in a half hour, Joe.\" \"", "Can you... walk me home?\" \"", "You scared of the Axeman?\" \"", "Everyone is scared.\" \"", "It's Tuesday night.\" \"", "He's gonna kill somebody.\" \"", "Well, he's not gonna lay a finger on you.\" \"", "Rumor has it he's got a thing for jazz, and you've got, uh, rhythm in your soul, baby.\" \"", "I gave fair warning, girl.\" \"", "I made my intentions clear to the world.\" \"", "Yes.\" \"", "Just as expected.\" \"", "Death.\" \"", "You have no one to blame but yourself.\" \"", "That reading was for you.\" \"", "American Horror Story S03E06 \"The Axeman Cometh\"\" \"A hundred years ago, this academy was packed to capacity.\" \"", "They had bunk beds and slept eight to a room.\" \"", "Now...\" \" Notice anything?\" \" ", "Yeah.\" \"", "Luke's not here.\" \"", "His mom keeps slamming the door on me.\" \"", "Nan, stay with me.\" \"", "Look at the pictures.\" \"", "Our numbers have gone down every year for a century straight.\" \"", "Witches are dying.\" \"", "In Salem, there were hundreds of us.\" \"", "Now there's three.\" \"", "Used to be four, until...\" \"Madison went missing or dead.\" \"", "And no one in charge has done shit.\" \"", "We'll go to Fiona.\" \"", "Last I checked, she was setting witches on fire.\" \"", "Okay.\" \"", "Madison wants us to find her, and we can't afford to lose a single witch if we want to survive.\" \"", "From now on... we watch each other's backs.\" \"", "Look, I've been taking care of myself for a really long time, so I'm not sure\" \"I need some white girl sorority sisters to cover my ass.\" \"", "And what is this green shit?\" \"", "It's not a sorority.\" \"", "It's a coven.\" \"", "And this is absinthe, drink of the divine.\" \"", "Which we are.\" \"", "Where'd you find the spirit board?\" \"", "More like it found me.\" \"", "Do you know what these things do?\" \"", "Contact the dead.\" \"", "You don't know shit.\" \"", "Spirit boards have two stages: contact and release.\" \"", "I saw my grandma use one once.\" \"", "She thought it was cool, too, till a bad spirit came out, burned her house to the ground and took half her face off with it.\" \"", "There's three of us.\" \"", "You want to find Madison?\" \"", "Witch up.\" \"", "So, what do we do?\" \"", "Ask the questions.\" \"", "Be polite.\" \"", "Are we alone?\" \"", "Did you die here?\" \"", "Were you murdered?\" \"", "Yes.\" \"", "Who killed you?\" \"\"", "You did.\"\" \"", "Madison, is this you?\" \"", "Who are you?\" \"", "Axeman.\" \"", "Wait, stop.\" \"", "Stop, stop!\" \"", "If survival is so important to you, you better find out who you're talking to.\" \"", "Oncology.\" \"", "Paging palliative services, extension 3609.\" \"", "Oncology, we're paging palliative services...\" \"It's all bullshit.\" \"", "Punch a clock.\" \"", "Scrimp and save?\" \"", "And for what?\" \"", "I'm taking my sick leave in Vegas.\" \"", "Time to play.\" \"", "Never had the gift of mind-reading before.\" \"", "Is it the medication?\" \"", "It took her so long to find the right man.\" \"", "Lord, please!\" \"", "Don't let me spoil my baby's special day.\" \"", "Just let me walk down the aisle.\" \"", "Nothing was ever good enough.\" \"", "And I swear, Heavenly Father, that very night...\" \"I picked him apart every chance I got.\" \"...", "my soul is yours to keep.\" \"", "And here he is, week after week, holding my hand,\" \"Cleaning up my vomit.\" \"", "Ms. Goode?\" \"", "You haven't finished your treatment yet.\" \"", "I got to get out of here.\" \"", "I can't stand it.\" \"", "It's so noisy.\" \"", "That'll go away soon.\" \"", "I put a sedative in your I.V. to quell your nerves.\" \"", "But you're doing great, and you're almost finished.\" \"", "No, don't patronize me.\" \"", "I never wanted to be here.\" \"", "Please take a seat and finish your treatment?\" \"", "My daughter needs me as she's never needed me before.\" \"", "I'm doing this for her.\" \"", "Not... for me.\" \"", "You understand?\" \"", "If I do everything you people tell me to...\" \"I'll beat this thing, right?\" \"", "We've chosen a very aggressive form of treatment, and we always hope for the best.\" \"", "Yeah.\" \"", "So,\" \" when am I gonna lose my hair?\" \" ", "You may not.\" \"", "Everyone responds differently to the medication.\" \"", "There.\" \"", "Ugh.\" \"", "I'm just not...\" \"I'm just not ready to go quite yet.\" \"", "I want one more great love affair in my life.\" \"", "Now I think what I really want is just to belong to somebody.\" \"", "It's not too late for that, is it?\" \"", "No.\" \"", "My mom met someone on Eharmony, and they just went on a cruise to Nova Scotia.\" \"", "Hmm.\" \"", "You're gonna make it to your daughter's wedding, so you should go out and buy yourself a great dress.\" \"", "Blow the bank on it.\" \"", "Is there anyone that doesn't have a fan site?\" \"", "I don't.\" \"", "Did you find anything new?\" \"", "The Axeman killed eight people, scared the crap out of the city, never got caught.\" \"", "Listen to this.\" \"\"", "If women will not dance\" \"\"to the sound of my axe,\" \"I shall gladly make them dance with the other.\"\" \"", "Do you know a saxophone is called an axe?\" \"", "So he chopped women up 'cause they wouldn't be his groupies?\" \"", "Plus men who protected them.\" \"", "We never got to ask about Madison.\" \"", "Good.\" \"", "A spirit'll say anything to get released.\" \"", "They mess with you.\" \"", "Is that why he said we killed him?\" \"", "No.\" \"", "He thinks we're them.\" \"", "Class of 1919.\" \"", "The same year the Axeman disappeared.\" \"\"", "This jazz killer\" \"\"has killed long enough.\" \"\"", "This city is done trembling.\" \"", "Tonight it ends.\"\" \"", "Witches killed the Axeman.\" \"", "If there's even a chance he knows where Madison is, we got to make contact.\" \"", "No!\" \"", "No.\" \"", "No way I'm helping you release the Axeman.\" \"", "Nan?\" \"", "I'm out.\" \"", "You left your lives and came all the way across the country just to puss out now?\" \"", "If this is all the fight we have left in us at the end of our race, witches deserve to die.\" \"", "Where's Madison?\" \"", "Tell me and I'll give you what you want.\" \"", "I know what you like.\" \"", "I can give it to you.\" \"", "Release.\" \"", "Don't you want release?\" \"\"", "A...\"\" \"\"T...\"\" \"\"T...\"\" \"\"I...\"\" \"\"C.\"\" \"She made it up the stairs on her own.\" \"", "Of course she did.\" \"", "She's tough.\" \"", "She's a survivor.\" \"", "She's right here.\" \"", "Why are there roses in here?\" \"", "Why, I thought you might enjoy them.\" \"", "They're the very last of your heirlooms.\" \"", "Roses pull in love and romance.\" \"", "That's not what I'm looking for right now.\" \"", "I need chrysanthemums.\" \"", "All kinds of them, for strength and protection.\" \"", "Well, doctor said, uh, bed rest for at least a week, hmm?\" \"", "Who is she?\" \" ", "Who is the redhead?\" \" ", "Whoa!\" \"", "Whoa, whoa, whoa, baby.\" \"", "I don't know what you're talking about.\" \"", "Enough bullshit!\" \"", "Anything else you want to tell me now?\" \"", "Because I will see it sooner or later.\" \"", "I had to go blind to see things about you I couldn't see before.\" \"", "A bad cosmic joke.\" \"", "It's a different\" \"Kind of clarity, an absolute clarity I've never had.\" \"", "The images almost vibrate\" \" with light.\" \" ", "Thank Christ she's finally\" \" got your number.\" \" ", "She's high as a kite.\" \"", "You know what they gave her before we left the hospital?\" \"", "I'm high all right, but it's not the drugs, and rest assured, you will be accountable for every single betrayal, no matter how deep you think your secrets are buried.\" \"", "Now get out of here.\" \" ", "Get out!\" \" ", "Baby.\" \"", "Now, you're my...\" \"you're my heart.\" \"", "I'd get out while you still can, jug head.\" \"", "I wanted to sever his arms and throw him out the window.\" \"", "I had to stop myself.\" \"", "You've been given the sight.\" \"", "It comes in bits and pieces.\" \"", "It's the greatest gift to have.\" \"", "And the hardest one to live with.\" \"", "Let me help, honey.\" \"", "Oh.\" \"", "Why didn't you tell me?\" \"", "What?\" \"", "What?\" \"", "What did you see?\" \"", "Auntie Myrtle.\" \"", "I wanted to tell you, Delia, but you were in so much pain, and\" \"I didn't want to add to it.\" \" ", "Burned at the stake.\" \" ", "Yes.\" \"", "For what she did to you, yes.\" \"", "No.\" \"", "That cannot be.\" \"", "I'm sorry you had to find out this way.\" \"", "Ah.\" \"", "I think it's best if I... let you be alone for a while.\" \"", "I'll ask\" \"Delphine to come and check on you.\" \"", "Fiona's leaving in a taxi.\" \"", "All right, you twisted, tea-serving necrophiliac.\" \"", "It's time to fess up.\" \"", "You killed Madison.\" \" ", "What's he thinking?\" \" ", "He's not afraid of children.\" \"", "Really?\" \"", "Yeah.\" \"", "We all know exactly how tough he is.\" \"", "Here's how this works, asshole.\" \"", "We ask the questions, you think the answers, she reads your mind.\" \"", "Fiona's not here to help you now, riffraff.\" \"", "Best be straight.\" \"", "You killed Madison, didn't you?\" \"", "Yes.\" \"", "Yes.\" \"", "Why?\" \"", "I'm a man of uniquely developed appetites.\" \"", "Sex.\" \"", "Was she your first?\" \"", "Yes.\" \"", "I had to have her.\" \"", "Madison Montgomery, she was so beautiful.\" \"", "The moment we met, I knew that only by sliding myself into her cold, stiff, unyielding mound would I ever feel like a real man again.\" \"", "His first.\" \"", "Yes.\" \"", "Ask yourselves, what will you tough little witches do now?\" \"", "Turn me in to the authorities, exposing the coven, bringing us all to ruin?\" \"", "I think you're smarter than that.\" \"", "What's he saying?\" \"", "That we can't do shit.\" \"", "I can.\" \"", "That's enough.\" \"", "Fine.\" \"", "We'll wait till he wakes up to kill him.\" \"", "I want him to feel it.\" \"", "We're not going to kill him.\" \"", "I'm not sure he really killed Madison.\" \"", "He admitted it.\" \"", "I read his mind.\" \"", "He grew up in a house full of witches.\" \"", "And he knows how to keep secrets.\" \"", "Bet he's learned a trick or two.\" \"", "So if he didn't kill her, who did?\" \"", "You like my swamp water, don't you?\" \"", "Got to have patience.\" \"", "Won't be long now.\" \"", "Oh, my Lord.\" \"", "It's you.\" \"", "What are you doing here?\" \"", "Where've you been?\" \"", "You look like you been rode hard and put up wet.\" \"", "My daddy used to say that.\" \"", "Oh.\" \"", "You need a bath.\" \"", "Ooh.\" \"", "You smell like a pack of polecats.\" \"", "Hey.\" \"", "Hey.\" \"", "Oh, for Christ's sake, Kyle.\" \"", "It's just me.\" \"", "Okay...\" \"Shh, shh, shh.\" \"", "Okay.\" \"", "Come on.\" \"", "All clean.\" \"", "Come on.\" \"", "Kyle?\" \"", "Kyle?\" \" ", "No!\" \" ", "Kyle, it's okay.\" \"", "Hey!\" \"", "You stop that!\" \"", "Stop that!\" \"", "You don't want to piss me off!\" \"", "I could be your only friend!\" \"", "Kyle!\" \"", "Hey!\" \"", "Hey, what's wrong with you?\" \"", "It's okay...\" \"No, no, no, no.\" \"", "No, no, no, no!\" \"", "No!\" \"", "Why would you do that?\" \"", "Why...\" \"You...\" \"Wh...\" \"You're just a big ol' monster.\" \"", "Oh, my God.\" \"", "Get him out of here.\" \"", "He broke Stevie.\" \"", "I'm taking you both out of here.\" \"", "I need your help.\" \"", "We have a problem.\" \"", "It's okay.\" \"", "It's okay.\" \"", "You're okay.\" \"", "He likes you.\" \"", "You two belong together.\" \"", "Not likely.\" \"", "He murdered his mother.\" \"", "What can you do?\" \"", "I can help you dig a hole.\" \"", "She's already rotting.\" \"", "Plus, she's missing an arm.\" \"", "I have it.\" \"", "I can sew it back on her like I did with kyle.\" \"", "Have you seen his scar?\" \"", "You're not so hot with a needle and thread.\" \"", "Come on.\" \"", "We'll find a soft spot in the yard.\" \"", "No.\" \"", "You have the power of resurgence.\" \"", "You have to bring her back.\" \"", "Give me some of that mud.\" \"", "I need your help.\" \"", "Too much death inside her.\" \"", "Put your hands on her stomach and push.\" \"", "Keep pushing!\" \"", "Hmm.\" \"", "I need a cigarette.\" \" ", "You risk an awful lot coming here, you know that.\" \" ", "You didn't give me much of a choice.\" \"", "An acid attack?\" \"", "Was that supposed to speed things along?\" \"", "You just made my job more complicated.\" \"", "You think I did that?\" \"", "I look like the Taliban to you?\" \"", "If I wanted to blind your little wifey,\" \"I wouldn't have to leave my room.\" \"", "Well, something's happened.\" \"", "She's acquired some kind of second sight.\" \"", "She's starting to see things.\" \"", "We have to do something.\" \"\"", "We\", mon cher?\" \"", "I believe I already did.\" \"", "I thought I'd hired me a professional witch hunter.\" \"", "Coming here in the light of day.\" \"\"", "We got a problem.\"\" \"", "I got a problem.\" \"", "You.\" \"", "Six years in that house and for what?\" \"", "Access.\" \"", "You know that.\" \"", "You said you wanted more than just the witches at the academy.\" \"", "You said you wanted all the Salem descendants.\" \"", "That's what I've been giving you.\" \"", "I'm really glad you decided to come and see us, Kaylee.\" \"", "Well, to be honest, I mostly wanted to see Bourbon Street and eat at Emeril's restaurant.\" \"", "This other stuff?\" \"", "I don't know.\" \"", "Th-this place?\" \"", "I'm not really sure it's for me.\" \"", "This isn't a nunnery.\" \"", "It's not a jail.\" \"", "It's a haven where you can learn about who and what you are.\" \"", "What do you think I am?\" \"", "I don't think you're an arsonist.\" \"", "Which is what you've been charged with.\" \"", "Twice.\" \"", "But not convicted.\" \"", "Not yet.\" \"", "Why don't you tell me about the last fire?\" \"", "You said that you loved me.\" \"", "I changed my mind.\" \"", "I can't marry you.\" \"", "I'm sorry.\" \"", "But why?\" \"", "Will you just give me one goddamn reason?\" \"", "There's something not right about you, okay?\" \"", "You make my friends squirm.\" \"", "My mother says if I married you I would regret it as long as I live, okay?\" \"", "And I think she's right.\" \"", "I'm sorry, Kaylee.\" \"", "I don't really like to talk about this.\" \"", "You have genuine power.\" \"", "Nothing to be ashamed of, but it is something you need to learn how to control.\" \"", "Wouldn't you like to be surrounded by people with similar gifts?\" \"", "Truth be told, Mrs. Foxx, I...\" \"I really don't want to be powerful.\" \"", "I just want to find a good husband and have three kids.\" \"", "I think I have a really good shot.\" \"", "I work out, and I play fantasy football.\" \"", "Nine Salem descendants in just three years.\" \"", "Five of them I never would have found without Delia's research.\" \"", "Maybe we should take you off the payroll and put her on it.\" \"", "Sounds like she doing all the work.\" \" ", "This is what we agreed to!\" \" ", "No.\" \"", "What we agreed to is that you would clean house, not \"play\" house.\" \" ", "What's that supposed to mean?\" \" ", "What you think it means?\" \"", "She made you hard.\" \"", "You went soft!\" \"", "You're in love with that sorry witch.\" \" ", "Bullshit.\" \" ", "Bullshit is right.\" \"", "You're supposed to be ridding me of my enemies.\" \"", "Instead, they're mouthier than ever!\" \"", "Showing up on my doorstep, disrespecting me, digging up my enemies.\" \"", "When I plant a fat-assed cracker bitch,\" \"I expect her to stay planted, not come back up like goddamned ragweed!\" \"", "And that Fiona...\" \"doing my Bastien like that.\" \"", "Bastien.\" \"", "My poor Bastien.\" \"", "They desecrated you.\" \"", "And I brought you back life, and she took it away again?\" \"!\" \"", "Well, now we take hers and all.\" \"", "No more nonsense.\" \"", "You go back there, and you bring me their heads.\" \"", "All of them.\" \"", "What?\" \"", "Fiona, her daughter and every witch bitch in that house.\" \"", "You bring me their heads, all of them.\" \"", "Then you burn that place to the ground.\" \"", "Uh, Marie... you do it, and you do it quick.\" \"", "And I let you live.\" \"", "I know you went all Malcolm X and shit, but this house is now a carnival of crazy.\" \"", "How are you gonna explain this to Fiona?\" \"", "I'm not.\" \"", "No one says a word to Fiona.\" \"", "We have to keep Madison under the radar until she's better.\" \"", "And I'll...\" \"I'll figure out what to do with Kyle.\" \"", "I'm not taking him.\" \"", "He's a walking tornado.\" \"", "You made him.\" \"", "He's your problem now.\" \"", "Okay.\" \"", "Who's taking me home?\" \"", "It's late.\" \"", "Why don't you stay the night, sleep in a real bed for a change?\" \"", "No, thanks.\" \"", "I need to be alone.\" \"", "I thought you were looking for your tribe.\" \"", "I was... and I am.\" \"", "This ain't it.\" \"", "I got bad vibes.\" \"", "Real bad.\" \"", "There's something foul in this house.\" \"", "I always hated this room.\" \"", "Was I in a car crash?\" \"", "Drink this.\" \"", "Ginger'll help your stomach.\" \"", "Oh.\" \"", "Do you know who you are?\" \"", "I'm...\" \"I'm Madison Montgomery.\" \"", "I...\" \"I make $7 million a picture.\" \"", "I have two teen choice awards.\" \"", "You died.\" \"", "We brought you back.\" \"", "What's the last thing you remember?\" \"", "Red.\" \"", "A... after that, it's all... dark.\" \"", "Did you see a bright light?\" \"", "No.\" \"", "There's nothing on the other side.\" \"", "It's just black...\" \"Forever.\" \"", "Who are you?\" \"", "What do you want?\" \"", "Release.\" \"", "I can't do that.\" \"", "Don't think so, dirty pussy cat?\" \"", "Goddamn witches.\" \"", "They ended me once right here in this very room.\" \"", "And for years after, the parties and the music and the dancing raged wild outside while I sat trapped inside these four ugly walls.\" \"", "Now, last night, this sweet young witch comes along and offers me my release, and I said,\" \"\"Oh, yes, ma'am, yes, please.\" \"", "What do you need?\"\" \"", "She asks her favor, and I provide.\" \"", "The thing is, when the time comes for her to ante up, bitch lies, leaving me betwixt, between and ready to pop.\" \"", "Huh?\" \" ", "You died.\" \" ", "Uh-huh.\" \"", "And now you're trapped.\" \"", "Right here with you.\" \"", "The only way I can help you is if you let me out of here.\" \"", "No.\" \"", "Nobody leaves this room.\" \"", "You see, I had a...\" \"a contract.\" \"", "Promises were made, and all you've got to do is sing and dance... and call the witches who owe me my freedom.\" \"", "And I'll provide the music.\" \"", "Cordelia?\" \"!\" \"", "It's locked.\" \" ", "It's the Axeman.\" \" ", "You released him?\" \"!\" \"?\" \"", "I told him I would.\" \"", "I lied!\" \"", "This don't end till I get out.\" \"", "Get those witches in here and release me now!\" \"", "Go to hell!\" \" ", "Ladies first.\" \"", "Now dance.\" \"", "We need a spell to make him move on.\" \"", "I told you not to mess with that spirit board.\" \"", "Yeah, there's a shit ton of books in there, and not one of them is written in english.\" \"", "This one's it.\" \"", "Give me your hands.\" \"", "Solvo liberatum spirito malus nequam pessimus pelor...\" \"♪ get rich or die trying, like 50 cent ♪\" \"♪ I'm just a young gunner tryna get that 50 bread... ♪\" \"Well, hello, pretty lady.\" \"", "What you drinking?\"" ]

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[ "local json = require \"json\"\nlocal database = require \"database\"\nlocal exit = require \"exit\"\n\nlocal template = require'template'\ntemplate.caching(false)\n-- Compile template, disable cache, enable plain text view to skip filesystem loading\nlocal view = template.compile([[<!DOCTYPE html><html><head><title>Fortunes</title></head><body><table><tr><th>id</th><th>message</th></tr>{% for _,f in ipairs(fortunes) do %}<tr><td>{{ f.id }}</td><td>{{ f.message }}</td></tr>{% end %}</table></body></html>]], nil, true)\n\n\nlocal function process (db)\n\tlocal fortunes = db:find({Fortune = {}})\n\ttable.insert(fortunes, {id = 0, message = \"Additional fortune added at request time.\"})", "\n\ttable.sort(fortunes, function(a, b)\n\t\treturn a.message < b.message\n\tend)\n return fortunes\nend\n\n\nlocal status, db = pcall(database.connect)\nif not status then exit(db) end\n\nlocal status, res = pcall(process, db)\ndb:close()\n\nif status then\n\tlocal html = view({fortunes = res})\n\tngx.header.content_type = 'text/html; charset=utf-8'\n\tngx.header.content_length = #html\n\tngx.print(html)\nelse\n\texit(res)\nend" ]

{ "pile_set_name": "Github" }

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[ "Q:\n\nnot supported by the language\n\nI code regularly in C++, and for the specific project I'm working on right now, I'm writing a C++ lib whose methods are to be used in a C# lib, whose methods are to be used in a C# app.", "\nI use Microsoft Visual Studio 2017 on Windows 10. ", "\nI created a solution with 3 projects : \n\nA C++/CLI dynamic lib (New Project => Visual C++ => CLR => Class Library)\nA C# lib (New Project => Windows Classic Desktop => Class Library (.NET Framework))\nAnd a C# app (New Project => Windows Classic Desktop => Console App (.NET Framework))\n\nFor now, I'm just trying to make the 3 projects communicate together, and I seem to have problems between the C++ lib and the C# lib.", "\nThe code in my C++ lib is the following ;\ncppLib.h\n#pragma once\n#include <string>\n\nusing std::string;\n\nusing namespace System;\n\nnamespace cppLib {\n public ref class cppClass\n {\n public:\n static string test();\n static double add(double arg1, double arg2);\n };\n}\n\ncppLib.cpp\n#include \"cppLib.h\"\n\nnamespace cppLib {\n string cppClass::test() {\n return \"Hello World from C++ lib.\";", "\n }\n\n double cppClass::add(double arg1, double arg2) {\n return arg1 + arg2;\n }\n}\n\nThe code in my C# lib is the following :\nWrapper.cs\nusing cppLib;\n\nnamespace CsWrapper\n{\n public class Wrapper\n {\n //static public string TestCppLib()\n //{\n // return cppClass.test();\n //}\n\n static public double Add(double arg1, double arg2)\n {\n return cppClass.add(arg1, arg2);\n }\n\n public string WrapperTest()\n {\n return \"Hello World from C# lib.\";", "\n }\n }\n}\n\nAs is, this code builds without errors nor warnings. ", "So I can call my static double add(double arg1, double arg2); method from my C++ lib in my C# lib method static public double Add(double arg1, double arg2), BUT if I try to uncomment the following code in Wrapper.cs :\n //static public string TestCppLib()\n //{\n // return cppClass.test();\n //}\n\nI get the 'cppClass.test(?)' ", "is not supported by the language error message :\nSeverity Code Description Project File Suppression State\nError CS0570 'cppClass.test(?)' ", "is not supported by the language CsWrapper D:\\documents\\...\\CsWrapper\\Wrapper.cs Active\n\nWhat does it mean? ", "How can I call one method from my C++ lib in my C# lib without problem, but the other I can't? ", "My public string WrapperTest() method returns a string all right that I can use in my C# app (it works, I can display it), so why can't I call that specific C++ method in my C# lib? ", "It's also really my first time coding in C#.", "\n\nA:\n\nIn C++/CLI, a string cannot be returned as a native C++ template type if the method is to be used by a C# app / lib, because the C# code won't know how to use it. ", "\nThe managed (.Net variant) of the type has to be used; for a C++ string, it's a String^. The ^ indicates that it is a ref class (managed) pointer.", "\nThe code becomes :\ncppLib.h\n#pragma once\n#include <string>\n\nusing std::string;\n\nusing namespace System;\n\nnamespace cppLib {\n public ref class cppClass\n {\n public:\n static String^ test();\n static double add(double arg1, double arg2);\n };\n}\n\ncppLib.cpp\n#include \"cppLib.h\"\n\nnamespace cppLib {\n String^ cppClass::test() {\n return \"Hello World from C++ lib.\";", "\n }\n\n double cppClass::add(double arg1, double arg2) {\n return arg1 + arg2;\n }\n}\n\nThe rest stays the same.", "\n\n" ]

{ "pile_set_name": "StackExchange" }

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[ "\n140 B.R. 790 (1992)\nIn re BLINDER, ROBINSON & CO., ", "INC., ", "Debtors.", "\nGlen E. KELLER, Jr., Trustee for the Estate of Blinder, Robinson & Co., Inc., Plaintiff/Appellee,\nv.\nMeyer BLINDER, et al., ", "Defendants/Appellants.", "\nCiv. ", "A. No. ", "90-K-1904, Bankruptcy No. ", "90 B 12654 SBB, Adv. ", "No. ", "90 1381 CEM.", "\nUnited States District Court, D. Colorado.", "\nMay 1, 1992.", "\n*791 William A. Bianco, Davis, Graham & Stubbs, Denver, Colo., for plaintiff-appellee.", "\nRonald G. Rossi, and Paul T. Maricle, Rossi & Judd, Denver, Colo., for Blinders.", "\nJames T. Ayers, Denver, Colo., for Intercontinental.", "\n\nMEMORANDUM OPINION AND ORDER\nKANE, Senior District Judge.", "\nMeyer Blinder, Lillian Blinder, American Rare Coin Exchange, Ltd., Intercontinental *792 Enterprises, Inc. and Redmey Management Company (collectively, the Appellants) appeal the bankruptcy court's October 12, 1990 judgment ordering them to turn over property, including legal files, to Glen E. Keller, Jr., Trustee of Blinder, Robinson & Co., Inc.'s estate (Trustee). ", "They argue that the court's order was in error because (1) certain files were not property of the estate, (2) turnover of files relating to Meyer Blinder violated his Fifth Amendment right against compelled self-incrimination, and (3) the bankruptcy court should have conditioned its order on the Trustee's agreement to adhere to any joint defense privilege. ", "I affirm.", "\n\nI. Facts.", "\n\nOn October 2, 1990, the Trustee filed a complaint against the Appellants for turnover of property of the estate and for injunctive relief. ", "The Trustee alleged that the Appellants had in their custody and control property of the estate that must be delivered to the Trustee under 11 U.S.C. § 542(a). ", "On October 10, 1990, the bankruptcy court held a hearing on the complaint.", "\nThe proceedings focused on certain legal files held by the former legal staff of Blinder, Robinson who were employed by Intercontinental Enterprises, Inc. after Blinder, Robinson was placed into liquidation under the Securities Investor Protection Act. ", "The Appellants argued that these files fell into three categories. ", "The first were files relating to actions in which Blinder, Robinson was the sole defendant. ", "The Appellants did not object to the turnover of these documents. ", "The second were files involving some joint interest between Blinder, Robinson and another party, such as an agreement by Blinder, Robinson to indemnify that party or the availability of a common defense. ", "The Appellants offered to turn these documents over to the Trustee subject to his guarantee that he would not waive any joint privilege. ", "The third were files involving only third parties. ", "The Appellants refused to turn over these documents, citing the attorney-client privilege.", "\nAt the conclusion of the hearing, the bankruptcy court granted the relief requested in the Trustee's complaint. ", "In its October 12 order, the court adopted the classification offered by the Appellants, but held that documents in all three categories were property of the estate which must be turned over to the Trustee under § 542(a). ", "As to the third category, however, the court granted the Appellants' motion for stay pending appeal, subject to the condition that they provide the Trustee with a list \"identifying the files for which they are asserting any privilege by number, name and general contents,\" setting forth \"the privilege they assert and the basis on which they assert the privilege may be impaired by delivery of that file to the Trustee.\" (", "R. Vol. ", "I, Doc. ", "8 at 1.) ", "The court further ordered the Appellants to provide a list of the third parties, their counsel and the addresses for both. (", "Id.) On October 19, 1990, the Appellants filed their notice of appeal.", "\n\nII. ", "Merits.", "\n\nA. Status of Legal Files Involving Third Parties Only.", "\nThe Appellants' first argument is that the third category of documents, legal files involving third parties only and not Blinder, Robinson, are not property of the estate or otherwise subject to turnover. ", "Section 542 of the Bankruptcy Code sets forth a two-part scheme for turnover of property of the estate or other information related to the debtor's property or financial affairs. ", "Under section 542(a), an entity\nin possession, custody, or control, during the case, of property that the trustee may use, sell or lease under section 363 of this title, or that the debtor may exempt under section 522 of this title, shall deliver to the trustee, and account for, such property or the value of such property, unless such property is of inconsequential value or benefit to the estate.", "\n11 U.S.C. § 542(a). ", "Thus, \"[s]ubsection (a) of this section requires anyone holding property of the estate on the date of the filing of the petition, or property that the trustee may use, sell or lease under section 363, to deliver it to the trustee.\" ", "Id. advisory committee note.", "\n*793 In contrast, subsection (e) of § 542 is directed to persons holding recorded information that is not property of the estate but is otherwise relevant to the debtor's property or financial affairs. ", "It provides:\nSubject to any applicable privilege, after notice and a hearing, the court may order an attorney, accountant, or other person that holds recorded information, including books, documents, records, and papers, relating to the debtor's property or financial affairs, to turn over or disclose such recorded information to the trustee.", "\nId. § 542(e). ", "This subsection \"was intended to prevent attorneys, accountants, and others similarly protected by state law, from asserting a lien on the debtor's property to obtain repayment of their fees `in full ahead of other creditors.'\" ", "4 Collier on Bankruptcy ¶ 542.06 at 542-27 (L. King 15th ed. ", "1992) (citing legislative history). ", "Thus, under this statutory framework, \"[d]ocuments or books belonging to the debtor and of value or benefit to the estate must be turned over as property of the estate under section 542(a). ", "If the documents or books are not property of the estate, [subsection (e)] applies to require disclosure of the information in such books or records.\" ", "Id. at 542-24.", "\nTo prevail on this argument, the Appellants must show that the bankruptcy court clearly erred in finding that Blinder, Robinson's legal files concerning cases in which Blinder, Robinson was not a defendant were property of the estate under § 542(a). ", "They have failed to make this showing.", "\nHere, the undisputed evidence indicates that all of the legal files sought by the Trustee were created and maintained by Blinder, Robinson's former in-house counsel or their support staff. ", "The Trustee testified at trial that he determined that all of the files and records were compiled by Blinder, Robinson's former legal personnel, they were located in space leased and on materials provided by Blinder, Robinson, and the legal staff were all paid by Blinder, Robinson. (", "See R.Vol. ", "I, Tr. ", "at 16, 95.) ", "The Appellants did not attempt to establish that any of the files were produced or maintained by an entity other than Blinder, Robinson, though there was evidence that some of information placed in the files were generated by other sources. ", "Furthermore, the Appellants' counsel conceded that the personnel who prepared the files were employees of Blinder, Robinson at the time, though they later became employed by Intercontinental Enterprises, Inc. (See id. at 110.)", "\nUnder § 541 of the Code, \"property of the estate\" is broadly defined to include \"all legal or equitable interests of the debtor in property as of the commencement of the case.\" ", "Id. § 541(a)(1). ", "In an action to compel turnover of property of the estate under § 542(a), the trustee has the initial burden of proving by clear and convincing evidence that the property in issue is property of the estate under § 541. ", "Evans v. Robbins, 897 F.2d 966, 968 (8th Cir.1990); Express Am., ", "Inc. v. Sivley (In re Express Am., ", "Inc.), 130 B.R. 196, 198 (Bankr. ", "W.D.Pa.1991).", "\nThe Appellants argue that the relevant factor in determining whether these files are property of the estate is the \"client\" for whom the Blinder, Robinson attorneys were working at the time. ", "They fail to explain, however, how these attorneys could be working solely for another party without having an impact on Blinder, Robinson itself. ", "The single concrete example cited in the record related to files containing information prepared by an outside law firm for an action in which only Meyer Blinder was a named defendant. ", "When asked by the court why Blinder, Robinson maintained a file on this matter, Appellants' counsel conceded that these materials were retained because Blinder, Robinson had a duty to indemnify Mr. Blinder. (", "See R.Vol. ", "II, Tr. ", "at 112.) ", "In this light, this file is more properly characterized under category two, as involving a case in which there is some kind of joint interest between Blinder, Robinson and the third party.", "\nIn sum, the record simply does not support the existence of any category three documents. ", "Yet, assuming they exist, the court was correct in ruling that they were *794 property of the estate. ", "Whether or not the underlying lawsuit involved Blinder, Robinson or an independent third party is irrelevant. ", "For whatever reason, the legal staff of Blinder, Robinson found it necessary to retain these documents in a file in the corporation's offices. ", "Property of the estate includes books and records produced during a corporation's existence. ", "See 11 U.S.C. § 521(4) (requiring the debtor to turn over to the trustee \"any recorded information, including books, documents, records, and papers, relating to the property of the estate\"). ", "The Trustee is entitled to review these materials to determine whether they impact the administration of the estate.", "\nAccordingly, the bankruptcy court's factual finding that the category three files were property of the estate was not clearly erroneous, and the court correctly ordered these files to be turned over to the Trustee under § 542(a). ", "Since turnover was proper under § 542(a), I need not consider whether § 542(e) applies.", "\nB. Fifth Amendment Privilege and Right to Effective Counsel.", "\nThe Appellants' second argument is that the forced turnover of documents relating to a criminal action against Meyer Blinder violates his Fifth Amendment privilege against compelled self-incrimination and his right to effective assistance of counsel. ", "The Trustee responds that Mr. Blinder's Fifth Amendment rights are not violated because he is not compelled to do anything, and that his right to effective assistance of counsel is not significantly impaired. ", "The Appellants bear the burden of establishing the existence of the privilege. ", "See Roach v. National Transp. ", "Safety Bd., ", "804 F.2d 1147, 1151 (10th Cir. ", "1986), cert. ", "denied, 486 U.S. 1006, 108 S.Ct. ", "1732, 100 L.Ed.2d 195 (1988).", "\nI agree with the Trustee's position. ", "First, it does not appear that any of the records in question are in Mr. Blinder's or his private counsel's possession. ", "The Fifth Amendment privilege is a personal right and does not extend to documents held by third parties. ", "See In re Standard Fin. ", "Management Corp., 77 B.R. 324, 327 (Bankr.", "D.Mass.1987).", "\nAssuming that Mr. Blinder does hold some of the files, the Fifth Amendment privilege protects only testimonial acts. ", "See Fisher v. United States, 425 U.S. 391, 408, 96 S.Ct. ", "1569, 1579, 48 L.Ed.2d 39 (1976). ", "While in limited circumstances the production of documents or records is, by its very nature, testimonial, see id. at 406, 96 S.Ct. ", "at 1578 (noting instance where conceding the existence or possession of document could establish liability), Mr. Blinder has not demonstrated how the production of documents in this case is communicative or testimonial in any way. ", "The existence of these files is not incriminating of itself. ", "See United States v. Doe, 465 U.S. 605, 610-11, 104 S.Ct. ", "1237, 1240-41, 79 L.Ed.2d 552 (1984) (contents of documents and records not privileged under Fifth Amendment); Couch v. United States, 409 U.S. 322, 328, 93 S.Ct. ", "611, 615, 34 L.Ed.2d 548 (1973) (\"Fifth Amendment privilege is a personal privilege: it adheres basically to the person, not to information that may incriminate him\"). ", "Compare Baltimore City Dept. ", "of Social Servs. ", "v. Bouknight, 493 U.S. 549, 561, 110 S.Ct. ", "900, 908, 107 L.Ed.2d 992 (1990) (complying with government's demand to produce child could be testimony as to defendant's control and possession of child). ", "Therefore, I conclude that the Appellants have failed to demonstrate that the bankruptcy court's order violates Mr. Blinder's Fifth Amendment rights.", "\nThe Appellants' parallel argument — that production of the files would prevent the effective assistance of counsel — is likewise without merit. ", "The Appellants claim that turnover of the files will chill counsel's defense of Mr. Blinder in the criminal action:\nThe facts are that a Bankruptcy Trustee is now attempting to obtain possession of a file which concerns the criminal defense of Meyer Blinder in Las Vegas, Nevada. ", "Such intrusion obviously interferes with counsel's effort in representing Mr. Blinder. ", "Should counsel know that his file is going to be reviewed by *795 complete strangers, he will certainly not record his research impressions and theories. ", "He also would not record anything his client tells him.", "\n(Opening Br. ", "of Appellants at 7-8.) ", "This argument is premised on the effect that turnover will have on counsel's future actions. ", "The premise is flawed.", "\nThe turnover order is directed to documents that were created and were in Blinder, Robinson's files at the time the SIPA liquidation commenced. ", "Some of those files may contain information relating to the criminal action against Mr. Blinder in Nevada. ", "For the chilling effect described above to take place, the Trustee would have to be entitled to continuing access to the files created by Mr. Blinder's criminal defense counsel, thereby causing Mr. Blinder's criminal defense counsel to limit his written work product. ", "The turnover order, however, does not address anything other than documents in existence at the time the SIPA decree was entered and cannot possibly effect counsel's future actions in representing Mr. Blinder in the criminal action. ", "The bankruptcy court's order was not deficient for failing to address this purported but illusory chilling effect on attorney-client communications.", "\nC. Joint Defense Privilege.", "\nThe Appellants' final argument is that the bankruptcy court should not have ordered the turnover of category two documents, involving some joint interest or defense between Blinder, Robinson and a third party, without establishing some guarantee that the Trustee would not divulge confidences running to both parties. ", "In my opinion, this request exceeded the scope of the matters raised by the Trustee's turnover complaint.", "\nThe sole issue before the court was whether the legal files were property of the estate subject to turnover under § 542(a). ", "The Appellants' concede that the category two files concerning legal matters in which Blinder, Robinson had a direct interest, even though they may also have involved third parties, were property of the estate. ", "They suggest, however, that whenever turnover of these files would implicate the joint defense privilege, the court has an absolute duty to provide for some control over the trustee's divulgence of jointly-held confidences. ", "I can find no support for this proposition.", "\nThe joint defense privilege is self-executing. \"", "An exception to the general rule that disclosure to a third party of privileged information thereby waives the privilege, a joint defense privilege cannot be waived without the consent of all parties who share the privilege.\" ", "In re Grand Jury Subpoenas 89-3 & 89-4, 902 F.2d 244, 248 (4th Cir.1990). ", "Therefore, were the Trustee to waive the privilege with respect to any of the documents provided under the turnover order, that waiver would be ineffective as to any appellant in this case who could establish the existence of a joint defense. ", "See John Morrell & Co. v. Local Union 304A, 913 F.2d 544, 555-56 (8th Cir.1990) (documents inadvertently provided to adversary by one party signatory to a joint defense agreement shielded for use against other signatory party by attorney-client privilege), cert. ", "denied, ___ U.S. ___, 111 S.Ct. ", "1683, 114 L.Ed.2d 78 (1991).", "\nMoreover, the few cases in which the courts have considered whether one party to the privilege may take offensive action against another party to prevent disclosure to an adversary indicate that the court's power is limited in this regard. ", "For example, in Nestle Foods Corp. v. Aetna Casualty & Sur. ", "Co., 129 F.R.D. 483 (D.N.J. 1990), the court denied a protective order to a party who could not establish good cause, despite its allegation that disclosure of certain documents would violate the joint defense privilege. ", "In a footnote, the court noted a trend among counsel to seek protective orders to prevent the disclosure of information subject to the joint defense privilege.", "\nSince most often the parties will consent to such non-disclosure, the parties seek only the Court's imprimatur to their agreement and do not come forward with any showing of good cause. ", "However, when as here, consent is unavailing, the *796 movant seems unwilling or unable to make the required showing — appearing to believe that a protective order should be available for the asking. ", "The law is to the contrary. ", "Parties should not assume that the court will accede to a protective order because no substantial harm to the party opposing the application can be shown; the requirements of Rule 26 must be satisfied by the movant in each case.", "\nId. at 485 n. 4; see also Waller v. Financial Corp. of Am., ", "828 F.2d 579, 584 (9th Cir.1987) (prospect that terms of settlement agreement could result in violation of joint defense privilege insufficient to give party standing to object to agreement).", "\nIn this case, there is even less of a compelling need for a protective decree. ", "The Trustee, when asked about documents subject to the joint defense privilege, freely agreed to adhere to his responsibilities under this doctrine, including providing the Appellants with notice before surrendering any information. (", "See R.Vol. ", "II, Tr. ", "at 92, 94.) ", "Under these circumstances, the court did not err by failing to include a provision in the turnover order expressly providing for enforcement of the privilege. ", "See also In re Michigan Boiler & Engineering Co., 87 B.R. 465, 471 (Bankr.", "E.D.Mich.1988) (joint defense privilege not a barrier to trustee's discovery of documents held by debtor's former corporate counsel).", "\n\nIII. ", "Conclusion.", "\n\nThe bankruptcy court's judgment is AFFIRMED. ", "The Appellants have not established that documents created and maintained by Blinder, Robinson's legal staff were not property of the estate, that disclosure of some of these documents violates Mr. Blinders Fifth Amendment privilege or right to effective assistance of counsel, or that there was a concrete prospect that the Trustee would reveal information subject to the joint defense privilege.", "\n" ]

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[ "Montgomery voting guidelines for primary announced\n\nMONTGOMERY,\nAlabama -- Alabamians will place their primary votes March 13, and the city of\nMontgomery wants to make sure its residents are ready.", "\n\nCitizens\nmust be registered and qualified to vote in order to participate in the Primary\nElection, and the last day to register is Friday, March 2. ", "To register to vote,\ncontact the Montgomery County Board of Registrar's Office at 334-832-1215.", "\n\nAbsentee\nvoting is currently underway. ", "Qualified voters must complete an absentee ballot\napplication and designate their preferred political party on the form before\nreceiving a ballot. ", "An absentee ballot application can be obtained by calling\n334-832-1281, by downloading the application from www.montgomeryelectioncenter.org\nor by visiting The Montgomery Election Center at 125 Washington Ave.", "\n\nThe last day\nto apply for an absentee ballot is Thursday, March 8. ", "Hand delivery deadline\nfor an absentee ballot is Monday, March 12. ", "Postmark deadline for an absentee\nballet is Monday, March 12, but it must be received by noon Tuesday, March 13.", "\n\nElection Day\nis Tuesday, March 13 from 7 a.m. to 7 p.m. at the voter's designated polling\nplace. ", "There is a tool on the center's website where you can find your polling\ncenter." ]

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[ "Q:\n\nTilde expansion not working when I hit tab on ubuntu 10.10\n\nI try to do this:\ncd ~git\\t\n\nwhere the \\t is tab character and I expect it to be expanded by bash_completion to this:\ncd ~gitolite/\n\nbut it doesn't. ", "I've uncommented the following lines in /etc/bash.bashrc and logged out and back in.", "\n# enable bash completion in interactive shells\nif [ -f /etc/bash_completion ] && ! ", "shopt -oq posix; then\n . ", "/etc/bash_completion\nfi\n\nWhat gives? ", "\n\nA:\n\nYou probably have:\ncomplete -d cd\n\ntry running this:\ncomplete -o bashdefault -d cd\n\nthen try your cd ~git\\t again.", "\nIf that works, add complete -o bashdefault -d cd to your ~/.bashrc, or wherever you put your configs for bash.", "\n\n" ]

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[ "[Effects of elaboration on retrieval of words in incidental memory].", "\nThe present study was carried out to investigate the mechanism of retrieval of words in incidental memory. ", "Thirty college students were asked to generate free associates to each target word followed by unexpected free recall and recognition tests. ", "In the free recall test, subjects were instructed to recall both targets and generated associates. ", "The probability of targets which elicited more associates correctly recalled was higher than that of those which did less when their associates previously recalled. ", "The above result was interpreted as showing that the more target words had retrieval route from the generated associates the more they were recalled. ", "False recognition score as an index of between-item elaboration was higher to an associate elicited by three targets than by two or one. ", "No clear effects of between-item elaboration were observed for free recall performance of targets. ", "These results were discussed in term of between-item and within-item elaboration." ]

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[ "/******************************************************************************\n* SOFA, Simulation Open-Framework Architecture *\n* (c) 2006 INRIA, USTL, UJF, CNRS, MGH *\n* *\n* This program is free software; you can redistribute it and/or modify it *\n* under the terms of the GNU Lesser General Public License as published by *\n* the Free Software Foundation; either version 2.1 of the License, or (at *\n* your option) any later version. ", " *\n* *\n* This program is distributed in the hope that it will be useful, but WITHOUT *\n* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or *\n* FITNESS FOR A PARTICULAR PURPOSE. ", "See the GNU Lesser General Public License *\n* for more details. ", " *\n* *\n* You should have received a copy of the GNU Lesser General Public License *\n* along with this program. ", "If not, see <http://www.gnu.org/licenses/>. ", " *\n*******************************************************************************\n* Authors: The SOFA Team and external contributors (see Authors.txt) *\n* *\n* Contact information: contact@sofa-framework.org *\n******************************************************************************/\n#ifndef SOFA_GPU_CUDA_CUDAMESHMATRIXMASS_CPP\n#define SOFA_GPU_CUDA_CUDAMESHMATRIXMASS_CPP\n\n#include <sofa/gpu/cuda/CudaMeshMatrixMass.inl>\n#include <SofaMiscForceField/MeshMatrixMass.inl>\n#include <sofa/core/behavior/Mass.inl>\n#include <sofa/core/behavior/ForceField.inl>\n\n#include <SofaBaseTopology/PointSetGeometryAlgorithms.inl>\n#include <SofaBaseTopology/TriangleSetGeometryAlgorithms.inl>\n#include <SofaBaseTopology/TetrahedronSetGeometryAlgorithms.inl>\n#include <SofaBaseTopology/QuadSetGeometryAlgorithms.inl>\n#include <SofaBaseTopology/HexahedronSetGeometryAlgorithms.inl>\n\n#include <sofa/defaulttype/VecTypes.h>\n#include <sofa/core/ObjectFactory.h>\n#include \"CudaTypes.h\"\n\nnamespace sofa\n{\n\nnamespace component\n{\n\nnamespace mass\n{\n\ntemplate class SOFA_GPU_CUDA_API MeshMatrixMass<sofa::gpu::cuda::CudaVec3fTypes, float>;\ntemplate class SOFA_GPU_CUDA_API MeshMatrixMass<sofa::gpu::cuda::CudaVec2fTypes, float>;\ntemplate class SOFA_GPU_CUDA_API MeshMatrixMass<sofa::gpu::cuda::CudaVec1fTypes, float>;\n\n#ifdef SOFA_GPU_CUDA_DOUBLE\ntemplate class SOFA_GPU_CUDA_API MeshMatrixMass<sofa::gpu::cuda::CudaVec3dTypes, double>;\ntemplate class SOFA_GPU_CUDA_API MeshMatrixMass<sofa::gpu::cuda::CudaVec2dTypes, double>;\ntemplate class SOFA_GPU_CUDA_API MeshMatrixMass<sofa::gpu::cuda::CudaVec1dTypes, double>;\n#endif // SOFA_GPU_CUDA_DOUBLE\n\n\n} // namespace mass\n\n} // namespace component\n\nnamespace gpu\n{\n\nnamespace cuda\n{\n\nint MeshMatrixMassClassCudaClass = core::RegisterObject(\"Supports GPU-side computations using CUDA\")\n .add< component::mass::MeshMatrixMass<CudaVec3fTypes, float > >(true)\n .add< component::mass::MeshMatrixMass<CudaVec2fTypes, float > >()\n .add< component::mass::MeshMatrixMass<CudaVec1fTypes, float > >()\n#ifdef SOFA_GPU_CUDA_DOUBLE\n .add< component::mass::MeshMatrixMass<CudaVec3dTypes, double > >()\n .add< component::mass::MeshMatrixMass<CudaVec2dTypes, double > >()\n .add< component::mass::MeshMatrixMass<CudaVec1dTypes, double > >()\n#endif // SOFA_GPU_CUDA_DOUBLE\n ;\n\n} // namespace cuda\n\n} // namespace gpu\n\n} // namespace sofa\n\n#endif //SOFA_GPU_CUDA_CUDAMESHMATRIXMASS_CPP\n\n" ]

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[ "\"One should either write ruthlessly what one believes to be the truth, or else shut up.\" — ", "Arthur Koestler\n\nThe women I know who have given birth, whether pro-life or pro-choice, do not romanticize it. ", "They speak, of course, of the miracle that it is. ", "But they also speak, often rather too frankly, of how difficult and often disgusting the process is. ", "If a substantial number of pro-lifers are women who have given birth–and they are–then we pro-choicers can’t simply tell ourselves that it’s because they haven’t really thought about what birth entails.", "\n\nSo this is what is at the bottom of the pro-choice argument — they are “disgusted” by pregnancy and birth? ", "I thought it was supposed to be the crazy fundamentalists that hated the human body and feared sex. ", "How sick do you have to be to be revolted by the process that brings new life, that brought your life, into being?", "\n\nWhat accounts for these differences in attitude? ", "Anti-natalist sentiments are a natural byproduct of the Contraceptive Culture, which propagates the belief that sex without pregnancy is normal, and where pregnancy is considered a rare medical anomaly.", "\n\nThis way of thinking — nowadays so common that we don’t even recognize it as an ideological phenomenon — is an inversion of nature.", "\n\nFrom a strictly biological point of view, procreation is the only purpose of sex. ", "People who like to condemn conservatives as being “anti-science” because we don’t go along with the global-warming crusade ought to be asked to explain why they are so hostile to the scientific purpose of sex, i.e., making babies.", "\n\nAh, but for the past half-century, Big Science has been in the business of preventing childbirth, you see. ", "So the anti-baby industry has diligently promoted all the arguments and attitudes necessary to the marketing of contraceptive products and services. ", "And this marketing campaign — for that’s what it was — has succeeded so phenomenally that the Contraceptive Culture is now nearly ubiquitous, and people don’t even stop to ask themselves: “Why do we think this way?”", "\n\nA little history: In 1957, at the peak of the Baby Boom, the U.S. total fertility rate (TFR) — the average number of births per woman, over the course of her lifetime, based on annual rates — reached 3.74. ", "As any student of statistics should see, this number meant that the typical American woman was far more likely to have four children than to have only three.", "\n\nToday, the U.S. TFR is about 2.1, which means that the typical woman is about equally likely to have only one baby as to have three.", "\n\nAnd it also means that U.S. women now are about as likely to have zero babies as to have four.", "\n\nWhenever you discuss such demographic trends, you can expect to be met with arguments that socioeconomic changes explain the trend: More young people are going to college, couples are delaying marriage, divorce is more prevalent, more women are working, etc.", "\n\nYet all of those factors — attending college, marriage, divorce, working — involve individual choices. ", "The conjuring of trends to explain these decisions requires us to believe that we are mere puppets dancing on the strings manipulated by impersonal forces beyond our control, and that our individual choices are pre-determined.", "\n\nI do not believe that. ", "Rather, it seems obvious to me that personal beliefs influence people’s choices and decisions, and that personal beliefs have shifted as a result of a nearly unnoticed process of indoctrination, the rise of a belief system called the Contraceptive Culture.", "\n\nRevulsion toward the thought of childbearing — an averse response to giving birth as “difficult and often disgusting” — is exactly what we would expect such indoctrination to produce. ", "One need not “romanticize” childbirth to see that those in whom an anti-natalist attitude has been carefully inculcated would dwell on the messy, painful and sometimes hazardous aspects of the process.", "\n\nWhy? ", "Because childbirth is now viewed as a choice, merely one optional outcome of sexual activity, rather than as a routine and natural consequence. (", "Childbirth is almost certainly more “difficult” in Mali, yet the average woman in Mali will give birth to 7.34 children in her lifetime.)", "\n\nWhat bothers me most about unthinking acceptance of the Contraceptive Culture is that it reflects a failure of imagination, and a death of hope. ", "When I tell people that my wife and I have six children, the reaction is often disbelief: “How can you possibly cope? ", "I can’t imagine it!” ", "And yet we do, somehow.", "\n\nWe have never been rich and have often been quite poor, but we have hope, a hope informed by the knowledge that other people have overcome hardships far more difficult than our own, by a sense of duty to fulfill the obligations entrusted to us, and by the belief that God will give us no burden that we are incapable of carrying.", "\n\nYou may believe otherwise. ", "But you ought to ask yourself why you believe what you believe.", "\n\n“In the hands of a skillful indoctrinator, the average student not only thinks what the indoctrinator wants him to think . . . ", "but is altogether positive that he has arrived at his position by independent intellectual exertion. ", "This man is outraged by the suggestion that he is the flesh-and-blood tribute to the success of his indoctrinators.”", "\n– William F. Buckley Jr., Up From Liberalism(1959)\n\nSHAMELESS CAPITALISM\n\nThe Other McCain is a participant in the Amazon Services LLC Associates Program, an affiliate advertising program designed to provide a means for this blog to earn fees by linking to Amazon.com and affiliated sites." ]

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[ "---\nabstract: 'We develop a nonperturbative method to calculate the electron propagator in low-dimensional and strongly correlated electron systems. ", "The method builds on our earlier work using a Hubbard-Stratonovich transformation to map the tunneling problem to the x-ray edge problem, which accounts for the infrared catastrophe caused by the sudden introduction of a new electron into a conductor during a tunneling event. ", "Here we use a cumulant expansion to include fluctuations about this x-ray edge limit. ", "We find that the dominant effect of electron-electron interaction at low energies is to correct the noninteracting Green’s function by a factor $e^{-S/\\hbar}$, where $S$ can be interpreted as the Euclidean action for a density field describing the time-dependent charge distribution of the newly added electron. ", "Initially localized, this charge distribution spreads in time as the electron is accommodated by the host conductor, and during this relaxation process action is accumulated according to classical electrostatics with a screened interaction. ", "The theory applies to lattice or continuum models of any dimensionality, with or without translational invariance. ", "In one dimension the method correctly predicts a power-law density of states (DOS) for electrons with short-range interaction and no disorder, and when applied to the solvable Tomonaga-Luttinger model, the exact DOS is obtained.'", "\nauthor:\n- 'Kelly R. Patton and Michael R. Geller'\nbibliography:\n- '/Users/mgeller/Papers/bibliographies/MRGhall.bib'\n- '/Users/mgeller/Papers/bibliographies/MRGmanybody.bib'\n- '/Users/mgeller/Papers/bibliographies/MRGbooks.bib'\n- '/Users/mgeller/Papers/bibliographies/MRGgroup.bib'\n- 'cumulantnotes.bib'\ndate: 'September 23, 2005'\ntitle: 'Infrared catastrophe and tunneling into strongly correlated electron systems: Beyond the x-ray edge limit'\n---\n\nIntroduction\n============\n\nIn the conventional many-body theory treatment of tunneling, the low-temperature tunneling current between an ordinary metal and a strongly correlated electron system is controlled by the single-particle density of states (DOS) of the correlated system. ", "Tunneling experiments are therefore often used as a probe of the DOS. ", "In a wide variety of low dimensional and strongly correlated electron systems, including all 1D metals, the 2D diffusive metal, the 2D Hall fluid, and the edge of the sharply confined Hall fluid, the DOS exhibits anomalies such as cusps, algebraic suppressions, and pseudogaps at the Fermi energy. ", "We have recently proposed that the origin of these anomalies is the infrared catastrophe caused by the response of the host electron gas to the sudden introduction of a new particle that occurs during a tunneling event.", "\n\nThe infrared catastrophe is a singular screening response of a degenerate Fermi gas to a localized potential applied abruptly in time, which is known to be responsible for the anomalous x-ray optical and photoemission edge spectra of metals, the Anderson orthogonality catastrophe,[@AndersonPRL67; @HamannPRL71] and the Kondo effect.[@AndersonPRL69; @YuvalPRB70] Imagine an electron in a tunneling process being replaced by a negatively charged, distinguishable particle with mass $M$. In the $M \\! ", "\\rightarrow \\! ", "\\infty$ limit, the time-dependent potential produced by the particle being added to the origin at time $\\tau = 0$ and removed at a later time $\\tau_0$ is[@stepfunctionnote] $$\\phi_{\\rm xr}({\\bf r},\\tau) = U({\\bf r}) \\Theta(\\tau) \\Theta(\\tau_{0}-\\tau),\n\\label{phixr}$$ where $U$ is the two-particle interaction. ", "$\\phi_{\\rm xr}$ is identical, up to a sign, to the abruptly turned-on hole potential of the x-ray edge problem, so an infrared catastrophe would be expected. ", "Tunneling of a real, finite-mass electron is different because it recoils, softening the potential produced. ", "The real electron is also an indistinguishable fermion, unable to tunnel into the occupied states below the Fermi energy.", "\n\nIn Ref.", "  we introduced an exact functional-integral representation for the interacting propagator, and developed a nonperturbative technique for calculating it by identifying a “dangerous\" scalar field configuration of the form (\\[phixr\\]), and then treating this special field configuration by using methods developed for the x-ray edge problem. ", "All other field configurations were ignored, thereby reducing the tunneling problem to an x-ray edge problem. ", "Nonetheless, qualitatively correct results were obtained for the 1D electron gas and the 2D Hall fluid using this approach. ", "In this paper we attempt to go beyond this so-called x-ray edge limit by including fluctuations about $\\phi_{\\rm xr}$. We find that by including fluctuations through the use of a simple functional cumulant expansion, a qualitatively correct DOS is obtained for electrons with short-range interaction and no disorder in one, two, and three dimensions. ", "We also show that and when applied to the solvable Tomonaga-Luttinger model, the low-energy fixed-point Hamiltonian for most 1D metals, the exact DOS is obtained. ", "A preliminary account of this work has appeared elsewhere.[@Geller02]\n\ngeneral formalism and cumulant expansion method {#general formalism section}\n===============================================\n\nWe assume a grand-canonical Hamiltonian $H =H_0 + V$, where $$H_0 \\equiv \\sum_\\sigma \\int d^{\\scriptscriptstyle D}r \\ \\psi^\\dagger_\\sigma({\\bf r}) \\, \\bigg[ {\\Pi^2 \\over 2m} + v({\\bf r}) - \\mu \\bigg] \n\\psi_\\sigma ({\\bf r})$$ is the Hartree mean-field Hamiltonian, and $$V \\equiv {\\textstyle{1 \\over 2}} \\int d^{\\scriptscriptstyle D}r \\ d^{\\scriptscriptstyle D} r' \\, \\delta n({\\bf r}) \\, U({\\bf r}-{\\bf r}') \\, \\delta n({\\bf r}').", "\n\\label{interaction hamiltonian}$$ Here ${\\bf \\Pi} \\equiv {\\bf p} + {\\textstyle{e \\over c}} {\\bf A}$, and $v({\\bf r})$ is any single-particle potential, which may include a periodic lattice potential or disorder or both, and which also includes the Hartree interaction with the self-consistent density $n_0({\\bf r})$. The interaction term is written in terms of the density fluctuation $$\\delta n({\\bf r}) \\equiv \\sum_\\sigma \\psi^\\dagger_\\sigma({\\bf r}) \n\\psi_\\sigma({\\bf r}) \\ - \\ n_0({\\bf r}).$$ Following Ref.", " , we use a Hubbard-Stratonovich transformation to write the exact Euclidean propagator $$G({\\bf r}_{\\rm f}\\sigma_{\\rm f},{\\bf r}_{\\rm i} \\sigma_{\\rm i},\\tau_0) \\equiv - \\big\\langle T \\psi_{\\sigma_{\\rm f}}({\\bf r}_{\\rm f} \n, \\tau_0) {\\bar \\psi}_{\\sigma_{\\rm i}}({\\bf r}_{\\rm i} ,0) \\big\\rangle_{\\! ", "H},\n\\label{G definition}$$ in the form $$G({\\bf r}_{\\rm f} \\sigma_{\\rm f}, {\\bf r}_{\\rm i} \\sigma_{\\rm i},\\tau_0) = {\\cal N} \\, {\\int \\! ", "D\\phi \\, e^{-{1 \\over 2} \\! ", " \\int \\! ", "\\phi {U}^{-1} \\! ", "\\phi} \ng({\\bf r}_{\\rm f} \\sigma_{\\rm f}, {\\bf r}_{\\rm i} \\sigma_{\\rm i}, \\tau_0 | \\phi) \\over \\int \\! ", "D\\phi \\, e^{-{1 \\over 2} \\! ", "\\int \\! ", "\\phi {U}^{-1} \\! ", "\\phi}} \n\\label{exact form}$$ where $$g(\\phi) \\equiv - \\big\\langle T \\psi_{\\sigma_{\\rm f}}({\\bf r}_{\\rm f},\\tau_0)\n{\\bar \\psi}_{\\sigma_{\\rm i}}({\\bf r}_{\\rm i},0) \\, e^{i \\int \\! ", "\\phi({\\bf r},\\tau) \\, \\delta n({\\bf r},\\tau) } \\big\\rangle_0 \n\\label{correlation function definition}$$ is a noninteracting correlation function in the presence of a purely imaginary scalar potential $i\\phi({\\bf r},\\tau)$, and ${\\cal N} \\equiv \\langle T \n\\exp(-\\int_0^\\beta d \\tau \\, V) \\rangle_0^{-1}$ is a constant, independent of $\\tau_{0}$. Eq.", " (\\[exact form\\]) is an exact expression for the interacting Green’s function.", "\n\nThe region of function space that contributes to the functional integrals in (\\[exact form\\]) is controlled by the width of the Gaussian, which in the small $U$ limit becomes strongly localized around $\\phi=0$. By expanding (\\[correlation function definition\\]) in powers of $\\phi$ and doing the functional integrals term by term, one simply recovers the standard perturbative expansion for $G({\\bf r}_{\\rm f}\\sigma_{\\rm f},{\\bf r}_{\\rm i} \\sigma_{\\rm i},\\tau_0)$ in powers of $U$. Therefore, it will be necessary to go beyond a perturbative expansion for $g({\\bf r}_{\\rm f} \\sigma_{\\rm f}, {\\bf r}_{\\rm i} \\sigma_{\\rm i},\\tau_0 | \\phi)$. We evaluate $g({\\bf r}_{\\rm f} \\sigma_{\\rm f}, {\\bf r}_{\\rm i} \\sigma_{\\rm i},\\tau_0 | \\phi)$ approximately, using a second-order functional cumulant expansion. ", "Such an expansion amounts to a resummation of the most divergent terms in the perturbation series when $\\phi=\\phi_{\\rm xr}$ and the infrared catastrophe occurs. ", "Indeed, one can view our resulting expression for $g({\\bf r}_{\\rm f} \\sigma_{\\rm f}, {\\bf r}_{\\rm i} \\sigma_{\\rm i},\\tau_0 | \\phi)$ as a functional generalization of Mahan’s “perturbative\" result for a similar correlation function.[@MahanPR67] Furthermore, for field configurations far from $\\phi_{\\rm xr}$, the cumulant expansion will yield a result that is, by construction, exact through second order in $U$. After carrying this out we obtain $$\\begin{aligned}\ng(\\phi) &\\approx& G_0({\\bf r}_{\\rm f} \\sigma_{\\rm f}, {\\bf r}_{\\rm i} \\sigma_{\\rm i}, \\tau_0) \\nonumber \\\\\n&\\times& e^{ \\int C_1({\\bf r} \\tau) \\, \\phi({\\bf r},\\tau) + \\int C_2({\\bf r} \\tau, {\\bf r}' \\tau' ) \\, \\phi({\\bf r},\\tau) \\, \\phi({\\bf r}', \\tau') },\n\\label{cumulant expansion}\\end{aligned}$$ where $$C_1({\\bf r} \\tau) = { g_1({\\bf r} \\tau) \\over \nG_0({\\bf r}_{\\rm f} \\sigma_{\\rm f},{\\bf r}_{\\rm i} \\sigma_{\\rm i},\\tau_0)}$$ and $$C_2({\\bf r} \\tau, {\\bf r}' \\tau' ) = { g_2({\\bf r} \\tau , {\\bf r}' \n\\tau') \\over \nG_0({\\bf r}_{\\rm f} \\sigma_{\\rm f},{\\bf r}_{\\rm i} \\sigma_{\\rm i},\\tau_0)} -\n{ g_1({\\bf r} \\tau) \\, g_1({\\bf r}' \\tau') \\over 2 \\, \n[G_0({\\bf r}_{\\rm f} \\sigma_{\\rm f},{\\bf r}_{\\rm i} \\sigma_{\\rm i},\\tau_0)]^2}.$$ Here $$\\begin{aligned}\n&g_n({\\bf r}_1 \\tau_1 , \\cdots , {\\bf r}_n \\tau_n) \\equiv \\nonumber\\\\ &- \\, \n{i^n \\over n!} \\, ", "\\big\\langle T \\psi_{\\sigma_{\\rm f}}({\\bf r}_{\\rm f} ,\\tau_0)\n{\\bar \\psi}_{\\sigma_{\\rm i}}({\\bf r}_{\\rm i} ,0) \\, \\delta n({\\bf r}_1 \\tau_1) \\,\n\\cdots \\, \\delta n({\\bf r}_n \\tau_n) \\big\\rangle_0 \\end{aligned}$$ is the coefficient of $\\phi^n$ appearing in the perturbative expansion of (\\[correlation function definition\\]), as in $$\\begin{aligned}\ng&({\\bf r}_{\\rm f} \\sigma_{\\rm f}, {\\bf r}_{\\rm i} \\sigma_{\\rm i},\\tau_0\n| \\phi) = G_0({\\bf r}_{\\rm f} \\sigma_{\\rm f}, {\\bf r}_{\\rm i} \\sigma_{\\rm i},\n\\tau_0) \\nonumber \\\\ +&\\sum_{n=1}^\\infty \\int g_n({\\bf r}_1 \\tau_1, \\cdots, \n{\\bf r}_n \\tau_n) \\, \\phi({\\bf r}_1,\\tau_1) \\cdots \\phi({\\bf r}_n,\\tau_n).", "\n\\label{formal perturbation expansion}\\end{aligned}$$ The cumulants $C_1$ and $C_2$ in terms of $G_{0}$ are $$C_1({\\bf r} \\tau) = - i\\sum_\\sigma\n{G_0({\\bf r}_{\\rm f} \\sigma_{\\rm f}, {\\bf r} \\sigma , \\tau_0 - \\tau) \\, \nG_0({\\bf r} \\sigma , {\\bf r}_{\\rm i} \\sigma_{\\rm i}, \\tau) \\over \nG_0({\\bf r}_{\\rm f} \\sigma_{\\rm f}, {\\bf r}_{\\rm i} \\sigma_{\\rm i}, \\tau_0)}$$ and (suppressing spin for clarity) $$\\begin{aligned}\n&C_2({\\bf r} \\tau,{\\bf r}' \\tau')=\\frac{1}{2G_0({\\bf r}_{\\rm f}, {\\bf r}_{\\rm i}, \\tau_0)^{2}}\\nonumber \\\\ & \\times\\Big\\{[G_0({\\bf r}, {\\bf r}', \\tau-\\tau')G_0({\\bf r}_{\\rm f}, {\\bf r}_{\\rm i}, \\tau_0)\\nonumber \\\\ & -G_0({\\bf r}, {\\bf r}_{\\rm i}, \\tau)G_0({\\bf r}_{\\rm f}, {\\bf r}', \\tau_0-\\tau')][{\\bf r}\\leftrightarrow {\\bf r}',\\tau \\leftrightarrow\\tau']\\Big\\}\\end{aligned}$$\n\nThe functional integral in (\\[exact form\\]) can now be done exactly, leading to $$G({\\bf r}_{\\rm f} \\sigma_{\\rm f}, {\\bf r}_{\\rm i} \\sigma_{\\rm i},\\tau_0)\n= {\\cal A}(\\tau_0) \\ G_0({\\bf r}_{\\rm f} \\sigma_{\\rm f}, {\\bf r}_{\\rm i} \n\\sigma_{\\rm i},\\tau_0) \\ e^{-S(\\tau_0)}, \n\\label{general result}$$ where $$\\begin{aligned}\n{\\cal A} & \\equiv {\\cal N} \\, {\\int D\\phi \\ e^{-{1 \\over 2} \\int \\phi ({ U}^{-1}\n- 2 C_2) \\phi} \\over \\int D\\phi \\ e^{-{1 \\over 2} \\int \\phi { U}^{-1} \\phi}}\n\\nonumber \\\\ &= {\\cal N} \\big[ \\det\\, (1-2 C_2 { U}) \\big]^{-{1 \\over 2}} , \n\\label{A definition}\\end{aligned}$$ and $$S \\equiv {1 \\over 2} \\int_0^\\beta \\! \\! ", "d\\tau \\, d\\tau' \\! ", " \\int \\! ", "d^{\\scriptscriptstyle D}r \\, d^{\\scriptscriptstyle D}r' \\rho({\\bf r},\\tau) \\, \nU_{\\rm eff}({\\bf r} \\tau, {\\bf r}' \\tau') \\, \\rho({\\bf r}',\\tau'). ", "\n\\label{action}$$ Here $$\\begin{aligned}\n&\\rho({\\bf r},\\tau) \\equiv -i \\, C_1({\\bf r} \\tau) \\\\& = - \\sum_\\sigma {G_0({\\bf r}_{\\rm f} \\sigma_{\\rm f}, {\\bf r} \\sigma , \\tau_0 - \\tau) \\, \nG_0({\\bf r} \\sigma , {\\bf r}_{\\rm i} \\sigma_{\\rm i}, \\tau) \\over G_0({\\bf r}_{\\rm f} \\sigma_{\\rm f}, {\\bf r}_{\\rm i} \\sigma_{\\rm i}, \\tau_0)} ,\n\\label{tunneling charge definition}\\end{aligned}$$ and $$U_{\\rm eff}({\\bf r} \\tau, {\\bf r}' \\tau') \\equiv \\big[{ U}^{-1}({\\bf r}- {\\bf r}') \\delta(\\tau- \\tau') - 2 C_2({\\bf r} \\tau, {\\bf r}' \\tau') \n\\big]^{-1}\n\\label{Ueff definition}$$ is a screened interaction.", "\n\nBecause spin-orbit coupling has been neglected in $H$, the noninteracting Green’s function is diagonal in spin, and $$\\begin{aligned}\n\\rho({\\bf r},\\tau) = - \n{G_0({\\bf r}_{\\rm f} \\sigma_{\\rm i}, {\\bf r} \\sigma_{\\rm i}, \\tau_0 - \\tau) \\, G_0({\\bf r} \\sigma_{\\rm i} , {\\bf r}_{\\rm i} \\sigma_{\\rm i}, \\tau) \\over \nG_0({\\bf r}_{\\rm f} \\sigma_{\\rm i}, {\\bf r}_{\\rm i} \\sigma_{\\rm i}, \\tau_0)} \\ \\delta_{\\sigma_{\\rm i} \\sigma_{\\rm f}} .", "\n\\label{tunneling charge with spin conserved}\\end{aligned}$$ Eq.", " (\\[general result\\]) is the principal result of this work.", "\n\nCHARGE SPREADING INTERPRETATION\n===============================\n\nWe interpret (\\[general result\\]) as follows: $S$ is the Euclidean action[@functionalnote] for a time-dependent charge distribution $\\rho({\\bf r},\\tau)$. We shall show that $\\rho({\\bf r},\\tau)$ acts like a charge density associated with an electron being inserted at ${\\bf r}_{\\rm i}$ at $\\tau \\! ", "= \\! ", "0$ and removed at ${\\bf r}_{\\rm f}$ at $\\tau_0$. This charge density interacts via an effective interaction $U_{\\rm eff}({\\bf r} \\tau, {\\bf r}' \\tau')$ that accounts for the modification of the electron-electron interaction by dynamic screening.[@photonfootnote] Our result can therefore be regarded as a variant of the intuitive but phenomenological “charge spreading” picture of Spivak[@spivak] and of Levitov and Shytov.[@Levitov97] However, here the dynamics of $\\rho({\\bf r},\\tau)$ is completely determined by the mean-field Hamiltonian, and has the dynamics of essentially noninteracting electrons.", "\n\nFirst consider the integrated charge, $$\\begin{aligned}\nQ(\\tau) &\\equiv& \\int d^{\\scriptscriptstyle D}r \\ \\rho({\\bf r},\\tau) \\nonumber \\\\\n&=& -\\frac{\\int d^{\\scriptscriptstyle D}r\\ G_{0}({\\bf r}_{\\rm f},{\\bf r},\\tau_{0}-\\tau)G_{0}({\\bf r},{\\bf r}_{\\rm i},\\tau)}{G_{0}({\\bf r}_{\\rm f},{\\bf r}_{\\rm i},\\tau_{0})}.", "\n\\label{integrated charge}\\end{aligned}$$ Using exact eigenfunction expansions for the Green’s functions we obtain\n\n$$Q(\\tau)= -\\frac{\\displaystyle\\sum_{\\alpha}\\Phi^{*}_{\\alpha}({\\bf r}_{\\rm f})\\Phi_{\\alpha}({\\bf r}_{\\rm i})e^{-(\\epsilon_{\\alpha}-\\mu)\\tau_{0}}\n\\left\\{[n_{\\rm F}(\\epsilon_{\\alpha}-\\mu)-1]^{2}\\Theta(\\tau_{0}-\\tau)\\Theta(\\tau)+n_{\\rm F}(\\epsilon_{\\alpha}-\\mu)[n_{\\rm F}(\\epsilon_{\\alpha}-\\mu)-1]\n\\left[\\Theta(-\\tau)+\\Theta(\\tau-\\tau_{0})\\right]\\right\\}}{\\displaystyle\\sum_{\\alpha}\\Phi^{*}_{\\alpha}({\\bf r}_{\\rm f})\\Phi_{\\alpha}({\\bf r}_{\\rm i})e^{-(\\epsilon_{\\alpha}-\\mu)\\tau_{0}}[n_{\\rm F}(\\epsilon_{\\alpha}-\\mu)-1]}.$$\n\nwhere $n_{\\rm F}$ is the Fermi distribution function and the $\\Phi_\\alpha$ are the single-particle eigenfunctions of $H_0$. In the zero temperature limit $$Q(\\tau)=-\\frac{\\displaystyle\\sum_{\\alpha}\\Phi^{*}_{\\alpha}({\\bf r}_{\\rm f})\\Phi_{\\alpha}({\\bf r}_{\\rm i})e^{-(\\epsilon_{\\alpha}-\\mu)\\tau_{0}}\\left\\{(N_{\\alpha}-1)^{2}\\Theta(\\tau_{0}-\\tau)\\Theta(\\tau)+N_{\\alpha}(N_{\\alpha}-1)\\left[\\Theta(-\\tau)+\n \\Theta(\\tau - \\tau_{0})\\right]\\right\\}}{\\displaystyle\\sum_{\\alpha}\\Phi^{*}_{\\alpha}({\\bf r}_{\\rm f})\\Phi_{\\alpha}({\\bf r}_{\\rm i})e^{-(\\epsilon_{\\alpha}-\\mu)\\tau_{0}}(N_{\\alpha}-1)},\n\\label{general sum rule}$$\n\nwhere $N_{\\alpha}$ is the ground-state occupation number of state $\\alpha$, which in the absence of ground state degeneracy takes the value of $0$ or $1$. In this case (\\[general sum rule\\]) reduces to $$Q(\\tau) = \\Theta(\\tau_0 - \\tau)\\Theta(\\tau).", "\n\\label{sum rule}$$ When the sum rule (\\[sum rule\\]) holds, the net added charge, as described by $\\rho({\\bf r},\\tau)$, is unity (in units of the electron charge) for times between $0$ and $\\tau_{0}$, and zero otherwise. ", "This behavior correctly mimics the action of the field operators in (\\[G definition\\]).", "\n\nAt short times, $\\tau \\ll \\tau_0$, the charge density is approximately $$\\rho({\\bf r},\\tau) \\sim -G_{0}({\\bf r},{\\bf r}_{\\rm i},\\tau)$$ which is localized around ${\\bf r}={\\bf r}_{\\rm i}$. As time evolves this distribution relaxes. ", "Then as $\\tau$ approaches $\\tau_{0}$ the charge density again becomes localized around ${\\bf r}={\\bf r}_{\\rm f},$ $$\\rho({\\bf r},\\tau)\\sim -G_{0}({\\bf r}_{\\rm f},{\\bf r},\\tau_0 -\\tau).$$ A plot of $\\rho({\\bf r},\\tau)$ for the 1D electron gas is given in Fig.", " \\[rhofig\\].", "\n\n![", "\\[rhofig\\] Charge density $\\rho (x,\\tau)$ for the 1D electron gas at two times, showing Friedel oscillations and gradual spreading.](fig1.eps){width=\"8.0cm\"}\n\nThe dynamics of $\\rho({\\bf r},\\tau)$ can be shown to be governed by the equation of motion $$\\left[\\partial_{\\tau}+H_{0}({\\bf r})\\right]\\rho({\\bf r},\\tau)=-\\delta({\\bf r}_{\\rm f}-{\\bf r})\\delta({\\tau}_{0}-\\tau')+\\delta({\\bf r}-{\\bf r}_{\\rm i})\\delta({\\tau}).", "\n\\label{equation of motion}$$ This can be seen by noting that the noninteracting Green’s function satisfies $$\\left[\\partial_{\\tau}+H_{0}({\\bf r})\\right]G_{0}({\\bf r},{\\bf r'},\\tau,\\tau')=-\\delta({\\bf r}-{\\bf r}')\\delta({\\tau}-\\tau').$$ Then, using the definition (\\[tunneling charge definition\\]) one can obtain (\\[equation of motion\\]). ", "Again, we stress that $\\rho({\\bf r},\\tau)$ is describing the dynamics of noninteracting electrons, governed by the mean-field Hamiltonian $H_0$.\n\nAlthough $\\rho({\\bf r},\\tau)$ has many properties that make it reasonable to interpret as the charge density associated with the added and subsequently removed electron in the Green’s function (\\[G definition\\]), one should not take this interpretation too literally. ", "For instance, the sum rule (\\[sum rule\\]) only holds in the zero temperature limit and in the absence of ground state degeneracy. ", "Also, as will be seen below in Sec.", " \\[TL model section\\], $\\rho({\\bf r},\\tau)$ may even be complex valued.", "\n\nAPPLICATIONS OF THE CUMULANT METHOD\n===================================\n\nIn the following examples we will assume electrons with a short-range interaction $U$, no disorder, and no magnetic field. ", "In Sec.", " \\[fermi liquid section\\] we show that our method correctly predicts a constant DOS near the Fermi energy in 2D and 3D, and in Sec.", " \\[luttinger liquid section\\] we obtain a power-law DOS in 1D, in qualitative agreement with Luttinger liquid theory.[@TomonagaPTP50; @MattisJMP65; @DzyaloshinskiiJETP74; @HaldaneJPC81; @HaldanePRL81; @KanePRB92; @Fisher97] Finally, in Sec.", " \\[TL model section\\] we use our method to calculate the DOS for the solvable Tomonaga-Luttinger model, obtaining the exact DOS exponent.", "\n\n2D and 3D electron gas: Recovery of the Fermi liquid phase {#fermi liquid section}\n----------------------------------------------------------\n\nThe sum rule (\\[sum rule\\]) allows one to determine the energy dependence of the DOS in $D$ dimensions, asymptotically in the low-energy limit, as follows: In the absence of disorder, a droplet of charge injected into a degenerate Fermi gas with velocity $v_{\\rm F}$ will relax to a size of order $\\ell \\sim v_{\\rm F} \\tau$ after a time $\\tau$. Approximating $\\rho({\\bf r},\\tau)$ to be of uniform magnitude in a region of size $\\ell$ and vanishing elsewhere, the sum rule then requires the magnitude or $\\rho$ to vary as $\\ell^{-D} \\! ", ".$ The interaction energy of such a charge distribution (assuming a short-range interaction) is $$E = {U \\over 2} \\int d^{\\scriptscriptstyle D}r \\, [\\rho({\\bf r})]^2 \\sim \\frac{U}{\\ell^D},$$ which varies with time as $\\tau^{-D}$. The action accumulated up to time $\\tau_0$ therefore scales as $$S \\sim \\frac{U}{\\tau_0^{D-1}} \\ \\ \\ \\ {\\rm if} \\ \\ \\ \\ D\\ge2 \n\\label{FL spreading}$$ or $$S \\sim U \\ln \\tau_0 \\ \\ \\ \\ {\\rm if} \\ \\ \\ \\ D=1. ", "\n\\label{LL spreading}$$\n\nThe cases (\\[FL spreading\\]) and (\\[LL spreading\\]) are dramatically different: In 2D and 3D the action vanishes a long times, and the propagator (\\[general result\\]) is therefore not appreciably affected by interactions. ", "The resulting DOS is energy independent at low energies, and the expected Fermi liquid behavior is recovered. ", "In 1D, however, the action diverges logarithmically, leading to an algebraic DOS.", "\n\n1D electron gas: Recovery of the Luttinger liquid phase {#luttinger liquid section}\n-------------------------------------------------------\n\nThe scaling argument of the previous section showed that the DOS in the 1D electron gas with short-range interaction is algebraic, as expected. ", "In this section we calculate the associated exponent.", "\n\nWe proceed in two stages. ", "Initially we keep only the first cumulant $C_1$, and then afterwards we discuss the effect of $C_2$. In 1D it is possible to calculate the action (\\[action\\]) exactly in the long-time asymptotic limit at the first-cumulant level. ", "Setting $x_{\\rm f}=x_{\\rm i}=0$, we have \\[see (\\[general result\\])\\] $$G(\\tau_0) = {\\rm const} \\times G_0(\\tau_0) \\ \\! ", "e^{-S(\\tau_{0})}.", "\n\\label{tree-level result}$$ Considering a local interaction of the form $U(x-x') = U_0 \\lambda \\delta(x-x')$ the action is $$S(\\tau_0) = {U_0 \\lambda \\over 2} \\int_0^\\beta \\! ", "d\\tau \\int_{-\\infty}^\\infty \\! ", "\ndx \\ \\! ", "\\big[ \\rho(x,\\tau) \\big]^2.", "\n\\label{1D action}$$ By linearizing the spectrum around the Fermi energy, the zero-temperature propagator at low energies is $$\\begin{aligned}\nG_0(x,\\tau) &=& {1 \\over \\pi} \\ \\! {", "\\rm Im} \\ \\! ", "\\bigg( {e^{i k_{\\rm F}x} \\over x \n+ i v_{\\rm F} \\tau } \\bigg) \\nonumber \\\\\n&=& {x \\sin k_{\\rm F}x - v_{\\rm F} \\tau \\cos k_{\\rm F}x \\over \\pi (x^2 + \nv_{\\rm F}^2 \\tau^2 )}.", "\n\\label{1D propagator}\\end{aligned}$$ The charge density (\\[tunneling charge definition\\]) in this case is $$\\begin{aligned}\n\\rho(x,\\tau) &=& {v_{\\rm F} \\tau_0 \\over \\pi} \\ \\! {", "x \\sin k_{\\rm F}x - v_{\\rm F} \n(\\tau_0 - \\tau) \\cos k_{\\rm F}x \\over x^2 + v_{\\rm F}^2 (\\tau - \\tau_0)^2} \n\\nonumber \\\\\n&\\times& {x \\sin k_{\\rm F}x - v_{\\rm F} \\tau \\cos k_{\\rm F}x \\over x^2 + \nv_{\\rm F}^2 \\tau^2}.\\end{aligned}$$ Fig.", " (\\[rhofig\\]) shows the charge density $\\rho(x,\\tau)$ as it spreads in time from its initially localized position.", "\n\nBy a lengthy but straightforward calculation it can be shown that $$S(\\tau_0) = {3 \\over 8 } {U_0 \\lambda \\over v_{\\rm F}\\pi} \\ln \\bigg({\\tau_0 \n\\over a}\\bigg) ,$$ where $a$ is a microscopic cutoff. ", "This leads to a power-law decay of the interacting propagator as $$G(\\tau) \\sim {1 \\over \\tau^\\alpha},$$ where $$\\alpha = {3 \\over 8} {U_0 \\lambda \\over v_{\\rm F}\\pi} + 1$$ is the propagator exponent. ", "The DOS exponent $\\delta$, defined as $$N(\\epsilon) = {\\rm const} \\times \\epsilon^\\delta,$$ is given in this case by $$\\delta = {3 \\over 8 } {U_0 \\lambda \\over v_{\\rm F}\\pi}.", "\n\\label{cumulant DOS exponent}$$\n\nThe effects of the second cumulant $C_2$ are now straightforward to understand: In addition to introducing a slowly varying prefactor ${\\cal A}$, whose only $\\tau_0$ dependence comes from the time dependence of the screening in (\\[Ueff definition\\]), the second cumulant screens the bare interaction and does not prevent the logarithmic divergence of the action, but it does modify the DOS exponent. ", "It is interesting, however, that in the large $U$ limit, the effective interaction becomes independent of $U,$ a clear indication of nonperturbative behavior.", "\n\nIt is illustrative to compare (\\[cumulant DOS exponent\\]) to the prediction of the perturbative x-ray edge limit of Ref.", " , where one neglects all field configurations in (\\[exact form\\]) except $\\phi_{\\rm xr}$. There we found (for this same short-range interaction model), $$\\delta=2 \\, {U_0 \\lambda \\over v_{\\rm F}\\pi} \n\\label{xray limit exponent}$$ to leading order in $U.$ The DOS exponents (\\[cumulant DOS exponent\\]) and (\\[xray limit exponent\\]) are in qualitative agreement, but the inclusion of fluctuations about $\\phi_{\\rm xr}$ in (\\[cumulant DOS exponent\\]) softens the exponent by almost a factor of four, as one might expect.", "\n\nThe exact DOS exponent is not known for this model. ", "In the next section we apply the cumulant method to the Tomonaga-Luttinger model, for which the exact propagator can be calculated using bosonization.", "\n\nTomonaga-Luttinger model\\[TL model section\\]\n--------------------------------------------\n\nWe consider the spinless or $U(1)$ Tomonaga-Luttinger model. ", "The noninteracting spectrum is $$\\epsilon_k = \\mu + v_{\\rm F}(\\pm k - k_{\\rm F}),$$ where the upper sign refers to the right branch and the lower to the left one. ", "The interaction is $$\\begin{aligned}\nV &=& {1 \\over 2} \\int dx \\ \\delta n_i(x) \\, U_{ij} \\, \\delta n_j(x) , \\\\ \n\\delta n_{\\pm}(x) &\\equiv& \\lim_{a \\rightarrow 0} : \\! ", "\\psi_{\\pm}(x+a) \n\\psi_{\\pm}(x) \\! :,", "\\end{aligned}$$ where the normal ordering is with respect to the noninteracting ground state. ", "The matrix $U$ has the form $${\\bf U}=\\left(\\begin{array}{cc}U_{4} & U_{2} \\\\U_{2} & U_{4}\\end{array}\\right).$$\n\nWe want to calculate $$G_{\\pm}(x_{\\rm f} \\tau_{\\rm f}, x_{\\rm i} \\tau_{\\rm i}) = - {\\cal N} \\, \n\\langle T \\psi_{\\pm}(x_{\\rm f},\\tau_{\\rm f}) {\\bar \\psi}_{\\pm}(x_{\\rm i}, \n\\tau_{\\rm i}) \\, e^{- \\int d\\tau V(\\tau)} \\rangle.$$ Make a Hubbard-Stratonovich transformation of the form $$e^{-{1 \\over 2} \\int \\delta n_i \\, U_{ij} \\, \\delta n_j} = {\\int D\\phi_{-} \\,\nD\\phi_{+} \\ e^{-{1 \\over 2} \\int \\phi_i U_{ij}^{-1} \\phi_j} \\, e^{i\\int \\phi_i\n\\, \\delta n_i} \\over \\int D\\phi_{-} \\, D\\phi_{+} \\ e^{-{1 \\over 2} \\int \\phi_i\nU_{ij}^{-1} \\phi_j}},\n\\label{TL Hubbard-Stratonovich transformation}$$ which leads to $$\\begin{aligned}\n&G_{\\pm}(x_{\\rm f} \\tau_{\\rm f}, x_{\\rm i} \\tau_{\\rm i}) =\\nonumber \\\\ & {\\cal N} \\, \n{\\int D\\phi_{-} \\, D\\phi_{+} \\ e^{-{1 \\over 2} \\int \\phi_i U_{ij}^{-1} \\phi_j}\n\\ g_{\\pm}(x_{\\rm f} \\tau_{\\rm f}, x_{\\rm i} \\tau_{\\rm i} | \\phi_{-},\\phi_{+}) \\over \\int D\\phi_{-} \\, D\\phi_{+} \\ e^{-{1 \\over 2} \\int \n\\phi_i U_{ij}^{-1} \\phi_j}} ,\n\\label{TL exact form}\\end{aligned}$$ where $$\\begin{aligned}\n&g_{\\pm}(x_{\\rm f} \\tau_{\\rm f}, x_{\\rm i} \\tau_{\\rm i} |\\phi_{+},\\phi_{-} ) \\equiv \\nonumber \\\\ &-\n\\big\\langle T \\psi_{\\pm}(x_{\\rm f} \\tau_{\\rm f}) {\\bar \\psi}_{\\pm}(x_{\\rm i} \n\\tau_{\\rm i}) \\, e^{i \\int_0^\\beta d \\tau \\int dx \\, \\phi_{i}(x,\\tau) \\, \n\\delta n_{i}(x,\\tau) } \\big\\rangle_0. ", "\n\\label{TL correlation function definition}\\end{aligned}$$ The correlation function (\\[TL correlation function definition\\]) can also be written as $$g_{\\pm}(x_{\\rm f} \\tau_{\\rm f}, x_{\\rm i} \\tau_{\\rm i}| \\phi_{+},\\phi_{-}) = g_{\\pm}\n(x_{\\rm f} \\tau_{\\rm f}, x_{\\rm i} \\tau_{\\rm i}| \\phi_{\\pm}) \\cdot \nZ_{\\mp}[\\phi_{\\mp}],$$ where $$Z_{\\pm}[\\phi_{\\pm}] \\equiv \\big\\langle T e^{i \\int_0^\\beta d \\tau \\int dx \\, \\phi_{\\pm}(x,\n\\tau) \\, \\delta n_{\\pm}(x,\\tau) } \\big\\rangle_{{0,\\pm}},\n\\label{TL effective partition function}$$ and $$\\begin{aligned}\n&g_{\\pm}(x_{\\rm f} \\tau_{\\rm f}, x_{\\rm i} \\tau_{\\rm i} |\\phi_{\\pm}) =\\nonumber \\\\ &-\n\\big\\langle T \\psi_{\\pm}(x_{\\rm f} \\tau_{\\rm f}) {\\bar \\psi}_{\\pm}(x_{\\rm i} \n\\tau_{\\rm i}) \\, e^{i \\int_0^\\beta d \\tau \\int dx \\, \\phi_{\\pm}(x,\\tau) \\, \n\\delta n_{\\pm}(x,\\tau) } \\big\\rangle_{{0,\\pm}}. ", "\n\\label{reduced TL correlation function definition}\\end{aligned}$$ Next we cumulant expand both (\\[TL effective partition function\\]) and (\\[reduced TL correlation function definition\\]) to second order. ", "For (\\[TL effective partition function\\]) $$Z_{\\pm}[\\phi_{\\pm}] \\approx e^{\\frac{1}{2}\\int d \\tau d\\tau' \\int dx dx' \\,\\Pi_{\\pm}(x-x',\\tau-\\tau')\\phi_{\\pm}\\phi'_{\\pm}}$$ Where $\\Pi_{\\pm}$ is the noninteracting density-density correlation function $$\\Pi_{\\pm}(x,\\tau) \\equiv - \\big\\langle T \\delta n_{\\pm}(x,\\tau) \\, \n\\delta n_{\\pm}(0) \\big\\rangle_{0,\\pm} ,\n\\label{TL polarization definition}$$ which can be written as $$\\Pi_{\\pm}(x,\\tau) = G_{0,\\pm}(x, \\tau) \\, G_{0,\\pm}(-x,-\\tau).$$ The noninteracting chiral propagator is $$G_{0,\\pm}(x, \\tau) = \\pm {1 \\over 2 \\pi i} \\ {e^{\\pm i k_{\\rm F} x} \\over x \\pm\ni v_{\\rm F} \\tau}.$$ For (\\[reduced TL correlation function definition\\]) $$\\begin{aligned}\n&g_{\\pm}(x_{\\rm f} \\tau_{\\rm f}, x_{\\rm i} \\tau_{\\rm i} | \\phi_{\\pm})\\approx G_{0,\\pm}(x_{\\rm f} \\tau_{\\rm f}, x_{\\rm i} \\tau_{\\rm i} | \\phi_{\\pm}) \\nonumber \\\\\n& \\times e^{\\int dx d\\tau\\, C_{1,\\pm}\\phi_{\\pm}+\\int dxdx' d\\tau d\\tau'\\, C_{2,\\pm}\\phi_{\\pm}\\phi'_{\\pm}}\\end{aligned}$$ where $$C_{1,\\pm}(x,\\tau)=-i{G_{0,\\pm}(x_{\\rm f}, x, \\tau_0 - \\tau) \\, G_{0,\\pm}(x, x_{\\rm i}, \\tau),\n\\over G_{0,\\pm}(x_{\\rm f}, x_{\\rm i}, \\tau_0)}$$ and $C_{2,\\pm}$ for this model reduces to $$C_{2,\\pm}(x-x',\\tau-\\tau')=\\frac{1}{2}\\,\\Pi_{\\pm}(x-x',\\tau-\\tau').$$\n\nNow we solve for $U_{\\rm eff},$ defined by $$\\begin{aligned}\n&\\int dx''d\\tau''{\\bf U}_{\\rm eff}^{-1}(x-x'',\\tau-\\tau''){\\bf U}_{\\rm eff}(x''-x',\\tau''-\\tau')=\\nonumber \\\\\n&\\delta(x-x')\\delta(\\tau-\\tau')\\openone,\n\\label{TL Ueff}\\end{aligned}$$ where $$\\begin{aligned}\n&U^{\\rm eff}_{ij}(x,\\tau)=\\nonumber \\\\ &\\left[{U}_{ij}^{-1}(x,\\tau)-{\\Pi}_{\\pm}(x,\\tau)\\delta_{i+}\\delta_{j+}-{\\Pi}_{\\mp}(x,\\tau)\\delta_{i-}\\delta_{j-}\\right]^{-1}\\end{aligned}$$ and $\\openone$ is a $2\\times 2$ identity matrix. ", "To achieve this we Fourier transform (\\[TL Ueff\\]). ", "This reduces (\\[TL Ueff\\]) to a matrix equation which gives $${\\bf U}_{\\rm eff}(k,\\omega)=\\left[ \\left(\\begin{array}{cc}U_{4} & U_{2} \\\\U_{2} & U_{4}\\end{array}\\right)^{-1}-\\left(\\begin{array}{cc}\\Pi_{\\pm}(k,\\omega) & 0 \\\\0 & \\Pi_{\\mp}(k,\\omega)\\end{array}\\right)\\right]^{-1}.$$ The $++$ or $--$ component is $$U_{\\rm eff}(k,\\omega)=\\frac{U_{4}-(U^{2}_{4}-U^{2}_{2})\\Pi_{\\mp}(k,\\omega)}{1-U_{4}\\Pi_{t}(k,\\omega)+(U^{2}_{4}-U^{2}_{2})\\Pi_{+}(k,\\omega)\\Pi_{-}(k,\\omega)}$$ where $$\\Pi_{\\rm t}(k,\\omega) =\\Pi_{+}(k,\\omega)+\\Pi_{-}(k,\\omega)=\n- {1 \\over \\pi} \\, { k^2 \\over (\\omega + ik) (\\omega - ik) }.$$ The effective interaction for right movers is (with $v_{\\rm F}=1$) $$U_{\\rm eff}(k,\\omega) = U_4 \\, {(\\omega + ik) ( \\omega - i u k) \\over \n(\\omega + i v k) (\\omega - i v k) },$$ where $$u \\equiv 1 + {(U_4 / 2 \\pi)^2 - (U_2/2 \\pi)^2 \\over (U_4 / 2 \\pi)}$$ and $$v \\equiv \\sqrt{ \\bigg( 1 + {U_4 \\over 2 \\pi} \\bigg)^2 - \n\\bigg( {U_2 \\over 2 \\pi} \\bigg)^2 }.$$ The action can be written as $$S = {1 \\over 2} \\int {dk \\over 2 \\pi} {d \\omega \\over 2 \\pi} \\ \n\\rho_{\\pm}(-k, -\\omega) \\, U_{\\rm eff}(k,\\omega) \\, \\rho_{\\pm}(k, \\omega).", "\n\\label{TL action}$$ The chiral tunneling charge density is $$\\rho_{\\pm}(x,\\tau) = - {G_{0,\\pm}(x_{\\rm f}, x, \\tau_0 - \\tau) \\, G_{0,\\pm}(x, x_{\\rm i}, \\tau)\n\\over G_{0,\\pm}(x_{\\rm f}, x_{\\rm i}, \\tau_0)}.$$\n\nWe now specialize to the DOS case where $x_{\\rm i} = x_{\\rm f} = 0$ and assuming right movers we set $\\rho_{+}\\equiv \\rho$. The tunneling charge density is $$\\rho(x, \\tau ) = {v_{\\rm F} \\tau_0 \\over 2 \\pi}{1 \\over (x + i v_{\\rm F} \\tau)\n[x + i v_{\\rm F} (\\tau - \\tau_0)]},$$ which satisfies $$\\int dx \\ \\rho(x, \\tau ) = \\Theta(\\tau) \\, \\Theta(\\tau_0 - \\tau).$$\n\nFourier transforming, we find that $$\\rho(k,\\omega) = {1 \\over i \\omega - v_{\\rm F}k} \\big[ \\big(e^{i \\omega \n\\tau_0} -1 \\big) \\, \\Theta(k) + \\big( e^{i \\omega \\tau_0} - e^{v_{\\rm F} k \n\\tau_0} \\big) \\Theta(-k) \\big]$$ and $$\\rho(k,\\omega) \\, \\rho(-k,-\\omega) = {1 \\over (\\omega +ik)^2} \\bigg[ \\bigg(\n1 - e^{i \\omega \\tau_0} e^{- k \\tau_0} + e^{-k \\tau_0} - e^{-i \\omega \\tau_0}\n\\bigg) \\Theta(k) + \\bigg(1 - e^{i \\omega \\tau_0} + e^{k \\tau_0} - \ne^{-i \\omega \\tau_0} e^{k \\tau_0} \\bigg) \\Theta(-k) \\bigg].$$ The action therefore is $$\\begin{aligned}\nS(\\tau_{0})=&{1 \\over 2} \\int {dk \\over 2 \\pi} {d \\omega \\over 2 \\pi}\\, {(\\omega + ik) ( \\omega - i u k) \\over \n(\\omega + i v k) (\\omega - i v k) } \\ {U_4 \\over (\\omega +ik)^2}\\nonumber \\\\ &\\times \\bigg[ \\bigg(\n1 - e^{i \\omega \\tau_0} e^{- k \\tau_0} + e^{-k \\tau_0} - e^{-i \\omega \\tau_0}\n\\bigg) \\Theta(k) + \\bigg(1 - e^{i \\omega \\tau_0} + e^{k \\tau_0} - \ne^{-i \\omega \\tau_0} e^{k \\tau_0} \\bigg) \\Theta(-k) \\bigg].\\end{aligned}$$ The action maybe written as $S=S_{>}+S_{<}$ where $$\\label{pos action}\nS_{>}=\\frac{U_{4}}{8 \\pi^2}\\int\\limits_{0^+}^{\\infty}dk\\,\\int\\limits_{-\\infty}^{\\infty}d\\omega \\, { ( \\omega - i u k) \\over \n(\\omega + i v k) (\\omega - i v k) (\\omega+ik)}\\bigg(\n1 - e^{i \\omega \\tau_0} e^{- k \\tau_0} + e^{-k \\tau_0} - e^{-i \\omega \\tau_0}\n\\bigg)$$ and $$S_{<}=\\frac{U_{4}}{8 \\pi^2}\\int\\limits_{-\\infty}^{0^-}dk\\,\\int\\limits_{-\\infty}^{\\infty}d\\omega \\,\\, { ( \\omega - i u k) \\over \n(\\omega + i v k) (\\omega - i v k) (\\omega+ik)}\\bigg(1 - e^{i \\omega \\tau_0} + e^{k \\tau_0} - \ne^{-i \\omega \\tau_0} e^{k \\tau_0} \\bigg).$$\n\n$S_{>}=S_{<}$ under change of coordinates $k\\rightarrow -k$ and $\\omega \\rightarrow -\\omega$, so $S=2S_{>}$. To proceed we need the large-$\\tau_0$ asymptotic result $$I(\\tau_0) \\equiv \\int_{0^+}^\\infty dk \\ {e^{-k \\tau_0} \\over k}\n\\longrightarrow - \\ln \\tau_0$$ where the additive constant, not shown explicitly, is cutoff dependent. ", "These lead, in the large $\\tau_0$ limit, to $$S=\\frac{U_4}{4\\pi}\\left[\\frac{2(1+u)}{(1+v)(1-v)}-\\frac{u+v}{v(1-v)}\\right]\\ln(\\tau_{0})$$ or $$S=\\frac{U_4}{4\\pi}\\left[\\frac{v-u}{v(1+v)}\\right]\\ln(\\tau_{0}).$$ Finally, we obtain $$S = \\delta \\ln \\tau_0 + {\\rm const} + O(1/\\tau_0)$$ and $$N(\\epsilon) = {\\rm const} \\times \\epsilon^\\delta ,$$ where $$\\begin{aligned}\n\\delta &=& {U_4 \\over 4 \\pi} \\ {v-u \\over v(1+v)} = {(u-v)(1-v) \n\\over 2 v(1+u)} \\\\ \n&=& {1 + {U_4 \\over 2 \\pi v_{\\rm F}} - \\sqrt{ \\big(1 + {U_4 \\over 2 \\pi \nv_{\\rm F}} \\big)^2 - \\big({U_2 \\over 2 \\pi v_{\\rm F}} \\big)^2 } \\over 2 \\sqrt{ \n\\big(1 + {U_4 \\over 2 \\pi v_{\\rm F}} \\big)^2 - \\big({U_2 \\over 2 \\pi \nv_{\\rm F}} \\big)^2 }} .\\end{aligned}$$ This is in exact agreement with the bosonization result $$\\delta = {g + g^{-1} \\over 2} - 1$$ with $$g = \\sqrt{{1 + {U_4 \\over 2 \\pi v_{\\rm F}} - {U_2 \\over 2 \\pi v_{\\rm F}} \\over\n1 + {U_4 \\over 2 \\pi v_{\\rm F}} + {U_2 \\over 2 \\pi v_{\\rm F}}}}.$$\n\nWhy does the cumulant method give the exact result for this model? ", "The answer is that a second order cumulant expansion of the form used here is exact for free bosons, which are the exact eigenstates of the Tomonaga-Luttinger model.[@vignalenote]\n\nDISCUSSION\n==========\n\nOur principal result (\\[general result\\]) suggests that the dominant effect of interaction on the low-energy DOS in a variety of strongly correlated electron systems is to add a semiclassical time-dependent charging energy contribution to the total potential barrier seen by a tunneling electron, as in Ref.", " . ", "The energy is computed according to classical electrostatics with a dynamically screened two-particle interaction. ", "In 2D and 3D the added charge is accommodated efficiently and reaches a zero-action state at long times. ", "In 1D the added charge leads to diverging action, and hence suppressed tunneling.", "\n\nThe robustness of our method has not been fully explored, although it is known to fail qualitatively in systems with ground state degeneracy, such as in the quantum Hall fluid. ", "We believe the cause of this failure to be the non-satisfiability of the sum rule (\\[sum rule\\]) in such situations. ", "In the future we plan to apply this method to other exactly solvable systems, such as the 1D Hubbard and Calogero-Sutherland models.", "\n\nThis work was supported by the National Science Foundation under CAREER Grant No.", " DMR-0093217, and by a Cottrell Scholars Award from the Research Corporation. ", "It is a pleasure to thank Phil Anderson, Matthew Grayson, Dmitri Khveshchenko, Allan MacDonald, Emily Pritchett, David Thouless, Shan-Ho Tsai, and Giovanni Vignale for useful discussions. ", "M.G. would also like to acknowledge the Aspen Center for Physics, where some of this work was carried out.", "\n" ]

{ "pile_set_name": "ArXiv" }

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[ "/*\n * Copyright 1992 by Jutta Degener and Carsten Bormann, Technische\n * Universitaet Berlin. ", " See the accompanying file \"COPYRIGHT\" for\n * details. ", " THERE IS ABSOLUTELY NO WARRANTY FOR THIS SOFTWARE.", "\n */\n\n#ifndef\tGSM_H\n#define\tGSM_H\n\n#include\t<stdio.h>\t\t/* for FILE * \t*/\n\n/*\n *\tInterface\n */\n\ntypedef struct gsm_state * \tgsm;\ntypedef short\t\t \t\tgsm_signal;\t\t/* signed 16 bit */\ntypedef unsigned char\t\tgsm_byte;\ntypedef gsm_byte \t\t\tgsm_frame[33];\t\t/* 33 * 8 bits\t */\n\n#define\tGSM_MAGIC\t\t0xD\t\t \t/* 13 kbit/s RPE-LTP */\n\n#define\tGSM_PATCHLEVEL\t\t10\n#define\tGSM_MINOR\t\t\t0\n#define\tGSM_MAJOR\t\t\t1\n\n#define\tGSM_OPT_VERBOSE\t\t1\n#define\tGSM_OPT_FAST\t\t2\n#define\tGSM_OPT_LTP_CUT\t\t3\n#define\tGSM_OPT_WAV49\t\t4\n#define\tGSM_OPT_FRAME_INDEX\t5\n#define\tGSM_OPT_FRAME_CHAIN\t6\n\ngsm gsm_create \t(void);\n\n/* Added for libsndfile : May 6, 2002 */\nvoid gsm_init (gsm);\t\n\nvoid gsm_destroy (gsm);\t\n\nint gsm_print (FILE *, gsm, gsm_byte *);\nint gsm_option (gsm, int, int *);\n\nvoid gsm_encode (gsm, gsm_signal *, gsm_byte *);\nint gsm_decode (gsm, gsm_byte *, gsm_signal *);\n\nint gsm_explode (gsm, gsm_byte *, gsm_signal *);\nvoid gsm_implode (gsm, gsm_signal *, gsm_byte *);\n\n#endif\t/* GSM_H */\n/*\n** Do not edit or modify anything in this comment block.", "\n** The arch-tag line is a file identity tag for the GNU Arch \n** revision control system.", "\n**\n** arch-tag: 8cfc7698-5433-4b6f-aeca-967c6fda4dec\n*/\n\n" ]

{ "pile_set_name": "Github" }

[ 0.031914893617021274, 0, 0, 0.007670182166826462, 0, 0 ]

[ "Legend:\n\nThe 'unordered-containers' package implements hashing-based containers that trade some functionality (lack of ordering) for speed. ", "The 'hashable' package provides a type class that, like Ord, is implemented by all types that can be used as keys in these containers." ]

{ "pile_set_name": "Pile-CC" }

[ 0, 0.007462686567164179 ]

[ "The present invention relates to a shielded device containment vessel for storing, transporting and detonating an explosive device and method of operating the same.", "\nBomb containment vessels are used for transporting and storing explosives, as well as containing an explosion. ", "Typically, containment vessels are spherical or rectangular units having an external shell and a series of reinforcements and shock absorbing material between the shells. ", "Containment vessels contain and absorb an explosion, accidental or intentional, to prevent damage to surrounding persons, environment, or structures. ", "However, if radioactive explosives are stored or detonated within the containment vessel, the containment vessel does not prevent dispersal of radiation from the vessel. ", "Thus, the containment vessel provides no protection to surrounding persons, environment, or structures from radiation exposure." ]

{ "pile_set_name": "USPTO Backgrounds" }

[ 0, 0, 0, 0, 0, 0 ]

[ "\"Come this way.\" \"", "Men wounded in battle we can deal with.\" \"", "But this strange disease....\" \"Thirty men dead yesterday.\" \"", "Eighteen, the day before.\" \"", "We need supplies.\" \"", "Plasma, penicillin.\" \"", "We'll get you everything you need, doctor.\" \"", "You're Americans.\" \"", "Please... get me out of this shithole.\" \"", "Hey, buddy, that's what we're here for.\" \"", "We're gonna take you home.\" \"", "But first we're gonna take a little blood sample, all right?\" \" ", "I'm gonna die, right?\" \" ", "No.\" \"", "You're not gonna die.\" \"", "Tell my girl I love her.\" \"", "I'm not gonna tell her.\" \"", "You're gonna tell her yourself, all right?\" \"", "The soldiers inside are in the early stages of the disease.\" \"", "By tomorrow night they will look like this.\" \"", "Mother of God.\" \"", "I'll authorize an immediate airdrop, doctor.\" \"", "It's even worse than I thought.\" \"", "Get the plane here by 1900 hours.\" \" ", "Well, shouldn't we at least--?\" \" ", "Get the plane, Billy.\" \"", "Come on.\" \"", "All right.\" \"", "Isn't this your last day?\" \"", "Yeah.\" \"", "I bet that feels good, right?\" \"", "Oh, come on, now, it's almost over.\" \"", "Almost over.\" \"", "That's it.\" \"", "Attaboy.\" \"", "Doesn't that feel good, Lewis?\" \"", "Doesn't that feel good?\" \"", "Oh, you're such a good boy.\" \"", "Yes.\" \"", "Come on.\" \"", "Sam, are you there?\" \"", "Pick up the phone if you're there.\" \"", "We got a situation in Zaire.\" \"", "It doesn't look good at all.\" \" ", "You guys stay there.\" \"", "I'll be right back.\" \" ", "Hemorrhagic fever, high mortality.\" \" ", "We picked up a satellite relay from Cairo.\" \" ", "I said stay!\" \"", "No!\" \" ", "Sam.\" \" ", "Hi, Billy.\" \"", "What's up?\" \"", "Looks like we have a Level 4, Sam.\" \" ", "How many dead?\" \" ", "Don't know.\" \"", "There aren't any numbers yet.\" \" ", "What do you think it is?\" \" ", "Too early to say.\" \"", "The World Health Organization is preparing a team, but I want you there first.\" \"", "Taking you off Hanta and flying you to Zaire.\" \"", "Okay, let me get my crew together.\" \"", "I'll get back to you.\" \"", "Bye.\" \"", "I can't believe this.\" \"", "You're wet.\" \"", "Right?\" \"", "You guys are wet.\" \"", "Which one disobeyed me first?\" \"", "Lewis, it was you, wasn't it?\" \"", "You guys are busted.\" \"", "You look very guilty.\" \"", "Come on.\" \"", "Lewis, come on.\" \"", "No.\" \"", "Sit down.\" \"", "How you doing?\" \"", "Hey, boys.\" \"", "Hey.\" \"", "How you doing, guys?\" \"", "How you doing, guys?\" \"", "What are you doing?\" \"", "Where are you?\" \"", "You miss me?\" \"", "Come here.\" \"", "Come here.\" \"", "Who wants some breakfast?\" \"", "Your paper.\" \"", "You here to get your stuff?\" \"", "Come on, boys.\" \"", "Bagels, huh?\" \"", "Who wants bagels?\" \"", "Who wants some breakfast?\" \" ", "Who wants some breakfast?\" \"", "Yeah.\" \" ", "I've, uh....\" \"I've got to go away.\" \"", "Where?\" \"", "Zaire.\" \"", "They think there's been some cases of hemorrhagic fever in a village there.\" \" ", "Is Casey going?\" \" ", "Yeah.\" \"", "And Jaffe.\" \"", "The whole crew.\" \"", "Most of it.\" \" ", "So you want me to take the dogs?\" \" ", "It's just three or four days.\" \"", "Okay, but I'm going to Atlanta on Friday.\" \"", "If you're late, the dogs go with me.\" \" ", "Fair enough.\" \" ", "Come on.\" \"", "What are you gonna be doing at CDC?\" \"", "Working BL-4.\" \"", "Same as you.\" \"", "My job.\" \"", "Well, I'd like to think of it as my job.\" \"", "And I won't have the Pentagon breathing down my neck.\" \" ", "This is mine.\" \" ", "Take it.\" \"", "And the rest of your stuff is in boxes in there.\" \"", "I can hang onto it till you come back... or whatever.\" \"", "You know that you're giving me all the pictures of us?\" \"", "Yeah.\" \"", "You can keep them.\" \"", "You keep them.\" \"", "I don't want them, Sam.\" \"", "Well, I don't want them either, Robby.\" \"", "Thursday.\" \"", "Oh, yeah.\" \"", "I want a turn-up.\" \"", "On the mark, lieutenant.\" \" ", "Yes, colonel.\" \" ", "Let's move it.\" \"", "Come on, let's go!\" \"", "Let's go!\" \"", "This plasma goes in the rig under the right wing.\" \" ", "Casey.\" \"", "Where is Jaffe?\" \" ", "Wife went into labor.\" \"", "I put him on leave.\" \" ", "Who's gonna read the tissue samples?\" \" ", "You don't trust me?\" \" ", "Come on.\" \" ", "Fine.\" \"", "You want the hotshot scope-jockey they sent out of Walter Reed?\" \"", "Frankly I'm hurt.\" \" ", "Who cut his orders?\" \" ", "The old man himself.\" \"", "Hasn't been up this early since Nixon was in office.\" \" ", "I'm gonna tell him you said that.\" \" ", "I'll deny it.\" \" ", "Good to see you, sir.\" \" ", "Sam.\" \"", "Thought if I showed my star around here it might speed things up for you.\" \" ", "Is it working?\" \" ", "No.\" \"", "Personnel file on your new man.\" \"", "Plus telex traffic to date, and satellite photos from the last bird over the area.\" \" ", "Sam.\" \" ", "Sir?\" \"", "Get in, get out.\" \"", "As much as I hate having you around to make my life miserable...\" \"I really don't want to lose you to some bug.\" \" ", "One question, sir.\" \" ", "Go on.\" \"", "What have I ever done to make your life miserable, sir?\" \"", "You got up this morning, didn't you?\" \"", "Thank you, Billy.\" \"", "Major Salt.\" \"", "May I say what an honor it is to have this opportunity\" \"Sit down.\" \"", "Your background's first-rate.\" \"", "West Point, helicopter flight school.\" \"", "How many hours did you log?\" \" ", "Eighty-five, sir.\" \" ", "Married?\" \" ", "Yes, sir.\" \" ", "Good luck.\" \"", "You've never been in the field?\" \"", "No, sir.\" \"", "But I'm fully trained and highly motivated.\" \"", "No, I'm talking about landing in a hot zone.\" \"", "It's a unique situation.\" \"", "Have you ever seen the effects of hemorrhagic fever?\" \" ", "No, sir.\" \" ", "Allow me, sir.\" \" ", "Major.\" \" ", "Yes, major.\" \"", "When the patient gets the virus he complains of flu-like symptoms.\" \"", "In two or three days pink lesions appear all over his body, along with small pustules... that soon erupt with blood and pus.\" \"", "A milky substance begins to\" \"These lesions become full-blown, feel like mush to the touch.\" \"", "There's vomiting, diarrhea, bleeding in the nose, ears, gums.\" \"", "The eyes hemorrhage, internal organs shut down.\" \"", "They liquefy.\" \"", "Very good, major.\" \"", "We've read that in a book too... but in about 16 hours you are about to see it.\" \"", "In the flesh, so to speak.\" \"", "I feel confident I can handle anything we encounter.\" \" ", "If one of us panics, it puts us all in danger.\" \" ", "He's under orders not to die out there.\" \"", "And that's one set of orders he's actually planning on following.\" \"", "That must be it.\" \"", "He's losing it.\" \" ", "No.\" \"", "No.\" \"", "Just hang on.\" \" ", "Keep his helmet on.\" \" ", "Don't take your helmet off.\" \" ", "I can't breathe!\" \"", "Keep your helmet\" \" Casey.\" \"", "Keep his helmet on.\" \"", "Don't let him expose himself, Casey.\" \"", "Goddamn it.\" \"", "Isolate him.\" \"", "Isolate him.\" \"", "Don't worry... it's not airborne.\" \"", "Sam Daniels, USAMRIID.\" \"", "Benjamin Iwabi.\" \"", "We've been expecting you.\" \"", "We came as soon as we could.\" \"", "Not soon enough.\" \"", "The village is dead.\" \"", "Do you know the incubation period?\" \"", "No.\" \"", "But it kills in two or three days.\" \"", "The mortality rate is 100 percent.\" \"", "Jesus.\" \"", "Could an infected person have gotten out of the village?\" \"", "If he did, he'd be dead or dying in the jungle.\" \"", "And it's 50 miles to the nearest village.\" \"", "First case?\" \"", "Patient zero?\" \"", "A young man called Murazo.\" \"", "Worked with a white man to build a road into Kinshasa.\" \" ", "And when he returned, he was sick.\" \" ", "I see.\" \"", "And he drank from this well.\" \"", "From there, it spread through the entire village.\" \"", "Did you identify the carrier?\" \"", "The host?\" \"", "No.\" \"", "When we arrived, the boy was incoherent.\" \"", "He died two hours later.\" \"", "He couldn't tell us how he got it.\" \"", "He's not sick.\" \"", "He's a local juju man.\" \"", "Witch doctor.\" \"", "He stayed in his cave a whole week.\" \" ", "I'd like to talk to him too.\" \" ", "No, he talks to me.\" \"", "You see, he believes that the gods were awoken from their sleep... by the men cutting down the trees... where no man should be.\" \"", "And the gods got angry.\" \"", "This... is a punishment.\" \"", "Alarmingly high fatality... all localized within a 3-mile radius.\" \"", "Incubation period short, appears contained.\" \"", "Alarmingly.\" \"", "Casey, you didn't put \"alarmingly.\"\" \"", "It's an adverb, Sam.\" \"", "It's a lazy tool of a weak mind.\" \"", "Period.\" \"", "Done.\" \"", "I want to add this:\" \"Billy... this is the scariest son of a bitch I've ever seen.\" \"", "And you know I've seen a lot.\" \"", "Fine.\" \"", "Fax it to Ford's house.\" \" ", "Sorry, sir.\" \" ", "It's all right.\" \"", "I've never seen anything like it before.\" \"", "I put the team in danger, sir.\" \"", "We're still here.\" \"", "I got scared, sir.\" \"", "You know, fear gets a bad rap, Salt.\" \"", "I don't want anybody working with me who isn't scared.\" \" ", "Okay?\" \" ", "Well, then I'm your man, sir.\" \" ", "Sir, I sent you the fax six hours ago.\" \" ", "Sam, I am not going to issue an alert.\" \"", "I don't wanna bust up your party, but you gotta issue an alert.\" \" ", "You said it was contained.\" \" ", "I said containment was probable.\" \" ", "You should be monitoring the airports\" \" Remember 1989?\" \"", "You found two lousy cases of Congo fever in Nairobi... and we put a note in every American kid's lunchbox.\" \"", "Remember?\" \" ", "Yeah, I was wrong.\" \" ", "You were wrong.\" \"", "What about 1992?\" \"", "Lassa fever?\" \" ", "I was wrong.\" \"", "Yup.\" \" ", "Wrong again.\" \" ", "But you're right about this?\" \" ", "I could be\" \"Yet you waltz into my party smelling like dirty socks... snatch me away from Senator Rosales, whom I need not remind you... is head of the Senate Arms Services subcommittee in charge of our budget.\" \"", "Forget Ebola, forget Lassa.\" \"", "This bug kills so fast, Billy...\" \" you could be dead in\" \" Keep your voice down.\" \" ", "Now, that is exactly my point, Sam.\" \" ", "What?\" \"", "It is the very lethality of this virus which is working for us here.\" \"", "These people don't live long enough to spread the goddamn thing around.\" \" ", "So you're right, it is contained.\" \" ", "I hope so.\" \" ", "Just\" \" I'm through talking, okay?\" \" ", "Okay.\" \"", "Because you never understood the concept of real time.\" \"", "What day is it?\" \" ", "Sunday.\" \" ", "And what day did you say you'd be home?\" \" ", "Friday.\" \" ", "Thursday, Sam.\" \"", "I said Thursday.\" \"", "I meant Thursday.\" \"", "Because Thursday and Friday sound so much alike, even I confuse them.\" \"", "Why didn't I just go to Atlanta like I said I would?\" \"", "Because you're a decent human being.\" \"", "If you\" \"Fuck you, Sam.\" \"", "You said you were gonna be home Thursday so I could fly Friday... go to my apartment on Saturday, buy a toaster, treat myself... and maybe on Sunday have a day of rest.\" \"", "Now, I have to go to the airport at 2, won't get in till 7.\" \"", "It'll be too late to buy a toaster.\" \"", "It'll be too late to\" \"Know what?\" \"", "I can't unpack... because I have a 9:00 \"Hello, how do you do?\" ", "cocktail party.\" \"", "Lewis, move over.\" \"", "Get over.\" \"", "Get over there.\" \"", "Get over.\" \" ", "Get over!\" \"", "Move over!\" \"", "Get\" \" You're scaring him.\" \"", "Lewis.\" \"", "That's because you let him get on the couch.\" \"", "Here.\" \"", "Okay.\" \"", "We can go now.\" \"", "How long are you keeping the dogs?\" \"", "Sam, the dogs are going with me to Atlanta.\" \"", "But they're my dogs too.\" \"", "I miss them.\" \"", "Okay.\" \"", "Do you want the dogs, Sam?\" \"", "They either go with me or stay with you.\" \"", "We're not gonna split them up and we can't share them.\" \"", "Decide.\" \"", "A negotiation.\" \"", "Okay.\" \"", "Wait.\" \"", "Wait.\" \"", "Wait.\" \"", "You win.\" \"", "You keep them.\" \"", "Okay, we can go now.\" \"", "Wait, wait, wait, I just wanted to tell you something, it's important.\" \"", "Now I forgot.\" \" ", "Sam, I'm gonna miss my flight.\" \" ", "Wait a minute, I remember.\" \"", "When you go to the pet store, remember that they like those medium-size bones.\" \"", "No, no, I know.\" \"", "The little barbecued ones, I know.\" \"", "That's right.\" \"", "You look tired, Sam.\" \"", "Was it that bad in Zaire?\" \"", "Could've been better.\" \"", "You be careful.\" \"", "I wish you luck.\" \"", "You better tell him to go.\" \"", "We can go now.\" \"", "No, Casey, that's not what I said.\" \"", "You're not getting this.\" \"", "Try to be objective.\" \"", "So let me just understand this.\" \"", "You didn't want photos, but you wanted the dogs?\" \" ", "You're missing the point.\" \" ", "Was there a photo of the dogs?\" \"", "Could have taken that and solved your problems.\" \" ", "I open my heart and you make jokes.\" \" ", "I'm not.\" \" ", "When we got the dogs, they were puppies.\" \" ", "Cute.\" \" ", "That's not my point.\" \" ", "Still cute.\" \"", "Now that we're no longer together, they're not ours.\" \"", "The dogs are a case for the Supreme Court.\" \"", "Just asking if you think I'm right or wrong.\" \"", "We're about to look at the most deadly virus you and I have seen.\" \" ", "Your mind should be in that neighborhood.\" \" ", "Right or wrong.\" \"", "It's a question.\" \"", "She's starting a new job at the CDC.\" \"", "No, she's got the same job as you at the CDC.\" \" ", "Good for her.\" \" ", "Anyway, she's starting a new life.\" \"", "She's happy.\" \"", "She's not coming back.\" \"", "It's nobody's fault.\" \"", "It's over.\" \"", "Move on.\" \"", "Frankly, I'm sick of hearing about it.\" \"", "All right, all right.\" \"", "What do you mean, it's over?\" \"", "Oh, you really need to seek some help.\" \"", "I think a state-sanctioned divorce signed by both parties... is evidence something was off.\" \" ", "Did you talk to her?\" \"", "Did she say it was off?\" \" ", "Do you know how I managed...\" \" to remain friends with the two of you?\" \" ", "How?\" \" ", "I don't have conversations like this.\" \" ", "Not asking you to take sides.\" \"", "She didn't take the dogs to be mean, I'm asking you your opinion.\" \" ", "What is this?\" \" ", "What?\" \"", "You didn't check your suit.\" \"", "There's a tear in it.\" \"", "Kind of takes your breath away.\" \"", "Thank you.\" \" ", "Good morning, colonel.\" \" ", "Good morning.\" \"", "I took the liberty of bringing in the samples myself, sir.\" \" ", "Casey, we got an early riser.\" \" ", "Hey, I was up at 4.\" \"", "Okay, let's go to work.\" \"", "I want to separate those samples, thaw them and throw them under the scope.\" \"", "Done.\" \"", "We'll have the results in a couple of hours.\" \"", "Very good, major.\" \"", "Listen to the way it rolls off your tongue.\" \"", "Motaba.\" \"", "Well, you know, it sounds like a perfume.\" \"", "One drop and you'll feel so different.\" \"", "Your lover will melt in your arms.\" \"", "Here, try a sample.\" \"", "Quick hands.\" \"", "But not as quick as mine.\" \"", "Don't mess with this stuff.\" \"", "You gotta be ready for anything.\" \"", "Nothing in here that can't kill you.\" \"", "Including the air.\" \"", "Okay, sirs, here we go.\" \"", "These were taken over a period of eight hours.\" \"", "Normal, healthy kidney cells before meeting the virus.\" \"", "In the space of an hour, a single virus has invaded, multiplied and killed the cell.\" \"", "In just over two hours... its offspring have invaded nearby cells here, and here.\" \"", "Continually multiplying.\" \"", "Jesus Christ, five hours?\" \"", "It infects the cell, replicates and kills this fast?\" \"", "These numbers can't be right.\" \"", "Ebola takes days to do this damage.\" \"", "Sirs, the numbers are correct.\" \"", "I wish to God they weren't.\" \"", "One goes in, millions come out.\" \"", "Every cell is dead.\" \"", "Now we see them individually... searching for their next victim... until there's nothing left to kill.\" \"", "Mark this day, Salt.\" \"", "We could spend our whole careers waiting to see a new virus.\" \"", "Sirs...\" \"Mr. Motaba... up close and personal.\" \"", "I hate this bug.\" \"", "Come on, Casey.\" \"", "You have to love its simplicity.\" \"", "It's one billionth our size and it's beating us.\" \"", "So what do you want to do?\" \"", "Take it to dinner?\" \" ", "No.\" \" ", "What then?\" \"", "Kill it.\" \"", "You know, Colonel Daniels is not going to like...\" \" us going behind his back like this.\" \" ", "Then we'll kill him.\" \"", "Lighten up, Billy.\" \"", "We have no alternative.\" \"", "You're so goddamned sentimental.\" \"", "That's the trouble with this country.\" \"", "Sir, the micrographs are ready.\" \"", "They're ready.\" \"", "Oh, my God.\" \"", "It's our African friend.\" \"", "It's back.\" \"", "We have to be very careful now, Billy.\" \"", "We wiped out a whole camp to keep this bug secret.\" \" ", "Right.\" \" ", "Lock it up.\" \"", "Shelve it.\" \"", "You know about this, I know about this, nobody else.\" \"", "Get your friend Daniels off the case.\" \"", "I don't want that nosy little bastard messing up 30 years of our work.\" \"", "Sir.\" \" ", "Hi, Marilyn.\" \"", "Is he in there?\" \" ", "Colonel, just a minute, please.\" \"", "Come in, Sam.\" \"", "Lieutenant, would you be kind enough to get us some coffee?\" \" ", "Would you like anything, Sam?\" \" ", "Why am I off Motaba, Billy?\" \" ", "Nothing for the colonel.\" \" ", "Yes, sir.\" \"", "Sit down, Sam.\" \"", "Now, did you or did you not say that Motaba was contained?\" \"", "It's gonna pop up again.\" \"", "We don't have a blood test... don't know how it's transmitted, diddlysquat.\" \"", "There's a fresh outbreak of the Hanta virus in New Mexico.\" \" ", "CDC needs help, so we're sending you.\" \" ", "No.\" \"", "Send Peterson's team.\" \"", "Don't tell me who to send on an assignment, colonel!\" \"", "I told Senator Rosales I'd send my best man.\" \"", "That's you.\" \" ", "Now, get the hell on out of here.\" \" ", "We've got baseline information on Hanta.\" \"", "What am I gonna do there?\" \"", "Trap rats, Billy?\" \"", "We got the bug growing.\" \"", "We got most of the protein isolated.\" \"", "We'll have an antibody test within a week.\" \"", "Casey put the bug in rodents and rhesus... if everything goes well, we'll know the genetic sequence within a month.\" \"", "If you leave us alone, we'll map this guy down to its last gene.\" \"", "Make you famous.\" \" ", "Sam.\" \" ", "Yeah.\" \"", "Odds of Motaba causing any more problems are a million to one.\" \"", "You know that.\" \" ", "No.\" \"", "I don't know that.\" \" ", "Well, you should.\" \"", "And you would if you didn't harbor this morbid desire to face the end of the world.\" \"", "You know it's the biggest thing we've ever seen.\" \"", "Jesus, you're killing me.\" \" ", "Fresh, brand-new virus.\" \" ", "You're still killing me.\" \"", "Put it over there.\" \"", "Whoa, it's bumpy, baby.\" \"", "It's okay, baby.\" \"", "You'll be out of here in no time.\" \"", "Yeah, I promise.\" \" ", "When did you get it?\" \" ", "Just today, Rudy.\" \" ", "We still on?\" \" ", "Yeah, I still want it.\" \"", "Great.\" \"", "Great.\" \"", "Oh, I see.\" \"", "So your ship came in again, eh, Jimbo?\" \"", "Our ship, Neil.\" \"", "Our ship.\" \"", "Africa, land of great beauty and untold riches.\" \" ", "Absolutely untold.\" \" ", "Keep it that way.\" \"", "Take care.\" \" ", "Tell them to send out an alert.\" \" ", "No, I won't.\" \" ", "Why are you fighting me?\" \" ", "I'm not gonna base one of my first... official decisions on a hunch when the Army won't back you.\" \"", "It's not a hunch.\" \"", "I'm faxing you the epidemic.\" \"", "I got a lab full of dead animals here.\" \"", "There's no response to intravenous acyclovir, okay?\" \"", "They're all dead.\" \"", "Of course they're dead, you stuck them with the same needle.\" \" ", "Where's the evidence it's coming here?\" \" ", "I don't need evidence, I got a feeling.\" \"", "You got a feeling.\" \"", "Your feeling is in my notes.\" \"", "This is not complicated, it's simple.\" \"", "This thing kills everything in its path.\" \" ", "Tell them to put out an alert.\" \" ", "This is starting to sound familiar.\" \" ", "Is that an order, colonel?\" \" ", "I cannot believe you're taking...\" \" a virus, turning it into a family matter.\" \" ", "This is not personal, Sam.\" \"", "Robby, look, I can't do this back and forth.\" \"", "Once in your life, take a chance.\" \"", "You know what, Sam?\" \"", "I did.\" \"", "I married you.\" \"", "You hung up, didn't you?\" \"", "Shit.\" \"", "First it was the dogs, now we're fighting over a virus.\" \"", "I can't believe it.\" \"", "What is the matter?\" \"", "You know, music is supposed to soothe the savage beast.\" \"", "What?\" \"", "Oh, Christ, you little shit.\" \" ", "Rudy.\" \" ", "Hey, fella.\" \"", "Welcome back.\" \" ", "Look, look, look.\" \" ", "All right.\" \"", "Put it on the shelf.\" \"", "Let's have a look.\" \" ", "You got the papers and everything?\" \" ", "Yeah, papers.\" \"", "That's a good one.\" \"", "Look at her.\" \"", "You asked for a monkey, I got you the monkey.\" \" ", "What do you mean, look at her?\" \" ", "What do you mean, what do I mean?\" \" ", "I told you a male.\" \" ", "No, you said, \"she.\"\" \"", "I said, \"male.\" ", "Customer's already got a female.\" \"", "He wants to breed them.\" \" ", "Goddamn.\" \" ", "You okay?\" \"", "It's okay.\" \"", "It's okay.\" \"", "It's okay.\" \" ", "All right, all right.\" \"", "Look, I'll sell her cheap.\" \" ", "No, no, no.\" \" ", "I've done a lot of favors for you.\" \" ", "We had a deal and you screwed it up.\" \"", "I can't even sell that one.\" \"", "Here, look at this.\" \"", "Well, it serves you right.\" \"", "What am I gonna do with her?\" \"", "The warning will be included in our weekly report, Dr. Keough.\" \"", "That doesn't go out till Wednesday...\" \"Colonel Daniels believes this is serious enough to send out a special alert.\" \"", "Do you know how much it costs to send out a special alert to 400,000 health workers?\" \"", "In '89, he predicted Hanta and it hit.\" \"", "Well, I suppose I understand your allegiance to your ex-husband... but both you and I know... that the chances of this virus showing up in the U.S. are virtually nil.\" \"", "Go on, girl.\" \"", "Yeah, it's freedom.\" \"", "Look at the trees.\" \"", "Look, it's like home.\" \"", "There you go.\" \"", "That's it.\" \"", "Oh, no.\" \"", "Don't give me that look.\" \"", "No.\" \"", "No, go on.\" \"", "No.\" \"", "Wha--?\" \"", "I'd keep you, but I'm already hitched.\" \"", "Come on.\" \"", "Go on.\" \"", "There you go.\" \"", "That's it.\" \"", "Folks, this is Captain Carter again.\" \"", "At this time I'd like to ask you to return to your seats... as we're about to commence our approach to Boston Logan Airport.\" \"", "Hey, buckaroo.\" \" ", "We should be on the ground in 25 minutes.\" \" ", "So cute.\" \"", "Hey, mister.\" \"", "Are you gonna eat the rest of that cookie?\" \"", "No.\" \"", "You can have it, sheriff.\" \"", "No, no, no.\" \"", "Bobby, don't bother the nice man.\" \"", "It's no problem.\" \"", "I don't want no trouble with the law.\" \"", "Jimbo.\" \"", "I missed you so much.\" \"", "You look like shit, baby.\" \"", "What's the matter?\" \"", "I don't know.\" \"", "Something I ate, or something.\" \"", "Jimbo?\" \"", "What is it?\" \"", "Sweetie, talk to me.\" \"", "What is it?\" \"", "Jimbo.\" \"", "Help!\" \"", "Morning, Rudy.\" \"", "Lucrecia won't touch those shredded beef wafers so we'll have to go back to the veal.\" \"", "What's wrong?\" \"", "Rudy, can you hear me?\" \"", "Come on, help me.\" \"", "Squeeze my hand.\" \"", "Looks like toxic shock.\" \" ", "Fred said he was fine yesterday.\" \" ", "Come on, Rudy.\" \"", "I've been reading about bad strep cases in Newsweek.\" \"", "Maybe I should subscribe.\" \"", "Henry... get me a blood culture, chemistry profile, and a blood count.\" \"", "Goddamn it.\" \"", "Come on, Rudy!\" \"", "wins it with his second home run... of the year by a final score of 6 to 3.\" \"", "Shit.\" \"", "Well, here are the totals for tonight's game for the San Francisco Giants.\" \"", "Three runs, seven hits, no errors and four left\" \"Fuck!\" \" ", "What about AIDS or hepatitis?\" \" ", "We'll have the blood tested.\" \"", "I'm sure there's nothing to worry about.\" \"", "Maybe give me gamma globulin?\" \"", "I wouldn't want to give anything to my girlfriend.\" \"", "Flowers would be nice on occasion, don't you think?\" \" ", "Well, you should eat.\" \" ", "You shouldn't eat that crap.\" \"", "It's bad.\" \"", "Come on, you know you want one.\" \"", "Here.\" \"", "You got something for me.\" \"", "E. coli outbreak in Michigan in a steak-house franchise.\" \"", "And a couple fevers of unknown origin up in Boston.\" \"", "Their infectious disease docs can't figure them out.\" \"", "Wouldn't be African explorers back from Zaire, would they?\" \" ", "Yeah, right.\" \" ", "Yeah?\" \"", "No, just a couple American kids.\" \"", "No unusual travel.\" \"", "Bet you some atypical strain of Lyme and those Boston doctors missed the boat.\" \"", "Lisa... get me on a plane to Boston.\" \"", "Right in here.\" \"", "Right over here.\" \"", "James.\" \"", "Jimbo, can you hear me?\" \"", "Jimbo.\" \"", "We're here to help, but we need to know how you got sick.\" \"", "Can you talk to me?\" \"", "Jimbo?\" \"", "Hello?\" \"", "Jimbo, were you in contact with any animals?\" \" ", "Doctor, should we call a code?\" \" ", "Turn it off.\" \" ", "What is this?\" \" ", "I'm here to find out.\" \" ", "We're gonna need a post.\" \" ", "No way.\" \"", "I'm not gonna cut myself and get what he's got.\" \" ", "I don't do autopsies.\" \" ", "You?\" \" ", "I'll do it.\" \" ", "Oh, God.\" \"", "He's dead, isn't he?\" \" ", "Oh, God, please...\" \" Honey.\" \" ", "please don't let him die.\" \" ", "We're doing what we can.\" \" ", "I need you to help me.\" \"", "Look at me, Alice.\" \" ", "Jimbo, say something.\" \"", "Alice, did Jimbo tell you anything?\" \" ", "Oh, God.\" \"", "Oh, God.\" \" ", "Did he talk to you?\" \"", "Very slow.\" \"", "Maximum sharps precautions.\" \"", "Slow.\" \"", "Give me the scalpel.\" \"", "You assist me.\" \"", "He worked at an animal quarantine facility in San Jose.\" \"", "Might have gotten it there.\" \"", "We're monitoring all of his co-workers.\" \"", "The host could be there, don't let anybody out of that place.\" \"", "We're isolating everybody.\" \"", "I've quarantined the med staff...\" \"EMS crews, girl's neighbors.\" \"", "Christ, Sam, I opened this guy up, it looked like a bomb went off inside.\" \"", "His pancreas, liver, kidneys, spleen, all the organs were liquefied.\" \"", "Christ, I should have forced the alert.\" \"", "You tried, but it wouldn't help those kids.\" \"", "Get tissue samples to our labs.\" \"", "I'll confirm that it's Motaba.\" \" ", "Robby, is anybody else showing symptoms?\" \" ", "No, not yet.\" \"", "CDC has a Stage 3 alert out.\" \"", "If there are any new cases...\" \"God, we'll find out about them.\" \"", "Oh, what about that girl?\" \"", "She died when I was in post.\" \"", "She wasn't on the plane.\" \"", "So the first time she had contact with him was at the airport.\" \"", "Plane got in at 9:00, she was admitted 6:00 the next morning.\" \"", "At the most, we're talking a 24-hour incubation period.\" \" ", "God, this thing moves so fast.\" \" ", "Sure, but that's good for us.\" \"", "We can see it.\" \"", "Nobody gets sick within 24 hours, we're in the clear.\" \"", "This doesn't sound like you.\" \" ", "What?\" \" ", "Imagining the best-case scenario.\" \"", "Why not?\" \"", "I still think there's hope for us.\" \"", "Honey, are you all right?\" \"", "I'm gonna get something to drink.\" \"", "Honey?\" \"", "What's your problem?\" \"", "Excuse me.\" \" ", "Water.\" \" ", "You have to wait your turn, sir.\" \"", "Help me.\" \"", "I need water.\" \"", "Henry.\" \"", "We caught it early, and you're gonna make it.\" \"", "But I need you to fight.\" \"", "Dr. Mascelli.\" \"", "Dr. Mascelli to ER, stat.\" \"", "Look who's here.\" \"", "Hi.\" \"", "You gotta fight, okay, Henry?\" \"", "Gotta fight.\" \"", "Doctor, she got sick really fast, doctor.\" \"", "I thought it was the flu.\" \"", "She fainted.\" \" ", "Doc, she's burning up.\" \" ", "It's gonna be all right.\" \"", "They keep coming in.\" \"", "What's wrong with these people?\" \"", "I don't know, Emma.\" \"", "I don't know.\" \"", "Get me the county health department, now.\" \"", "Are you sure?\" \"", "Are you sure?\" \"", "Every last one?\" \"", "Okay, great.\" \"", "Thank you.\" \"", "Okay, the airline passengers checked out clean.\" \"", "No further infection at Boston Municipal.\" \"", "We're in the clear.\" \"", "Yes.\" \"", "Congratulations.\" \"", "Robby, Dr. Reynolds.\" \"", "Fifteen cases.\" \" ", "There's another outbreak?\" \"", "Besides Boston?\" \" ", "Yeah.\" \"", "I don't understand why you're reluctant.\" \"", "CDC, USAMRIID... are the only agencies capable of dealing with a virus like this.\" \"", "That's why I want to get out of here tonight.\" \"", "Sorry, Sam, can't do that.\" \"", "Why in God's name would you keep me out of there?\" \"", "It's a civilian matter, Sam.\" \"", "CDC is on it.\" \"", "Let them do their job.\" \"", "We don't have a charter.\" \"", "Fuck the charter.\" \"", "It's not about a charter.\" \"", "People are dying.\" \"", "It's about being a doctor!\" \"", "It's about that sacred oath that we took, remember?\" \"", "We've been friends 20 years.\" \"", "Yes, we're friends, Sam, but I'm also your boss!\" \"", "I run this outfit!\" \"", "It's not run by committee!\" \"", "You do what the hell I say you do!\" \"", "I'm your boss.\" \"", "I have my boss.\" \"", "Is that clear to you?\" \"", "Yeah, get your boss on the phone.\" \"", "Tell him to put me on a plane before the two of you kill a lot of people.\" \"", "I'm gonna suggest that you shut up now before you say something else.\" \" ", "Don't forget who you're talking to.\" \" ", "I don't know who I'm talking to anymore.\" \"", "Am I talking to USAMRIID, the Pentagon, the CIA, McClintock?\" \" ", "Dugway?\" \"", "Tell me who I'm talking to.\" \" ", "This conversation is over.\" \" ", "Can you tell me--?\" \" ", "You're on a plane to New Mexico.\" \"", "I suggest you get packed or whatever you have to do, and I suggest you do it now.\" \"", "All right, sergeant, who screwed up?\" \"", "Why wasn't my pilot given the new orders?\" \"", "New orders?\" \"", "General Ford called me 0200, told me to get my ass to Cedar Creek, California.\" \"", "I got you going to Albuquerque\" \"No, I'm not going to Albuquerque!\" \"", "I'm going to Cedar Creek!\" \"", "Get General Ford on the phone and you get him to confirm.\" \"", "No, don't get a confirmation.\" \"", "Give me that phone.\" \" ", "No, I better a\" \" You know what time it is?\" \"", "It's 2:30.\" \"", "That's right.\" \"", "You redirect on my orders.\" \"", "Call and change my flight plans.\" \"", "Put your finger on the phone.\" \"", "Your finger on the phone.\" \" ", "This could mean my stripes, sir.\" \" ", "Gonna mean your ass if you don't.\" \"", "Finger the phone.\" \"", "Finger it.\" \"", "Thank you.\" \"", "The governor's asked the president for federal help.\" \"", "So you can proceed there with the 1st Battalion of the 8th Infantry.\" \"", "We need transmission rates of every possible carrier.\" \"", "Insect, marine, animal, human.\" \"", "If this thing is spreading... we need to know where it's going and how fast it's getting there.\" \"", "And Billy... they placed us in a hold mode for Clean Sweep.\" \"", "Donny, you and I both know we can throw these people a lifeline.\" \"", "No, we have to proceed with conventional containment.\" \"", "And you have to maintain an absolute media blackout.\" \"", "Control your subordinates.\" \"", "Is Daniels in line?\" \"", "Yes, sir.\" \"", "I'll believe that when I see it.\" \"", "Anything else?\" \" ", "No, sir.\" \" ", "Good luck, Billy.\" \"", "Get the supplies.\" \"", "Bring them in.\" \" ", "What could be holding them up?\" \" ", "There they are now.\" \"", "Ray Fowler, Chief of Police.\" \"", "This is Mayor Gaddis.\" \"", "Hi, I'm Dr. Keough from CDC.\" \"", "This is Dr. Aronson and Dr. Ruiz.\" \"", "Cedar Creek is a small town, doctor.\" \"", "We're like a family.\" \"", "Everybody's scared.\" \"", "I know and we're here to help you in any way we can.\" \"", "I'll be in charge.\" \"", "I thought he was in charge.\" \" ", "Sam.\" \" ", "Hi, Robby.\" \"", "They just set up the BL4 mobile unit.\" \"", "What are you doing here?\" \"", "I thought Ford sent you to New Mexico.\" \"", "He did.\" \"", "We have got everybody running.\" \"", "I am running out of everything, people.\" \"", "We're keeping the patients isolated in here.\" \"", "There's so many.\" \"", "So many, so fast.\" \"", "Apparently they all got it at a movie theater.\" \" ", "Dr. Daniels?\" \" ", "Yeah.\" \"", "There's something I think you should see.\" \"", "This way.\" \"", "The patient was admitted a week ago after a car accident.\" \"", "He's had no contact with anyone in isolation.\" \"", "It's all right, honey.\" \"", "It's airborne.\" \"", "General Ford?\" \"", "I'm Lt. ", "Colonel Briggs, sir.\" \"", "Welcome.\" \"", "Thank you, colonel.\" \"", "The SITREP?\" \"", "Well, since 0620 this morning we've had an outer and inner perimeter established.\" \"", "No one has violated our cordon.\" \"", "Before, I can't give any guarantee.\" \"", "Colonel, there are 2618 people in this town.\" \"", "I want every one of them accounted for by 0900.\" \"", "Guarantee me that.\" \"", "Very well, sir.\" \"", "We're on it.\" \"", "Quarters in here, sir.\" \"", "By the way, Colonel Daniels is in town against orders.\" \" ", "Locate him.\" \"", "Arrest him.\" \" ", "Yes, sir.\" \"", "Clear this area, now!\" \"", "Hey, we have rights!\" \"", "Stop.\" \"", "Stop.\" \"", "What are you doing?\" \"", "You can't do this to us!\" \"", "This is a different strain.\" \"", "This one is the one we got from Jimbo Scott, the one from Zaire.\" \"", "This new one is the one from Cedar Creek.\" \"", "They look the same.\" \"", "But... closer... and closer.\" \"", "See the differences?\" \" ", "The spikes here and here.\" \" ", "Yes.\" \"", "The protein code has changed, which allows it to survive longer in the air.\" \"", "So it spreads like the flu.\" \"", "Okay, Casey, tree of death.\" \"", "Assuming the new strain originated with Seward... bing, bang, bong, he infects the whole theater.\" \"", "Go back further.\" \"", "He's a medical worker.\" \"", "He was sprayed with a blood sample taken from Alvarez.\" \"", "And Alvarez tells us what?\" \"", "Zip, he was dead before we got here.\" \"", "But listen.\" \"", "Alvarez died of the original strain.\" \"", "Seward died of the new strain.\" \"", "These are too close together on the tree for the virus to spontaneously mutate... so I think... that the host animal is carrying both strains.\" \"", "Pretty good.\" \"", "Pretty good.\" \"", "Alvarez, Jimbo, what's the connection?\" \" ", "I can't find one.\" \" ", "Wait a minute.\" \" ", "Alvarez worked at a pet store.\" \" ", "I'm just learning this now?\" \"", "We just got it, Sam.\" \"", "Jesus, if the host is there, then it's carrying antibodies to both strains.\" \"", "I'm at the pet store.\" \" ", "Salt, get on the new strain from scratch.\" \" ", "Yes, sir.\" \" ", "Casey, blood test.\" \" ", "Right away.\" \"", "Damn you.\" \"", "Get back here!\" \"", "General, you got a minute?\" \"", "There you are, Sam.\" \"", "Colonel Briggs, take this man into custody.\" \"", "We're in deep shit, Billy.\" \"", "The virus has aerosolized.\" \" ", "What are you talking about?\" \" ", "It's gone airborne.\" \" ", "Colonel, would you excuse us?\" \" ", "Certainly, sir.\" \"", "Motaba is only spread through direct human contact.\" \"", "Now, you said that yourself, Sam.\" \"", "I know what I told you, but now we're facing a new strain.\" \" ", "What?\" \" ", "It spreads like the flu.\" \" ", "Impossible.\" \" ", "Fine.\" \"", "Go to the hospital, check it.\" \"", "Go without a mask, you'll see more clearly.\" \"", "You got 19 dead, you got hundreds more infected and it's spreading like a brushfire.\" \"", "You gotta isolate the sick, and I mean really isolate them.\" \"", "We gotta get everybody else back into their houses.\" \" ", "We're doing that!\" \" ", "No, we're not doing it!\" \"", "Because I just drove through 100 people!\" \"", "If one of them has got it, then 10 of them have it.\" \"", "If one gets out of Cedar Creek, Billy, then we're in deep fucking shit!\" \"", "And we're already in deep fucking shit!\" \" ", "If you're gonna arrest me, arrest me now!\" \" ", "All right, Sam!\" \"", "Don't threaten me.\" \"", "Don't threaten my crew.\" \"", "Please.\" \"", "Leave us to do our work.\" \"", "All right, Sam.\" \"", "All right.\" \" ", "You were never here.\" \" ", "No, I was here.\" \"", "I followed the bug here.\" \"", "I've always been here.\" \"", "And you remember that.\" \"", "The U.S. Army and the CDC report... that the virus which has struck this Northern California town... is being contained while they search for answers.\" \"", "A tight quarantine has been established for the protection of neighboring townships... and extends to the Pacific Ocean, just a scant mile away.\" \"", "You are entering a restricted area.\" \"", "Turn your aircraft around.\" \"", "This is a no-fly zone.\" \"", "Careful of the glass.\" \"", "Return to your homes!\" \"", "Do not congregate in the street!\" \"", "Return to your homes!\" \"", "Mouse.\" \"", "Robby.\" \"", "Could this be the host?\" \"", "This monkey's sick.\" \"", "It can't be our host.\" \"", "We need to run an ELISA.\" \"", "Let's get back to the lab.\" \"", "No one is permitted to leave the town.\" \"", "Anybody attempting to do so will be placed under arrest.\" \"", "I repeat, we are turning you around.\" \"", "Hey, hey, what the hell is Bobby doing?\" \"", "Tommy, follow us.\" \"", "We gotta get out of here.\" \"", "Kids, get down.\" \"", "Remain calm.\" \"", "We are turning you around.\" \"", "Go for it, Bobby.\" \"", "Gotta get to the trees.\" \"", "Halt your vehicles.\" \"", "Halt your vehicles, then dismount.\" \"", "Shit.\" \"", "They're bluffing.\" \"", "Keep going.\" \"", "Keep going.\" \"", "You have entered a restricted area.\" \"", "We will fire.\" \"", "This is your last warning.\" \"", "Damn.\" \" ", "Jesus Christ, they're shooting.\" \" ", "Damn it, people, there's no place to go.\" \"", "Go!\" \"", "We're almost there!\" \"", "What the hell are they trying to do?\" \"", "Get out of that vehicle, now!\" \" ", "Come on.\" \" ", "Let me see your hands!\" \" ", "All right, lady, get out!\" \"", "Come on!\" \"", "Let's go!\" \" ", "Move!\" \"", "Move!\" \" ", "Salt, how are we doing?\" \" ", "Just a moment.\" \" ", "Tell me as soon as you got something.\" \" ", "Yes, sir.\" \"", "Anything?\" \"", "Sir, this monkey's been infected with the original strain.\" \"", "No antibodies, nothing.\" \"", "Okay.\" \"", "That means the monkey caught it before the mutation.\" \"", "Maybe he was on the boat next to the real host, maybe he caught it at Biotest.\" \"", "Not Biotest.\" \"", "CDC's turned that place inside out.\" \"", "All Motaba negative.\" \" ", "No, test it again.\" \" ", "My people know what they're doing.\" \"", "Robby, get your people over there, tell them to test it again and again.\" \"", "And after they've tested it, tell them to test it again.\" \"", "Welcome home.\" \"", "Military have escalated their quarantine at Cedar Creek... doubling their presence in this small town.\" \"", "Authorities remain silent about the details of the situation... continuing the media blackout.\" \"", "We can only guess at the seriousness of the spread of the disease.\" \"", "Our sources number the dead as low as 10, as high as 50.\" \"", "It's like a war zone out here, and we can only imagine... the fear and frustration of the citizens of this once very quiet rural town.\" \"", "Their voices too are silent to us.\" \"", "All phone communications have been cut off.\" \"", "And those we can hear... those with the information, will not speak.\" \"", "It is, in a word, frightening.\" \"", "A military curfew is now in effect.\" \"", "Return to your homes immediately.\" \"", "Anyone found on the streets after 1900 hours, or 7:00 p.m... will be arrested and confined.\" \"", "Return to your homes.\" \"", "You will be safe there.\" \"", "Return to your homes immediately.\" \"", "The town has been secured.\" \"", "All civilians are in their homes.\" \"", "Only minimal protective gear is required for all military personnel.\" \" ", "Got it?\" \" ", "I got it.\" \"", "Bring it in.\" \"", "Billy.\" \"", "She was one of the first ones infected.\" \"", "What's E-1101?\" \"", "It's an experimental antiserum from Yale Virology.\" \"", "I figured it might be worth a try.\" \"", "I read the journals.\" \"", "I haven't read a word about E-1101.\" \"", "Where'd you get it, Billy?\" \" ", "You know I can call Yale in a second.\" \" ", "I want to save these people same as you.\" \"", "I'm using everything in the arsenal.\" \"", "We have to work together, Sam.\" \"", "Are we?\" \"", "Are we what?\" \"", "Are we working together, sir?\" \"", "Oh, shit.\" \"", "Don't waste your time making phone calls, Sam.\" \" ", "Salt?\" \" ", "Excuse me.\" \" ", "Salt, come here.\" \" ", "Yes, sir.\" \"", "Give this to the rhesus and put it with some virus and pull it apart.\" \"", "Yeah?\" \"", "Yes, sir.\" \"", "What is it?\" \" ", "What's it look like?\" \" ", "It isn't orange juice.\" \"", "No, it's not.\" \" ", "Colonel?\" \" ", "Yeah.\" \"", "What is it?\" \"", "I don't know.\" \"", "Maybe he'll tell us.\" \"", "If you're feeling sick in any way... you should hang a pillowcase or any piece of white cloth on your front door.\" \"", "Soldiers will take you to a testing facility and you'll know the results within hours.\" \"", "Early stages resemble the flu.\" \"", "Coughing and high fever.\" \"", "Anyone showing these signs should report them immediately.\" \"", "Doctors have the situation well in hand... and are working day and night to find a cure.\" \"", "I'm only gonna be gone for a few hours.\" \"", "Well, I might have to spend the night.\" \"", "So you girls be good, okay?\" \"", "Make sure you brush your teeth before you go to bed.\" \" ", "Erica, don't touch your mommy.\" \" ", "Oh, baby, I can't.\" \"", "I love you.\" \"", "Bye.\" \"", "Bye.\" \"", "Positive.\" \"", "Positive, damn it.\" \"", "The whole damn town's infected.\" \"", "Watch your step.\" \"", "Just follow the line.\" \"", "This way, folks.\" \"", "One straight line.\" \"", "Down the hall.\" \"", "Out into the field.\" \"", "This way, folks.\" \"", "One straight line.\" \"", "You will be given paperwork to complete.\" \"", "Stay in the tent to which you are assigned.\" \"", "We'll keep you informed.\" \"", "You'll be allowed to contact your families as soon as possible.\" \"", "Do not leave the tent to which you are assigned.\" \"", "No.\" \"", "No animals have been removed from here for the last 14 days.\" \"", "I double-checked the storage lists, the manifests, the vet profiles.\" \"", "Nothing.\" \"", "Talk to every single employee.\" \"", "Every one.\" \"", "Somebody's got to know something.\" \"", "The source of this whole mess is there.\" \"", "The host is there, Casey.\" \"", "He didn't talk to everyone.\" \"", "You said he did.\" \" ", "Sam.\" \" ", "This coffee sucks.\" \" ", "Why don't you try to get a little sleep.\" \" ", "Why don't you?\" \" ", "I slept back in July.\" \" ", "Well, I got work to do.\" \"", "Don't tell me when I need sleep, Casey.\" \"", "I don't tell you when you need sleep.\" \"", "What happened, Casey?\" \"", "Oh, nothing.\" \"", "I just got a sudden case of the willies.\" \"", "You okay?\" \"", "I can finish up.\" \"", "No, no, no, I'm fine.\" \"", "I'm fine.\" \"", "I just-- You know, I hate them willies, you know?\" \"", "They ought to call them \"the Sams,\" don't you think?\" \"", "You're tired, huh?\" \" ", "Yeah.\" \" ", "Yeah.\" \"", "The most optimistic projection USAMRIID is willing to make... for the spread of the virus is this: 24 hours... 36 hours... 48 hours.\" \"", "The curtailment procedure must be viewed objectively.\" \"", "Be compassionate, but be compassionate globally.\" \"", "Thank you.\" \"", "All right, all right.\" \"", "Please.\" \"", "Please.\" \"", "The President's ETA from the East Asia Economic Summit is in 20 hours.\" \"", "He wants a recommendation by then from this group.\" \"", "As I understand it, you want to firebomb the town of Cedar Creek... population 2600, with something called a fuel-air bomb... the most powerful non-nuclear weapon in our arsenal.\" \"", "The way it works, it explodes, sucks in all available oxygen to the core... vaporizes everything within a mile:\" \"men, women, children and one airborne virus.\" \"", "Destruction complete, case closed, crisis over.\" \"", "This Constitution of the United States, I've read it cover to cover.\" \"", "I don't find anything in it about vaporizing 2600 American citizens.\" \"", "But it does say, several times... that \"no person shall be deprived of life, liberty or property... without due process.\"\" \"", "So couple things before Clean Sweep is even considered:\" \"One... unanimous, unwavering support for the president on this one.\" \"", "And I mean public.\" \"", "Stand shoulder to shoulder with him.\" \"", "He goes down, you go down!\" \"", "And the second thing is...\" \"I want an army of experts citing hundreds and thousands of lab experiments... telling any idiot with a camera that there was no other way!\" \"", "You got that?\" \"", "No member of this government is gonna go sneaking off to the Washington Post... telling them how they were the sole voice of opposition.\" \"", "If there is a voice of opposition out there, I want him in here.\" \"", "Now.\" \"", "Those are the citizens of Cedar Creek.\" \"", "Go on!\" \"", "Look at them!\" \"", "These are not statistics, ladies and gentlemen.\" \"", "They're flesh and blood!\" \"", "And I want you to burn those into your memories.\" \"", "Because those images should haunt us till the day we die.\" \"", "1918.\" \"", "Remember your history, Donny?\" \"", "The great influenza pandemic.\" \"", "Circled the globe in nine months.\" \"", "Killed 25 million people.\" \"", "My father lost three brothers in that.\" \"", "So?\" \"", "What if there were men who could have stopped it, only they didn't?\" \"", "How do you think history would judge such men?\" \"", "Oh, baloney.\" \"", "FDR stopped Stilwell going into Indochina.\" \"", "He caused the Vietnam War.\" \"", "What's history say about him?\" \"", "Truman dropped the bomb on the Japanese.\" \"", "Saved thousands of American lives.\" \"", "Now your revisionist historians say he dropped that bomb to scare the Russians.\" \"", "Those men were at war, Donny.\" \"", "We're not.\" \"", "We are at war, Billy.\" \"", "Everybody is at war.\" \"", "I have a presidential green light on Operation Clean Sweep... and I am going forward.\" \"", "Donny... these people are Americans.\" \"", "Twenty-six hundred dead or dying Americans.\" \"", "If that bug gets out of there, Billy, 260 million Americans will be dead or dying.\" \"", "Those people are casualties of war, Billy.\" \"", "I would give them all a medal if I could... but they are casualties of war.\" \"", "That'll be all, Joe.\" \"", "Come on.\" \" ", "Neil, is it?\" \" ", "Yes, sir.\" \"", "I have to ask you a few questions.\" \"", "Have a seat.\" \"", "Okay.\" \"", "Jimbo, Jimbo, Jimbo, how did he get it?\" \"", "You know, maybe we're on the wrong track.\" \"", "Maybe Alice gave it to him.\" \"", "No, his tissue sample showed twice the viral amplification of Alice's.\" \" ", "So we're stuck.\" \" ", "We're doing the best we can, Sam.\" \"", "No we're not.\" \"", "We're not.\" \"", "Look, let's wait for the comprehensive results to come in.\" \" ", "Just\" \" Robby.\" \" ", "Yeah?\" \" ", "Can I ask you a personal question?\" \"", "What did you do with the dogs?\" \"", "God.\" \"", "Please don't tell me you put them in a kennel.\" \"", "Think I tied them to a tree and left a five-pound bag of dog chow nearby?\" \" ", "That's what you did when you left me.\" \" ", "Sam, we're gonna start over, okay?\" \"", "It's Alvarez, Jimbo, Biotest.\" \"", "Jesus.\" \"", "Look.\" \"", "Guys, guys, the monkey.\" \"", "Turn around.\" \"", "Oh, my sweet Jesus.\" \"", "He should be dead by now.\" \" ", "I guess the orange juice worked.\" \" ", "It doesn't work on humans.\" \"", "No, it doesn't on Cedar Creek Motaba, Sam.\" \"", "This monkey was infected with the original strain.\" \"", "You're right.\" \"", "And do you know what that means?\" \"", "This is no experimental antiserum.\" \"", "E-1101 was designed to kill African Motaba.\" \"", "And they had it all the time.\" \"", "Casey!\" \"", "Casey, come on, buddy!\" \"", "Salt!\" \"", "How's his breathing?\" \"", "He's gonna arrest!\" \"", "We need blood, fluid, oxygen, ice, now!\" \"", "Come on, Casey.\" \" ", "Let's go.\" \"", "Put it in his armpits.\" \" ", "Come on, Case.\" \"", "I need to get in there.\" \" ", "Under his armpits.\" \" ", "Pressure.\" \" ", "I need his arm.\" \" ", "Give me his temperature.\" \"", "I need pressure.\" \" ", "Tell me what his temperature is.\" \" ", "106!\" \"", "We need suction!\" \"", "We need more ice, now!\" \"", "Okay, Casey.\" \"", "Let me in here.\" \"", "Come on.\" \"", "You slept long enough.\" \"", "Come on.\" \"", "Come on.\" \"", "Open your eyes!\" \"", "Open!\" \"", "Open!\" \"", "Open!\" \"", "Open!\" \"", "Open!\" \"", "Open!\" \"", "Look at me.\" \"", "Look at me.\" \"", "Casey, right here.\" \"", "Here I am, here I am.\" \"", "Here I am.\" \"", "See me?\" \"", "There you are.\" \"", "There you are.\" \"", "How you doing?\" \"", "I had a wonderful dream, Auntie Em.\" \"", "Yeah?\" \"", "You were there.\" \"", "You were there.\" \"", "Stay here.\" \"", "Stay with me.\" \"", "Yeah, you were there too.\" \"", "You had about 106 fever.\" \"", "We're going to take you down.\" \"", "Stay with me.\" \"", "Come on, don't fuck around.\" \"", "How many brain cells did I kill?\" \"", "How many?\" \"", "About a billion.\" \"", "Now I'm only as smart as you.\" \"", "What can we give him to kill his sense of humor?\" \"", "We gotta get a line!\" \"", "We gotta get a line!\" \"", "Hold him.\" \"", "Hold him.\" \" ", "Hold his head!\" \" ", "I got it.\" \"", "What?\" \"", "What?\" \"", "Talk to me.\" \"", "What?\" \"", "It didn't get past the outer glove.\" \"", "Just hold him down and give him a line.\" \"", "What do you mean?\" \"", "Come here.\" \"", "I was with him.\" \"", "I should've known something was wrong.\" \" ", "Maybe it didn't puncture.\" \" ", "It did.\" \" ", "Let me see.\" \" ", "It did, Sam.\" \" ", "Okay, let me get some iodine on it.\" \" ", "I did that already.\" \" ", "We'll get it.\" \" ", "I did it, Sam!\" \"", "Oh, God.\" \"", "Oh, God, I know how to work with needles.\" \"", "I just....\" \" Why didn't I wait?\" \" ", "Robby.\" \" ", "Okay, listen to me.\" \" ", "Sam, not now, okay?\" \"", "Not now.\" \" ", "Robby!\" \" ", "What?\" \" ", "Listen to me!\" \" ", "There's nothing to say, Sam.\" \"", "There is.\" \"", "Watch it.\" \"", "Yes, Sam?\" \"", "You knew about Motaba all along.\" \"", "E-1101 was the antiserum.\" \"", "You could've stopped this outbreak before it mutated.\" \"", "But you didn't.\" \" ", "We couldn't.\" \" ", "We?\" \" ", "We.\" \" ", "We?\" \" ", "We.\" \"", "That's all you need to know.\" \" ", "No, you gotta tell me what the host is.\" \"", "We never found the host.\" \"", "We had to synthesize the antiserum.\" \"", "Sure.\" \"", "To protect the troops.\" \"", "But now the virus comes here and two kids die.\" \"", "We could've stopped it then... but we don't because we have to protect the perfect biological weapon.\" \"", "But then the virus mutates and we can't stop it now and we could've then.\" \"", "The decision was made in the interest of national security.\" \"", "At the time, it was felt that we could afford a certain number of losses.\" \"", "Robby's infected.\" \"", "I'm sorry.\" \"", "Is \"we\" sorry too?\" \"", "Billy, \"we\" is responsible for a town dying.\" \"\"", "We\" is a party to Casey dying.\" \"", "My wife is dying.\" \"", "Isn't she your ex-wife, Sam?\" \"", "I'm sorry.\" \"", "What's your point?\" \"", "My point is your penchant for distorting the facts.\" \"", "You and Robby are, in fact, divorced.\" \"", "Who is \"we\"?\" \"\"", "We\" includes you, Sam.\" \"", "Unless you resigned from the Army the last week.\" \"", "You don't just do research and it ends there, Sam.\" \"", "We have to defend ourselves against the other maniacs... who are developing biological weapons.\" \"", "That's the way the game is played.\" \"", "Yes, it was a terrible mistake to withhold E-1101... but we're beyond that now.\" \"", "We've done all we can as doctors.\" \"", "We have to go on... as soldiers.\" \"", "You're gonna wipe out the town.\" \"", "You're gonna eradicate the mutation and then your weapon is intact.\" \"", "That's why the troops are moving out, right, Billy?\" \"", "It's already been ordered.\" \"", "When is it, Billy?\" \"", "2000 hours.\" \"", "By order of the president.\" \"", "What do you mean, the president?\" \"", "He was shown the projections.\" \"", "He was advised by an expert panel of virologists.\" \"", "I wasn't there.\" \"", "It's not about a weapon, Sam.\" \"", "When the president saw that within 48 hours... this virus could be crawling across the White House lawn, he gave the order.\" \"", "I wasn't invited.\" \"", "Suppose you had been, Sam... what would have been your advice?\" \" ", "What?\" \" ", "Colonel...\" \" Ruiz called.\" \" ", "Yeah?\" \"", "Apparently he scared a security guard into telling him Jimbo Scott... smuggled an animal out of Biotest.\" \" ", "Jesus.\" \"", "What kind of animal?\" \" ", "He couldn't say.\" \"", "Had to be small enough to fit in the back seat of a car.\" \"", "Colonel, we do know it came in on a ship from Africa around September 1st.\" \"", "It's something at least, maybe it's enough\" \"We gotta find that ship.\" \"", "You better pack, we got work to do.\" \"", "Yes, sir.\" \" ", "Colonel Briggs.\" \" ", "Yes, sir.\" \"", "Daniels was here?\" \"", "In here?\" \" ", "Yes, he was, general.\" \" ", "Why was I not informed?\" \"", "Sir, you were sleeping.\" \"", "I am never that asleep, Briggs.\" \"", "Now, you find him and you arrest him.\" \"", "Code blue.\" \"", "Emergency Room 3, stat.\" \"", "We are so close now, Robby, we have a real chance.\" \"", "I know.\" \" ", "Do you believe that?\" \" ", "I believe you, Sam.\" \" ", "You gotta go.\" \" ", "Okay.\" \"", "Listen to me...\" \"I don't know how to say this... but if I'm not back by 1800... and you're not symptomatic... leave.\" \" ", "What are you saying?\" \" ", "Leave town.\" \"", "Robby, have you seen the troops moving out?\" \"", "They can't do that.\" \"", "They're doing it, Robby.\" \"", "Colonel.\" \"", "Sir, I think we should go very soon.\" \"", "Like, right now.\" \"", "Let's go.\" \"", "Where's Colonel Daniels?\" \"", "In the hospital?\" \"", "Yes, he's upstairs, I could\" \"Upstairs.\" \"", "Let's go.\" \" ", "How many hours of flight school?\" \" ", "60 hours plus, sir.\" \" ", "Actual flying time?\" \" ", "Every minute.\" \"", "I was yanking and banking.\" \"", "Anybody seen Colonel Daniels?\" \" ", "Colonel Daniels.\" \" ", "We're looking for Colonel Daniels.\" \"", "Have you seen him?\" \"", "Tall, big guy?\" \"", "Sure, sure.\" \"", "There.\" \"", "I want the rotors re-checked.\" \"", "Let's see some activity on these birds, people.\" \" ", "We got four flights to pull today.\" \" ", "Sir.\" \"", "I want a fuel niner-three and I want a turn niner-one.\" \"", "Let's go.\" \" ", "Sergeant.\" \" ", "Can I help you, sir?\" \"", "Sergeant, where's your pilot?\" \"", "General Ford just called from CP.\" \"", "We've got helicopter priority to deliver flash traffic.\" \"", "Where is he?\" \"", "My pilot, sir, he's, he's, he's....\" \"Your pilot's what, sergeant?\" \"", "Sir, my pilot's taking a leak.\" \"", "Taking a leak?\" \"", "No shit.\" \"", "Well, in that case, we'll just wait in the Loach.\" \"", "Sir.\" \" ", "Tell him to squeeze it off, sergeant.\" \" ", "How about you give him a hand, sergeant?\" \"", "Yeah, okay.\" \"", "Mr. Robertson.\" \"", "Mr. Robertson, get out here on the double.\" \"", "Mr. Robertson.\" \"", "Anybody seen Colonel Daniels?\" \"", "They're down below.\" \"", "Let's go.\" \"", "They're in the helicopter.\" \"", "Pull them out.\" \"", "Move.\" \"", "Stop that chopper.\" \"", "That's an order.\" \" ", "Stop them.\" \" ", "Hold your fire.\" \"", "Hold your fire.\" \"", "Watch it.\" \"", "Hit the decks, troops.\" \"", "We're airborne.\" \"", "Com Center, flight line.\" \"", "Com Center.\" \"", "Com Center, flight line.\" \"", "Shit.\" \"", "Get us to San Francisco, Salt.\" \"", "They'll be on our tail, so follow the coast.\" \"", "The fog might give us cover.\" \" ", "Fog, sir?\" \" ", "Yeah, fog.\" \"", "You've flown through fog, right?\" \"", "I read about it, sir.\" \"", "Daniels commandeered one of our choppers.\" \"", "What?\" \"", "Dare I ask how?\" \"", "Don't waste time thinking about it, Briggs.\" \"", "Find him.\" \"", "If he resists, shoot him.\" \" ", "I understand, sir.\" \" ", "Wait, wait.\" \" ", "Donnie, you don't have to do this.\" \" ", "He's a carrier of the disease.\" \"", "Do it now.\" \"", "I'm doing it, sir.\" \"", "Donnie, you go after him like this, the press is gonna swarm all over it.\" \"", "You're creating a panic.\" \"", "You always have the wrong priority, Billy.\" \"", "He's not infected, Donnie.\" \"", "You damn well know it.\" \"", "I know that he has been in direct contact with Motaba patients.\" \"", "You know something beyond that?\" \"", "You should have arrested him when you had the chance.\" \"", "Launch AWACS.\" \" ", "Yes, sir.\" \" ", "Shut up.\" \" ", "Yes, sir.\" \" ", "Holy shit.\" \"", "I got it.\" \"", "Back up, coming through.\" \"", "Make a hole, people.\" \"", "Back it up.\" \"", "Colonel Daniels from USAMRIID.\" \"", "Sorry.\" \"", "Yes, and I'm George from Sioux City, South Dakota.\" \"", "Back of the line, colonel.\" \"", "We got a terrible epidemic.\" \"", "We're from Cedar Creek.\" \" ", "We're from Cedar Creek, California.\" \" ", "Cedar Creek, site of the viral infection.\" \"", "George, you heard about this virus?\" \"", "Need we say more?\" \" ", "No.\" \" ", "We need all the bills of lading... from ships arriving from Africa in the last 3 months.\" \"", "George.\" \" ", "Shall I cough on you, George?\" \" ", "No.\" \" ", "Mrs. Pananides.\" \" ", "Now you're talking, George.\" \" ", "Mrs. Pananides...\" \" What?\" \"", "I think these men need some help.\" \"", "Biotest has to be very careful in its paperwork.\" \" ", "Live cargo, federal regulations.\" \" ", "Thank you.\" \"", "Here's our list.\" \"", "Compare it with your Biotest list.\" \" ", "You ready?\" \" ", "Yes, sir.\" \" ", "Number one, Petrov.\" \" ", "Same.\" \" ", "Number two, Venus.\" \" ", "Same.\" \" ", "Number three, Patricia.\" \" ", "Same.\" \"", "Number four, Tae Kuk.\" \" ", "Tae Kuk.\" \" ", "No, sir.\" \" ", "No?\" \" ", "No, sir.\" \"", "San Francisco a week ago, carrying a monkey.\" \" ", "Delivered to Biotest.\" \" ", "Negative, sir.\" \" ", "It's not on the list?\" \" ", "No, sir.\" \" ", "That's our vessel.\" \"", "That's the boat.\" \" ", "Sir, sir.\" \" ", "The Tae Kuk has set out to sea already.\" \" ", "So what?\" \" ", "How are we gonna locate it?\" \" ", "I got a friend in the Coast Guard.\" \"", "I can make a call, easy.\" \"", "How close a friend?\" \"", "Closer than his wife would like.\" \"", "Get me on that ship.\" \"", "It can't be far, it just left this morning.\" \"", "You want me to fly you out to sea... drop you onto a freighter?\" \"", "Sir, with all due respect, that is idiotic.\" \"", "Idiotic?\" \"", "Let me ask you a question, are we fugitives from the law?\" \" ", "Right.\" \" ", "Idiocy is our only option.\" \"", "Find the boat.\" \"", "So, what is this?\" \"", "She's a monkey.\" \"", "Her name's Betsy.\" \" ", "A monkey?\" \"", "I could tell.\" \" ", "I'm feeding her, see?\" \" ", "She lives in the woods.\" \" ", "Do a lot of monkeys live in the woods?\" \"", "No, just Betsy.\" \"", "She comes to visit me.\" \"", "Does Betsy like apples like my little monkey loves apples?\" \"", "She does.\" \"", "Tae Kuk, Tae Kuk, this is Army Helo 1350 on guard.\" \"", "Say your position, over.\" \"", "Try another frequency.\" \"", "It won't work, colonel, they'll be monitoring marine channels.\" \" ", "Have to rely on the Coast Guard reports.\" \" ", "Just don't get negative.\" \"", "Affirmative.\" \" ", "You sure you got the coordinates right?\" \" ", "Yes, sir.\" \" ", "How much fuel have we got?\" \" ", "Don't worry about it.\" \"", "This bird will go 400 miles without refueling.\" \" ", "Wait.\" \" ", "What?\" \"", "There.\" \"", "Tae Kuk, Seattle.\" \"", "That's it.\" \"", "There it is.\" \" ", "Thank you, Mrs.\" \" What's her name?\" \" ", "Pananides.\" \"", "Thank you, ma'am.\" \" ", "I can't land this thing on that ship, sir.\" \" ", "You gotta get me on it.\" \" ", "I'll get you close enough, colonel.\" \" ", "Close enough for what?\" \"", "Close enough to jump, sir.\" \"", "You're not serious.\" \"", "All right, you fly, I'll jump, colonel.\" \"", "Just get closer.\" \" ", "Just get very close.\" \" ", "Yes, sir.\" \"", "Colonel, that lifeboat down there is your best shot.\" \"", "How do I get back up here?\" \"", "Just get them to clear me an area.\" \"", "Or I can throw you a rope.\" \"", "Just kidding, sir.\" \"", "Trying to keep you loose.\" \"", "Closer!\" \"", "Get me closer!\" \"", "Does anyone here speak English?\" \"", "English?\" \" ", "A little.\" \" ", "I need information... about an animal that was on this ship.\" \"", "Okay, you don't understand.\" \"", "Look, this is a medical emergency.\" \"", "I'm an American Army doctor.\" \" ", "Doctor.\" \"", "Doctor.\" \" ", "Doctor.\" \"", "Doctor.\" \"", "Doc\" \"Come.\" \"", "Look.\" \" ", "Is there anyone else sick on this ship?\" \" ", "No.\" \"", "No, sick.\" \"", "Can you take me to this man's sleeping quarters?\" \"", "Upstairs.\" \"", "Where's his locker?\" \"", "There's our host.\" \" ", "Hey.\" \" ", "Hey.\" \"", "How are you?\" \"", "I'm good.\" \"", "I'm good, Case.\" \"", "Robby...\" \" Yeah, case?\" \" ", "you should be nice to Sam, you know.\" \"", "He's got a big crush on you.\" \"", "I'm so scared.\" \"", "Would you please hold my hand?\" \"", "I'm right here, Casey.\" \"", "The president's scientific advisors at FEMA... have assured me that there is no threat... of the further spread of this disease at the present time.\" \"", "In a related story, the two men who escaped... from the Cedar Creek quarantine this morning... and are believed to be infected with the disease\" \"Stay back.\" \"", "Just relax.\" \"", "This is a military emergency.\" \"", "Back up.\" \"", "Back up.\" \"", "It's all right.\" \"", "It's all right.\" \"", "Back up.\" \"", "Everybody back up.\" \"", "This is a military emergency.\" \"", "Stay calm.\" \"", "Stay calm.\" \" ", "Everybody stay calm.\" \" ", "It's all right.\" \"", "It's okay.\" \"", "That's the guys.\" \"", "Two, get your camera on them.\" \" ", "Tell me which camera to talk into?\" \" ", "Right there.\" \"", "My name is Colonel Sam Daniels, I'm here with Major Salt.\" \"", "We are not infected with the Motaba virus, but many other people are.\" \"", "We have identified the animal... carrying the virus and we need your help in finding it.\" \"", "The animal who is carrying the Motaba virus is a monkey.\" \"", "This is a photo of the animal.\" \"", "Can you get in close, please?\" \"", "Can you get a shot of it, please?\" \"", "Somebody?\" \"", "Get in as close as you can.\" \"", "It's a small monkey, about the size of a cat.\" \"", "It has a white face, it has dark fur running down its back.\" \"", "Please do not attempt to capture it yourself.\" \"", "Don't even go near it.\" \"", "What you can do is if you see this monkey... call this number at the Center for Disease Control in Atlanta.\" \"", "The area code is 404, and it's 555-9653.\" \"", "Again, if you see this monkey...\" \" do not go near it.\" \"", "Do not\" \" Kate!\" \"", "Hold your fire.\" \"", "Right.\" \"", "Palisades.\" \"", "Dr. Reynolds, I just want to read this back to make sure I've written it down correctly.\" \"", "That's 211 Sycamore Road, Palisades... and the woman's name is Jeffries.\" \" ", "Thank you very much.\" \" ", "Thank God that woman called the CDC.\" \"", "You're not kidding.\" \"", "What have we got?\" \"", "Jimbo takes the monkey to Cedar Creek, tries to sell it but can't.\" \"", "So he drives to San Francisco, he gets on an airplane for Boston...\" \" but without the animal.\" \" ", "Must have released it somewhere.\" \"", "Right in between Cedar Creek and San Francisco is what?\" \" ", "Palisades.\" \"", "That's it.\" \" ", "That's it.\" \" ", "We're there.\" \" ", "There it is.\" \" ", "That's it.\" \" ", "There it is.\" \" ", "We're there, colonel.\" \"", "We are there.\" \" ", "There it is.\" \"", "Intercepted a phone transmission.\" \"", "They're headed there, I got two teams on standby.\" \"", "Good.\" \"", "A potential screwup you managed to avoid among many others you have not.\" \"", "Who do you think should handle this now?\" \"", "You, sir?\" \"", "You kiss ass with the best of them, Briggs.\" \" ", "You hope to make general one day?\" \" ", "Yes, sir.\" \"", "Well, you won't.\" \"", "Now, get me on one of those choppers.\" \"", "She won't come.\" \"", "She won't come, except to me.\" \"", "I'm her only friend.\" \"", "I trust you are the very best helicopter pilot in this man's army?\" \" ", "Yes, sir.\" \" ", "That's a relief.\" \"", "Viper 2, Lead, left echelon.\" \"", "Viper 2, line the skids, I'm at your six.\" \"", "We're looking for a Loach, side number 1350.\" \" ", "1350, sir.\" \" ", "Make this easy for me, all right?\" \"", "Yes, sir.\" \" ", "Katie.\" \" ", "What?\" \"", "Have you ever been sick?\" \" ", "Yes.\" \" ", "It's not much fun, is it?\" \" ", "No.\" \" ", "Well... there's a whole lot of people that are sick right now.\" \"", "A whole town.\" \"", "And you know how much that you love your mommy?\" \"", "Well, that's how much I love my wife.\" \"", "And my wife is one of the people who's very sick... and I want her to get better.\" \"", "And\" \" Is it Betsy?\" \"", "Betsy can help make everybody better because she's got this medicine inside her.\" \"", "And that's what makes her very special.\" \"", "Do you understand?\" \" ", "You won't hurt her?\" \" ", "No.\" \"", "She'll just go to sleep for a little while.\" \"", "That doesn't hurt, does it?\" \"", "No.\" \"", "Promise you won't hurt her?\" \"", "I promise.\" \"", "If I hurt her, you can punch me in the nose.\" \"", "A serious punch... for a very serious nose.\" \"", "All stations this net, this is Viper 6.\" \"", "The commander in chief has issued final authorization.\" \"", "We are ordered to proceed.\" \"", "Some of us have doubts about what we are about to do.\" \"", "We'd be less than human if we didn't.\" \"", "But the fate of the nation... perhaps the world, is in our hands.\" \"", "We are the last line of defense.\" \"", "We cannot, we dare not refuse this burden.\" \"", "I'm confident that each of us... each of you, will do his duty.\" \"", "Viper 6 out.\" \"", "Viper Command, Sandman is rolling.\" \"", "Over.\" \"", "God forgive us.\" \"", "Betsy.\" \"", "Here, girl.\" \"", "Here, Betsy.\" \"", "Here, girl.\" \"", "Here, Betsy.\" \"", "Here, Betsy.\" \"", "Betsy.\" \"", "Here, Betsy.\" \"", "Here, girl.\" \"", "Oh, God, be careful.\" \"", "Here, Betsy.\" \"", "He won't hurt her.\" \"", "Here, Betsy.\" \"", "Here, girl.\" \"", "Here, Betsy.\" \"", "Here, Betsy, girl.\" \" ", "I can't stand this.\" \" ", "Betsy.\" \"", "It won't be long.\" \"", "Here, Betsy.\" \"", "There you are.\" \"", "Careful.\" \"", "Careful.\" \"", "Here, Betsy.\" \"", "Here, Betsy.\" \"", "No.\" \"", "Jesus.\" \"", "Come on, Katie, move.\" \"", "Come on.\" \"", "No.\" \"", "Oh, baby.\" \"", "Move.\" \"", "Come on.\" \"", "Betsy, come on.\" \"", "Here, Betsy.\" \"", "Here, girl.\" \" ", "Shoot.\" \" ", "Damn it, Salt.\" \"", "We're approaching the destination, sir.\" \"", "Fellas, our fugitive is a carrier of the disease... and we're going to take him into quarantine at Travis, all right?\" \"", "Let's go.\" \"", "Big Eye, Big Eye, Viper flight is airborne, do you see us?\" \"", "Viper, Big Eye.\" \"", "Paint you flight of two.\" \"", "Standing by.\" \"", "Over.\" \"", "Come on, major, don't give me any shit and listen carefully.\" \"", "Put Ford on the phone, tell him it's Colonel Daniels, it's urgent.\" \"", "Sam?\" \"", "Where the hell are you?\" \"", "Billy, we're on our way back.\" \"", "We got the host.\" \" ", "You what?\" \" ", "We found the host, Billy.\" \"", "Thank God.\" \"", "Sir, you've got to call off the bombing.\" \"", "Well, I'll buy you some time, that's all I can do.\" \" ", "You get your ass back here quickly, safely.\" \" ", "Yes, sir.\" \"", "Sam, you may run into resistance on your way back.\" \"", "Resistance?\" \"", "That makes it a little tough to get back safely, doesn't it, Billy?\" \"", "Good luck.\" \"", "Let's go.\" \" ", "Problems, colonel?\" \" ", "Of course.\" \"", "Sandman flight, this is Viper 6.\" \"", "Stand down, stand down.\" \"", "Return to base.\" \"", "Viper 6, Sandman.\" \"", "Roger.\" \"", "Return to base.\" \" ", "Salt.\" \" ", "Yes, sir.\" \"", "Take a look.\" \" ", "Is that resistance?\" \" ", "That's resistance.\" \"", "Hold on.\" \" ", "There's our Loach, sir.\" \" ", "Where?\" \"", "Army 1350, this is Viper Lead at your 8 o'clock.\" \"", "Acknowledge.\" \"", "Over.\" \"", "Viper, I hear you.\" \"", "Army 1350, stand by to turn into formation... to accompany us to Travis Air Force Base.\" \"", "Over.\" \"", "Travis?\" \"", "On whose authority?\" \" ", "Mine.\" \" ", "Who are you?\" \"", "Major General Donald McClintock, senior officer in this area.\" \"", "Over.\" \"", "I didn't know you were behind us.\" \"", "You'll be happy to know we have the host animal.\" \"", "We are headed back to the lab at Cedar Creek.\" \"", "Your orders are to accompany me to Travis Air Force Base.\" \"", "Over.\" \"", "General, you don't understand, there's nobody sick at Travis.\" \"", "Don't make this difficult for me, Colonel Daniels.\" \"", "They're lining up in attack formation.\" \"", "They don't want us anywhere but down.\" \"", "I don't think you want to destroy an Army helicopter over California in broad daylight.\" \"", "With all due respect, colonel, if you do not follow us to Travis Air Force Base...\" \"I will blow you out of the sky.\" \"", "General, with all due respect, fuck you, sir.\" \"", "Under my authority, go weapons hot.\" \"", "Viper 2, This is General McClintock.\" \"", "Go weapons hot.\" \"", "Hold on, colonel.\" \"", "We're going low.\" \" ", "Anything I can do to help?\" \" ", "Just don't make me nervous.\" \"", "The river bends to the right.\" \"", "We've gotta cut them off.\" \"", "Viper 2, break right.\" \"", "Two, breaking right.\" \"", "I don't see them back there.\" \"", "I think we lost them.\" \"", "Oh, shit.\" \"", "Hang on colonel.\" \"", "Two is masked.\" \"", "No shot, no shot.\" \" ", "See that bridge up ahead, colonel?\" \" ", "Yes.\" \"", "Over or under, sir?\" \"", "Why don't you decide, I'm really not up to it, I'm\" \" Hang on.\" \" ", "I would have said over.\" \"", "Wires, wires.\" \"", "Two is off left.\" \" ", "What should I do, sir?\" \" ", "Just stay on him, get him out of the air.\" \"", "Don't go under the bridge!\" \" ", "You're missing him.\" \" ", "Fuck.\" \" ", "Go into it.\" \" ", "You're missing him.\" \"", "Hang on, colonel.\" \"", "That's it, sir.\" \"", "That's it.\" \"", "We got it.\" \" ", "If you're in trouble, I want to know.\" \" ", "Hang on.\" \"", "Salt, you gotta warn me before you pull a stunt like that again.\" \"", "I didn't know I was gonna do it until it was done, sir.\" \"", "Viper 2, where are the hell are you?\" \"", "Lead, Viper 2 closing in on you now.\" \"", "He just pulled a 180, he's coming right back at you.\" \"", "Viper Lead, they're coming straight at us.\" \"", "I'm going weapons hot.\" \" ", "Holy shit!\" \"", "Break, break!\" \" ", "Break now!\" \" ", "Where's he gone?\" \" ", "I don't know, sir.\" \"", "Son of a bitch.\" \"", "He did that on purpose.\" \" ", "Salt.\" \" ", "Yes, sir.\" \" ", "Are those rockets on the side of this thing?\" \" ", "They are.\" \"", "Fire a couple into those trees.\" \"", "Hey, look there.\" \"", "Lead, we got fire in the trees at 2 o'clock.\" \"", "Verify.\" \"", "Viper 2, Lead.\" \"", "Can you get down there and search for wreckage?\" \"", "Lead, Two.\" \"", "Negative.\" \"", "It's too thick down there.\" \"", "Big Eye, Viper.\" \"", "We think the Loach is down.\" \"", "What do you see?\" \"", "Viper, we had three contacts and then an explosion.\" \"", "Now we've only got two.\" \"", "Everything else is ground clutter on the highway.\" \"", "Over.\" \"", "Flying a little low, aren't we, Salt?\" \"", "Avoiding radar, sir.\" \"", "She's still out.\" \"", "How you doing, Betsy?\" \" ", "Salt.\" \" ", "Sir.\" \"", "Use the E-1101 as a map to synthesize an antiserum.\" \" ", "I'll get right on it.\" \" ", "Got an awful lot of people here.\" \" ", "I'll copy it big time.\" \" ", "I want liters of it.\" \"", "Yes, sir.\" \"", "I want everything in place if Robby responds.\" \" ", "You got it?\" \" ", "Yes, sir.\" \"", "Okay.\" \"", "Sir, there's no sign of wreckage.\" \"", "We've been decoyed.\" \"", "You son of a bitch.\" \"", "How are you doing, kid?\" \"", "Sam.\" \"", "You're gonna be okay.\" \"", "We found the host.\" \"", "You don't have to say that, Sam.\" \"", "No, it's true.\" \"", "Would I kid you?\" \"", "Salt's cooking up the good stuff.\" \"", "So let's hang out for a while.\" \" ", "Sam.\" \" ", "Okay?\" \"", "I love your face.\" \"", "Keep talking to me, Robby.\" \"", "Robby.\" \"", "Robby.\" \"", "Robby.\" \"", "Please don't leave me, Robby.\" \"", "Sam... don't.\" \"", "Sam.\" \"", "Sam, don't.\" \"", "No.\" \"", "Sam.\" \"", "It's okay.\" \"", "Colonel, I got it.\" \" ", "Your helmet.\" \" ", "Come on, come on, put it up.\" \"", "We got it.\" \"", "Okay.\" \"", "You ready?\" \" ", "Say when.\" \" ", "Now.\" \"", "I got it.\" \"", "I got it.\" \" ", "Get the lab geared up.\" \" ", "Yes, sir.\" \"", "Make more, we got a town waiting.\" \" ", "It's gonna work, sir.\" \" ", "Go, go.\" \"", "Come on.\" \"", "The time's now.\" \"", "You delayed the bombing.\" \"", "That more of your sentimental bullshit?\" \"", "For God's sake, Donnie, there's a chance we can save these people.\" \"", "You're nuts.\" \"", "Sandman 1, Viper 1.\" \"", "How copy?\" \"", "Over.\" \"", "Viper 1, Sandman 1.\" \"", "Send your traffic.\" \"", "Over.\" \"", "We had the antiserum and didn't use it.\" \" ", "Don't you think that's gonna come out?\" \" ", "I can defend that.\" \"", "It's not about saving our asses anymore, Donnie.\" \"", "You are to proceed immediately with Operation Clean Sweep.\" \"", "Is that understood?\" \"", "Over.\" \"", "Daniels knows about the African camp.\" \"", "Roger, Viper.\" \"", "Sandman is proceeding.\" \"", "Out.\" \"", "Salt.\" \"", "Her temperature's coming down.\" \" ", "It's working, she's normalizing.\" \"", "Come here.\" \" ", "But, sir, they're coming.\" \"", "I picked up a transmission.\" \"", "The plane is in the air.\" \"", "They're coming, colonel.\" \"", "Come on.\" \" ", "Where are we going?\" \" ", "Come on.\" \"", "Come on!\" \" ", "Where are we going?\" \" ", "Gotta get through to the pilot.\" \" ", "Can you do it?\" \" ", "Yes.\" \"", "Guard channel.\" \"", "Every aircraft has it.\" \" ", "All right, get this thing up.\" \" ", "Where are we going?\" \"", "I don't know.\" \"", "Get us in the air.\" \"", "Shouldn't we contact the command center?\" \"", "We have the antiserum.\" \" ", "Don't care.\" \"", "They want to bury the town.\" \" ", "This is crazy.\" \" ", "They want their weapon.\" \" ", "Kill all those people?\" \" ", "They want their weapon.\" \" ", "Sit and watch all those people die?\" \"", "Yes, they want their weapon.\" \"", "No.\" \"", "Viper, Sandman.\" \"", "We are at the IP commencing bomb run now.\" \"", "Three minutes to target area.\" \"", "Over.\" \"", "Sandman, Viper Command.\" \"", "Bomb release is go.\" \"", "I say again, bomb release is go.\" \"", "Over.\" \"", "Where are we going?\" \"", "What are we doing?\" \"", "Get me on the Guard channel, I wanna talk to the pilot.\" \" ", "Go.\" \" ", "To the aircraft approaching Cedar Creek... this is Colonel Sam Daniels, a doctor with USAMRIID.\" \" ", "Do you read me?\" \" ", "We read you.\" \"", "Over.\" \"", "Okay.\" \"", "You must not bomb this town.\" \"", "I repeat, do not drop the bomb.\" \" ", "We have produced an antiserum....\" \" That son of a bitch.\" \"", "Sandman, Viper Command.\" \"", "You're being spoofed by com chatter.\" \" ", "Charlie Mike, over.\" \" ", "Viper Command, Sandman.\" \"", "Authenticate Hotel Alpha.\" \"", "Over.\" \"", "Sandman, this is Viper Command.\" \"", "I authenticate...\" \"Juliette, over.\" \"", "Unfortunately, your commanders do not have the current data.\" \"", "We do.\" \"", "We have an antiserum.\" \"", "As we speak, it's being administered.\" \"", "Every infected person within a matter of hours will have their dosage... you must abort the mission.\" \"", "This is urgent.\" \"", "Answer me.\" \"", "Do you read me?\" \"", "You cannot bomb this town.\" \"", "You must abort.\" \"", "I am talking to the pilots in the bomber.\" \"", "Do you read me?\" \"", "Do you read me?\" \" ", "Where is he, Briggs?\" \" ", "Can you hear me?\" \"", "Can he prevent the bombing?\" \"", "Can he cause them to abort their run?\" \"", "If he gets in the way of that inbound aircraft.\" \"", "You get something up in the air and blow him the Christ out of there!\" \" ", "Now.\" \" ", "Yes sir, major.\" \" ", "What have we got in the way of Stingers?\" \" ", "Can we not stop his transmission?\" \"", "Do you read me?\" \"", "You must abort.\" \"", "They won't answer you, colonel, they've been trained not to.\" \"", "You hear me, don't you, guys?\" \"", "I'll say it one last time.\" \"", "These people that you're gonna bomb are not the enemy.\" \"", "We can kill the virus without killing these people.\" \"", "And I swear to you on my soul... that the president does not have the facts.\" \"", "He does not know we have a serum that is working.\" \"", "Do you really think he wants to blow up the town?\" \"", "Oh, Christ, guys, if you think I'm lying, drop the bomb.\" \"", "If you think I'm crazy, drop the bomb.\" \"", "But don't drop the bomb just because you're following orders.\" \"", "What you haven't been told is your superiors have another agenda.\" \"", "Don't you understand that below you in Cedar Creek, there's a biological weapon... that they've been manufacturing illegally for the last 30 years?\" \"", "Hey, I guarantee you... that the disease has spread beyond the perimeters of this town.\" \"", "People, we're in a state of national emergency.\" \" ", "You can't tell me that virus\" \" We are under executive orders.\" \" ", "--what the serum is.\" \" ", "See it through.\" \"", "And if you incinerate Cedar Creek, you incinerate the serum.\" \"", "Billy, can you hear me?\" \"", "Why don't you do something?\" \"", "Call this thing off.\" \"", "Don't kill all these people to protect your lie.\" \"", "This is murder, Billy, any way you fucking slice it.\" \"", "If you manipulate the truth, the president, the country, the Constitution... then it's not just a town you're killing, it's a big piece of the American soul, sir.\" \"", "Billy, why aren't you at Cedar Creek, man?\" \"", "Colonel Daniels, this is General Ford.\" \"", "I remind you that you are interfering with presidential authority.\" \"", "Sandman has a specific line to the target.\" \"", "If you are in his way, he cannot complete his bombing run... and there will be hell to pay.\" \"", "Do you understand?\" \"", "Over.\" \" ", "Why'd he say that?\" \" ", "Beats the hell out of me.\" \"", "Billy, are you dumb or something?\" \"", "You just told him how to stop the\" \"Okay.\" \"", "Okay.\" \"", "Colonel, there it is.\" \"", "I see it.\" \" ", "Okay, man, you up for this?\" \" ", "Yes, sir.\" \"", "Viper Command, he's over the target area.\" \"", "Please advise.\" \"", "Over.\" \"", "Sandman, Viper Command.\" \"", "We have final clearance.\" \"", "Do not deviate.\" \"", "Over.\" \"", "Guys.\" \"", "I'm talking to the pilots coming toward us in the bomber.\" \"", "I know what you're about to do doesn't come easy to you, but what...\" \"I've been telling you is truth, so help me God.\" \"", "You will release that weapon on time and on target!\" \"", "Whatever you do in the next 30 seconds will be your testimony to life.\" \"", "Sandman, Viper Command.\" \"", "You know what's riding on this.\" \"", "Please, try to remain calm.\" \"", "Okay, guys, no more words.\" \"", "But we're not moving from your path.\" \"", "Do you hear us?\" \"", "I said we're not moving from your path.\" \"", "I've never seen anything like this, I swear to God.\" \"", "Never seen anything.\" \"", "Sandman, Viper Command.\" \"", "I don't care if you have to fly through those bastards.\" \"", "This is what you've been trained for.\" \"", "Hold your course and drop.\" \"", "Over.\" \"", "You'll have to take us out with you.\" \"", "We're not moving!\" \"", "We're not moving!\" \"", "They're dropping it.\" \"", "Thank you, guys.\" \"", "Sandman, Viper Command.\" \"", "How did you release that weapon?\" \"", "Over.\" \"", "Viper Command, this is Sandman.\" \"", "We have detonation over the water.\" \"", "It might have been wind shear.\" \"", "Over.\" \"", "Sandman, you understand that it is my belief... that you have deliberately contravened a direct order.\" \"", "Now, you return to base for immediate rearming.\" \"", "Over.\" \"", "Give me the microphone, general.\" \"", "I beg your pardon, Billy?\" \"", "Give me the mike, general.\" \"", "Sandman, this is General Ford.\" \"", "You will ignore that order.\" \"", "For the record, I am relieving General McClintock of command... for withholding vital information from the president of the United States.\" \"", "I have in no way withheld vital information from the president of the United States.\" \" ", "Colonel Briggs.\" \" ", "Sir.\" \"", "You will place General McClintock under arrest.\" \"", "If I go down for this, Billy, you go down for it.\" \"", "It's out of our hands now, Donnie.\" \"", "You silly, sentimental son of a bitch.\" \"", "Nobody puts me under arrest.\" \"", "Nobody.\" \"", "Colonel Briggs... what a wonderful moment this must be for you.\" \"", "Sam.\" \"", "Yes.\" \"", "Boy, that was a good nap, kid.\" \"", "You look better.\" \"", "The gown becomes you.\" \" ", "How're they doing on the antiserum?\" \" ", "Great.\" \"", "They're cranking it out by the liter.\" \"", "How much are they giving the contact patients?\" \"", "Two-hundred mls.\" \"", "Is that what they gave you?\" \"", "I didn't think I'd ever see you again.\" \"", "I didn't think you'd make it.\" \"", "It's a pretty unique experience.\" \"", "Sort of like living with me.\" \"", "Would you go through it again?\" \"", "Maybe.\" \"", "Now that I have the antibodies.\" \"[", "ENGLISH]\"" ]

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[ "Jews Choosing Life\n\nMatthew Berke\n\nThe sanctity and infinite worth of every human being is a quintessential Jewish value, grounded in the biblical notion that man is made in the image and likeness of God. ", "According to the Mishnah (Sanhedrin 4:5): \"Whoever destroys one life is as if he destroyed a whole world, and whoever preserves a life is as if he preserved the whole world.\"", "\n\nAgainst this background, it is ironic and vexatious for many pro–life activists that American Jews tend to line up on the \"pro–choice\" side in the struggle over abortion. \"", "Affirming the Sanctity of Human Life,\" a conference held last November 12 in Washington, D.C., brought together a hundred or so Jews who are troubled by the Jewish community’s stance toward the unborn, particularly concerning the gruesome late–term procedure known as \"partial–birth abortion.", "\"{1}\n\nThe assembly was, if not representative, at least diverse: secular and religious, prominent public personages and private individuals, the well informed and those trying to become informed. ", "Organized by Chris Gersten of the Washington–based Institute for Religious Values, and sponsored by a grant from Our Sunday Visitor Institute, a Catholic organization, the conference was held at the Catholic University of America. ", "Even for someone accustomed to interreligious gatherings, the anomaly was striking. ", "Happily, it was not of the \"what’s wrong with this picture\" variety, but rather, what’s right with it: ordinary Jews and rabbis of all denominations (several with long, hasidic–style beards) engaged in dialogue with each other and with the evangelical Protestant and Catholic pro–lifers in attendance. ", "Only in America, one might say—and perhaps only when the issues truly involve life and death.", "\n\nThe morning session consisted of panel presentations by three Orthodox Jews and a maverick Reform rabbi. ", "Marshall Breger, a law professor and political writer, lamented the fact that Jews support \"abortion rights\" more than any religious or ethnic group: they are consistently 15 to 20 percent above the norm, he said, even when controlling for various factors such as religious belief or unbelief, political ideology, social class, etc. ", "He attributed this support, in part, to fears that governmental restrictions on abortion would abridge personal autonomy and impose Christian religious standards on Jewish life. ", "He said that \"gray areas\" in Jewish law—its combination of silence and ambiguity regarding the fetus’ status, its handful of exceptional situations allowing abortion—have confused Jews about the permissibility of abortion in general.", "\n\nBarry Freundel, an Orthodox rabbi from Georgetown, seconded Breger’s sociological account of Jewish fears about abortion as being \"symbolic\" of the wider Jewish culture clash with conservative Christian movements. \"", "It’s hard to have a conversation about abortion,\" he said, \"that doesn’t become a conversation about something else.\" ", "Even among his own Orthodox congregants, Freundel said, his pro–life preaching is treated as the rabbi \"getting up on his soapbox\" again. ", "Nevertheless, he said, he feels obliged to inform them that the absolute license to abort, as practiced in the United States today, is \"simply impossible to reconcile\" with traditional Jewish teaching. ", "Judaism, he said, permits abortion in a few limited circumstances, such as to save the life of the mother. ", "He indicated that there is some difference of rabbinic opinion about these circumstances, but stressed that there is no warrant for the overwhelming number of abortions now performed in the U.S. He said that classic Jewish sources really don’t say much about the general moral or metaphysical status of the fetus; but, he added, we have an \"intuitive response\" that the fetus is \"not like an appendix or an in–grown toe nail\" that can simply be removed at will.", "\n\nDavid Novak, a theologian and rabbi who holds a chair in Jewish Studies at the University of Toronto, further developed the theme that Jewish thinking on abortion tends to be less theoretical than practical. ", "And the guide to practice is sometimes ambiguous: The great medieval teacher Rashi, for instance, implies in one case that the fetus has no rights, but elsewhere seems to imply the opposite. ", "No Jewish source, however, accepts abortion for the purpose of birth control or sterility, a practice that \"cheapens human life\" and public morality. ", "Novak suggested that Jewish casuistry regarding permissible versus impermissible abortions could leaven the general societal debate on this vexed issue. ", "But he warned against having the Jewish witness be limited to pleading \"exceptions\" and hard cases; it is corrupting, he argued, to allow exceptional cases to dictate general rules, or, worse, to be the occasion for erasing rules altogether. ", "Despite his emphasis on the practical over the metaphysical, Professor Novak did, finally, open the door to the kind of wider considerations assumed by Christian pro–life advocates when he spoke of Judaism’s overall thrust toward \"greater inclusiveness in the human community.\"", "\n\nYehuda Levin, an Orthodox rabbi from Brooklyn—a conference participant though not a panel member—said that the Orthodox community has a special responsibility to present to the wider public the authentic pro–natal, pro–life Jewish view on abortion. ", "Levin, well known in the New York area for taking the conservative cultural agenda to the streets and to talk radio, said Jews are obliged not just to cultivate righteousness within their own community but also to be \"a light unto the nations\"; specifically, he argued, Orthodox institutions should lobby to protect life as earnestly as they seek tuition tax credits or vouchers for religious schools.", "\n\nClifford E. Librach, a Reform rabbi from Sharon, Massachusetts, picked up on the theme of greater inclusiveness. ", "He turned the tables on his own liberal Reform movement, which frequently justifies changes in Jewish law on the grounds that the ancient rabbis lacked modern, scientific knowledge. ", "What, then, Rabbi Librach asked, if the sages had known that, from the moment of conception, twenty–three chromosome pairs form the signature of each human being, or that a fetus exhibits brain waves at just ten weeks, or that fetuses are sensitive to music and human voices? ", "Though the Reform movement has uncritically supported \"abortion rights\" in its political activities, Librach found a source of possible hope in its rabbinic wing, which has occasionally displayed a measure of moral seriousness on the issue. ", "In 1996, for instance, it refused to give legal approval for an abortion to a couple that claimed giving birth to a handicapped child \"would impose an undue hardship on their other children.\" ", "According to the rabbinic responsum: \"The secrets of God . . . ", "are not knowable,\" and \"We do not encourage abortion, nor favor it for trivial reasons, nor sanction it on demand.\" ", "At other times, however, Librach noted, the Reform rabbinate exhibits pro–choice obfuscation, euphemism, and self–contradiction, as in its 1994 home prayerbook, which offers the following prayer \"upon termination of a pregnancy\": \"Mother of all life: I need You. ", "I need Your comfort and love; I yearn to rest my head on Your tender breast. ", "Rock me in Your arms as I reflect upon the meaning of life and loss. . . . ", "Awed by the creative powers within my body, I look back with sadness on the life that could not be.\"", "\n\nSimilar ambivalence characterizes the thinking of Conservative movement rabbis, Librach said. ", "He quoted a 1998 Conservative rabbinic manual, whose section on \"grieving ritual following termination of pregnancy\" is hopelessly self–contradictory in its attitude toward the unborn: in some passages referring to the fetus as \"a thing,\" a mere \"stirring\" or \"seed\" of life \"that could not grow into a child\" and therefore \"could not be,\" but in other places as a \"baby,\" even praying \"Shelter this baby, O God, under Your care.\"", "\n\nAs part of a successful strategy to reduce abortion, Librach cited the need to celebrate the \"autonomy\" of the fetus and its potential for uniqueness and creativity. ", "Hesed, the Hebrew word for lovingkindness, with its implication of self–sacrifice and surrender, should be part of the mother’s attitude toward the unborn life within her, and of society’s toward her in her dilemma. ", "We must \"acknowledge . . . ", "the difficulty in addressing both the morality of the act [of abortion] and the fragile loneliness of the mother, who is both a person and a vessel . . . [", "and who] desperately needs a friend more than a lecture.\" ", "He recalled God’s solicitude for Hagar (in Genesis 16) as a model for our response to women who feel abandoned, bereft, and alone.", "\n\nThe luncheon speaker was actor Ben Stein, who argued for the importance of bringing the pro–life case to Hollywood’s liberal Jewish elite. ", "Though that elite is not particularly religious, it will, over the long term, take notice if groups of rabbis persistently argue against abortion and for life. ", "Given that so many people take their cultural and moral cues from movies and TV, it is vital, he said, that Hollywood be converted to the pro–life cause. ", "He expressed a wish that the TV series Touched by an Angel would have a pregnant young woman receive the message that the life inside her is a human being; that, he said, would be a cultural turning point. ", "Already, he noted, there is some \"upward seepage\" of pro–life sentiment in Hollywood coming from the industry’s blue–collar support people—grips, light men, hairdressers, make–up artists, and others.", "\n\nIn the afternoon, there were two impassioned pleas for Jewish opposition to the late–term procedure frequently called \"dilation and extraction\" but commonly known as \"partial–birth abortion.\" ", "As the speakers all indicated, \"partial–birth\" is the more accurate description because labor is induced to the point that the majority of the body comes out the birth canal, while the head, still remaining inside, is punctured with scissors and the brain suctioned out by a catheter in order to facilitate removal of the collapsed skull. ", "The procedure is, according to every speaker at the conference, clearly in violation of Jewish law, which says that if either a baby’s head or the majority of its body emerges from the womb it is considered a human being and may not be harmed.", "\n\nSandi Merle, a Manhattan–based writer and founder of STOP (Standing Together Opposing Partial–birth), said recent election results and congressional votes seem to confirm that \"American culture is becoming a culture of violence and death. ", "Worst of all are the murders of convenience, very much like the killing of unwanted babies in the days of Moses. ", "It is an infamous sign of human regression if we are to become the murderous pharaohs rather than the life–saving midwives. . . . ", "As a people with a tribal memory, instinct tells us we must fight for the survival of those most vulnerable among us—in this case those without a voice, innocent unborn children.\" ", "She called for educational efforts, political activism, and a simple truthfulness that doesn’t try to \"cleanse\" or \"sterilize\" the reality of partial–birth abortion by describing it simply as a late–term abortion. \"", "Be not afraid. ", "Say the vile words: ‘Partial–birth,’ ‘suction tubes,’ ‘infanticide,’ ‘murder.’ ", "Describe the procedure to all who will listen. ", "Make them feel the scissors’ thrust. ", "Otherwise we will be meeting here again next year, and we will remain polite, and kind, and timid, and proper, and—I’m afraid—doomed.\"", "\n\nMoses A. Birnbaum, a Conservative movement rabbi from Plainview, Long Island, was among the 450 rabbis who, under the sponsorship of the Institute for Religious Values, recently published an open letter to Jewish members of the U.S. Senate, urging an override of President Clinton’s veto of a bill to ban partial–birth abortion. ", "The National Council of Jewish Women countered with a pro–abortion letter signed by a group of 500 rabbis; but, Rabbi Birnbaum said, they were unable to refute either the medical or religious arguments of the original letter. ", "Troubled by the idea that religiously knowledgeable Jews could sign such an anti–life document, Birnbaum concluded that \"Many rabbis, difficult as it is to believe, are not aware of the horrific details of the partial–birth abortion procedure.\" ", "Nevertheless, he said, he has been able to convert many of them to a pro–life position by explaining its details and assuring them that the legislation makes full provision to protect the life of the mother.", "\n\nHe said there is much misgiving and guilt in the Jewish community over partial–birth abortion, and people are hungering for an authentic Jewish response. ", "Although Jews cannot, like Catholics, accept a total ban on all abortions, according to Rabbi Birnbaum, it is imperative to \"unite with our Christian brothers and sisters\" against partial–birth, \"a procedure unique in its total violation of Jewish law\" and \"tantamount to infanticide.\" ", "He said Jews should not worry about partial–birth legislation leading to a wider ban on abortion, but should consider one issue at a time. ", "He decried the \"mantra of choice,\" arguing that sometimes people must simply \"choose life—the best choice of all, the only choice.\"", "\n\nRabbi Eliezer Goldstock of Brooklyn, a Lubavitcher hasid, criticized today’s \"morality of convenience\" which is always \"looking for an excuse\" even as \"children are being killed.\" ", "Rabbi Goldstock, who is director of Heart to Heart—an agency that counsels women with unborn children of imperfect health to carry their pregnancies to term, gives post–birth assistance, and, where necessary, provides adoption services—said fetal handicap does not justify abortion, since we are all born with a grave handicap: our mortality.", "\n\nThough the key conference participants and attendees were learned in Jewish law and tradition, one should not underestimate the importance of the ordinary Jews, whether religious or not, whose presence seemed to me a great sign of hope. ", "If these Jews in all their diversity and independence could see the rightness of the pro–life cause (in whatever measure), so, I thought, might many others. ", "As more and more Jews begin to feel comfortable discussing protection for the unborn, what was previously unthinkable becomes suddenly thinkable, even do–able. ", "Education is key, Andrea Seawald, a social worker from Pittsburgh, told me; eventually there will have to be a national Jewish pro–life organization.", "\n\nConference organizer Chris Gersten thanked the pro–life movement and Catholic University for \"creating space\" for a specifically Jewish pro–life group that is unified, at least for now, only in its opposition to partial–birth abortion. ", "That might be the beginning of a larger Judeo–Christian consensus on life, but to help end this one particularly heinous procedure would, in itself, be a great good. ", "As Sandi Merle put it: \"Ultimately, we will have to explain to our children, and our children’s children. ", "L’dor va–dor, from generation to generation, we may have to explain the evil that lives after us.\"", "\n\nMatthew Berke is Managing Editor of First Things.", "\n\nEndnotes\n\n{1} For more information or a transcript of the conference, contact Chris Gersten by e-mail <<<Gersten1@aol.com>>> or by fax at (540) 668-6757." ]

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[ "Like some sort of perverted Noah’s Ark, Primal will trap Nicolas Cage on a ship full of predatory animals. ", "And honestly, what the hell more do you need? ", "Can’t you just see that movie in your head already? ", "See Cage running around, screaming that scream of his, as CGI animals leap about with fangs bared? ", "I know I can. ", "And I want it in front of my face immediately.", "\n\nHow’s this for a synopsis? “", "A big game hunter finds himself trapped on a cargo ship when his predatory animals are set loose by a dangerous criminal out to kill everyone on board.” ", "Still not sold? ", "Well, what if I told you this movie starred Nicolas Cage? ", "Is Cage playing the big game hunter? ", "I have no idea – I certainly hope so. ", "But just the thought of Cage trapped on a ship with killer animals is good enough for me. ", "Also, here’s an image.", "\n\nThe movie also stars Famke Janssen, Kevin Durand, and Michael Imperioli, and comes from Nick Powell, a stuntman turned director. ", "That suggests – I think – that Primal is going to be big on stunts. ", "So now you can imagine Nic Cage running around, jumping over stuff, and screaming as he’s chased by a tiger or something like that. ", "I don’t know about you, but I’m very excited about all of this.", "\n\nI know it’s easy to think of Nicolas Cage of a walking, talking meme – especially when he does stuff like this. ", "But he’s an actor who never phones in a performance. ", "He always gives 100% – hell, sometimes he gives 200%. ", "He goes above and beyond and brings his absolutely gonzo approach to acting to whatever part he’s playing. ", "I have no doubt he’ll turn in yet another memorable performance in Primal.", "\n\nThis is just one of several projects Cage has on the horizon. ", "The actor will also appear in the Richard Stanley H.P. Lovecraft adaptation Color Out of Space, the Sion Sono flick Prisoners of the Ghostland, and Jiu Jitsu, about a ninja fighting an alien. ", "You will watch all of those – don’t even pretend you won’t.", "\n\nPrimal hits theaters and VOD on November 8, 2019." ]

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[ "The Ovivo® Reactor ClarifierTM solids contact clarifiers are high rate vertical flow units combining chemical mixing, flocculation, coagulation settling and clarification in a single circular tank. ", "Applications may include lime softening, color removal and turbidity removal in drinking water treatment. ", "Ovivo also has an extensive knowledge and experience in the application of this technology to Oil and Gas and other industrial markets." ]

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[ "Meta\n\nTag: Climate Alarmists\n\nClimate alarmists have finally admitted that they’ve got it wrong on global warming.", "\n\nThis is the inescapable conclusion of a landmark paper, published in Nature Geoscience, which finally admits that the computer models have overstated the impact of carbon dioxide on climate and that the planet is warming more slowly than predicted.", "\n\nThe paper – titled Emission budgets and pathways consistent with limiting warming to 1.5°C – concedes that it is now almost impossible that the doomsday predictions made in the last IPCC Assessment Report of 1.5 degrees C warming above pre-industrial levels by 2022 will come true.", "\n\nIn order for that to happen, temperatures would have to rise by a massive 0.5 degrees C in five years.", "\n\nSince global mean temperatures rarely rise by even as much as 0.25 degrees C in a decade, that would mean the planet would have to do 20 years’ worth of extreme warming in the space of the next five years.", "\n\nThe video is well produced and cleverly constructed – designed to look measured and reasonable rather than yet another shoddy hit job in the ongoing climate wars.", "\n\nSundry “experts”, adopting a tone of “more in sorrow than anger” gently express their reservations about the reliability of the satellite data which, right up until the release of this video, has generally been accepted as the most accurate gauge of global temperatures.", "\n\nThis accuracy was acknowledged 25 years ago by NASA, which said that “satellite analysis of the upper atmosphere is more accurate, and should be adopted as the standard way to monitor temperature change.”", "\n\nMore recently, though, climate alarmists have grown increasingly resentful of the satellite temperature record because of its pesky refusal to show the warming trend they’d like it to show. ", "Instead of warming, the RSS and UAH satellite data shows that the earth’s temperatures have remained flat for over 18 years – the so-called “Pause.”", "\n\nHence the alarmists’ preference for the land- and sea-based temperature datasets which do show a warming trend – especially after the raw data has been adjusted in the right direction. ", "Climate realists, however, counter that these records have all the integrity of Enron’s accounting system or of Hillary’s word on what really happened in Benghazi.", "\n\nGiven the embarrassment the satellite data has been causing alarmists in recent years – most recently at the Ted Cruz “Data or Dogma” hearing last December – it was almost inevitable that sooner or later they would try to discredit it.", "\n\nIn the video, the line taken by the alarmists is that the satellite records too have been subject to dishonest adjustments and that the satellites have given a misleading impression of global temperature because of the way their orbital position changes over time." ]

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[ "Q:\n\nkineticjs 'on mousemove' does not track outside shapes\n\nI have a simple kineticjs program with two rectangles. ", "One is called \"rect\", the other is called \"grow\". ", "When the user clicks and drags in the \"grow\" I want to grow the other rectangle. ", "So when I get a mousedown in grow I do a 'on mousemove' on the grow rect ( have also tried layer and stage ). ", "This works fine except for the user moves the mouse quickly and the mouse moves outside the grow rect. ", "I have tried putting the 'mousemove' function on the layer and the stage hoping this would allow the growing to continue even after the mouse has left the grow box but this doesn't seem to work.", "\nThe code, in it's entirety, is:\n<html>\n<body>\n\n<br>debug:\n<div id=\"debug\">start</div>\n<div id=\"container\"></div>\n\n<script src=\"http://d3lp1msu2r81bx.cloudfront.net/kjs/js/lib/kinetic-v4.5.4.min.js\"></script>\n\n<script defer=\"defer\">\nvar stage = new Kinetic.", "Stage({\n container: 'container',\n width: 500,\n height: 500\n });\nvar layer = new Kinetic.", "Layer();\nvar rect = new Kinetic.", "Rect({\n x : 10,\n y : 10,\n width : 90,\n height : 90,\n fill : \"green\"\n});\nvar grow = new Kinetic.", "Rect({\n x : 80,\n y : 80,\n width : 20,\n height : 20,\n fill : \"red\"\n});\nlayer.add(rect);\nlayer.add(grow);\nlayer.draw();\nstage.add(layer);\nstage.draw();\n\nvar anchor = 0\n\nfunction debug(s) {\n var div = document.getElementById(\"debug\");\n div.innerHTML = s;\n}\n\nfunction doGrow() {\n debug(\"doGrow\");\n var mousePos = stage.getMousePosition();\n var dx = mousePos.x - anchor.x;\n var dy = mousePos.y - anchor.y;\n rect.setWidth(rect.getWidth() + dx);\n rect.setHeight(rect.getHeight() + dy);\n grow.setX(grow.getX() + dx);\n grow.setY(grow.getY() + dy);\n anchor = mousePos;\n layer.draw();\n}\n\ngrow.on('mousedown', function(e) {\n debug(\"down\");\n anchor = stage.getMousePosition();\n //grow.on('mousemove', doGrow); // These are my three attempts\n //layer.on('mousemove', doGrow);\n stage.on('mousemove', doGrow);\n});\n</script>\n</body>\n</html>\n\nSo the deal is, it works except for the user moves too fast and the grow function doesn't continue to get called.", "\nAny help would be greatly appreciated. ", "Thank you.", "\n\nA:\n\nIt looks like KineticJS will only issue a mousemove event if there's an element you're moving over. ", " So two possibilities spring to mind:\n1) Add a background rectangle that covers the entire layer; you can make it transparent, I assume.", "\n2) Attach a mousemove handler via other means, like jQuery, or directly in JavaScript.", "\nYou can see the second approach in action here:\nhttp://jsfiddle.net/SdXqA/\n\n" ]

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[ "Background\n==========\n\nNon-alcoholic fatty liver disease (NAFLD) is the most prevalent chronic liver disease in the world, and is growing especially quickly in Asia. ", "It is regarded as a hepatic manifestation of metabolic syndrome (MetS) because of its close concomitance with obesity, type 2 diabetes mellitus and dyslipidemia \\[[@B1],[@B2]\\]. ", "Patients with NAFLD, who are at increased risk of atherosclerotic cardiovascular disease, are also at risk of progression to non-alcoholic steatotic hepatitis (NASH), cirrhosis or hepatocellular carcinoma \\[[@B3],[@B4]\\]. ", "Our previous study clearly documented a very high prevalence (57.8%) of fatty liver, as assessed by abdominal ultrasound, in adult Taiwanese \\[[@B5]\\]. ", "Previous study has also shown that compared to Caucasians, Asians (mostly Chinese) have a greater fat accumulation in the body and viscera for a given body mass index (BMI) \\[[@B6]\\]. ", "Understanding the consequences and how to prevent the development of fatty liver are extremely important for Asians.", "\n\nNAFLD, defined as hepatic steatosis with an intrahepatic triglyceride (TG) content \\> 5% of the liver volume or weight, develops owing to an imbalance between fatty acid (FA) input and output. ", "Physiologically, the hepatic TG content results from a complex interaction of lipid homeostasis, including (1) fatty acid influx derived by adipose lipolysis (contributing 60% of hepatic FA), (2) dietary fat intake from chylomicron (10- 15%), (3) *de novo* lipogenesis from plasma glucose (25- 30%), (4) fatty acid β-oxidation and (5) fatty acid export by esterification to secrete as a very low-density lipoprotein (VLDL) \\[[@B7],[@B8]\\]. ", "The mechanism of excess hepatic fat accumulation is attributed generally to enhanced FA delivery from adipose lipolysis and increased *de novo* lipogenesis in the liver itself, while β-oxidation and VLDL export play minor roles \\[[@B8]\\].", "\n\nFatty acid synthase (FAS), catalyzing the final step in FA biosynthesis, is well known to be the major determinant of the generation of hepatic FA by *de novo* lipogenesis. ", "Altered FAS expression has been correlated with obesity related insulin resistance and hepatic steatosis. ", "Therefore, circulating FAS has been suggested to be a possible surrogate marker of insulin resistance \\[[@B9],[@B10]\\]. ", "In the FA metabolism, adipose triglyceride lipase (ATGL) and hormone-sensitive lipase (HSL) are responsible for \\> 95% of TG hydrolysis. ", "Both ATGL and HSL regulate the basal lipolysis, whereas only HSL determines the stimulated lipolysis. ", "HSL, catalyzing diacylglycerol and monoacylglycerol into free fatty acids, determines the rate-limiting step to modulate complete lipolysis \\[[@B11],[@B12]\\]. ", "HSL is also engaged in the mobilization of FA from intracellular lipid stores in tissues. ", "Insulin represents the most potent inhibitor of HSL to shut down lipolysis, and HSL expression has often been correlated with the pathogenesis of type 2 diabetes, abdominal obesity and MetS \\[[@B13]-[@B15]\\]. ", "Insulin resistance is the pathophysiologic hallmark of the development of NAFLD. ", "As there is a very low expression of ATGL in the liver, the activities of FAS and HSL seem to be essential for the regulation of fatty acid metabolism in the formation of NAFLD.", "\n\nGenetic susceptibility to hepatic lipid accumulation is also considered important because of the evidence that approximately one-third of NAFLD occurs in subjects without the documented risk factors of obesity and insulin resistance. ", "The *Ile* 1483 variant of the FAS gene was reported to have a protective effect, with a lower BMI, waist hip ratio, fasting glucose and blood pressure \\[[@B16]\\]. ", "The well-studied promoter variant of HSL (−60 C \\> G), exhibiting a 40% decline in promoter activity, plays a critical role in fat metabolism in some diseases in a sex-, race- and insulin-dependent manner \\[[@B17],[@B18]\\].", "\n\nA combination of genetic and environmental risk factors, for example, diet, obesity or diabetes, is well known to cause the development of NAFLD \\[[@B4],[@B19]\\]. ", "However, the risk interaction and the relative impact on the development of NAFLD of individual genes and related metabolic biomarkers have not been thoroughly investigated. ", "We designed this study to clarify the impact of metabolic abnormalities on the relationship between fatty liver and glucose intolerance. ", "The differential impact of confounding risks for the development of NAFLD was analyzed after stratification of the fasting glucose. ", "The results could have eventual clinical utility to help establish a practical treatment strategy for NAFLD in distinct populations with normal or abnormal glucose tolerance.", "\n\nMethods\n=======\n\nSelection criteria\n------------------\n\nSubjects were recruited from the Department of Preventive Medicine at KMUH in 2005 under the approval and supervision of the Institutional Review Board of Kaohsiung Medical University Hospital (KMUH-IRB-980323). ", "All of the serum was obtained from the tissue bank in our hospital and de-identified from participant's names and personal characteristics. ", "To avoid gender bias, a cross-sectional population of 1056 males was randomly enrolled within 3 months. ", "The detailed medical history of each subject was evaluated by an experienced physician. ", "Twenty-seven participants were excluded due to recognized dyslipidemia secondary to poorly-controlled DM, documented DM with medication, Cushing's syndrome, hypothyroidism, nephrotic syndrome, chronic liver disease, heavy alcohol use (drinking more than once weekly) or use of lipid-lowering agents. ", "A total of 1029 male subjects were eligible for further study, and were stratified by fasting glucose into normal glucose tolerance (NGT, \\< 100 mg/dl) and glucose intolerance (GI, ≥ 100 mg/dl) groups.", "\n\nLaboratory measurements\n-----------------------\n\nAfter overnight fasting, blood samples were collected and analyzed for serum glucose, aspartate aminotransferase (AST), alanine aminotransferase (ALT), total cholesterol, serum triglyceride, HDL-cholesterol, and LDL-cholesterol, using a multichannel autoanalyser. ", "Serum insulin was measured using commercial radioimmunoassay kits (Diagnostic Products Corporation, Los Angeles, CA, USA). ", "Serum non-esterified fatty acid (NEFA) was measured by colorimetry (Wako Pure Chemical Industries, Ltd, Osaka, Japan). ", "The objectively quantitative expression of the relative hepatic insulin resistance was indicated by the homeostatic model assessment of insulin resistance (HOMA-IR index = insulin (μU/mL) × glucose (mmol/L)/22.5). ", "The adipose insulin resistance was expressed as the adipose insulin resistance (Adipo-IR index = fasting serum NEFA (μmol/L) × fasting serum insulin \\[μU/mL\\]) \\[[@B20],[@B21]\\].", "\n\nSearch strategy\n---------------\n\nEDTA-treated blood samples were used for DNA extraction by standard methods. ", "The TaqMan genotyping assay was performed to detect the sequence of fatty acid synthase *FAS* polymorphisms (**[rs2228305]{.ul}** for Ile1483Val, **[rs2228307]{.ul}** for Val1888Ile) and *HSL* promoter polymorphism (**[rs34845087]{.ul}** for C-60G, *LIPE* 14672 C \\> G). ", "These assays were designed according to the SNP reference data in the NCBI GenBank database. ", "The ABI PRISM 7500® sequence detection system was use to determine the sequence of the gene variants (Applied Biosystems, Roche, Taipei, Taiwan).", "\n\nEvaluation of fatty liver\n-------------------------\n\nSonographic diagnosis of fatty liver was performed by abdominal B-mode ultrasound (3.5 MHz convex transducer, Toshiba SSA-250; Toshiba, Tokyo, Japan) carried out by experienced hepatologists trained at the same institution to ensure interobserver consistency. ", "Diagnosis of fatty liver was based on the brightness of the liver on ultrasound as compared with the kidney, vascular blurring of the hepatic vein trunk, and deep attenuation in the right hepatic lobe. ", "The absence of fatty liver change (AFL) was defined as a normal echo texture without visible fatty change. ", "The presence of fatty liver (FL) was defined as an increase in the fine echoes of hepatic parenchyma with impaired visualization of the intrahepatic vessels and diaphragm.", "\n\nStatistical analysis\n--------------------\n\nThe SPSS 18.0 statistical package for Windows (SPSS Inc., Chicago, IL, USA) was used for all of the statistical analyses. ", "Continuous variables were represented as the means ± SD. ", "Nonparametric tests (Kruskal--Wallis test or Mann--Whitney rank-sum test) were used when the original measurements were highly skewed. ", "Allele frequency was estimated by direct counting, while genotype distribution with Hardy--Weinberg equilibrium was tested using the chi-square test. ", "Two-way analysis of variance (ANOVA, α = 0.05) was carried out to evaluate the metabolic profiles by the interaction effects between fatty liver and glucose intolerance. ", "Student's *t*-test with Bonferroni comparisons post hoc analysis was conducted within the NGT and GI groups. ", "Multivariate regression analysis was further employed using fatty liver as a dependent variable, while body mass index (BMI), HOMA-IR, Adipo-IR and HSL (GG + GC vs CC) genotype were selected as independent variables based on significance in univariate analyses. ", "To avoid multicollinearity in the regression model, serum insulin and NEFA were not included as independent variables in the multivariate regression model. ", "Separate multiple regression analyses stratified by fasting glucose were further used to evaluate the effects of BMI, HOMA-IR, Adipo-IR, fatty liver, and HSL promoter genotypes (GG + GC vs CC) on serum TG. ", "In addition, to compare the parameter estimates between NGT and GI, a single multiple regression model was conducted with the additional interactions of glucose intolerance vs BMI, HOMA-IR, Adipo-IR, fatty liver, and HSL promoter (GG + GC vs CC). ", "Statistical significance was defined as a *P* value of \\< 0.05 using a two-tailed test.", "\n\nResults\n=======\n\nTo standardize the *de novo* lipogenesis by fasting plasma glucose, our purely male population was divided into NTG (n = 729) and GI (n = 299) groups. ", "The age of the participants ranged from 20 to 70 years, the majority (\\>80%) being distributed in the range of 40--65 years. ", "The prevalence of GI was 29.1% in our adult population. ", "There was a high prevalence of MetS abnormalities (obesity 30.6%, GI 29.1%, hyperTG 42.2%, low HDL-C 19.6% and hypertension 51.6%) in subjects with NAFLD. ", "Minor allele A of FAS (Val1483Ile) and G of FAS (Val1888Ile) polymorphism was nearly absent, with a monogenic distribution of Val1483 (99.6%) and Val 1888 (100%). ", "The genetic effect of FAS was not further analyzed in the development of fatty liver. ", "The frequency of the minor G allele of the HSL promoter (−60 C \\> G) was 9.9%, while the genotype frequency of CC: CG: GG was distributed as 80.8: 18.4 : 0.8% in Hardy--Weinberg equilibrium. ", "There was no significant difference in the frequency distribution of the HSL promoter (−60 C \\> G) genotype between the NGT and GI groups.", "\n\nAs shown in Table [1](#T1){ref-type=\"table\"}, the prevalence of FL (67.2%) in the GI group was significantly higher than in the NGT group (55.7%) (*p* = 0.001, chi-square test). ", "Within the NGT or GI groups, there were significantly greater metabolic abnormalities in the presence of FL. ", "The metabolic profiles, such as BMI, serum insulin and HOMA-IR, were significantly attributed to a synergistic effect of FL and GI. ", "However, the metabolic abnormalities in the group of NGT and FL seemed equivalent or even worse than those in the GI group without FL. ", "The metabolic abnormalities occurred more in the presence of FL.", "\n\n###### \n\nComparison of the metabolic abnormalities between glucose tolerance and fatty liver\n\n **Groups/variables** **Normal Glucose Tolerance (NGT)** **Glucose Intolerance (GI)** ***P*for effect of FL vs AFL** ***P*for effect of GI vs NGT** ***P*for interaction of FL and GI** \n ------------------------ ------------------------------------ ------------------------------ -------------------------------- -------------------------------- ------------------------------------- ----------- -------\n Age (yrs) 45.63 ± 8.10 44.60 ± 8.65 48.68 ± 6.89 49.21 ± 8.69 0.675 \\< 0.0001 0.195\n BMI (kg/m^2^) 23.16 ± 2.51 25.64 ± 3.06\\* 22.79 ± 3.31 26.16 ± 3.03\\* \\< 0.0001 0.716 0.035\n Serum insulin (μIU/ml) 2.22 ± 2.47 4.28 ± 4.48\\* 3.77 ± 6.73 7.74 ± 12.00\\* \\< 0.0001 \\< 0.0001 0.044\n NEFA (μmol/L) 509.81 ±192.78 575.03 ± 227.93\\* 589.47 ±230.07 646.75 ± 264.183 \\< 0.0001 \\< 0.0001 0.811\n HOMA-IR 0.48 ± 0.53 0.94 ± 0.99\\* 1.28 ± 2.89 2.47 ± 4.49\\* \\< 0.0001 \\< 0.0001 0.027\n Adipo-IR 1.11 ± 1.22 2.57 ± 3.95\\* 2.10 ± 3.86 4.50 ± 5.24\\* \\< 0.0001 \\< 0.0001 0.083\n SBP (mmHg) 123.5 ± 15.3 126.2 ±15.1\\* 126.86 ± 16.86 130.44 ±18.20 0.007 0.001 0.701\n DBP (mmHg) 76.2 ± 10.9 79.1 ± 10.6\\* 78.55 ± 11.49 82.45 ± 11.83\\* \\< 0.0001 \\< 0.0001 0.530\n AST (IU/L) 27.20 ±11.81 29.97 ± 11.41\\* 28.77 ±16.31 34.22 ± 18.71\\* \\< 0.0001 0.004 0.163\n ALT (IU/L) 25.28 ± 19.78 34.35 ± 20.64\\* 25.94 ± 20.91 40.70 ± 33.01\\* \\< 0.0001 0.037 0.090\n Cholesterol (mg/dl) 175.13 ± 31.00 184.24 ± 32.65\\* 173.98 ± 28.97 188.17 ± 34.57\\* \\< 0.0001 0.548 0.274\n Triglyceride (mg/dl) 104.78 ± 58.24 158.29 ± 115.18\\* 129.99 ± 111.28 163.97 ± 102.82\\* \\< 0.0001 0.028 0.165\n HDL-C (mg/dl) 53.75 ± 12.87 49.12 ± 11.55\\* 50.09 ± 10.67 48.30 ± 10.68 0.002 0.034 0.176\n LDL-C (mg/dl) 115.27 ± 31.50 130.27 ± 32.97\\* 117.23 ± 28.96 129.08 ± 33.12\\* \\< 0.0001 0.895 0.584\n\n\\*P \\< 0.025 = 0.05/2 (Bonferroni test, two sample comparison within the normal glucose tolerance and glucose intolerance groups).", "\n\nAFL indicates absence of fatty liver, FL indicates fatty liver. ", "BMI indicates body mass index. ", "SBP and DBP indicate systolic and diastolic blood pressure.", "\n\nNEFA indicates non-esterified fatty acid.", "\n\nIn the development of FL, risk analysis was conducted to compare the odds ratios of BMI, HOMA-IR, Adipo-IR and HSL promoter genotypes (CC vs CG + GG) (Table [2](#T2){ref-type=\"table\"}). ", "Analysis showed that BMI and Adipo-IR, rather than HOMA-IR and HSL promoter polymorphism, are independent risk factors for the formation of FL.", "\n\n###### \n\nLogistic regression using fatty liver as a dependent variable in normal glucose tolerance and glucose intolerance groups\n\n **Independent variables** **Odds ratio** ***P*value**\n ---------------------------------------- ------------------ --------------\n **Normal glucose tolerance** \n  BMI 1.31 (1.22-1.41) \\< 0.0001\n  HOMA-IR 0.98 (0.55-1.77) 0.948\n  Adipo-IR 1.36 (1.06-1.75) 0.016\n  HSL promoter genotype (CC vs CG + GG) 1.41 (0.71-2.16) 0.122\n **Glucose intolerance** \n  BMI 1.50 (1.32-1.69) \\< 0.0001\n  HOMA-IR 0.85 (0.64-1.13) 0.258\n  Adipo-IR 1.41 (1.11-1.78) 0.005\n  HSL promoter genotype (CC vs CG + GG) 1.03 (0.49-2.18) 0.940\n\nObesity plays a central role in MetS. Our study demonstrated that the frequency of FL and the metabolic profiles of MetS were positively parallel to BMI, with the exception of GI (Table [3](#T3){ref-type=\"table\"}). ", "The frequency of FL is greater than that of GI for a given BMI. ", "Relevant metabolic abnormalities, including 38.4% for fatty liver, 33.4% for hypertension, 26.4% for glucose intolerance, 18.2% for hypertriglyceridemia and 10.1% for low HDL-C, existed in normal BMI subjects; this has previously been regarded as metabolic obese normal weight (MONW). ", "This means that hepatic steatosis is not only dependent on the BMI status, and the threshold for hepatic fat accumulation essentially differs greatly between individuals.", "\n\n###### \n\nPrevalence of fatty liver and indexes of metabolic syndrome by BMI status\n\n **BMI status (kg/m^2^)** **\\< 24 (n = 434)** **24- 26.9 (n = 379)** **≥ 27 (n = 216)** ***P***\n -------------------------- --------------------- ------------------------ -------------------- -----------\n Fatty liver 38.4% 67.3% 86.1% \\< 0.0001\n Hypertension 33.4% 53.0% 57.9% \\< 0.0001\n Glucose intolerance 26.4% 29.2% 34.9% 0.086\n Hypertriglyceridemia 18.2% 37.4% 49.3% \\< 0.0001\n HDL \\< 40 mg/dl 10.1% 22.6% 24.6% \\< 0.0001\n\nHypertension is defined as systolic BP ≥ 130 or diastolic BP ≥ 80 mmHg.", "\n\nGlucose intolerance is defined as fasting glucose ≥ 100 mg/dl.", "\n\nHypertriglyceridemia is defined as fasting triglyceride ≥ 150 mg/dl.", "\n\nPower calculation was more than 80% in the whole population when the pooled standard deviation of TG is estimated around 90 mg/dl. ", "In the NGT group, the presence of FL followed by high Adipo-IR and BMI significantly contributed to a raised serum TG (Table [4](#T4){ref-type=\"table\"}). ", "However, the effect of BMI on serum TG disappeared in the GI group. ", "Conversely, the HSL promoter genotype (CG + GG vs CC) demonstrated a significant strong impact elevating serum TG in the GI but not the NGT group. ", "Comparison of the parameter estimates of the impact on serum TG, indicated by interactions, showed a significant difference in the HSL promoter (GG + GC vs CC) (*p* = 0.005) between the NGT and the GI groups. ", "Therefore, it means that the TG level is very dependent upon the status of the subject's glucose in-tolerance or not.", "\n\n###### \n\nMultiple regression using triglyceride as a dependent variable in the normal glucose tolerance and glucose intolerance groups\n\n **Independent variables** **Parameter estimates (B)** **95% Confidence interval** ***P*value** \n --------------------------------------- ----------------------------- ----------------------------- -------------- -----------\n **Normal glucose tolerance** \n BMI 4.30 2.41 6.20 \\< 0.0001\n HOMA-IR −31.06 −41.11 −21.01 \\< 0.0001\n Adipo-IR 17.04 14.35 19.74 \\< 0.0001\n FL vs AFL 27.50 16.41 38.58 \\< 0.0001\n HSL promoter genotype (CG + GG vs CC) −3.05 −16.14 10.04 0.648\n **Glucose intolerance** \n BMI −0.32 −3.82 3.82 0.860\n HOMA-IR −11.01 −16.26 −5.76 \\< 0.0001\n Adipo-IR 11.50 7.04 15.96 \\< 0.0001\n FL vs AFL 29.40 3.74 55.05 0.025\n HSL promoter genotype (CG + GG vs CC) 34.10 9.16 60.04 0.010\n\nFL indicates fatty liver, AFL indicates absence of fatty liver.", "\n\nDiscussion\n==========\n\nOur study demonstrated that BMI and Adipo-IR significantly contributed to FL formation. ", "Men's BMI is reported to predict approximately 93% of the variance linked to obesity-related adipocyte size, fat cell mass and fat distribution \\[[@B22]\\]. ", "Accordingly, BMI could be used as a clinically practical parameter in males to represent the obesity-related fat metabolism. ", "There is substantial evidence that obesity is related to excess fat cell mass leading to increased basal lipolysis \\[[@B11]\\]. ", "Insulin resistance is well-documented as the hallmark of MetS, but occurs with a differential response intensity of target tissues such as adipose, liver and muscle tissues to a given insulin level \\[[@B23]\\]. ", "The Adipo-IR index is a simple way of measuring the inhibiting response of lipolysis by insulin in adipose tissue. ", "Our results rationally suggest that people with a higher BMI usually have a greater fat cell mass, increased basal lipolysis leading to higher NEFA and greater insulin resistance (represented by Adipo-IR), which will result in hepatic FFA overflow and FL formation. ", "The genetic effect of the HSL promoter (CC vs CG + GG) in relevant lipolysis and FL formation may be overcome by the greater impact of obesity-related lipolysis and insulin resistance of adipose (Adipo-IR). ", "This finding is compatible with the fact that increased plasma FFA from adipose lipolysis is the major provider of lipids in the steatotic liver \\[[@B8],[@B20],[@B24]\\].", "\n\nNAFLD has been regarded as the hepatic manifestation of MetS. However, debate continues regarding the progression of MetS to NAFLD or vice versa \\[[@B25],[@B26]\\]. ", "NAFLD has been reported to be a better independent risk factor for cardiovascular disease than MetS in some studies \\[[@B3],[@B27]\\]. ", "Liver fat is an independent determinant of the hepatic glucose output, which is sensitive to insulin. ", "The liver is the primary site regulating 50-70% of insulin clearance \\[[@B28]\\]. ", "Increased hepatic steatosis is associated with impaired insulin clearance and hepatic insulin resistance, which results in plasma glucose elevation, compensatory hyperinsulinemia and progression to type 2 DM. ", "Hepatic insulin resistance also accelerates VLDL secretion, contributing to hypertriglyceridemia and low-HDL cholesterol concentration. ", "Thus, hyperinsulinemia is regarded to be a consequence rather than a cause of NAFLD. ", "Furthermore, hyperinsulinemia, stimulating the sympathetic tone and enhancing renal sodium reabsorption, contributes to hypertension \\[[@B28],[@B29]\\]. ", "HOMA-IR, an indirect estimate of insulin resistance, is usually used to represent the inhibition of hepatic glucose output by insulin, which is maintained by a balance between the liver and β-cells \\[[@B20]\\]. ", "As suggested by Kotronen et al., ", "the HOMA-IR index, which overestimates the insulin resistance in subjects with NAFLD, is more likely to reflect impaired insulin clearance and secretion than insulin sensitivity \\[[@B29]\\]. ", "Our results revealed an inconsistent effect of HOMA-IR, whereas Adipo-IR showed a consistent trend in regulating NAFLD formation or serum TG. ", "This highly suggests Adipo-IR as an index of insulin sensitivity in NAFLD or MetS research. ", "In our study, subjects with FL and NGT complicated more metabolic abnormalities than subjects with AFL and GI. ", "The coexistence of FL and GI exerts a significant synergistic effect raising BMI, serum insulin and HOMA-IR. ", "This indicates that FL may develop earlier in the progression of MetS and the coexistence of FL and GI may magnify obesity and insulin resistance.", "\n\nNo matter how MetS is defined, visceral obesity is an obligatory component of MetS based on the recommendations of the International Diabetes Federation consensus \\[[@B30]\\]. ", "However, there is still no convenient, practical worldwide indicator to define visceral obesity. ", "As our study has shown, metabolic abnormalities are considerably prevalent in a MONW population. ", "Visceral obesity is not easily defined by BMI alone since the threshold for hepatic lipid accumulation (a critical visceral adiposity) differs individually \\[[@B4]\\]. ", "The liver is a pivotal organ to regulate the homeostasis of fat and glucose. ", "It also plays a central role linking the interaction of obesity, GI, hypertension and dyslipidemia. ", "Previous evidence has shown that hepatic steatosis rather than extrahepatic adiposity is more correlated with insulin resistance, especially in normal-weight non-diabetic subjects. ", "NAFLD is an early manifestation of MetS and its severity is positively parallel to the degree of obesity. ", "Therefore, hepatic steatosis may be the earliest sign in the pathogenesis of MetS and may be a better marker of visceral obesity for defining MetS, especially in a MONW population \\[[@B4],[@B26],[@B31]\\]. ", "Compared with the gold standard of liver biopsy to diagnose FL, abdominal ultrasound is a noninvasive, convenient and accurate tool with high sensitivity and specificity. ", "Therefore, we propose that a steatotic liver evaluated by ultrasound is a more sensitive indicator than BMI for defining visceral obesity.", "\n\nFacing an increased FA influx and *de novo* lipogenesis, the hepatic FA pool is regulated by β-oxidation, with biosynthesis of TG for secretion as VLDL-C particles or storage as intrahepatic lipid. ", "Current evidence suggests that hepatic TG synthesis and VLDL-TG secretion protect against lipotoxicity by buffering hepatic FFA influx \\[[@B8]\\]. ", "Fasting serum TG is carried predominantly in the particles of VLDL secreted from the liver, which is inhibited by insulin. ", "In subjects without FL, nearly 70% of FA incorporated into VLDL-TG is derived from plasma FA sources, and the rest originates from hepatic *de novo* lipogenesis and lipolysis of intrahepatic lipids. ", "The VLDL-TG secretion rate is greater in subjects with FL than those without FL \\[[@B4],[@B7]\\]. ", "Our results demonstrated that the impact of increased circulating TG is significantly regulated by the presence of FL, Adipo-IR and BMI in sequence. ", "This is compatible with the reported fact that a higher BMI, greater insulin resistance to adipose (Adipo-IR) and more liver fat is compensated with higher secretion of VLDL-TG \\[[@B4],[@B7],[@B8],[@B30]\\]. ", "Therefore, the presence of FL essentially could result in dyslipidemia and related atherosclerosis. ", "Our results demonstrated a differential intensity of HOMA-IR inhibition of VLDL-TG secretion in the NGT and GI groups. ", "In the GI state, it still demonstrated an inhibiting impact on VLDL-TG secretion coexistent with the impaired hepatic output in a given HOMA-IR, which implies differential insulin sensitivity to regulate fat and glucose metabolism in the liver, such as by inhibiting VLDL-TG secretion and hepatic glucose output. ", "However, greater insulin resistance has been shown to lead to greater VLDL-TG secretion and higher serum TG \\[[@B12]-[@B14]\\]. ", "Thus our variable TG regulation responses when using HOMA-IR as an insulin resistance index suggest the need for a more appropriate index to represent insulin resistance for glucose or fatty acid metabolism. ", "Adipo-IR, representing the circulating FFA influx relative to insulin, can be regarded as a good indicator of insulin resistance in studies of TG metabolism and NAFLD.", "\n\nThere are many reports in the literature investigating C-60G gene polymorphism in the HSL promoter. ", "The Ely study showed a gender specific effect on insulin and lipid levels in--60G carriers. ", "Men carrying the --60G allele had significantly lower fasting NEFA and LDL-cholesterol than non-carriers \\[[@B18]\\]. ", "Ordovas et al. ", "reported that male carriers of the --60G allele who were not alcohol drinkers had higher glucose levels than non-carriers \\[[@B32]\\]. ", "In addition, the C-60G polymorphism is associated with increased waist circumference in lean subjects \\[[@B33]\\]. ", "The interaction between body fat mass and physical activity is closely associated with the C-60G polymorphism in male carriers. ", "The Quebec Family study showed that men who were G allele carriers were less likely to lose adiposity by physical activity than non-carriers \\[[@B34]\\]. ", "Talmud et al. ", "found no significant difference in fasting lipid, glucose, BMI, waist/hip ration or blood pressure between C and G allele carriers but the G allele carriers had significant lower HOMA index in healthy young men \\[[@B35]\\]. ", "Taken together, these previous reports reveal that HSL promoter polymorphisms play a critical role in the regulation of fat and glucose metabolism and are also highly correlated with insulin resistance. ", "The apparent discrepancies between these studies, however, are hard to rationally explain via pathophysiologic mechanisms. ", "To avoid confounding effects, multivariate regression analysis was carried out focusing only on male gender stratified by fasting glucose so insulin resistance is clearly defined. ", "Our results demonstrated different impacts on serum TG by insulin resistance, BMI and the HSL promoter genotype after stratification by serum glucose. ", "Since serum insulin, HOMA-IR and BMI were significantly attributable to a synergistic effect of glucose intolerance and FL, it is necessary to compare the interaction of these confounding factors together on serum TG. ", "We observed no difference in anthropometric or metabolic parameters and related insulin resistance indexes between genotype (CG + GG) and (CC) carriers in the NTG group, except for significantly higher serum TG levels found in carriers of the G allele in the GI group (Additional file [1](#S1){ref-type=\"supplementary-material\"}: Table S1 and S2).", "\n\nRecent evidence has shown that the accumulation of diacylglycerol in the liver might activate protein kinase C, induce insulin resistance and increase VLDL-TG secretion. ", "HSL is involved in a rate-limiting step to catalyze diacylglycerol and monoacylglycerol into free fatty acids, so HSL activity determines the tissue content of diacylglycerol and the degree of insulin resistance \\[[@B20],[@B26]\\]. ", "Reid et al. ", "found that hepatic overexpression of HSL promotes β-oxidation of the fatty acid to ameliorate steatosis \\[[@B36]\\]. ", "Taken together, HSL activity has a critical role in the development of NAFLD. ", "The G allele of the HSL promoter (C-60G) exhibited a 40% decline in promoter activity, which may theoretically cause greater accumulation of diacylglycerol in the liver. ", "This could lead to greater insulin resistance, less β-oxidation and more VLDL-TG secretion. ", "The HSL activity is negatively regulated by insulin and up-regulated by glucose. ", "There are multiple prominent *cis-*regulatory elements, including the insulin response element (IRE), glucose response element (GRE) and fat specific element (FSE), along with other transcriptional factor binding elements, residing in the proximal promoter regions of the human HSL gene. ", "All these *cis-*acting elements act as critical transcriptional regulators for promoter activity \\[[@B37],[@B38]\\]. ", "A literature review by Ling et al. ", "pointed out that the epigenetic effect of DNA methylation always occurs in CG dinucleotides and is modified by environmental exposure to nutrients in complex multifactorial diseases such as type 2 DM. ", "The relative ratio of insulin, glucose and fat levels may act on the *cis*-regulating elements to modulate promoter function and transcriptional initiation \\[[@B39]\\]. ", "Our results showed a genetic effect of the HSL promoter (C-60G) regulating serum TG only in the GI group and not in the NGT group. ", "It is rational to speculate that the G allele of the HSL promoter may express a differential susceptibility to the complex interaction between serum insulin, glucose and fat to determine lipolysis, such as lowering lipolytic activity only under a dependable range of insulin resistance. ", "Because this is a cross-sectional study, further prospective and large-scaled study is suggested to verify this preliminary observation.", "\n\nConclusion\n==========\n\nThe risk interaction between genetic susceptibility, obesity and insulin resistance contribute different impacts on the development of NAFLD. ", "Adipo-IR, rather than HOMA-IR, is proposed as a consistent insulin resistance index for the study of NAFLD. ", "BMI and Adipo-IR were independent risk factors for the formation of FL. ", "In a GI state, HSL promoter (CG + GG) contributed the greatest impact on raising serum TG, followed by FL and Adipo-IR in sequence.", "\n\nAbbreviations\n=============\n\nNAFLD: Non-alcoholic fatty liver disease; MetS: Metabolic syndrome; NASH: Non-alcoholic steatotic hepatitis; BMI: Body mass index; TG: Triglyceride; FA: Fatty acid; VLDL: Very low-density lipoprotein; FAS: Fatty acid synthase; ATGL: Adipose triglyceride lipase; HSL: Hormone-sensitive lipase; NGT: Normal glucose tolerance; GI: Glucose intolerance; AST: Aspartate aminotransferase; ALT: Alanine aminotransferase; NEFA: Non-esterified fatty acid; HOMA-IR: Homeostatic model assessment of insulin resistance; Adipo-IR: Adipose insulin resistance; FL: Fatty liver; AFL: Absent fatty liver; MONW: Metabolic obese normal weight; IRE: Insulin response element; GRE: Glucose response element; FSE: Fat specific element.", "\n\nCompeting interests\n===================\n\nAll of the authors contributed substantially to this study. ", "All of the authors fully declare that there is no conflict of interest prejudicing the text of this article.", "\n\nAuthors' contributions\n======================\n\nPJH involved research design, quality control of the genetic experiments, and writing the manuscript. ", "ZCC designed the research. ", "WWH searched the literature and analyzed data. ", "YHCY contributed to using analytic tools for statistical analysis and involved the statistical analysis. ", "MYL collected data for analysis. ", "JFH contributed on patients enrollment. ", "KKK supervised the project, edit and revise the manuscript. ", "All authors read and approved the final manuscript.", "\n\nPre-publication history\n=======================\n\nThe pre-publication history for this paper can be accessed here:\n\n<http://www.biomedcentral.com/1471-2350/14/54/prepub>\n\nSupplementary Material\n======================\n\n###### Additional file 1: Table S1\n\nComparison of biochemistry between genotypes (CG+GG) and (CC) of the hormone sensitive lipase (HSL) promoter in the normal glucose tolerance group (n=729). **", "S2.** ", "Comparison of biochemistry between genotypes (CG+GG) and (CC) of the hormone sensitive lipase (HSL) promoter in the glucose intolerance group (n=299).", "\n\n###### \n\nClick here for file\n\nAcknowledgements\n================\n\nThis study was sponsored by grants from the cooperative research program at Chi-Mei Medical Center and Kaohsiung Medical University, CMFHR9647. ", "We are sincerely grateful to Shu-Ting Lee for technical assistance.", "\n" ]

{ "pile_set_name": "PubMed Central" }

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[ "Statistical analysis and optimization of frequency-domain fluorescence lifetime imaging microscopy using homodyne lock-in detection.", "\nFluorescence lifetime imaging microscopy is used widely in biological research, but the accuracy and precision of lifetime measurements are limited. ", "Photon noise is an inherent error source that cannot be eliminated. ", "In this paper, we present a general approach to compute the probability density of the estimated lifetime for frequency-domain fluorescence lifetime imaging microscopy using homodyne lock-in detection. ", "The analysis for commonly used excitation methods, including sinusoidal modulation, square-wave modulation, and a periodically pulsed light source, are given and compared to the results of Monte Carlo simulations. ", "The optimum parameters of the excitation waveforms to minimize the variance of the estimated lifetimes are also derived and compared to previously published results." ]

{ "pile_set_name": "PubMed Abstracts" }

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[ "The present invention is directed to polyvalent immunizing preparations composed of nontoxic serotype-specific polysaccharide preparations. ", "More particularly, the invention described herein relates to the treatment of purified capsular polysaccharides (CPS) derived from Klebsiella species bacilli, hereinafter referred to as Klebsiella, with a deacylating agent such as sodium hydroxide (NaOH) to yield a nonpyrogenic, immunogenic CPS preparation. ", "The present invention also relates to the use of immunogenic Klebsiella species CPS to provide protection against Klebsiella infections. ", "A vaccine formulated from such antigens can be utilized to actively immunize individuals at risk to Klebsiella infections.", "\nThe frequency of infections due to gram-negative aerobic bacilli, such as Klebsiella, has increased dramatically over the preceding three decades, concommitant with the widespread use of broad spectrum antibiotics. ", "Of these infections, those classified as pneumonia or bacteremia carry the highest attendant fatality ratios which average roughly 25% and are in the range of 10% to 50%. ", "As described in McGowan, J. E., Barnes, M. W., Finland, M., \"Bacteremia at Boston City Hospital: occurrence and mortality during 12 selected years (1935-1972), with special reference to hospital acquired cases,\" J. Infect. ", "Dis. ", "132: 316-335, 1975; Bryan C. S., Reynolds, K. L., Brenner, E. R., \"Analysis of 1,186 episodes of gram-negative bacteremia in non-university hospitals: the effects of antimicrobial therapy,\" Rev. Infect. ", "Dis. ", "5: 629-638 1983; Graybill, J. R., Marshall, L. W., Charache, P., Wallace, C. K., Melvin, V. B., \"Nosocomial pneumonia. ", "A continuing major problem,\" Am. ", "Rev. Resp. ", "Dis. ", "108: 1130-1140, 1973; and Cross, A., Allen, J. R., Burke, J., Ducel, G., Harris, A., John, J., Johnson, D., Lew, M., MacMillan, B., Meers, P., Skalova, R., Wenzel, R., Tenney, J., \"Nosocomial Infections due to Pseudomonas aeruginosa: review of recent trends,\" Rev. Infect. ", "Dis. ", "5 (Suppl.): ", "S837-S845, 1983, Klebsiella is a leading cause of such life-threatening infections, being the most frequently isolated gram-negative bacterium from the lower respiratory tract and the second most common cause of bacteremia. ", "At present, there exists no effective immunological means for the control of Klebsiella infections.", "\nNumerous bacterial species, among them Klebsiella, possess a well-defined capsule which surrounds the bacterial cell in a viscous layer. ", "The capsule is composed of repeating units of monosaccharides which form a high molecular weight polymer. ", "Such capsular polysaccharides (CPS) confer the K (or capsular) antigenic specificity upon their respective bacterial cells.", "\nStudies such as described in Riottot, M. M., Fournier, J. M., Pillot, J., \"Capsular serotype specificity of the protection conferred on mice by Klebsiella pneumoniae ribosomal preparations,\" Infect. ", "Immun. ", "24: 476-482, 1979; Riottot, M. M., Fournier, J. M., Jouin, H., \"Direct evidence for the involvement of capsular polysaccharide in the immunoprotective activity of Klebsiella pneumoniae ribosomal preparations,\" Infect. ", "Immun. ", "31: 71-77, 1981; and Cooper, J., McA., Rawley, D., \"Resistance to Klebsiella pneumoniae and the importance of two bacterial antigens,\" Austral. ", "J. Expt. ", "Biol. ", "Med. ", "Sci. ", "60: 629-641, 1982, have shown that an experimental ribosomal vaccine and an experimental killed whole-cell vaccine are capable of providing a degree of protection against Klebsiella infections in experimental animal models. ", "Protection was found to correlate with the induction of a serotype-specific anti-CPS immune response. ", "However, prior attempts to evoke a protective immune response in mice by vaccination with CPS have been heretofore unsuccessful, and this failure has been attributed to the poor immunogenicity of CPS in mice, as noted in J. M. Fournier, C. Jolivet-Reynaud, M. M. Riottot and H. Jouin, Infect. ", "Immun. ", "32: 420-426, 1981.", "\nIt has now been discovered that immunogenic preparations of CPS can be obtained from the culture supernatant of Klebsiella cultivated in a medium designed to support capsule production. ", "These CSP antigens can subsequently be purified to a high degree, and this highly purified product has been shown to be immunogenic and non-pyrogenic in animals, as described in Cryz, S. J., Jr., Furer, E., Germanier, R., \"Purification and vaccine potential of Klebsiella capsular polysaccharide,\" Infect. ", "Immun. ", "50: 225-280, 1985; and Cryz, S. J., Jr., Furer, E., Germanier, R., \"Safety and Immunogenicity of Klebsiella pneumoniae Kl Capsular Polysaccharide Vaccine in Humans,\" The Journal of Infectious Diseases, Vol. ", "151, No. ", "4, April, 1985. ", "Furthermore, as noted in Cryz, S. J., Jr., Furer, E., Germanier, R., \"Prevention of fatal experimental burn wound sepsis due to Klebsiella pneumoniae KP1-0 by immunization with homologous capsular polysaccharide,\" J. Infect. ", "Dis. ", "150: 817-822, 1984 and Cryz, S. J., Jr., Furer, E. Germanier, R., \"Protection against fatal Klebsiella pneumoniae burn wound sepsis by passive transfer of anticapsular polysaccharide,\" Infect. ", "Immun. ", "45: 139-142, 1984, anti-serotype-specific CPS has been shown to be highly effective at preventing fatal experimental Klebsiella infections." ]

{ "pile_set_name": "USPTO Backgrounds" }

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[ "Rogers Media uses cookies for personalization, to customize its online advertisements, and for other purposes. ", "Learn more or change your cookie preferences. ", "Rogers Media supports the Digital Advertising Alliance principles. ", "By continuing to use our service, you agree to our use of cookies.", "\n\nWe use cookies (why?) ", "You can change cookie preferences. ", "Continued site use signifies consent.", "\n\nWinning the wage war\n\nPerhaps she shouldn’t have been surprised. ", "After all, big business and big politics have long been the almost exclusive playground for big boys. ", "But still, when lobbyist Pamela Jeffery stepped up to a male Ontario cabinet minister at Queen’s Park to set up a meeting, she was taken aback when he asked her on a date instead. “", "I’d be happy to get together with you,” he cooed, looking at Jeffery with a glint in his eye, “but I’d prefer if it were just the two of us… over drinks or dinner.”", "\n\nThe eyebrows of the minister’s aide shot up with surprise, and Jeffery’s heart sank with disappointment. “", "No, I’m sorry,” she told him. ", "Before leaving, Jeffery whispered to the aide that she felt the minister’s behaviour was inappropriate. ", "He nodded knowingly.", "\n\nThat was back in 1989, when Jeffery was in her late 20s. ", "Today, 21 years later, she heads up her own consulting firm, The Jeffery Group, and she is the founder of the Women’s Executive Network. ", "She says conditions are better for working women today, but when you read recent news reports about how women are treated in the workplace, it’s hard to see where her optimism comes from.", "\n\nCurrently, women hold just 10% of board seats in Canadian public companies. ", "Canada ranks 25th on the World Economic Forum’s ranking of countries in terms of women’s equality, behind South Africa and Lesotho. ", "Worst of all, the average full-time female worker earns just 71% of what a man does—$44,700 compared with $62,600—and that percentage has barely budged in recent years. ", "Katherine Scott, director of programs at the Vanier Institute of the Family, says sexism is a big part of the problem—and she doesn’t think that will change soon. ", "To assume that there will one day be pay equity, she says, is to assume “that the institutional barriers that exist today will be addressed somehow. ", "I see no evidence that will be the case.”", "\n\nYoung girls club?", "\nLiberal newspapers, university gender studies departments and women’s advocacy groups have long held the same view: women are paid less than men because of ingrained sexism, they say, and we’ll never get that sexism out of the system. ", "But it turns out the hard numbers don’t back that up. ", "To find out what’s really going on, MoneySense decided to look at the long-term trend in income, rather than the current gap, to see what kind of progress we’re making. ", "We hired researcher Roger Sauvé, president of People Patterns Consulting, to spend months digging through Statistics Canada data, with a focus on how the income for different age groups and genders has changed over the 30-year period between 1978 and 2008, the most recent year for which the data is available.", "\n\nWe were shocked when he presented us with his findings. ", "It turns out that women have been making impressive gains in total income relative to men over the last 30 years, especially young women. ", "When he focused on workers between the ages of 25 to 34, Sauvé found that over those three decades women enjoyed an impressive 27% surge in income, while men saw their income drop by 11%. (", "All figures have been adjusted for inflation, so those are real gains and losses.) ", "And that’s just up to 2008—it’s likely that in the recession which followed, the gap narrowed even more.", "\n\nIf the trend continues, says Sauvé, the wage gap for young workers will completely disappear within the next 30 or so years. ", "The gap for older workers is wider and closing more slowly, but as those younger workers climb the corporate ladder, they’ll likely bring pay equity with them. ", "It may be hard to believe for those who have spent a lifetime in the trenches fighting gender-based discrimination in the workplace—but it looks like women are winning the wage war. ", "Rather than being an intractable problem, the unfair gap in income between men and women seems to be headed for extinction, and soon. “", "Absolutely, I think it could happen,” says Linda Duxbury, a professor at the Sprott School of Business at Carleton University in Ottawa. “", "You could even see the reverse—men earning less than women.”", "\n\nTo predict what the future will bring, it helps to look at the past. ", "When we do, we find that the recent gains women have made in the workplace are not a new phenomenon. ", "Women have actually been making huge gains for more than a century.", "\n\nJust 200 years ago—not a huge amount of time in historical terms—women weren’t even thought of as proper members of society. ", "They generally had no legal standing independent of their fathers or husbands, no means of making a living independent of the family enterprise, and very limited access to education. ", "In the early part of the 20th century, women were given the right to vote and hold office. ", "Contrary to popular belief, females didn’t suddenly enter the work force en masse in the 1960s. ", "The number of women in paid employment steadily increased starting in the 1870s, and this continued for almost a century. ", "The big change was that in the 1960s, married women—in particular married women with children—began to seek, and get, paid employment.", "\n\nAt first they were confined largely to “pink collar jobs”—secretaries, nurses and school teachers. ", "But pressure from the feminist movement helped women gain access to law schools, business schools and advanced degree programs. ", "Meanwhile legal challenges led to the passing of anti-discrimination laws, and birth control gave women more control over childbearing. ", "Increasing numbers of women went to university and college, and not just to get their ‘M.R.S. degree,’ as the old expression goes—meaning a stint at college to scope out a successful man to marry.", "\n\nIn the decades to come, it will be gains in education access that fuel women’s progress in the workplace. “", "It’s an education story first and foremost,” says James Chung, founder of New-York based consumer research firm Reach Advisors. ", "Already, 71% of Canadian women ages 25 to 34 have post-secondary degrees or diplomas, compared to just 62% of men, a trend that looks likely to continue, because girls are currently getting better grades in school than boys.", "\n\nTrading places\nWomen are also moving into fields of work traditionally held by men that have opportunities for higher wages. ", "The fastest-growing job categories for women are drillers and blasters (up 750% between 1996 and 2006), petroleum engineers (up 384%) and structural metal and platework fabricators and fitters (up 321%). “", "Women have been acting more like men over the last 30 years so it’s no wonder that we’re closing the gap towards wage parity,” says Armine Yalnizyan, senior economist with the Canadian Centre for Policy Alternatives. ", "Men, meanwhile, are moving in the other direction. ", "It’s telling that the fastest growing job categories for the XY-chromosome set are library and information jobs, as well as estheticians and electrologists.", "\n\nThe wage gap isn’t closing just because women’s income is rising. ", "It’s also closing because men’s income is falling. ", "Our data shows that between 1978 and 2008, men aged 25 to 34 saw a dramatic 11% drop in income, while men aged 35 to 44 saw a 2% decline. ", "This is a more difficult trend to explain, although many experts attribute it largely to the loss of male-dominated high-paying manufacturing jobs. ", "Many of these jobs have been replaced by automation or they have moved overseas to countries where labour is cheaper. ", "These days, an uneducated male worker tends to end up in a lower-paying service job.", "\n\nUnemployment rates are now consistently higher for men than they are for women, a situation that was exacerbated during the recent recession. ", "Indeed, each of the recessions we’ve experienced in the last few decades have caused a contraction in men’s incomes. ", "As family incomes dropped, many women picked up the slack, increasing their working hours and income.", "\n\nAs a result of all of these changes, many young women entering traditionally male occupations are now finding that gender isn’t such a big deal. ", "Virginia Au, a 29-year old graduate of the University of British Columbia’s Sauder School of Business, says she hasn’t encountered many bumps on the path to her current job, where she earns a six-figure salary as a mutual fund portfolio manager for Invesco Trimark in Toronto. “", "I’ve noticed that gender is not really an issue, not from my experience anyway,” she says. “", "I was fortunate to be able to work with a lot of good bosses who gave me the opportunity to show people who I am.”", "\n\nAs women make gains in the office, their home life is changing too. ", "Many women are finding themselves to be the main breadwinner, while their husbands take care of the kids. ", "That’s the situation for Susan Philipson, a 43-year-old who lives in a small town near Newmarket, Ont. ", "She works as a human resources consultant, pulling in $80,000 a year—almost double the salary of her husband, Rick. ", "Because his lower-paying job is less demanding, Rick is the primary caregiver for their seven-year-old daughter Jenny and 16-year-old son Lucas (names have been changed to protect the family’s privacy). “", "When we were dating, I said to Susan, ‘You’ll never earn more than me,’ ” says Rick, who is now 44 and working at a nearby hospital, “but I guess she’s proved me wrong.”", "\n\nThere’s no doubt that women have made some impressive gains over the last 30 years. ", "The big question now is whether that trend will continue. ", "Will the gap in income continue to narrow, or is sexism so deeply imbedded in the workplace that true equality is impossible?", "\nThe first thing to acknowledge is that when it comes to equal pay for equal work—the rallying cry for social activists—we’re already a lot closer than you might think. ", "Women’s groups often cite the statistic we presented earlier indicating that women only earn 71% of what men do. ", "But when you look a little closer at that number, it begins to look misleading.", "\n\nThe main reason women earn less than men, it turns out, is because they have less experience, work fewer hours, and they choose lower-paying professions. ", "Indeed, when you look at the gender gap in terms of hourly wages—a more accurate measure than income—and you control for such things as qualifications, academics estimate that women get paid 85% to 93% of what men are paid, a percentage that’s trended upward steadily over the last three decades. “", "The reality is that many women work part-time, so you have to compare hourly wages to get the bigger picture,” says University of British Columbia economics professor Nicole Fortin. “", "When you do that, the gender wage gap doesn’t look as dire as people make it out to be.”", "\n\nThe reasons women enter lower paying fields are complicated, but it’s clear that gender segregation is lessening. ", "While some fields, such as construction, continue to hold little appeal to women, many professional fields are becoming more diverse. ", "Often what happens is that once a certain threshold of women enter the field, they are able to change the culture to be more friendly to women and they serve as role models, leading to a large influx of females into the field.", "\n\nPink collar or blue?", "\nHowever, many women still continue to choose feminized fields that pay less, either because they prefer the work or they want more flexible careers to balance with their family responsibilities. ", "Women also tend to choose lower-paying areas inside of their fields. ", "The majority of students in medical school are now women, for example, but female graduates are more likely to become general practitioners rather than higher-earning specialists. ", "Another factor may be salary negotiations—many women feel uncomfortable playing hardball when talking about salaries with prospective bosses.", "\n\nAt the heart of all of this, of course, is the simple fact that it’s still women who bear the children. ", "This naturally leads to taking time off for a maternity leave, working reduced hours and, in some cases, following less ambitious career paths so they can spend time with the kids. ", "But as more women out-earn their husbands, more men will take on primary caregiver responsibilities, and the drag on income caused by being absent from the workplace will be more evenly distributed across the sexes. ", "As well, more families are choosing to delay having children or not have them at all, a factor that may contribute to economic problems such as labour shortages—but will likely bode well for women’s salaries.", "\n\nWhen you take kids out of the equation, you find that in many cases women are already out-earning men. ", "A recent study by Reach Advisors showed that in 366 metropolitan areas of the U.S., women in their 20s who are single and have no children already have a median income that is 8% higher than men’s. “", "The reverse gender gap is not just a U.S. phenomenon,” says Reach Advisors’ Chung. “", "We’ve looked at Canadian data and we’re seeing similar patterns.”", "\n\nThe women’s advocacy movement isn’t wrong about sexism in the workplace though. ", "Even when you account for education, experience, and hours worked, there still is a stubborn gap between men and women’s pay. ", "It’s hard for researchers to say exactly what causes it, but it is likely that some of it is caused by old-fashioned discrimination. ", "Men still hold the reins of power in the majority of our institutions, and they still tend to hire and promote those who are the same gender as themselves.", "\n\n“We see some consistent barriers that are identified in terms of advancement,” says Deborah Gillis, Toronto-based vice-president of Catalyst, an international organization that promotes opportunities for women in business. “", "They include a lack of role models and informal networks where they can share information and build relationships. ", "Women just don’t have the same access to mentors and sponsors.”", "\n\nBut as young people enter the workforce and move up through the ranks, this too could change. ", "Our statistics show that the wage gap is closing most quickly among the young, and other studies have found that sexism seems to be on the wane among the next generation. ", "Today’s teens and twentysomethings genuinely seem to be appalled by the notion that if two people are doing the same job, one could be paid less just because she happens to be a woman. ", "Research by University of Lethbridge sociologist Reginald Bibby clearly shows that teens take equality much more seriously than the generation that came before them, with the percentage who consider the unequal treatment of women to be a serious social issue doubling between 1984 and 2008.", "\n\nIndeed, when Pamela Jeffery—the lobbyist who worked at Queen’s Park—gets discouraged, she only has to look to her teenaged sons for hope. ", "When she does, it’s hard for her to believe that equal pay for equal work is all that far off. “", "In their generation, they see their female classmates as equals,” she says. “", "When they enter the workplace, they’re going to take their views of equality with them and apply that in their organizations. ", "So I’m very optimistic.”", "\n\nAlmost Done!", "\n\nPlease confirm the information below before signing up.", "\n\n{* #socialRegistrationForm *}\n{* socialRegistration_firstName *}\n{* socialRegistration_lastName *}\n{* socialRegistration_emailAddress *}\n{* socialRegistration_displayName *}\nBy clicking \"Create Account\", I confirm that I have read and understood each of the website terms of service and privacy policy and that I agree to be bound by them." ]

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[ "José F. Sosa\n\nJosé F. Sosa (born December 25, 1950) is an American Republican Party politician who served in the New Jersey General Assembly from the 7th Legislative District from 1992 to 1994. ", "Sosa was the state's second Hispanic legislator, after Bob Menendez.", "\n\nSosa had served on the Mount Holly Township Council and as the township's mayor.", "\n\nTogether with Frank Catania, Sosa was one of the major sponsors of a measure that reduced the state sales tax from 7% to 6%, a measure that reduced taxation on residents by $600 million, as part of the Republican effort to roll back the $2.8 billion in tax increases that had been made by the Democratic-controlled legislature under Governor James Florio.", "\n\nHe has been a resident of Westampton Township, New Jersey.", "\n\nReferences\n\nCategory:1950 births\nCategory:Living people\nCategory:Mayors of places in New Jersey\nCategory:Members of the New Jersey General Assembly\nCategory:New Jersey Republicans\nCategory:People from Mount Holly, New Jersey\nCategory:People from San Juan, Puerto Rico\nCategory:People from Westampton Township, New Jersey\nCategory:American politicians of Puerto Rican descent" ]

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[ "Leopold Halliday Savile\n\nSir Leopold Halliday Savile, KCB (31 August 1870 – 28 January 1953) was a Scottish civil engineer.", "\n\nSavile was born at Bridge of Earn, Perthshire, the son of Lieutenant-Colonel John Walter Savile and Sarah Emma Stoddart. ", "He was a great grandson of the MP Christopher Atkinson (later Savile). ", "He was educated at Marlborough College and King's College London. ", "He was a pupil of Sir John Wolfe Barry and Henry Marc Brunel from 1891–96.", "\n\nIn 1931, Savile was elected a member of the Smeatonian Society of Civil Engineers and was their president in 1948. ", "Savile was appointed to the panel of qualified civil engineers required by the Reservoirs Act of 1930 where he was responsible for the design, construction and inspection of reservoirs. ", "At this time he was working for Alexander Gibb and partners. ", " He served as president of the Institution of Civil Engineers between November 1940 and November 1941. ", "\n\nHe was appointed a Companion of the Order of the Bath on 1 January 1925. ", "He was appointed a Knight Commander of the same order on 1 March 1929.", "\n\nIn 1904, Savile married Evelyn Stileman, daughter of Frank Stileman, consulting engineer to the Furness Railway Company. ", "They had one daughter. ", "After her death died in 1920, he married secondly, in 1929, Lilith Savile (who was his first cousin once removed), daughter of Brigadier-General Walter Clare Savile.", "\n\nHe died in 1953.", "\n\nReferences \n\n \n \n \n \n \n \n\nCategory:1870 births\nCategory:1953 deaths\nCategory:People educated at Marlborough College\nCategory:Alumni of King's College London\nCategory:British civil engineers\nCategory:Scottish civil engineers\nCategory:Presidents of the Institution of Civil Engineers\nCategory:Presidents of the Smeatonian Society of Civil Engineers\nCategory:Knights Commander of the Order of the Bath" ]

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[ "Dinosaur World in Somerville\n\nHooray for summer! ", "It’s time to start venturing outdoors to enjoy all the great things the Great Outdoors has to offer. ", "One such place that you should add to your visit list if you're heading down to the Mornington Peninsula is Dinosaur World, a themed tourist attraction in Somerville.", "\n\nDinosaur World closes for winter but opens on 1st September each year, just in time for the warmer weather. ", "This prehistoric themed outdoor activity, situated at the rear of the popular Somerville Christmas Tree Farm, is a joy for any dino loving child. ", "The front shed-like entrance boasts a bad-ass prehistoric beast out front, so you can be sure you’ve found the right spot!", "\n\nYou initially walk through an impressive gift shop filled with more dinosaur toys than you'll find in any retail shop, although you can save your take-home treats for later, it’s the \"real\" dinosaurs your kids will want to see. ", "As you enter Dinosaur World’s park, you will follow a path scattered with animatronic dinosaurs big and small. ", "Hear the roar of the dinosaurs and read up on the history of each beast as you walk through the foliage.", "\n\nWatch out for the T-Rex!", "\n\nAfter your kids have spotted all the dinosaurs on site, there’s an opportunity for your children to meet \"Wilson\" the walking dinosaur. ", "He comes out to play at various times throughout each day. ", "Then there is \"Wilbur\", a wee baby raptor who wants to meet your kids for photo opportunities.", "\n\nAnother extra is the ‘dig and discover’ activity, whereby your kids can work on their palaeontology skills and dig for fossils and chisel away at their found blocks to see what’s inside.", "\n\nAlthough small, there is enough to keep small people interested, so take your time and bring a picnic. ", "There are BBQ’s available, tables and umbrellas right next to the children’s dino-themed playground.", "\n\nDinosaur World can be found on the corner of Frankston-Flinders and Oneills Road in Somerville just 5 minutes from Peninsula Link." ]

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[ "NEW ORLEANS — A Catholic school official said Monday that a suburban New Orleans school has rescinded its policy forbidding hair extensions.", "\n\nBut it remains unclear whether a sixth-grader who left school in tears last week after running afoul of the rule will return to Christ the King school.", "\n\nVideo of Faith Fennidy dejectedly walking out of school last week drew accusations that the rule targeted black students. ", "A state judge blocked enforcement of the rule after the families of Faith and another girl, Tyrielle Davis, filed suit.", "\n\nA lawyer for the Fennidy family, James Williams, and officials with the archdiocese said last week they would meet on Monday. ", "But a statement from RaeNell Houston, the superintendent Archdiocese of New Orleans schools, says the family postponed, then canceled the meeting. ", "Emails to the Williams' law firm were not immediately returned Monday night.", "\n\nHouston's statement said Fennidy's family, and the family of Tyrielle Davis, another student who joined in a lawsuit over the policy, were told last week that Christ the King's hair extension policy had been rescinded.", "\n\n\"When this issue arose, the school immediately reviewed its policy and recognized that there may have been sensitivities that needed to be addressed,\" Houston's statement said. \"", "They then reached out for input from the Office of Catholic Schools, the Office of Black Catholic Ministries, other principals, and parents.\"", "\n\nHouston said she will work with school officials to \"create a uniform policy that is sensitive to all races, religions, and cultures.\"", "\n\nThe video that sparked the controversy went virile after Faith's brother posted it on Facebook. ", "He included an explanation that there were practical reasons for Faith's use of extensions." ]

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[ "1. ", "Field of the Invention\nThe present invention is directed to a confectionary, which provides instantaneous cooling and immediate intense sweetness and a process of making that confectionary. ", "More particularly, the present invention is directed to a confectionary, which includes a solid whose surface is sanded with crystals of a sugar alcohol having a negative heat of solution.", "\n2. ", "Background of the Prior Art\nOne of the sweeteners employed in the manufacture of confectioneries is xylitol. ", "Xylitol, although a non-cariogenic sweetener, leaves little unfavorable aftertaste and simulates the texture and confectionary characteristics of conventional cariogenic confectioneries. ", "As taught in U.S. Pat. ", "Nos. ", "3,899,593 and 3,914,434, xylitol not only possesses non-cariogenic properties but also has substantially the same sweetening power as conventional cariogenic-producing sugars, including sucrose. ", "Moreover, xylitol is highly soluble in water and possesses a relatively large negative heat of solution and is thus capable of producing significant cooling effects in the mouth.", "\nA recent development in the confectionary arts has been the development of confectionaries, which impart intense cooling flavor upon initial contact in the mouth. ", "To effectuate this feeling compounds well known for their physiological cooling effect on the skin and the mucous membranes of the mouth have been employed in such confectionaries. ", "A particularly favored compound in this application is menthol. ", "Menthol and other like materials, although imparting cooling effect to the mouth, also emit very strong undesirable odor and bitter taste. ", "This is caused by the high volatility of menthol and like additives.", "\nThe above remarks establish a need in the art for a sweetener which provides the advantages of strong sweetening effects, the absence of exposure to cariogenic agents and, most importantly, high intense cooling effect without attendant undesirable odor or flavor.", "\nSweetening agents are employed in confectioneries as internal components. ", "Sweetening agents, however, have also been employed as surface additives to confectionaries. ", "Molded jellies and pastries are often “sanded” with sugars. ", "Sugar sanding of these confectioneries provides an attractive appearance, keep molded pieces from sticking together during production and enhance initial sweetness.", "\nSanding of confectioneries with sugar alcohols having a negative heat of solution, however, has not been practiced in the prior art. ", "It is emphasized that “dusting” of confectioneries have been practiced in the art. ", "Sanding and dusting are distinguished processes in the confectionary arts. ", "Dusting is defined as the application of a uniform coating of fine powder particles to a surface, such as the surface of a confectionary. ", "Sanding, by definition, consists of making fine sugar crystals that adhere to the surface of the products by moistening them beforehand using techniques known in the art, such as by utilizing dry steam, or a hot solution of gum arabic or maltodextrin, and then subsequently drying the products. ", "Sanding, thus, involves the embedding of solid crystals below the surface of the confectionary. ", "Whereas dusting provides a uniform height of fine particles, sanding, involving as it does random penetration of the surface, results in contact with solid particles of varying height and thus different concentration of the particles.", "\nAnother distinction between dusting and sanding is that dusted particles are far smaller, resulting in higher surface areas per unit volume than the larger particles employed in sanding. ", "This results in shorter duration of the effect of dusted particles than sanded particles.", "\nAs stated above, sanding of certain confectionaries is known in the art, although sanding of confectioneries with sugar alcohols has not been practiced in the prior art. ", "Although one can only speculate as to the reason for this absence in the prior art, it is believed that because sugar alcohols have a high degree of hydroscopicity, one of ordinary skill in the art would not have thought of using sugar alcohols for the purpose of sanding.", "\nThe above remarks establish the need in the art for a sanded confectionary, providing intense initial cooling accompanied by corresponding intense sweet flavor." ]

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[ "A reader of this blog with whom I am connected on LinkedIn — if you and I aren’t connected there yet, what are you waiting for? — ", "asked me to do a post about this discrimination claim. ", "Right before I put fingers to keyboard, I noticed in my RSS feed that Dan Schwartz had already blogged about this at his Connecticut Employment Law Blog.", "\n\nDan’s dynamic post is a great mix of news and analysis. ", "And I have nothing to add…other than this link to the Telemundo call of Carli Lloyd’s incredible gooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooolazo from midfield in the 2015 World Cup final." ]

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[ "[The Zero-Mass Limit Problem for a Relativistic Spinless Particle in an Electromagnetic Field ]{}\n\n[Takashi Ichinose and Taro Murayama]{}\n\nDivision of Mathematical and Physical Sciences, Graduate School of Natural Science and Technology, Kanazawa University Kakuma-machi, Kanazawa, 920-1192, Japan\n\n[**Abstract:**]{} It is shown that mass-parameter-dependent solutions of the imaginary-time magnetic relativitstic Schrödinger equations converge as functionals of Lévy processes represented by stochastic integrals of stationary Poisson point processes if mass-parameter goes to zero.", "\n\n[**2010 Mathematics Subject Classification:**]{} 60G51; 60F17; 60H05; 35S10; 81S40.", "\n\n[**Key words:**]{} magnetic relativistic Schrödinger operator, imaginary-time relativistic Schrödinger equation, Lévy process, path integral formula, Feynman-Kac-Itô formula.", "\n\nIntroduction and results.", "\n=========================\n\nKasahara-Watanabe [@K; @and; @W; @86] discussed limit theorems in the framework of semimartingales represented by stochastic integrals of point processes. ", "In fact, they considered a sequence of point processes and their certain functionals represented by stochastic integrals, and proved their convergence in that context.", "\n\nIn this paper we treat a sequence of a slightly more general functionals of special kind of Lévy processes, which have no Gaussian part stemming from relativistic quantum mechanics, to discuss its convergence. ", "Naturally we have in mind the following relativistic Schrödinger equation which describes a spinless quantum particle of mass $m>0$ (for example, pions) in $\\R^{d}$ under the influence of the vector and scalar potentials $A(x), V(x) \\colon$ $$\\begin{aligned}\n&i\\frac{\\partial}{\\partial t} \\psi(x, t) = [H_{A}^{m} - m + V]\\psi(x,t)\n\\quad (t>0), \\end{aligned}$$ where $x\\in\\R^d$. In this paper, to see the main idea, we only consider the case that $A\\in C^{\\infty}_0 (\\R^d;\\R^d)$ and $V \\in C_0(\\R^d;\\R)$. Here then $H_A^m$ is defined by $$\\begin{aligned}\n &(H^{m}_{A}f)(x) :=\\text{Os-}\\frac{1}{(2\\pi)^{d} } \\iint_{\\R^{d}\\times \\R^{d}} \\nonumber \ne^{i(x-y)\\cdot \\xi} \\sqrt{\\left| \\xi -A(\\tfrac{x+y}{2})\\right|^{2}+m^{2}}f(y)dy d\\xi \\nonumber \\end{aligned}$$ for $f \\in C_{0}^{\\infty}(\\mathbf{R}^{d})$, where Osmeans [*oscillatory integral*]{}. ", "$H_{A}^{m}$ is called the [*Weyl pseudo-differential operator with mid-point prescription*]{}, corresponding to the classical relativistic Hamiltonian $\\sqrt{|\\xi-A(x)|^{2}+m^{2}}$. It is essentially selfadojoint in $L^{2}(\\R^{d})$ on $C_{0}^{\\infty}(\\R^{d})$ and bounded from below by $m$ ([@I; @89],[@I; @and; @T; @93]). ", "We have $H_{0}^{m}= \\sqrt{-\\Delta +m^{2}}$ for $A \\equiv 0$, where $-\\Delta$ is the Laplacian in $\\R^{d}$. The light velocity $c$, electric charge $e$ and Planck’s constant $h$ are taken to be $1$, $1$ and 2$\\pi$ respectively.", "\n\nThe operator $H_{A}^{m}-m+V$ was first studied in [@I; @and; @T; @86] by one of the authors of this paper to treat the [*pure imaginary-time*]{} relativistic Schrödinger equation $$\\begin{aligned}\n&\\frac{\\partial}{\\partial t} u(x, t) = -[H_{A}^{m} - m + V]u(x,t)\n\\quad (t>0), \\end{aligned}$$ where $x \\in \\R^d$. An imaginary-time path integral formula was given on path space $D_{0}$ to represent the solution of the Cauchy problem for (1.2). ", "Here $D_{0}$ is the set of the right-continuous paths $X: [0,\\infty) \\to \\mathbf{R}^{d}$ with left-hand limits and $X(0)=0$.\n\nWe use the probability space $(D_0, \\mathcal{F}, \\lambda^{m})$ treated in [@I; @and; @T; @86] with the natural filtration $\\{\\mathcal{F}(t)\\}_{t \\geq 0}$, where $\\mathcal{F}(t):=\\sigma(X(s); s \\leq t)\\subset \\mathcal{F}$. $\\{X(t)\\}_{t \\ge 0}$ is Lévy process, namely, it has stationary independent increments and is stochastically continuous (cf., [", "@I; @and; @W; @81], [@S; @99], [@A; @09]). ", "$\\lambda^m(X; X(t) \\in dy)$ is equal to $k^{m}_{0}(y, t)dy$, where $k^{m}_{0}(y, t)$ is the integral kernel of the operator $e^{-t(\\sqrt{-\\Delta +m^{2}}-m)}$ and has an explicit expression $$\\begin{aligned}\n k_{0}^{m}(y,t) \n = \\begin{cases} \n\\displaystyle 2 \\left( \\frac{m}{2\\pi}\\right)^{(d+1)/2}\\frac{te^{mt} K_{(d+1)/2}(m(|y|^{2}+t^{2})^{1/2})}{(|y|^{2}+t^{2})^{(d+1)/4}}, \\quad & m>0,\n \\\\ \n \\displaystyle \\frac{\\Gamma ((d+1)/2)}{\\pi^{(d+1)/2}} \\frac{t}{(|y|^{2}+t^{2})^{(d+1)/2}}, & \nm=0.", "\n \\end{cases}\\end{aligned}$$ Here $K_{\\nu}$ stands for the modified Bessel function of the third kind of order $\\nu$.\n\nThe characteristic function of $X(t)$ is $$\\begin{aligned}\n & E^{m}[ e^{i \\xi \\cdot X(t)}]=e^{-t(\\sqrt{|\\xi|^{2}+m^{2}}-m)}, \\quad \\xi \\in \\mathbf{R}^{d},\\end{aligned}$$ where $E^{m}$ denotes the expectation over $D_0$ with respect to $\\lambda^{m}$. By the [*Lévy-Khintchine formula*]{}, $$\\begin{aligned}\n \\sqrt{ |\\xi|^{2} + m^{2}} - m \n = - \\int_{|y| > 0} \\big( \n e^{i\\xi \\cdot y} - 1 - i\\xi \\cdot y\\mathbf{1}_{|y|<1} \\big)\n n^{ m} (dy). ", "\\end{aligned}$$ Here $n^{m}(dy)$ is the [*Lévy measure*]{}, that is a $\\sigma$-finite measure on $\\mathbf{R}^{d}\\setminus \\{0\\}$ satisfying $\\int_{|y|>0}(1 \\wedge |y|^{2})n^{m}(dy) < \\infty$, and having density $$\\begin{aligned}\n\\label{eq:eq levy measure}\nn^{m}(y)=n^{m}(|y|) \n= \\begin{cases}\n\\displaystyle 2\\left (\\frac{m}{2\\pi}\\right)^{(d+1)/2}\\frac{K_{(d+1)/2}(m|y|)}{|y|^{(d+1)/2}}, \n\\quad & m>0, \n\\\\\n \\displaystyle \\frac{\\Gamma ((d+1)/2)}{\\pi^{(d+1) /2}} \\frac{1}{|y|^{d+1}}, & m=0.", "\n\\end{cases}\\end{aligned}$$ As shown in [@I; @89], $H_{A}^{m}$ has another expression connected with the Lévy measure $n^{m}(dy)$ $$\\begin{aligned}\n(H_{A}^{m}f)(x)=mf(x) -\\lim_{r \\downarrow 0}\\int_{|y|\\geq r} \\big[e^{-iy\\cdot A(x+\\frac{1}{2}y)} f(x+y) -f(x) \\big]n^{m}(dy).\\end{aligned}$$\n\nFor $X \\in D_0$, let $N_{X}(dsdy)$ be a counting measure on $(0, \\infty) \\times (\\mathbf{R}^{d} \\setminus \\{0\\})$ defined by $$\\begin{aligned}\n&N_{X}(E):=\\# \\{ s >0; (s,X(s)-X(s-)) \\in E\\}\\end{aligned}$$ for $E \\in \\mathcal{B}(0, \\infty) \\times \\mathcal{B}(\\mathbf{R}^{d} \\setminus \\{0\\})$, where $\\mathcal{B}(\\cdots)$ are $\\sigma$-algebras of Borel sets. ", "$N_{X}(dsdy)$ is the stationary Poisson random measure with intensity measure $ds n^{m}(dy)$ with respect to $\\lambda^{m}$. Let $\\widetilde{N_{X}^{m}}(dsdy):= N_{X}(dsdy)-ds n^{ m}(dy)$. By the [*Lévy-Itô theorem*]{}, $$\\begin{aligned}\n\\label{eq:eq levy-ito}\nX(t) =\\int_{0}^{t} \\int_{|y| \\geq 1} y N_{X}(dsdy) \n+ \\int_{0}^{t} \\int_{0< |y| < 1} y \\widetilde{N_{X}^{m}}(dsdy),\\quad \\lambda^{m}\\text{-a.s. }", "X \\in D_{0}. ", "\\end{aligned}$$ Here and below, we should understand $\\int_0^t: =\\int_{(0, t]}$. It can be proved that the solution of (1.2) with initial data $u^{m}(x,0)=g(x)$ is given by $$\\begin{aligned}\nu^{m}(x,t) &:= E^{m}[e^{-S^{m}(t,x,X)}g(x+X(t))],\\\\ \n S^{m}( \\cdot) & := i Y^m(t, x,X) + \\int_{0}^{t} V(x+X(s))ds, \\\\\n Y^m (\\cdot) &:= \\int_{0}^{t}\\int_{|y| \\geq 1} A(x+X(s-)+\\tfrac{1}{2}y) \\cdot y N_{X}(dsdy) \\nonumber \\\\\n& \\quad + \\int_{0}^{t} \\int_{0<|y| < 1} A(x+X(s-)+\\tfrac{1}{2}y) \\cdot y \\widetilde{N_{X}^{m}}(dsdy)\\nonumber \\\\\n& \\quad + \\int_{0}^{t} ds\\int_{0<|y|<1} \\Big[ A(x+X(s)+\\tfrac{1}{2}y) -A(x+ X(s))\\Big] \\cdot y n^{m}(dy). ", " \\nonumber \\end{aligned}$$ In (1.7) and (1.9) above, the integration regions $|y| \\geq 1$ and $0<|y| <1$ may be replaced by $|y| \\geq \\delta$ and $0< |y| < \\delta$ respectively, for any $\\delta >0$.\n\nWe note that these relativistic quantities, $H^{m}_{A}-m+V$, $\\sqrt{|\\xi|^{2}+m^{2}}-m$, $D_{0}$, $\\lambda^{m}$, $k_{0}^{m}(y,t)$ and $X(t)$, correspond to the nonrelativistic ones $\\frac{1}{2m}(-i \\nabla -A)^{2}+V$, $\\frac{|\\xi |^{2}}{2m}$, $ C_{0}$, [*Wiener measure*]{}, the heat kernel $(\\tfrac{m}{2\\pi t })^{d/2}e^{-\\tfrac{m}{2t}|y|^{2}}$, [*Brownian motion*]{} $B(t)$, respectively. ", "Here $C_{0}$ is the space of continuous paths $B: [0,\\infty) \\to \\mathbf{R}^{d}$ with $B(0)=0$. Furthermore, (1.8) with (1.9) is what [*does*]{} correspond to [*Feynman-Kac-Itô formula*]{} ([@S; @79]).", "\n\nThe purpose of this paper is to answer the following question:\\\n(Q) [*When the mass $m > 0$ of the particle becomes sufficiently small, how does its property vary ?*]{}", "\n\n$\\lambda^{m}$ converges weakly to $\\lambda^{0}$ as $m \\downarrow 0$.\n\n$u^{m}(\\cdot, t)$ converges to $u^{0}(\\cdot,t )$ on $L^{2}(\\mathbf{R}^{d})$ as $m \\downarrow 0$, uniformly on $[0, T]$.\n\nHere and below, $0 < T < \\infty$ can be taken arbitrary. ", "Theorem 2 implies the strong resolvent convergence of $H^{m}_{A}-m+V$ to $H^{0}_{A}+V$ (\\[13, IX, Theorem 2.16\\]). ", "An immediate consequence is the following result for the solution $\\psi^{m}(x,t)$ of the Cauchy problem for (1.1).", "\n\n$\\psi^{m}(\\cdot,t)$ converges to $\\psi^{0}(\\cdot ,t)$ on $L^{2}(\\mathbf{R}^{d})$ as $m \\downarrow 0$, uniformly on $[0, T]$.\n\nWe will prove Theorem 2 by using following:\n\n$u^{m}(\\cdot, t)$ converges to $u^{0}(\\cdot,t )$ on $C_{\\infty}(\\mathbf{R}^{d})$ as $m \\downarrow 0$, uniformly on $[0, T]$, where $C_{\\infty}(\\mathbf{R}^{d})$ is the space of the continuous functions $g :\\mathbf{R}^{d} \\to \\mathbf{C}$ with $|g(x)| \\to 0$ as $|x| \\to \\infty$ with norm $\\|g\\|_{\\infty}:= \\sup_{x\\in \\R^{d} }|g(x)|$.\n\nThe crucial idea of proof is to do a change of variable path. ", "In Sections 2,3 and 4, these theorems are shown by probabilistic method, although one can more easily show Theorem 2 by operator-theoretical one [@I; @92], and also by pseudo-differential calculus [@N; @and; @U; @90]. ", "In this paper, as we mentiond before, we treat the problem under a rather mild assumption on the potentials $A(x), V(x)$. We will come to more general case in a forthcoming paper, together for the other two different magnetic relativistic Schrödinger operators ([@I; @2012], [@I; @2013]) corresponding to the same classical relativistic Hamiltonian. ", "Another limit problem when the light velocity $c$ goes to infinity ([*nonrelativistic limit*]{}) was studied in [@I; @87].", "\n\nProof of Theorem 1.", "\n===================\n\nWe observe the following three facts which imply Theorem 1 (\\[2,Theorem 13.5\\]):\\\n(i) The finite dimensional distributions with respect to $\\lambda^{m}$ converge weakly to those with respect to $\\lambda^{0}$ as $m \\downarrow 0$.\\\n(ii) For any $t > 0$, $\\lambda^0(X; X(t)-X(t-\\varepsilon)\\in dy )$ converges weakly to Dirac measure concentrated at the point $0\\in \\R^d$ as $\\varepsilon \\downarrow 0$.\\\n(iii) There exist constants $\\alpha > \\frac{1}{2}$, $\\beta > 0$ and a nondecreasing continuous function $F$ on $[0,\\infty)$ such that $$\\begin{aligned}\n& E^{m}\\left[ |X(s)-X(r)|^{\\beta} |X(t)-X(s)|^{\\beta}\\right] \\leq [F(t)-F(r)]^{2\\alpha}, \\quad 0 < m < 1, \\ 0 \\leq r < s < t.\\end{aligned}$$ [*Proof.*]{} (", "i) follows from (1.4), and (ii) from the stochastic continuity of $\\{X(t)\\}_{t \\geq 0}. ", "$ (iii) Since $\\tfrac{d}{d\\tau} \\tau^{\\nu} K_{\\nu}(\\tau)=$ $-\\tau^{\\nu}K_{\\nu-1}(\\tau) $ ($\\tau>0, \\nu >0$) (\\[3, (21), p.79\\]) and $\\nu \\mapsto K_{\\nu}(\\tau)$ is strictly increasing in $(0, \\infty)$ (\\[3, (21), p.82\\]), we have $(d/d\\tau)(e^{\\tau}\\tau^{\\nu}K_{\\nu}(\\tau))= e^{\\tau}\\tau^{\\nu} (K_{\\nu}(\\tau)-K_{\\nu-1}(\\tau))<0$ if $0< \\nu <\\frac{1}{2}$. Therefore $\\tau \\mapsto e^{\\tau}\\tau^{\\nu} K_{\\nu}(\\tau)$ is strictly decreasing in $(0,\\infty)$ and so \\[3, (41),(42), (43), p.10\\] $$\\begin{aligned}\ne^{\\tau} \\tau^{\\nu}K_{\\nu}(\\tau) \\leq \\lim_{\\tau \\downarrow 0} \\tau^{\\nu}K_{\\nu}(\\tau)\n =2^{\\nu-1} \\Gamma(\\nu).\\end{aligned}$$ Then we have for $0\\leq r< s< t$, $\\frac{1}{2}< \\beta < 1$, $$\\begin{aligned}\n E^{m}\\left[ |X(s)-X(r)|^{\\beta} |X(t)-X(s)|^{\\beta}\\right]\n& = \\int|y|^{\\beta}k_{0}^{m}(y, s-r)dy \\int|y|^{\\beta}k_{0}^{m}(y, t-s)dy\\\\\n&= C(d, \\beta)^{2} ((s-r)(t-s) )^{\\beta} \\\\\n& \\quad \\times e^{m(s-r)} (m(s-r))^{ \\frac{1-\\beta}{2 }}K_{\\frac{1-\\beta}{2}} (m(s-r))\\\\\n& \\quad \\times e^{m(t-s)} (m(t-s))^{ \\frac{1-\\beta}{2 }}K_{\\frac{1-\\beta}{2}} (m(t-s))\\\\\n&\\leq C(d, \\beta)^{2} 2^{-(1+2\\beta)}\\Gamma(\\tfrac{1-\\beta}{2})^{2}(t-r)^{2\\beta},\\end{aligned}$$ where in the second equality we use \\[4, Lemma 3.3(ii)\\] with a constant $C(d, \\beta)$ depending on $d$ and $\\beta$. Therefore (iii) holds for $\\frac{1}{2}< \\beta < 1$ and $\\alpha = \\beta$ and $F(p):= C(d, \\beta)^{1/\\beta} 2^{-(1+2\\beta)/2\\beta}\\Gamma(\\tfrac{1-\\beta}{2})^{1/\\beta}p$.$\\square$\n\nProof of Theorem 2.", "\n===================\n\nWe will prove Theorem 2 by assuming validity of Theorem 3. ", "In this and the next section, we assume $V \\geq 0$ without loss of generality, since in the general case, we have only to replace $V$ in (1.8), (1.9) by $V -\\inf V \\geq 0$.\\\nStep I: Let $g \\in C_{0}^{\\infty}(\\R^{d})$. For $R >0$, we have $$\\begin{aligned}\n\\|u^{m}(\\cdot, t )-u^{0}(\\cdot, t )\\|_{2}\n&\\leq \\|u^{m}(\\cdot, t )-u^{0}(\\cdot, t )\\|_{L^{2}(|x|< R)} +\\|u^{m}(\\cdot, t )-u^{0}\n(\\cdot, t )\\|_{L^{2}(|x|\\geq R)}\\nonumber \\\\\n{} &=: I_{1}( t, m,R)+I_{2}( t, m,R).\\end{aligned}$$ From Theorem 3, $I_{1}( t, m,R)$ converges to zero as $m \\downarrow 0$ uniformly on $t \\leq T$. From (1.8), we have $$\\begin{aligned}\nI_{2}(t, m,R)& \\leq \\|u^{m}(\\cdot,t)\\|_{L^{2}(|x| \\geq R)} + \\| u^{0}(\\cdot,t)\\|_{L^{2}(|x| \\geq R)} \\nonumber \\\\\n&\\leq \\Big(\\int_{|x| \\geq R}dx \\int k_{0}^{m}(y,t)|g(x+y)|^{2}dy\\Big)^{\\frac{1}{2}} \\\\\n& \\quad + \\Big(\\int_{|x| \\geq R} dx \\int k_{0}^{0}(y,t)|g(x+y)|^{2}dy\\Big)^{\\frac{1}{2}} \\\\\n&=: J( t, m,R)+J(t,0,R).\\end{aligned}$$ Let $\\chi$ be a nonnegative $C^{\\infty}_{0}(\\mathbf{R}^{d})$ function such that $\\chi(x)=1$ if $|x| \\leq \\frac{1}{2}$ and $=0$ if $|x| \\geq 1$. Put $h(x)=|g(x)|^{2}$. Since $\\mathbf{1}_{|x|< R} \\geq \\chi(\\frac{x}{R})$, we have $$\\begin{aligned}\nJ( t, m,R)^{2} \n& \\leq \\int(1-\\chi(\\tfrac{x}{R}) )dx\\int k_{0}^{m}(y,t)h(x+y)dy \\\\\n& = \\frac{1}{(2\\pi)^{d}} \\bigg [\\widehat{h}(0) \\int \\left( 1- \\exp \\{ -t[\\sqrt{\\tfrac{|\\eta|^{2}}{R^{2}}+m^{2}}-m] \\} \\right) \\overline{\\widehat{\\chi}(\\eta)} d\\eta \\\\\n& \\qquad \\qquad + \\int ( \\widehat{h}(0)) - \\widehat{h}(\\tfrac{\\eta}{R})) \\exp \\left\\{ -t\\left[\\sqrt{\\tfrac{|\\eta|^{2}}{R^{2}}+m^{2}}-m\\right] \\right\\}\\overline{\\widehat{\\chi}(\\eta)} d\\eta \\bigg],\\end{aligned}$$ which converges to zero as $R \\to \\infty$ uniformly on $t \\leq T$ and $0\\leq m \\leq1$. Here, for $\\varphi \\in \\mathcal{S}(\\R^{d})$, $\\widehat{\\varphi}$ is the Fourier transform of $\\varphi$ given by $\\widehat{\\varphi}(\\xi)=\\int e^{-ix \\cdot \\xi}\\varphi(x)dx$ ($\\xi \\in \\R^{d}$).", "\n\nFrom (1.3) and (2.1), it follows that $k^{m}_{0}(y,t) \\to k_{0}^{0}(y,t)$ as $m \\downarrow 0$, and then $ J( t, 0,R)^{2}\\leq \\liminf_{m \\downarrow 0} J( t, m,R)^{2}$ by Fatou’s lemma. ", "Therefore we have Theorem 2 for this step.\\\nStep II: Let $g \\in L^{2}(\\mathbf{R}^{d})$. There is a sequence $\\{ g_{n}\\} \\subset C^{\\infty}_{0}(\\mathbf{R}^{d})$ such that $g_{n} \\to g$ in $L^{2}(\\mathbf{R}^{d})$ as $n \\to \\infty.$ Put $u^{m}_{n}(x,t):= E^{m}[e^{-S^{m}(t,x,X)}g_{n}(x+X(t))]$. Then we have $$\\begin{aligned}\n\\| u^{m}(\\cdot, t )-u^{0}(\\cdot, t )\\|_{2} \n&\\leq \\| u^{m}(\\cdot, t )-u^{m}_{n}(\\cdot, t )\\|_{2}+ \\| u^{m}_{n}(\\cdot, t )-u^{0}_{n}(\\cdot, t )\\|_{2}\\\\ \n& \\quad + \\| u^{0}_{n}(\\cdot, t )-u^{0}(\\cdot, t )\\|_{2}\\\\ \n&\\leq 2\\|g_{n}-g\\|_{2}+\\| u^{m}_{n}(\\cdot, t )-u^{0}_{n}(\\cdot, t ) \\|_{2}.\\end{aligned}$$ By Step I, we have $$\\begin{aligned}\n\\limsup_{m \\downarrow 0}\\sup_{t \\leq T}\\| u^{m}(\\cdot, t )-u^{0}(\\cdot, t ) \\|_{2} \\leq 2 \\|g_{n}-g\\|_{2},\\end{aligned}$$ which converges to zero as $n \\to \\infty$. $\\square$\n\nProof of Theorem 3.", "\n===================\n\nFrom (1.8), we have to prove that $$\\begin{aligned}\nu^{m}(x,t) &= E^{m}[e^{-S^{m}(t,x,X)}g(x+X(t))] \\nonumber \\\\\n & \\to E^{0}[e^{-S^{0}(t,x,X)}g(x+X(t))] = u^{0}(x,t)\\end{aligned}$$ as $m \\downarrow 0$ in $C_{\\infty}(\\mathbf{R}^{d})$. But its direct proof seems difficult since both the integrand $e^{-S^{m}(t,x,X)}g(x+X(t))$ and the probability measure $\\lambda^{m}$ depend on $m$. So we change $E^{m}[\\cdots]$ to $E^{0}[\\cdots]$ by a [*change of variable*]{} (i.e., [*change of probability measure*]{}) $\\lambda^{m}=\\lambda^{0} \\Phi_{m}^{-1}$ with path space transformation $\\Phi_{m}: D_0 \\to D_0 $. ", "If there is such a $\\Phi_{m}$, we can see by (1.4) and (1.5) that the difference between the path $X(t)$ and the transformed path $\\Phi_{m}(X)(t)$ is expressed in terms of the difference between the two Lévy measures $n^{0}(dy)$ and $n^{m}(dy)$, so that it is presumed to hold that $n^{m}(dy)=n^{0}\\phi_{m}^{-1}(dy)$ for some map $\\phi_{m}\\colon {\\mathbf{R}^{d}\\setminus \\{0\\} }$ $\\to$ $\\mathbf{R}^{d}\\setminus \\{0\\}$.\n\nWe will determine $\\phi_{m}$ in such a way that (1) $n^{m}(dy)=n^{0}\\phi_{m}^{-1}(dy)$, (2) $\\phi_{m} \\in C^{1}(\\mathbf{R}^{d}\\setminus \\{0\\}; \\mathbf{R}^{d}\\setminus \\{0\\})$, (3) $\\phi_{m}$ is one to one and onto, (4) $\\det D\\phi_{m}(z) \\ne 0$ for all $z \\in \\R^{d}\\setminus \\{0\\}$, where $D\\phi_{m}(z)$ is the Jacobian matrix of $\\phi_{m}$ at the point $z$.\n\nLet $U:= \\{y \\in \\R^{d} \\setminus \\{0\\}; |y| \\in U'\\}$ for $U' \\in \\mathcal{B}(0, \\infty)$. Introducing the spherical coordinates by $z=r \\omega$, $r>0$, $\\omega \\in S^{d-1}$, we have $$\\begin{aligned}\nn^{m}(U)=\\int_{U}n^{m}(|y|)dy \n= C(d)\\int_{U'}n^{m}(r)r^{d-1}dr,\\end{aligned}$$ where $C(d)$ is the surface area of the $d$-dimensional unit ball.", "\n\nLet us assume that $\\phi_{m}^{-1}(z) = l_{m}(|z|)\\tfrac{z}{|z|}$ for some non-decreasing $C^{1}$ function $l_{m}:(0, \\infty) \\to (0, \\infty)$. Then we have $$\\begin{aligned}\nn^{0}\\phi_{m}^{-1}(U) \n&= \\int_{U}n^{0}(l_{m}(|z|)) |z|^{-(d-1)} l_{m}(|z|)^{d-1}l_{m}'(|z|) dz\\nonumber \\\\\n& = C(d)\\int_{U'} n^{0}(l_{m}(r)) l_{m}(r)^{d-1} l_{m}'(r) dr,\\end{aligned}$$ where $l_{m}'(r)=(d/dr)l_{m}(r).$ Therefore we have $$\\begin{aligned}\nn^{m}(r)r^{d-1}= n^{0}(l_{m}(r)) l_{m}(r)^{d-1} l_{m}'(r), \\quad \\text{a.s. } ", "r > 0. ", " \\end{aligned}$$ If $m > 0$, from (1.6), we have $$\\begin{aligned}\n&-\\frac{d}{dr}l_{m}(r)^{-1}= 2^{-\\frac{d-1}{2}} \\Gamma(\\tfrac{d+1}{2})^{-1} m^{\\frac{d+1}{2}}r^{\\frac{d-3}{2}} K_{\\frac{d+1}{2}}(mr).\\end{aligned}$$ We solve this differential equation under boundary condition $l_{m}(\\infty) = \\infty$ to get $$\\begin{aligned}\nl_{m}(r)= \\frac{2^{\\frac{d-1}{2}} \\Gamma (\\frac{d+1}{2})}{ m^{\\frac{d+1}{2}} \\int_{r}^{\\infty} u^{\\frac{d-3}{2}} K_{\\frac{d+1}{2}}(mu)du }.\\end{aligned}$$ Here we note that $0<\\int_{r}^{\\infty} u^{\\frac{d-3}{2}} K_{\\frac{d+1}{2}}(mu) du < \\infty$ by $K_{\\frac{d+1}{2}}(\\tau) > 0$ for $\\tau > 0$, and \\[3, (37), (38), p.9\\] $$\\begin{aligned}\nK_{\\frac{d+1}{2}}(\\tau) =\\left(\\frac{\\pi}{2}\\right)^{1/2} \\tau^{-1/2}e^{-\\tau} (1+o(1)), \\quad \\tau \\uparrow \\infty.\\end{aligned}$$\n\n[(i)]{} $l_{m}(r)$ is a strictly increasing $C^{\\infty}$ function of $r\\in(0, \\infty)$ and $l_{m}(+0)=0$, $l_{m}(\\infty)=\\infty$.\\\n[(ii)]{} For all $r>0$, $l_{m}(r)$ converges to $r$, strictly decreasingly, as $m \\downarrow 0$.\n\n[*Proof.*]{} (", "2.1) implies $l_{m}(+0)=0$. The other claims of (i) follow from (4.1) and the fact that $K_{(d+1)/2}(\\tau)$ is a $C^{\\infty}$ function in $(0,\\infty)$. The claim (ii) can be proved by the fact that $\\tau^{\\nu}K_{\\nu}(\\tau)$ is strictly decreasing in $(0, \\infty)$ (cf. ", "Section 2, Proof of (ii)), (2.1) and the monotone convergence theorem. ", "$\\square$\n\nIf $m=0$, let $l_{0}(r):=r$. Let us put $\\phi_{0}(z):=z$ and for $m >0$, $$\\begin{aligned}\n\\phi_{m}(z):= \\l_{m}^{-1}(|z|) \\frac{z}{|z|}, \\quad z \\in \\R^{d}\\setminus \\{0\\}.\\end{aligned}$$ Then we have $$\\begin{aligned}\n\\phi_{m}^{-1}(z)= \\l_{m}(|z|) \\frac{z}{|z|}, \\quad z \\in \\R^{d}\\setminus \\{0\\}.\\end{aligned}$$ We note that $$\\begin{aligned}\n\\phi_{m}(z) \\to z, \\; |\\phi_{m}(z)|= l_{m}^{-1}(|z|) \\uparrow |z|\\end{aligned}$$ $m \\downarrow 0$ by Proposition 1 (ii).", "\n\nLet us define $\\Phi_{0}(X):=X$ and for $m >0$, $$\\begin{aligned}\n\\Phi_{m}(X)(t) \n& := \\int_{0}^{t}\\int_{|y| \\geq 1}y N_{X}(ds \\phi_{m}^{-1}(dy)) + \\int_{0}^{t} \\int_{0< |y| < 1} y \\widetilde{N_{X}^{0}}(ds \\phi_{m}^{-1}(dy)) \\nonumber \\\\\n& = \\int_{0}^{t} \\int_{|z| \\geq l_{m}(1)} \\phi_{m}(z) N_{X}(ds dz)+\\int_{0}^{t}\\int_{0< |z| < l_{m}(1)} \\phi_{m}(z) \\widetilde{N_{X}^{0}}( ds dz)\\nonumber \\\\\n& = \\int_{0}^{t} \\int_{|z| \\geq 1}\\phi_{m}(z) N_{X}(ds dz)+ \\int_{0}^{t}\\int_{0< |z| < 1} \\phi_{m}(z) \\widetilde{N_{X}^{0}}( ds dz).\\end{aligned}$$\n\nFor every sequence $\\{m\\}$ with $m \\downarrow 0$, there exists a subsequence $\\{m'\\}$ such that $$\\begin{aligned}\n\\sup_{t \\leq T}|\\Phi_{m'}(X)(t)-X(t)|\\to 0 \\text{ as } m' \\downarrow 0, \\lambda^{0}\\text{-a.s. } ", "X \\in D_0.\\end{aligned}$$\n\n[*Proof.*]{} ", "From (1.7) and (4.3), we have $$\\begin{aligned}\n \\sup_{t \\leq T}|\\Phi_{m}(X)(t)-X(t)|\\nonumber & \\leq \\int_{0}^{T}\\int_{|z| \\geq 1}| \\phi_{m}(z)-z|N_{X}(dsdz)\\\\ \n& \\quad + \\sup_{t \\leq T}\\Big| \\int_{0}^{t}\\int_{0< |z| <1} (\\phi_{m}(z)-z) \\widetilde{N_{X}^{0}}(dsdz)\\Big| \\nonumber\\\\\n&=: I_{1}(m, X)+ \\sup_{t \\leq T}|I_{2}(t, m, X)|.\\end{aligned}$$ We have $I_{1}(m, X) \\to 0$ as $m \\downarrow 0$ by (4.2) and $\\int_{0}^{T}\\int_{|z|\\geq 1}|z|N_{X}(dsdz) \n< \\infty$. We note that $I_2(t,m,X)$ is the $L^2(D_0;\\lambda^0)$-limit of the right-continuous $\\{\\mathcal{F}(t)\\}_{t \\geq 0}$-martingale $\\{I_2^{\\varepsilon}(t,m,X)\\}_{t \\geq 0}$ with $I_2^{\\varepsilon}(t,m,X):= \\int_0^t\\int_{\\varepsilon<|z|<1}(\\phi_m(z)-z)\\widetilde{N_X^0}(dsdz)$ as $\\varepsilon \\downarrow 0$, with convergence being uniform on $t \\leq T$. By taking a subsequence if necessary, $I_2^{\\varepsilon}(t,m,X)$ converges to $I_2(t,m,X)$ as $\\varepsilon \\downarrow 0$ uniformly on $t \\leq T$, $\\lambda^0$-a.s., ", "and hence $I_2(t,m,X)$ is right-continuous on $t \\leq T$, $\\lambda^0$-a.s. (", "\\[11, p.73, Proof of Theorem 5.1\\], \\[15, p.128-129, Proofs of Lemmas 20.6, 20.7\\]). ", "Then we use Doob’s martingale inequality [@A; @09] to have $$\\begin{aligned}\nE^{0}\\left[ \\sup_{t \\leq T}|I_{2}(t, m, X)|^{2} \\right]\n &\\leq 4E^{0}\\left[| I_{2}(T, m, X)|^{2} \\right]\\nonumber \\\\\n& \\leq 4T \\! \\! ", "\\int_{0<|z|<1}\\!\\! \\!\\!\\!\\!\\!\\!\\!\\!\\! ", "\\!| \\phi_{m}(z)-z|^{2} n^{0}(dz),\\nonumber \\end{aligned}$$ which converges to zero as $m \\downarrow 0$ by (4.2) and $\\int_{0< |z|<1} |z|^{2}n^{0}(dz) < \\infty$. $\\square$\n\nBy (1.8) and $\\lambda^{m}=\\lambda^{0} \\Phi_{m}^{-1}$, we have $$\\begin{aligned}\nu^{m}(x,t)= E^{0}[ e^{-S^{m}(t, x, \\Phi_{m}(X))} g(x+ \\Phi_{m}(X)(t))],\\end{aligned}$$ and then $$\\begin{aligned}\n\\sup_{t \\leq T} \\|u^{m}(\\cdot,t) -u^{0}(\\cdot,t)\\|_{\\infty}\n \\leq & \\| g \\|_{\\infty} \\sup_{t \\leq T, \\ x \\in \\mathbf{R}^{d}} E^{0} \\left[\\left| e^{-S^{m}(t,x, \\Phi_{m}(X))} - e^{-S^{0}(t, x, X)} \\right| \\right] \\nonumber \\\\ \n& +E^{0}\\left[ \\sup_{t\\leq T} \\|g(\\cdot + \\Phi_{m}(X)(t)) - g(\\cdot + X(t))\\|_{\\infty} \\right].\\end{aligned}$$ Since $g\\in C_{\\infty}(\\R^{d})$ is uniformly continuous and bounded on $\\R^{d}$, the second term on the right of (4.4) converges to zero as $m \\downarrow 0$.\n\nNext we consider the first term on the right of (4.4). ", "By $N_{\\Phi_{m}(X)}(dsdy) = N_{X}(ds \\phi_{m}^{-1}(dy))$, we have $$\\begin{aligned}\n\\label{eq;eq S}\n&S^{m}(t, x, \\Phi_{m}(X)) \\nonumber \\\\\n&= i\\bigg(\\int_{0}^{t} \\int_{|z|\\geq 1} A(x+ \\Phi_{m}(X)(s-)+\\tfrac{1}{2}\\phi_{m}(z))\\cdot \\phi_{m}(z) N_{X}(dsdz) \\nonumber \\\\\n &\\quad + \\int_{0}^{t} \\int_{0< |z|<1} A(x+ \\Phi_{m}(X)(s-)+\\tfrac{1}{2}\\phi_{m}(z))\\cdot \\phi_{m}(z) \\widetilde{N_{X}^{0}}(dsdz) \\nonumber \\\\\n& \\quad +\\int_{0}^{t} ds \n \\int_{0<|z| < 1} \\left[A(x+\\Phi_{m}(X)(s)+\\tfrac{1}{2}\\phi_{m}(z))-A(x+\\Phi_{m}(X)(s))\\right] \\cdot \\phi_{m}(z) n^{0}(dz) \\bigg) \\nonumber \\\\\n&\\quad + \\int_{0}^{t} V(x+ \\Phi_{m}(X)(s))ds \\nonumber \\\\\n& =: i \\Big( S_{1}^{m} (t,x,X)+S_{2}^{m}(t,x,X)+ S_{3}^{m} (t,x,X) \\Big) + S_{4}^m(t,x,X). ", " \\nonumber \\end{aligned}$$ By the inequality $$|e^{-(ia+b)}-e^{-(ia'+b')}| \\leq e^{-b}|e^{-ia}-e^{-ia'}|+|b-b'|$$ for any $a,a'\\in\\mathbf{R}$, $b, b' \\geq 0$, $\\sup E^{0}[\\cdots]$ of the first term on the right of (4.4) is less than or equal to $$\\begin{aligned}\n & E^{0}\\Big[\\sup_{t \\leq T} \\|e^{-i S^m_{1}(t, \\cdot, X)}- e^{-i S^0_{1}(t, \\cdot,X)} \\|_{\\infty} \\Big] + \\sup_{x \\in \\mathbf{R}^{d}}E^{0}\\Big[ \\sup_{t \\leq T} | S^m_{2}(t, x, X)- S^0_{2}(t, x,X) |\\Big] \\nonumber \\\\\n & \\quad +E^{0}\\Big[ \\sup_{t \\leq T} \\| S^m_{3}(t, \\cdot, X)-S^0_{3}(t, \\cdot,X) \\|_{\\infty} \\Big] + E^{0}\\Big[\\sup_{t \\leq T} \\| S^m_{4}(t, \\cdot, X) -S^0_{4}(t, \\cdot,X) \\|_{\\infty} \\Big]. ", "\\end{aligned}$$ Now, let $\\{m\\}$ be a sequence with $m \\downarrow 0$ and $\\{m'\\}$ any subsequence of $\\{m\\}$. By Proposition 2, there exists a subsequence $\\{m''\\}$ of $\\{ m'\\}$ such that $\\sup_{t \\leq T}|\\Phi_{m''}(X)(t)-X(t)|\\to 0$ $m'' \\downarrow 0$, $\\lambda^{0}$.\n\nTo prove that each term of (4.5) converges to zero as $m'' \\downarrow 0$, we first note that $$\\begin{aligned}\n S^{m''}_{1}(t, x, X) -S_{1}^0(t, x,X) & = \\int_{0}^{t} \\int_{|z| \\geq 1 }\n\\big( A(x+\\Phi_{m''}(X)(s-) + \\tfrac{1}{2}\\phi_{m''}(z)) \\nonumber \\\\\n&\\qquad \\qquad \\qquad - A(x+X(s-)+\\tfrac{1}{2}z)\\big)\\cdot \\phi_{m''} (z) N_{X}(dsdz)\\\\\n& \\quad +\\int_{0}^{t} \\int_{|z| \\geq 1 } A(x+X(s-)+\\tfrac{1}{2}z)\\cdot (\\phi_{m''}(z)- z) N_{X}(dsdz).\\end{aligned}$$ Then the integrand of the first term of (4.5) is less than or equal to $$\\begin{aligned}\n& \\!\\int_{0}^{T} \\int_{|z| \\geq 1} \\sup_{x\\in \\R^{d}}\\left|A(x\\!+\\!\\Phi_{m''}(X)(s-) + \\tfrac{1}{2}\\phi_{m''}(z)) - A(x+X(s-)+\\tfrac{1}{2}z)\\right| |z| N_{X}(dsdz)\\\\\n& +\\sup_{x \\in \\R^{d}}|A(x)|\\!\\int_{0}^{T}\\!\\! ", "\\int_{|z| \\geq 1 }\\!\\!\\!\\!\\! ", " |\\phi_{m''}(z)\\!-\\! ", "z| N_{X}(dsdz),\\end{aligned}$$ which converges to zero as $m'' \\downarrow 0$ since $A \\in C_{0}^{\\infty}(\\R^{d};\\R^{d}) $ is uniformly continuous on $\\R^{d}$.\n\nNext, since $S_2^m(t,x,X)$ is seen to be right-continuous, by Schwarz’s inequality and Doob’s martingale inequality, $E^{0}[\\cdots]$ of the second term of (4.5) is less than or equal to $$\\begin{aligned}\n& 2E^{0}\\Big[ \\int_{0}^{T} ds \\int_{0<|z| <1} \\big|A(x\\!+\\!\\Phi_{m''}(X)(s-)+\\tfrac{1}{2} \\phi_{m''}(z))\\cdot\\phi_{m''}(z)\\\\\n &\\qquad \\qquad \\qquad \\qquad \\quad - A(x+X(s-)+\\tfrac{1}{2}z) \\cdot z \\big|^{2} n^{0}(dz) \\Big ]^{\\frac{1}{2}}.\\nonumber \\end{aligned}$$ By the inequality $( a+ b)^{2}\\leq 2(a^{2}+b^{2})$ for any $a,b \\in \\R$, $E^{0}[\\cdots]$ above is less than or equal to $$\\begin{aligned}\n& 2\\bigg\\{E^{0}\\bigg[ \\int_{0}^{T}ds \\int_{0<|z| <1} \\sup_{x\\in \\R^{d}} |A(x+\\Phi_{m''}(X)(s-) +\\tfrac{1}{2} \\phi_{m''}(z)) \\\\\n& \\qquad \\qquad \\qquad \\qquad \\qquad \\qquad - A(x+X(s-)+\\tfrac{1}{2} z) |^{2} |z|^{2} n^{0}(dz)\\bigg] \\nonumber \\\\\n& \\quad + T \\sup_{x\\in \\R^{d}}|A(x)|^{2}\\int_{0<|z| <1} |\\phi_{m''}(z)-z|^{2} n^{0}(dz)\\bigg\\}, \\nonumber \\end{aligned}$$ which converges to zero as $ m'' \\downarrow 0$. As for the third term of (4.5), by the mean value theorem, we have $$\\begin{aligned}\n& S^{m''}_{3}(t, x, X)-S^{0}_{3}(t, x,X) \\\\\n&= \\frac{1}{2}\\int_{0}^{t}ds \\int_{0<|z| <1} n^{0}(dz)\\int_{0}^{1} \\big[ \\big(W^{m''}_{x,X}(s,\\theta) \\phi_{m''}(z) \\big)\\cdot \\phi_{m''}(z) - \\big( W^{0}_{x,X}(s,\\theta) z \\big) \\cdot z \\big]\nd\\theta.\\end{aligned}$$ Here $W^{m''}_{x,X}(s,\\theta) $ and $W^{0}_{x,X}(s,\\theta) $ are $d\\times d$ matrices defined by $$\\begin{aligned}\n&W^{m''}_{x,X}(s,\\theta) = DA (x+ \\Phi_{m''}(X)(s)+\\tfrac{1}{2}\\phi_{m''}(z) \\theta),\\\\\n&W^{0}_{x,X}(s,\\theta) = DA (x+ X(s)+\\tfrac{1}{2}z \\theta),\\end{aligned}$$ where $DA(\\cdot )$ is the Jacobian matrix of $A$. ", "Since $$\\begin{aligned}\n&\\big(W^{m''}_{x,X}(s,\\theta) \\phi_{m''}(z) \\big) \\cdot \\phi_{m''}(z)\n- \\big(W^{0}_{x,X}(s,\\theta) z \\big) \\cdot z \\\\\n&= \\big(W^{m''}_{x,X}(s,\\theta) \\phi_{m''}(z) \\big) \\cdot \n \\big(\\phi_{m''}(z) - z \\big) + \\big( (W^{m''}_{x,X}(s,\\theta)-W^{0}_{x,X}(s,\\theta))\\phi_{m''}(z) \\big) \\cdot z \\\\\n&\\quad + \\big( W^{0}_{x,X}(s,\\theta)(\\phi_{m''}(z) - z) \\big) \\cdot z , \\end{aligned}$$ the integrand of the third term of (4.5) is less than or equal to $$\\begin{aligned}\n&T \\sup_{x \\in \\R^{d}}\\| DA(x)\\| \\int_{0< |z| <1} |\\phi_{m''}(z) -z| |z| n^{0}(dz)\\\\& +\\frac{1}{2} \\int_{0}^{T}ds \\int_{0 < |z| <1} |z|^{2} n^{0}(dz) \\int_{0}^{1} \\sup_{x \\in \\R^{d}} \\| W^{m''}_{x,X}(s,\\theta)- W^{0}_{x,X}(s,\\theta)\\|d\\theta,\\nonumber \\end{aligned}$$ where $\\| \\cdot \\|$ is the norm of matrices. ", "This is less than or equal to $$\\begin{aligned}\n3T \\sup_{x\\in \\R^{d}}\\| DA(x)\\| \\int_{0< |z| <1} |z|^{2} n^{0}(dz) < \\infty,\\end{aligned}$$ and converges to zero as $m'' \\downarrow 0$ because each component of $DA$ is uniformly continuous on $\\R^{d}$.\n\nFinally, the fourth term of (4.5) is less than or equal to $$\\begin{aligned}\nE^{0}\\left[\\int_{0}^{T}\\|V(\\cdot+ \\Phi_{m''}(X)(s))- V(\\cdot+ X(s))\\|_{\\infty}ds\\right],\\end{aligned}$$ which converges to zero as $m'' \\downarrow 0$ since $V \\in C_{0}(\\R^{d};\\R )$ is uniformly continuous on $\\R^{d}$. Thus we have $\\sup_{t \\leq T} \\|u^{m''}(\\cdot,t) -u^{0}(\\cdot,t)\\|_{\\infty}\\to 0$ as $m'' \\downarrow 0$, and hence $\\sup_{t \\leq T} \\|u^{m}(\\cdot,t) -u^{0}(\\cdot,t)\\|_{\\infty}\\to 0$ as $m \\downarrow 0$. $\\square$\n\n**Acknowledgements.** ", "The author (T. I.) is grateful to Professor Yuji Kasahara for a number of helpful discussions with suggestion on the subject at a very early stage of this work and Professor Masaaki Tsuchiya for frequent valuable and helpful discussions from the beginning. ", "The other author (T.M.) would like to thank Professor Hidekazu Ito for his kind guidance, many helpful advices and warm encouragement during the preparation of this work. ", "The authors are indebted to the anonymous referee for valuable comments and suggestions.", "\n\n[16]{} D. Applebaum, [*Lévy Processes and Stochastic Calculus*]{}, 2nd ed., ", "Cambridge Studies in Advanced Mathematics, 116, Cambridge Univ. ", "Press, Cambridge, 2009. ", "P. Billingsley, [*Convergence of Probability Measures*]{}, 2nd ed., ", "Wiley Series in Probability and Statistics: Probability Statistics, New York, 1999. ", "A. Erdélyi, W. Magnus, F. Oberhettinger and F. G. Tricomi, [*Higher Transcendental Fnctions*]{}, [*Vol. ", "II*]{}, McGraw-Hill, New York, 1953. ", "T. Ichinose, The nonrelativistic limit problem for a relativistic spinless particle in an electromagnetic field, J. Funct. ", "Anal. **", "73** (1987), no. ", "2, 233–257. ", "T. Ichinose, Essential selfadjointness of the Weyl quantized relativistic Hamiltonian, Ann. ", "Inst. ", "H. Poincaré, Phys. ", "Théor. [**", "51**]{} (1989), no.3, 265–297. ", "T. Ichinose, Remarks on the Weyl quantized relativistic Hamiltonian, Note Mat. **", "12** (1992), 49–67. ", "T. Ichinose, On three magnetic relativistic Schrödinger operators and imaginary-time path integrals, Lett. ", "Math. ", "Phys **101** (2012), 323–339. ", "T. Ichinose, Magnetic relativistic Schrödinger operators and imaginary-time path integrals, in [*Mathematical Physics, Spectral Theory and Stochastic Analysis*]{}, Oper. ", "Theory Adv. ", "Appl., ", "232, Birkhäuser/Springer Basel AG, Basel, 2013, pp.247–297. ", "T. Ichinose and H. Tamura, Imaginary-time path integral for a relativistic spinless particle in an electromagnetic field, Commun. ", "Math. ", "Phys. **", "105** (1986), no. ", "2, 239–257. ", "T. Ichinose and T. Tsuchida, On essential selfadjointness of the Weyl quantized relativistic Hamiltonian, Forum Math. [**", "5**]{} (1993), no. ", "6, 539–559. ", "N. Ikeda and S. Watanabe, [*Stochastic Differential Equations and Diffusion Processes*]{}, North-Holland Mathematical Library, 24, North-Holland, Amsterdam, 1981. ", "Y. Kasahara and S. Watanabe, Limit theorems for point processes and their functionals, J. Math. ", "Soc. ", "Japan [**38**]{} (1986), no. ", "3, 543–574. ", "T. Kato, [*Perturbation Theory for Linear Operators*]{}, 2nd ed., ", "Springer, Berlin, 1976. ", "M. Nagase and T. Umeda, Weyl quantized Hamiltonians of relativistic spinless particles in magnetic fields, J. Funct. ", "Anal. **", "92** (1990), no. ", "1, 136–154. ", "K. Sato, [*Lévy Processes and Infinitely Divisible Distributions*]{}, translated from the 1990 Japanese original, Cambridge Studies in Advanced Mathematics, 68, Cambridge Univ. ", "Press, Cambridge, 1999. ", "B. Simon, [*Functional Integration and Quantum Physics*]{}, Pure and Applied Mathematics, 86, Academic Press, New York, 1979; 2nd ed., ", "AMS Chelsea Publishing, Providence, RI, 2005.", "\n" ]

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[ "[Tumor necrosis factor and possibilities of correction of its production in patients with suppurative-septic complications in terminal states].", "\nThe production of tumor necrosis factor (TNF) by mononuclears was studied in 37 patients after critical states of various origins. ", "A relationship was revealed between the TNF production and the patient's condition severity and the development of pyoseptic complications. ", "Use of thymohexin, a new drug for correction, provided a modulating effect and helped reduce the excessively increased TNF production both in vitro and in the patients with pyoseptic complications." ]

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[ "Lemon Law Lawyers In El Centro California\n\nEl Centro (formerly, Cabarker), is Spanish for \"the center\". ", "The name is fitting, because it is the core urban area and principal city of the El Centro metropolitan area which encompasses all of Imperial County. ", "The city is the county seat of Imperial County, the largest city in the Imperial Valley and the east anchor of the Southern Border. ", "El Centro is also the largest American city to lie entirely below sea level (- 50 feet). ", "The city is conveniently near the global cities of San Diego and Los Angeles as well as placed between the major cities of Phoenix and San Diego. ", "Founded in 1906 W. F. Holt and C.A. Barker purchased the land on which El Centro was eventually built for about forty dollars an acre and invested $100,000 in improvements. ", "As one historian of Valley life put it, \"in only five months El Centro went from a barley field to a city...\". ", "Fast forward to modern times and El Centro is the center of one of Southern California's most promising new commercial and industrial regions. ", "It is home to retail, transportation, wholesale, and agricultural industries. ", "There are also two international border crossings nearby for commercial and noncommercial vehicles. ", "The city's population was 37,835 at the 2000 census. ", "The 2006 population is 40,563.", "\n\nWhat is lemon law?", "\n\nLemon laws provide a remedy for purchasers of cars that repeatedly fail to meet standards of quality and performance. ", "These cars are called lemons. ", "The federal lemon law, the Magnuson-Moss Warranty Act, protects citizens of all states. ", "State lemon laws vary by state and may not necessarily cover used or leased cars. ", "The rights afforded to consumers by lemon laws may exceed the warranties expressed in purchase contracts. ", "Lemon law is the common nickname for these laws, but each state has different names for the laws and acts." ]

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[ "Kurityán\n\nKurityán is a village in Borsod-Abaúj-Zemplén county, Hungary.", "\n\nEtymology\nThe name comes from the Slavic/Early Slovak koryto (manger) with the suffix -ťany used to derive place names referring to people. ", "Initially the name of the valley. ", " 1280/1413 Koryth.", "\n\nReferences\n\nExternal links \n Street map \n\nCategory:Populated places in Borsod-Abaúj-Zemplén County" ]

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[ "Angor District\n\nAngor is a raion (district) of Surxondaryo Region in Uzbekistan. ", "The capital lies at Angor.", "\n\nCategory:Districts of Uzbekistan" ]

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[ "1. ", "Field of the Invention\nThe present invention relates to a structure for mounting a camera to a vehicle, and in particular it relates to a structure for attaching a stereoscopic camera system for a vehicle by which a plurality of cameras are attached to a body frame of the vehicle in order to stereoscopically capture images of the area surrounding the vehicle.", "\n2. ", "Description of Related Art\nA technology has been developed, which captures the images of an area surrounding a vehicle while the vehicle is running and when it stops, and the technology utilizes the image information for traveling Support, etc. ", "As one of the representative technologies, a stereoscopic camera technology is known which stereoscopically recognizes the surrounding images on the basis of images captured by two cameras and grasps the positional relationship in front of and behind an object.", "\nIn such a structure for attaching a stereoscopic camera system, two cameras are attached to a vehicle body. ", "One camera is attached on each end of a horizontally long lateral stay in order to prevent die optical axes of both cameras from deviating due to a distortion of a body of the vehicle, and only the middle part of the lateral stay is fixed in the body (For example, refer to Japanese Unexamined Patent Application, First Publication No. ", "2001-88623). ", "That is, since the optical axes of the respective cameras are maintained so as to be constant by the lateral stay, and both the end portions of the lateral stay are not fixed on the vehicle, no bending stress is applied onto the lateral stay, resulting from distortion, etc., ", "of the vehicle body.", "\nHowever, since, with the above-described attaching structure, two cameras, which are heavy devices, are supported on the vehicle only at the middle part of the lateral stay, it is difficult to suppress looseness and shaking of the cameras.", "\nIn particular, when there is no way other than disposing both the cameras with a spacing secured therebetween in order to secure focal distances of the cameras (in this case, it is necessary to lengthen the lateral stay) and when cameras are installed at the front side of a vehicle subjected to large vibrations, there is a concern that looseness and shaking of the cameras are further increased." ]

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[ "Two great TOTWs in a row? ", "I think so!", "\n\nTwo great TOTWs in a row? ", "I think so!", "\n\n\n\nMessi, Kane, Aguero, Mbappe. ", "What more could you want?", "\n\n\n\nHamsik, Benatia, Lukaku! ", "All those beautiful cards should be in TOTW and we should see some TOTW SBCs to pack them in!", "\n\n\n\nJoe Allen or Choupo-Moting should get one for Stoke win.", "\n\n\n\nSome other questionable choices, but overall we haven’t had many games played so there’s a good chance for hitting high numbers in predictions!", "\n\n\n\nLet’s see what we’ll get on Wednesday\n\n\n\nGood Luck!", "\n\n\n\n\n\nStarting 11:\n\n\n\nGK:Andrea Consigli(Sassuolo) – 82>84– 6 saves and pen save and cs in 1-0 win (SAT)\n\nCB:Michael Keane (Everton FC) – 81>84– Cs and MOTM in 0-0 draw(SAT)\n\nCB:Mehdi Benatia (FC Juventus) – 84>86>87– 1 goal and cs in 1-0 win (SAT)\n\nCB:Inigo Martnez (Real Sociedad) – 81>84- 1 goal and 1 assist in 3-1 win (WED)\n\nLWB: Jordan Lukaku (Lazio) – 77>81– 1 goal and 1 assist in 4-0 win (SAT)\n\nCM:Joe Allen (Stoke City) – 77>82 – 1 goal and 1 assist in 3-1 win(SAT)\n\nCM:Antonin Barak (Udinese) – 72>80 – 2 goals and 1 assists in 4-0 win(SAT)\n\nRW:Juan Mata (Manchester United) – 84>86- 2 goals in 2-2 draw (SAT)\n\nST: Harry Kane(Spurs) – 86>87>88>89>90- 3 goals in 3-0 win(SAT)\n\nRF:Lionel Messi (FC Barcelona) – 93>94>95– 1 goal and 1 assist in 3-0 win(SAT)\n\nST:Sergio Aguero (Manchester City) – 89>90>91- 2 goals and 1 assist in 4-0 win (SAT)\n\n\n\nSubs:\n\n\n\nGK:Claudio Ramos (Tondela) – 71>78– 6 saves and cs in 1-0 win (FRI)\n\nST: Lennart Thy(VVV-Venlo)- 69>76- 3 goals in 3-1 win (SUN)\n\nCDM:Luiz Gustavo (OM)- 80>83>85 – 1 goal in 3-1 win(THU)\n\nRW:Kylian Mbappe (PSG) – 83>85>86>87- 1 goal and 1 assist in 3-1 win(THU)\n\nLM:Takashi Inui(SD Eibar) – 78>82– 2 goals in 4-1 win(THU)\n\nST:Nicolai Jorgensen (Feyenoord) –78>82- 2 goals and 1 assist in 5-1 win (SUN)\n\nRW:Hirving Lozano(PSV) –78>82>84– 1 goal and 1 assist in 2-1 win (SAT)\n\n\n\nReserves:\n\n\n\nST:Mattia Destro (Bologna)- 76>82 – 2 goals in 3-2 win (FRI)\n\nCM:Marek Hamsik (Napoli)- 87>88 – 1 goal in 3-2 win(SAT)\n\nST:Sergi Guardiaola (Cordoba) – 66>75– 3 goals and 1 assist in 5-0 win(WED)\n\nST:Will Grigg (Wigan Athletic) – 69>75 – 3 goals and 1 assist in 7-0 win(SAT)\n\nST:Bobo (Sydney FC) – 74>80- 3 goals and 1 assist in 4-1 win(SAT)" ]

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[ "Q:\n\nAre workflows sensitive to data changes?", "\n\nI want to make a workflow that will move an item from one list to another once the current date exceeds the archive date. ", "\nI was wondering, do workflows just save the values they are given once they are started, or are the constantly querying the list object they act on so they can pick up changes?", "\nFor example, if I do a \"pause until date\" action and I set the value of the date to pause until to a field in the list item, if the item is updated, will it pause until the original date or the updated date?", "\n\nA:\n\nPause activity require to know how long it should Pause. ", "So once it entered the Pause state it will wait till the time frame mentioned as part of initialization.", "\nIn your case if the date field changes you should start another workflow which basically kills the previous and start a new Pause activity based on the new date.", "\n\n" ]

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[ "SCENE AND WE'LL HAVE LIVE\nUPDATES TOMORROW MORNING.", "\nHAVE YOU EVER GOTTEN A PHONE\nCALL FROM YOUR OWN NUMBER OR ONE\nTHAT WAS JUST A FEW DIGITS OFF?", "\nIT'S CALLED NEIGHBORHOOD\nSPOOFING AND IT'S THE LATEST\nILLEGAL SCAM TO GET YOU TO\nANSWER YOUR PHONE.", "\nTHAT HAD GENE FROM HASTINGS AND\nSANDY FROM WILMER WONDERING HOW\nDOES SPOOFING WORK?", "\nWHEN YOU FIRST HAD YOUR OWN\nNUMBER CALL YOU, WHAT DID YOU\nTHINK?", "\nIT WAS KIND OF CRAZY.", "\nIT HONESTLY WAS KIND OF\nSCARY.", "\nI WASN'T SURE IF THERE WAS\nSOMETHING WRONG WITH VERIZON.", "\nI WAS NERVOUS.", "\nI THOUGHT\nSOMETHING HAD HAPPENED TO A\nFAMILY MEMBER IN THAT AREA.", "\nTHEY'RE 99.999% ILLEGITIMATE\nCALLS.", "\nReporter: CYBER SECURITY\nEXPERT.", "\nWHAT IS ILLEGAL IS CALLER\nI.D.\nSPOOFING FOR THE INTENT OF\nCOMMITTING A FRAUDULENT ACT.", "\nANY IDEA HOW THEY ACTUALLY DO\nTHAT?", "\nNO CLUE.", "\nI DON'T KNOW WHERE THEY'RE\nGETTING MY PHONE NUMBER FROM.", "\nYOU HAVE TO REALIZE THAT THE\nPHONE NETWORK ISN'T JUST A\nSINGLE NETWORK.", "\nIT'S SEVERAL DIFFERENT\nNETWORKS STRUNG TOGETHER WITH\nDIFFERENT TECHNOLOGIES.", "\nBECAUSE THE TELEPHONE NETWORK\nIS BY ITS NATURE VERY OPEN, THAT\nALLOWED THE SCAMMERS AND\nSPAMMERS AND TELEMARKETERS TO\nCONNECT INTO THAT PHONE NETWORK.", "\nTHEY CAN DO THOUSANDS OF\nPHONE CALLS AT A TIME AND YOU\nHAPPENED TO BE THE ONE THAT\nPICKS UP.", "\nYEAH.", "\nTHEY'RE ESSENTIALLY JUST\nUSING SOFTWARE THAT ROUTES THEIR\nPHONE SYSTEM.", "\nIT'S VERY EASY TO DO.", "\nReporter: HOW EASY?", "\nIT TOOK CHRIS LESS THAN 30\nSECONDS USING AN APP FROM THE\nAPP STORE.", "\nTHIS IS LEGAL AS LONG AS WE'RE\nNOT TRYING TO SCAM SOMEONE.", "\nLEGITIMATE BUSINESSES USE\nSPOOFING ALL THE TIME LIKE WHEN\nALL THE LINES IN ONE BUILDING\nSHOW UP AS ONE NUMBER.", "\nMY OWN NUMBER IS GOING TO\nCALL ME.", "\nReporter: HE TYPED MY\nNUMBERS INTO THE APP ON HIS\nPHONE.", "\nOH, MY GOSH.", "\nI'M GOING TO STEP AWAY SO I\nCAN HEAR YOU.", "\nHELLO?", "\nHELLO, HEATHER.", "\nMY NAME IS HEATHER AND I'M\nCALLING TO SEE IF YOU'D LIKE TO\nHAVE A FREE CRUISE.", "\nIT'S CRAZY WHAT TECHNOLOGY IS\nDOING TO US.", "\nWE THINK THERE'S BENEFITS TO IT\nBUT THERE'S ALSO SOME CON.", "\nIT CAN BE ANYTHING FROM A\nSINGLE PERSON SITTING IN THEIR\nHOME, USING AN APP IN THEIR\nPHONE.", "\nTHERE CAN BE BUSINESSES DESIGNED\nTO BE CALL CENTER IN SCOPE AND\nSIZE.", "\nI DON'T KNOW WHAT THE REAL\nANSWER IS.", "\nI JUST KNOW SOMETHING NEEDS TO\nBE DONE.", "\nReporter: HEATHER BROWN,\nWCCO 4 NEWS.", "\nOUR EXPERT SAYS STOPPING\nTHESE CALLS IS NOT AS SIMPLE AS\nTHE GOVERNMENT CRACKING DOWN.", "\nHE SAYS NEW LAWS ARE NEEDED\nALONG WITH THE TECHNOLOGY TO END\nROBO CALLS.", "\nTHE FCC SAYS DO NOT ANSWER\nTHESE CALLS.", "\n" ]

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[ "Morphological tuning, self-assembly and optical properties of indium oxide nanocrystals.", "\nIn this paper, weak acids, weak bases or their mixtures were used as reaction media/coordinating ligands to achieve systematic morphological control over amphoteric indium oxide nanostructures. ", "Different indium/oleic acid molar ratios from 1 : 0, 1 : 1, 1 : 2, 1 : 3, 1 : 6 and 1 : 15 in non-coordinating, weakly coordinating, strongly coordinating and their mixed media were adopted to prepare irregular aggregated nanoparticles and uniform regular/truncated octahedra, etc. ", "In addition to their strong size-dependent absorption, single-crystalline indium oxide octahedra also gave a strong band-edge emission while irregular indium oxide aggregated nanoparticles only exhibited a weak deep-trap emission. ", "Meanwhile, the truncated octahedra were self-assembled into either zigzag lines or pentagram patterns, and the regular octahedra and truncated cubes were self-assembled into hexagonally packed nanocrystal arrays. ", "In addition, the formation mechanism of the various nanostructures under different conditions was investigated in detail." ]

{ "pile_set_name": "PubMed Abstracts" }

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[ "---\nabstract: 'Nearly five decades have elapsed since the seminal 1966 paper of P.W. Anderson on the flow of superfluid helium, $^4$He at that time. ", "Some of his “Considerations” – the role of the quantum phase as a dynamical variable, the interplay between the motion of quantised vortices and potential superflow, its incidence on dissipation in the superfluid and the appearance of critical velocities, the quest for the hydrodynamic analogues of the Josephson effects in helium – and the way they have evolved over the past half-century are recounted below. ", "But it is due to key advances on the experimental front that phase slippage could be harnessed in the laboratory, leading to a deeper understanding of superflow, vortex nucleation, the various intrinsic and extrinsic dissipation mechanisms in superfluids, macroscopic quantum effects and the superfluid analogue of both [*ac*]{} and [*dc*]{} Josephson effects – pivotal concepts in superfluid physics – have been performed. ", "Some of the experiments that have shed light on the more intimate effect of quantum mechanics on the hydrodynamics of the dense heliums are surveyed, including the nucleation of quantised vortices both by Arrhenius processes and by macroscopic quantum tunnelling, the setting up of vortex mills, and superfluid interferometry.'", "\nauthor:\n- Eric Varoquaux\ntitle: |\n Anderson’s considerations on the flow of superfluid helium:\\\n some offshoots\n---\n\nSuperfluids display quantum properties over large distance. ", "Superfluid currents may persist indefinitely unlike those of ordinary fluids [@Reppy:65]; the circulation of flow velocity has been found quantised over meter-size paths [@Verbeek:74]. ", "These manifestations of macroscopic quantum phenomena have constituted one of the early hallmarks of experimental condensed matter physics as reviewed over the years by a number of authors.[^1] They are viewed as supporting the concept of a macroscopic wavefunction extending over the whole superfluid sample as put forward by @London:54. ", "Together with Landau’s views on the irrotational nature of superfluid motion [@Landau:41], these ideas form the basis of the two-fluid model, summarised in Sec.\\[basics\\], which not only describes the hydrodynamics of superfluids [@Khalatnikov:65] but has been extended to other fields of physics like superconductivity, the Bose-Einstein condensed gases$\\ldots$ [@Enz:74]\n\nHydrodynamics, and superfluid hydrodynamics in its wake, is expected to break down at small scale when the typical lengths of the problem at hand are no longer much larger than the interatomic separation or other microscopic lengths characteristic of the internal structure of the fluid, the “size” of Cooper pairs in superfluid $^3$He for instance. ", "It has however been known for a long time, notably from the ion propagation measurements of @Rayfield:64 that the relevant scale in superfluid $^4$He is surprisingly small, of the order of ångströms. ", "In these experiments, the velocity of vortex rings could be measured in a direct way and compared to the usual outcome of classical hydrodynamics (see Sec.\\[VortexDynamics\\]). ", "Rayfield and Reif found that, at first sight at least, hydrodynamics remains valid down to atomic sizes. ", "Their result holds for $^4$He, which is a dense fluid of bosons. ", "The relevant scale is much larger in superfluid $^3$He, a BCS-type p-wave superfluid in which the characteristic length is fixed by the “size” of the Cooper pair. ", "This article aims at reviewing how the hydrodynamics of superfluid $^4$He and $^3$He evolves from large to small scale and ultimately breaks down at close distance, revealing the more intimate quantum properties of these fluids. ", "This is no mean feat, as noted long ago by Uhlenbeck, who is quoted to have said “[*One must watch like a hawk to see Planck’s constant appear in hydrodynamics*]{}” [@Putterman:74].", "\n\nThe main object of study in the following is the time and space evolution of the phase of the macroscopic wavefunction, often simply referred to as “the phase”, in so-called aperture flow. ", "This concept of “phase” with wave-mechanical properties governing the evolution of macroscopic quantities has become so well-spread that its meaning is, wrongly perhaps, taken for granted. ", "It was put forward by P. W. Anderson in 1966, following the lead of @Feynman:55, mainly by the recognition of the phase as the quantity commandeering in superfluids both the putative Josephson-type effects and dissipation caused by vortex motion. ", "The dynamics of quantised vortices, central to Anderson’s ideas, is outlined in Sec.\\[VortexDynamics\\]. ", "A detailed understanding of these phenomena is of fundamental importance as they govern the breakdown of viscousless flow – the most noteworthy feature of superfluidity – and the appearance of an entirely new class of phenomena – the hydrodynamic analogues of the Josephson effects – that underpin the sort of interferometry that can be performed with the superfluid wavefunction.", "\n\nThese ideas were agitated in the mid-sixties, in particular at the Sussex Meeting in 1965, by @Anderson:66b, and by a number of prominent physicists, notably Nozières and Vinen. ", "Reliable experimental observations were performed twenty years later only, as recalled in Sec.\\[slippage\\], giving a host of new results and insights on superfluid hydrodynamics, notably an improved understanding of critical velocities and of the nucleation of vortices, topics discussed in Secs.\\[CriticalVelocities\\] and \\[PhaseSlipCriticalVelocity\\], of possible mechanisms for formation of vortex tangles, described in Sec.\\[AllThat\\], of the appearance of the Josephson regime of superflow through tiny apertures, described in Sec.\\[Josephson\\].", "\n\nPresented below is a coverage of some of the ramifications of Anderson’s ideas on phase slippage in superfluids. ", "It is intended to provide a gangway between the many excellent monographs[^2] that provide the background material on this subject and the more specialised research publications in the literature that give the full, raw, sometimes arcane, coverage. ", "As such, it does not constitute a comprehensive review - space and time constraining - but touches on a few selected issues that provide the backbone of this subfield of superfluid hydrodynamics. ", "Reviews with different flavours span over a quarter of a century and show how this field has evolved.[^3]\n\nParticularly worthy of notice are the reviews of closely related subjects, Sonin’s description of vortex dynamics ([@Sonin:87; @Sonin:15], the Landau critical velocity in superfluid $^4$He by @McClintock:95 and in superfluid $^3$He-B by @Dobbs:00, and vortex formation and dynamics in superfluid $^3$He by @Eltsov:05 [@Salomaa:87; @Volovik:03]. ", "The later references also cover the exciting field of exotic topological defects in superfluid $^3$He under rotation, not considered here.", "\n\nThe basic superfluid: He-4 {#basics}\n==========================\n\nHelium-4 undergoes an ordering transition toward a superfluid state at $T\\sim\n2.17$ K under its saturated vapour pressure (SVP), which is now commonly viewed as a form of Bose-Einstein condensation. ", "A similar transition occurs in helium-3 at $T\\lesssim 2.7$ mK when Cooper pairing in a state with parallel spin $S=1$ and relative orbital momentum $l=1$ occurs.", "\n\nThe two-fluid hydrodynamics {#TwoFluidModel}\n---------------------------\n\nThe flowing superfluid helium must obey some form of hydrodynamic equations given by the general conservation laws, Galilean invariance, and the thermodynamic equation of state that should also include its superfluid properties. ", "These equations were written down for $^4$He by @Landau:41 [@Landau:Hydro; @Khalatnikov:65] who made the key assumption that in order to describe the viscous-less fluid flow the independent hydrodynamical variables must include a velocity field $\\mb v_\\m s$, to which is associated a fraction $\\rho_\\m s/\\rho$ of the total density of the liquid, $\\rho=m_4/v_4$ being the $^4$He atomic mass divided by the volume occupied by one atom. ", "This ideal inviscid fluid velocity field conforms to the Euler equation for ideal fluid flow. ", "As a consequence, it also obeys the Kelvin-Helmholtz theorem, which states that the vorticity $\\nabla \\times \\mb v_\\m s$ remains constant along the fluid flowlines.[^4] In addition to vorticity conservation, a more stringent condition was assumed by @Landau:41, namely that the superfluid velocity field be at any instant irrotational at all points in the superfluid:[^5]\n\n$$\\label{rotvs0}\n \\nabla \\times \\mb v_\\m s = 0 \\; .$$\n\nThe superfluid fraction velocity therefore derives from a velocity potential. ", "This property will be shown below to be intimately related to the microscopic description of the superfluid and to have far-reaching consequences.", "\n\nThe remainder of the fluid, the normal fraction $\\rho_\\m n = \\rho - \\rho_\\m\ns$, to which is associated a “normal” velocity $\\mb v_\\m n$, obeys an equation similar to the Navier-Stokes equation of viscous flow. ", "The total momentum density of the helium liquid is the sum of the contributions of these two fluids: $$\\mb j = \\rho_\\m s\\mb v_\\m s + \\rho_\\m n\\mb v_\\m n \\; .$$\n\nThe superfluid part of the flow being assumed ideal, it carries no entropy. ", "The fluid entropy is transported by the normal fluid described by Landau as a gas of thermally-excited elementary excitations, the phonons – or sound quanta – at long wavelengths and the rotons at wavelengths of the order of interatomic spacing, as sketched in Fig.\\[DispersionCurve\\].", "\n\n![", "\\[DispersionCurve\\] Dispersion curve of the elementary excitations in superfluid $^4$He as devised by @Landau:47. ](", "Fig01.pdf){height=\"50mm\"}\n\nLandau attributed the non-viscous property of $^4$He flow to the intrinsic shape of this spectrum. ", "There exists no elementary excitation with a finite momentum $\\bf p =\\hbar\\,\\bf k$ and a small enough energy $\\epsilon(\\bf p)$ to couple to a solid obstacle or a wall at rest while conserving energy and momentum. ", "At least for small enough superflow velocities. ", "This requirement sets the Landau criterion for dissipationless flow: $v_\\m s<v_\\m L$. The intricate problem of critical velocities above which dissipation arises in superfluid flow is dealt with in Sec.\\[CriticalVelocities\\].", "\n\nWhen $\\rho_\\m n$ and $\\rho_\\m s$ can be assumed incompressible – [*i.e.*]{}, for small flow velocities, the separation between potential flow for $\\mb v_\\m\ns$ and a Poiseuille flow for $\\mb v_\\m n$ becomes exact.[^6] In this approximation, superflow is effectively decoupled from normal fluid motion. ", "It has become customary to talk somewhat loosely of the motion of the superfluid as fully distinct from that of the normal fluid. ", "This simplified view is adopted here but, occasionally, it fails [@Idowu:00a; @Idowu:00b].", "\n\nLandau’s two-fluid hydrodynamics, based on early experiments on superfluids and preceded by the original suggestion of @Tisza:38, accounts remarkably well for a whole class of thermodynamical and hydrodynamical properties, notably for the existence of second sound and for the non-classical rotational inertia in Andronikashvili oscillating-disks experiments [@Andronikashvili:66]. ", "It features full internal consistency; it assumes that the motion of $\\rho_\\m s$ is pure potential (irrotational) flow and carries no entropy, and it reaches the conclusion that, below $v_\\m\nL$, this motion is indeed fully inviscid. ", "It has been universally adopted.", "\n\nThe two-fluid hydrodynamics has been extended to the superfluid phases of $^3$He. ", "A number of new features appear owing to the anisotropy introduced by the Cooper pairing in a $l=1$ state of orbital momentum. ", "Some of these features are discussed in Sect.\\[CPR\\], but the separation of the hydrodynamics between a superfluid component and a “normal” component still holds as well as the existence of a Landau critical velocity.", "\n\nHowever, this model has a number of shortcomings pointed out, among others, by @London:54. ", "In particular, for the purpose of this review, it does not discuss the roots of the irrotationality condition, Eq.(\\[rotvs0\\]), which are to be found in the existence of a complex scalar order parameter arising from the transition to a Bose-condensed state, as recognised at a very early stage of the study of superfluids by @London:38.[^7] It gives no clue as to when the hydrodynamics of the superfluid fails at close distance as any macroscopic approach to hydrodynamic is bound to. ", "Namely, it provides no way of estimating the superfluid coherence length - or healing length of the macroscopic wavefunction. ", "It also completely disregards the existence of quantised vorticity,[^8] which, as recognised by @Feynman:55 and @Anderson:65, is responsible for dissipation of the superfluid motion and for different, and more commonly met in practice, critical velocity mechanisms than that of $v_\\m L$.\n\nAs already noted, the Landau criterion for critical velocities rests on the fact that the elementary excitation energy spectrum is sharply defined, that is, it rises linearly as $\\epsilon = \\m c p$ with no spread in energy: there are [*no*]{} excitations with low energy and small moment capable of exchanging momentum with the superfluid in slow motion, thus causing dissipation. ", "This sharpness of the energy spectrum $\\epsilon(p)$ has been checked directly by neutron scattering measurements of the dynamic structure factor as discussed in particular by @Glyde:93 [@Glyde:13].", "\n\nIt may be pointed out here that $^3$He in the normal Fermi liquid state does display an elementary excitation spectrum with a phonon branch and a roton minimum in neutron diffraction experiments [@Stirling:76; @Griffin:87]. ", "However, that spectrum is broad; $^3$He does not exhibit superfluid properties until Cooper pairs of fermions form and Bose-condense. ", "As stressed by @Feynman:72, it really is the lack – the “scarcity” in Feynman’s words – of low-lying energy levels at finite momenta, a property of the $N$-boson groundstate with a macroscopic number of particles in it and the existence of few excited states well-separated in energy, that results in superfluidity.", "\n\nThe superfluid order parameter {#OrderParameter}\n------------------------------\n\nA different approach to superfluidity in which a central role was attributed to the phase of the order parameter (assumed to describe this superfluidity) was sketchily framed by Onsager in 1948, as reported by @London:54.[^9] London himself did not make much use of this concept of phase, although, on the one hand, he was the first to propose that superfluidity arises from Bose-Einstein condensation and the appearance of a “macroscopic wave function”, and on the other hand, he had earlier realised the important significance of the phase factor in quantum mechanical wavefunctions.", "\n\nIndeed, as soon as wavefunctions are considered, the concept of quantum phase becomes relevant. ", "Its early origin can be found in a formalisation of electrodynamics by Weyl [@Yang:03], in which a gauge transformation explicitly introduces a factor $\\m e^{\\theta}$ in the theory. ", "A change of gauge, $\\mb A' \\longrightarrow \\mb A +\\nabla\\theta$, combined with a change of the wavefunction $\\psi' \\longrightarrow \\psi\\, \\exp\\{\\m i\\,e\\theta/\\hbar\nc\\} $ leaves the Schrödinger equation unchanged. ", "The application of Weyl’s prescription to quantum-mechanical systems led F. London to turn the exponent $\\theta$ into a purely imaginary quantity $\\m i\\varphi$, $\\varphi$ then having the significance of an actual phase [@Yang:03]. ", "These historical developments explain the somewhat inadequate terminology that refers to changes of the phase as gauge transformations [@Greiter:05].[^10]\n\nBut the unifying power of quantum field gauge theories ultimately carried the day. ", "The fact that a droplet of superfluid randomly picks up a (well-defined) quantum phase when it nucleates out of vapour or out of normal fluid in a confined geometry, is referred to as the breaking of gauge symmetry. ", "The term “Bose broken-symmetry” promoted in particular by @Griffin:87 to describe the appearance of a macroscopic number of particles in the groundstate of a Bose system with the same one-particle wavefunction exhibiting the same phase factor only gained limited acceptance.", "\n\nThe ground state wavefunction of a homogeneous system of structureless bosons such as superfluid $^4$He at rest can be shown quite generally to have no node;[^11] it reduces to a complex scalar with a constant phase and a modulus that remains finite at every point in the sample. ", "Atomic motion results in small scale, small amplitude fluctuations of this complex scalar. ", "Averaging these fluctuations over finite, but still small, volume elements leaves a “coarse-grained” average wavefunction. ", "If the system is inhomogeneous on a scale much larger than the coarse-graining volume, the modulus and phase are slowly varying functions of the position $\\mb r$, $$\\label{MacroscopicWaveFunction}\n \\mi\\Psi(\\mb r) = f(\\mb r)\\, \\m e^{\\ts{\\m i\\varphi(\\mb r)}} \\; .$$\n\nThis in essence is the macroscopic wavefunction considered by @London:38, @Onsager:49, @London:54 and @Feynman:55 [@Feynman:72]. ", "The information on the localisation of the bosons at $\\mb r_1,\\mb r_2,\\ldots,\\mb r_\\m N$ and on their short-range correlations has been lost in Eq.(\\[MacroscopicWaveFunction\\]), which is not an exact many-body ground state wavefunction anymore.[^12] However, considered as a “macroscopic matter field” in Anderson’s own words, it has provided a lot of mileage in describing the properties of superfluids.", "\n\nThe superfluid velocity\n-----------------------\n\nThe particle density $n(\\mb r)$ at point $\\mb r$ of the $N$-boson system is given in terms of this macroscopic wavefunction, Eq.(\\[MacroscopicWaveFunction\\]), by $$\\label{NumberDensity}\n n(\\mb r) = \\int \\m d^3\\mb r_1 \\ldots \\m d^3\\mb r_\\m N\\, \n \\mi\\Psi^\\star(\\mb r)\\mi\\Psi(\\mb r)\\,\n \\sum_{i=1}^{\\m N}\\delta(\\mb r -\\mb r_i) \\; ,$$ and the particle current density by $$\\label{Current}\n\\begin{split} \n \\mb j(\\mb r) &= \\int \\m d^3\\mb r_1 \\ldots \\m d^3\\mb r_\\m N \n \\\\\n &\\sum_{i=1}^{\\m N} \\frac{\\hbar}{2 \\m i m_4}\n \\bigg[ \\mi\\Psi^\\star(\\mb r)\\delta(\\mb r -\\mb r_i)\\mb \\nabla_\\mb r \\mi\\Psi(\\mb r) +\n \\mi\\Psi(\\mb r) \\mb \\nabla_\\mb r \\delta(\\mb r -\\mb r_i) \\mi\\Psi^\\star(\\mb r) \\bigg]\n \\\\\n &= \\int \\m d^3\\mb r_1 \\ldots \\m d^3\\mb r_\\m N\n \\\\\n &\\sum_{i=1}^{\\m N} \\frac{\\hbar}{2 \\m i m_4}\\, \\delta(\\mb r -\\mb r_i)\n \\bigg[ \\mi\\Psi^\\star(\\mb r) \\nabla_\\mb r \\mi\\Psi(\\mb r) - \\mi\\Psi(\\mb r) \n \\nabla_\\mb r \\mi\\Psi^\\star(\\mb r) \\bigg] \n \\\\\n &= n(\\mb r) \\frac{\\hbar}{m_4} \\nabla \\varphi(\\mb r) \\; . ", "\n\\end{split}$$ Equation (\\[Current\\]) leads as a matter of course to the definition of the local mean velocity of the bosons as $$\\label{vs}\n \\mb v_\\m s = \\frac{\\hbar}{m_4} \\nabla \\varphi(\\mb r) \\; .$$ According to this definition, the quantity $\\mb v_\\m s$ derives from the velocity potential $ (\\hbar/m_4) \\varphi(\\mb r)$ and is identified to the quantity introduced in the two-fluid hydrodynamics under the same notation. ", "This identification implies that the quantity $ n(\\mb r)$ given by Eq.(\\[NumberDensity\\]) stands for the superfluid number density $\\rho_\\m s/m_4$. The strong correlations between bosons in the dense system – in particular, the hard core interactions – are averaged out in the coarse-graining procedure.", "\n\nDefinition (\\[vs\\]) of the superfluid velocity and the identification of $f(\\mb r)$ in Eq.(\\[MacroscopicWaveFunction\\]) with $(\\rho_\\m\ns\\,/\\,m_4)^{1/2}$ thus appears as a necessary formal construction that reproduces, in the classical limit, the quantity postulated by Landau to set up the two-fluid hydrodynamic model. ", "At finite temperature, the number of atoms involved in Eqs.(\\[NumberDensity\\]) and (\\[Current\\]) is simply proportional to $\\rho_\\m s(T)/\\rho$. The macroscopic wavefunction thus takes the following form: $$\\label{MacroscopicWavefunction2}\n \\mi\\Psi(\\mb r) = n_\\m s(\\mb r)^{1/2} \\m e^{\\ts{\\m i \\varphi(\\mb r)}} \\; .$$\n\nA more microscopic approach {#MicroscopicApproach}\n---------------------------\n\nSo far, the discussion has been based on the general properties of the groundstate wavefunction of $N$-boson systems, turned into a “macroscopic wavefunction” by coarse-grained averaging. ", "No precise prescription on how this averaging can be carried out in practice, no clue as to the suspected relationship between Bose-Einstein condensation and superfluidity at the microscopic level have been given. ", "Off-diagonal long range order (ODLRO) represents the commonly acknowledged fundamental concept that achieves this connection, underlying both superconductivity and superfluidity. ", "It defines the kind of order that prevails in a superfluid or a superconductor as put forward by @Yang:62 extending earlier work by @Penrose:56 while a parallel route was taken by Bogolyubov and other representatives of the Russian school,[^13] and in particular @Beliaev:58 for the system of interacting bosons.[^14]\n\nODLRO stands for the correlation that exists between atoms in Bose-Einstein condensates. ", "In its simplest form, for a gas of $N$ non-interacting Bose particles in a box of volume $V$, it is expressed by the single-particle density matrix $$\\begin{aligned}\n \\label{DensityMatrix}\n {\\mbox{{{\\usefont{U}{psy}{m}{n}r}}}}_1(\\mb r,\\mb r') &=& (N/V)\\,\\int \\m d\\mb r_2 \\ldots \\m d\\mb r_N \n \\nonumber \\\\\n && \\mi\\Psi_{\\m N}^\\star(\\mb r,\\mb r_2,\\ldots,\\mb r_N) \\mi\\Psi_{\\m N}(\\mb r',\\mb r_2,\\ldots,\\mb r_N)\n \\; ,\\end{aligned}$$ where $\\mi\\Psi_{\\m N}$ is the eigenfunction of the groundstate of the $N$-boson system at $T=0$ satisfying the boundary conditions at the box wall (rigid walls, or periodic). ", "As the particles of an ideal gas do not interact, the many-body wavefunction $\\mi\\Psi_{\\m N}$ is simply the product of $N$ identical single-particle wavefunctions $\\psi(\\mb r)$ evaluated at $\\mb r =\\mb\nr_i$, the particle locations, suitably normalised and symmetrised. ", "Upon integration over the $N-1$ particles $\\mb r_2 \\ldots \\mb r_N$, all what is left is the product $$\\label{IdealBEDensityMatrix}\n {\\mbox{{{\\usefont{U}{psy}{m}{n}r}}}}_1(\\mb r,\\mb r') = (N/V) \\psi^\\star(\\mb r)\\,\\psi(\\mb r') \\; ,$$ of single-particle wavefunctions, which is quite simple but highly anomalous in that it does not vanish when the two locations $\\mb r$ and $\\mb r'$ become far apart as it would do for a classical ideal gas. ", "This simple remark has startling consequences. ", "Even though the boson particles are assumed not to interact in the ideal gas, they still show a large degree of correlation. ", "These correlations of statistical origin[^15] preclude the use of the grand canonical ensemble because two widely separated parts of the system cannot be assumed to behave independently [@Ziff:77].", "\n\nThe extension of the anomalous result Eq.(\\[IdealBEDensityMatrix\\]) to non-ideal Bose gases is non-trivial – one may remember for instance that a minute attractive interaction between bosons destabilises the gas. ", "And yet a further extension to non-equilibrium situations is mandatory to describe superflow.", "\n\nSuch an extension to the weakly–repulsive Bose gas is implicit in the pioneering work of @Bogolyubov:47 who showed how second quantisation techniques could be used to derive the property of linearity of the energy spectrum at long wavelengths, $\\epsilon = cp$, as asserted for the dense superfluid helium by Landau. ", "Further progress was carried out by @Beliaev:58 using field-theoretical techniques to express the relationship between the particle number density $n$, the chemical potential $\\mu$, and the particle number density in the condensate $n_0$, which differs from $n$ because the interaction between particles prevent all of them to fall into the lowest energy state.", "\n\nVarious refinements have led to what now constitutes the conventional way[^16] to describe the nearly-ideal BEC gas with a number density of atoms $n$, the Bose order parameter being written as a complex number $\\sqrt{n_0}\\exp{(\\m{i}\\varphi)}$ involving the number density of atoms in the ground state $n_0$, as expounded, for instance, by @Dalfovo:99. ", "This description is only well-grounded for small depletion of the condensate, [*i.e.*]{}, for $n_0/n$ not too far from unity. ", "For a dense, strongly interacting, Bose system such as liquid $^4$He, this condition is not fulfilled. ", "The zero-momentum ground state is strongly depleted.", "\n\nThe spirit of the definition of the order parameter for helium was given by @Penrose:56, based on an analysis of the large-scale correlations in the various terms of the single-particle density matrix.", "\n\nIn a usual fluid, the on-diagonal elements ${\\mbox{{{\\usefont{U}{psy}{m}{n}r}}}}_1(\\mb r,\\mb r)$ are of order of the particle number density $n(\\mb r)$. Particle correlations decrease rapidly as [**r-r**]{}$'$ increases and so do the off-diagonal terms with $\\mb r\n\\neq \\mb r'$. By contrast, a superfluid can sustain a persistent current: large scale correlations should be strong so that, when a particle is deflected at [**r**]{} by an obstacle and kicked out of the condensate, a twin-sister particle is immediately relocated in the condensate at [**r**]{}$'$ with no loss of order in momentum space. ", "Such correlations should be described in the density matrix by a term embodying the condensate of the same “structure” as the product in Eq.(\\[IdealBEDensityMatrix\\]), supplemented by other terms for the part of the system that cannot be accommodated in the ground state because of interparticle collisions. ", "Thus, following Penrose and Onsager, the criterion for Bose-Einstein condensation must be traced to the existence of one element of the form (\\[IdealBEDensityMatrix\\]), namely a product $ \\Phi^*(\\mb r)\\Phi(\\mb r')$ with a macroscopic size relative to other elements, so that the density matrix takes the form: $$\\label{ODLRODensityMatrix}\n {\\mbox{{{\\usefont{U}{psy}{m}{n}r}}}}_1(\\mb r,\\mb r')= \\Phi^*(\\mb r)\\Phi(\\mb r') + \n \\sum{\\mbox{other matrix elements}}\n\\; .$$ The sum in the right hand side of Eq.(\\[ODLRODensityMatrix\\]) is a mixed bag of terms describing the correlations between particles outside the condensate as well as terms involving both condensate and non-condensate particles. ", "The function $\\Phi(\\mb r)$ can be viewed as playing the role of a single-particle wavefunction of the interacting particles in the condensate, $n_0 = (1/V)\n\\int |\\Phi(\\mb r)|^2 \\m d\\mb r$ being the mean number density of those particles.[^17] This number density $n_0$ can be orders of magnitude smaller than the total density $n$, but is assumed to still remain macroscopic.", "\n\nAs the ground state wavefunction for a boson system is everywhere non-zero, its absolute value for a homogeneous system, $|\\Phi(\\mb r)|$, is equal to $\\sqrt{n_0}$ to the extent that $n_0$ is constant in space. ", "This reasoning can be extended to situations that are slightly non-uniform in space. ", "The term $\\Phi^*(\\mb r)\\Phi(\\mb r')$ in Eq.(\\[ODLRODensityMatrix\\]) does not decay as the particle locations $\\mb r$ and $\\mb r'$ become far apart compared to interatomic distances: it describes the long-range correlations in the condensate, or ODLRO. ", "The excited states with $\\mb k \\neq 0$ and distribution $n_{\\mb k}$ are not macroscopically populated and only have short range coherence. ", "The summation over all these remaining contributions in Eq.(\\[ODLRODensityMatrix\\]) may also amount to a macroscopic term $\\sum_\\mb\nk n_\\mb k$, of order $N$. Each of these terms decays as $|\\mb r - \\mb r'|$ becomes large but there are a large number of them: the whole of the excited states is also macroscopically populated.", "\n\nNeedless to say, the single particle wavefunction $\\Phi(\\mb r)$ in Eq.(\\[ODLRODensityMatrix\\]) bears no relationship to that for free particles in Eq.(\\[IdealBEDensityMatrix\\]) for the ideal gas. ", "Neither the $\\Phi^*(\\mb\nr)\\Phi(\\mb r')$ term in Eq.(\\[ODLRODensityMatrix\\]) nor the incoherent terms have been expressed in full for the dense helium 4,[^18] contrarily to near-ideal BEC gases and to the BCS theory (for Cooper pairs and superfluid $^3$He). ", "But in superfluid $^4$He as in these other situations, ODLRO is found to be present and to constitute a unifying feature sufficient to ensure flux quantisation (BCS superconductors) or velocity circulation quantisation (dense superfluid helium). ", "That the simple factorisation of the coherent part of the density matrix ensures superfluidity is a remarkable result. ", "It has been established on general grounds by @Yang:62.", "\n\n@Penrose:56 used various approximate forms for the groundstate wavefunction of dense helium-4 at $T=0$ to illustrate the splitting of the density matrix, Eq.(\\[ODLRODensityMatrix\\]), and to evaluate the depletion of the condensate, [*i.e.*]{}, the value of $n_0$. They have used in particular Feynman’s simple ansatz for the superfluid wavefunction [@Feynman:55], which assumes strong hard-core repulsion and weak 2-body attraction with a minor role in interparticle correlations. ", "Only the former can be kept for an approximate evaluation of $n_0$.\n\nBuilding on this remark, Penrose and Onsager noticed that the depletion under scrutiny can conveniently be derived from the (known) pair distribution for a classical gas of hard spheres such as the one pictured in Fig.2. ", "They found that collisions between hard spheres with diameter 2.6 Å , 3.6 Å  apart, leave only about 8 % of the helium atoms in the zero-momentum state. ", "This value of $n_0/n$ in $^4$He has been confirmed by more elaborate theories and by experiment.[^19] While the depletion of the condensate is a small effect in low density atomic gases [@Dalfovo:99], it is considerable in liquid helium.", "\n\n 3D view of 2.6 Å diameter hard spheres randomly distributed in a 10x10x10 Å cube with a 3.6 Å mean spacing, as for liquid helium-4 at SVP. ", "In helium, atoms are both strongly confined by hard core repulsion and dynamically delocalised by the zero point energy motion. ", "Courtesy Nelle Varoquaux. ](", "Fig02.pdf){width=\"60mm\"}\n\nThis large depletion raises the following question: how is it that the condensate fraction is only 8 % at $T$ = 0 while the superfluid fraction in the two-fluid model is 100 % ? ", "The answer is simple: these are not the same quantities.[^20] The superfluid density stands for the inertia of the superfluid fraction, as measured for instance by a gyroscopic device sensitive to trapped superfluid currents [@Reppy:65] or, less directly, by the decoupling of the superfluid component in an oscillating disk experiment [@Andronikashvili:66]. ", "In these experiments, only the elementary quasiparticles couple to the transverse oscillations of the cell walls; the remaining of the superfluid is not set into motion.", "\n\nThe superfluid fraction superfluid $\\rho_\\m s/\\rho$ is not directly related to the probability of finding bosons in the $\\mb k =0$ quantum state. ", "The occupation of the condensate is seen experimentally as a hump at zero energy transfer in the dynamic structure factor measured by neutron inelastic scattering [@Glyde:13], a quantity rather well-hidden from experimentalists’sight in helium. ", "When the superfluid is set into motion, the condensate enforces long-range order and drags the excited states along through the short-range correlations; there is entrainment of the atoms in the fluid by the condensate. ", "Microscopic theory is needed to describe this process in detail.", "\n\nDeferring to the end, §\\[Conclusion\\], further discussion on the merits of, and differences between, the microscopic approach – the ODLRO concept of @Penrose:56 and @Yang:62 – and the macroscopic quantum field point of view – a discussion found in Appendix A1 of @Anderson:66a – the superfluid order parameter in $^4$He will be taken in the following as the macroscopic wavefunction Eq.(\\[MacroscopicWavefunction2\\]), namely $\\mi\\Psi(\\mb r) = f(\\mb r) \\m\ne^{\\m i\\varphi(\\mb r)}$ with $f = n_\\m s^{{1/2}}$, $n_\\m s$ being the superfluid number density. ", "This choice conforms to that of §\\[OrderParameter\\] and leads straightforwardly to the two-fluid model. ", "The alternate choice to set $f = n_0^{{1/2}}$ would be less productive: the condensate density $n_0$ remains half-buried in the formalism and is difficult to access experimentally. ", "This situation differs markedly from that in cold atomic gases. ", "There, the condensate can be imaged directly in momentum space; it comprises most of the particles in the gas so that $n_0 \\simeq n $; the corresponding order parameter emerges seamlessly from perturbation theory applied to the weakly-interacting Bose gas following Bogolyubov’s prescriptions.", "\n\nFor weakly interacting bosons, the macroscopic wavefunction dynamics is governed by the Gross-Pitaevskii equation.[^21] The relevance of the Gross-Pitaevskii equation to the Bose-condensed systems has been put in a bright new perspective for ultra-cold atoms in a trap, for which it constitutes an excellent description [@Dalfovo:99; @Cohen-Tannoudji:01]. ", "However, the approach based on this equation turns out to be less adequate for the dense superfluid, sometimes not even qualitatively correct, as found for instance by @Pomeau:93 in the context of the breakdown of superflow. ", "It will not be pursued here, except to mention that it does provide an estimate of the distance over which the two-fluid hydrodynamics needs to be supplemented by quantum corrections, as discussed in Sect.\\[Josephson\\].", "\n\nIn all cases, the phase, a variable of lesser relevance in the older quantum mechanics, is now assigned the role of governing superfluid dynamics. ", "A fundamental result, established early by @Beliaev:58, relates the phase of the condensate particles to the chemical potential, $\\varphi = \\mu \\,\nt/\\hbar $, where $t$ is time. ", "The deep significance of this odd-looking relation only became apparent later, when the Josephson effects came on stage.", "\n\nThe role of the phase as a dynamical variable was extended to superfluid helium by @Anderson:64 [@Anderson:65; @Anderson:66b; @Anderson:84b] who noted that phase and particle number are canonically conjugate variables. ", "This property is well-known in quantum electrodynamics for photons in a cavity. ", "The number of photons in a given mode and their phase, defined for coherent electromagnetic fields in the cavity, are non-commuting operators. ", "As such, they obey an uncertainty relation [@Heitler:54] that reads: $$\\label{NumberPhaseUn} \n {\\mbox{\\small{{\\usefont{U}{psy}{m}{n}d}}\\hskip 0.05ex}}N \\,{\\mbox{\\small{{\\usefont{U}{psy}{m}{n}d}}\\hskip 0.05ex}}\\varphi \\sim 1 \\; .$$ As remarked by Heitler, “[*if the number of quanta of a wave are given it follows from eq.(\\[NumberPhaseUn\\]) that the phase of this wave is entirely undetermined and vice versa. ", "If for two waves the phase difference is given (but not the absolute phase) the total number of light quanta may be determined, but it is uncertain to which wave they belong*]{}”. ", "This remark will bear implications throughout this review.", "\n\nSuperfluidity is more than simply the absence of viscosity supplemented by the condition that vortices have quantised circulation. ", "The urge to observe the role of the phase in a Josephson-type effect – and the failure to do so for a long period of time – became quite pressing to confirm the picture drawn by Anderson of helium as obeying quantum mechanics in a more profound way than simply as an ideal inviscid fluid with quantised velocity circulation.", "\n\nAnderson[’]{}s phase slippage {#PhaseSlippage}\n-----------------------------\n\nAnderson’s famed “Considerations” on the flow of superfluid $^4$He [@Anderson:66b] provided the conceptual basis for this experimental search for Josephson-type effects in neutral matter. ", "Their underlying aim was to convey a physical, laboratory-oriented, meaning to order parameter Eq.(\\[MacroscopicWavefunction2\\]) and, in particular, to its phase. ", "These Considerations provided the groundwork for phase slippage experiments in $^4$He ; they were gradually fostered in a series of Lectures Notes [@Anderson:64; @Anderson:65; @Anderson:84b] and built upon the ideas of @London:54, @Feynman:55, and @Penrose:56, and also on the quantum field theoretic approach of @Beliaev:58.", "\n\nIn the absence of a fully-established microscopic theory of dense boson systems, these considerations rest on the following set of well-argumented conjectures:\n\n1. ", "  By extrapolation of the properties of the coherent photon fields in quantum electrodynamics recalled above, $N$ and $\\varphi$ are taken in dense liquid helium as canonically conjugate dynamical (quantum) variables in the sense that $N \\leftrightarrow \\m i(\\partial/\\partial\\varphi)$ and $\\varphi \\leftrightarrow -\\m i(\\partial/\\partial N)$.\\[sec:2\\]\n\n As such, they obey the uncertainty relation (\\[NumberPhaseUn\\]). ", "For a closed system with a fixed number of particles, the phase is completely undetermined. ", "For the phase to be determined within ${\\mbox{\\small{{\\usefont{U}{psy}{m}{n}d}}\\hskip 0.05ex}}\\varphi \\ll 1$, $N$ must be allowed to vary, that is, the condensate must be able to exchange particles with other parts of the complete physical system, which includes the non-condensate fraction of the bosons and the eventual measuring apparatus.", "\n\n For the Josephson-effects experiments specifically considered by Anderson, the two weakly-coupled helium baths also exchange particles. ", "For all these reasons, $N$ is allowed to fluctuate locally so that ${\\mbox{\\small{{\\usefont{U}{psy}{m}{n}d}}\\hskip 0.05ex}}N$ takes a non-zero value. ", "It can be shown [@Beliaev:58] that ${\\mbox{\\small{{\\usefont{U}{psy}{m}{n}d}}\\hskip 0.05ex}}N$ is of order $N$ rather than unity, so that ${\\mbox{\\small{{\\usefont{U}{psy}{m}{n}d}}\\hskip 0.05ex}}\\varphi \\sim {\\cal O}(1/N)$ and $\\varphi$ is well defined.", "\n\n2. ", " A Hamiltonian $\\cal H$ should therefore exist such that, $N$ being free to vary, $$\\begin{aligned}\n \\label{Hamilton1}\n \\hbar \\frac{\\partial N}{\\partial t}&=& \\mbox{ }\\frac{\\partial\\cal\n H}{\\partial\\varphi} \\; ,\n \\\\ \\label{Hamilton2} \n \\hbar \\frac{\\partial \\varphi}{\\partial t}&=& -\\frac{\\partial\\cal\n H}{\\partial N} \\; .\\end{aligned}$$\n\n Upon coarse-graining, the quantum operators become quasi-classical and their coarse-grained average obey equations formerly identical to (\\[Hamilton1\\]) and (\\[Hamilton2\\]). ", "Eq.(\\[Hamilton1\\]) defines the particle current $J=\n \\partial{ E}/\\hbar\\partial \\varphi$ since $\\partial{\\cal H}/\\partial \\varphi\n \\Longrightarrow \\partial E/\\partial\\varphi$ upon averaging. ", "Likewise with $\\partial{\\cal H}/\\partial N \\Longrightarrow \\partial E/\\partial N = \\mu +\n \\slantfrac{1}{2} m_4 v_\\m s^2$ where $\\mu$ is the chemical potential in the fluid at rest, namely $\\mu = m_4 P/\\rho +m_4 gh+s_4 T$ with the usual notations, Eq.(\\[Hamilton2\\]) becomes $$\\label{acJosephson}\n \\hbar \\frac{\\partial\\varphi}{\\partial t} = -(\\mu + \\slantfrac{1}{2} m_4 v_\\m\n s^2) \\; .$$\n\n Eq.(\\[acJosephson\\]) states that, whenever there exists a chemical potential difference between two points 1 and 2 in a superfluid (or a superconductor), the phase of the order parameter varies in time with a rate proportional to $\\mu_1 - \\mu_2$: this [*ac*]{}-effect is quite detectable and has nowadays many applications. ", "It was first discussed by @Josephson:62 [@Josephson:64] for the tunnelling current between superconductors coupled through a thin barrier. ", "A full derivation for superfluid helium can be found in the monograph by Nozières and Pines.[^22]\n\n Upon taking the gradient of both left and right-hand sides, Eq.(\\[Hamilton2\\]) becomes, using the definition (\\[vs\\]) of $v_\\m s$, $$\\label{SimpleEuler}\n \\frac{\\partial v_\\m s}{\\partial t} + \\nabla\\left(\\frac{P}{\\rho}+\n \\frac{v_\\m s^2}{2} \\right) = 0\\; ,$$ which is nothing else but the Euler equation for an inviscid fluid with no vorticity ($\\bs{\\omegaup} = \\nabla\\times \\mb v_\\m s = 0$). ", "Equation (\\[SimpleEuler\\]) is precisely the same as that for the velocity of the superfluid component in Landau’s two-fluid hydrodynamics.", "\n\n3. ", " [ Anderson assumed that Eq.(\\[acJosephson\\]) for the time variation of the order parameter phase holds with no solution of continuity between the classical inviscid fluid case and the quantum tunnelling one and, [*i.e.*]{}, that it has universal applicability. ", "This unifying approach is, in a broad sense, internally consistent but details are missing of how the normal component interacts with the superfluid component, which brings dissipative terms into Eq.(\\[SimpleEuler\\]), and how the definition of $v_\\m s$ as $(\\hbar/m)\\,\\nabla\\varphi$ breaks down at small distances where coarse-graining cannot be performed. ", "These fine points have been raised in the discussion at the end of Anderson’s communication at the Sussex Symposium on Quantum Fluids [@Anderson:66a]. ", "His views are that the phase equation (\\[acJosephson\\]), being more fundamental than (\\[SimpleEuler\\]), always hold. ", "This equation describes both simple superfluid acceleration, expressed by (\\[SimpleEuler\\]), the ideal tunnelling situation envisioned by Josephson (see Sect.\\[Josephson\\]), and when the variation of the phase is caused by the motion of vorticity. ]{}", "\n\n4. ", " [The last conjecture asserts that the dissipation of the kinetic energy of a superflow is, when averaged over time, proportional to the rate at which vorticity crosses the superflow streamlines. ", "In fact, a stronger statement has been rigorously proved by @Huggins:70, which governs the detailed transfer of energy between the potential flow of the superfluid and moving vorticity. ", "This process is pivotal to the understanding of superflow decay and, more generally, of vortex dynamics as discussed in Sec.\\[VortexDynamics\\]. ]{}", "\n\nAnderson’s ideas on phase slippage, linked to the motion of vortices, have provided the conceptual framework for the experiments on the onset of dissipation and the Josephson effects in superfluids, discussed below in Sect.\\[slippage\\] and \\[CPR\\]. ", "All facets of these experiments in superfluid $^4$He and $^3$He can be very well accounted for with the help of the macroscopic quantum phase $\\varphi$. However, these ideas are still surrounded by an aura of mystery that lingers on in spite of the facts that: (1) the formal theoretical groundwork has been put on a firmer basis;[^23] (2) the implications of the uncertainty relation to laboratory observations, as well as of the other conjectures of Anderson, have been clarified by the developments of the experiments in the past forty and so years since they were formulated.", "\n\nThis review will tackle some of these advances, in particular, by showing what the phase slippage experiments really consist of, how phase slippage proceeds from a dissipative regime governed by vortex dynamics to a true dissipationless Josephson regime, and that this truly quantum behaviour manifests itself in matter waves interferometric measurements.", "\n\nQuantised vortex dynamics close to $T$=0 {#VortexDynamics}\n========================================\n\nVortex filaments are extended quasi-one-dimensional structures in the superfluid, line vortices. ", "At the core of these defects, the superfluid order parameter is either zero as in $^4$He or heavily distorted as in $^3$He. ", "They form the prevalent topological defects in superfluids.[^24]\n\nAt distances larger than the core size, superfluid vortices behave according to the laws of ideal fluid hydrodynamics, that is, as classical vortices with a given, quantised, vorticity. ", "Classical vortices have been studied for many decades [@Lamb:45; @Saffman:92]. ", "Their properties have been the subject of detailed studies in recent years in order to clarify in a number of standing problems, their mass and impulse, the Magnus and Iordanski forces, the eigenmodes of isolated vortices - the Kelvin waves, the collective behaviour of vortex arrays - the Tkachenko waves, the reconnection of two vortices, superfluid vortex tangles, and lastly, the formation of vortices and their annihilation. ", "This review is concerned mainly with the last topic but use will be made of other properties of vortices, either single or few at a time, mostly without consideration to the normal fluid background. ", "These properties bear a close resemblance to those of magnetic vortices in superconductors as spelled out by @Sonin:94.", "\n\nAt temperatures below 1 K, vortices in superfluid $^4$He experience negligible friction from the normal fluid, the fraction of which becomes very small. ", "If they deform only little and slowly, they constitute stable fluid eddies: their velocity circulation is conserved (and furthermore, quantised) and they cannot vanish to nothing. ", "Their core radius, $a_0$, is of the order of the superfluid coherence length, a few Å in $^4$He [@Glaberson:86; @Donnelly:91], one to two orders of magnitude larger in $^3$He depending on pressure [@Vollhardt:90]. ", "As the temperature increases, the scattering of phonons and rotons by the vortex cores causes dissipation. ", "Mutual friction between the superfluid vortices and normal fluid sets in. ", "Close to the superfluid transition temperature, the core size increases and eventually diverges.", "\n\nSome of the properties of vortices that have a relevance to phase slippage are summarised below. ", "Extended coverage of this topic can be found in the monographs by @Donnelly:91 and by @Sonin:15. ", "Here, the dynamical properties of superfluid vortices are derived directly from the existence of a superfluid order parameter. ", "Some simplifying approximations are made in order to get a simpler physical description of a vortex element, treated more in the manner of a quasiparticle with mass, energy and impulse. ", "The following discussion then rests on physical concepts such as energy conservation or the balance of forces. ", "It follows largely the approach of @Sonin:87. ", "It differs from the more traditional and rigorous fluid-mechanical approach, as can be found for instance in the monograph by @Saffman:92. ", "It provides a more intuitive feel for the behaviour of superfluid vortices that will prove useful in the description of phase slips.", "\n\nQuantisation of circulation\n---------------------------\n\nSuperfluid vortices have quantised circulation. ", "This property comes about because their core is non-superfluid: it disrupts the order parameter field and constitutes a topological defect in the superfluid. ", "The circulation of the superfluid velocity $\\mb v_{\\m s}$ on any path around such a defect, $$\\label{VelocityCirculation}\n \\oint {\\bf v_{\\m s}\\cdot}{\\m d}{\\mb l} =\n \\frac{\\hbar}{m_4}\\,\\oint\\nabla\\varphi\\cdot{\\m d}{\\mb l}$$ amounts to $\\kappa_4 = 2\\pi\\hbar/m_4$[^25] because the phase $\\varphi$ of the order parameter can change only by multiples of $2\\pi$ along any closed contour [*entirely*]{} located in the superfluid. ", "This property holds for the true condensate wavefunction as a basic requirement of quantum mechanics. ", "It is not altered in the coarse-graining average.", "\n\nConsider the velocity circulation from point 1 to point 2 in Fig.\\[paths\\] along a path $\\Gamma$ entirely located in the superfluid: $$\\label{Quantisation}\n \\kappa = \\int_1^2 {\\bf v_{\\m s}.}{\\m d}{\\bf l}\n = \\frac{\\hbar}{m_4}\\int_1^2 {\\bf \\nabla\\varphi.}{\\m d}{\\bf l}\n = \\frac{\\hbar}{m_4} (\\varphi_2 - \\varphi_1) \\; .$$ Along another path $\\Gamma'$ also going from 1 to 2, as shown in Fig.\\[paths\\], the circulation is $ (\\hbar/m_4)(\\varphi_2 - \\varphi_1 +\n2n\\pi)$. If $\\Gamma^\\prime$ can be deformed into $\\Gamma$ continuously while remaining in the superfluid, then $n=0$ . ", "If this cannot be done, $n$ may be a non-zero integer, 1 in the case under consideration.", "\n\nThus, when path $\\Gamma´$ crosses the core of a $^4$He vortex, in which superfluidity is destroyed and the order parameter amplitude goes to zero, $n$ changes by 1 because $^4$He vortices carry a single quantum of circulation for reasons discussed below. ", "Conversely, when a vortex crosses a superfluid path from 1 to 2, the circulation along that path changes by one quantum and the phase difference by $2\\pi$. This simple property forms the basis of the phase slip phenomenon described in Sec.\\[slippage\\].", "\n\n![", "\\[paths\\]Two different situations for the path of integration in Eq.():", " (a) [[G]{}]{} can be deformed continuously into [[G]{}]{}’; both paths give the same phase difference between point 1 and point 2. (", "b)  vortex V stands between the two paths; the phase differences along [[G]{}]{} and [[G]{}]{}’ differ by $2\\pi$.](Fig03.pdf){width=\"7cm\"}\n\nExperiments have confirmed to a high accuracy the quantisation of hydrodynamic circulation both in $^4$He and in $^3$He [@Davis:91]. ", "This feature constitutes a cornerstone of superfluid physics, and evidence for the reality of the superfluid quantum phase.", "\n\nVortex flow field and line energy {#VortexlineEnergy}\n---------------------------------\n\nThe flow velocity induced by a straight vortex filament, chosen along the unit vector $\\mb{\\hat z}$, at a distance $\\mb r$ measured in the plane perpendicular to $\\mb{\\hat z}$ is easily expressed from the quantisation of the velocity circulation and the symmetry around the vortex axis as $$\\label{VortexFlow}\n\\oint\\mb v \\cdot \\m d\\mb l = \\kappa_4 \\; \\Longrightarrow \\;\n\\mb v_{\\m v} = \\frac{\\kappa_4 }{2\\pi} \\mb{\\hat z}\\times \\frac{\\mb{\\hat r}}{r} \\;,$$ provided that $r$ is larger than $a_0$. For $r \\lesssim a_0$, the detailed structure of the core becomes important.[^26] The quantity $\\mb v_{\\m v}$ is the vortical flow due to the vortex element. ", "The superfluid velocity $\\mb v_{\\m s}$ is the sum of an eventual potential flow $\\mb v_{\\m p}$ existing independently of the vortex, for instance applied externally, and of $\\mb v_{\\m v}$. The contribution of $\\mb v_{\\m p}$ to the loop integral in Eq.(\\[VortexFlow\\]) is nil and leaves the circulation unchanged. ", "Straight vortex filaments are created by rotating the helium container; they have been the object of very detailed studies.[^27]\n\nEquation (\\[VortexFlow\\]) can be extended to [*curved*]{} vortices, provided that their radii of curvature are much larger than the core radius $a_0$. It bears a direct analogy with Ampère’s law, $\\mb v$ standing for the magnetic field and $\\kappa$ for the electric current carried by the conductor.[^28] The velocity at point $\\mb r$ induced by a [*closed*]{} vortex filament lying along the curve $\\mb s$ is then given by the analogue of the Biot-Savart law in electrodynamics:[^29] $$\\label{BiotSavart}\n\\mb v_\\m v(\\mb r) = \\frac{\\kappa_4 }{4\\pi} \\oint\\m d\\mb l\\times \n \\frac{\\mb r -\\mb s(l)}{|\\mb r-\\mb s(l)|^3} \\;.$$ The geometrical representation of the vortex loop by $\\mb s$ is such that $\\m\nd\\mb l = \\m d \\mb s$ is a vector oriented along the tangent to the loop $\\mb{\\hat t}$ of infinitesimal length $\\m d l$, $l$ being the arc length of the loop (see the sketch in Fig.\\[SolidAngle\\]). ", "The tangent $\\mb{\\hat t}$ is the unit vector $\\m d\\mb s/\\m d l =\\m d\\mb l/\\m d l $. ", "Its derivative with respect to $l$ defines the normal to the loop $\\mb{\\hat n}$ and the radius of curvature $R$: $\\m d\\mb{\\hat t}/\\m d l = \\m d^2\\mb s/\\m d l^2 = \\mb{\\hat\n n}/R$. As noted above, the radius of curvature $R$ should be large – and the change of orientation of the tangent $\\m d\\mb{\\hat t}/\\m d l$ small – with respect to the core radius for this representation of the vortex element as a one-dimensional line to be valid.", "\n\nThe integrand in Eq.(\\[BiotSavart\\]) gives the contribution of the vortex element $\\m d \\mb l$ located at $\\mb s$ on the loop to the full velocity field. ", "An integration by parts yields $$\\label{VectorPotential}\n\\mb v_\\m v(\\mb r) = \\frac{\\kappa_4}{4\\pi}\\nabla\\times\\oint \\frac{\\m d\\mb l}\n {|\\mb r-\\mb s(l)|} = \\nabla\\times \\mb A(\\mb r) \\;,$$ which defines a vector potential for the vortex velocity field, $\\mb v_\\m\nv = \\nabla\\times \\mb A$.", "\n\nEquation (\\[VectorPotential\\]) fulfils the mantra of conventional mathematical physics according to which a vector field can be split into an irrotational part, which derives from a scalar potential, and a remainder, the solenoidal part, which is not curl-free and which derives from a vector potential.", "\n\nWhile utterly correct in mathematical terms, this point of view may be slightly misleading for the superfluid velocity fields. ", "The latter are a subset only of the more general vector fields in the sense that vorticity is localised in space to the vortex cores and that the vortex line can be treated as a line singularity. ", "The Biot-Savart law (\\[BiotSavart\\]) can then be put under the following form [^30] $$\\label{ScalarPotential}\n\\mb v_\\m v(\\mb r) = \\frac{\\kappa_4}{4\\pi}\\,\\nabla_{\\mb r}\\,\n\\left\\{\\iint_S \\frac{\\mb r-\\mb R}{|\\mb r-\\mb R|^3} \\cdot \\m d\\mb S \\right\\}\n= \\frac{\\hbar}{m_4}\\,\\nabla \\varphi_\\m v \\; ,$$ the infinitesimal surface element $\\m d\\mb S$ being located at position $\\mb\nR$. Thus the velocity fostered by the vortex derives from a scalar potential as well as a vector potential. ", "Everywhere in the superfluid but at the precise location of the vortex cores, the superfluid velocity $v_\\m s$ is indeed irrotational and derives from a scalar potential, the quantum phase.[^31]\n\n The geometrical representation of a vortex loop, an arbitrary surface $S$ spanning the loop, with element $\\m d \\mb S$, and the solid angle $\\Omega$ subtended by the loop from point $\\mb r$, the tangent $\\mb{\\hat t}$, normal $\\mb{\\hat n}$, and binormal $\\mb{\\hat b}$ at point $\\mb s$. The flow lines of the vortex velocity field (dashed line) thread surface $S$ where the phase changes determination by $2\\pi$. Solid angle $\\Omega$ offers a geometrical representation of the integrand in Eq.(\\[ScalarPotential\\]).](Fig04.pdf){width=\"3.8cm\" height=\"4.5cm\"}\n\nThe velocity induced by a vortex loop decreases at large distance from the loop as that of a dipole in the electromagnetic analogy, that is as $1/r^3$, much faster than the $1/r$ dependence for straight vortex filaments (see Eq.(\\[VortexFlow\\])). ", "The $1/r$ dependence can still be expected to hold at a distance away from the core smaller than the local radius of curvature of the vortex filament. ", "At distances larger than the loop size, the velocity field rapidly dies away. ", "This property is well known for magnetic fields generated by electric current loops. ", "It means, for practical purposes, that vortex loops far apart interfere very weakly and that distant boundaries have negligible effect. ", "These simplifying features will often be assumed in the following.", "\n\n### Vortex line energy\n\nThe flow around the core of a vortex element carries kinetic energy, obtained by integration of $\\int (1/2) \\rho_{\\mathrm s} v^2_{\\mathrm v} {\\mathrm\n d}\\tau\\,$ over the volume $V$ in which this flow extends. ", "The quantity $\\rho_{\\mathrm s}$ is the superfluid density. ", "This integral is evaluated by introducing the vector potential $\\mb A$, Eq.(\\[VectorPotential\\]), from which derives the vortical flow field, as follows: $$\\begin{split}\n E_\\m v &= \\frac{\\rho_\\m s}{2}\\,\\int_\\m V \\!\\!\\m d\\tau\\,\\mb v_\\m v\\cdot\\mb v_\\m v =\n \\frac{\\rho_\\m s}{2}\\,\\int_\\m V \\!\\! ", "\\m d\\tau\\, \\mb v_\\m\n v\\cdot\\nabla\\times\\mb A \\\\\n &= \\frac{\\rho_\\m s}{2}\\,\\int_\\m V \\!\\!\\m d\\tau\\,\\nabla\\cdot(\\mb A \\times \\mb v_\\m v) \n + \\frac{\\rho_\\m s}{2}\\,\\int_\\m V \\!\\!\\m d\\tau\\,\\mb A \\cdot(\\nabla\n \\times \\mb v_\\m v) \\; . ", " \n \\end{split}$$ The last line is obtained with the help of vector identity $\\nabla\\cdot(\\mb\na\\times\\mb b)=\\mb b\\cdot(\\nabla\\times \\mb a) - \\mb a\\cdot(\\nabla\\times\\mb b)$. It consists of the sum of two volume integrals. ", "The first can be changed into a surface integral over $\\mb A\\times\\mb v$ with the divergence theorem. ", "By taking the volume boundary sufficiently far from the vortex element, supposed isolated in a large volume, the surface integral can be made negligible. ", "In the second integral, the curl of $\\mb v_\\m v$ is zero everywhere but on the vortex core, where it is singular: $\\nabla\\times\\mb v_\\m v = \\kappa_4\\,\\mb{\\hat\n t}\\,\\delta_2(\\mb r-\\mb s)$. Integration over the two-dimensional delta function $\\delta_2(\\mb x)$, defined in the plane normal to the tangent $\\mb{\\hat t}$ to the loop, reduces this volume integral to a line integral over the vortex element: $$\\label{ReducedEv}\n E_\\m v = \\frac{\\rho_\\m s \\kappa_4}{2}\\,\\oint\\m d\\mb l\\cdot\\mb A \\; .$$ The vortex kinetic energy is the circulation of the vector potential along the the vortex filament.", "\n\nBy substitution of the expression (\\[VectorPotential\\]) for the vector potential $\\mb A$ in Eq.(\\[ReducedEv\\]), the vortex energy can be expressed by a double contour integral over the vortex loop:[^32] $$\\label{ReducedEv2}\n E_\\m v = \\frac{\\rho_\\m s \\kappa_4^2}{8\\pi}\\,\\oint\\!\\!\\oint \\frac{\\m d\\mb s(l_1)}{\\m d l_1}\n \\cdot \\frac{\\m d\\mb s(l_2)}{\\m d l_2} \n \\frac{\\m d l_1\\,\\m d l_2}{\\left| \\mb s(l_1)-\\mb s(l_2)\\right|}\n \\; .$$ Because $E_\\m v$ in Eq.(\\[ReducedEv2\\]) varies as $\\kappa_4^2$, loops carrying two quanta of circulation would have four times the line energy of single charge ones. ", "Vortices with multiple quanta of circulation are thus strongly disfavoured on energy grounds compared to separate singly-charged vortices with the same total vorticity charge; they are energetically unstable and decay spontaneously into several singly-charged entities. ", "Only loops and filaments carrying one quantum of circulation are considered here.", "\n\nFor a circular ring of radius $R$ the integral can be evaluated in terms of elliptic functions[^33] and expanded in terms of the small parameter $a_0/R$. The kinetic energy associated with the ring velocity field is then given by $$\\label{RingEnergy}\n E_\\m R = \\frac{1}{2}\\rho_\\m s \\kappa_4^2 R\\,\\ln \\frac{8R}{a_0} \n + {\\cal O}\\left(\\frac{a_0}{R}\\right) \\; .$$\n\nFor a straight vortex filament, the integral for the kinetic energy in the volume comprised between two planes perpendicular to the filament stems out directly from Eq.(\\[VortexFlow\\]). ", "For a unit length of vortex the result reads: $$\\label{FlowEnergy}\n{\\mathsf{\\epsilon}}_{\\m f} = \\frac{\\rho_{\\m s}\\kappa_4^2}{4\\pi}\n \\ln\\left(\\frac{r_{\\m m}}{a_0}\\right)\\; .$$ The logarithmic divergence is cut at short distance to $a_0$, taken as the definition of the core radius. ", "Its value, of the order of one Å  at low pressure, is obtained from experiment [@Rayfield:64]. ", "The far distance cut-off $r_{\\m m}$ is the minimum distance over which the vortex flow field is undisturbed: it is the smallest of 1) the size of the container, 2) the average radius of curvature of the vortex, 3) the distance to neighbouring vortices. ", "For ångström-size vortices, taking $r_{\\m m}/a_0=10$, ${\\mathsf{\\epsilon}}_{\\m v} \\sim 2$ kelvin per ångström: vortices are high-energy excitations of the superfluid as compared to thermal excitations, phonons or rotons. ", "Changes in $r_{\\m m}$ along the vortex line are disregarded because they enter logarithmic terms and yield small corrections only for $r_\\m m \\gg a_0$: when the vortex deforms, its energy changes mostly as its length, and little with its shape.", "\n\nThe line energy of the core, usually taken as $${\\mathsf{\\epsilon}}_{\\m{sb}} = -\\frac{7}{4}\\,\\frac{\\rho_{\\m s}\\kappa_4^2}{4\\pi} \\; ,$$ for a core rotating as a solid body,[[^34]]{} must be added to Eq.(\\[FlowEnergy\\]) to obtain the full vortex energy per unit length $$\\label{LineTension}\n\\mathsf{\\epsilon}_{\\m v} = \\mathsf{\\epsilon}_{\\m f}\\,+\\,\\mathsf{\\epsilon}_{\\m{sb}}\n = \\frac{\\rho_{\\m s}\\kappa_4^2}{4\\pi} \\left\\{\\ln\\left(\\frac{r_{\\m m}}{a_0}\n \\right) - \\frac{7}{4}\\right\\} \\; .$$ The full energy of a curved vortex line is thus approximated by $\\mathsf{\\epsilon}_{\\m v}$ times its total length. ", "For instance, the energy of a vortex ring, Eq.(\\[RingEnergy\\]), stems from Eq.(\\[FlowEnergy\\]) if $r_{\\m m}$ is taken to be $8R$.\n\nExpression (\\[LineTension\\]) holds for straight vortex lines, rings, curved filaments or general loops provided than $r_{\\m m} \\gg a_0$. It can be viewed as a force developing along the vortex axis, a line tension that tends to shorten the vortex length. ", "That is, the vortex line pulls on its ends: if an end becomes loose it shrinks to zero. ", "Stable vortices in finite size containers either are closed on themselves in loops or connect to the container walls.", "\n\n### Stable vortices\n\nIt follows from the existence of a positive line tension that a vortex loop would tend to spontaneously reduce its length and minimise the line energy. ", "However, the energy so released by the vortex loop in its motion can be disposed of into the surrounding fluid only in certain conditions of flow. ", "The line tension is opposed by other forces that arise from the vortex motion in the fluid or from its interaction with the boundaries, namely, the Magnus force and pinning forces.", "\n\nAs stand-alone loops or pinned filaments, their length is constant as long as they cannot exchange energy with the rest of the fluid (or the external world). ", "In the presence of hard walls, their flow field must be such as to satisfy the condition that no fluid can penetrate into the wall. ", "A convenient way of satisfying such a boundary condition is to continue the vortex filament into the wall, forming an imaginary image vortex. ", "Such a continuation procedure can be shown to be possible and to yield a unique velocity field.[^35] Vortices meeting with walls usually satisfy the condition of no flow through a solid boundary by standing perpendicular to it.[^36] Thus, finite length vortices always close on themselves or end at walls. ", "In this latter case, they also form closed loops if their image is taken into account. ", "The opposite view, namely that vortices are most of the time infinitely long as, for instance, vortices formed under rotation in a cylindrical helium bucket, is also held.[^37] The process of nucleation of vortices considered below obviously requires that their size be finite (otherwise, the energy involved would be infinite): the isolated vortex loops dealt with in the following have a finite size, usually small.", "\n\n### Vortex line impulse {#ImpulseAndMass}\n\nIf an external potential flow with velocity $\\mb v_\\m p = (\\hbar/m_4)\\,\n\\nabla\\varphi_\\m p$ imposed by moving boundaries, a piston for instance, or by nearby vortices, the kinetic energy of the combined flow $\\mb v_\\m p + \\mb\nv_\\m v$ in a given volume $V$ is the sum of the kinetic energy of the remotely applied superflow $\\mb v_\\m p$, that of the vortex loop, obtained from Eq.(\\[ReducedEv2\\]), and the volume integral of the cross term of the scalar product of $\\mb v_\\m p$ and $\\mb v_\\m v$. This last term reads $$\\label{CrossIntegral}\n E_\\m {\\,I} = \\rho_{\\m s}\\int_V \\mb v_{\\m p}\\cdot\\mb v_{\\m v} \\,\\m d\\tau \n = \\rho_\\m s\\,\\frac{\\hbar^2}{m_4^2} \\int_V \\nabla \\varphi_{\\m p}\n \\cdot \\nabla \\varphi_{\\m v} \\,\\m d\\tau \\; ,$$ and represents the energy of interaction between the vortex and the applied flow. ", "Making use of Green’s first identity,[^38] the integral in Eq. (", "\\[CrossIntegral\\]) can be rewritten as $$\\label{CrossIntegral2}\n E_\\m {\\,I} = \\rho_{\\m s} \\frac{\\hbar}{m_4}\n \\int_S \\varphi_{\\m v}\\, \\mb v_\\m p\\cdot \\m \\,d\\mb S \\; ,$$ where $\\varphi_{\\m v}$ is the phase change contributed by the vortex own flow field.", "\n\nThe bounding surface $S$ yields not one but two contributions to the integral in Eq.(\\[CrossIntegral2\\]), the outer surface bounding $V$ and, quite importantly, the cut spanning the vortex loop over which $\\varphi_{\\m v}$ changes discontinuously by $2\\pi$ (see Fig.\\[SolidAngle\\]). ", "If $V$ can be chosen large enough, the velocity induced by the vortex on its surface is negligible and $\\varphi_{\\m v}$ is a constant: the contribution to Eq.(\\[CrossIntegral2\\]) of the outer surface reduces to the net flux of $\\mb\nv_\\m p$, which is zero. ", "The contribution of the cut is $2\\pi$ times the flux of $\\mb v_\\m p$ through the vortex loop. ", "Introducing the mass flux of the applied potential flow through the vortex loop, $J_\\m p$, the contribution of the cross term (\\[CrossIntegral\\]) takes the very simple form $$\\label{CrossIntegral3}\n E_\\m {\\,I} = \\rho_{\\m s} \\frac{2\\pi\\hbar}{m_4}\n \\int_{\\m{loop}} \\mb v_\\m p\\cdot \\,\\m d\\mb S = \\kappa_4 J_{\\m p} \\; .$$ Thus, an applied flow contributes to the vortex loop energy by the additional mass flux $J_{\\m p}$ that it causes through the loop times the quantum of circulation. ", "This result will be derived below in §\\[EnergyExchange\\] from the more general phase-slippage theorem governing the exchange of energy between potential and vortical flows.", "\n\nIn the event that $\\mb v_\\m p$ can be considered as constant over the surface spanned by the vortex loop, Eq.(\\[CrossIntegral3\\]) becomes even simpler: $$\\label{CrossIntegral4}\n E_\\m {\\,I} = \\rho_{\\m s} \\kappa_4 \\mb S\\cdot \\mb v_\\m p \\; ,$$ in which $\\mb S$ is the vectorial area of the loop, $\\int \\m d\\mb S =\n(1/2)\\,\\oint \\mb r\\times\\m d \\mb l$, $\\m d\\mb l$ being the line element at point $\\mb s$ of the oriented loop.", "\n\nThe total energy of the vortex immersed in an applied flow field is the sum of its energy in the rest frame, $E_0$, given by Eq.(\\[ReducedEv2\\]), and the energy of interaction with the potential flow, $E_\\m {\\,I}$. For Eq.(\\[CrossIntegral4\\]), this reads $$\\label{Impulse}\n E_\\m v = E_0 + \\mb P\\cdot \\mb v_\\m p\\; , {\\mbox{ with }} \\mb P =\n \\rho_\\m s \\kappa_4 \\mb S \\; ,$$ where $\\mb P$ ican be defined as the impulse of the vortex loop.", "\n\nFor a circular loop of radius $R$, a vortex ring, Eq.(\\[Impulse\\]) gives the well-known result [@Lamb:45]: $$\\label{RingImpulse}\n P_\\m R = \\pi \\rho_\\m s \\kappa_4 R^2 \\; .$$ It emerges from this derivation (and the various approximations made along the way) that, under a Galilean boost, vortex loops do behave as Landau quasiparticles, with an energy proportional to their length and an impulse proportional to their area. ", "This approach puts some flesh on the bare bones of the conventional (and exact) fluid-mechanical vortex dynamics; it gives substance to the intuitive view than they can be treated as independent elementary entities. ", "This physically meaningful manner of separating the vortical flow from the local value of the remotely potential superflow $v_{\\m\n p}$ will prove quite useful in the following.", "\n\n### Vortex self-velocity\n\nThe impulse is not simply a plain geometrical quantity as Eqs.(\\[CrossIntegral4\\]) or (\\[Impulse\\]) would let think. ", "It is the resultant of the impulsive pressures that must be applied to the fluid at rest to create the vortex loop from rest.[^39] It possesses some of the properties of a true momentum. ", "For instance, the propagation velocity of the vortex ring, Eq.(\\[RingVelocity\\]), can be expressed as the group velocity associated with the energy (\\[RingEnergy\\]) and impulse (\\[RingImpulse\\]) [@Langer:70; @Roberts:70]: $$\\label{GroupVelocity}\n v_\\m R = \\frac{\\m d E_\\m R}{\\m d P_\\m R} = \n \\frac{\\kappa_4}{4\\pi R}\\,\\left(\\ln\n \\frac{8R}{a_0}-\\frac{3}{4}\\right) \\; ,$$ Expression (\\[GroupVelocity\\]) tends asymptotically to the actual velocity of a ring with a hollow core as computed directly from the Biot and Savart law,[^40] which moves along its symmetry axis $\\hat{\\mb n}$ with velocity $$\\label{RingVelocity}\n \\frac{\\m d\\mb s}{\\m d t} = \\mb v_\\m R = \n \\frac{\\kappa_4}{4\\pi R}\\,\\left(\\ln\n \\frac{8R}{a_0}-\\frac{1}{4}\\right)\\hat{\\mb n} \\; .$$\n\nHowever, these simple properties do not imply that a vortex has actual linear momentum. ", "The vortical impulse is more elusive. ", "For instance, it can be shown that a vortex ring moving freely under its own force at velocity $v_\\m R$ and impinging on a wall exerts no force on it [@Fetter:72]. ", "This somewhat counter-intuitive result arises from the distribution of the flow around the vortex loop [@Cross:74]. ", "The contribution of the flow that goes in the forward direction, and which causes the ring free motion, does impart a momentum impulse into the wall equal to $P_\\m R$, but the returning fluid away from the ring, the backflow, yields an opposite contribution that leads to full cancellation of the momentum transfer recorded over an infinitely extended wall for the complete collision event. ", "This push and pull action constitutes a reminder that actual momentum is carried by the individual fluid elements and that a vortex is a hydrodynamical object made up of many of those elements.", "\n\nIsolated circular rings propagate undistorted under their own velocity field in the superfluid at rest for symmetry reasons.. Only a few vortex shapes propagate undistorted in their own velocity field. ", "Straight vortex pairs and helical vortices are other examples [@Langer:70].", "\n\nFor an arbitrarily curved vortex, the self-velocity of each curve element can be approximated by Eq.(\\[RingVelocity\\]), $R$ being replaced by the local radius of curvature, $r_\\m m= |\\m d^2 \\mb s/ \\m d\\xi^2|^{-1}$, parameter $\\xi$ being the line length of the curve represented by $\\mb s(\\xi)$. The validity of this “local induction” approximation, which requires that $r_\\m m$ be large with respect to the vortex core radius, has been discussed in particular by @Schwarz:78 [@Schwarz:85] who has used it in extensive numerical simulations of 3D vortex motion.", "\n\n### The vortex mass {#VortexMass}\n\nThe impulse of a vortex discussed above is in no way related to the vortex self-velocity as the product of this velocity by an inertial mass. ", "The problem of the mass of a vortex has been a long lasting riddle, which has now been resolved in a satisfactory way in superfluid $^4$He.[^41]\n\nThis mass arises from several contributions. ", "If it is assumed that the vortex has a hollow core of radius $a_0$ and that the compressibility of the surrounding superfluid in rapid rotation can be neglected, the vortex mass is simply the mass of the displaced fluid. ", "For a cylindrical body, this amounts to $\\pi \\rho_\\m s a_0^2$ per unit length, a standard result of classical fluid dynamics [@Lamb:45]. ", "The minuteness of $a_0$ in $^4$He, $1\\sim2$ Å, of the same order as the interparticle spacing, makes this contribution very small.", "\n\nHowever, compressibility cannot be neglected in the vicinity of the vortex core because the peripheral velocity, Eq.(\\[VortexFlow\\]), becomes large. ", "The corresponding pressure drop is given by the Bernoulli equation: $$\\label{Bernoulli}\n \\frac{{\\mbox{\\small{{\\usefont{U}{psy}{m}{n}d}}\\hskip 0.05ex}}P}{\\rho_\\m s} = -\\frac{1}{2} {\\mbox{\\small{{\\usefont{U}{psy}{m}{n}d}}\\hskip 0.05ex}}(v^2_\\m s) = 0 \\; .$$ The change in density at distance $r$ from the core where the velocity is $\\kappa_4/2\\pi r$ is then: $$\\label{DensityChange}\n {\\mbox{\\small{{\\usefont{U}{psy}{m}{n}d}}\\hskip 0.05ex}}\\rho_\\m s = \\frac{{\\mbox{\\small{{\\usefont{U}{psy}{m}{n}d}}\\hskip 0.05ex}}P}{c_1^2} =\n \\frac{\\kappa_4^2}{8\\pi^2}\\,\\frac{\\rho_s}{c_1^2}\\, \\frac{1}{r^2} \\; ,$$ using the relation between the (first) sound velocity and the compressibility $c_1 = (\\partial P/\\partial \\rho)^{-1/2}$,[^42] which is justified when the normal fluid fraction is small ($\\rho_\\m\ns \\simeq \\rho$). ", "The overall change of mass about a unit length of vortex filament arising from the fluid compressibility is obtained by integrating Eq.(\\[DensityChange\\]) over space: $$\\label{CompressibilityMass}\n \\mu_\\m v = \\int_{a_0}^{r_\\m m}\\!\\!\\int_0^{2\\pi}\\!\\!\\int_0^1 \n {\\mbox{\\small{{\\usefont{U}{psy}{m}{n}d}}\\hskip 0.05ex}}\\rho_\\m s r \\m d r\\m d \\theta\\m d z =\n \\frac{\\kappa_4^2}{4\\pi}\\,\\frac{\\rho_s}{c_1^2}\\, \\ln\\frac{r_\\m m}{a_0} \\; .$$ The vortex mass per unit length $\\mu _\\m v$diverges logarithmically with $r_\\m\nm$ and ranges from negligible for $r_\\m m \\sim$ a few core radii to important for large vortices, $r_\\m m/a_0 \\gtrsim 10^3$. However, in most cases, the mass of the vortex remains small and can be neglected except for high frequency phenomena [@Baym:83; @Sonin:87] and, possibly, for quantum tunnelling [@Volovik:97].", "\n\nThe Bernoulli effect, Eq.(\\[DensityChange\\]), also causes $^3$He impurities and ions to be trapped on the vortex cores because their chemical potential decreases with the $^4$He density. ", "They prefer to sit in low density regions of the fluid. ", "Trapped impurities add their own inertial mass $m_\\m I$ to that of the core. ", "In superfluid $^3$He, the core is large and yields the dominant contribution to the vortex mass [@Kopnin:78; @Kopnin:95; @Duan:92; @Volovik:97].", "\n\nEnergy exchange between potential and vortical flows {#EnergyExchange}\n----------------------------------------------------\n\n Stream of vortices $\\m v_1$, $\\m\n v_2$, $\\m v_3$, … crossing a path between point 1 and point 2, moving from bottom to top. ", "The vortices are represented by dots and are assumed perpendicular to the figure and nearly straight in the vicinity of 1-2. ", "Each contributes angle $\\theta_i$ to the phase difference recorded between 1 and 2. ", "In its travel from far below to far above line 1-2, each vortex contributes $2\\pi$ to the phase difference. ", "According to the [*ac*]{} Josephson effect, a pressure difference develops in the superfluid due to the stream of vortices (see Eq.(\\[AndersonPhaseSlippage\\]). ](", "Fig05.pdf){width=\"4cm\"}\n\nFollowing the insight of @Anderson:66a, the idea that phase slippage by moving vorticity causes dissipation in superfluids and superconductors has become conventional wisdom. ", "If, referring for instance to the situation of Fig.\\[LiftForce\\], there is not just one vortex as in Fig.\\[paths\\] but a constant stream of vortices crossing the path 1-2 at a rate of $n$ per second, driven by some external force, a pressure difference develops in the superfluid according to the Josephson [*ac*]{}-relation (\\[acJosephson\\]). ", "When the superfluid is free to move, it is accelerated by the cross stream of vortices: work is done onto the superfluid by the applied external force, for instance an electric field acting on charges trapped in the vortex cores. ", "This Section dwells on the mechanism for this exchange of energy between the purely potential superflow and vorticity.", "\n\n@Anderson:66a noted in an appendix entitled “A ‘new’ corollary in classical hydrodynamics” that, whenever there exists a steady stream of vortices, for instance at the mouth of an orifice, the quantum phase in the superfluid would change there at a constant rate and, according to Eq.(\\[acJosephson\\]), the following chemical potential difference would build up $$\\label{AndersonPhaseSlippage}\n \\hbar \\frac{\\m d n_{\\m{vortices}}}{\\m d t}\\Big |_1^2 = \\bigg < \\hbar \\,\\frac{\\m\n d(\\varphi_2 - \\varphi_1)}{\\m d t} \\bigg > = \\big < \\mu_2 - \\mu_1 \\big > \\; .$$ In Eq.(\\[AndersonPhaseSlippage\\]), the brackets stand for time-averaging and the quantity $\\m d n_{\\m{vortices}} / \\m d t$ for the rate of passage of vortices across a line joining points 1 and 2, as depicted in Fig.\\[LiftForce\\].", "\n\nThis result is of no special importance in classical hydrodynamics because the velocity circulation carried by each vortex, albeit constant, can take any value, while in the superfluid it is directly related to the phase of the macroscopic wavefunction and quantised . ", "A formal proof of this conjecture, based on the standard decomposition of any vector field into an irrotational contribution and a solenoidal one was given by @Huggins:70.[^43] The following derivation is based on the more physical approach to vortex dynamics, which makes use of the concepts of force and energy.", "\n\n### The Magnus force\n\nConsider the interaction energy between a vortex loop and a potential flow $\\mb v_\\m p$, Eq.(\\[CrossIntegral4\\]). ", "Under an infinitesimal displacement ${\\mbox{\\small{{\\usefont{U}{psy}{m}{n}d}}\\hskip 0.05ex}}\\mb x$ of a small line element $\\Delta \\mb l$, as shown in Fig.\\[VirtualDisplacement\\], the energy of the vortex loop changes according to $$\\label{DerivativeEI}\n {\\mbox{\\small{{\\usefont{U}{psy}{m}{n}d}}\\hskip 0.05ex}}(\\Delta E_\\m I) = \\kappa_4 \\rho_\\m s\\, {\\mbox{\\small{{\\usefont{U}{psy}{m}{n}d}}\\hskip 0.05ex}}\\mb x\\times \\Delta \\mb l\\cdot \n \\mb v_\\m l \n = \\kappa_4 \\rho_\\m s\\, \\Delta \\mb l\\times \\mb v_\\m l \\cdot{\\mbox{\\small{{\\usefont{U}{psy}{m}{n}d}}\\hskip 0.05ex}}\\mb x \\; ,$$ where $\\mb v_\\m l$ is the local superflow velocity as seen by the vortex element standing still. ", "The local flow velocity $\\mb v_\\m l$ is the sum of the applied superflow $\\mb v_{\\m p}$ and the flow induced by the other parts of the vortex loop, $\\mb v_\\m v$. Equation (\\[DerivativeEI\\]) expresses the functional derivative ${\\mbox{\\small{{\\usefont{U}{psy}{m}{n}d}}\\hskip 0.05ex}}(\\Delta E_\\m I)/ {\\mbox{\\small{{\\usefont{U}{psy}{m}{n}d}}\\hskip 0.05ex}}\\mb x$ of the energy with respect to an infinitesimal deformation of the vortex line.", "\n\n![ ", "\\[VirtualDisplacement\\] Virtual displacement by ${\\mbox{\\small{{\\usefont{U}{psy}{m}{n}d}}\\hskip 0.05ex}}x$ of a small line element $\\Delta l$. ](Fig06.pdf){width=\"2.5cm\"}\n\nIf the vortex loop moves along at velocity $\\mb v_{\\m{loop}}$ together with the element under consideration in the rest frame of the observer, $\\mb v_\\m l$ in Eq.(\\[DerivativeEI\\]) becomes $\\mb v_\\m l - \\mb v_{\\m{loop}}$ and this force takes the same form as the Magnus force for a line vortex in classical hydrodynamics with a fluid density $\\rho_\\m s$:[^44] $$\\label{MagnusForce}\n \\frac{{\\mbox{\\small{{\\usefont{U}{psy}{m}{n}d}}\\hskip 0.05ex}}(\\Delta E_\\m I)}{{\\mbox{\\small{{\\usefont{U}{psy}{m}{n}d}}\\hskip 0.05ex}}\\mb x} =\n \\Delta \\mb F_\\m M = \\kappa_4 \\rho_\\m s (\\mb v_{\\m{loop}} - \\mb v_\\m l)\\times\n \\Delta\\mb l \\; ,$$ The Magnus force, Eq.(\\[MagnusForce\\]), has a simple physical origin. ", "It is due to the Bernoulli effect that arises from the rotational flow around the vortex core. ", "As shown in Fig.\\[MagnusBernoulli\\], this flow adds to the potential flow in the lower half-plane and subtracts from it in the upper half-plane. ", "Integrating the resulting pressure difference obtained from the Bernoulli Eq.(\\[Bernoulli\\]) over the cylinder yields a downward force expressed by Eq.(\\[MagnusForce\\]).", "\n\n![ ", "\\[MagnusBernoulli\\] (Color online) Potential streamlines past the cylindrical vortex core flowing from left to right in thin plain lines. ", "The flow from the vortex, in dashed lines, subtracts from the potential flow in the upper half and adds to it in the lower half, inducing a Bernoulli pressure difference between top and bottom. ](", "Fig07.pdf){width=\"7cm\"}\n\nThe Magnus force on each element of the vortex line arises ultimately from momentum conservation in the fluid and comes into play whenever the vortex trajectory differs from that of the local fluid particles. ", "When no other force acts on the vortex core (such as, e.g., an electric field on charges trapped in the core, or friction from the normal fluid component, …) $\\mb F_\\m M$ must be zero, hence $\\mb v_{\\m{loop}} = \\mb v_\\m l$: the vortex core moves with the local superfluid velocity. ", "The velocity of the core at point ${\\mb\n s}$ is the sum of the velocity of the local potential flow ${\\mb v}_\\m p$ at ${\\mb s}$ when there is no vortex, and of the velocity ${\\mb v}_{\\m v}$ induced at ${\\mb s}$ by the other parts of the vortex. ", "If no flow is applied, $\\mb v_\\m p =0$, then $\\mb v_{\\m{loop}} = \\mb v_\\m v$: the vortex loop moves under its own flow field in the superfluid at rest at large distance. ", "The vortex thus appears to behave as a quasiparticle in its own right although it stands only for the vortical part of the total flow. ", "The physical picture that emerges from this approach rings a familiar bell to condensed matter physicists.", "\n\n### Quantised vorticity and the Kelvin-Helmholtz theorem\n\nThat free vortex loops moves with the local fluid particles conforms to the Kelvin-Helmholtz theorem. ", "This result has been obtained here as a consequence of the quantisation of circulation, Eq.(\\[VortexFlow\\]). ", "The Kelvin-Helmholtz theorem is usually derived from the Euler equation and the implicit assumption that the motion of the fluid is isentropic [@Landau:Hydro].[^45] A further implicit assumption is that the velocity field and the loop deformation are well-behaved analytically, that is, continuous in space and time.[^46] The relevance of these remarks will become apparent in Sect.\\[VortexNucleation\\] on vortex nucleation, which deals with the spontaneous appearance of vorticity, in other words, the violation of the Kelvin-Helmholtz theorem. ", "The derivation given above does not hide these fine points under the rug; it explicitly rests on the quantisation of circulation, hence its conservation, and also implies isentropic and continuous superfluid motion. ", "When this fails new phenomena occur: vortices may be nucleated.", "\n\nAs the effect of external forces and mutual friction has been set aside for simplicity, no work is done on the vortex itself except by the interaction with the local superflow. ", "Thus any gain or loss of energy by the vortex balances that lost or gained by the potential flow. ", "The way by which this conservation of energy proceeds is instructive; the detailed analysis is given in the following.", "\n\n### The phase slippage theorem\n\nIf ${\\mbox{\\small{{\\usefont{U}{psy}{m}{n}d}}\\hskip 0.05ex}}\\mb x$, used in Eq.(\\[DerivativeEI\\]) as a virtual displacement to compute the forces acting on $\\Delta \\mb l$, becomes a real displacement $\\mb\nv_{\\m{loop}} \\Delta\\m t$, actual work during the time $ \\Delta\\m t$ is done by the applied potential flow on the vortex loop. ", "The energy balance is expressed by rewriting Eq.(\\[DerivativeEI\\]) as $$\\label{EnergyBalance}\n \\begin{split}\n {\\mbox{\\small{{\\usefont{U}{psy}{m}{n}d}}\\hskip 0.05ex}}(\\Delta E_\\m I) &= \\kappa_4 \\rho_\\m s\\, \\Delta \\mb l\\times \n (\\mb v_\\m p+\\mb v_\\m v)\\cdot {\\mbox{\\small{{\\usefont{U}{psy}{m}{n}d}}\\hskip 0.05ex}}\\mb x \\\\\n &= \\kappa_4\\rho_\\m s\\,\\Delta\\mb l\\times \\mb v_\\m p\\cdot \\mb v_{\\m{loop}} \\Delta t +\n \\kappa_4 \\rho_\\m s\\,\\Delta \\mb l\\times \\mb v_\\m v\\cdot \\mb v_{\\m{loop}} \\Delta t \n \\; . ", " \n \\end{split}$$ In free motion – disregarding friction of the core on the normal component and with no force applied externally – the vortex loop follows the fluid stream: $\\mb v_{\\m{loop}} = \\mb v_\\m l=\\mb v_\\m p+\\mb v_\\m v$. The triple products are equal in magnitude and opposite in sign. ", "The energy increment expressed by Eq.(\\[EnergyBalance\\]) is equal to zero. ", "Total energy is conserved in the course of the vortex motion by the balance of the two terms in the last equality (\\[EnergyBalance\\]). ", "The first, rewritten as $$\\label{PotenialFlowCutEnergyChange}\n {\\mbox{\\small{{\\usefont{U}{psy}{m}{n}d}}\\hskip 0.05ex}}(\\Delta E_\\m I)_1 = \\kappa_4 \\rho_\\m s\\, ( \\mb\n v_{\\m{loop}} \\Delta t \\times \\Delta \\mb l) \\cdot \\mb v_\\m p \\; ,$$ is readily seen proportional to the rate at which the potential flow streamlines are crossed by the vortex element $\\Delta \\mb l$. It expresses the change of the potential flow kinetic energy when its streamlines are crossed by the vortex line, causing a change of the phase difference of $2\\pi$ along them.", "\n\nThe second term requires a little more formal work to be recognised as a contribution to the vortex self-energy $E_\\m v$. What needs to be shown is that it corresponds to the energy variation for a small, local deformation of the vortex loop. ", "This is established in Appendix A with the following result, $$\\label{VortexSefEnergyChange}\n {\\mbox{\\small{{\\usefont{U}{psy}{m}{n}d}}\\hskip 0.05ex}}(\\Delta E_\\m I)_2 = \\kappa_4\\rho_\\m s\\,\\Delta\\mb l\\times \\mb v_\\m v\\cdot\n \\mb v_{\\m{loop}} \\Delta t \n = \\Delta E_\\m v({\\mbox{\\small{{\\usefont{U}{psy}{m}{n}d}}\\hskip 0.05ex}}\\mb x,\\mb v_{\\m{loop}}) \\; ,$$ for the displacement ${\\mbox{\\small{{\\usefont{U}{psy}{m}{n}d}}\\hskip 0.05ex}}\\mb x = \\mb v_{\\m{loop}} \\Delta t$ of the loop element $\\Delta \\mb l$.\n\nThe energy balance expressed by Eq.(\\[EnergyBalance\\]) between the potential flow kinetic energy and the vortex self-energy constitutes the fundamental relation governing phase slippage. ", "In integral form, it yields Eq.(\\[CrossIntegral3\\]). ", "It shows the way by which a vortex loop of arbitrary shape can form by expanding from an infinitesimal loop.", "\n\nThe gist of Eq.(\\[VortexSefEnergyChange\\]) is that whenever a vortex cuts potential flow streamlines, it reversibly exchanges energy with the potential flow and it concurrently changes the velocity circulation along these streamlines by one quantum unit, causing slippage of the quantum phase. ", "This process takes place in real time and locally, not only in a time-averaged fashion as in Anderson’s conjecture, Eq.(\\[AndersonPhaseSlippage\\]). ", "If the potential flow is divergent – for instance outward the mouth of a duct where the streamlines flare out, the vortex expands in length, collects energy from the flow and slows it down. ", "If the vortex runs away from that point to a far off distance and never comes back, this energy is irreversibly lost for the potential flow: dissipation of superflow energy has occurred. ", "Reversing the flow direction, which then becomes convergent, results in the vortex shrinking and the potential flow picking up energy: a collapsing vortex dumps its energy into the potential flow and speeds it up.", "\n\nThese processes alter the quantum phase and will be discussed in Sec.\\[HalfRingModel\\] on the phase slip mechanism. ", "But before turning to the inner details of the phase slips, their experimental observations will be briefly sketched in the following Section.", "\n\nPhase slippage experiments {#slippage}\n==========================\n\nAs the [*dc*]{} and [*ac*]{} effects predicted in the early sixties by Brian Josephson [@Josephson:62; @Josephson:64; @Josephson:65] to take place between two suitably coupled superconductors were quickly observed [@Anderson:63; @Shapiro:63], the search for analogous effects in superfluids also begun, with the tantalising goal of observing unique quantum-mechanical effects in hydrodynamics. ", "This search for a long time gave inconclusive results,[^47] or led to blind alleys.[^48] It was only in the mid-eighties that decisive steps forward were taken.[^49]\n\nThe Richards-Anderson experiment\n--------------------------------\n\n![ ", "\\[RichardsAndersonCell\\] The Richards-Anderson cell (1965).](Fig08.pdf){height=\"9cm\"}\n\nIn order to observe the Josephson [*ac*]{}-effect in superfluid helium, @Richards:65 designed an experiment based on the beat note expected to form between the sound wave emitted by a quartz transducer immersed in the superfluid and the internal pressure fluctuation due to the [*ac*]{}-effect. ", "In this historical setup, shown in Fig.\\[RichardsAndersonCell\\],[^50] two identical coaxial capacitors are suspended over a liquid helium bath cooled at a temperature below the lambda point (of the order of 1.15 K). ", "One of the capacitors is fully open-ended, the other is partially closed at the bottom by nickel foil with a very small aperture. ", "The foil is 25 micrometres thick, in which a 15 micrometre aperture had been punched with a sharp needle: the pinhole thus manufactured constitutes the “weak link” between the two superfluid pools.", "\n\nIf a helium level difference $\\Delta z$ between the two coaxial capacitors is created by lowering and raising the whole assembly over the liquid helium bath, the return to hydrostatic equilibrium is impeded by the pressure head of the steady stream of vortices corresponding to Eq.(\\[AndersonPhaseSlippage\\]). ", "The level difference can be precisely monitored by a capacitance bridge. ", "When an ultrasound wave is shone by a quartz transducer facing the micro-aperture as shown in Fig.\\[RichardsAndersonCell\\], it can couple to the stream of vortices and modulate the flow.", "\n\nSteps in the return to equilibrium were indeed observed at level differences which were multiples and submultiples of the fundamental head difference frequency expected from the Josephson [*ac*]{} relation: $\n\\Delta z = n\\,\\hbar\\omega\\, /\\,n'\\,m_4 g \\; \n$ where $n$ and $n'$ are integers, and $g$ the acceleration of gravity. ", "Richards and Anderson’s results were reproduced by other researchers using similar setups, notably @Khorana:67, @Khorana:69, @Hulin:71, and @Hulin:72. ", "Different setups, involving rotating or oscillating toroidal cells [@Guernsey:71; @Gregory:72], vortices accelerated by ions [@Carey:73], a two-orifice flow arrangement [@Gamota:74] were also tried but with mixed success at best, suffering from lack of reproducibility and poised with numerous unexpected features.", "\n\nIt eventually became clear that the early claims of observation of the Josephson [*ac*]{} effect by synchronisation of the pressure head on the sound frequency did not meet universal acceptance. ", "On the contrary, an alternate explanation in terms of acoustic standing waves in the cell was put forward on experimental grounds by @Leiderer:73, as well as @Musinski:72 [@Musinski:73], and on theoretical grounds by @Rudnick:73. ", "It was nonetheless argued by @Anderson:75a that, although acoustic resonances in the cell could be a concern, they could not account for all of the features observed in their experiments.", "\n\nThese efforts directed toward the demonstration of the hydrodynamic Josephson effects, together with direct studies of the critical velocity itself [@Trela:67; @Gamota:73], did bring experimental confirmation of the views of Feynman and Anderson that vortices were associated with the appearance of dissipation in superfluid flow. ", "However, quantitative studies leading to a clear picture of how these vortices were created and how they interacted with the superflow were lacking. ", "A consensus grew that somehow their formation and evolution had a chaotic character, presumably due to random pre-existing vorticity in the superfluid and to a probable evolution toward some form of turbulent motion of the quantised vortices, a belief confirmed in part by the more recent studies described in Sec.\\[AllThat\\]. ", "The flurry of activity stirred by the initial reports of observations related to the Josephson effects in helium receded almost completely.", "\n\nWith the hindsight gained from the experiments described further on, it can now be concluded that the synchronisation envisioned by @Richards:65 would be nigh impossible to achieve. ", "A particularly clear exposition of this synchronisation experiment is given by @Anderson:84 in terms of parametric effects due to the system non-linearities, of the same kind as frequency pulling in radiofrequency oscillators. ", "These effects require that energy be stored reversibly in a non-linear element, here the Josephson junction or, for [*rf*]{}-devices, a non-linear inductance. ", "In $^4$He far from the [[l]{}]{}-point the relation between the current and the phase difference across the weak link shows no non-linearities. ", "The energy that the vortices gather from the potential flow is carried swiftly away from the orifice and is irreversibly lost. ", "It can be used to pull or push the flow in synchronism with the sound excitation for a very brief lapse of time only, much shorter than the period of the audiofrequencies used in these experiments.[^51] Furthermore, for the comparatively large orifices used then, vortices appear in a rather irregular fashion, not individually but in lumps with varying numbers, as discussed in Sec.\\[LargeSlips\\]. ", "These peculiarities hamper the eventual synchronisation to a regular pattern of steps.", "\n\nThe hydromechanical resonator\n-----------------------------\n\nIn the early eighties, several groups went on striving to improve the detection techniques used in the search for the hydrodynamical Josephson effects. ", "The use of a diaphragm-driven hydromechanical resonator fully immersed in the superfluid was pioneered by Zimmermann, Jr., and his students.[^52] A similar device with two chambers was built by @Manninen:83 for critical velocity measurements in superfluid $^3$He, and used by @Lounasmaa:83 for the search of an [*ac*]{} Josephson effect in superfluid $^3$He, a topic that will be covered in Sect. ", "\\[CPR\\]. ", "The expertise developed at Cornell on torsional oscillators was put to use in superfluid $^3$He by Reppy and his students [@Crooker:84]. ", "Again, the hydrodynamic Josephson effects could not be observed in these various experiments, for one or several of the following reasons:\n\n[$\\bullet$ the apertures used as weak links were too large;]{}\n\n[$\\bullet$ the mass flow rate sensitivity was marginally adequate only;]{}\n\n[$\\bullet$ the superfluid motion was driven from current sources that were too stiff to let the response of the weak link be seen;]{}\n\n[$\\bullet$ and, last but not least, the cells were too bulky and too sensitive to external mechanical vibrations to allow for non-invasive measurements.]{}", "\n\nThe first reason was clearly perceived as essential. ", "Efforts shifted from superfluid $^4$He to the newly discovered superfluid $^3$He because the coherence length is two orders of magnitude larger, putting the fabrication of a genuinely-weak superfluid link within reach of experimental low temperature physicists. ", "Work was carried out in that direction by @Wirth:81, who were the first to use sub-micronic orifices in free-standing ultra-thin foils, and others [@Sudraud:87],[@Amar:90].", "\n\nThe detection of the minute mass currents that would flow in micro-apertures improved markedly in the early eighties as reliable [*rf*]{}-SQUIDs became available.[^53] Ultra-sensitive pressure and displacement gauges could then be developed [@Avenel:86].", "\n\nEarly phase slippage experiments \n---------------------------------\n\n![", "\\[Cell\\] Schematic drawing of the flexible-diaphragm double-hole hydromechanical resonator. ", "The dashed line shows a closed loop threading the two holes – micro-aperture and long channel – located entirely in the superfluid. ](", "Fig09.pdf){width=\"45\"}\n\nThe phase slippage experiments that were carried out starting from the mid-eighties using these refined techniques [@Varoquaux:87; @Avenel:85] confirmed Feynman and Anderson’s views on dissipation in superflows and brought a large measure of clarification to the critical velocity problem [@Varoquaux:91] and to the formation of vortices in superfluid $^4$He [@Avenel:93]. ", "These experimental results and their interpretation have since been largely confirmed by other workers.[^54]\n\nThe design of the first weak link in which hydrodynamical Josephson effects were seen [@Sudraud:87] struck a compromise between to two conflicting requirements, that it be weak enough to effectively depress the wavefunction amplitude while preserving the macroscopic coherence of the superfluid, and that it be big enough to let a measurable flow of liquid go through. ", "A slit geometry was chosen for the micro-aperture, the smaller dimension of which was comparable with the coherence length in superfluid $^3$He, $\\xi_0$, which is in the sub-micron range (see §\\[CPR\\]). ", "This orifice was micro-machined by ion-milling in a free standing foil the thickness of which was also comparable to $\\xi_0$. The third dimension of the slit was made large to provide a substantial cross sectional area through which the superfluid would flow.", "\n\nPhase slippage was studied with the help of a miniature hydromechanical device, represented schematically in Fig.\\[Cell\\], which is basically a flexible-wall Helmholtz resonator with two vents, immersed in the superfluid bath.[^55] The flexible wall is constituted by a Kapton membrane coated with aluminium. ", "In the version shown in Fig.\\[Cell\\], there are two openings connecting the resonator chamber to the main superfluid bath. ", "One is a micro-aperture in which the critical velocity is reached. ", "The critical event consists in a sudden change of the resonance amplitude corresponding to a departure from the expected classical hydrodynamics response of the flow velocity through the micro-aperture as discussed in the following. ", "The other opening is a relatively open duct and provides a parallel path to the superfluid, along which the quantum phase remains well determined in all circumstances. ", "The velocity circulation along the superfluid closed loop threading the two openings shown in Fig.\\[Cell\\] changes by an integral number of quanta for each critical event.", "\n\n-3mm ![", "\\[PhaseSlipsCanJPhys\\] Time chart of the peak resonance amplitude of the resonator membrane, in nm, for positive and for negative excursions. ", "Each dot represents a measurement. ", "The time interval between individual measurements is half a period, 177 ms here. ", "The ticks labelled “in” and “out” indicate whether the jumps occur when the liquid flows in or out of the cell. ", "The drive power applied to drive the resonance is very small ($2.4 \\; 10^{-18}$ W). ", "When the peak amplitude is subcritical, its value builds up linearly with time as seen at the left of the chart. ", "The critical events are sharply defined and quite reproducible but occur at a threshold that varies slightly from event to event. ", "The superfluid $^4$He contained 100 to 300 ppb of $^3$He and was cooled to about 10 mK under a very small hydrostatic pressure head. ", "From [@Avenel:85]. ](", "Fig10.pdf \"fig:\"){width=\"80mm\"}\n\nThe operation of these resonators is described in detail in the literature.[^56] Flow is driven in and out of the resonator by an electrostatic [*ac*]{}-drive applied to the aluminium-coated Kapton membrane. ", "The membrane is mounted in such way as to be as flexible as possible; it provides the restoring elastic force in the resonator. ", "The “common mode” flow of liquid in and out of the cell body through the two vents of the resonator provides a force of inertia to the hydromechanical device. ", "These inertial and elastic terms determine the resonance frequency. ", "The device is usually driven at or close to resonance in continuous mode. ", "The raw data consist of peak amplitude charts as represented in Fig.\\[PhaseSlipsCanJPhys\\]. ", "A strong impulsive force may also be applied to the membrane; the large transient response of the resonator reveals additional features when it becomes non-linear.", "\n\nIn the absence of dissipation, the resonance motion under a small steady [ *ac*]{} drive increases linearly in amplitude under the action of the drive as energy gradually gets stored in the resonator. ", "This linear rise on the left of the trace in Fig.\\[PhaseSlipsCanJPhys\\] proceeds until the flow velocity in the micro-aperture becomes critical. ", "Sudden drops of the peak amplitude from one half-cycle to the next then appear. ", "These drops signal that a lump of resonator energy has been lost between two successive recordings of the absolute peak amplitude. ", "Quite importantly, these lumps are identical – to experimental uncertainty – from event to event.", "\n\nThese events are interpreted as the footprint left by vortices crossing the potential flow pattern in the vicinity of the micro-aperture. ", "In their course, they cut all potential flow lines, pick up energy at the expense of the potential flow of the resonator and change the phase difference along these flow lines by $2\\pi$. Hence the name “phase slips”. ", "These slips of the phase are sudden and take place at a fairly well defined threshold, which defines the phase slip critical velocity. ", "It will become apparent in the following that this critical velocity, while signalling a breakdown of superfluidity, differs from other quantities also called “critical velocities”. ", "These features are discussed in detail further on, in Secs.\\[PhaseSlipCriticalVelocity\\] and \\[HalfRingModel\\].", "\n\nPhase-slippage experimental results\n-----------------------------------\n\nThe observation of phase slips in $^4$He has led to a number of quite significant results. ", "They brought a confirmation of Anderson’s ideas, much welcome in view of the controversies about previous experiments. ", "And quite importantly, they have shed light on the previously indecipherable problems of the critical velocity and of vortex nucleation. ", "Below are summarised their most important qualitative features and some of their implications.", "\n\n1. ", " [ The critical velocity threshold, which can be seen on time charts such as that shown in Fig.\\[PhaseSlipsCanJPhys\\], is markedly temperature-dependent down to below 200 mK and reaches a well-defined plateau below 150 mK. These features are shown in Fig.\\[vc\\] and are analysed in Sec.\\[PhaseSlipCriticalVelocity\\] below. ", "As the thermodynamic properties of superfluid $^4$He are very nearly independent of temperature below 1 K, this observation indicates that the critical process in action is not governed solely by hydrodynamics. ", "Statistical mechanics may well play the leading role. ]{}", "\n\n2. ", " [ Aperture size is not found to be a relevant factor, as long as it is “small enough”, roughly below a few m. This feature and the temperature dependence mentioned above are in sharp contrast with the Feynman critical velocity, which, as discussed below in §\\[FeynmanCriticalVelocity\\], exhibits a well-characterised dependence on size and none on temperature (except very close to the ${\\mbox{\\footnotesize{{\\usefont{U}{psy}{m}{n}l}}}}$ transition).]{}", "\n\n3. ", " [ The actual velocity threshold for phase slips shows significant scatter from one slip to the next in a given sequence, as can be seen in Fig.\\[TimeChart\\]. ", "This scatter lies much above the instrumental noise level of peak amplitude detection. ", "It represents a genuine stochastic property of the physical process at work, which turns out to display a temperature dependence similar to that of the critical velocity itself, as shown in Fig.\\[Delta-vc\\]. ]{}", "\n\n4. ", " [ The phase slip pattern shows quite reproducible properties in the course of a given cool-down as long as the experimental cell is kept at a temperature below 10$\\sim$15 K. If the temperature is cycled up to liquid nitrogen temperature and down again, small changes to the critical threshold and to the pattern itself can occur. ", "These changes reveal the importance of minute alterations in the surface state of the cell, e.g., contamination of the micro-aperture walls by solidified gases during thermal cycling. ]{}", "\n\n5. ", " [ Quite importantly, phase slips are the signature that [*quantised vortices*]{} are created in aperture flow above a well-defined threshold of flow velocity. ", "This statement is based on the measured value of the phase change, found to be $2\\pi$ to the accuracy of the experiment [@Avenel:85]. ", "This amounts to a change of precisely one quantum of circulation in the superfluid loop threading the micro-aperture and the long parallel channel.[^57] A detailed scenario for the occurrence and development of these phase slips has been described by @Burkhart:94 and is discussed below in Sec.\\[HalfRingModel\\]. ]{}", "\n\nCritical velocities and phase slips in the superfluid phases of $^3$He show different features that will be briefly touched upon in Sect.\\[AllThat\\].", "\n\nCritical velocities in superfluids {#CriticalVelocities}\n==================================\n\nThe critical velocity in a superfluid is defined as the threshold above which the flow of the superfluid component becomes dissipative, that is, the property of superfluidity is lost. ", "This rather broad definition encompasses a number of different physical situations. ", "This Section begins with an overview of the different brands of “critical” velocities that comply with this definition. ", "It will end up by focusing on that which involves the phase slip phenomenon, namely, the nucleation of superfluid vortices.", "\n\nNeither the problem of critical velocities in superfluids nor that of the nucleation of vortices are new. ", "The former is as old as the discovery of superfluidity (see the monograph by @Wilks:67). ", "The latter, first discussed by Vinen in the early sixties [@Vinen:63], has met an even more tortuous fate. ", "It was first thought, still was in some quarters not so long ago, to be nigh impossible: such an extended hydrodynamical object as a vortex line with a finite circulation involving the collective motion of a large number of helium atoms would have a vanishingly small probability of occurring spontaneously. ", "More recent experiments probing superflow on a finer scale of length have shown otherwise.[^58]\n\nThe Landau criterion\n--------------------\n\nAs discussed previously in §\\[TwoFluidModel\\], @Landau:41[^59] explained the absence of dissipation in the flow of helium-4 by the existence of a sharply defined dispersion curve for elementary excitations, the phonons and the rotons. ", "This property is now associated with the phenomenon of Bose-Einstein condensation [@Griffin:87; @Griffin:93], as has long been suspected [@London:54]. ", "Elementary excitation energy levels $\\epsilon(\\mb p)$ are well defined. ", "They have a negligible spread in energy. ", "States with very low energy are thus extremely rare. ", "This scarcity of low-lying states is held responsible for the inviscid property of $^4$He.", "\n\nAn impurity, or a solid obstacle, can only exchange an energy $\\epsilon(\\mb\np)$ at momentum $\\mb p$ that exactly matches the energy of an elementary excitation of the fluid. ", "If the superfluid moves at velocity $\\mb v_\\m s$, the energy of elementary excitations in the frame of reference at rest becomes $\\epsilon-\\mb v_\\m s\\cdot \\mb p$ [@Wilks:67; @Baym:69]. ", "The same holds for a moving obstacle, by Galilean invariance. ", "If this energy turns negative, elementary excitations proliferate and superfluidity is lost. ", "The condition on the superfluid velocity for this to happen reads: $$\\label{LandauVelocity}\n v_\\m s \\geqslant v_\\m L = \\frac{\\epsilon(p)}{p}\\Big|_\\m{min} \\simeq \n \\frac{\\epsilon(p)}{p}\\Big|_\\m{roton} \\; .$$ Unless this condition is met, there is no dissipative interaction between the fluid and its surroundings: the flow is viscousless.", "\n\nThe minimum value of $\\epsilon/p$ for helium lies very close to the roton minimum, as shown in Fig.\\[DispersionCurve\\]. ", "This means that rotons are created when the Landau critical velocity is reached in $^4$He. ", "At low pressure, the roton minimum parameters are such that $v_\\m L \\simeq 60$ m/s. The Landau critical velocity has been observed under certain conditions in the propagation of ions in which rotons are created in $^4$He as reviewed by @McClintock:95. ", "The much less dense Bose-Einstein Condensed gases sustain a phonon-like energy spectrum at low momentum [@Bogolyubov:47] and no roton-like features; the Landau velocity is the sound velocity, $c=\\epsilon(p)/p|_{p=0}$ and phonons are emitted. ", "The Landau critical velocity $v_\\m L$ in superfluid $^4$He is smaller than the sound velocity ($c=220$ m/s at low pressure) but is still quite larger than the critical velocities observed in most experiments.", "\n\nFeynman’s approach {#FeynmanCriticalVelocity}\n------------------\n\n@Feynman:55 realised, following Onsager, that not only would vorticity be quantised in $^4$He in units of the quantum of circulation $\\kappa_4=2\\pi \\hbar/m_4$ but, preceding Anderson, that these vortices would be responsible for the onset of dissipation and for a critical velocity in the superfluid. ", "In Feynman’s views, vortices would be puffed out of the mouth of orifices much in the way of smoke rings – or von Karmann alleys past obstacles in classical (Navier-Stokes) fluids.", "\n\nSuch vortex rings can be treated as elementary excitations of the superfluid, which they rightfully are from the vantage point taken in Sec.\\[VortexDynamics\\]. ", "Hence Landau’s criterion applies. ", "The limiting velocity associated with these vortex rings, assumed to be circular, can be evaluated from the expressions for the energy $E_\\m R$ and impulse $P_\\m R$, Eqs.(\\[RingEnergy\\]) and (\\[RingImpulse\\]). ", "The critical value set by Eq.(\\[LandauVelocity\\]) is reached for a radius $R$ such that $E_\\m R/P_\\m\nR$ is at a minimum, which occurs when $R$ is as large as feasible, that is, of the order of the orifice size $d$. This minimum value sets the lowest velocity at which vortices can start to appear and defines the Feynman critical velocity: $$\\label{FeynmanVelocity}\n v_\\m F \\simeq \\frac{\\kappa_4}{2\\pi d} \\ln\\left(\\frac{d}{a_0}\\right) \\; .$$ As discussed below, $v_\\m F$ is much closer to experimental values than the Landau critical velocity for rotons. ", "Although this agreement is heartening, it also raises questions: how do these vortices come about and how do they evolve?", "\n\nSeveral kinds of critical velocities\n------------------------------------\n\nThe compilation of the critical velocity data in various apertures and channels from various sources available at the time of the Exeter Meeting in 1990 [@Varoquaux:91] is shown in Fig.\\[TwoCriticalVelocities\\] together with more recent data. ", "Two different critical velocity regimes appear clearly on this graph, a fast regime for small apertures, of the phase-slip type, which is temperature-dependent, and a slower regime for larger channels, of the Feynman type, which is temperature-independent. ", "The data points from various sources for these two different types of critical velocity do not fall on well-defined lines but merely bunch into clusters of points. ", "As already stated, critical velocities in apertures and capillaries are not very reproducible from experiment to experiment indicating that, besides size, temperature, and pressure, some less-well-controlled parameters also exert an influence. ", "In some occasions, switching between these two types of critical velocity has been observed in the course of the same cool-down [@Hulin:74; @Zimmermann:93].", "\n\nThe critical velocity that depends on channel size does follow on average relation (\\[FeynmanVelocity\\]) for the Feynman mechanism. ", "The higher critical velocities, bunched around 5 to 10 m/s, faster than the Feynman $v_{\\m F}$ even for the smallest apertures but still considerably slower than Landau’s $v_{\\m L}$ relate to the phase slip phenomenon and are discussed below.", "\n\n![ ", "\\[TwoCriticalVelocities\\] (Color online) Critical velocity data [*vs*]{} channel width ($\\diamond$) – @Wilks:67; ($\\circ$) and ($\\scriptstyle\\triangle$) – temperature-dependent and temperature-independent data as compiled by@Varoquaux:91; ($\\blacktriangleleft$) – [@Shifflett:95]; ($\\star$) – [@Flaten:06a]; ($\\square$) – @Steinhauer:95 as reanalysed by @Varoquaux:96. ", "For the temperature-dependent data, the highest value, [*i.e.*]{}, that at the lowest temperature, has been retained. ", "The dashed line is obtained from Eq. ", "for the Feynman critical velocity.](Fig11.pdf){height=\"65\"}\n\nAs a basis for comparison, it is worthwhile to summarise the findings of the ion propagation studies in superfluid $^4$He at various pressures, which have been reviewed by @McClintock:91 [@McClintock:95]. ", "Ions can be created in liquid helium and accelerated by electric field until they reach a limiting velocity. ", "The resulting drift velocities are measured by time-of-flight techniques. ", "For negative ions, hollow bubbles 30 Å in diameter with an electron inside, two different behaviours are observed:\n\n[$\\bullet$]{}\n\nBelow about 10 bars, vortex rings are created, on the core of which single electrons get trapped: the drift velocity suddenly drops from that of the negatively charged bubbles to that of the much slower vortex rings [@Rayfield:64].", "\n\nAbove 10 bars, the accelerated ion runs into the roton emission mechanism before vortex rings can be created. ", "The Landau critical velocity is observed to be $\\approx$ 46 m/s at 24 bars down from a calculated value of 60 m/s at SVT as the roton parameters change with pressure while the vortex creation velocity increases with pressure [@Varoquaux:96a].", "\n\nAround 10 bars, both critical velocities, the Landau critical velocity for the formation of rotons and that for the formation of vortex rings can be observed to occur simultaneously because ions can be accelerated above the threshold for roton emission.", "\n\nThese ion propagation measurements provide a vivid illustration not only of the existence of a critical velocity obeying the Landau criterion but also that roton creation and vortex formation constitute different phenomena and can exist concurrently.[^60] The vortex emission threshold displays other noteworthy features. ", "It depends on temperature in a non-trivial way, comparable to that of the phase-slip and also shows the marked dependence on $^3$He impurity concentration observed for phase slips in micro-aperture flows but not in larger channels. ", "In both ion propagation and aperture flow measurements, vortex formation displays similar features.", "\n\nAltogether, a study of the experimental data in superfluid $^4$He reveals three different, well-defined, types of critical velocities; one, the celebrated Landau critical velocity, $v_\\m L$, observed in $^4$He only for ion propagation; another, $v_\\m F$, that appears to follow the Feynman criterion as shown in Fig.\\[TwoCriticalVelocities\\] with all the uncertainties on the hydrodynamical process of vortex creation in larger channels; and a third, $v_\\m c$, for phase slips, in want of an explanation: how are the vortices of phase slips in aperture flow created, and how does the situation differ from that in larger channels?", "\n\nThe short answer, based on qualitative evidence, is that the temperature dependence of $v_\\m c$ and its stochastic properties clearly point toward a process of nucleation by thermal activation above $\\sim$150 mK or so and by quantum tunnelling below. ", "This conclusion contradicts the common-place daily observations of the formation of whirlpools and eddies, and also the widely held belief that large scale topological defects with a quantum charge of circulation cannot appear out of nowhere in the superfluid. ", "It will be seen to hold in $^4$He only because the nucleated vortices have nanometric size, a fact that came to be appreciated because of the detailed analysis of phase slippage observations related below.", "\n\nPhase slip critical velocity: a stochastic process {#PhaseSlipCriticalVelocity}\n==================================================\n\nA more firmly established answer to the question formulated above comes from a quantitative analysis of the experimental data for phase slips. ", "The clues given below conclusively show that, in small apertures, vortices are nucleated by thermal activation above about 150 mK, and by quantum tunnelling below.[^61]\n\nThe first piece of evidence for the nucleation of vortices, that is their creation [*ex nihilo*]{}, rests on the temperature dependence of the phase-slip critical velocity shown in Fig.\\[vc\\]. ", "This figure, as Fig.\\[TwoCriticalVelocities\\] (and Fig.\\[Delta-vc\\] to be discussed further on), represents an attempt to compare data from different groups. ", "The data points are scattered but a general trend emerges. ", "The phase slip critical velocity increases in a near-linear manner when the temperature decreases from 2 K to $\\sim\\,$0.2 K. That is, the functional dependence of $v_{\\m c}$ upon $T$ goes as $v_{\\m c} =\nv_0(1-T/T_0)$. The data depart from this linear dependence below 200 mK, where they reach a plateau, and above 2 K because the critical velocity goes to zero at $T_{{\\mbox{\\footnotesize{{\\usefont{U}{psy}{m}{n}l}}}}}$.\n\nThis temperature dependence, first observed in 1985 at Orsay [@Varoquaux:87; @Varoquaux:01a] and now a well-established experimental fact [@Zimmermann:98], [@Steinhauer:95] is very telling. ", "It came as a surprise at first because the critical velocities observed before were temperature-independent below $\\sim$1 K. As the quantum fluid is nearly fully in its ground state below 1 K – the normal fluid fraction becomes less than 1 % – one is led to suspect that a Arrhenius-type process must come into play. ", "If such is the case, that is, if thermal fluctuations in the fluid with an energy of at most a few $k_\\m B T$ can trigger the appearance of fully-formed vortex out of nowhere, the energy of this vortex must also be of the order of a few $k_\\m B T$: it must be a very small vortex. ", "But very small vortices require rather large superfluid velocities to sustain themselves – as seen on Eq.(\\[RingVelocity\\]). ", "That these requirements can be met emerges from a detailed quantitative analysis of the experimental data in the framework of nucleation process.", "\n\nThe nucleation rate for a thermally activated process is expressed by Arrhenius’s law: $$\\label{Kramers}\n{\\mathit\\Gamma}_{\\mathrm K} =\n\\frac{\\omega_0}{2\\pi}\\,\\left[(1+\\alpha^2)^{1/2}-\\alpha\\right] \n \\exp\\left\\{-\\frac{E_\\m a}{k_{\\m B}T}\\right\\}\\;.$$ where $\\omega_0/2\\pi$ is the attempt frequency and $E_\\m a$ the activation energy of the process, which depends on the velocity $v_\\m p$ and, more weakly, on the pressure $P$ and the temperature $T$. The correction for dissipation in the square brackets has been introduced by @Kramers:40 to describe the escape of a particle trapped in a potential well and interacting with a thermal bath in its environment. ", "The particle undergoes Brownian motion fluctuations and experiences dissipation. ", "This dissipation is characterised by a dimensionless coefficient $\\alpha = 1/(2\\omega_0\\tau)$, $\\tau$ being the time of relaxation of the system toward equilibrium. ", "In superfluid helium, dissipation is small. ", "Although some dissipation is necessary for the system to reach equilibrium with its environment, its influence on the thermal activation rate is very small and will be neglected in the following. ", "However, this will not be anymore so in the quantum regime, considered below, because dissipation causes decoherence.", "\n\nThe expression for the critical velocity that stems from the Arrhenius rate, Eq.(\\[Kramers\\]), is derived as follows. ", "In experiments such as those shown in Fig.\\[PhaseSlipsCanJPhys\\], the velocity varies periodically at the resonance frequency as $v_\\m p\\,\\cos(\\omega t)$, $v_\\m p$ being the peak velocity of the potential flow. ", "The probability that a phase slip takes place during the half-cycle $\\omega t_\\m i = -\\pi/2\\, ,\\; \\omega t_\\m f = \\pi/2$ is $$\\begin{aligned}\n \\label{probability}\n p &=& 1 - \\exp\\left\\{-\\int_{t_\\m i}^{t_\\m f}\n \\mathit\\Gamma_{\\m K}(P,T,v_\\m p\\cos(\\omega t')\\right\\} dt'\n \\\\ \n &=& 1 - \\exp\\left\\{\n -\\frac{\\omega_0}{2\\pi\\omega}\\sqrt{\\frac{-2\\pi k_\\m B T}\n {v_\\m p \\left. ", "\\left. ", "\\partial{E_\\m a} \\right/ \\partial{v} \\right|_{\\m t=0}}}\n \\exp \\left\\{ -\\frac{E_\\m a}{k_\\m B T} \\right\\}\n \\right\\} . ", " \\nonumber \\end{aligned}$$ The last equation (\\[probability\\]) results from an asymptotic evaluation of the integral at the saddle point $t=0$.\n\n-5 mm  Critical velocity, normalised to the zero temperature linear extrapolation value $v_0$, [*vs*]{} $T$, in kelvin: ($\\diamond$), @Avenel:93, for ultra-pure $^4$He; ($\\scriptstyle\\triangle$), @Zimmermann:98. ", "The plain curves are computed from the half-ring model (see §\\[HalfRingModel\\]) for $a_0$ = 2.2, 3.2, 4.5, 6.0 Å and are normalised to match the experimental value at 0.5 K. The inset shows the influence of $^3$He impurities on $v_\\m c$: ($\\circ$), 3 ppb $^3$He in $^4$He; ($\\scriptstyle\\triangle$), 45 ppb, from @Varoquaux:93. ", "Adapted from [@Varoquaux:01a]. ](", "Fig12.pdf \"fig:\"){width=\"85\"}\n\nThe critical velocity $v_\\m c$ is defined as the velocity for which $p=1/2$. This definition is independent of the experimental setup, except for the occurrence in Eq.(\\[probability\\]) of the natural frequency of the hydromechanical resonator $\\omega$. The implicit relation between $v_\\m c$ and $E_\\m a$ then reads: $$\\label{CriticalVelocity}\n\\frac{\\omega_0}{2\\pi\\omega}\\sqrt{\\frac{-2\\pi k_\\m BT}\n {v_\\m c \\left. ", "\\left. ", "\\partial{E_\\m a} \\right/ \\partial{v}\n \\right|_{v_\\m c}}}\n \\exp \\left\\{ -\\frac{E_\\m a(P,T,v_\\m c)}{k_\\m B T} \\right\\} = \\ln 2 \\; .$$\n\nIn Eq.(\\[CriticalVelocity\\]), the attempt frequency is normalised by the resonator drive frequency: the Brownian particle attempts to escape from the potential well at rate $\\omega_0/2\\pi$ but an escape event is likely only in the time window in a given half-cycle of the resonance during which the energy barrier stays close to its minimum value $E_\\m a(v_\\m c)$. This time interval is inversely proportional to $\\omega$, which explains why an instrumental parameter gets its way into Eqs.(\\[probability\\]) and (\\[CriticalVelocity\\]).", "\n\n Statistical width of the critical velocity transition, normalised to the linear extrapolation limit at $T=0$, $v_0$, in terms of temperature: ($\\diamond$), @Avenel:93; ($\\scriptstyle\\triangle$), @Zimmermann:98; ($\\times$), @Steinhauer:95. ", "The plain curves are computed as in Fig.\\[vc\\] for four values for $a_0$. Adapted from @Varoquaux:01a.](Fig13.pdf){width=\"75mm\"}\n\nThe velocity at which each individual critical event takes place is a stochastic quantity. ", "Its statistical spread can be characterised by the \\`\\`width” of the probability distribution defined [@Avenel:93; @Zimmermann:90] as the inverse of the slope of the distribution at $v_\\m c$, $\\left({\\partial p/\\partial\n v|_{v_\\m c}}\\right)^{-1}$. This critical width is found to be expressed by: $$\\label{Width}\n\\Delta v_\\m c = - \\frac{2}{\\ln 2}\n \\left[\n \\frac{1}{2}\\left\\{\n \\frac{1}{v_\\m c}+\\left.\\left. ", "\\frac{\\partial^2E_\\m a}{\\partial\n v^2}\\right|_{v_\\m c}\n \\right/\\left.\\frac{\\partial E_\\m a}{\\partial v}\\right|_{v_\\m c}\n \\right\\}\n + \\frac{1}{k_\\m B T}\\left.\\frac{\\partial E_\\m a}{\\partial\n v}\\right|_{v_\\m c}\n \\right]^{-1} \\; .$$\n\nThe quantities $v_\\m c$ and $\\Delta v_\\m c$ are derived from $p$, itself obtained by integrating the histograms of the number of nucleation events ordered in velocity bins. ", "The outcome of this procedure is illustrated in Fig.\\[PR02-pure-proba\\]: $p$ shows an asymmetric-[*S*]{} shape characteristic of the double exponential dependence of $p$ on $v$, Eq.(\\[probability\\]), a consequence of Arrhenius’s law, Eq.(\\[Kramers\\]), being plugged into a Poisson probability distribution. ", "The observation of this asymmetric-[*S*]{} probability distribution constitutes an additional experimental clue for the existence of a nucleation process. ", "The quantities $v_\\m c$ and $\\Delta v_\\m c$ are easily extracted from the probability curves $p(v)$, but the inverse path from $v_\\m c$ and $\\Delta v_\\m\nc$ back to $E_\\m a(v)$ and $\\omega_0$ by numerical integration of the differential equation (\\[CriticalVelocity\\]) leads to inaccurate results.", "\n\n![ ", "\\[PR02-pure-proba\\] (Color online) Probability $p$ [*vs*]{} phase slip velocity in winding number. ", "The plain curve is a non-linear least square fit to the analytic form Eq.(\\[probability\\]), which contains two adjustable parameters, $v_\\m c$ and $\\Delta v_\\m c$. The critical velocity resulting from this distribution of the measured values is defined as the fit value for $p=1/2$. The critical velocity distribution width is given by the slope at $p=1/2$. From @Varoquaux:03.](Fig14.pdf){width=\"65mm\"}\n\nIn view of these difficulties @Varoquaux:03 improved the data analysis by obtaining the escape rate $\\mathit\\Gamma(v)$ directly from the phase slip data. ", "This rate is the ratio in any velocity bin of the number of slips that have occurred at that velocity to the total time spent by the system at that given velocity. ", "The outcome of this procedure is illustrated in Fig.\\[PR02-pure-rate\\]. ", "The slope of $\\ln \\mathit\\Gamma(v)$ directly yields $\\left.{\\partial E_\\m a/\\partial v} \\right|_{v_\\m c}$; the value of $\\ln \\mathit\\Gamma$ at $v_\\m c$ gives a combination of $\\ln\\omega_0$ and $E_\\m\na(v_\\m c)$.\n\nThe need to solve Eq.(\\[CriticalVelocity\\]) has been alleviated but to cleanly disentangle these two quantities and solve this inverse problem is still error prone. ", "At this point experiment itself offers help as will shortly be shown.", "\n\n![ ", "\\[PR02-pure-rate\\] Nucleation rate $\\mathit\\Gamma$ expressed in s$^{-1}$ on a semi-logarithmic scale [*vs*]{} slip velocity in winding number in ultra-pure $^4$He at 17.70 mK and saturated vapour pressure. ", "The line is a linear fit to the data. ", "From @Varoquaux:03. ](", "Fig15.pdf){width=\"70mm\"}\n\nVortex nucleation: thermal [**[*vs*]{}**]{} quantum {#VortexNucleation}\n----------------------------------------------------\n\nBelow $\\sim$ 0.15 K, the phase slip critical velocity $v_\\m c$ suddenly ceases to vary with $T$, as seen in Fig.\\[vc\\] for ultra-pure $^4$He, $v_\\m c(T)$ remains flat down to the lowest temperatures ($\\sim\\,$12 mK). ", "The effect of $^3$He impurities, shown in the inset, could mimic the appearance of such a plateau but is ruled out because of the extreme purity of the $^4$He sample, which contains less than 1 part in 10$^9$ of $^3$He impurities. ", "The crossover between these two regimes is very sharp. ", "At the same crossover temperature $T_\\m q$, $\\Delta v_\\m c$ also levels off sharply. ", "It is believed on experimental grounds that this saturation is intrinsic and is not due to stray heating or parasitic mechanical vibrations [@Avenel:93].", "\n\nIf the nucleation barrier were undergoing an abrupt change at $T_\\m q$, for instance because of a bifurcation toward a vortex instability of a different nature [@Josserand:95], in all likelihood $\\Delta v_\\m c$ would jump to a different value characteristic of the new process (presumably small since $v_\\m c$ reaches a plateau). ", "Such a jump is not observed in Fig.\\[Delta-vc\\]. ", "Furthermore, $v_\\m c$ levels off below $T_\\m q$, which would imply through Eq.(\\[CriticalVelocity\\]) that $E_a$ becomes a very steep function of $v$, but $\\Delta v_\\m c$ also levels off, which, through Eq.(\\[Width\\]), would imply the contrary. ", "This discussion leads one to investigate the possibility that, below $T_\\m q$, thermally-assisted escape over the barrier gives way to quantum tunnelling under the barrier [@Ihas:92]. ", "This switch from thermal to quantum does induce plateaus below $T_\\m q$ for both $v_\\m c$ and $\\Delta v_\\m c$.\n\nIndependently of these phase slippage studies, the group of Peter McClintock at Lancaster had also reached the conclusion from their ion propagation experiments of the existence of a crossover around 300 mK from a thermal to a quantum regime for the nucleation of vortices [@Hendry:88], as predicted by Muirhead, Vinen, and Donnelly [@Muirhead:84]. ", "There certainly are significant differences between the ion limiting drift velocity and aperture critical flow – in particular, the latter is nearly one order of magnitude smaller – but the qualitative similarities are strikingly telling. ", "The two completely different types of experiments indicate that vortices would appear as a result of a nucleation process on a nanometric scale, both in a thermal regime above $T_\\m q$ and in a quantum one below.", "\n\nThe macroscopic quantum tunnelling rate\n---------------------------------------\n\nTaking this hint at face value, zero point fluctuations are now assumed to overtake thermal fluctuations below $T_\\m q$: the potential barrier is not surmounted with the assistance of a large thermal fluctuation, it is tunnelled under quantum-mechanically; the quantum-tunnelling event is “assisted” by the zero point fluctuations, so to speak [@Martinis:88], in the same manner as the Arrhenius process is assisted by thermal fluctuations. ", "What is remarkable here, and not so easy to admit at first, is that such a tunnelling process affects a macroscopic number of atoms, those necessary to form a vortex of about 50 Å in length, as turns out to be the case.", "\n\nThese “macroscopic quantum tunnelling” (MQT) processes have been the object of numerous experimental and theoretical studies, mainly in superconducting Josephson devices [@Caldeira:83a] . ", "The case for vortices in helium can be worked out in a similar manner.", "\n\nThe quantum tunnelling rate of escape of a particle out of a potential well $V(q)$ is a textbook problem.[^62] The rate is proportional to $\\exp{-S/\\hbar}$, $S$ being, in the WKB approximation, the action of the escaping particle along the saddle-point trajectory at the top of the potential barrier, the so-called “bounce” [@Coleman:77]. ", "For a particle of mass $m$ and energy $E$ escaping from a one-dimensional barrier $V(q)$, this action reads $$\\label{Action}\n S = 2 \\int_{q_1}^{q_2} \\m d q \\sqrt{2m[V(q)-E]} \\; .$$ The determination of the bounce yields the generalised coordinates $q_1$ and $q_2$ of the points at which the particle enters and leaves the barrier. ", "A discussion of the quantum tunnelling of vortices in terms of Eq.(\\[Action\\]) thus requires a Lagrangian formulation of vortex dynamics. ", "Such a formulation has been carried out in particular by @Sonin:95 [^63] and by @Fischer:00. ", "However, analytic results can be obtained only at the cost of approximations that yield a less than fair comparison with experiments as discussed by @Varoquaux:01a.", "\n\nA simplified and more productive approach can be borrowed from the literature for Josephson devices. ", "Extending the work of @Caldeira:83a, and @Larkin:84 to vortices in helium, @Varoquaux:06 has used for $V(q)$ a simple analytic form reduced to a sum of two terms, respectively parabolic and cubic in $q$: $$\\label{CubicParabolic}\n V(q) = V_0 + \\frac{1}{2}m\\omega_0^2 q^2 \n \\big(1-\\frac{2q}{3q_\\m b}\\big)\\; ,$$ where $\\omega_0$ is the angular frequency of the lowest mode of the trapped particle (that will be found comparable to the attempt frequency) and $q_\\m b$ the generalised coordinate of the barrier top location. ", "The barrier height $E_\\m\nb$ is expressed in terms of these two parameters by $m\\omega_0^2 q_\\m b^2/6$.\n\nEquation (\\[CubicParabolic\\]) expresses the vanishing potential barrier height when the applied velocity reaches the limiting velocity, $v_{\\m c0}$ at which the system “runs away”, the so-called “lability” point.[^64] At this point where the system becomes labile, the critical velocity is reached even in the absence of thermal or quantum fluctuations. ", "Such a hydrodynamic instability threshold at which vortices appear spontaneously has been shown to occur in numerical simulations of flows past an obstacle using the Gross-Pitaevskii equation by @Frisch:92 and others.[^65]\n\nThe zero-temperature WKB tunnelling rate for the phenomenological cubic-plus-parabolic potential $E_\\m b$, Eq.(\\[CubicParabolic\\]), is found to be [@Caldeira:83a] $$\\label{ZeroTemperature}\n \\mathit\\Gamma_0 =\\frac{\\omega_0}{2\\pi}\\, \\left(120\\pi\\, \\frac{S_0}{\\hbar}\\right)^{1/2}\n \\exp -\\frac{S_0}{\\hbar} \\; ,$$ the action $S_0$ being equal to $36 E_\\m b/5\\omega_0$.\n\nFrom this result, it can be anticipated that the crossover between the quantum and the thermal regime lies around a temperature close to that for which the exponents in Eqs.(\\[Kramers\\]) and (\\[ZeroTemperature\\]) are equal, namely $T = 5\\omega_0/36 k_\\m B$ – assuming that the activation energy in Eq.(\\[Kramers\\]), $E_\\m a$, reduces to the simple cubic-plus-parabolic form, $E_\\m b$. A more precise study of the mathematical properties of the quantum channel for escape leads to the following relation [@Melnikov:91] $$\\label{Crossover}\n \\hbar \\omega_0 = 2 \\pi k_B T_\\m q \\; .$$ Thus, from the experimental knowledge of the temperature of the crossover from thermal to quantal, $\\omega_0$ is fixed to pinpoint accuracy by Eq.(\\[Crossover\\]). ", "Its value agrees with that (less precisely determined) obtained from the analysis of the Arrhenius regime outlined in the previous paragraph: some degree of self-consistency has been achieved. ", "The values of the barrier height $E_\\m b$ at each given velocity then follow easily, using the full expressions for the rate in terms in terms of $E_\\m b$, $\\omega_0$ and, also, for the damping parameter $\\alpha$ as discussed below.", "\n\nFriction in MQT {#Friction}\n---------------\n\nDamping turns out to matter significantly for quantum tunnelling of semi-macroscopic objects, contrarily to the thermal regime. ", "The relevance and applicability of the concept of quantum tunnelling to macroscopic quantities such as the electric current through a Josephson junction or the flow of superfluid through a micro-aperture, although still sometimes questioned, have been checked in detail for the electrodynamic Josephson effect [@Martinis:87]. ", "One of the conceptual problems is that, when a macroscopic quantum system is coupled to an environment that acts as a thermal bath, the coupling gives rise to a source of classical fluctuations and friction. ", "The quantum process suffers decoherence and is profoundly affected.", "\n\nThis issue was tackled by Caldeira and Leggett [@Caldeira:83a], and a number of other authors.[^66] For weak frequency-independent damping ($\\alpha \\ll 1$) and the cubic-plus-parabolic potential, the tunnelling rate takes the form: [^67] $$\\label{QuantumRate}\n \\begin{split}\n {\\mathit\\Gamma}_{\\m{qt}}= \n & \\frac{\\omega_0}{2\\pi}\n \\,\\left(864\\pi\\,\\frac{E_\\m b}{\\hbar\\omega_0}\\right)^{1/2} \n \\times\\exp\\left\\{-\\,\\frac{36}{5}\\,\\frac{E_\\m b}{\\hbar\\omega_0}\n \\left[1+\\frac{45\\zeta(3)}{\\pi^3}\\alpha\\right]^{} \\right.", "\n \\\\\n &\\left. ", "+\\frac{18}{\\pi}\\alpha\\,\\frac{T^2}{T_\\m q^2}+\n {\\mathcal O}\\left(\\alpha^2,\\,\\alpha\\,\\frac{T^4}{T_\\m q^4}\\right)\\right\\}\n \\; .", "\n \\end{split}$$ According to Eq.(\\[QuantumRate\\]), damping depresses the MQT escape rate at $T=0$ – $\\alpha$ being a positive quantity – and introduces a temperature dependence that increases the rate as $T$ increases. ", "These effects are large, even for weak damping, because they enter the exponent of the exponential factor in Eq.(\\[QuantumRate\\]). ", "Relation (\\[Crossover\\]) between $T_\\m q$ and $\\omega_0$ is nearly unaffected by damping: $\\omega_0$ is simply changed into $\\omega_0[(1+\\alpha^2)^{1/2} -\\alpha]$ according to Eq.(\\[Kramers\\]), a minor modification for $\\alpha\\ll 1$.\n\n![ ", "\\[PotentialWell\\] Potential well trapping a particle in one dimension. ", "The particle can escape to the continuum of states to the right. ", "The lowest mode at the bottom of the well has angular frequency $\\omega_0$; $\\omega_\\m b$ would be the corresponding quantity if the potential was inverted bottom over top. ", "For the simple case of Eq.(\\[CubicParabolic\\]), $\\omega_0=\\omega_\\m b$. There can exist intermediate energy levels within the well, which are populated according to the Boltzmann factor. ", "Particle escape can take place by quantum tunnelling “under” the barrier or by thermal activation “over” the barrier. ", "The intermediate energy levels can be used as ladder rungs by the particle attempting to escape. ", "These processes are embedded in Eq.(\\[GeneralKramers\\]).](Fig16.pdf){width=\"40\"}\n\nEquation (\\[QuantumRate\\]) is valid up to about $T_\\m q/2$. From $T_\\m q/2$ to $\\sim T_\\m q$, one has to resort to numerical calculations [@Grabert:87]. ", "In the thermal activation regime, $T\\gtrsim T_\\m q$, quantum corrections affect the Kramers escape rate up to about $3\\,T_\\m q$ and can be evaluated analytically. ", "These high-temperature quantum corrections depend only weakly on friction. ", "A complete solution of the problem of the influence of friction, weak, moderate or strong, has first been worked out in the classical regime ($T\\gg T_\\m q$) by @Grabert:88 and extended to the temperature range $T\\gtrsim T_\\m q$ by @Rips:89 who showed that the rate for arbitrary damping can be factorised in three terms, $$\\label{GeneralKramers}\n{\\mathit\\Gamma} = \\,f_\\m q\\,{\\mathit\\Upsilon}\\,\\mathit\\Gamma_\\m K \\;,$$ each term having a well-defined physical meaning: ${\\mathit\\Gamma}_\\m K$ is the classical Kramers rate, $f_\\m q$ the quantum correction factor, and $\\mathit\\Upsilon$ the depopulation factor. ", "The high temperature limit of $f_\\m q$ is $$\\label{LeadingQuantumCorrection}\nf_\\m q =\n\\exp \\left\\{\\frac{\\hbar^2}{24} \\frac{(\\omega_0^2+\\omega_\\m b^2)}{(k_{\\m B}T)^2}\n +{\\mathcal O}(\\alpha/T^3,1/T^4)\\right\\} \\; ,$$ in which $\\omega_0$ and $\\omega_\\m b$ are the confining potential parameters depicted in Fig.\\[PotentialWell\\]. ", "Analytic results for $f_\\m q$ are known to slightly below $T_\\m q$ [@Grabert:87; @Hanggi:90].", "\n\nThe depopulation factor $\\mathit\\Upsilon$ arises from the depletion of the occupancy of the energy levels inside the potential well in the course of the escape process. ", "This depletion occurs when the intermediate levels, if they exist, are not replenished fast enough by the thermal fluctuations. ", "For the nucleation of vortices, friction turns out to always be both sufficient and not too large so that depopulation corrections remain small and $\\mathit\\Upsilon \\sim 1$.\n\n![ ", "\\[EscapeRate\\] Logarithm of the escape rate normalised to the attempt frequency in terms of inverse temperature, also normalised to $\\omega_0$ for various values of the damping parameter $\\alpha$ [@Grabert:87]. ", "The dotted line is a hand-sketch of the situation where $\\alpha$ increases with temperature, starting from zero at $T=0$ (see §\\[Friction\\]). ", "From @Varoquaux:03. ](", "Fig17.pdf){width=\"55mm\"}\n\nThe escape rate can be calculated over the full temperature range by piecing together Eqs.(\\[Kramers\\]), (\\[QuantumRate\\]), (\\[GeneralKramers\\]) and (\\[LeadingQuantumCorrection\\]). ", "The results for three values of the damping parameter $\\alpha$ are shown in Fig.\\[EscapeRate\\]. ", "A hand-sketched line pictures the escape rate for $\\alpha$ varying from zero at $T=0$ to 0.5 above $T_\\m q$: it is seen to actually decrease when the temperature increases from absolute zero. ", "This unique situation is found in the nucleation of vortices in $^4$He as will now be described.", "\n\nExperimental energy barrier and damping coefficient {#ExperimentalEnergyBarrier}\n---------------------------------------------------\n\nThe knowledge of the rate $\\mathit\\Gamma$ makes it possible to extract from the measured nucleation rate and crossover temperature the values of the energy barrier in terms of $v_\\m c$. The value of $\\omega_0$ given by Eq.(\\[Crossover\\]) ($\\omega_0/2\\pi = 2\\times10^{10}$ Hz for $T_q$=0.147 K) is consistent with the attempt frequency appropriate to the thermally-activated regime [@Varoquaux:86] and that found directly from the fits to the probability $p$ as shown in Fig.\\[PR02-pure-proba\\]. ", "This agreement has been mentioned above.", "\n\nThis value of $\\omega_0$ is comparable to the highest Kelvin mode eigenfrequency that a vortex filament in $^4$He can sustain. ", "The Kelvin modes are helical waves with a dispersion relation expressed for a straight isolated vortex by $$\\label{KelvinMode}\n\\omega^{\\ts\\pm} = \\frac{\\kappa_4}{\\pi\\,a_0^2}\\left[1\\pm\n \\left\\{1 +ka_0\\left[\\frac{\\mbox{K}_0(ka_0)}{\\mbox{K}_1(ka_0)}\n \\right]\\right\\}^{\\frac{1}{2}}\\right] \\;,$$ where $\\mbox{K}_0$ and $\\mbox{K}_1$ are the modified Bessel functions of zeroth and first orders.[^68] In the short wavelength limit, $k^{-1} \\rightarrow 0$, the high frequency mode reduces to: $$\\label{HighFrequency}\n\\omega^{\\ts +} = \\frac{\\kappa_4}{\\pi a_0^2} \\;.$$ Equation (\\[HighFrequency\\]) sets the shortest time scale on which vortices can be expected to respond.", "\n\nBy analogy with the 2D-motion of point electric charges subjected to a [*rf*]{} magnetic field [@Muirhead:85], this frequency is sometimes called the “cyclotron” frequency. ", "This frequency is that of the cycloidal motion taken by a long hollow cylinder impulsively pulled sideways in an inviscid fluid [@Donnelly:91]. ", "The cylinder stands for the vortex core, assumed to be hollow and with radius $a_0$. The displaced mass per unit length of such a cylinder is $\\rho \\pi a_0^2$. For high frequency motions, the vortex mass is modified as discussed in §\\[ImpulseAndMass\\], and Eq.(\\[HighFrequency\\]) is renormalised to $\\omega^{+}= \\kappa_4/[\\pi a_0^2 {\\m{ln}}(r_\\m m/a_0)]$, $r_\\m m$ being defined below Eq.(\\[FlowEnergy\\]). ", "With $a_0=2.5$Å and $r_\\m m/a_0 \\sim 10$, $\\omega^{\\ts +}/2\\pi = 3.5\\, 10^{10}$ Hz, a value comparable to the attempt frequency given by Eq.(\\[Crossover\\]). ", "That the attempt frequency be linked to the highest frequency that the nucleating vortex can sustained makes good physical sense.", "\n\nWith the known value of $\\omega_0$, the energy barrier $E_\\m b$ can be extracted from the measured rate with the help of Eqs.(\\[QuantumRate\\]) and (\\[GeneralKramers\\]). ", "These values of $E_\\m b$ for the experiments on ultra-pure $^4$He analysed by @Varoquaux:03 are shown in Fig.\\[ExperimentalEb\\]. ", "The high $T$ and low $T$ analyses are seen to yield consistent results in the region where they overlap.", "\n\n The barrier energy $E_\\m b$ in kelvin [*vs*]{} $v$, the mean velocity in the aperture expressed in phase winding numbers and obtained from the nucleation rate data of @Varoquaux:03: ($\\scriptstyle{\\blacksquare}$), low temperature data transformed using the numerical tables of @Grabert:87; ($\\lozenge$), high temperature data. ", "From @Varoquaux:03. ](", "Fig18.pdf){width=\"68mm\"}\n\n Arrhenius plot $\\ln\n \\mathit\\Gamma(v)$ [*vs*]{} $1/T$, $\\mathit\\Gamma$ being expressed in s$^{-1}$ and $T$ in kelvin, as measured at varying $T$ and $v_\\m c$ for two ultra-pure $^4$He samples ($\\lozenge$) and ($\\triangle$); ($\\ast$) and ($\\blacktriangle$) after correction for the change of the velocity with $T$. The plain and the dot-dot curves are calculated from the experimental barrier energy $E_\\m b$ represented in Fig.\\[ExperimentalEb\\]. ", "From @Varoquaux:03. ", "In the inset, $\\ln \\mathit\\Gamma(v_\\m q)$, ($\\scriptstyle\\blacksquare$), has been obtained with smoothed values of $v_\\m c$. The curves represent the calculated values of $\\ln {\\mathit\n \\Gamma(v_\\m q)}$ with $\\alpha= 0$ (dash-dash) or varying with $T$ (plain). ", "The latter gives a better representation of the data and illustrates the influence of damping depicted by the dot-dot line in Fig.\\[EscapeRate\\]. ](", "Fig19.pdf){width=\"85mm\" height=\"65\"}\n\nThe quantitative analysis can be carried out one step further using the variation of the barrier energy $E_\\m b$ in terms of $v$ to construct a Arrhenius plot – the logarithm of the escape rate $\\mathit\\Gamma$ in terms of the inverse temperature [*for a fixed potential well*]{} – from the experimental data and comparing directly the outcome to the results from theory. ", "Arrhenius plots are drawn at constant $E_\\m b$ and varying temperature but the experimental results are obtained at velocities that vary with temperature, hence at varying $E_\\m b$. The correction can be computed from the experimentally determined $E_\\m b$ given in Fig.\\[ExperimentalEb\\]. ", "The final outcome for the nucleation rate data of @Varoquaux:03 in ultra pure $^4$He is plotted in Fig.\\[ArrheniusPlot\\].", "\n\nAs can be noted in Fig.\\[ArrheniusPlot\\], the raw experimental, velocity-dependent rates exhibit little variation over the range of parameters: escape rates are only observed in a certain window determined by the measuring technique. ", "At low temperatures, $T< T_\\m q$, the critical velocity is close to its zero temperature limit $v_\\m q$ and the corrections to $\\mathit\\Gamma$ are small. ", "As $T$ increases above $T_\\m q$, $v_\\m c$ decreases and $\\mathit\\Gamma$ has to be determined by piece-wise integration of $\\m d \\ln\\mathit\\Gamma / \\m d v$. The high temperature extrapolation for $\\mathit\\Gamma$ obtained in such a manner does display the usual $1/T$ dependence.", "\n\nIn the intermediate temperature range, the corrected $\\mathit\\Gamma$ shows, as can be seen in the inset of Fig.\\[ArrheniusPlot\\], a small but real drop below its zero temperature limit as the temperature is raised. ", "This drop reveals the influence of damping on the escape rate illustrated in Fig.\\[EscapeRate\\]. ", "A damping coefficient $\\alpha$ that increases from 0 at $T=0$ to $\\sim\\,0.1$ around $T_\\m q$ and more slowly above accounts for the observed drop [@Varoquaux:03]. ", "This $T$-dependent dissipation also makes the crossover between the thermal and the quantum regimes even sharper than for $\\alpha = 0$, and closer to observations. ", "The nucleation of vortices in $^4$He thus offers a rare observation of the effect of damping on MQT.", "\n\nThe vortex half-ring model\n--------------------------\n\n  \\[HalfRingModel\\]\n\nThe case has been put so far for the nucleation of vortices, thermal or quantal. ", "The nucleation barrier $E_\\m b$ is of the order of a few kelvins (see Fig.\\[ExperimentalEb\\]) and the attempt frequency $\\sim 2\\times10^{10}$ Hz, close to that of the highest Kelvin wave mode.", "\n\nA simple model accounts for these features. ", "This model – the nucleation of vortex half-rings at a prominent asperity on the walls – finds its roots in the work of @Langer:67b, @Langer:70, @Volovik:72, and @Muirhead:84. ", "It was further developed and put on the firm experimental findings described above by @Avenel:93.", "\n\nThe model premises are the following. ", "Consider, as done by @Langer:70, the homogeneous nucleation of a vortex ring in a homogeneous flow $v_\\m s$ extending over large distances. ", "When the ring has grown to reach radius $R$ in a plane perpendicular to the flow, its energy in the laboratory frame, where the observer is at rest and sees the superfluid moving at velocity $v_\\m s$, is expressed by $$\\label{VortexFreeEnergy}\n E_\\m v = E_\\m R - P_\\m R v_\\m s \\; .$$ The rest energy $E_\\m R$ and impulse $P_\\m R$ of the vortex ring are given by Eqs.(\\[RingEnergy\\]) and (\\[RingImpulse\\]). ", "The minus sign in the right hand side of Eq.(\\[VortexFreeEnergy\\]) arises because the vortex opposes the flow, that is, its impulse $P_\\m R$ points straight against $v_\\m s$: this configuration minimises $E_\\m v$.\n\n![ ", "\\[Ev\\] Energy barrier $E_\\m v$ normalised by $\\rho_\\m s\n \\kappa_4^2 a_0$ and expressed in kelvin [*vs*]{} the vortex radius $R/a_0$ for the vortex half-ring model. ", "This figure illustrates various potential forms given by Eq.(\\[VortexFreeEnergy\\]) at various superfluid flow velocities taken from the data in Fig.\\[vc\\] at, from top down, $T\\rightarrow T_{{\\mbox{\\footnotesize{{\\usefont{U}{psy}{m}{n}l}}}}}$, 1 K, 0.5 K and at the quantum crossover $T_\\m q$. The lowest curve illustrates the situation in which the potential barrier vanishes and the trapped particle runs away, the so-called lability point. ", "Adapted from @Avenel:93. ](", "Fig20.pdf){width=\"70mm\"}\n\nThe rest energy $E_\\m R$ increases with vortex size as $R\\ln R$ and the impulse $P_\\m R$ as $R^2$: the impulse term becomes dominant at large radii and causes $E_\\m v$ to become negative. ", "The variation of $E_\\m v$ in terms of $R$ has the shape of a confining well potential, which becomes shallower and shallower with increasing $v_\\m s$, as depicted in Fig.\\[Ev\\]. ", "The barrier height can easily be computed numerically and plugged into the expression for $v_\\m c$, Eq.(\\[CriticalVelocity\\]). ", "An analytic approximation for $v_\\m c$ involving the neglect of logarithmic terms and valid for large vortices ($R\\gg a_0$) has been given by @Langer:70.", "\n\nThis critical process would yield a mist of vortices in the bulk of the superfluid. ", "This sort of vorticity condensation does not take place for two reasons. ", "First, the velocity of potential flows, which follows from the Laplace equation, reaches its maximum value at the boundaries, not in the bulk. ", "Secondly, the nucleation of a vortex half-ring at the boundary itself involves, for the same radius hence the same self-induced velocity, a half of the energy given by Eq.(\\[VortexFreeEnergy\\]); for that reason alone, half-ring nucleation at walls is always much more probable at the same velocity $v_\\m s$ than full ring nucleation in the bulk.", "\n\nHalving the full-ring energy for the half-ring holds for classical hydrodynamics, the other half being taken care of by the image in the plane boundary. ", "For a superfluid vortex, the actual energy of a half-ring is smaller than in the classical ideal fluid because the superfluid density is depleted at the solid wall and the core radius increases.", "\n\nThe half-ring model for the nucleation of vortices has been proposed for ion critical velocity by @Muirhead:84 and for aperture flows by @Burkhart:94.[^69] A variant, based on a different accounting of the vortex core energy, has been studied by @Zimmermann:98. ", "Other mechanisms have been discussed [@Josserand:95; @Josserand:95b; @Andreev:04] for which it is unclear that the end product of the nucleation process is actually a vortex.", "\n\nThe barrier height for the vortex half-ring nucleation can easily be computed and plugged into the expressions for $v_\\m c$ and $\\Delta v_\\m c$, Eqs.(\\[CriticalVelocity\\]) and (\\[Width\\]). ", "Critical velocities $v_\\m c$ and statistical widths $\\Delta v_\\m c$ computed in such a manner are shown as a function of temperature by the solid lines in Figs.\\[vc\\] and \\[Delta-vc\\] for several values of the vortex core parameter $a_0$. A value of 4.5 Å gives near-quantitative agreement with the experimental observations over the entire temperature range. ", "This value exceeds that in the bulk ($a_0\\simeq 2.5$ Å). ", "This is thought to reflect the proximity of the wall as discussed by @Varoquaux:01a. ", "With this value, the nucleating half-ring has a radius of approximately 15 Å at the top of the barrier and a self-velocity of $v_\\m R = 13.5$ m/sec from Eq.(\\[GroupVelocity\\]); this value compares well with the values shown by open circles in Fig.\\[TwoCriticalVelocities\\].", "\n\n![ ", "\\[trajectory\\] Schematic views in 2D (top) and 3D (bottom) of the vortex half-ring trajectory over a point-like pinhole punched in an infinite horizontal plane. ", "The dashed lines on the 2D plot are the potential flow streamlines that emerge from the pinhole. ", "The 3D view shows the vortex half-ring being first pushed by the potential flow to the right and then flying back over the pinhole to finally drift away to the upper left. ", "Adapted from [@Varoquaux:06].](Fig21a.pdf){width=\"43mm\"}\n\nOnce nucleated, the vortex half-ring floats away, carried out by the superfluid stream at the local superfluid velocity and by its own velocity, $v_\\m R = \\partial E_\\m R/\\partial P_\\m R$. It can be noted that, at the top of the barrier, $\\partial E_\\m v/\\partial R =0$: the vortex self-velocity $v_\\m R$ exactly balances the applied $v_\\m s$; the nucleating vortex is at a near standstill.", "\n\nIf the flow were uniform, with parallel streamlines, nothing much would happen. ", "Downstream from the aperture however, the flow is divergent, as pictured in Fig.\\[trajectory\\]. ", "The vortex half-ring tends to follow the local streamlines and grow under the combined action of the potential flow and its own self-velocity: it then gains energy at the expense of the potential flow as explained in §\\[EnergyExchange\\]. ", "In such a way, it expands from nanometric to micrometric sizes and above, and wanders away. ", "Interaction with the normal fluid, encounters with other vortices and friction on the solid boundaries cause a loss of vortex energy that eventually leads to its disappearance. ", "The vortex in its motion away from the micro-aperture takes a given finite lump of energy to remote places of the cell and never returns.", "\n\nThis scenario for a phase slip produces a change of the phase difference between the two sides of the micro-aperture of exactly $2\\pi$ because the vortex ends up crossing all the streamlines, as pictured in Fig.\\[trajectory\\]. ", "This crossing causes the velocity circulation to change by exactly one quantum $\\kappa_4$ on all the superfluid paths extending from one side of the aperture to the other. ", "Such a dissipative event gives the signature of single phase slips that are seen in Fig.\\[PhaseSlipsCanJPhys\\]. ", "Extensive numerical simulations by @Schwarz:93 [@Schwarz:93c] and @Flaten:06b fully confirm the above scenario for phase slips.", "\n\nThe effect of $^3$He impurities on the phase slip critical velocity at low temperature is striking, as seen in the inset of Fig.\\[vc\\]. ", "It is due to the condensation of these impurities on the vortex cores, which changes their line energy and the potential barrier for nucleation. ", "This impurity dependence, studied in detail by @Varoquaux:93, was used as a local probe of the superfluid velocity at which vortices nucleate. ", "This velocity was found to be 22 m/s, an important piece of information in reasonable agreement with the value derived from the vortex half-ring model.", "\n\nIn all, the model parameters hang fairly well together, showing that specific finer details are probably not very relevant and that the model simplifications are reasonably well founded. ", "It nonetheless remains that the nature and geometry of a typical nucleation site are wholly unspecified and that the enhancement factor between the mean aperture velocity and the velocity at the nucleation site is not under control, as shown in particular by @Shifflett:95.", "\n\nVortex pinning, mills and flow collapse {#AllThat}\n=======================================\n\nSingle phase slips are observed in experimental situations that may be loosely characterised as “clean”, broadly speaking for uncontaminated apertures of relatively small sizes (a few micrometres at the most), with low background of mechanical and acoustical interferences ..., and with probing techniques that do not manhandle the superfluid, namely, with low frequency hydromechanical resonators.", "\n\nWhen these conditions are not met, flow dissipation occurs in a more erratic manner in large bursts – multiple phase slips or “collapses” of the superflow. ", "Such collapses of the superflow through an orifice were first observed by Sabo and Zimmermann, Jr. [^70] and by @Hess:77.", "\n\nMultiple phase slips and collapses constitute an apparent disruption of the vortex nucleation mechanism described in the previous Section. ", "Their properties have been studied in detail by @Avenel:95 and are briefly mentioned below, together with possible mechanisms for their formation. ", "It is likely that these events provide a bridge between the “clean” single phase slip case and the usual situation of the Feynman-type critical velocities that are temperature-independent below 1 K and dependent on the channel size. ", "Preexisting vorticity is widely suspected to come into play in these “extrinsic” critical velocities.", "\n\nPinned vorticity\n----------------\n\n@Awschalom:84 have directly shown the existence of remanent vorticity in $^4$He, which had long been assumed, and have given an estimate of its background level. ", "These authors studied the propagation of ions in the presence of vortex lines. ", "Ions get trapped in the vortex cores and completely change course, revealing the presence of these vortex lines. ", "These vortices, presumably nucleated at the [[l]{}]{} transition when the critical velocity is low and critical fluctuations large, remain stuck in various places of the superfluid sample container. ", "This trapped vorticity, according to @Adams:85, either is quite loosely bound to the substrate and disappears rapidly, or is strongly pinned and dislodged only by strong perturbations.", "\n\nTo achieve a stable configuration, a pinned vortex has to take on a shape such that its local radius of curvature results in a self-velocity that exactly opposes at each of its points the local value of the superflow. ", "This dynamic equilibrium is what is meant here by pinning. ", "Vortex pinning exists in bulk $^4$He as discussed here,[^71] in films,[^72] in $^3$He,[^73] in neutron stars [^74] …\n\nTo account for laboratory observations and with the outcome of extensive numerical simulations of vortex dynamics, Schwarz has proposed the following formula for the velocity at which such strongly pinned vortices unpin [@Schwarz:81; @Schwarz:85],[^75] $$\\label{Unpin}\n v_\\m u \\lesssim \\frac{\\kappa_4}{2\\pi D}\\,\\ln\\left(\\frac{b}{a_0}\\right) \\;,$$ $D$ being the size of the pinned vortex and $b$ being a characteristic size of the pinning asperity. ", "Equation (\\[Unpin\\]) bears a strong resemblance with that for the Feynman critical velocity, Eq.(\\[FeynmanVelocity\\]).", "\n\nAs a rule of thumb, the pinning energy of the vortex line on such an asperity with radius $b$ is approximately equal to $b$ times the line tension of the vortex given by Eq.(\\[LineTension\\]). ", "Long vortices unpin at very low velocities unless they are perched on a tall pedestal, but very small vortices pinned on microscopic defects can survive a wide range of superflow velocities; according to Eq.(\\[Unpin\\]), a straight vortex filament pinned at both ends on 20 Å asperities 200 nm apart resists transverse flows of velocities up to 20 cm/s.\n\nSuch pinned vorticity has long been thought to play a role in critical velocities. ", "The long standing suggestion by @Glaberson:66 of vortex mills had its time of fame [@Amar:92]. ", "In these authors’s views, imposing a flow on a vortex pinned between the opposite lips of an aperture would induce deformations such that the vortex would twist on itself, self-reconnect, and mill out fresh vortex loops. ", "Upon scrutiny however, vortex mills are not so easy to set up.", "\n\nThe first thing to realise is that such a mill must involve a pinned vortex of sub-micrometric size so that it is not washed away by any flow velocity above a few cm/s. Pinned vorticity in large channels cannot withstand the Feynman-type critical velocities shown in Fig.\\[TwoCriticalVelocities\\].", "\n\nLess obviously, vortices are not prone to twist on themselves and foster loops. ", "As shown by numerical simulations of 3D flows involving few vortices only,[^76] vortex loops and filaments are found to be stable against large deformations: it takes the complex flow fields associated with fully developed vortex tangles to produce small rings [@Svistunov:95; @Tsubota:00].[^77] And it takes some quite special vortex pinning geometry to set up a mill that actually works.", "\n\n@Schwarz:90 has demonstrated the existence of such a mill by numerical simulations. ", "Imagine a vortex filament pinned at one end in a region close to the aperture mouth or the channel entrance where it bends sharply to withstand the local superflow. ", "This end of the vortex is at a near-stagnation point. ", "Its other end is being carried away by the flow along the streamlines; it moves freely with its end sliding perpendicular to the wall. ", "The filament develops a helical instability as depicted in Fig.\\[Schwarz:90-Fig3\\], a sort of driven Kelvin wave, and reconnects sporadically to the wall when the amplitude of the helix grows large enough. ", "The freed bit immediately stands against the flow and forms a vortex half-ring: such a helical vortex mill, which has to be of sub-micrometric size to withstand the near-by flow, does churn out fresh vortices.", "\n\nThe occurrence of multiple slips such as those shown in Fig.\\[TimeChart\\], is probably caused by such a form of vortex mill on a microscopic size. ", "Before coming to this topic, a description of multiple slips in greater details must be provided.", "\n\n![", "\\[Schwarz:90-Fig3\\] Operation of a helical vortex mill: (a) Spiral-helix configuration of a streamwise vortex filament pinned at the centre of the bottom left section of the channel. ", "The helical vortex self-velocity opposes the superflow while the vortex filament grows in size and spirals on itself. (", "b) End-on view of subsequent reconnections. ", "The vortex is pinned near the upper left of the channel cut view. ", "The outwardly growing spiral sporadically reconnects to the wall and releases a new line segment, which then moves to the lower right. ", "These numerical simulations are carried out in the presence of a sizeable mutual friction with the normal component in order to stabilise the numerical algorithms, which is why the generated half-rings rapidly decrease in size. ", "From @Schwarz:90.](Fig22.pdf){width=\"45\" height=\"67\"}\n\nThe two types of large slips {#LargeSlips}\n----------------------------\n\nExamples of multiple slips are shown on the peak amplitude charts in Fig.\\[TimeChart\\] and in Fig.\\[collapse\\] for two different runs in the same experimental cell. ", "They display rather different patterns. ", "In Fig.\\[TimeChart\\], multiples slips are fairly frequent and their winding number multiplicity remains moderate. ", "As the probability for a one-slip event per half-cycle is not large, that for a double slip is small, and it becomes negligible for higher multiples. ", "A separate mechanism for their formation must be found. ", "The event shown in Fig.\\[collapse\\] is quite spectacular as it leads to a near-extinction of the resonance.", "\n\nIn Figs. ", "\\[TimeChart\\] and \\[collapse\\] aperture velocities are expressed by the number of turns $\\delta \\varphi /2\\pi$ by which the quantum-mechanical phase winds across the aperture. ", "Phase winding numbers are related to mean flow velocities in cm/s by multiplication by $\\ell_{\\m h}/\\kappa_4$, the “hydraulic” length $\\ell_{\\m h}$ characterising the extension of the aperture along the flow. ", "For a phase slip by 2$\\pi$, the phase winding number changes by one unit and the trapped circulation in the resonator loop by one quantum.", "The hydraulic length is defined by lumping the (classical) kinetic energy of the fluid moving with velocity $\\mb v$ inside the aperture of cross-section $s_{\\m h}$ and in its vicinity according to: $$\\label{HydraulicLength}\n \\ell_\\m h = s_{\\m h}\\,\\int_V \\mb\n v(\\mb r)^2 \\m d^3 \\mb r \\,\\big/\\, \\big(\\int_S\\mb v(\\mb r)\\cdot \\m d^2 \\mb\n r\\big)^2 \\; .$$ The actual flow velocity averaged over the cross-section of the micro-aperture is proportional to $\\delta \\varphi$, the multiplying factor being $\\hbar /m_4 \\ell_\\m h$. The hydraulic length $\\ell_\\m h$ of the micro-aperture is of the order of 1 m in the experiments shown in Fig.\\[PhaseSlipsCanJPhys\\].", "\n\nSome degree of understanding of the formation of multiple slips can be gained by plotting the mean value of the phase slip multiplicity, expressed in number of quanta, against the flow velocity at which the slips take place [@Varoquaux:95]. ", "This flow velocity is close to the critical velocity for single phase slips, [*i.e.*]{} the vortex nucleation velocity; it varies with temperature, pressure, and resonator drive level. ", "A plot summarising these variations is shown in Fig.\\[MultiSlip\\] for $<\\!n_{_{+}}\\!\\!>$, [*i.e.*]{}, in the flow direction conventionally chosen as the $(+)$ direction. ", "Slips in the opposite $(-)$ direction behave qualitatively in the same manner but the phenomenon displays a clear quantitative asymmetry.", "\n\nAs can be seen in Fig.\\[MultiSlip\\], the mean slip multiplicity decreases, as does the nucleation velocity, on either side of the quantum plateau – a $^3$He impurity effect on the low–$T$ side – a thermal effect on the high–$T$ side. ", "At 16 bars, $<\\!n_{_{+}}\\!\\!>$ increases from $\\approx 1$ at 12 mK where the velocity is 43.2 in winding number to $15 \\sim 20$ on the plateau of $v$ with a winding number of 48; $<\\!n_{_{+}}\\!\\!>$ drops back to 1 at 225 mK and the velocity to $\\sim 46.2$. The same trend is observed at 24 bars, with a lower velocity on the plateau of 46.4 and a higher mean multiplicity of $\\sim$ 23. ", "Rather oddly, the slip multiplicity $<\\!n_{_{+}}\\!\\!>$ increases with pressure while the mean velocity at which these multiples occurs decreases. ", "One would have expected – naively it seems – that more slips would be ushered into faster streams. ", "The opposite may show that the phenomenon under study is not purely ruled by hydrodynamics in the fluid bulk.", "\n\nAnother important feature of the data shown in Fig.\\[MultiSlip\\] concerns the dependence of the velocity threshold for the appearance of multiple slips on hydrostatic pressure. ", "The $P$-dependence of the upturn of $<\\!n_{_{+}}\\!\\!>$ in terms of $v$ exactly tracks that of $v_\\m c$, the critical velocity for single phase slip nucleation: multiple slips occur when single slips occur. ", "Would multiple slips appear because of an alteration, or as a consequence, of single slip nucleation?", "\n\nThe very large drops in the resonance amplitude of the resonator such as the event shown in Fig.\\[collapse\\] and in the inset sometimes result in a complete collapse of the resonance. ", "Under the conditions of this particular exper-\n\n![ ", "\\[TimeChart\\] Absolute peak amplitude $A_\\m p$ normalised to the amplitude jump of a single slip $\\Delta A_1$ during successive half-cycles of the resonance plotted as a function of half-cycle index (time runs from left to right) at 100.7 mK (top) and 201.5 mK (bottom) in nominal purity helium at SVP. ", "The expanded traces at the very top and bottom of the graph show the slip sizes in signed winding numbers (according to flow direction, in and out of the resonator chamber). ", "The numerous multiple slips seen on these charts occur at or close to the critical velocity for single slips. ", "From [@Varoquaux:03]. ](", "Fig23.pdf){height=\"160mm\"}\n\niment [@Avenel:95], these events were rare (one in $10^4 \\mbox{ to }\n10^5$ slips). ", "A striking feature is that they may occur at velocities much below the vortex nucleation threshold, down to less than a third of $v_c$, the critical velocity for phase slips. ", "These intriguing “singular” collapses, first studied by @Hess:77, differ from the multiple slips of Fig.\\[MultiSlip\\]. ", "The underlying mechanisms responsible for each are bound to be different, as discussed below [@Varoquaux:01a].", "\n\nThe pattern of formation of multiple slips and collapses changes on cycling the cell from room temperature and back but remains stable during each given cool-down. ", "It depends on the degree of contamination of the cell, degree which cannot easily be controlled experimentally. ", "The detailed microscopic configuration of the aperture wall where nucleation takes place has a strong influence on multiple slip formation.", "\n\n-5 mm ![", "\\[collapse\\] Absolute peak amplitudes at successive half-cycles of the resonator motion, normalised as in Fig.\\[TimeChart\\], [*vs*]{} half-cycle index in a $^4$He sample containing 100 ppb of $^3$He impurity, at 24.0 bars and 12.5 mK. The resonance half-period is 31.8 msec. ", "The top trace shows a succession of amplitude drops which correspond, for its main part, to phase slips by $2\\pi$ of opposite sign, with occasional larger slips – the multiple slips of Fig.\\[TimeChart\\]. ", "The large feature around the 1000$^{th}$ half-cycle is a “singular” collapse, as defined in this Section. ", "The insert shows the details of this collapse, ($\\bullet$) being for positive peaks, ($\\circ$) for negative peaks. ", "It is preceded by a slip by -2 ($\\times 2\\pi$) and followed by a slow recovery of the peak amplitude caused by the applied drive, punctuated by single and double slips. ", "The time-resolved evolution of this collapse has actually been tracked. ", "See @Avenel:95. ](", "Fig24.pdf \"fig:\"){height=\"70\"}\n\n![", "\\[MultiSlip\\] Mean size of (positive) multiple slips [*vs*]{} velocity in phase winding number in nominal purity $^4$He (100 ppb $^3$He): ($\\triangle$) pressure sweep from 0.4 to 24 bars at 81.5 mK (for all even values of the pressure $P$, and 0.4, 1, 3, 5, and 7 bars) – ($\\diamond$) temperature sweep at 16 bars – ($\\circ$) temperature sweep at 24 bars - ($\\ast$) drive level sweep at 24 bars, 81.5 mK – ($\\scriptscriptstyle\\blacksquare$) temperature sweep at 0 bar. ", "Lines connect successive data points in the temperature and pressure sweeps. ", "For the temperature sweeps, from 14 to 200 mK approximately, $v$ first increases when the $^3$He impurities evaporate from the vortex core, reaches the quantum plateau and then decreases, following the same pattern as shown in the insert of Fig.\\[vc\\] for $v_\\m c$. Adapted from @Varoquaux:01a. ](", "Fig25.pdf){width=\"80\" height=\"70\"}\n\nExtrinsic critical velocities\n-----------------------------\n\nTo try and clarify these matters, a series of experiments was conducted by @Hakonen:98b[@Varoquaux:98], in which the experimental cell was deliberately heavily contaminated by atomic clusters of air and of H$_2$ in order to favour the pinning of vortices. ", "Numerous multiple slips and collapses of the “singular” type occurred. ", "The peak amplitude charts of the resonator became very difficult to interpret except in few instances. ", "In one of these, two apparent critical velocities for single phase slips were observed. ", "The higher critical velocity corresponded to the one observed in the absence of contamination. ", "The lower critical velocity was thought to reveal the influence of a vortex pinned in the immediate vicinity of the prevailing nucleation site.", "\n\nFollowing this interpretation, the pinned vortex induces a local velocity which adds to that of the applied flow and causes an apparent decrease in the critical velocity for phase slips. ", "Because of this change, the presence of the pinned vortex can be monitored. ", "The lifetime in the pinned state and the unpinning velocity can be measured, yielding precious information on the pinning process, reported in detail by @Hakonen:98b.[^78]. ", "This observation also brings evidence that pinned vorticity can alter the vortex nucleation process responsible for phase slips.", "\n\nWith such pinned vortices hanging around, multiple slips could formed according to the following scheme [@Varoquaux:01a]. ", "First, a vortex half-ring is nucleated at a prominent nucleation site. ", "It pins shortly after nucleation when its velocity relative to the boundary is still small and the capture by a pinning site easy. ", "A micro-mill is thus formed, which remains active as long as the flow is sufficient to maintain the helical instability. ", "As it is set up to withstand one flow direction, it is destroyed when the flow velocity reverses itself in the resonance motion. ", "It eventually re-establishes itself during a subsequent resonance cycle, causing a new multiple slip. ", "This process depends on the precise details of the pinning site configuration and of the primordial vortex trajectory, factors which allow for the variableness of multiple slips on contamination and pressure.", "\n\nIn the same experiments by @Hakonen:98b, a large number of unpinning events were also observed to take place at an “anomalously low” unpinning velocity. ", "A parallel can be made [@Varoquaux:98] with the singular collapses that also occur at “subcritical” velocities and that were also quite frequent in the same experiments, suggesting that the two effects might have a common cause. ", "Noting furthermore that pinning and unpinning processes were also quite frequent, releasing a fair amount of vagrant vorticity, it appears quite plausible that both singular collapses and low velocity unpinning events are caused by vagrant vortices hopping from pinning sites to pinning sites, eventually hovering over a pinned vortex or a vortex nucleation site. ", "The transient boost to the local velocity may push the pinned vortex off its perch, or may cause a burst of vortices to be shed.", "\n\nThese observations, albeit incidental, have important consequences for the critical velocity problem: existing vortices, either pinned or free-moving, can contribute to the nucleation of new vortices at the walls of the experimental cell at apparent velocities much lower than the critical velocity for phase slips. ", "A mechanism is thus provided by which superflow dissipation sets in at large scale for mean velocities much smaller than the velocity for vortex nucleation on the microscopic scale, possibly bridging the gap between phase slip and Feynman-type critical velocities.", "\n\nTo conclude this Section, the critical velocities in superfluids that are true and proven include the Landau critical velocity for roton creation in ion propagation [@McClintock:95], the formation of vortices by a hydrodynamical instability in BEC gases [@Madison:01] and in $^3$He [@Eltsov:05], the nucleation of vortices by thermal activation and quantum tunnelling in $^4$He, both for ion propagation and in aperture flow.", "\n\nThere is also rather compelling experimental evidence for the interplay on a microscopic scale between vortex nucleation and pinned vorticity; this evidence points toward the existence of helical vortex micro-mills that can generate bursts of vortices, even, in some cases, at fairly low flow velocities. ", "Finally, vagrant vortices interacting with these mills, or with the vortex nucleation sites are found to generate enough vorticity to completely kill the superflow and explain singular collapses.", "\n\nHow these different events occur is illustrated in detail by the numerical simulations of the onset and decay of vortex tangles in large channels [@Schwarz:83; @Schwarz:91], of the influence of surface roughness on the critical velocity for a self-sustaining vortex tangle [@Schwarz:92], and of the evolution of phase-slip cascades from a single remnant vortex as a function of channel size [@Schwarz:93]. ", "These processes depend on the cell geometry but not on temperature.", "\n\nA fair degree of understanding of the possible mechanisms behind the Feynman critical velocity has thus been achieved by the study of phase slippage signatures of these various large slips.", "\n\nJosephson-type effects in superfluids {#Josephson}\n=====================================\n\nAnderson’s conjectures, seen in the previous Sections to be fully confirmed in the hydrodynamic (macroscopic) limit of quantised vortex dynamics, have also been carried over to the microscopic limit of quantum tunnelling, as described below.", "\n\nThe reasoning goes that Eqs.(\\[Hamilton1\\]) and (\\[Hamilton2\\]) are [ *fundamental*]{} [^79] enough to carry the day both at large and short distances, namely when the coherence length is either small or large with respect to characteristic dimensions of the hydrodynamic weak link. ", "The former case has been covered in the previous Sections. ", "In the latter case – weak quantum coupling between two superfluid baths – the contention is that effects analogous to the famed Josephson effects between two weakly-coupled bits of superconducting material must also exist between two loosely-connected pools of superfluid provided that superfluid coherence is not entirely lost through the connection. ", "These Josephson-type effects in superfluids are dealt with below.", "\n\nA simple model {#SimpleModel}\n--------------\n\nThe Hamilton equations (\\[Hamilton1\\]) and (\\[Hamilton2\\]) express in a quite general way the time evolution of $\\varphi$ and $N$, as discussed in Sec.\\[OrderParameter\\]. ", "These equations hold in fact for the operators $\\hat{N}$ and $\\hat{\\varphi}$ but their coarse-grained averages can be treated as [*c*]{}-numbers to a very good approximation because their relative quantum uncertainties are very small. ", "Averaging over a volume of superfluid small compared to the size of the sample but still containing a large number of atoms leads to Eq.(\\[acJosephson\\]): $$\\hbar \\frac{\\partial\\varphi}{\\partial t} = -(\\mu +\n\\slantfrac{1}{2} m_4 v_\\m s^2) \\; .$$ Equation (\\[acJosephson\\]) describes the Josephson [*ac*]{} effect.[^80]\n\n![", "\\[Weak link\\] Schematic representation of a two–dimensional weak link: (top) cut view of the elongated slit in the partitioning wall; (bottom) amplitude of the macroscopic wavefunction $\\Phi$ in the region in which it is depleted by the energy barrier of height $U$ and extent $l_\\m b$ due to the constricting walls. ](", "Fig26.pdf){width=\"27\"}\n\nWhen applied to the gradient of the phase, it can be cast, using Eq.(\\[vs\\]), into the Euler equation (\\[SimpleEuler\\]): $$\\frac{\\partial \\mb v}{\\partial t} + \\nabla (v_{\\mathrm{ a}} P +\n\\frac{1}{2} m_{\\mathrm{ a}}v^2) = 0 \\;,$$ $m_{\\mathrm a}$ being the atomic mass of the effective boson.", "\n\nEquations (\\[acJosephson\\]) and (\\[SimpleEuler\\]) look plainly classical enough. ", "Quantum mechanics hides in the possible multiple determinations of the overall phase $\\varphi(t,\\mb r)$ of the order parameter, yielding a quantised circulation of the fluid velocity, and, in a subtler manner, when $\\hat{N}$ cannot be coarse-grained averaged because the amplitude of the order parameter vanishes or varies too rapidly over short distances. ", "A (quantum) mechanism is then provided for $\\varphi$ to vary discontinuously from one determination to another, violating the Kelvin-Helmholtz theorem.", "\n\nThe second Heisenberg equation of motion, that for $\\dot N$, expresses particle number conservation: $$\\label{numberconservation} \n \\hbar\\,\\frac{\\partial N}{\\partial t} = \\frac{\\partial\n E}{\\partial \\varphi} \\;.$$ As stressed by @Anderson:66b, the range of validity of Eqs.(\\[acJosephson\\]) and (\\[numberconservation\\]) is quite wide. ", "They will still hold when hydrodynamics breaks down as for tunnelling supercurrents. ", "In this kind of situations, the internal energy $E$ depends in a non-trivial way on $\\varphi$, as may be expected from Eq.(\\[numberconservation\\]).", "\n\nWhen applied between two regions of the superfluid, Eqs.(\\[acJosephson\\]) and (\\[numberconservation\\]) describe the supercurrent flowing from one region to the other. ", "This situation becomes especially interesting when the two regions, the two superfluid baths, are sufficiently well separated so that they only [*weakly coupled*]{}: a well-defined phase difference between them, ${\\mbox{{{\\usefont{U}{psy}{m}{n}d}}}}\\varphi$, can then be sustained.", "\n\nSuch a situation can be modelled by a potential barrier, as in Fig.\\[Weak link\\]. ", "The thin partition separating the two baths presents a thin elongated slit through which a trickle flow only of superfluid can leak. ", "If the two smaller dimensions of the slit are comparable to the superfluid coherence length — the distance over which its wavefunction can heal — the amplitude of the wavefunction is reduced in the narrow passage, as pictured in the bottom panel of Fig.\\[Weak link\\]. ", "In superconductivity, such weak links, or micro-bridges, are known to lead to the same kind of effects as tunnel junctions [@Likharev:79; @Golubov:04].", "\n\nFor superflows through such a micro-aperture, the problem can be restricted to one dimension along $z$ and, to simplify further, the barrier (the weak link) can be taken as a square potential wall of height $U$ over length $l_\\m b$. [^81]\n\nIn the bulk of the fluid, the wave function corresponding to a state with energy $E$ is taken as a plane wave with identical amplitude $|\\mi\\Phi|=(\\rho_\\m s/m_\\m a)^{1/2}$ on both sides of the barrier ($ m_\\m\na = 2 m_3$ for superfluid $^3$He), but with phases that differ by ${\\mbox{{{\\usefont{U}{psy}{m}{n}d}}}}\\varphi$: these are the boundary conditions at the weak link walls at $z=0$ and $z=l_\\m b$.\n\nInside the barrier $|\\mi\\Phi(z)|$ is assumed to be severely depressed: the interactions within the fluid can be neglected.[^82] With this approximation of weak coupling, the tenuous fluid inside the weak link behaves as a simple non-interaction gas and the equation of motion reduces to a one-particle Schrödinger equation: $$\\m{i}\\hbar\\frac{\\partial \\mi\\Phi}{\\partial t} =\n-\\frac{\\hbar^2}{2m_{\\mathrm{ a}}} \\nabla^2\\mi\\Phi + U\\mi\\Phi \\; , \\hskip 2mm U\n> E \\;,$$ and also has a plane wave solution $\\exp\\{-\\mathrm{i}(Et/\\hbar -\nkz)\\}$. The momentum takes two values corresponding to the two possible directions of (damped) propagation: $$k_{\\ts\\pm} = \\pm (\\m{i}/\\hbar)\\sqrt{2m_{\\mathrm{ a}}(U-E)} \\;.$$ Let $b_\\m b=\\hbar/\\sqrt{2m_{\\mathrm{ a}}(U-E)}$: the barrier height is characterised by a penetration length. ", "The wave function inside the barrier is found by standard methods: $$\\mi\\Phi(z) = \\frac{|\\mi\\Phi|}{{\\sinh}(l_\\m b/b_\\m b)}\n \\left\\{{\\sinh} \\left(\\frac{z}{b_\\m b}\\right)\\,{\\mbox e}^{\\ts\n {\\m i{\\mbox{{{\\usefont{U}{psy}{m}{n}d}}}}\\varphi}} - {\\sinh}\\left(\\frac{z-l_\\m b}{b_\\m b}\\right)\\right\\}\n\\; .$$ The modulus of $\\mi\\Phi$ midway in the barrier is expressed by $$\\label{Modulus} \n \\mi\\Phi^*(l_\\m b/2)\\,\\mi\\Phi(l_\\m b/2) =\n \\frac{\\rho_\\m s/m_\\m a}{2 \\cosh^2(l_\\m b/2b_\\m b)}[1+\\cos {\\mbox{{{\\usefont{U}{psy}{m}{n}d}}}}\\varphi] \\;,$$ and is a $2\\pi$-periodic function that vanishes for ${\\mbox{{{\\usefont{U}{psy}{m}{n}d}}}}\\varphi =\n\\pi\\,\\pm 2n\\pi$. The weak coupling condition is satisfied in superfluid helium for $l_\\m b \\gtrsim b_\\m b$.\n\nKnowing the wavefunction, the current density, Eq.(\\[Current\\]), can be straightforwardly computed. ", "The total current through a micro-aperture of effective cross-section $s_\\m b$ is found to be: $$\\begin{aligned}\n J &=& \\frac{\\hbar s_\\m b}{2\\m i b_\\m b}\n \\frac{\\rho_\\m s/m_\\m a}{{\\sinh}^2\\left(l_\\m b/b_\\m b\\right)}\n \\left\\{\\left[{\\sinh}\\left(\\frac{z}{b_\\m b}\\right)\\,\n {\\mbox{e}}^{\\ts{ -\\m{i}{\\mbox{{{\\usefont{U}{psy}{m}{n}d}}}}\\varphi}} - {\\sinh}\n \\left(\\frac{z-l_\\m b}{b_\\m b}\\right)\\right]\\times\\right. ", " \\nonumber \n \\\\ &&\\hskip -5mm\n \\left. ", "\\left[{\\cosh}\\left(\\frac{z}{b_\\m b}\\right) {\\mbox{e}}^{\\ts{\n \\m{i}{\\mbox{{{\\usefont{U}{psy}{m}{n}d}}}}\\varphi}} - {\\cosh}\\left(\\frac{z-l_\\m b}{b_\\m\n b}\\right)\\right] - {\\mbox{complex conjugate}}\\right\\} \\nonumber \n \\\\ &=& \n J_\\m c\\, \\sin\\left({\\mbox{{{\\usefont{U}{psy}{m}{n}d}}}}\\varphi\\right)\\,, \\;\\;{\\mbox{with}}\\;\n J_\\m c = \\frac{\\hbar}{m_\\m a}\\,\\frac{s_\\m b}{b_\\m b}\\,\n \\frac{\\rho_\\m s}{{\\sinh(l_\\m b/b_\\m b)}} \\;.", "\n\\label{dcJosephson}\\end{aligned}$$ Equation (\\[dcJosephson\\]) describes the Josephson [*dc*]{} effect. ", "Although this equation has been obtained here in a drastically simplified manner, it is nearly identical to the result of more involved theories, each with its own set of approximations – the Ginzburg-Landau model [@Monien:86], an ideal tunnel junction [@Rainer:87], or a strictly point-like orifice [@Kurkijarvi:88].", "\n\nThe supercurrent $J$ is periodic by $2\\pi$ in ${\\mbox{{{\\usefont{U}{psy}{m}{n}d}}}}\\varphi$ as it must be since changing the phase by $2\\pi$ on one side of the barrier must leave the overall physical situation unchanged. ", "It vanishes for ${\\mbox{{{\\usefont{U}{psy}{m}{n}d}}}}\\varphi = \\pm\n\\pi$ not because the velocity, proportional to ${\\mbox{{{\\usefont{U}{psy}{m}{n}d}}}}\\varphi$, goes to zero but because the superfluid density, which is proportional to $|\\m\\Phi|^2\n\\sin({\\mbox{{{\\usefont{U}{psy}{m}{n}d}}}}\\varphi)/{\\mbox{{{\\usefont{U}{psy}{m}{n}d}}}}\\varphi$ inside the barrier, does; the modulus of the wave function at midpoint in the barrier, Eq.(\\[Modulus\\]), vanishes: superfluidity is actually destroyed at that point, which is why the supercurrent goes to zero and the phase can slip by $2\\pi$ (or lumps of $2\\pi$).", "\n\nIf the coupling is not weak, a more elaborate calculation is necessary: the sine function is replaced by a general $2\\pi$–periodic function $f_{2\\pi}({\\mbox{{{\\usefont{U}{psy}{m}{n}d}}}}\\varphi)$, the current-phase relation, or CPR, for a “non-ideal” weak link. ", "Often, this relation is not even single-valued and, when the phase is varied, the current may jump discontinuously from one determination to another: the weak link is then said to be hysteretic. ", "This behaviour is due to the nucleation of topological defects such as vortices as seen in the previous Section. ", "It is accompanied by dissipation while the ideal Josephson case (when $f_{2\\pi}({\\mbox{{{\\usefont{U}{psy}{m}{n}d}}}}\\varphi)$ is a sine function) is dissipation-less [@Likharev:79; @Thuneberg:05; @Viljas:05].", "\n\nIn the transition between the “ideal”, non-hysteretic, purely sinusoidal CPR’s and the mostly linear CPR seen, for example, in Fig.\\[PhaseSlipsCanJPhys\\], a slanted sine function is often observed. ", "Part of this distortion arises from purely classical fluid flow in the vicinity of the micro-aperture. ", "The full phase difference across the weak link, $\\varphi_\\m w$, includes, besides the phase difference across the barrier $\\varphi_\\m b$, the rather trivial velocity potential drop in the vicinity of the weak link where the superfluid velocity $v_\\m s$, and the corresponding phase gradient, behave in accord with classical ideal fluid dynamics.", "\n\nIn order to account in a simple manner for this classical contribution, it is convenient to introduce the equivalent “hydraulic” length and cross-sectional area of these regions, $\\ell_\\m h$ and $s_\\m h$, in such a way that the flow is described in a ‘rod-like’’ manner.[^83]. ", "The superfluid velocity is then expressed simply by $v_\\m s = (\\hbar/m_\\m a){\\mbox{\\small{{\\usefont{U}{psy}{m}{n}d}}\\hskip 0.05ex}}\\varphi_\\m h/\\ell_\\m h $ and the current by $J = \\rho_\\m s s_\\m h v_\\m s$.\n\nThe total phase difference ${\\mbox{\\small{{\\usefont{U}{psy}{m}{n}d}}\\hskip 0.05ex}}\\varphi$ is the sum of the phase drop through this “hydraulic” region and through the barrier acting as the weak link, assumed ideal, [*i.e.*]{}, such that: $$\\label{TotalPhaseDrop}\n {\\mbox{\\small{{\\usefont{U}{psy}{m}{n}d}}\\hskip 0.05ex}}\\varphi = {\\mbox{\\small{{\\usefont{U}{psy}{m}{n}d}}\\hskip 0.05ex}}\\varphi_\\m h + {\\mbox{\\small{{\\usefont{U}{psy}{m}{n}d}}\\hskip 0.05ex}}\\varphi_\\m b\n = \\frac{m_\\m a \\ell_\\m h}{\\rho_\\m s \\hbar s_\\m h} \\, J \\; .$$ The same mass current also flows through the depletion region and varies, following Eq.(\\[dcJosephson\\]), as a sine function of the phase difference ${\\mbox{\\small{{\\usefont{U}{psy}{m}{n}d}}\\hskip 0.05ex}}\\varphi_\\m b$ as long as the coupling is weak.", "\n\nCombining Eqs.(\\[dcJosephson\\]) and (\\[TotalPhaseDrop\\]), and renaming the hydraulic part ${\\mbox{\\small{{\\usefont{U}{psy}{m}{n}d}}\\hskip 0.05ex}}\\varphi_\\m h$ of the phase difference $\\zeta$ to stress its ancillary role yields the relation between the current and the phase of a (slightly more) realistic micro-aperture: $$\\label{DeaverPierce} \n\\varphi = \\zeta + \\alpha \\sin\\zeta \\;,\\;\\;\\;\\;\\;\\ J=J_\\m c \\sin\\zeta \\; ,$$ with $\\alpha = (m_\\m a \\ell_\\m h / \\rho_\\m s s_\\m h \\hbar)\\, J_\\m c$ and $J_\\m\nc$ expressed from Eq.(\\[dcJosephson\\]).[^84] The non-ideality parameter $\\alpha$ and the critical current through the junction $J_\\m c$ are given a meaning in terms the geometrical details of the micro-aperture. ", "They can be derived from experiments and compared with the expected values. [", "^85]\n\nSince the healing length is of atomic dimensions for $^4$He, a near-ideal Josephson effect cannot be expected to be found in the micro-apertures that can be manufactured at present, except very close to the ${{\\mbox{\\footnotesize{{\\usefont{U}{psy}{m}{n}l}}}}}$ transition when this length diverges. ", "Experiments close to $T_{{\\mbox{\\footnotesize{{\\usefont{U}{psy}{m}{n}l}}}}}$ have been conducted successfully by @Sukhatme:01 and @Hoskinson:06-Nature and are described in §\\[LambdaPoint\\]. ", "The experiments that have first shown the existence of the Josephson [ *dc*]{}-effect in superfluids have been carried out in $^3$He [@Avenel:88].", "\n\nCurrent and phase in superfluid $^{\\mb 3}$He {#CPR}\n--------------------------------------------\n\nThe helium-3 nucleus is made up of two protons and one neutron: $^3$He is a fermion. ", "As for the abundant and heavier isotope, $^4$He, its zero-point energy in the condensed phase is large and it remains in the liquid phase down to absolute zero at pressures below about 35 bars. ", "It thus forms a Fermi liquid with a Fermi sphere over which Landau quasiparticles float. ", "Because the interatomic potential is attractive at large distance, these quasi-particles can form Cooper pairs and $^3$He was long suspected to become a BCS superfluid below some hard-to-predict temperature. ", "The discovery by Osheroff, Richardson and Lee of the transition to not one but two superfluid phases [@Osheroff:72] fixed the transition temperature to 2.49 mK on the melting curve, at a pressure of 34.34 bars and opened an exciting new chapter of low temperature physics.", "\n\nAs the experimental properties of these new superfluid phases were quickly unravelled [@Wheatley:75a; @Wheatley:75b; @Lee:78], they were identified from their nuclear susceptibility properties observed by NMR as resulting from the formation of Cooper pairs in a [*spin-triplet*]{} state [@Leggett:75]. ", "A new breed of superfluid was just born. ", "The overall antisymmetry of the wavefunction under the exchange of two fermions then requires an odd angular momentum state $l=1,\\,3\\,\\ldots$. The available experimental data, mainly the phase diagram, the specific heat, and the nuclear susceptibility, led to the identification of the A and B phases as p-wave Cooper-pair superfluids with total spin $S=1$ and total angular momentum $L=1$.\n\nThe formalism describing the properties of these anisotropic superfluid phases was quickly developed.[^86] It extended the Bardeen-Cooper-Schrieffer theory of s-wave superconductivity to the neutral triplet-spin-state superfluid. ", "The most general pair wavefunction with three possible substates for the spin and the orbital parts is an arbitrary superposition of these 3x3 substates, involving nine complex parameters. ", "Assuming weak coupling between the pairs – a surprisingly good assumption at low pressure – this extension of the BCS theory [@Leggett:75] leads to a 3x3 order parameter for B-phase of the form $$\\label{BPhaseOrderParameter}\n A_{\\mu i} = \\Delta(\\hat{\\bs{\\m k}}) \\m{e}^{\\ts{\\m i\\varphi}} \\, \n R_{\\mu i}(\\hat{\\bs{\\m n}},\\theta) \\; .$$ The gap parameter $\\Delta(\\hat{\\bs{\\m k}})$ and the phase factor $\\m{e}^{\\m i\\varphi}$ have the same interpretation as for s-wave superconductors. ", "The B-phase contains the $S_{\\m z}$ = 0, +1, and -1 pairs ($\\ket{\\uparrow\\downarrow + \\downarrow\\uparrow}$, $\\ket{\\uparrow\\uparrow}$, and $\\ket{\\downarrow\\downarrow}$) in equal amounts in zero applied magnetic field; $\\Delta(\\hat{\\bs{\\m k}})$ is isotropic and independent of $\\hat{\\bs{\\m k}}$, the direction on the Fermi sphere.", "\n\nThe matrix $R_{\\mu i}(\\hat{\\bs{\\m n}},\\theta)$ describes the rotation bringing the spin quantisation axis along the orbital quantisation axis. ", "This rotation is characterised by a unit vector $\\hat{\\bs{\\m n}}$ and an angle $\\theta$. Both the gap parameter $\\Delta(\\hat{\\bs{\\m k}})$ and the rotation are real quantities independent of the overall phase $\\varphi$. Therefore, the B-phase order parameter (\\[BPhaseOrderParameter\\]) takes the same form as that for $^4$He, namely, the product of a phase factor ${\\m{exp}}(\\m i\\varphi)$ with a well-defined phase $\\varphi$ and a phase independent modulus. ", "The same reasoning as for the $^4$He case applies when performing a Galilean transformation: mass transport in the pseudo-isotropic B-phase is related to the gradient of $\\varphi$.\n\nThe modulus of order parameter (\\[BPhaseOrderParameter\\]), or gap parameter $\\Delta$, can be thought of as the binding energy of a Cooper pair at $T=0$; it is of the order of $k_\\m B T_\\m c$,[^87] $T_\\m c$ being the superfluid transition temperature. ", "The smallest time lapse over which this energy can be defined is limited by the uncertainty relation for time–energy: ${\\mbox{\\small{{\\usefont{U}{psy}{m}{n}d}}\\hskip 0.05ex}}t\\simeq \\hbar / \\Delta$. During that time, the pair spreads over a length $\\xi_0 = \\hbar v_\\m F/\\Delta \\;, $ where $v_\\m F$ is the velocity of the $^3$He quasiparticles over the Fermi surface. [", "^88] It can be seen from this heuristic argument (@Lounasmaa:83, @Davis:02) that properties of the superfluid are well-defined only over distances larger than the coherence length $\\xi_0$, of the order of 600 Å at $T=0$ and low pressure – 120 Å  at melting pressure. ", "The prospect to observe quantum departures from classical hydrodynamics in $^3$He appears much more favourable than in the case of $^4$He:[^89] the coherence length is no longer very small compared to the size of apertures that can be micro-machined; genuine hydrodynamic Josephson effects can be expected to take place in the B-phase in submicron size apertures, or pinholes.", "\n\nWeak links in p-wave superfluids {#p-wave}\n--------------------------------\n\nWeak links for superfluids come in two breeds, single micro-apertures in thin wall partitions and larger scale arrays of such apertures geometrically arranged a few microns apart, actual pinholes for the former, a mock-up for tunnel junctions for the latter. ", "The flow patterns in the vicinity of each kind lead to different weak link behaviours.", "\n\nThe first successful Josephson-type experiments were carried out by @Avenel:88, using the same micro-resonator and single aperture as for their experiments on phase-slippage in $^4$He.[^90] Their observations spurred intense theoretical interest in the description of phase slippage in $^3$He.", "\n\nAnalytic calculations of the current through a pinhole orifice with all dimensions smaller than $\\xi_0$ and with specular reflection of the quasiparticles on the walls by @Kurkijarvi:88 in the framework of quasiclassical theory, following earlier work by @Kopnin:86 and @Monien:86, lead to the following current-phase relation: $$\\label{CPRKurki}\n J = \\mbox{\\tt a} s_{\\m h} v_{\\m F} N(E_{\\m F}) \\Delta(T)\n \\,\\sin\\big(\\frac{\\varphi}{2}\\big) \\,\\tanh\\bigg[\\mbox{\\tt b}\n \\frac{\\Delta(T)}{k_\\m B T} \\,\\cos\\big(\\frac{\\varphi}{2}\\big)\\bigg] \\, ,$$ where $N(E_{\\m F})$ is the density of states at the Fermi surface, $v_{\\m F}$ the Fermi velocity, $\\mbox{\\tt a}= \\pi /2 $, and $\\mbox{\\tt b} = 1/2$ for the B-phase. ", "Equation(\\[CPRKurki\\]) takes the same form as for a s-wave supercurrent through a superconducting micro-bridge.[^91] A similar form also holds approximately for the A-phase with $\\mbox{\\tt a}= \\pi /\\sqrt{6}$ and $\\mbox{\\tt b} = (3/8)\\sqrt{3/2}$, and for the planar phase, a phase which may possibly be stabilised within the micro-aperture by the walls.", "\n\n![", "\\[PRL88-fig2-staircase\\] Staircase patterns (peak resonance amplitude versus applied drive level, both in arbitrary units) in $^3$He-B at a pressure of about 0.2 bar. ", "The curves at various temperatures are shifted vertically for readability. ", "Drive frequencies at the various temperatures are shifted from resonance so as to set comparable resonance conditions. ", "From @Avenel:88. ](", "Fig27.png){width=\"70\"}\n\nExpression (\\[CPRKurki\\]) reduces in the limit $\\Delta(T)/k_\\m B T \\ll1$ to the sinusoidal dependence of Eq.(\\[dcJosephson\\]) for the current in terms of the phase difference across the barrier $\\varphi_\\m b$. This result has been obtained by a number of authors using a variety of techniques.[^92] It is no real surprise that the details of the structure of the order parameter disappear when the dimensions of the orifice are small with respect to the coherence length and that s-wave-like results are found for both the A and B phases. ", "Superfluid coherence is effectively weakened by the micro-orifice because the length over which it heals becomes larger than the physical size of the connecting duct; however, if the length of that duct is short enough, a sizeable supercurrent can still exist, sustained by the quantum tunnelling of quasi-particle pairs through the weak link.[^93]\n\nAt temperatures such that $\\Delta(T)/k_\\m B T$ is no longer a small quantity, Eq.(\\[CPRKurki\\]) becomes increasingly slanted with an abrupt slope close to $\\varphi=\\pi$ when ${\\m{cos}}\\,\\varphi/2$ changes sign while retaining the periodicity by $2\\pi$ in the phase difference. ", "It displays a discontinuity for $\\varphi = \\pi$ at $T=0$. This behaviour of the weak link comes on top of the effect of the hydraulic inductance of the Deaver-Pierce model: the CPR is bound to become hysteretic and multivalued even for an extremely small pinhole in the limit $T\\longrightarrow 0$.\n\nThis simple theoretical description accounts well for the experiments of @Avenel:88, whose results are reproduced in Fig.\\[PRL88-fig2-staircase\\]. ", "Similar findings have been reached by @Backhaus:97 in an array of pinholes. ", "Close to the superfluid transition, weakly-coupled reservoirs of superfluid $^3$He-B exhibit a behaviour that involves the direct analogues of both Josephson [*ac*]{} and [*dc*]{} effects in superconductors. ", "The relation between the superfluid current and phase – or CPR – is well represented by a slanted sine function. ", "In the range of applicability of Eq.(\\[CPRKurki\\]), single micro-apertures and arrays behave alike. ", "The existence in superfluids of the analogues of the Josephson effects in superconductors was thus established in 1988 on firm grounds, both experimentally and theoretically, but more features were soon revealed by further studies.", "\n\nMultivalued CPR’s, states and defects\n-------------------------------------\n\nWhile near-ideal Josephson behaviour prevails in $^3$He-B at low pressure close to $T_\\m c$, departures from a sinusoidal current-phase relation were observed by @Avenel:88 [@Avenel:89] in a single orifice and later by @Backhaus:97 [@Marchenkov:99] in an array of 0.1$\\mu$m–diameter apertures, evolving to a near-straight line relation below 0.6$T_\\m c$. The latter case is reminiscent of the situation in $^4$He, in which vortices are nucleated.", "\n\nAs the temperature is lowered further below $T_\\m c$, the superfluid coherence length becomes smaller than the aperture size used in present-day experiments. ", "This trend is even more pronounced at higher pressure, where $T_\\m c$ is higher (and $\\xi_0$ smaller). ", "Room is thus left for a wall dominated order parameter texture within the weak link or its immediate proximity: the p-wave nature of superfluid $^3$He can then reveal itself.", "\n\nVery detailed numerical simulations based on the time-dependent Ginzburg-Landau equations have been carried out by @Soininen:92 [^94] for a finite size aperture quite similar to the one used by @Avenel:88. ", "These simulations show in colourful figures the time evolution, when the $^3$He superfluid is set to flow through the micro-slit, of the components of the superfluid density tensor parallel to the two short dimensions of the slit. ", "Both the mass and the spin degrees of freedom of the spin-triplet p-wave order parameter take part in the phase slippage process. ", "The various components of the order parameter evolve separately in space and time and do not go to zero simultaneously at the same location in the micro-aperture. ", "The regions of space, in which the order parameter is depressed and about which the phase slips, peel off from the walls and traverse the slit at right angle with the flow direction. ", "Thus, phase slips in the p-wave superfluid exhibit a fairly complex spatial and temporal evolution both in the pseudo-isotropic B phase and in the anisotropic A phase. ", "In addition, the A phase may sustain core-less phase slippage as suggested by @Anderson:77 and as discussed below. ", "These simulations also illustrate the details of operation of a vortex mill [@Soininen:92] in which phase slip avalanches and multiple vortex creation take place. ", "The state of sophistication of\n\n![", "\\[Marchenkov:99-PiState\\] Current-phase relations in $^3$He-B observed in an array weak link. ", "The two panels show CPR’s for the low current state (left panel) and the high current state (right panel) for temperatures ranging from $T/T_\\m c\n = 0.850$ down to 0.450 $T/T_\\m c$ in steps of approximately 0.05$\\,T/T_\\m c$. The mass current through the weak link increases as the temperature is lowered. ", "At temperatures close to $T_\\m c$, the current-phase relations can be fit well with the Deaver-Pierce model. ", "At the temperature decreases (and the critical current increases), this model becomes inadequate as a $\\pi$-periodic component gradually sets in. ", "From @Marchenkov:99.](Fig28.pdf){width=\"150\" height=\"70mm\"}\n\nthe microscopic description of superfluid $^3$He makes it possible to obtain such detailed information.", "\n\nThe phase slippage observations in superfluid $^3$He reflects this wealth of riches. ", "While near-ideal Josephson behaviour prevails in $^3$He-B at low pressure close to $T_\\m c$, more complicated staircase patterns than those shown in Fig.(\\[PRL88-fig2-staircase\\]) develop below $0.7 T_\\m c$ [@Avenel:89], which cannot be described by the Deaver-Pierce model. ", "These patterns are not even reproducible from one cool-down through $T_\\m c$, or through the A to B transition, to the next. ", "It is likely that different order parameter textures and topological defects are coming into play.", "\n\nAmong those features, two notable ones were reported by @Backhaus:98 [@Marchenkov:99] and are shown in Fig.\\[Marchenkov:99-PiState\\] in $^3$He-B at saturated vapour pressure. ", "These authors used a two-hole micro-resonator with a weak link made of a 65x65 array of 100 nm round holes micro-machined in a 50 nm thick silicon nitride free-standing membrane. ", "The 4225 holes in parallel offer a large enough flow path for the mass flow rate under an applied pressure head to be closely monitored. ", "They operated the resonator in free ringing mode and recorded the transient response following a large impulsive drive excitation. ", "The phase is derived from the measurement of the pressure head between the two sides of the weak link by integration of Eq.(\\[acJosephson\\]). ", "The current-phase relations displayed in Fig.\\[Marchenkov:99-PiState\\] are obtained with this direct technique.[^95]\n\nThe first feature shown in Fig.(\\[Marchenkov:99-PiState\\]) is the existence of two possible CPR’s at the same temperature, one with a larger critical current than the other, the second, the appearance in the $2\\pi$-periodic CPR of an increasingly strong $\\pi$-periodic admixture as the temperature is lowered. ", "@Avenel:99 pointed out that this admixture could simply arise from the unavoidable dispersion between the sizes of the micro-holes in the array.[^96] This rather trivial explanation holds in part under all circumstances but is not the end of the story, as was soon shown by @Avenel:00’s own observations using a single micro-aperture for which there is obviously no scatter in critical currents or transit times.", "\n\n@Avenel:00 and @Mukharsky:04 took advantage of the Sagnac effect (see §\\[interferometry\\]) to ramp up and down in a precise manner the macroscopic phase difference $\\delta \\varphi$ applied across the weak link. ", "They reported the observation of several different CPR branches – usually more than two – most with $\\pi$-components and with different critical velocities at the same temperature but in different cooldowns through the superfluid transition temperature. ", "Each of these several $J(\\varphi)$’s was usually robustly fixed in each run and the general trend was to go from $2\\pi$ periodicity to $\\pi$ periodicity as the temperature is lowered, although, occasionally, no $\\pi$ periodicity was observed even at the lowest temperature. ", "At higher pressure (10 bars), hysteretic behaviour in the single micro-aperture was prevalent and up to three simultaneous branches for the CPR were observed. ", "Switching between these different branches could be triggered by applying strong transient drive voltage to the resonator, indicating that textural effects were most likely at play.", "\n\nSome of these features were actually predicted long before their observation by @Thuneberg:88 who worked out a numerical solution for the Ginzburg-Landau equations of the state of $^3$He-B confined inside a micro-aperture. ", "This author found two different CPR’s according to whether the $\\hat{\\bs{\\m n}}$-vector of the B-phase order parameter, assumed to lie perpendicular to solid walls, is in a parallel or antiparallel configuration on both sides of the membrane carrying the micro-aperture. ", "In the antiparallel configuration, the spin and mass currents are out of phase, resulting in a lower critical current. ", "Eventually, the decoupling between mass and spin currents leads to the admixture of a $\\pi$-periodic component to the 2$\\pi$-periodic CPR.", "\n\nThe experimental discovery of these effects by @Backhaus:98 and @Marchenkov:99 spurred theoretical interest. ", "Thuneberg’s numerical findings were soon confirmed and sharpened by the analytic investigations of @Yip:99 and @Viljas:99 [@Viljas:02-PRB] and extended numerical simulations for two-dimensional geometries by @Viljas:02-JLTP. ", "The upshots of these studies are the following:[^97]\n\n[$\\bullet$ Following @Yip:99 and @Viljas:99,[^98] the $\\pi$ states in $^3$He-B are due to the interference of currents carried by quasiparticles with different spins that acquire different excess phases from the internal spin structure of the order parameter while travelling through the weak link. ", "More specifically, the $\\ket{\\uparrow\\uparrow}$ and $\\ket{\\downarrow\\downarrow}$ Cooper pair populations may be viewed as independent superfluids, the phases of which may be slightly shifted with respect to one another because of a differing spin-orbit coupling. ", "Summing the corresponding mass currents, given by Eq.(\\[CPRKurki\\]), represented by slanted sine CPR’s shifted in phase by $\\pm \\delta \\varphi$ leads, if the shift is large enough, to a positive-slope branch in the CPR at $\\pi$: this $\\pi$-state mechanism relies on different spin-orbit orientations on both sides of the weak link and operates at the single pinhole level [@Viljas:02-JLTP].]{}", "\n\n[$\\bullet$  The Josephson coupling between two baths of $^3$He-B mixes the phase difference to the spin-orbit texture of the order parameter: the equilibrium configuration of the texture then depends on the phase bias applied to (hence on the current carried by) the weak link. ", "The texture is assumed fixed in the simpler calculations: this is the [*isotextural*]{} case, which offers only a coarse agreement with observations. ", "If the texture is allowed to adjust to the local mass and spin currents by expressing the balance between its stiffness and its interactions with the walls and with the mass current, a $\\pi$-state can also arise: this [ *anisotextural*]{} effect requires a self-adjusting string of calculations and provides quantitative agreement with pinhole array experiments [@Viljas:02-PRB].]{}", "\n\n[$\\bullet$ These refined calculations led to the realisation that multiple Andreev reflections and sub-gap structures also played a role in the transmission of the supercurrent through the weak link [@Asano:01],[^99] and that a A-like phase inside the superfluid junction could also result in the existence of a $\\pi$-state [@Nishida:02]. ]{}", "\n\n[$\\bullet$ Dissipation in pressure-driven [*dc*]{}-supercurrents [@Simmonds:00] could also be explained by multiple Andreev reflections [@Mukharsky:04-JLTP; @Viljas:05] or by time-dependent anisotextural effects and spin-wave emission, [@Viljas:04-PRL; @Viljas:05]: if a pressure difference is applied across the weak link, an [*ac*]{}-oscillation (at the [*ac*]{}-Josephson frequency) of the texture ensues, causing dissipation by spin-wave radiation. ", "The two dissipation mechanisms, sub-gap processes and textural losses, can come on top of one another. [", "^100]]{}\n\nObservations related to these topics are those of @Mukharsky:04 who, in the course of high-precision CPR measurements using the Sagnac effect described in §\\[interferometry\\], found the signature of a stable textural defect that sustains a change of the phase by $\\pi$ away from the weak link. ", "This differs from the $\\pi$-state discussed above. “", "Cosmic-like” solitons, proposed by @Salomaa:88, could constitute such a defect but they are thought to be unstable in the bulk of the superfluid.", "\n\nA comprehensive study of the possible planar interfaces between two domains of superfluid $^3$He-B has been conducted by @Silveri:14. ", "Of all the possible planar structures allowed by the symmetries of the B-phase order parameter, only one is found to be energetically stable in the presence of walls. ", "This particular interface is characterised by the vanishing of one of the components of the interfacial order parameter along a [*gap-node direction*]{} contained in the plane of the domain wall. ", "It sustains a phase change by $\\pi$ and can appear as a remnant of the A to B interface during cool-down through the transition.", "\n\nIn the perspective of the present article (see also the review by @Davis:02), these complex features of the Josephson supercurrents illustrate quite vividly the nature of the superfluid order parameter and of the phase coherence it entails. ", "But their detailed studies are complicated because they are entangled with order parameter textures, as mentioned above, but also because the state of the superfluid inside the micro-junction may not be precisely accounted for, as discussed in the next Section.", "\n\nThe peculiarities of the A-phase {#Peculiarities}\n--------------------------------\n\nThe A-phase takes over from the B-phase at the superfluid transition temperature above a pressure of 21.2 bars. ", "Strong coupling effects resulting from atomic localisation increase with density. ", "Part of these enhanced interactions is mediated by spin-spin exchange, the so-called paramagnons. ", "Because of these effects, the A-phase condensate only consists of $S_{\\m z}$ = +1 and -1 pairs, ($\\ket{\\uparrow\\uparrow}$ and $\\ket{\\downarrow\\downarrow}$), and the energy gap above the Fermi surface $|{\\m{\\bs \\Delta}}(\\hat{\\m{\\bs k}})|$ is strongly anisotropic while retaining the $L=1$ symmetry: it vanishes at a node in the direction of $\\hat{\\bs{\\m\n l}}$, the orbital quantisation axis. ", "As for its spin part, the A-phase behaves in some respect as an antiferromagnet with a spin quantisation axis $\\hat{\\bs{\\m d}}$. Its stability with respect to the B-phase is enhanced by an external magnetic field.", "\n\nThe A-phase order parameter in zero magnetic field is expressed in terms of three unit vectors, the spin quantisation axis $\\hat{\\bs{\\m d}}$, and the orthonormal vectors $\\hat{\\bs{\\m m}}$ and $\\hat{\\bs{\\m n}}$ forming a triad with $\\hat{\\bs{\\m l}}$, the direction of the orbital angular momentum of the pairs. ", "It is written in tensorial notation as: $$\\label{APhaseOrderParameter}\n A_{\\mu i} = \\Delta_{\\m A} \\hat{d_\\mu} (\\hat{m_i} + \\m i\\, \\hat{n_i}) \\; .$$\n\nIn $^4$He, the Bose order parameter is a simple complex number and the phase comes in quite naturally as it does for the BCS order parameter in s-wave superconductors, for ultracold atoms, and for the B-phase order parameter, Eq.(\\[BPhaseOrderParameter\\]), as discussed above.", "\n\nNo single phase factor appears spontaneously in expression (\\[APhaseOrderParameter\\]) for the A-phase order parameter. ", "However, the single-particle wave function in the condensate still possesses an overall phase among other components. ", "This phase goes over to the macroscopic Bose order parameter, which inherits of a global $U(1)$ phase rotation broken symmetry.", "\n\nBut this is not the whole story: a rotation of the triad $\\hat{\\bs{\\m\n l}},\\,\\hat{\\bs{\\m m}},\\,\\hat{\\bs{\\m n}}$ about the angular momentum directrix $\\hat{\\bs{\\m l}}$ by angle $\\gamma$ also contributes an overall phase factor to the A-phase order parameter. ", "This property can be seen readily by considering the complex plane perpendicular to $\\hat{\\bs{\\m l}}$ containing the complex vector $\\hat{\\bs{\\m m}}+\\m i\\,\\hat{\\bs{\\m n}}$ that appears in Eq.(\\[APhaseOrderParameter\\]): a rotation by angle $\\gamma$ in the complex plane transforms $\\hat{\\bs{\\m m}}+\\m i\\,\\hat{\\bs{\\m n}}$ into ${\\m{exp}}(-\\m\ni\\gamma)\\,(\\hat{\\bs{\\m m}}+\\m i\\,\\hat{\\bs{\\m n}})$. The Galilean invariance argument as used to derive the two-fluid model for $^4$He leads, when everything is told, to the following expression for the velocity of superfluid mass transport:[^101] $$\\label{AphaseSuperfluidVelocity}\n{\\mb v_\\m s} = -\\, \\frac{\\hbar}{2m_3}\\,(\\nabla\\gamma + \n \\cos \\beta\\,\\nabla\\alpha) \\;.$$ The Euler angles $\\alpha,\\beta,\\gamma$ fix the orientation of the orbital triad $\\hat{\\bs{\\m l}},\\,\\hat{\\bs{\\m n}},\\,\\hat{\\bs{\\m m}}$ in the chosen reference frame, $\\gamma$ expressing a rotation about $\\hat{\\bs{\\m l}}$ as already mentioned. ", "Two independent phase gradients appear in Eq.(\\[AphaseSuperfluidVelocity\\]). ", "In one, $-\\nabla\\gamma$, the angle plays the role of the usual phase $\\varphi$. This feature arises because the $U(1)$ phase rotation broken symmetry as already mentioned. ", "The other stems from the bending of the $\\hat{\\bs{\\m l}}$-texture. ", "Superflow is not simply governed by the gradient of the global phase alone. ", "The velocity field $\\bs{v_\\m s}$ is no longer irrotational in general, hence the circulation of $\\bs v_\\m s$ over a closed loop is no longer necessarily quantised.", "\n\nIn the presence of non-uniform $\\hat{\\bs{\\m l}}$ textures, the change of orientation of $\\hat{\\bs{\\m l}}$ in space may also contribute to the supercurrent. ", "The contour integral of Eq.(\\[AphaseSuperfluidVelocity\\]) along a closed loop $\\Gamma$ can be put under the form $$\\label{HoCirculationTheorem}\n{\\oint_{\\Gamma}\\,\\bs v_\\m s\\cdot\\m d\\bs r = \\frac{\\hbar}{2m_3}\\,\\big[ 2\\pi n + \n\\sigma(\\cal D}\\big ] \\;.$$ The first contribution to the rhs of Eq.(\\[HoCirculationTheorem\\] is recognised as the quantised velocity circulation around line singularities, as found in superfluid $^4$He, the second is expressed [@Ho:78] as the area circumscribed on the unit sphere by unit vector $\\hat{\\bs{\\m l}}$ when carrying the loop integral along contour $\\Gamma$. This last contribution is nil in the trivial case\n\n![", "\\[StaircasesAphase\\] Staircase patterns in the A-phase at 28.4 bars and $T=0.92 T_\\m c$ ($T_\\m c = 2.417$ mK). ", "The left and right panels show the patterns slightly above and below the resonator resonance at $\\omega_\\m m=1.783$ Hz, as observed (upper curves) and as computed (lower curve) with the Deaver-Pierce model. ", "From [@Avenel:89]. ](", "Fig29.pdf){width=\"120mm\" height=\"60\"}\n\nwhere $\\hat{\\bs{\\m l}}$ keeps pointing in a fixed direction. ", "There exist other less-trivial cases with $\\sigma({\\cal D})=0$ as discussed by @Ho:78, but, in general, this contribution is non-zero and the velocity circulation is non-quantised.", "\n\nThe interplay between superflow, vortices and textures of the order parameter becomes quite complex.[[^102]]{} In particular, the A-phase persistent superflow can be relaxed by textural motion alone without the creation of topological singularities of the order parameter such as vortices. ", "However, if large-scale motion of the texture is suppressed, dissipation can be quenched and persistent currents stabilised, as shown by the experiments of @Gammel:85. ", "The authors demonstrated the existence of such currents in the annular space of a torsional oscillator packed with 25 silicon carbide powder. ", "The effect of the powder was to immobilise $\\hat{\\bs{\\m l}}$. The (small) supercurrent was detected indirectly through its effect on the damping of the small-amplitude of the torsional oscillator. ", "This crafty experiment showed that the A-phase possesses, if to a less convincing extent than the B-phase, the distinctive attribute of dissipationless flow.", "\n\nThe phase slippage concept can also be extended to the A-phase, as proposed by @Anderson:77. ", "Josephson-type experiments can be contemplated with some uncertainty as to their outcome because of the lack of quantisation of the velocity circulation, and also because of the large dissipation associated with the motion of the order parameter gap in the direction of $\\hat{\\bs{\\m l}}$, where its nodes lie.", "\n\nThese experiments were attempted by @Avenel:89 with the same resonator as for their B-phase experiments. ", "They did observe staircase patterns in the A-phase both close to the superfluid transition temperature with a rather non-ideal current-phase relation, and further down in temperature where new features occurred. ", "The patterns shown in Fig.\\[StaircasesAphase\\] obtained in the A-phase at $T=0.92\nT_\\m c$ at frequencies slightly above and below the resonance frequency of the flexible wall resonator are quite well defined but differ markedly: they exhibit large dispersive effects, a sharply peaked resonance and low dissipation. ", "The outcome of numerical simulations of the resonator response using the Deaver-Pierce model, Eq.(\\[DeaverPierce\\]) are shown below the experimental data curves. ", "The resonance quality factor is high, $Q= 80$. The non-ideality parameter $\\alpha$ is equal to 5: the phase slips are hysteretic and weakly dissipative.", "\n\nGiven this observation that the A-phase phase-slip pattern seems to follow the ubiquitous Deaver-Pierce model at 0.92 $T_\\m c$, it could be expected to become more and more ideal when raising the temperature closer to $T_\\m c$. This trend could unfortunately not be ascertained in these experiments because the operating frequencies, which decrease as $\\rho_\\m s/\\rho$, become too low and the useful signal gets lost in the background $1/f$ mechanical noise of the detection device.", "\n\n![", "\\[ComparisonA-Bphase\\] Staircase patterns in the A and B phases at nearly identical frequencies and temperature. ", "The horizontal ticks mark the periodicity of the staircase pattern (top) and of the low-level structure (bottom). ", "This low-level structure has been attributed by the authors to solid friction of unknown origin somewhere in the resonator (but may also arise from sub-gap energy levels). ", "From [@Avenel:89].](Fig30.pdf){width=\"120mm\" height=\"60\"}\n\nFurther down in temperature, an instructive direct comparison between the A-phase response and that of the B-phase at high pressure can be carried out by taking advantage of the following circumstance: at 28.4 bars, the A to B transition occurs at about 0.81 $T_\\m c$; it is signalled by a sudden drop in resonance frequency caused by the drop in superfluid density accompanying the first order transition. ", "As the A-phase can be supercooled into the domain of stability of the B-phase, both phases can be studies at comparable frequencies.", "\n\nThe outcome of this comparison is shown in Fig.\\[ComparisonA-Bphase\\] and reveals a remarkable similarity between the two phases. ", "The response of the superfluid in the weak link depends little on whether the bulk of the liquid is in the A or the B phase. ", "As discussed by @Avenel:89, the observed behaviour inside the micro-slit corresponds well to the situation described by @Kurkijarvi:88 who finds that the current-phase relations for the A and B phases differ only little (see Eq.(\\[CPRKurki\\])). ", "It may also happen that the state of the superfluid in the weak link remains the same irrespective of the state in the bulk. ", "It has been predicted by @Li:88 and @Fetter:88 that the A-polar phase would be favoured by the depletion of some of the components of the A-phase order parameter close to the aperture walls.", "\n\nThe sub-gap structure, shown in Fig.\\[ComparisonA-Bphase\\], which develops for resonance amplitudes below the critical threshold at which dissipative phase slips start to occur, is quite intriguing. ", "It is interpreted by @Avenel:89 as arising from possible (aniso)-textural effects inducing solid friction. ", "It could also possibly be revealing the existence of sub-gap resonant levels.", "\n\nThese experiments establish very clearly that phase slippage takes place in the A phase, that persistent currents can be trapped in the loop threading the double-hole resonator, and that the velocity circulation along these trapped currents changes by multiples of the quantum of circulation in the same manner as in the B phase: it so turns out, as was the case in the persistent current experiments by @Gammel:85, that the $\\hat{\\bs{\\m l}}$-texture is sufficiently well pinned in the regions where ${\\bs v_\\m s}$ picks up significant speed.", "\n\nTopological defects, seen above to play an important role in phase slippage experiments, offer a vast and fascinating domain of study, both in the A and B phases. ", "The vortex core develops complex structures, as reviewed by @Salomaa:87. ", "Vortex sheets can form in rotating $^3$He-A, as observed by @Parts:94 using very sensitive NMR techniques, which have brought about a wealth of information on vortices in superfluids under rotation. ", "This work has been reviewed by @Finne:06. ", "Analogies can be drawn between the formation of defects in superfluid $^3$He and that of cosmic strings in the Early Universe because the order parameter symmetries that can be broken are the same. ", "These enticing prospects for experimental cosmology have been reviewed by @Eltsov:00, @Bauerle:00, @Bunkov:10 and @Volovik:03 in his wonderful book. ", "Phase slippage is beyond doubt relevant in these situations and will be used to study this vast new field.", "\n\n$^4$He close to the [[l]{}]{}–point {#LambdaPoint}\n-----------------------------------\n\nThe existence of Josephson-like effects was thus clearly established in superfluid $^3$He for the [*dc*]{}-effect and in both $^3$He and $^4$He superfluids for the [*ac*]{}–effect by Year 2000. ", "The remaining problem was the possible observation of a quasi-sinusoidal current-phase relation in $^4$He. ", "The minuteness of the coherence length in $^4$He makes the fabrication of a suitable weak link a tall order except in the immediate vicinity of the ${{\\mbox{\\footnotesize{{\\usefont{U}{psy}{m}{n}l}}}}}$-point, where it diverges as $\\xi=\\xi_0(1-T/T_{{\\mbox{\\footnotesize{{\\usefont{U}{psy}{m}{n}l}}}}})^{-2/3}$ with $\\xi_0 \\sim$ 1 to 2 Å [@Langer:70]. ", "At the ${{\\mbox{\\footnotesize{{\\usefont{U}{psy}{m}{n}l}}}}}$-point however, superfluidity is suppressed by thermal fluctuations. ", "Would the hydrodynamic Josephson effects not be even more readily washed out by the same token?[^103]\n\nThis concern was formalised by Zimmermann (1987) whose argument runs approximately as follows. ", "The Josephson coupling energy is obtained from the Josephson current, Eq.(\\[dcJosephson\\]), by integration with respect to $(\\hbar/m_\\m 4) {\\mbox{\\small{{\\usefont{U}{psy}{m}{n}d}}\\hskip 0.05ex}}\\varphi$. Its maximum value is therefore $(\\hbar/m_4)\\,J_\\m c$ and reads $$\\label{JosephsonEnergy}\nE_\\m J = \\left(\\frac{\\hbar}{m_4}\\right)^2\\,\\frac{s_\\m b}{b_\\m b}\\,\n \\frac{\\rho_\\m s}{\\sinh(l_\\m b/b_\\m b)} \\; .$$\n\nIn the weak coupling limit for which Eq.(\\[dcJosephson\\]) holds, the wavefunction is strongly depleted within the barrier and the penetration length is smaller than the length of the barrier, $b_\\m b \\lesssim l_\\m b$. Making use of the scaling relation between $\\rho_\\m s(T)$ and $\\xi(T)$ [@Josephson:66],[^104] $$\\label{ScalingRelation}\n \\rho_\\m s \\xi = (m_4/\\hbar)^2 k_\\m B T \\; ,$$ and since $\\sinh(l_\\m b/b_\\m b) > l_\\m b/b_\\m b$ it stems from Eq.(\\[JosephsonEnergy\\]) that $$\\label{ZimmermannCondition}\nE_\\m J \\lesssim \\frac{s_\\m b}{l_\\m b} \\,\\frac{k_\\m B T}{\\xi(T)}\n \\; .$$ For the round pinhole with diameter $d$ considered by Zimmermann, $s_\\m b =\n\\pi d^2/4$ and $l_\\m b > \\ell_\\m h$, the hydraulic length $\\ell_\\m h$ being $\\pi d /4$ for a circular orifice,[^105] so that $E_\\m J < k_\\m\nBT \\,d/\\xi(T)$. Zimmermann concludes from this upper bound for the Josephson energy that, as $\\xi(T)$ diverges upon approaching $T_\\m {{\\mbox{\\footnotesize{{\\usefont{U}{psy}{m}{n}l}}}}}$ from below, the Josephson coupling energy will end up being less than the thermal energy and that the Josephson [*dc*]{}-effect will be washed out by thermal fluctuations.", "\n\nSimilar concerns were spelled out by @Ullah:89 for their calculations of weak link properties in $^3$He-B in the Ginzburg-Landau regime: “[*We do not address the important problem of thermal fluctuations destroying the superfluidity in the very small volume of the weak link. ", "To our knowledge, there is no reliable, quantitative theory of the stability of the superfluid phase is severely confined geometries. ", "We believe that this question can be convincingly answered only by experiment*]{}”. ", "This remark is even more relevant to superfluid $^4$He close to $T_{{\\mbox{\\footnotesize{{\\usefont{U}{psy}{m}{n}l}}}}}$.\n\nThe first hint of a successful experimental observation was reported by @Sukhatme:01. ", "These authors used an array weak link of 24 micro-slits 3 m x 0.17 m about 10 m apart in a 0.15 m thick membrane. ", "Their findings are summarised in Fig.\\[Sukhatme-staircase\\]. ", "At 3.72 mK below $T_{{\\mbox{\\footnotesize{{\\usefont{U}{psy}{m}{n}l}}}}}$ – the bottom curve in the figure, the scale of which is shrunk – the critical velocity is well-marked, as well as the staircase steps, indicating a dissipative phase slippage process. ", "A phase-slip regime has been reached. ", "This was hoped for since the temperature-dependent coherent length 3.72 mK below $T_{{\\mbox{\\footnotesize{{\\usefont{U}{psy}{m}{n}l}}}}}$, $\\xi(T)=24$ nm,[^106] is smaller than the micro-slit width, but by less than one order of magnitude.", "\n\n-5 mm 6 mm ![", "\\[Sukhatme-staircase\\] (Color online) Staircase patterns in $^4$He close to $T_\\m{{\\mbox{\\footnotesize{{\\usefont{U}{psy}{m}{n}l}}}}}$ (amplitude, in picometres versus drive, in arbitrary units, from @Sukhatme:01) for $T_{{\\mbox{\\footnotesize{{\\usefont{U}{psy}{m}{n}l}}}}}-T=$ 61 $\\mu$K – curve i), 154 $\\mu$K – curve ii), and 3.72 mK – curve iii). ", "The plots are shifted vertically by 2 pm with respect to one another for clarity. ", "The data for curve iii) has been divided by 20 along the $x$-axis and by 10 along the $y$-axis. ", "As in the case of $^3$He-B – shown in Fig.\\[PRL88-fig2-staircase\\] – the height of the first step corresponds to the critical current $J_\\m c$. Each subsequent step corresponds to an additional phase difference of $2\\pi$ (Courtesy of Yuri Mukharsky). ](", "Fig31.pdf \"fig:\"){width=\"90\"}\n\nGetting closer to $T_{{\\mbox{\\footnotesize{{\\usefont{U}{psy}{m}{n}l}}}}}$ from below, successively at $T_{{\\mbox{\\footnotesize{{\\usefont{U}{psy}{m}{n}l}}}}}-T = 154\n$K, and 61 K, the expected trend toward a smoother, less dissipative staircase pattern is observed, much like in Fig.(\\[PRL88-fig2-staircase\\]) for $^3$He, supporting the conclusion that the same hydrodynamic ideal Josephson effect can be observed in superfluid $^4$He close to the superfluid transition temperature $T_{{\\mbox{\\footnotesize{{\\usefont{U}{psy}{m}{n}l}}}}} = 2.17$ K.\n\nThis conclusion raises questions, and possibly, some eyebrows as well:\n\n[$\\bullet$  Would, for some reason, Zimmermann’s argument be invalid?]{}", "\n\n[$\\bullet$  How come that dissipative phase slippage, the mechanism for which seems to rely on the nucleation of a single vortex and its crossing of all streamlines of the superfluid flow through a single micro-slit also operates for an extended array of them?]{}", "\n\nZimmermann’s original argument, outlined above, was applied to a single round hole. ", "@Sukhatme:01’s 24 parallel slits yield an estimated enhancement factor of 500 in the superflow passage area $s_\\m b$ that appears in Eq.(\\[ZimmermannCondition\\]), provided that the supercurrents in the apertures effectively sum up. ", "The overall Josephson energy is increased by the same factor and the disruptive effect of thermal fluctuations is pushed back much closer to $T_{{\\mbox{\\footnotesize{{\\usefont{U}{psy}{m}{n}l}}}}}$. This line of reasoning was pursued by @Chui:03, but its soundness depends on the answer to the second question, which turns out to be trickier.", "\n\nThe Berkeley group carried out a number of studies[^107] with aperture arrays similar to those used for $^3$He-B by @Marchenkov:99. ", "The size of the round pinholes in these arrays, 90 nm in diameter, is comparable to the coherence length one millikelvin away from the -point but the distance separating the pinholes, located on a 3 m square lattice, is much larger. ", "Two phase-slippage regimes are identified when the temperature is lowered below $T_\\m{{\\mbox{\\footnotesize{{\\usefont{U}{psy}{m}{n}l}}}}}$ as already reported by @Sukhatme:01. ", "At $\\sim$ 50 to 100 K below $T_\\m{{\\mbox{\\footnotesize{{\\usefont{U}{psy}{m}{n}l}}}}}$ (and slightly further down in temperature in the experiments by @Sato:06), a reversible (non-dissipative) Josephson regime is observed. ", "In this regime, the phase-slips occur in a fully [*synchronous*]{} manner. ", "Between approximately 0.3 to 15 mK below $T_\\m{{\\mbox{\\footnotesize{{\\usefont{U}{psy}{m}{n}l}}}}}$, a transition toward a dissipative phase-slip regime sets in as the synchronisation between the apertures gets lost. ", "Further below $T_\\m{{\\mbox{\\footnotesize{{\\usefont{U}{psy}{m}{n}l}}}}}$, the phase-slip regime becomes [ *asynchronous*]{}. ", "The amplitude of the resultant phase slippage signal from the array does not sum up to what it should be. ", "It also exhibits large slips and collapses somewhat similar to those described in §\\[LargeSlips\\] for a single orifice (but of a different sort, see below).", "\n\nIt is clear that inhomogeneities in aperture size and surface properties, the edge effects at the periphery of the array, and local critical fluctuations introduce a spread in the values of the critical current in the different apertures. ", "Phase slips occur at different times during resonator motion. ", "The summation of the currents through the various apertures, as attempted in the numerical simulations of arrays of superfluid Josephson junctions by @Avenel:99, @Pekker:07, and @Sato:07 has to be exercised with care.", "\n\nIt can be argued [@Chui:03] that the Josephson currents in the micro-apertures are small and perturb little the quantum phases in the bulk on both sides of the membrane supporting the weak link array. ", "Phases are well defined below $T_\\m{{\\mbox{\\footnotesize{{\\usefont{U}{psy}{m}{n}l}}}}}$ – for instance, the quantisation of circulation is enforced – and so should their difference. ", "This reasoning would appear to leave only one degree of freedom to undergo fluctuations, with a thermal energy of $k_\\m B\\,T/2$ to be shared among the $N$ apertures of the array: the effect of fluctuations in each individual aperture would effectively be quenched on taking the average over the whole array.", "\n\n![", "\\[Hoskinson:06-Interference\\] Superfluid Interferences in a two-aperture resonator.\\\nTop panel: (a) Sketch of the hydromechanical resonator. ", "The unshaded regions are filled with superfluid $^4$He. ", "The flexible metallised diaphragm at the top of the upper chamber serves both as a microphone to detect the resonant oscillations and as a pressure pump to drive the flow across the two aperture arrays indicated by crosses. ", "These arrays interrupt the superfluid channel enclosing the sense area. (", "b) Diagram of the resonator equivalent circuit showing the analogy with the electrodynamic dc-SQUID. ", "There are two superposed currents flowing through the weak links, one corresponding to the rotation flux picked-up by the sensing loop, Eq.(\\[Bias\\]), the other being the common-mode read-out current from the flexible diaphragm.\\\nBottom panel: Peak amplitude of the diaphragm displacement on resonance as a function of the rotation flux $2\\, {\\bf \\Omega}\\cdot{\\bf A}$ picked up by the superfluid loop enclosing the sense area – see §\\[interferometry\\] for a detailed description of these interferometer operation based on the Sagnac effect. ", "The measured data is shown by the symbols; the solid lines are fits to the data of the equation modelling the resonator motion as described by @Hoskinson:06. ", "The modulation curves were taken at temperatures $T_{{\\mbox{\\footnotesize{{\\usefont{U}{psy}{m}{n}l}}}}}\\,-\\,T =$ 12, 7.0, 4.0, 3.0, 2.0, 1.5, 0.9, 0.6, 0.4, and 0.3 mK from top to bottom. ", "This temperature span covers the coherent Josephson regime in the array discussed in §\\[LambdaPoint\\]. ", "From @Hoskinson:06 ](Fig32a.png \"fig:\"){width=\"55\"} ![", "\\[Hoskinson:06-Interference\\] Superfluid Interferences in a two-aperture resonator.\\\nTop panel: (a) Sketch of the hydromechanical resonator. ", "The unshaded regions are filled with superfluid $^4$He. ", "The flexible metallised diaphragm at the top of the upper chamber serves both as a microphone to detect the resonant oscillations and as a pressure pump to drive the flow across the two aperture arrays indicated by crosses. ", "These arrays interrupt the superfluid channel enclosing the sense area. (", "b) Diagram of the resonator equivalent circuit showing the analogy with the electrodynamic dc-SQUID. ", "There are two superposed currents flowing through the weak links, one corresponding to the rotation flux picked-up by the sensing loop, Eq.(\\[Bias\\]), the other being the common-mode read-out current from the flexible diaphragm.\\\nBottom panel: Peak amplitude of the diaphragm displacement on resonance as a function of the rotation flux $2\\, {\\bf \\Omega}\\cdot{\\bf A}$ picked up by the superfluid loop enclosing the sense area – see §\\[interferometry\\] for a detailed description of these interferometer operation based on the Sagnac effect. ", "The measured data is shown by the symbols; the solid lines are fits to the data of the equation modelling the resonator motion as described by @Hoskinson:06. ", "The modulation curves were taken at temperatures $T_{{\\mbox{\\footnotesize{{\\usefont{U}{psy}{m}{n}l}}}}}\\,-\\,T =$ 12, 7.0, 4.0, 3.0, 2.0, 1.5, 0.9, 0.6, 0.4, and 0.3 mK from top to bottom. ", "This temperature span covers the coherent Josephson regime in the array discussed in §\\[LambdaPoint\\]. ", "From @Hoskinson:06 ](Fig32b.png \"fig:\"){width=\"70mm\"}\n\nThis argument has to be stretched a long way to explain the large span in $T_{{\\mbox{\\footnotesize{{\\usefont{U}{psy}{m}{n}l}}}}} -T$ over which the synchronous phase-slippage regime subsides both very close to the [[l]{}]{}-point when quantum coherence should end up being killed by thermal fluctuations, and quite a way below it where it should be randomised by array imperfections. ", "In other words, the robustness of the coherence effect mentioned above against dephasing by environmental effects appears quite remarkable. ", "@Perron:13 have pointed out that the superfluid onset in the micro-slits used by @Sukhatme:01 is expected to be depressed by size effects to $T_{{\\mbox{\\footnotesize{{\\usefont{U}{psy}{m}{n}l}}}}} - T_\\m c \\simeq 430$ K whereas the Josephson effect could be tracked to as close as 28 K below $T_{{\\mbox{\\footnotesize{{\\usefont{U}{psy}{m}{n}l}}}}}$. Similarly, for the pinholes used by @Sato:06, $T_{{\\mbox{\\footnotesize{{\\usefont{U}{psy}{m}{n}l}}}}} - T_\\m c\n\\simeq 2.3$ mK while the Josephson effect survived up to possibly 0.5 mK from $T_{{\\mbox{\\footnotesize{{\\usefont{U}{psy}{m}{n}l}}}}}$. As concluded by @Perron:13, “[*in both experiments one obtains superflow in a temperature region where the helium in the isolated weak links should be normal. ", "Both of these experiments are thus relying on proximity effects, due to the surrounding bulk liquid, to maintain a non-zero order parameter in the weak links*]{}”.", "\n\nThese authors draw their conclusion from studies of the interconnection of an array of 2 m$\\times$2 m micro-pools linked through the film of superfluid $^4$He. ", "They have found from measurements of the specific heat and the superfluid fraction in the vicinity of $T_{{\\mbox{\\footnotesize{{\\usefont{U}{psy}{m}{n}l}}}}}$ that correlation effects are still effective at distances up to 100 times $\\xi(T,L)$, the finite-size correlation length suitably renormalised for confinement over the distance $L$, the size of the micro-pools boxes. ", "The unexpectedly large extent of the correlation observed between micro-pools can be likened to the robustness of the coherent behaviour of Josephson junction arrays close to $T_{{\\mbox{\\footnotesize{{\\usefont{U}{psy}{m}{n}l}}}}}$.\n\n@Pekker:07, besides their numerical studies referred to above, also treated the problem of aperture current summation in an irregular array as an order-disorder transition in a mean-field approximation approach. ", "They introduce a distribution of aperture critical currents and an effective inter-aperture coupling parameter. ", "They report qualitative agreement with the experiments of @Sato:06 including “[*system-wide avalanches*]{}”, both in the numerical simulations of the array behaviour and in the ordering transition approach.", "\n\nThe observed long range of cross-aperture coupling may arise from a simple classical hydrodynamics scheme, which is an extension to arrays of the putative mechanism for single-aperture large slips discussed in §\\[LargeSlips\\]. ", "Suppose that, during the surge of the superflow through the array, a (quantum) phase slip occurs early in one of the apertures, releasing a vortex half-ring that starts drifting (classically) sideways along the membrane supporting the array. ", "Soon, this vortex half-ring runs into the flow lines emerging from a nearby aperture, gaining energy from it to proceed in its course and, possibly, triggering the nucleation of another vortex half-ring, and so on. ", "This multiplication process may die by itself at the ebb of the flow. ", "Or, if it overcomes the friction on the normal component, it may trigger $2\\pi$ slips over all the microholes of the array, or, possibly, swell to the system-wide avalanches [@Pekker:07] observed by @Sato:06. ", "This mechanism for avalanches are thus intrinsic to aperture array dynamics and distinct from flow collapses in single apertures discussed in §\\[LargeSlips\\].", "\n\nEven more so than in single apertures, “macroscopic quantum coherence” manifests itself in the aperture array in a dual manner. ", "First, the condensate acts as an ideal Euler fluid, maintaining orderly streamlines throughout the superflow in accordance to the Kelvin-Helmholtz theorem. ", "Then, when a non-adiabatic process takes place, violating velocity circulation conservation, it does so in a quantum manner, allowing the phase to change by multiples of $2\\pi$, for instance by the nucleation of a quantised vortex or by the current source or sink provided by Josephson tunnelling through a thin barrier of normal fluid.", "\n\nConcluding comments {#conclusion}\n===================\n\nMatter waves and superfluid interferometry {#interferometry}\n------------------------------------------\n\nThe single-hole or two-hole hydromechanical resonators used in the phase slippage experiments described above have been presented so far as the analogues of [*rf*]{} or [*dc*]{} superconducting quantum devices (SQUIDs), a useful analogy to help understand the way they operate. ", "Another analogy is used in this Section to illustrate the concept of coherent matter fields, or [*matter waves*]{}, introduced for superfluid helium by Anderson in 1965. ", "These devices are now considered as the likes of optical Sagnac interferometers; as the latter, they can be used to measure absolute rotations with very high sensitivity.", "\n\nConsider a pool of superfluid in the shape of a conduit bending on itself as shown in Figs.\\[Hoskinson:06-Interference\\] or \\[Gyrometer\\]. ", "The circulation of the velocity is quantised [*in the inertial frame*]{} – the reference frame fixed with respect to the distant stars – along any closed contour $\\Gamma$ located entirely in the superfluid: $$\\oint_{\\Gamma} {\\bf v}_\\m s \\cdot{\\m d}{\\bf l}= \n \\frac{\\hbar}{m_\\m a}\\,\\oint_{\\Gamma}\\,\\nabla\\varphi \\cdot{\\m d}{\\bf l}\n = n\\kappa_\\m a \\; ,$$ where $\\kappa_\\m a=2\\pi\\hbar/2 m_3$ for $^3$He, 3/2 times that quantity for $^4$He, and $n$ is an integer.", "\n\nIf the cryostat housing the pool is set into rotation with rotation vector ${\\bf\n \\Omega}$, the velocity transforms in the new frame according to ${\\bf v}'_\\m\ns ={\\bf v}_\\m s - {\\bf \\Omega} \\times {\\bf r}$ and the quantisation of circulation condition now reads $$\\label{Circulation}\n \\oint_{\\Gamma}{\\bf v}'_\\m s\\cdot{\\m d}{\\bf l} \n = n\\kappa_\\m a - \\oint_{\\Gamma} {\\bf \\Omega} \\times {\\bf r}\\cdot{\\m d}{\\bf l}\n = n\\kappa_\\m a - 2\\,{\\bf \\Omega}\\cdot{\\bf S}_\\Gamma\\,,$$ ${\\bf S}_\\Gamma$ being the geometrical (oriented) area of the closed superfluid contour.", "\n\nFor an actual conduit with finite cross section such as the one pictured in Figs.\\[Hoskinson:06-Interference\\] and \\[Gyrometer\\], there is a variety of choices for the contour $\\Gamma$. The mean circulation of the velocity results from a suitable average over the various distinct superfluid contours threading the conduit. ", "Taking the average of Eq.(\\[Circulation\\]) over all the streamlines threading the conduit amidst stray thermal currents, pinned vortices, and textures, weighed according to the (infinitesimal) mass current that they carry, leads to [@Avenel:97]: $$\\label{Bias}\n\\left\\langle\\oint_{\\Gamma} {\\bf v}'_s\\cdot{\\m d}{\\bf l}\\right\\rangle \n = n\\kappa_\\m a + \\kappa_\\m b - 2\\,{\\bf \\Omega}\\cdot{\\left\\langle\\bf S\\right\\rangle} \\, ,$$ where $\\left\\langle{\\bf S}\\right\\rangle$ is the average of the contour areas over the conduit. ", "The average of the quanta of circulation carried by the various streamlines, $\\left\\langle n\\right\\rangle\\,\\kappa_\\m a$ has been written as $n\\,\\kappa_\\m a + \\kappa_\\m b$ to explicitly separate the non-quantised phase bias $\\delta\\varphi_{\\m b} = 2\\pi \\kappa_{\\m b}/\\kappa_{\\m\n a}$ arising from pinned vorticity from the strictly quantised contribution $2\\pi n$.\n\nThe last term to the right of Eq.(\\[Bias\\]) also amounts to a non-quantised contribution to the phase bias, which varies with the flux of the rotation vector ${\\bf\\Omega}$ through $\\left\\langle\\bf S\\right\\rangle$: the measurement of the corresponding phase difference with the interferometers depicted in Figs.\\[Hoskinson:06-Interference\\] or \\[Gyrometer\\], $\\delta\\varphi_\\m S= (m_\\m a/\\hbar)\\,2\\,{\\bf{\\Omega \\cdot \\left\\langle S\n \\right\\rangle}}$, gives access to the rotation velocity. ", "Alternatively, changing the orientation with respect to the North axis of the superfluid loop picks up more or less of the rotation flux due to the Earth rotation $\\Omega_\\oplus$. A known phase difference can be coupled to the weak link. ", "The experimenter is provided with a “gauge wheel” to steer the phase.[^108]\n\nExploiting the properties of superfluids to detect very slow rotations has been proposed even before the discovery of the Josephson effects in superfluids, understandably with some lack of accuracy as to how the experiment could be conducted. ", "Cerdonio and Vitale clarified in 1984 the way in which inertial and gravitational fields could be detected with superfluid $^4$He analogues of the [*rf*]{}-SQUID[@Cerdonio:84; @Bonaldi:90]. ", "A number of authors followed suit afterwards for superfluid $^3$He and $^4$He[@Varoquaux:92; @Packard:92b; @Hess:92], and for the Bose-Einstein condensed gases[@Stringari:01].", "\n\nDetailed schemes for the actual implementation of superfluid $^4$He gyros have been worked out with the help of numerical simulations[@Avenel:94] and from the analysis of the operation of existing double-hole hydromechanical resonators.[^109] The first measurement of $\\Omega_\\oplus$ with a superfluid device was performed using a resonator operating in hysteretic mode in superfluid $^4$He with a rotation-sensing loop of 4.0 cm$^2$ by @Avenel:96. ", "Soon after, the Berkeley group reported the observation of the effect of the rotation of the Earth with a similar device operated in the staircase mode, in much the same way as conventional [*rf*]{}-SQUID magnetometers.", "\n\n![", "\\[SagnacInterferometer\\] (Color online) Schematics of the optical Sagnac interferometer. ", "A collimated beam from the source enters the interferometer through a beam splitter and is separated into two beams travelling along the optical path defined by the three mirrors in opposite directions, as indicated by the arrows. ", "Re-entering the beam splitter, they recombine and produce a fringe pattern on the detector plate. ](", "Fig33.pdf){width=\"45\"}\n\nOne may mention for the record that early attempts to measure $\\Omega_\\oplus$ led to disappointing results to the dismay of experimenters[@Schwab:96a; @Schwab:96b; @Avenel:98]. ", "It was however quickly realised that the currents in the bulk of the cell outside the resonator[@Avenel:98; @Schwab:98], simply caused by the re-orientation of the cryostat, were interfering with, and possibly overwhelming, the relatively weak $\\Omega_\\oplus$–induced Sagnac current in the pick-up loop. ", "The influence of these stray currents can be made negligible by a proper design of the cell. ", "A sheath on the port connecting the resonator to the main body of the cell was used to that effect by @Avenel:96[@Avenel:97]. ", "The absence of such a decoupling device between the Sagnac current in the pick-up loop and the stray currents around the cell could cause uncontrolled inaccuracies of several tens of %[@Schwab:96a; @Schwab:97; @Schwab:98].", "\n\nThe potentialities of superfluid gyros as extremely sensitive and stable rotation sensors, able to track, [*e.g.*]{}, General Relativity effects, have been considered by @Avenel:98, @Chui:05, @Sato:12 and @Sato:14. ", "It appears that these gyros can compete with the most advanced rotation sensors, in particular because they are inherently driftless at very low temperatures.", "\n\nThese gyrometric devices are the direct superfluid analogues of the well-known Sagnac optical interferometers, as can be seen by inspection of the sketches of the latter in Fig.\\[SagnacInterferometer\\] and of the superfluid device in Fig.\\[Gyrometer\\]: the light source provides the incident light beam, the flexible membrane the supercurrent; counter-rotating waves travel along the square optical path, and along the coiled capillary, for the co-rotating part; the waves interfere in the beam splitter in the optical case, in the Josephson weak link in the superfluid case. ", "The interferometer shown in Fig.\\[Hoskinson:06-Interference\\] is closer to a Mach-Zehnder interferometer than to a Sagnac one but the analogy goes along in the same way.", "\n\nBut is this reasoning by analogy, or the display of clear fringe patterns such as those shown in Fig.\\[Hoskinson:06-Interference\\], sufficient proof that the Sagnac effect is involved in the operation of these superfluid interferometers?", "\n\n-2mm  Photograph and schematic view of the cell of @Avenel:04, approximately to scale for the inner parts, except for the loop, which is made of two turns of 0.4 mm internal diameter capillary (only one turn is shown) with total area $5.90\\,\\pm\\,0.10$ cm$^2$. The lower chamber of the resonator is a cylindrical duct, 1 mm in diameter, and connects the weak link to the flexible diaphragm (at the bottom) and to one end of the pickup loop (on the side); the upper chamber, a squat cylinder, is connected to the other end of the loop and to an inlet toward the main superfluid bath in which the resonator is immersed. ", "Two pairs of coils produce fields parallel and perpendicular to the flow through the weak link to control locally the order parameter texture in $^3$He. ", "The cryostat is rotated about the vertical axis $z$ by angle $\\beta$ from the North, shown by a compass needle; $\\lambda$ is the latitude, 48$^{\\circ}$43$^\\prime$ at Saclay. ", "This cell has been used to detect the rotation of the Earth from a “blind” laboratory with a sensitivity of $5\\times\n 10^{-3}\\,\\Omega_\\oplus\\mbox{ Hz}^{-1/2}$.](Fig34a.pdf \"fig:\"){width=\"42mm\"}  Photograph and schematic view of the cell of @Avenel:04, approximately to scale for the inner parts, except for the loop, which is made of two turns of 0.4 mm internal diameter capillary (only one turn is shown) with total area $5.90\\,\\pm\\,0.10$ cm$^2$. The lower chamber of the resonator is a cylindrical duct, 1 mm in diameter, and connects the weak link to the flexible diaphragm (at the bottom) and to one end of the pickup loop (on the side); the upper chamber, a squat cylinder, is connected to the other end of the loop and to an inlet toward the main superfluid bath in which the resonator is immersed. ", "Two pairs of coils produce fields parallel and perpendicular to the flow through the weak link to control locally the order parameter texture in $^3$He. ", "The cryostat is rotated about the vertical axis $z$ by angle $\\beta$ from the North, shown by a compass needle; $\\lambda$ is the latitude, 48$^{\\circ}$43$^\\prime$ at Saclay. ", "This cell has been used to detect the rotation of the Earth from a “blind” laboratory with a sensitivity of $5\\times\n 10^{-3}\\,\\Omega_\\oplus\\mbox{ Hz}^{-1/2}$.](Fig34b.pdf \"fig:\"){width=\"33mm\"}\n\nApparently not; superfluid gyros are still sometimes mistaken for purely inertial devices such as spinning tops, as discussed by @Varoquaux:08. ", "Clearly, the superfluid in a rotating bucket experiment is a dense medium. ", "It can be weighed on a scale. ", "For large enough rotation velocities, when enough vortex lines have been created, the fluid free surface eventually becomes concave, as in Newton’s rotating water bucket experiment. ", "For small velocities however, things are different: the superfluid does not even starts spinning because of the absence of viscosity. ", "Hence the common sense reluctance to admit that the far-fetched analogy between the behaviour of this condensed matter system and that of massless photons travelling at the velocity of light, or elementary particles like electrons or neutrons, or even confined ultra-cold atomic gases, holds any water.", "\n\nA more formal approach is the following. ", "As mentioned above, the Sagnac effect has been observed in a number of different physical systems, ranging from photon, electron, neutron and cold atomic gas interferometers to atomic clocks and the Global Positioning System.[^110] The unifying concept behind these widely different situations is provided by the transportation of Einstein clocks from location A to location B on a rotating platform [@Langevin:21; @Rizzi:04].", "\n\nConsider how these clocks can be synchronised, first when they are infinitely close to one another. ", "The space-time metric is characterised in the conventional notation by $ -\\m d s^2= g_{00}\\m d (x^0)^2 + 2g_{0i}\\m dx^0 \\m\ndx^i+g_{ii}\\m d(x^i)^2$. The infinitesimal time interval $\\m d t$ between two nearly simultaneous events taking place at this given location in space is such that $\\m ds^2 = g_{00}\\m d (x^0)^2 = -\\m c^2 \\m d t^2$, $\\m c$ being the velocity of light.", "\n\nIf the clocks are now separated in space by an infinitesimal amount $\\m d x^i$ and the two events taken, say at location A, as the ticking of clock A for one and as the signal transmitted by clock B of its ticking a small distance away for the second, the two ticks occur with a time lag given by $ \n \\m c \\m d t = - g_{0i} \\m d x^i\\,/\\,g_{00} \\; ,\n$ the repeated summation being on the space coordinates.", "\n\nIf clock B is now transported over a finite path $\\Gamma$ closing on itself in a frame rotating with velocity $\\mb\\Omega$, the total time shift results from an integration along path $\\Gamma$:[^111] $$\\label{TimeDifference} \n \\Delta t = \\frac{1}{\\m c}\\,\\oint_{\\Gamma} \\frac{g_{0i}\\m d x^i}\n {-g_{00}} \n =\\oint_{\\Gamma} \\frac{\\mb\\Omega \\!\\bs\\times\\! ", " \\mb r \\bs\\cdot\\m d\\mb r}\n {\\m c^2-(\\mb\\Omega\\!\\bs\\times\\!\\mb r)^2}\n \\simeq \\frac{2}{\\m c^2}\\, \\mb\\Omega \\bs\\cdot \\mb S \\; ,$$ $\\mb S$ being the vector area subtended by the loop $\\Gamma$.\n\nTime delay (\\[TimeDifference\\]) between the reading of the clock standing still on the rotating platform and that of the transported clock lies at the root of the Sagnac effect. ", "As it depends on the rotation velocity and the actual path $\\mathit \\Gamma$, absolute clock synchronisation cannot be achieved. ", "Sagnac corrections, Eq.(\\[TimeDifference\\]), must be performed as done routinely for Global Positioning Systems [@Ashby:04]. [", "^112]\n\nSo much with clocks. ", "For helium, a Lorentz invariant two-fluid model can be built over the usual Landau superfluid hydrodynamics as done by @Carter:92.[^113] The invariant velocity circulation, the generalisation of Eq.(\\[VelocityCirculation\\]), reads $$\\label{CovariantCirculation}\n \\int_\\Xi\\{ v'_0 \\m dx^0 + v'_i \\m dx^i\\} = n\\kappa \\; ,$$ where $(v'_o,v'_i)$ is the four-velocity in the rotating frame $(c^2+\\mb v'_\\m\nn\\bs\\cdot \\mb v'_{\\m s}\\,, -\\mb v'_\\m s)$. The normal fluid velocity $v'_\\m\nn$ and the superfluid velocity $v'_\\m s$ are very small compared to $\\m c$ so that the time-like component of the four-velocity reduces to $\\m c^2$. The integration over $\\Xi$ is an actual loop integral only for the space-like components. ", "The corresponding world line is not closed because the time for synchronised clocks varies according to Eq.(\\[TimeDifference\\]). ", "Upon integration, Eq.(\\[Circulation\\]) is recovered, $$\\label{Circulation2}\n \\oint_\\Gamma v'_i \\m dx^i = n\\kappa + \\int\\! ", "c^2 g_{0i} \\m dx^i/g_{00} \\simeq\n n\\kappa - 2\\,\\mb\\Omega\n \\bs\\cdot \\mb S \\; ,$$ which establishes the link between superfluid physics and the relativistic clock approach: the true and honest Sagnac effect described by the transported clocks, Eq.(\\[TimeDifference\\]), and the circulation quantisation condition in the rotating frame leading to Eq.(\\[Bias\\]) are one and the same.[^114]\n\nThus, Einstein-synchronised clocks provide the time standard by which phase differences can be kept track of in all the studied physical systems. ", "As appropriately summarised by @Greenberger:83 for neutron interferometry experiments: “[*the phase shift*]{} (in the rotating interferometer) [*is seen to be caused by the different rates at which a clock ticks along each of the two beams*]{}”. ", "The rate at which that clock ticks for helium depends on the chemical potential $\\mu$, due to the molecular field of the condensate as shown by Beliaev, and on the Sagnac phase shift.", "\n\nThe helium Sagnac experiments illustrate convincingly the reality of matter wave interference in the superfluid heliums, a substantially massive coherent field. ", "Coherent, as shown at some length here, means coherence of the quantum phase, giving a wave-like character to a bulky fluid. ", "A few remarks on this follow in a manner of conclusion.", "\n\nLandau’s two fluids, ODLRO, and macrorealism {#Conclusion}\n--------------------------------------------\n\nAnderson’s introductory words to the reprint of his 1966 paper in his book of 1994 are the following [^115]:“[*I feel this is the clearest discussion of superfluidity available. ", "Note that on many points this is contradictory or orthogonal to Landau orthodoxy as pronounced by Khalatnikov. ", "Whether Landau would have agreed was never clarified because of his accident”.*]{} ", "This remark poses the problem of the complementarity between the two-fluid model, the description of Bose condensation by the non-vanishing off-diagonal terms of the density matrix over a long range, and the macroscopic wavefunction approach.", "\n\nTwo crucial aspects of Landau’s legacy have been invoked here. ", "The two-fluid model has ruled once and for good on the separation between normal fluid and superfluid components, both for the thermodynamics and the hydrodynamics. ", "As used in this review in its reduced form for incompressible flows, which treats both components as independent, it has allowed to basically disregard the normal component. ", "There are obviously limits to this high-handed simplification, especially close to the -point, but it has provided the backbone of the simplified vortex dynamics of Sec.\\[VortexDynamics\\] and subsequent Sections on phase-slip processes. ", "The second pillar of Landau’s contributions to helium superflow is his criterion that many consider as the genuine [*intrinsic*]{} critical velocity in superfluids. ", "This criterion rests on the existence of a sharply-defined phonon-roton excitation spectrum, which allows for no low lying elementary excitations as Landau implicitly postulated.", "\n\nLandau’s foreknowledge was soon put on firm grounds by the work of Bogolyubov, Beliaev, Penrose, Onsager and others. ", "The formal description of the Bose condensate correlations ended up in the concept of off-diagonal long range order [@Yang:62] and a formal definition of the single wavefunction shared by the particles in the condensate. ", "For not-too-complicated superfluids – $^4$He and the B-phase of $^3$He – this wavefunction, or order parameter, has a definite overall phase.", "\n\nThe role of this phase actually came to the fore when @Anderson:66b gave it dynamical variable status and universal applicability. ", "In Appendix A of his paper, “[*ODLRO vs macroscopic particle fields*]{}”, he states explicitly that “[*recognising that in principle the relative phase of any two*]{} (superfluid) [*systems may always be measured by a Josephson-type experiment, one immediately has a usable local description*]{}” (of those systems).", "\n\nThis local description has been put to good use, as recounted in the foregoing at some length. ", "It has opened the way to a full understanding of the interaction of quantised vortices and superflow, put on firm classical hydrodynamics footing by @Huggins:70. ", "@Sonin:95 and others have further expanded the vortex velocity field idea into a workable scheme for vortex dynamics. ", "More importantly, it has bridged the gap between a predominantly “classical” two-fluid hydrodynamics and the more intimately quantum Josephson effects. ", "The experimental observation of these effects, and, in particular, the detailed way by which dissipative phase slippage, understood first as the nucleation and propagation of vortices, evolves into the purest brand of Josephson hydrodynamics effects, both for $^3$He and $^4$He superfluids, has brought fresh food for thought.", "\n\nDetailed numerical simulations of vortex dynamics have been conducted by Schwarz and others,[^116] in particular for the problems of the vortex in-an-aperture, or trapped on a thin wire, or else, pinned. ", "Collision between vortices, and the resulting reconnection, their multiplication by vortex mills churning out fresh quantised vorticity, the formation of vortex tangles, and the several ensuing critical velocities, are examples of the improved way of dealing with quantised vortices fostered one way or another by Anderson’s Considerations, which thus appear complementary to Landau’s views. ", "Experimental observations have fully borne out over the years this central concept of a macroscopic quantum phase governing the dynamical behaviour of the superfluid.", "\n\nAt least in [*one*]{} given pool of superfluid. ", "The idea that a given pool, or bucket, or droplet, of superfluid has its own phase has become so common place that the question of knowing if the quantum phase of an isolated droplet of superfluid has a value of its own as compared to an other one seems out of place. ", "As put by @Anderson:86: “[*[Do superfluids that have never seen each other have a well-defined relative phase]{}*]{}”?", "\n\nBefore answering by a qualified “yes”, it may be useful to consider the new inputs to this problem of the meaning, or reality, of the phase in Bose condensates that have emerged after 1996 from investigations in ultra-cold atomic systems. ", "This is not the topic of this review, but interference experiments with BEC gases do bear on some aspects of it.", "\n\nA seemingly curious fact was noted by @Javanainen:96 in their numerical simulations of the setting up of an interference pattern between two condensates formed in separate traps and left to overlap with one another.[^117] The initial number of particles in each condensate is well-defined in this computer experiment. ", "The phases of the condensate wavefunctions are in no instance invoked in the number crunching sequence describing the interference process. ", "Yet it does appear: the simple statistical count of bosons in separate bins suffices.", "\n\nThis finding is a manifestation for the special case of atoms in cold traps of the well-known tendency of bosons to “bunch” together. ", "This phenomenon is very clearly illustrated by @Castin:97 who tackled the same problem analytically. ", "Namely, they studied the evolution of the relative phase of two separate BE condensates of like-species of atoms confined separate traps and left at some instant to interact by leaking two small beams of atoms to a beam splitter. ", "The two outgoing split beams that have been mixed are read by two atom counters.", "\n\nFollowing these authors, consider first that only a single atom trap leaks atoms to the beam splitter. ", "Assume the first counting event to occur in counter (+). ", "The probability for this event to take place is 1/2. ", "Because of the Bose statistics, the next event has a probability 3/4 to take place in counter (+), in which the first event was recorded, and 1/4 for counter (-) that has not seen an atom yet [@Feynman:65]. ", "Iterating for $k$ such events in a row, @Castin:97 find that the probability that the $k$ atoms end up registered by counter (+) – and none by counter (-) – takes the following form, $${\\cal P}(k,0) = \\frac{1}{2}\\, \\frac{3}{4}\\,\\ldots \\frac{2k-1}{2k}\\, ,$$ which is quite different from the probability of the same final outcome for atoms with no quantum-statistical correlations, namely $1/2^k$. The latter becomes rapidly negligible for $k \\gg 1$ while the former decreases only as $k^{-1/2}$. Bosons have a strong tendency to crop or “bunch” together in states where they can find like-bosons.", "\n\n@Castin:97 proceed to study the case in which the two separate BE condensates are now leaking beams to the beam splitter. ", "If the two incident beams are described by fields with well-defined phases and identical amplitudes, $|\\psi_0| \\m e^{\\m i\\varphi_\\m A}$ and $|\\psi_0| \\m e^{\\m\n i\\varphi_\\m B}$, the mean intensities in the (+) and (-) output channels of the beam splitter are given by $$\\label{BeatIntensities}\n I_{\\ts +} = 2\\, |\\psi_0|^2 \\cos^2({\\mbox{\\small{{\\usefont{U}{psy}{m}{n}d}}\\hskip 0.05ex}}\\varphi/2) \\;\\mbox{ and }\\;\n I_{\\ts -} = 2\\, |\\psi_0|^2 \\sin^2({\\mbox{\\small{{\\usefont{U}{psy}{m}{n}d}}\\hskip 0.05ex}}\\varphi/2)$$ with ${\\mbox{\\small{{\\usefont{U}{psy}{m}{n}d}}\\hskip 0.05ex}}\\varphi = \\varphi_\\m B-\\varphi_\\m A$. ", "This matter wave interferometry measurement allows as expected the determination of the phase difference between the two condensates.", "\n\nWhat now if phases are not ascribed to the condensates but instead their particle numbers $N_\\m A$ and $N_\\m B$ are? ", "Assuming $N_\\m B = N_\\m A$ for simplicity (as in the simulations of @Javanainen:96) the two-condensate system is now described by a Fock state $\\bra {N_\\m A},\\ket {N_\\m A}$. Performing the same interferometry measurement by counting atoms in the (+) and (-) counters should end up yielding result (\\[BeatIntensities\\]). ", "It does, but the interesting thing is how a phase difference arises from the mere statistical count.", "\n\nThe detailed probability ${\\cal P}(k_{\\ts +},k_{\\ts -})$ of counting $k_{\\ts +}$ events in counter (+) and $k_{\\ts -}$ in counter (-) has been worked out analytically by @Castin:97. ", "The beat pattern given by Eq.(\\[BeatIntensities\\]) is found to emerge gradually from the successive counting events in the (+) and (-) counters. ", "The phase difference can be obtained from the tallied quantities $k_{\\ts +}$ and $k_{\\ts -}$: ${\\mbox{\\small{{\\usefont{U}{psy}{m}{n}d}}\\hskip 0.05ex}}\\varphi \\simeq \\arctan (\\sqrt{k_{\\ts -} /\n k_{\\ts +}})$. ", "The particle-like description turns into the wave-like description as the counting proceeds. ", "The sequence of measurements brings a definite quantum phase to states for which none had been assumed to start with: at the end of the day, one is left with a state containing $2N_\\m A-k$ atoms and a phase difference known to an accuracy of order $1/k$.\n\nThe phase difference is an unpredictable random variable, which takes a different value for any realisation of the counting experiment. ", "It appears as a mere by-product of the counting statistics. ", "No direct interaction between the atoms in the condensates has been assumed at any point. ", "The BEC gases are taken as perfect gases. ", "The effect purely originates from the quantum statistics of bosons. ", "As concluded by Castin and Dalibard, “[*the notion of phase-broken symmetry is therefore not indispensable in order to understand the beating of two condensates*]{}”.", "\n\nThis conclusion, which has gained wide acceptance, [^118] has been beautifully illustrated by the experiments of @Saba:05. ", "These authors dropped two condensates of like-species out of their traps and, during the course of their free fall and expansion, gently pushed with laser beams a few atoms from one to the other. ", "They dutifully observed the continuous emergence of a fringe pattern in a quintessential form, without beam splitters and interferometers nor destruction of the condensate clouds, thus realising a nearly non-invasive measurement of their relative phase.", "\n\nThese cold atom gases constitute model systems. ", "They can be studied to their minutest details starting from the basic principles of quantum mechanics. ", "Photons in cavities provide another such instance. ", "Quantum statistical correlations between indistinguishable bosons play the leading role. ", "Particle interactions play a minor role of decoherence and are neglected. ", "Particle-wave duality is demonstrated to near perfection.", "\n\nSuperfluids differ in a number of respects. ", "The macroscopic wavefunction introduced by Anderson is defined on the premises that the particle number $N$ and its possible variation $\\delta N$ are sufficiently large so that the uncertainty in $\\varphi$, expressed by Eq.(\\[NumberPhaseUn\\]), $\\delta N\n\\,\\delta \\varphi \\sim 1$, is small in most instances. ", "It is then neglected and the operators $\\hat N$ and $\\hat\\varphi$ are “projected” onto $c$-numbers. ", "They have acquired a value once and for good: the phase is forced to “exist” even if its actual value is not determined by the same token and its absolute meaning uncertain.", "\n\nActually, the above introduction of the superfluid phase resembles a leap of faith: it is there because it is needed to reproduce the hydrodynamics. ", "@Leggett:91 and @Leggett:95 have paid careful attention to this problem of the “existence” of the phase. ", "One of the many points raised by these authors is that, in order to attribute a well-defined meaning to an [*absolute*]{} phase, one has first to consider the [ *relative*]{} phase of one bucket of superfluid with respect to another – presumably measured by performing a Josephson experiment. ", "The various ways and constraints of such an experiment have been expounded in the Sections above: the “relative” phase between two weakly connected superfluid systems (1) an (2), ${\\mbox{{{\\usefont{U}{psy}{m}{n}d}}}}\\varphi_{12} = \\varphi_2 - \\varphi_1$, can be measured and indeed possesses a well-defined meaning. ", "Suppose now that systems (1) and (2) are separated and a third system brought in. ", "System (3) can be compared to (1), with the result ${\\mbox{{{\\usefont{U}{psy}{m}{n}d}}}}\\varphi_{13} = \\varphi_3 - \\varphi_1$: is it possible to infer that the phase difference between (2) and (3) is $ \\varphi_3 -\n\\varphi_2= {\\mbox{{{\\usefont{U}{psy}{m}{n}d}}}}\\varphi_{13} - {\\mbox{{{\\usefont{U}{psy}{m}{n}d}}}}\\varphi_{12}$? ", "If yes, then phases can be referred to a “standard” and acquire absolute meaning.", "\n\nThe not-so-trivial answer given by @Leggett:95 is “no” if the systems are let to settle to equilibrium with the environment and the two Josephson phase measurements are independent, but “yes” if they are done simultaneously. ", "In other words, maintaining a superfluid phase standard across the various Standards Laboratories of the planet would require connecting them with a continuous superfluid duct. ", "The phase information would have to be tapped from this standard at the same time and place, or else a host of corrections, such as that for local gravity or for the Sagnac effect – the synchronisation of the Einstein clocks – …, would have to be performed. ", "If the phase readings are not simultaneous, the correlation between phase measurements between systems (1) and (2), and then (1) and (3) is upset by the sole act of measuring, with a part played by the environment; decoherence takes its toll and phases ultimately randomise [@Sols:94; @Zapata:03].", "\n\nThe situation in simple superfluids such as $^4$He and $^3$He-B, in which macroscopic coherence holds over lengths of metres and more, and in which the Planck constant hides at the nanometric scale provides a quite extreme example of macroscopic matter field. ", "That the macroscopic field $\\Phi(\\mb r)$ standing as the single-particle wavefunction for condensate atoms possesses quantum properties is indisputable – the quantisation of velocity circulation and the existence of persistent currents offer bullet-proof examples. ", "However, the sort of coherence shown by ultra-cold atom condensates does not stand out readily for dense superfluids. ", "The description of the superfluid dynamics in terms the conjugate variables $N$ and $\\varphi$ belongs more to thermodynamics than to quantum mechanics. ", "The correlation between atoms in the dense helium fluid relies more on their hard-core repulsion than on their Bose statistics.", "\n\nYet, the quantum interferences by quantum tunnelling between macroscopically distinct states in superfluid Josephson junctions, the quantum nucleation of vortices clearly reveal the importance of the latter. ", "In these situations, the coarse-grained average fails and some other procedure, more in line with the basic rules of quantum mechanics, and, in particular, the principle of superposition, is in order. ", "Would it be possible to envision experiments showing actual macroscopic quantum [*coherence*]{} as discussed by @Leggett:80 and @Leggett:02 [@Annett:03]? ", "The superfluid quantum phase would then gain a dual acception, actual coherence in the superposition of different states at very small scale on the one hand and, on the other, the “rigidity”, in the language of F. London, of the velocity potential of the ideal Euler fluid and the quantisation of the velocity circulation.", "\n\nThe above remarks bring this “essay on criticism” of Anderson’s Considerations to a close. ", "At this stage, but one hard conclusion can be drawn: many offshoots have already sprung but more are to grow.", "\n\nAcknowledgement\n===============\n\nThis work has been supported over many years by Centre National de la Recherche Scientifique and by Commissariat à l’Énergie Atomique et aux Énergies Alternatives. ", "The author owes much to his many colleagues, foremostly Olivier Avenel and Yuri Mukharsky who have brought vital contributions to many of the topics discussed above.", "\n\nWhat need be shown is that the second term of the right-hand side of Eq.(\\[EnergyBalance\\]) corresponds to the variation of the vortex loop self-energy for the infinitesimal deformation $\\mb s(l)$ into $\\mb s(l)+\n{\\mbox{\\bf{{{\\usefont{U}{psy}{m}{n}e}}}}}\\, \\delta(l-l_0)$ . ", "This energy variation can be derived from the functional derivative of $E_\\m v[\\mb s]$, given by Eq.(\\[ReducedEv2\\]), with respect to the deformation ${\\mbox{\\small{{\\usefont{U}{psy}{m}{n}d}}\\hskip 0.05ex}}\\mb s$ : $$\\begin{aligned}\n \\label{FuncDeriv1} \n \\frac{{\\mbox{\\small{{\\usefont{U}{psy}{m}{n}d}}\\hskip 0.05ex}}E[\\mb s]}{{\\mbox{\\small{{\\usefont{U}{psy}{m}{n}d}}\\hskip 0.05ex}}\\mb s}\\biggl|_{l_0} \n &=& \\frac{\\rho_\\m s \\kappa_4^2}{8\\pi}\\,\n \\Biggl\\{-\\oint \\frac{\\m d\\mb s(l_0)}{\\m d l_0} \\cdot \n \\frac{\\m d\\mb s(l_2)}{\\m d l_2} \\,\n \\frac{\\mb s(l_0) -\\mb s(l_2)}{\\left| \\mb s(l_0)-\\mb s(l_2)\\right|^3} \\,\\m d l_2 \n \\nonumber\n \\\\ &+& \n \\;\\lim_{\\mbox{\\bf{{{\\usefont{U}{psy}{m}{n}e}}}} \\rightarrow 0}\\; \n \\oint\\!\\!\\oint {\\mbox{\\bf{{{\\usefont{U}{psy}{m}{n}e}}}}}\\cdot\\frac{\\m d\\mb\n s(l_2)}{\\m d l_2}\\delta'(l_1-l_0) \\frac{\\m d l_1\\,\\m d l_2}\n {\\left| \\mb s(l_1)-\\mb s(l_2)\\right|}\n \\nonumber\n \\\\ &+&\n \\; l_1 \\Longleftrightarrow l_2 \\Biggr\\} \\, .\\end{aligned}$$ The first term in the right hand side of Eq.(\\[FuncDeriv1\\]) results from the differentiation of $1/|\\mb s(l_1)- \\mb s(l_2)|$ with respect to $l_1$ and integration over the Dirac function representing the deformation at $l_1=l_0$. The integral over the derivative of the Dirac $\\delta$-function, which comes from the differentiation of $ \\m d\\mb s(l_1) / \\m d l_1$ yields the derivative of the integrand evaluated at $l_0$. The contribution of the integration over $l_2$ over the same contour with the same deformation is equal to that over $l_1$, expressed by the first two terms of the right hand side of Eq.(\\[FuncDeriv1\\]), and yields a factor of 2 in the final result.", "\n\nUsing the notation $\\mb{\\hat t}(l)= \\m d\\mb s(l)/\\m d l $ for the unit vector tangent to the vortex loop at location $\\mb s(l)$, Eq.(\\[FuncDeriv1\\]) can be written as $$\\label{FunctionalDerivative2}\n \\begin{split} \n \\frac{{\\mbox{\\small{{\\usefont{U}{psy}{m}{n}d}}\\hskip 0.05ex}}E[\\mb s]}{{\\mbox{\\small{{\\usefont{U}{psy}{m}{n}d}}\\hskip 0.05ex}}\\mb s}\\biggl|_{l_0} \n &= \\frac{\\rho_\\m s \\kappa_4^2}{4\\pi}\\,\\oint \n \\Biggl\\{\\mb{\\hat t}(l_0) \\cdot\\frac{\\mb s(l_0)- \\mb s(l_2)}\n {\\left| \\mb s(l_0)-\\mb s(l_2)\\right|^3} \\,\\mb{\\hat t}(l_2) \n \\\\& \\hskip 1.5 cm \n -\\; \\mb{\\hat t}(l_0)\\cdot\\mb{\\hat t}(l_2)\\,\\frac{\\mb s(l_0)- \\mb s(l_2)}\n {\\left| \\mb s(l_0)-\\mb s(l_2)\\right|^3} \\Biggr\\}\n \\,\\m d l_2\n \\\\& = \\frac{\\rho_\\m s \\kappa_4^2}{4\\pi}\\, \\mb{\\hat t}(l_0)\\times\\oint \n \\mb{\\hat t}(l_2)\\times\\frac{\\mb s(l_0)- \\mb s(l_2)} \n {\\left| \\mb s(l_0)-\\mb s(l_2)\\right|^3} \\,\\m d l_2 \n \\\\& = \\rho_\\m s\\kappa_4\\, \\mb{\\hat t}(l_0)\\times \\mb v_\\m v(l_0)\\,\\; . ", "\n \\end{split}$$ The double cross product in the second equality of (\\[FunctionalDerivative2\\]) appears because of the vector relation $(\\mb\na\\cdot\\mb c)\\,\\mb b -(\\mb a\\cdot\\mb b)\\,\\mb c =\\mb a\\times(\\mb b\\times\\mb\nc)$. The last equality is obtained using the Biot-Savart law, Eq.(\\[BiotSavart\\]), for $\\mb v_\\m v$ the velocity induced by the vortex loop on itself at $l_0$. The logarithmic divergences for $l_0 = l_2$ are cut-off at the core radius $a_0$.[^119] The change of the vortex self-energy is then expressed by $$\\begin{split}\n \\Delta E_\\m v &= \\int_l^{l+\\Delta l} \\,\\oint_{\\m{loop}}\\; \\frac{{\\mbox{\\small{{\\usefont{U}{psy}{m}{n}d}}\\hskip 0.05ex}}E[\\mb\n s]}{{\\mbox{\\small{{\\usefont{U}{psy}{m}{n}d}}\\hskip 0.05ex}}\\mb s}\\biggl|_{l_0} \\!\\! ", "\\cdot {\\mbox{\\small{{\\usefont{U}{psy}{m}{n}d}}\\hskip 0.05ex}}\\mb x\\, \\delta(l-l_0) \\m d l\\,\\m d l_0 \\\\\n &= \\int_l^{l+\\Delta l} \\rho_\\m s \\kappa_4 \\, \n \\hat{\\mb t}(l_0) \\times \\mb v_\\m v \\cdot \\mb v_\\m p \\Delta t\\,\\m d l_0 \\;.", "\n \\end{split}$$ Assuming the integrand constant over the small element $\\Delta \\mb l$, Eq.(\\[VortexSefEnergyChange\\]) ensues.", "\n\n[346]{}ifxundefined \\[1\\][ ifx[\\#1]{} ]{}ifnum \\[1\\][ \\#1firstoftwo secondoftwo ]{}ifx \\[1\\][ \\#1firstoftwo secondoftwo ]{}““\\#1””@noop \\[0\\][secondoftwo]{}sanitize@url \\[0\\][‘\\\n12‘\\$12 ‘&12‘\\#12‘12‘\\_12‘%12]{}@startlink\\[1\\]@endlink\\[0\\]@bib@innerbibempty (), @noop [****, ]{} (), @noop [**]{} ()  (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [ , ]{} (), in @noop [**]{},  () p.  (), in @noop [**]{}, Vol.", " ,  () p. ,  (), @noop [****, ]{} (), in @noop [**]{},  () p. ,  (), @noop [**]{} ()  (), in @noop [**]{},  () (), @noop [**]{} () (), in @noop [**]{},  () p.  (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{},  (), @noop [**]{} ()  (), @noop [****, ]{} (), “,” Chap.", "  () (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (),  () p.  (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), in @noop [**]{},  () p.  (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} , ,  and , Eds. (),", " @noop [**]{} ()  (), “,”  () p.  (), “,” Chap.", "  () p.  (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{},  (),  (), @noop [****, ]{},  (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [Ph.D. thesis]{} () (), @noop [****, ]{} (), @noop [****, ]{},  (), @noop [****, ]{} (), @noop [****, ]{},  (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [**** (), ]{} (), @noop [****, ]{} (), @noop [Ph.D. thesis]{} () (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [**]{} ()  (), @noop [****, ]{} (), @noop [**]{} () (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), in @noop [**]{}, Vol.", " , , Chap.", "  () p.  (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), in @noop [**]{}, Chap.", "  () p.  (), in @noop [**]{}, Vol.", " , Chap.", "  () p. ,  (), @noop [**]{} ()  (), @noop [**]{} () (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), in @noop [**]{}, Vol.", " , Chap.", "  ()  (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{},  (), @noop [Ph.D. thesis]{} (),  (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [**]{} () (), “,”  () p. ,  (), @noop [****, ]{} (), in @noop [**]{},  () p.  (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), in @noop [**]{}, Vol.", " ,  () p. ,  (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [**]{} ()  (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), in @noop [**]{},  () p.  (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [**]{} () (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{},  (), @noop [****, ]{},  (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [**]{} () (), @noop [****, ]{},  (), @noop [****, ]{},  (), @noop [**]{} () (), @noop [**]{} () (), @noop [**]{} () (), @noop [****, ]{} (), @noop [****, ]{} (), in @noop [**]{}, Vol.", " , Chap.", "  () p.  (), @noop [****, ]{},  (), @noop [“,” ]{} (), @noop [****, ]{} (), in @noop [**]{}, , Chap.", "  () (), @noop [****, ]{},  (), @noop [****, ]{} (), in @noop [**]{}, , Chap.", "  () (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [**]{} ()  (), @noop [****, ]{},  (), @noop [****, ]{} (), @noop [**]{}, Vol.", "  () (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (),  (), in @noop [**]{}, Vol.", " ,  () p.  (), @noop [****, ]{} (), @noop [****, ]{},  (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), “,”  () p.  (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [**]{}, Vol.", "  () Chap.", "  (), @noop [****, ]{},  (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{},  (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [**]{} () (), @noop [****, ]{},  (), @noop [****, ]{} (), @noop [**]{} ()  (), @noop [ , ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (),  (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), “,”  () p. ,  (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [**]{} () (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [Ph.D. thesis]{} (),  (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{},  (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), in @noop [**]{},  () p.  (), @noop [“,” ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [“,” ]{} (), @noop [****, ]{} (), @noop [**]{},  ed.", " () (), @noop [****, ]{},  (), @noop [****, ]{} (), @noop [****, ]{} (), “,” Chap.", "  ()  (), @noop [****, ]{} (), @noop [****, ]{} (), in @noop [**]{},  () p.  (), in @noop [**]{},  () p.  (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), in @noop [**]{},  () p.  (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (),  (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{},  (),  (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), in @noop [**]{} () p.  (), in @noop [**]{} () p.  (), @noop [****, ]{} (), @noop [**]{} () (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [**]{} ()  (), @noop [****, ]{} (), @noop [****, ]{} (), in @noop [**]{},  () p.  (), @noop [****, ]{} (), @noop [**]{} () (), @noop [****, ]{} ,  and , Eds. (),", " @noop [**]{} () (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{} (), @noop [****, ]{}\n\n[^1]: Among these reviews, see in particular @Vinen:63, @Khalatnikov:65, @Vinen:66, @Andronikashvili:66, @Vinen:68, @Putterman:71, @Nozieres:90, @Vollhardt:90, @Volovik:03, @Sonin:15.", "\n\n[^2]: See, for example, @Nozieres:90, @Tilley:90,@Vollhardt:90.", "\n\n[^3]: The reviews include the work of @Varoquaux:87, @Avenel:87, @Avenel:89, @Varoquaux:91, @Varoquaux:92, @Bowley:92, @Avenel:93, @Varoquaux:94, @Zimmermann:96, @Packard:98, @Varoquaux:99, @Varoquaux:01a, @Varoquaux:01b, @Davis:02,@Packard:04 and @Sato:12.", "\n\n[^4]: See  @Landau:Hydro, §8.", "\n\n[^5]: This fundamental assumption, which sets an important difference between superfluids and ideal Euler fluids, is discussed below in this Section. ", "It is best justified by its consequences, the subject matter of the principal part of this review.", "\n\n[^6]: See @Landau:Hydro, ch. ", "XVI.", "\n\n[^7]: @Landau:Hydro –§128 – trace its roots to the property of the energy spectrum for the low energy excitations of the superfluid, constituted by sound quanta, or phonons. ", "The Landau school (@Khalatnikov:65 – Ch 8 – and @Abrikosov:61) – §1.3) merely states the irrotationality condition as an assumption justified by its experimental implications. ", "@London:54 – §19 – actually derives this condition from a peculiar variation principle devised by @Eckart:38 but the actual significance of this principle has not been clarified, nor, as it seems, that of Eq.(\\[rotvs0\\]) (see, for example, the pedagogical review of @Essen:12 and the references therein on the similar problem of the Meissner effect in superconductivity.", "\n\n[^8]: This question was nonetheless treated by the Landau school [@Khalatnikov:65].", "\n\n[^9]: As implied in a footnote of a paper by @Onsager:49 and mentioned in the footnote in page 151 of London’s book.", "\n\n[^10]: In the words of C.N. Yang (2003) “[*Weyl in 1929 came back with an important paper that really launched what was called, and is still called, gauge theory of electromagnetism, a misnomer. (", "It should have been called phase theory of electromagnetism.)’*]{}’.", "\n\n[^11]: See @Feynman:55, @Penrose:56 or @Landau:Quantum §61.", "\n\n[^12]: A useful discussion of this topic can be found in @Nozieres:90, Ch. ", "5 and also in @Feynman:72. ", "The more rigorous approach discussed in §[\\[MicroscopicApproach\\]]{}, based on the density matrix formalism, shows how such a macroscopic wavefunction can be constructed.", "\n\n[^13]: See @Abrikosov:61.", "\n\n[^14]: See @Kadanoff:13 for an insightful account of the historical genesis of the idea of ODLRO and a discussion of the role of the condensate in superfluidity and superconductivity.", "\n\n[^15]: More is said on these correlations in Sec.\\[Conclusion\\]\n\n[^16]: See, for example, the monograph of @Griffin:93 and his historical note [@Griffin:99]\n\n[^17]: @Nozieres:90 give in Ch. ", "10 a very transparent account of ODLRO using the notation of field theory, in which the density matrix reads $$\\rho_1({\\mb r},{\\mb r}') = \\sum_n\n \\langle\\phi|{\\mbox{{{\\usefont{U}{psy}{m}{n}y}}}}^\\dagger({\\mb\n r})|\\phi_n\\rangle\\langle\\phi_n|{\\mbox{{{\\usefont{U}{psy}{m}{n}y}}}}({\\mb r}')|\\phi\\rangle \\; ,$$ ${\\mbox{{{\\usefont{U}{psy}{m}{n}y}}}}^\\dagger({\\mb r})$ and ${\\mbox{{{\\usefont{U}{psy}{m}{n}y}}}}({\\mb r}')$ being the boson creation and annihilation field operators, $|\\phi_n\\rangle$ a complete set of eigenstates of the system and $|\\phi\\rangle$ the state in which the average is expressed, which is taken as the ground state $|\\phi_0\\rangle$. Among the intermediate states $|\\phi_n\\rangle$, those of special relevance to the kicking-out and relocation processes discussed here connect the ground state with $N$ bosons to the ground state with $N-1$ bosons. ", "So attention must be focused on the following matrix element $$\\Phi({\\mb r}) = \\langle\\phi_0(N-1)|{\\mbox{{{\\usefont{U}{psy}{m}{n}y}}}}(\\mb r)|\\phi_0(N)\\rangle$$ that is taken to represent the condensate wavefunction.", "\n\n[^18]: As stated in the monograph of @Nozieres:90, §9.4\n\n[^19]: For a recent review, see @Glyde:13.", "\n\n[^20]: This point has been discussed by @Griffin:87 [@Griffin:93].", "\n\n[^21]: In the context of superfluids, see @Gross:61 [@Pitaevskii:61; @Langer:68; @Nozieres:90].", "\n\n[^22]: @Nozieres:90 §5.7.", "\n\n[^23]: Following for instance @Lifshitz:80, the density operator takes the form $\\hat{\\rho}(\\mb r)=\\sum_i{m_4\\delta(\\mb r_i-\\mb r)}$ and the current density operator the form $\\hat{\\mb j}(\\mb r) = \\frac{1}{2}\\sum_i{\\hat{\\mb p}_i \\delta(\\mb r_i-\\mb r) +\n \\delta(\\mb r_i-\\mb r)}\\hat{\\mb p}_i$ – compare with Eqs.(\\[NumberDensity\\]) and (\\[Current\\]). ", "The liquid velocity operator $\\hat{\\mb v}$ is in turn defined by $\\hat{\\mb j}(\\mb r) =\n \\frac{1}{2}(\\hat{\\rho}\\hat{\\mb v} + \\hat{\\mb v}\\hat{\\rho})$. These operators can then be shown to obey the commutation rule $\\hat{\\Phi}(\\mb\n r)\\hat{\\rho}(\\mb r') - \\hat{\\rho}(\\mb r')\\hat{\\Phi}(\\mb r) = -\\m i\\hbar \\delta(\\mb\n r -\\mb r')$, $\\hat{\\Phi}$ being here the potential for the velocity operator $\\hat{\\mb v} = \\nabla\\hat \\Phi$. The quantities $\\hat\\rho$ and $\\hat\\Phi$ are thus canonically conjugate. ", "Their fluctuations obey an uncertainty relation of the form $\\delta\\hat\\rho \\; \\delta\\hat\\Phi \\geq \\hbar/2$. Using the phase of the macroscopic wavefunction, Eq.(\\[vs\\]), instead of the velocity potential, uncertainty relation (\\[NumberPhaseUn\\]) is obtained.", "\n\n[^24]: There are a number of different topological defects in superfluid $^3$He owing to the large number of degrees of freedom of the order parameter as briefly discussed in §\\[CPR\\].", "\n\n[^25]: The quantum of circulation in $^4$He takes the value 9.97 $10^{-4}$ cm$^2$s$^{-1}$ and in $^3$He where the boson mass is $2m_3$, $\\kappa_3 = \\pi\\hbar/m_3 =6.65\\times10^{-4}$ cm$^2$s$^{-1}$.\n\n[^26]: See @Fetter:76, @Sonin:87, @Salomaa:88, @Dalfovo:92 for more extended discussions.", "\n\n[^27]: See @Hall:60, @Andronikashvili:66, @Sonin:87, @Krusius:93, @Finne:06.", "\n\n[^28]: See, for example, @Lamb:45, §147.", "\n\n[^29]: See @Saffman:92 §2.3.", "\n\n[^30]: Stokes’s theorem can be invoked to transform the line integral in Eq.(\\[BiotSavart\\]) into an integral over the surface spanned by the vortex loop, $$\\oint \\m d l\\times\\mb a = \\iint\n \\big[(\\nabla\\mb a)\\cdot\\m d \\mb S - \\nabla\\cdot\\mb a\\,\\m d\\mb S\\big]$$ with $\\mb a = (\\mb r -\\mb R)/|\\mb r -\\mb R|^3$. Equation (\\[ScalarPotential\\]) then follows.", "\n\n[^31]: The situation in superfluid $^3$He-A is more complicated, as discussed in §\\[Peculiarities\\].", "\n\n[^32]: See @Lamb:45, §153 or @Saffman:92, §3.11.", "\n\n[^33]: See @Lamb:45 §163.", "\n\n[^34]: Using the Gross-Pitaevskii equation, @Roberts:71 find that the prefactor 7/4 should be replaced by the not-so-different number 0.615\n\n[^35]: See @Saffman:92 §2.4.", "\n\n[^36]: It is understood here that the boundary does not carry vorticity. ", "A case of the contrary is discussed by @Sonin:94b.", "\n\n[^37]: Such a point of view is discussed by @Saffman:92 §1.4.", "\n\n[^38]: As expressed by $$\\int_V \\nabla\\Psi\\cdot\\nabla\\Phi \\,\\m d\\tau = \n \\int_S \\Phi\\,\\nabla\\Psi\\cdot \\m d\\mb S - \\int_V \\Phi\\nabla^2\\Psi\\, \\m d\\tau\n \\; ,$$ $S$ being the surface bounding volume $V$ and $\\m d\\mb S$ being the outward pointing surface element, and taking into account mass conservation of the fluid in incompressible flow ($\\nabla^2\\Psi=0$, $\\Psi =\n (\\hbar/m_4)\\,\\varphi_{\\m p}$ being the velocity potential of $\\mb v_\\m p$).", "\n\n[^39]: See @Lamb:45, §152.", "\n\n[^40]: See [@Lamb:45], §163.", "\n\n[^41]: Notably from the work of @Baym:83, @Duan:94, and @Sonin:98.", "\n\n[^42]: See @Landau:Hydro, §131.", "\n\n[^43]: See also [@Zimmermann:96] and @Greiter:05) for alternate derivations.", "\n\n[^44]: See @Sonin:97 for a complete discussion of the Magnus force in classical fluids, neutral superfluids and charged superfluids.", "\n\n[^45]: See §8.", "\n\n[^46]: For a discussion, see @Saffman:92 §1.6.", "\n\n[^47]: See the work of @Richards:65, @Khorana:67, @Khorana:69, @Richards:70, @Guernsey:71, [@Gregory:72], @Hulin:72.", "\n\n[^48]: As mentioned by @Schofield:71, @Musinski:72, @Musinski:73, @Gamota:74.", "\n\n[^49]: The work of @Avenel:85, @Avenel:86b, @Varoquaux:87, @Amar:90, @Amar:92, @Zimmermann:93b, @Zimmermann:96 is described below.", "\n\n[^50]: Later refined by @Richards:70\n\n[^51]: As will become clear in the discussion of phase slip mechanism in §\\[HalfRingModel\\]\n\n[^52]: Namely @Wirth:81 [@Anderson:84; @Beecken:87a].", "\n\n[^53]: SQUID is an acronym for Superconducting QUantum Interferometric Device. ", "The present sensitivity of [*dc*]{}-SQUID based displacement sensors used in the phase slippage described further on is $\\sim 10^{-15}$ m/$\\sqrt{\\m Hz}$, or one fermi per root hertz.", "\n\n[^54]: See the accounts of @Zimmermann:96, and @Packard:98.", "\n\n[^55]: Calling the device a “Helmholtz” resonator has been criticised as the compressibility of the fluid inside the chamber has a negligible effect at the low frequencies of the experiments, hence the little more convoluted appellation used here. ", "The term “hydromechanical resonator” is also used in this paper\n\n[^56]: See, for instance, @Varoquaux:87, @Avenel:87, @Beecken:87, @Varoquaux:94, @Avenel:95.", "\n\n[^57]: See Fig.\\[Cell\\], or Fig.\\[Gyrometer\\] for a more realistic cell.", "\n\n[^58]: As reported by @Muirhead:84, @Varoquaux:87, @Varoquaux:03.", "\n\n[^59]: For complete accounts of Landau’s work, see @Khalatnikov:65 and @Wilks:67..\n\n[^60]: A noteworthy attempt to by-pass this experimental finding is that of @Andreev:04\n\n[^61]: This Section is based on the work of @Varoquaux:01a, @Varoquaux:03, and @Varoquaux:06.", "\n\n[^62]: See for instance @Landau:Quantum §50.", "\n\n[^63]: See also Sonin’s book (2015), §12.2.", "\n\n[^64]: For an illustration, see Fig.2 in @Anderson:66a for the “tilted washboard” model.", "\n\n[^65]: For instance, @Nore:00, @Berloff:01, @Rica:01.", "\n\n[^66]: See, for instance, @Melnikov:91 and also @Varoquaux:03 for more references and details on this Section.", "\n\n[^67]: As explained by @Caldeira:83a, @Waxman:85, and @Grabert:87\n\n[^68]: See, for instance @Fetter:65, @Glaberson:86, @Sonin:87, or @Donnelly:91.", "\n\n[^69]: See also @Zimmermann:94 [@Burkhart:95; @Varoquaux:96].", "\n\n[^70]: As quoted by @Hess:77.", "\n\n[^71]: See @Varoquaux:98, @Donev:01, and @Neumann:14 for more references.", "\n\n[^72]: See @Ellis:93.", "\n\n[^73]: See, among others, @Hakonen:87,@Zieve:92, or @Krusius:93.", "\n\n[^74]: See @Packard:72, @Alpar:80, and @Langlois:00.", "\n\n[^75]: See also @Tsubota:94, @Neumann:14.", "\n\n[^76]: K.W. Schwarz: private communication to the author (1989).", "\n\n[^77]: See the review by @Tsubota:09\n\n[^78]: This topic is also covered by @Varoquaux:98, @Varoquaux:00a, @Varoquaux:00b, @Varoquaux:01a\n\n[^79]: See the discussion following Anderson’s talk at the Sussex University Symposium in 1965 [@Anderson:66a].", "\n\n[^80]: The contribution of the entropy to the chemical potential, ${\\mathcal S}T$, should also be taken into account in Eq.(\\[acJosephson\\]) if the temperature is not very low.", "\n\n[^81]: See the discussion given by @Vinen:68, still very relevant 40 and more years later, also @Varoquaux:92.", "\n\n[^82]: In the framework of the Gross-Pitaevskii equation, the interaction term $V_0(\\mi\\Phi^*\\mi\\Phi)\\mi\\Phi$ becomes small in the depleted region and can be neglected - see §\\[p-wave\\] for superfluid $^3$He\n\n[^83]: The hydraulic length $\\ell_\\m h$ is defined by Eq.(\\[HydraulicLength\\]. ", "The thickness of the tunnel barrier is neglected.", "\n\n[^84]: Relations (\\[DeaverPierce\\]) were proposed by @Deaver:72 for superconducting junctions. ", "See also @Likharev:79.", "\n\n[^85]: See @Avenel:88 for an example of this procedure and @Varoquaux:92 for a more complete analysis.", "\n\n[^86]: As related by @Leggett:75 and @Anderson:75 – see the monograph by @Vollhardt:90.", "\n\n[^87]: For $^3$He-B in weak coupling theory, $\\Delta(0)=ak_\\m B T_\\m c$ with $a\\leq 1.75$ @Leggett:75.", "\n\n[^88]: The zero temperature coherence length of the B-phase is given by $\\xi_0=\n [7\\zeta(3)/48\\pi^2]^{1/2}\\,[\\hbar v_\\m F/k_\\m B T_\\m c]$ (@Vollhardt:90, §3.4). ", "The temperature dependent coherent length diverges as $\\xi(T)=\\xi_0(1-T/T\\m c)^{-1/2}$ in the Ginzburg-Landau regime.", "\n\n[^89]: The state of the art in aperture manufacturing evolved with time from submicronic slits [@Sudraud:87] to nanometric holes [@Pereverzev:01].", "\n\n[^90]: See @Sudraud:87 for an account of earlier attempts and @Sato:12 for later developments.", "\n\n[^91]: As obtained by Kulik and Omel’yanchuk in 1977, see for instance @Likharev:79 or @Golubov:04.", "\n\n[^92]: See, in particular,@Monien:86, @Hook:87, @Ullah:89, @Kopnin:90, @Thuneberg:90, @Soininen:91, @Kopnin:91\n\n[^93]: A different situation has been examined by @Rainer:87, that of tunnelling through a very thin $^3$He-$^4$He film spanning a micro-hole, much like a soap bubble. ", "The barrier parameters $l_\\m b$ and $\\xi_\\m b (T)$ can be also evaluated explicitly in this idealised case as well as the critical current through the weak link.", "\n\n[^94]: Also by @Kopnin:90 [@Kopnin:92].", "\n\n[^95]: More experimental details and further references can be found in the reviews by @Davis:02 and @Sato:12.", "\n\n[^96]: An alternate explanation for the existence of $\\pi$-states is offered by @Eska:10 and is based on the built-in non-linearities of the single-hole resonator used in the experiments of @Backhaus:98 [@Marchenkov:99],\n\n[^97]: See also Janne Viljas’s Thesis (Espoo 2004) available at http://lib.hut.fi/Diss/, @Smerzi:01, @Zhang:01, @Nishida:02 and the very clear review by @Viljas:04-JLTP. ", "A related situation, that of “$\\pi$–junctions”, has been much studied in electrodynamic junctions [@Golubov:04].", "\n\n[^98]: Also @Zhang:01.", "\n\n[^99]: See also the contributions of @Smerzi:01, @Viljas:05 and @Thuneberg:05.", "\n\n[^100]: A related mechanism governing the vortex dynamics in Fermi superfluids at temperatures well below $T_\\m c$, reported by @Silaev:12, arises from the kinetics of localised excitations bound to the vortex cores and driven out of equilibrium by vortex motion. ", "The local heating of the vortex cores results in an energy flux carried by nonequilibrium quasiparticles and in a dissipation mechanism that can operate even at zero temperature.", "\n\n[^101]: See @Vollhardt:90, §7.1.", "\n\n[^102]: For a pointed but still gentle introduction to the intricacies of the A-phase hydrodynamics, see @Hall:86 who also covered the effect of magnetic fields, not considered here.", "\n\n[^103]: As already mentioned by @Anderson:64, p. 120.", "\n\n[^104]: See @Halperin:76 and @Hohenberg:77 for details.", "\n\n[^105]: As derived by @Anderson:66a, p.305\n\n[^106]: Approaching $T_{{\\mbox{\\footnotesize{{\\usefont{U}{psy}{m}{n}l}}}}}$ from below, $\\rho_\\m s$ is known to vanish as [@Langer:70] $$\\rho_\\m s \\simeq 2.4\\, \\rho_{{\\mbox{\\footnotesize{{\\usefont{U}{psy}{m}{n}l}}}}}(1-T/T_{{\\mbox{\\footnotesize{{\\usefont{U}{psy}{m}{n}l}}}}})^{2/3} \\; ,$$ where $\\rho_{{\\mbox{\\footnotesize{{\\usefont{U}{psy}{m}{n}l}}}}}$ is the density at the ${{\\mbox{\\footnotesize{{\\usefont{U}{psy}{m}{n}l}}}}}$ transition, 0.1459 g/cm$^3$. From relation (\\[ScalingRelation\\]), the temperature-dependent coherence length becomes $\\xi(T)= 0.338/(1-T/T_{{\\mbox{\\footnotesize{{\\usefont{U}{psy}{m}{n}l}}}}})^{2/3}$ in nm.", "\n\n[^107]: In particular, the work of @Hoskinson:06 [@Sato:06], and also of @Sato:08 [@Narayana:10; @Narayana:11].", "\n\n[^108]: The original “gauge wheel” proposal due to Liu has been discussed by @Ho:80a.", "\n\n[^109]: See @Aarts:94 [@Schwab:96a; @Schwab:96b] and the review by @Sato:12.", "\n\n[^110]: The literature on the Sagnac effect is extremely vast. ", "See @Hasselbach:93, @Stedman:97, @Neutze:98 for recent reviews on the effect with matter waves.", "\n\n[^111]: As done in the book of @Landau:ClassicalFields, §90.", "\n\n[^112]: It may be worth recalling that this clock transportation experiment was actually performed by @Hafele:72 who boarded eastward and westward bound commercial jetliners taking as luggage a portable atomic clock.", "\n\n[^113]: As also outlined by @Ho:80b.", "\n\n[^114]: See @Volovik:03 for an alternate approach and @Varoquaux:08 for additional references. ", "Equation (11) in the latter reference is misprinted.", "\n\n[^115]: @Anderson:94, p. 165.", "\n\n[^116]: See, for example, the contributions of D. C. Samuels, of O. C. Idowu et al., ", "and of M. Tsubota, T. Araki, and S. K. Nemirovskii in @Barenghi:01.", "\n\n[^117]: Such an experiment was successfully performed soon after by @Andrews:97 and others. ", "See also below.", "\n\n[^118]: See, for example, @Horak:99 [@Nienhuis:01].", "\n\n[^119]: Compare with Eqs.(3.7) and (3.15) in Sonin’s paper (1987).", "\n" ]

{ "pile_set_name": "ArXiv" }

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[ "FILE - In this July 17, 2019, photo, Democratic presidential candidate, Sen. Bernie Sanders, I-Vt., ", "speaks at George Washington University in Washington. ", "Sanders’ campaign is building an aggressive, in-house media operation to take its candidate’s message directly to voters. (", "AP Photo/Patrick Semansky)\n\nFILE - In this July 17, 2019, photo, Democratic presidential candidate, Sen. Bernie Sanders, I-Vt., ", "speaks at George Washington University in Washington. ", "Sanders’ campaign is building an aggressive, in-house media operation to take its candidate’s message directly to voters. (", "AP Photo/Patrick Semansky)\n\nWASHINGTON (AP) — When Bernie Sanders wanted to preview a speech about his signature health care plan, “Medicare for All,” he did not opt for a traditional interview.", "\n\nInstead, he made an appearance on “The 99,” his Democratic presidential campaign’s in-house livestreamed show, a controlled, decidedly on-message pro-Sanders program that streams on a variety of services including Twitch, a platform primarily used by gamers.", "\n\nFull Coverage: Bernie Sanders\n\nThe makeshift studio for the show is in a room with a long wooden table, walls decorated with Sanders campaign signs and tchotchkes including a Sanders action figure. ", "Sanders sat down for an interview — with his campaign manager, Faiz Shakir.", "\n\nADVERTISEMENT\n\n“We are doing these livestreams, we are talking to you directly,” Shakir said. “", "One of the reasons is while we appreciate our friends in the elite media, they don’t often cover the issues that truly matter to working Americans.”", "\n\nThe livestream represents just one spoke in a communications network that his campaign, frustrated by the coverage he gets in traditional media, has built to exclusively promote the candidate’s worldview. ", "Since Sanders announced his second bid for the presidency in February, the campaign has started not just a twice-weekly livestreaming show, but also a sleekly produced podcast, “Hear the Bern,” hosted by national press secretary Brihana Joy Gray. ", "On the first episode of the podcast, Gray described it as a “behind the scenes look at how campaigns work, how political movements grow and what motivates the man who has reintroduced big, transformative ideas into politics.”", "\n\nCandidates have long sought outlets to appeal directly to supporters without a media filter, and none more effectively than President Donald Trump. ", "But Sanders’ efforts have taken that approach a step further, and there’s some evidence that people are watching and listening. ", "His campaign says that the streaming show they aired before and after the first Democratic presidential debate had more than 300,000 views.", "\n\nFull Coverage: Election 2020\n\n“If you go on the premise that Bernie folks think they were boxed out of the mainstream party the last time around, I think the assumption that his folks made is they’ve just got to kind of build their own universe,” said Joel Payne, a Democratic strategist who worked on Hillary Clinton’s 2016 campaign.", "\n\nSanders’ campaign says he is to use the new platforms to anchor his base and to reach voters who may be disengaged with the political process currently but who could be animated by Sanders’ ideas and policies.", "\n\nADVERTISEMENT\n\n“This is different from a typical post on social media, which is putting out content. ", "With the live show, we can actually have a conversation with people. ", "It’s bringing our supporters into the conversation, but also to bring people who may disagree with us into the conversation,” said Josh Miller-Lewis, the campaign’s digital director.", "\n\nIn his second run for president, Sanders is finding that the attention he received in his run against Clinton is harder to come by in a field with two dozen candidates. ", "By expanding Sanders’ already robust social media presence with streaming shows where they have outsize control offers a test of whether he has found a new way to break through.", "\n\n“I think Bernie Sanders became accustomed to the level of news attention that a fresh face attacking the establishment normally gets and now thinks, (if) he got that attention in 2016, he should be getting it now, and, if not, there must be something wrong with the press,” said Kathleen Hall Jamieson, director of the University of Pennsylvania’s Annenberg Public Policy Center.", "\n\nHis campaign also says it’s a long-range strategy that looks ahead to a general election matchup with President Donald Trump. ", "Miller-Lewis says he believes that anyone who wants to defeat Trump in 2020 has to be able to “challenge Trump’s supremacy on digital platforms.”", "\n\nIn a recent episode of “The 99,” three top Sanders aides spent an hour discussing whether Sanders was “too consistent for corporate media,” at times dissecting individual headlines and stories they criticized.", "\n\nAri Rabin-Havt, Sanders’ chief of staff, argued that the media has a “bias for something new, for something exciting, for something salacious, and Bernie Sanders’ continual history of standing up for these issues over 40 years is not new and exciting for people.”", "\n\nIn that way, his consistency may have hurt his desire to get more attention. “", "News is something that’s new, and the best thing that Bernie has going for him is that he’s consistent, that he’s pushing for what he’s always pushed for,” said Rebecca Katz, a New York-based Democratic strategist. “", "The problem that Bernie has going for him is he’s not making news, he’s repeating news.”", "\n\nJoe Trippi, a Democratic consultant who managed Howard Dean’s 2004 presidential campaign, has heard the kind of complaints the Sanders campaign is making.", "\n\n“Every politician who’s ever had the problem of, it’s not going very well and they’re shrinking, complains about their coverage,” Trippi said. “", "The question they need to ask themselves is, Is the coverage diminishing because his support’s diminishing?”" ]

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[ "Disappearance of atrial natriuretic factor from circulation in the rat.", "\nThe rate of disappearance of radioiodinated forms of 3 different atrial natriuretic factors (ANF (Ser 99-Tyr 126), ANF (Arg 101-Tyr 126), ANF (Ser 103-Tyr 126)) from circulation in the rat was studied. ", "Before proceeding to study the half-life of these peptides, the biological activity of their cold iodinated forms was examined. ", "Upon incorporation of iodine into the ANF molecule, there was a 2 to 5-fold loss in their binding affinities to mesenteric arteries and adrenal capsules as compared to their respective uniodinated forms. ", "A similar loss in their potency to inhibit basal aldosterone release from adrenal zona glomerulosa cells was observed. ", "The rate of disappearance of the radioiodinated peptides from plasma was very fast; the half-life of ANF (Ser 99-Tyr 126) was 16.8 +/- 0.9 sec. ", "Similar values were also obtained for ANF (Arg 101-Tyr 126) and ANF (Ser 103-Tyr 126). ", "The in vivo disappearance of ANF from plasma is probably due to the binding to receptors in the cells since in vitro incubation of ANF (Ser 99-Tyr 126) with rat plasma caused only a slight loss in its immunoreactivity in the first 5 minutes. ", "Hepatectomy and nephrectomy did not cause any major prolongation of the disappearance rate suggesting that these two organs may not be the primary sites involved in the removal of this peptide from circulation." ]

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[ "New Order (Nazism)\n\nThe Neuordnung (often translated as the New Order) of Europe was the political order which Nazi Germany wanted to impose on the conquered areas under its dominion. ", "The establishment of the Neuordnung had already begun long before the start of World War II, but was publicly proclaimed by Adolf Hitler in 1941: \n\nAmong other things, it entailed the creation of a pan-German racial state structured according to Nazi ideology to ensure the supremacy of an Aryan-Nordic master race, massive territorial expansion into Central and Eastern Europe through its colonization with German settlers, the physical annihilation of the Jews, the Slavs (especially Poles and Russians), Roma (\"gypsies\") and others considered to be \"unworthy of life\" and the extermination, expulsion or enslavement of most of the Slavic peoples and others regarded as \"racially inferior\". ", "Nazi Germany's desire for aggressive territorial expansionism was one of the most important causes of World War II.", "\n\nHistorians are still divided as to its ultimate goals, some believing that it was to be limited to Nazi German domination of Europe, while others maintain that it was a springboard for eventual world conquest and the establishment of a world government under German control.", "\n\nOrigin of the term\n\nThe term Neuordnung originally had a different and more limited meaning than in its present usage. ", "It is typically translated as New Order, but a more correct translation would actually be more akin to reorganization. ", "When it was used in Germany during the Third Reich-era it referred specifically to the Nazis' desire to essentially redraw the contemporary state borders within Europe, thereby changing the then-existing geopolitical structures. ", "In the same sense it has also been used now and in the past to denote similar re-orderings of the international political order such as the Peace of Westphalia in 1648, the Vienna Congress in 1815, and the Allied victory in 1945. ", "The complete phrase which was used by the Nazi establishment was actually die Neuordnung Europas (the New Order of Europe), for which Neuordnung was merely a shorthand.", "\n\nAccording to the Nazi government this goal was pursued by Germany to secure a fair rearrangement of territory for the common benefit of a new, economically integrated Europe, which in Nazi terminology meant the continent of Europe with the exclusion of the \"Asiatic\" Soviet Union. ", "Nazi racial views regarded the \"Judeo-Bolshevist\" Soviet state both as a criminal institution which needed to be destroyed as well as a barbarian place as yet lacking any actual culture that would give it a \"European\" character. ", "Neuordnung was therefore hardly ever used in reference to Soviet Russia since theoretically there were no structures that could be re-organized along National Socialist designs.", "\n\nThe actual objective was to ensure a state of total post-war continental hegemony for Nazi Germany. ", "This was to be achieved by the expansion of the territorial base of the German state itself, combined with the political and economic subjugation of the rest of Europe to Germany. ", "Eventual extensions of the project to areas beyond Europe as well as on an ultimately global scale were anticipated for the future period in which Germany would have secured unchallenged control over her own continent first, but Neuordnung did not carry this extra-European meaning at the time.", "\n\nThrough its wide use in Nazi propaganda it quickly gained coinage in Western media. ", "In English-language academic circles especially it eventually carried a much more inclusive definition, and became increasingly known as a term used to refer to all the foreign and domestic politics and war aims of the Nazi German state as well as its dictatorial leader Adolf Hitler. ", "It therefore holds approximately the same connotations as the term co-prosperity sphere did in Japanese circles in reference to their planned imperial domain. ", "Nowadays it is most commonly used to refer to all the post-war planning and policies both in and outside of Europe that the Nazi government expected to implement after an anticipated victory for Germany and the other Axis powers in World War II.", "\n\nIdeological background\n\nRacialist doctrine\n\nThe Nazis claimed to scientifically measure a strict hierarchy of human race; the \"master race\" was said to be the most pure stock of the Aryan race, which was narrowly defined by the Nazis as being identical with the Nordic race, followed by other sub-races of the Aryan race. ", " The Nazis said that since Western civilization, created and maintained they asserted mostly by Nordics, was obviously superior to other civilizations, then the \"Nordic\" peoples were superior to all other races and thus, the Nazis believed, they were entitled to world domination. ", "This concept is known as Nordicism.", "\n\nGeopolitical strategy\n\nHitler’s ideas about eastward expansion that he promulgated in Mein Kampf were greatly influenced during his 1924 imprisonment by his contact with his geopolitical mentor Karl Haushofer. ", " One of Haushofer’s primary geopolitical concepts was the necessity for Germany to get control of the Eurasian Heartland in order for Germany to attain eventual world domination.", "\n\nAnticipated territorial extent of Nazi imperialism\n\nIn a subsequently published speech given at Erlangen University in November 1930 Hitler explained to his audience that no other people had more of a right to fight for and attain \"control\" of the globe (Weltherrschaft, i.e. \"world leadership\", \"world rule\") than the Germans. ", "He realized that this extremely ambitious goal could never be achieved without an enormous amount of fighting. ", "Hitler had alluded to future German world dominance even earlier in his political career. ", "In a letter written by Rudolf Hess to Walter Hewel in 1927, Hess paraphrases Hitler's vision: \"World peace is certainly an ideal worth striving for; in Hitler's opinion it will be realizable only when one power, the racially best one, has attained complete and uncontested supremacy. ", "That [power] can then provide a sort of world police, seeing to it at the same time that the most valuable race is guaranteed the necessary living space. ", "And if no other way is open to them, the lower races will have to restrict themselves accordingly\".", "\n\nHeinrich Himmler discussed the territorial aspirations of Germany during his first Posen speech in 1943. ", "He commented on the goals of the warring nations involved in the conflict, and stated that Germany was fighting for new territories and a global power status:\n\nImplementation in Europe\n\nMilitary campaigns in Poland and Western Europe\nThe initial phase of the establishment of the New Order was:\n First, the signing of the German–Soviet non-aggression agreement on 23 August 1939 prior to the invasion of Poland to secure the new eastern border with the Soviet Union, prevent the emergence of a two-front war, and to circumvent a shortage of raw materials due to an expected British naval blockade.", "\n Second, the Blitzkrieg attacks in northern and western Europe (Operation Weserübung and the Battle of France respectively) to neutralize opposition from the west. ", "This resulted in the conquest of Denmark, Norway, Luxembourg, Belgium, the Netherlands, and France, all of which were under German rule by the early summer of 1940.", "\n\nHad the British succumbed to Germany, the political re-ordering of Western Europe would have been accomplished. ", "There was to be no post-war general peace conference in the manner of the one held in Paris after the First World War, merely bilateral negotiations between Germany and her defeated enemies. ", " All still existing international organizations such as the International Labour Organization were to be dismantled or replaced by German-controlled equivalents. ", "According to captured German documents, the commander-in-chief of the German Army, Walther von Brauchitsch, directed that \"The able-bodied male population between the ages of 17 and 45 will, unless the local situation calls for an exceptional ruling, be interned and dispatched to the Continent.\" ", "This represented about 25% of the surviving population. ", "The United Kingdom was then to be plundered for anything of financial, military, industrial or cultural value, and the remaining population terrorized. ", "Civilian hostages would be taken, and the death penalty immediately imposed for any acts of resistance.", "\n\nThe deported male population would have most likely been used as industrial slave labor in areas of the Reich such as the factories and mines of the Ruhr and Upper Silesia. ", "Although they may have been treated less brutally than slaves from the East (whom the Nazis regarded as sub-humans, fit only to be worked to death), working and living conditions would still have been severe.", "\n\nIn late February 1943 Otto Bräutigam of the Reich Ministry for the Occupied Eastern Territories claimed he had the opportunity to read a personal report by General Eduard Wagner about a discussion with Heinrich Himmler, in which Himmler had expressed the intention to kill about 80% of the populations of France and England by special forces of the SS after the German victory. ", "In an unrelated event, Hitler had on one occasion called the English lower classes, descendants of Anglo-Saxons—a Germanic people, \"racially inferior\".", "\n\nBy annexing large territories in northeastern France, Hitler hoped to marginalize the country to prevent any further continental challenges to Germany's hegemony. ", "Likewise, the Latin nations of Western and Southern Europe (Portugal, Spain and Italy) were to be eventually brought into a state of total German dependency and control.", "\n\nEstablishment of a Greater Germanic Reich\n\nOne of the most elaborate Nazi projects initiated in the newly conquered territories during this period of the war was the planned establishment of a \"Greater Germanic Reich of the German Nation\" (Grossgermanisches Reich Deutscher Nation).", "\n\nEstablishment of German domination in Southeastern Europe\n\nImmediately prior to Germany's invasion of Russia, Slovakia, Hungary, Romania, Bulgaria, and Serbia (including the German-dominated autonomous area of Banat) were already satellites of Nazi Germany. ", "Montenegro was a satellite of Italy while Albania had been annexed by Italy. ", "Greece was under direct German-Italian military occupation because of the growing resistance movement. ", "Although technically in the Italian sphere of influence, Croatia was in reality a condominium puppet state of the two Axis powers, with Italy controlling the southwestern half, and Germany the northeastern half. ", "Hitler observed that permanent German bases might be established in Belgrade (possibly to be renamed to Prinz-Eugen-Stadt) and Thessaloniki.", "\n\nConquest of Lebensraum in Eastern Europe\n\nAdolf Hitler in Mein Kampf argued in the chapter \"Eastern Orientation or Eastern Policy\" that the Germans needed Lebensraum in the East and described it as a \"historic destiny\" which would properly nurture the future generations of Germans. ", "Hitler believed that \"the organization of a Russian state formation was not the result of the political abilities of the Slavs in Russia, but only a wonderful example of the state-forming efficacity of the German element in an inferior race.\" ", "Hitler spoke on 3 February 1933 to the staff of the army and declared that Germany's problems could be solved by \"the conquest of new living space in the east and its ruthless Germanization\". ", "His earlier invasions of Czechoslovakia and Poland can be directly resonate from his desire of Lebensraum in Mein Kampf.", "\n\nImplementation of the long term plan for the New Order was begun on June 22, 1941 with Operation Barbarossa, the invasion of the USSR. ", "The goal of the campaign was not merely the destruction of the Soviet regime—which the Nazis considered illegitimate and criminal—but also the racial reorganization of European Russia, outlined for the Nazi elite in the Generalplan Ost (\"General Plan for the East\"). ", "Nazi party philosopher Alfred Rosenberg (who, incidentally, protested against the inhumane policy shown toward the Slavs) was the Minister for the Eastern Territories, the person nominally in charge of the project, and Heinrich Himmler, head of the SS, was assigned to implement the General Plan for the East which detailed the enslavement, expulsion, and extermination of the Baltic peoples and Slavic peoples.", "\n\nFurthermore, Hitler hoped to turn Germany into a total blockade-proof autarky by exploiting the vast resources lying in Soviet territories: Ukraine was to provide grain, vegetable oil, fodder, iron ore, nickel, manganese, coal, molybdenum; Crimea natural rubber, citrus fruit and cotton; the Black Sea fish, and the Caucasus crude oil.", "\n\nBy 1942 the quasi-colonial regimes called the General Gouvernment in Poland, the Reichskommissariat Ostland in the Baltic states and Belarus, and the Reichskommissariat Ukraine in the Ukraine had been established. ", "Two more administrative divisions were envisaged: a Reichskommissariat Moskowien that would include the Moscow metropolitan area and vast tracts of European Russia, and a Reichskommissariat Kaukasus in the Caucasus. ", "This policy was accompanied by the annihilation of the entire Jewish population (the Final Solution) as well as the enslavement of their Slavic inhabitants, who it was planned would be made slave laborers on the estates to be granted to SS soldiers after the conquest of European Russia. ", "Each of these SS \"soldier peasants\" were expected to father at least seven children.", "\n\nGerman women were encouraged to have as many children as possible to populate the newly acquired Eastern territories. ", "To encourage this fertility policy, the lebensborn program was expanded and the state decoration known as the Gold Honor Cross of the German Mother was instituted, which was awarded to German women who bore at least eight children for the Third Reich. ", "There was also an effort by Martin Bormann and Himmler to introduce new marriage legislation to facilitate population growth, which would have allowed decorated war heroes to marry an additional wife. ", "Himmler envisaged a German population of 300,000,000 by 2000.", "\n\nRosenberg viewed that the political goal of Operation Barbarossa was not merely the destruction of the Bolshevik regime, but the \"reversing of Russian dynamism\" towards the east (Siberia) and the freeing of the Reich of the \"eastern nightmare for centuries to come\" by eliminating the Russian state, regardless of its political ideology. ", "The continued existence of Russia as a potential instigator of Pan-Slavism and its suggestive power over other Slavic peoples in the fight between \"Germandom\" and \"Slavism\" was seen as a major threat. ", "This was to be solved by exploiting ethnic centrifugal forces and limiting the influence of \"Greater Russiandom\" (Großrussentum) by promoting segmentation in the manner of divide and conquer.", "\n\nIn a memorandum sent to Rosenberg in March 1942, Nazi anthropologist Otto Reche argued for the disappearance of 'Russia' both as an ethnic and political concept, and the promotion of a new plethora of ethnicities based on medieval Slavic tribes such as the Vyatichs and Severians. ", "Even White Ruthenia, and in particular the Ukraine (\"in its present extent\") he deemed to be dangerously large. ", "Heinrich Himmler had already advocated for such a general policy towards Eastern Europe in 1940. ", "A top-secret memorandum in 1940 from Himmler entitled \"Thoughts on the Treatment of Alien Peoples in the East\" expressed that the Germans must splinter as many ethnic splinter groups in German-occupied Europe as possible, including Ukrainians, \"White Russians\" (Belarusians), Gorals (see Goralenvolk), Lemkos, and Kashubians and to find all \"racially valuable\" people and assimilate them in Germany. ", "The Eastern Ministry responded that Reche's emphasis on the plurality of ethnic groups in the Soviet Union was correct \"in itself\", but was skeptical about his proposal to resurrect obscure and extinct nationalities. ", "He defended his proposal by arguing that \"[sic] in the area of ethnicity much has already been successfully brought back to life!\", ", "but inquired as to whether names connected with the main towns in each area might serve this role instead. ", "A memo date written by Erhard Wetzel from the NSDAP Office of Racial Policy administration, on April 1942 details the splitting up of Reichskommissariat Moskowien into very loosely tied Generalkommissariats. ", "The objective was to undermine the national cohesion of the Russians by promoting regional identification; a Russian from the Gorki Generalkommissariat was to feel that he was different from a Russian in the Tula Generalkommissariat. ", "Also, a source of discussion in the Nazi circles was the replacement of the Cyrillic letters with the German alphabet. ", "In July 1944, Himmler ordered Ernst Kaltenbrunner, the head of the RSHA, to begin the exporting of the faith of the Jehovah's Witnesses to the occupied east. ", "Himmler considered the Jehovah's Witnesses of being frugal, hard-working, honest and fanatic in their pacifism, and that these traits were extremely desirable for the suppressed nations in the east — despite some 2,500 and 5,000 Jehovah's Witnesses becoming victims of the Holocaust.", "\n\nA series of \"semantic guidelines\" published by the Reich Interior Ministry in 1942 declared that it was permissible to use the word 'Russia' only in a reference to the \"Petersburg empire\" of Peter the Great and its follow-ups until the revolution of 1917. ", "The period from 1300 to Peter the Great (the Grand Duchy of Moscow and the Tsardom of Russia) was to be called the \"Muscovite state\", while post-1917 Russia was not to be referred to as an empire or a state at all; the preferred terms for this period were \"bolshevik chaos\" or \"communist elements\". ", "Furthermore, historic expressions such as Little Russia (Ukraine), White Russia (Belarus/White Ruthenia), Russian Sea (for the Black Sea), and Russian Asia (for Siberia and Central Asia) were to be absolutely avoided as terminology of the \"Muscovite imperialism\". \"", "Tatars\" was described as a pejorative Russian term for the Volga, Crimean, and Azerbaijan Turks which was preferably to be avoided, and respectively replaced with the concepts \"Idel (Volga)-Uralian\", \"Crimean Turks\", and Azerbaijanis.", "\n\nRe-settlement efforts\n\nBy 1942, Hitler's empire encompassed much of Europe, but the territories annexed lacked population desired by the Nazis. ", "After Germany had acquired her Lebensraum, she now needed to populate these lands according to Nazi ideology and racial principles. ", "This was to be accomplished before the end of the war by a \"reordering of ethnographical relations\". ", "The initial step of this project had already been taken by Hitler on 7 October 1939, when Himmler was named the Reich Commissar for the Consolidation of Germandom (Reichskommissar für die Festigung deutschen Volkstums) (RKFDV) (see also Hauptamt Volksdeutsche Mittelstelle, VoMi) This position authorized Himmler to repatriate ethnic Germans (Volksdeutsche) living abroad to occupied Poland. ", "Himmler's jurisdiction as the guardian of the Volksdeutsche re-settlement efforts was increased to other occupied territories to be Germanized as the war continued. ", "To make room for the German settlers, hundreds of thousands of Poles and French living in these lands were transferred across borders. ", "The great majority of Himmler's Volksdeutsche were acquired from the Soviet sphere of interest under the German–Soviet \"population exchange\" treaty.", "\n\nAt the end of 1942 a total of 629,000 Volksdeutsche had been re-settled, and preparations for the transfer of 393,000 others were underway. ", "The long-term goal of the VoMi was the resettlement of a further 5.4 million Volksdeutsche, mainly from Transylvania, Banat, France, Hungary and Romania. ", "The immigrants were classified either as racially or politically unreliable (settled in Altreich), of high quality (settled in the annexed eastern territories) or suitable for transit camps. ", "Himmler encountered considerable difficulties with the Volksdeutsche of France and Luxembourg, who often wished retain their former status as citizens of their respective countries.", "\n\nSpain and Portugal \nSpanish dictator General Francisco Franco contemplated joining the war on the German side. ", "The Spanish Falangists made numerous border claims. ", "Franco claimed French Basque departments, Catalan-speaking Roussillon, Cerdagne and Andorra. ", "Spain also wanted to reclaim Gibraltar from the United Kingdom because of the symbolic and strategic value. ", "Franco also called for the reunification of Morocco as a Spanish protectorate, the annexation of the Oran district from French Algeria and large-scale expansion of Spanish Guinea. ", "This last project was especially unfeasible because it overlapped German territorial ambition to reclaim German Cameroon and Spain would most likely be forced to give up Guinea entirely. ", "Spain also sought federation with Portugal on common cultural and historical grounds (such as the Iberian Union).", "\n\nAfter the Spanish refusal to join the war, Spain and Portugal were expected to be invaded and become puppet states. ", "They were to turn over coastal cities and islands in the Atlantic to Germany as part of the Atlantic Wall and to serve as German naval facilities. ", "Portugal was to cede Portuguese Mozambique and Portuguese Angola as part of the intended Mittelafrika colonial project.", "\n\nPlans for other parts of the world outside Europe\n\nPlans for an African colonial domain\n\nHitler's geopolitical thoughts about Africa always occupied a secondary position to his expansionist aims in Europe itself. ", "His public announcements prior to outbreak of the war that Germany's former colonies be returned to it served primarily as bargaining chips to further territorial goals in Europe itself. ", "Africa was nevertheless expected to fall under German control in some way or another after Germany had first achieved supremacy over its own continent.", "\n\nHitler's overall intentions for the future organization of Africa divided the continent into three overall. ", "The northern third was to be assigned to its Italian ally, while the central part would fall under German rule. ", "The remaining southern sector would be controlled by a pro-Nazi Afrikaner state built on racial grounds. ", "In early 1940 Foreign Minister Ribbentrop had communicated with South African leaders thought to be sympathetic to the Nazi cause, informing them that Germany was to reclaim its former colony of German South-West Africa, then a mandate of the Union of South Africa. ", "South Africa was to be compensated by the territorial acquisitions of the British protectorates of Swaziland, Basutoland and Bechuanaland and the colony of Southern Rhodesia. ", "On the division of French African colonies between the Spanish and Italian governments Hitler refused to provide any official promises during the war, however, fearful of losing the support of Vichy France.", "\n\nIn 1940 the general staff of the Kriegsmarine (navy) produced a much more detailed plan accompanied by a map showing a proposed German colonial empire delineated in blue (the traditional color used in German cartography to indicate the German sphere of influence as opposed to the red or pink that represented the British Empire) in sub-Saharan Africa, extending from the Atlantic Ocean to the Indian Ocean. ", "The proposed domain was supposed to fulfill the long-sought territorial German goal of Mittelafrika, and even further beyond. ", "It would provide a base from which Germany would achieve a pre-eminent position on the African continent just as the conquest of Eastern Europe was to achieve a similar status over the continent of Europe.", "\n\nIn contrast to territories that were to be acquired in Europe itself (specifically European Russia), these areas were not envisaged as targets for extensive German population settlement. ", "The establishment of a vast colonial empire was to serve primarily economic purposes, for it would provide Germany with most natural resources that it would not be able to find in its continental possessions, as well as an additional nearly unlimited supply of labor. ", "Racialist policies would nevertheless be strictly enforced on all inhabitants (meaning segregation of Europeans and blacks and punishing of interracial relationships) to maintain \"Aryan\" purity.", "\n\nThe area included all pre-1914 German colonial territories in Africa, as well as additional parts of the French, Belgian and British colonial holdings in Africa. ", "These included the French and Belgian Congos, Northern and Southern Rhodesia (the latter going perhaps to South Africa), Nyasaland, southern Kenya with Nairobi (northern Kenya was to be given to Italy), Uganda, Gabon, Ubangui-Chari, Nigeria, Dahomey, the Gold Coast, Zanzibar, nearly all of Niger and Chad, as well as the naval bases of Dakar and Bathurst.", "\n\nA second part of the plan entailed the construction of a huge string of fortified naval and air bases for future operations against the Western hemisphere, spanning much of the Atlantic coastline of Europe and Africa from Trondheim in Norway all the way down to the Belgian Congo, as well as many off-lying islands such as Cape Verde and the Azores. ", "A less extensive but similar initiative was intended for the east coast of Africa.", "\n\nDivision of Asia between the Axis powers\n\nIn 1942, a secret diplomatic conference was held between Nazi Germany and the Japanese Empire in which they agreed to divide Asia along a line that followed the Yenisei River to the border of China, and then along the border of China and the Soviet Union, the northern and western borders of Afghanistan, and the border between Iran and British India (which included what is now Pakistan). ", "This treaty, of which a draft was presented to the Germans by ambassador Hiroshi Ōshima, was rejected by the German Foreign Office and the Navy, as it allocated India to Japan and limited the Kriegsmarine'''s operations in the Indian Ocean. ", "Hitler, however, found the treaty acceptable, leading to its signing on 18 January 1942.", "\n\nThe treaty proved to be detrimental for Axis strategic cooperation in the Indian Ocean, as crossing the boundary line required tedious prior consultation. ", "This made any joint German-Japanese offensive against British positions in the Middle East impossible. ", "Japanese operations against Allied shipping lines during the Indian Ocean raid had been highly successful along with the attack against Ceylon, but these were not followed due to the non-existent German-Japanese strategic cooperation. ", "The Germans vigorously maintained watch on the demarcation line, and objected to any Japanese incursion to the \"German sphere\" of the Axis-divided world. ", "Thus the Japanese were forced to cancel a planned massive attack against Madagascar, as the island had been delegated to Germany in the treaty.", "\n\nConcession of Oceania to Japan\n\nGermany's former colonial possessions in the Pacific (German New Guinea and German Samoa), which had been allocated to Japan after World War I as C-Class Mandates according to the Treaty of Versailles, were to be sold to Japan (both Weimar and Nazi-era Germany never relinquished claims to their pre-war colonial territories) at least temporarily in the interest of the Tripartite Pact, its alliance with that country. ", " Australia and New Zealand were designated as future Japanese territories, although Hitler lamented his belief that the white race would disappear from those regions. ", "He nevertheless made it clear to his officials that \"the descendants of the convicts in Australia\" were not Germany's concern and that their lands would be colonized by Japanese settlers in the immediate future, an opinion also shared by Joseph Goebbels, who expressed his conviction in his diary that the Japanese had always desired \"the fifth continent\" for emigration purposes. ", "In his only recorded lengthy discussion on the subject he argued that its people still lived in trees and had not yet learned to walk upright. ", "Historian Norman Rich stated that it can be assumed that Hitler would have attempted to recruit the Anglo-Saxons of these two countries as colonists for the conquered east; some of the English were to share the same fate.", "\n\nMiddle East and Central Asia\n\nAfter the projected fall of the Soviet Union, Hitler planned to intensify the war in the Mediterranean. ", "The OKW produced studies concerning an attack against the Suez Canal through Turkey, an offensive towards Baghdad-Basra from the Caucasus (most of which was already under German occupation as a result of Fall Blau) in support of revolting Arab nationalists, and operations in Afghanistan and Iran directed against British India. ", "Hitler did not envision German colonization of the region, and was most likely to allow Italian dominance at least over the Levant.", "Weinberg (2005), p. 19 The Jews of the Middle East were to be murdered, as Hitler had promised to the Grand Mufti of Jerusalem in November 1941 (see Einsatzgruppe Egypt).", "\n\nTurkey was favored as a potential ally by Hitler because of its important strategic location on the boundaries of Europe, Asia, and Africa, as well as its extensive history as a state hostile against the Russian Empire and the later Soviet Union. ", "To assure that Germany wanted to work with them on a long-range basis, the Turks were guaranteed an equal status in the German-dominated order, and were promised a number of territories which they might desire for reasons of security. ", "These encompassed Edirne (Adrianople) and an expansion of Turkish frontiers at the expense of Greece, the creation of buffer states in the Caucasus under Turkish influence, a revision of the Turkish-Syrian frontier (the Baghdad Railway and the State of Aleppo) and the Turkish-Iraqi frontier (the Mosul region), as well as a settlement of \"the Aegean question\" to provide Turkey with suitable protection against encroachments from Italy. ", "The Black Sea (which Hitler derided as \"a mere frog-pond\") was also to be conceded to Turkey as part of its sphere of influence, for this would negate the need of stationing a German navy in the region to replace the Soviet Black Sea Fleet. ", "Crimea (tentatively dubbed Gotenland by the Nazis) was nevertheless to be fortified to ensure permanent German possession of the peninsula, and the Black Sea exploited as an \"unlimited\" resource of seafood.", "\n\nAllied-occupied Iran was also to be drawn into the Axis camp, possibly by the means of an uprising. ", "The possibility of Iran as an anti-Soviet bastion was already considered in the 1930s, and coincided with Hitler's declaration of Iran as an \"Aryan state\" (the name Iran literally means \"homeland of the Aryans\" in Persian). ", "The changing of Persia's name to Iran in 1935 was done by the Shah at the suggestion of the German ambassador to Iran as an act of \"Aryan solidarity\". ", "However the Iranians had always called their country \"Iran\", a name that predated the rise of Nazi Germany by more than a thousand years. ", "On the eve of World War II Germany was already Iran's single-biggest trading partner, followed by the Soviet Union, United Kingdom, and the United States.", "\n\nDuring pre-war diplomatic maneuvers, the NSDAP Foreign Affairs Office took special interest in Afghanistan, believing that the German Empire had failed to exploit the country diplomatically during the First World War despite the Niedermayer-Hentig Expedition. ", "The objective was to ensure that the country would remain neutral during a possible German-British conflict, and even use it militarily against British India or Soviet Russia. ", "Despite the NSDAP Foreign Office's good relations with the Afghan government, the Foreign Ministry under Ribbentrop favored overthrowing the current government and restoration of the rule of Amānullāh Khān, who had been living in exile since 1929. ", "Hitler eventually came to support Rosenberg's office on this issue.", "After the German-French armistice of 1940, the Kabul government tried to question Berlin on German plans concerning the future of Afghanistan. ", "Of special interest were the post-war borders of the country - the Afghan government hoped to see the liberation of 15 million ethnic Pashtuns living in British India, and the securing of the northern Indian border so that an expansion towards the Indian Ocean became possible (See Pashtunistan). ", "As the Nazi–Soviet Axis talks of October–November were then underway (and the possible expansion of the Soviet sphere of influence in south-central Asia and India was on the table), Berlin was reluctant to give any binding offers to Kabul.", "\n\nThe Third Saudi State under Ibn Saud was seen as a natural ally, and was to be given territorial concessions in south-west Arabia and Transjordan. ", "Also, a post-war satellite Greater Arab Union was discussed.", "\n\nAlthough initially intending to concede Italy control of the region, after that country had defected to the Allied camp in 1943 Hitler came to regard the Islamic countries and the Pan-Arab movement increasingly more as the natural ally of National Socialist Germany, as opposed to the \"treacherous\" Italians. ", "On 17 February 1945 in particular he explained to his entourage his regrets that Germany's prior alliance with its southern neighbor had prevented her from pursuing a more revolutionary policy towards the Arab world, which would have also allowed its exit from the British and French spheres of influence in the area:\n\nHitler's plans for India\n\nHitler's views on India were disparaging. ", "He considered the British colonial rule of the subcontinent as an exemplary one and intended the German rule in the occupied East to resemble it. ", "Hitler thought little of the Indian independence movement, declaring the freedom fighters to be racially inferior \"Asiatic jugglers\". ", "As early as 1930 he spoke of the Indian freedom movement as the rebellion of the \"lower Indian race against the superior English Nordic race\", and that the British were free to deal with any subversive Indian activists as they liked. ", "In 1937 he told the British Foreign Secretary Lord Halifax that the British should \"shoot Gandhi, and if this doesn't suffice to reduce them to submission, shoot a dozen leading members of the Congress, and if that doesn't suffice shoot 200, and so on, as you make it clear that you mean business.\" ", "During the same discussion Hitler reportedly told Halifax that one of his favorite films was The Lives of a Bengal Lancer, because it depicted a handful of \"superior race\" Britons holding sway over an entire continent.", "\n\nNazi ideologist Alfred Rosenberg stated that although the Vedic culture was Aryan in origin, any Nordic blood had long since been lost due to racial mixing. ", "Like Hitler, he viewed the British rule in India as being desirable. ", "Asit Krishna Mukherji, with support of the German consulate, published The New Mercury, a National Socialist magazine and was lauded by Baron von Selzam in a \"communiqué to all German legations in the Far East that no one had rendered services to the Third Reich in Asia comparable to those of Sir Asit Krishna Mukherji's.\" ", "Savitri Devi, who would later marry him, shared his beliefs \"in the pan Aryan revival of India\", as well as in Hindu nationalism, and once World War II started, both \"undertook clandestine war work on behalf of the Axis powers in Calcutta.\"", "\n\nDuring the first years of the war in Europe, as Hitler sought to reach an arrangement with the British, he held the notion that India should remain under British control after the war, as in his mind the only alternative was a Soviet occupation of the subcontinent. ", "As the British had rejected German peace offers, Hitler ordered on 17 February 1941 to prepare a military study for a post-Barbarossa operation in Afghanistan against India. ", "The goal of this operation was not so much to conquer the subcontinent, but to threaten British military positions there to force the British to come to terms. ", "A week later the Afghanistan operation was the subject of a discussion between head of the Army General Staff Franz Halder, Oberbefehlshaber des Heeres Walter von Brauchitsch and chief of the Operationsabteilung OKH Adolf Heusinger. ", "In an assessment produced on 7 April 1941, Halder estimated that the operation would require 17 divisions and one separate regiment. ", "A Special Bureau for India was created with these goals in mind.", "\n\nIndian revolutionary Subhas Chandra Bose escaped from India on 17 January 1941 and arrived in Berlin via Moscow. ", "There he proposed organizing an Indian national government in exile and urged the Axis to declare their support for the Indian cause. ", "He eventually managed to extract such promises from Japan after the Fall of Singapore and later on from Italy as well, but the Germans refused. ", "Bose was granted an audience with Benito Mussolini, but Hitler initially refused to see him, although he did acquire access to Joachim von Ribbentrop after much difficulty. ", "The German Foreign Ministry was skeptical of any such endeavors, as the German goal was to use Bose for propaganda and subversive activity, especially following the model of the 1941 pro-Axis coup in Iraq. ", "These propaganda measures included anti-Raj radio broadcasts and the recruitment of Indian prisoners of war for the \"Free India Legion\". ", "Bose eventually met with Hitler on 29 May 1942. ", "During the discussion, which mostly consisted of Hitler monologing to Bose, Hitler expressed his skepticism for India's readiness for a rebellion against the Raj, and his fears of a Soviet takeover of India. ", "He stated that if Germany had to do anything about India it would first have to conquer Russia, for the road to India could only be accomplished through that country, although he did promise to financially support Bose and help relocate him to the Far East. ", "Bose later described the encounter by stating that it was impossible to get Hitler involved in any serious political discussion.", "\n\nOn 18 January 1942, it was decided that the Indian subcontinent was to be divided between the Axis powers. ", "Germany was to take the part of British India roughly corresponding to the western part of modern day Pakistan, while the rest of British India, along with Afghanistan, was marked for Japan.", "Weinberg (2005), p. 13.", "\n\n Hitler's plans for North America \n\nBefore completing the expected German conquest of Europe, the Nazi leadership hoped to keep the United States out of the war. ", "In an interview with Life in the spring of 1941, Hitler stated that a German invasion of the Western Hemisphere was as fantastic as an invasion of the moon, and he said he was convinced that the idea was being promoted by men who mistakenly thought that war would be good for business.", "\n\nU.S. pro-Nazi movements such as the Friends of the New Germany and the German-American Bund played no role in Hitler's plans for the country, and received no financial or verbal support from Germany after 1935. ", "However, certain Native American advocate groups, such as the fascist-leaning American Indian Federation, were to be used to undermine the Roosevelt administration from within by means of propaganda.", "\"American Indian Federation\" at the Encyclopedia of Oklahoma History & Culture Fictitious reports about Berlin declaring the Sioux as Aryans were circulated by the German-American Bund with the aim of increasing tensions between Native Americans and the Government of the United States, impelling Native Americans to resist being drafted or registered by the Bureau of Indian Affairs; such rumours were reported by John Collier, commissioner of Indian Affairs, to the Congress as true, thus not merely spreading them further but also legitimating them in the eyes of many. ", "As a boy, Hitler had been an enthusiastic reader of Karl May westerns and he told Albert Speer that he still turned to them for inspiration as an adult when he was in a tight spot.", "\n\nApproximately nine months before the United States joined the Allies, U.S. President Franklin D. Roosevelt made a reference to the New Order in a speech he gave on March 15, 1941, recognizing Hitler's hostility towards the United States and the destructive potential it represented, about which Roosevelt was quite acutely aware:\n\nHitler held U.S. society in contempt, stating that the United States (which he consistently referred to as the \"American Union\") was \"half Judaized, and the other half Negrified\" and that \"in so far as there are any decent people in America, they are all of German origin\". ", "As early as 1928, he had maintained that National Socialist Germany must prepare for the ultimate struggle against the U.S. for hegemony. ", "In mid-late 1941, as Hitler became overconfident of an Axis victory in Europe against the UK and the Soviet Union, he began planning an enormous extension of the Kriegsmarine, projected to include 25 battleships, 8 aircraft carriers, 50 cruisers, 400 submarines and 150 destroyers, far exceeding the naval expansion that had already been decided on in 1939's Plan Z. Historian Gerhard L. Weinberg stated that this super-fleet was intended against the Western Hemisphere. ", "Hitler also considered the occupation of the Portuguese Azores, Cape Verde and Madeira and the Spanish Canary islands to deny the British a staging ground for military actions against Nazi-controlled Europe, and also to gain Atlantic naval bases and military airfields for operations against North America. ", "Hitler desired to use the islands to \"deploy long-range bombers against American cities from the Azores\", via a plan that actually arrived on Hermann Göring's RLM office desks in the spring of 1942 for the design competition concerning such an aircraft. ", "In July 1941, Hitler approached Japanese ambassador Ōshima with an offer to wage a joint struggle against the U.S.—Japan's own Project Z aircraft design program was one possible manner in which such a goal could be accomplished, all during the timeframe that the USAAC had itself, on April 11, 1941, first proposed a competition for airframe designs for the same sort of missions against the Axis forces, the Northrop XB-35 and the Convair B-36, flying directly from North American soil to attack Nazi Germany.", "\n\nIn this final battle for world domination, Hitler expected the defeated British to eventually support the Axis forces with its powerful navy. ", "He stated that \"England and America will one day have a war with one another, which will be waged with the greatest hatred imaginable. ", "One of the two countries will have to disappear.\" ", " and \"I shall no longer be there to see it, but I rejoice on behalf of the German people at the idea that one day we will see England and Germany marching together against America\".", "\n\nThe actual physical conquest of the United States was unlikely, however, and the future disposition of U.S. territories remained cloudy in Hitler's mind. ", "He perceived the anticipated battle with that country, at least under his own rule, to be a sort of \"battle of the continents\"—possibly along the lines of then-contemporary U.S. thought, such as the opening text from the second film in Frank Capra's Why We Fight series, illustrating one U.S. viewpoint of what Hitler could have thought on such matters while viewing the crowds at the 1934 Nuremberg rally—with a Nazi-dominated Old World fighting for global dominance against the New World, in which Germany would attain leadership of the world rather than establish direct control over it. ", "Further decisions down the line were left up to future generations of German rulers.", "\n\nCanada featured fairly little in Nazi conceptions of the post-war world. ", "Because Hitler's political objectives were primarily focused on Eastern Europe before and during the war — in contrast to his own opinions towards the United States from 1928 in his unpublished volume, Zweites Buch—Hitler considered the United States a negligible political factor in the world, while Canada interested him even less. ", "He politically grouped the country together with the United States in a U.S.-dominated North America, and considered it equally as \"materialistic, racially bastardized, and decadent\" as its southern neighbor. ", "In 1942, when expressing his fear of an imminent collapse of the British Empire which he preferred to remain intact, Hitler believed that the United States would seize and annex Canada at the first opportunity, and that the Canadians would be quick to welcome such a move.", "\n\nThis lack of policy direction from the top meant that Nazi politicians concerned with representing Germany's interests and relations with Canada had to resort to an improvised line of policy which they believed to be in accordance with Hitler's wishes. ", "The country was noted for its abundance of natural resources, and because of its great geographic size coupled with a low population density was characterized as \"a country without people\", in contrast to Germany which was considered \"a people without space\". ", "In his 1934 travelogue account of Canada, Zwischen USA und dem Pol (), German journalist Colin Ross described Canadian society as artificial because it was composed of many different parts that weren't tied together by either blood or long-standing traditions (highlighting the differences between the French and English Canadians in particular), and that for this reason one could not speak of either a Canadian nation or Volk. ", "As a result the country's political system was also considered mechanic and non-organic, and that Ottawa did not constitute \"the heart of the nation\". ", "Because of both these factors the Canadians were deemed incapable of comprehending \"true culture\", and German immigration in Canada was considered a mistake because they would be forced to live in an \"empty civilization\".", "\n\nPlans for economic domination in South America\nNeither Hitler nor any other major Nazi leader showed much interest towards South America, except as a warning example of \"racial mixing\". ", "However, the NSDAP/AO was active in various South American countries (notably among German Brazilians and German Argentines), and trade relations between Germany and the South American countries were seen as of great importance. ", "During 1933–1941, the Nazi aim in South America was to achieve economic hegemony by expanding trade at the expense of the Western Powers. ", "Hitler also believed that German-dominated Europe would displace the United States as the principal trading partner of the continent. ", "Long-term Nazi hopes for political penetration of the region were placed on the local Fascist movements, such as the Integralists in Brazil and right-wing nationalists in Argentina, combined with the political activation of the German immigrant communities. ", "Hitler also had hopes of seeing German immigrants \"returning\" from the Western Hemisphere to colonize the conquered East. ", "Despite being occasionally suspicious of the South American Germans of adopting a \"South attitude towards life\", top Nazis believed that their experience working in underdeveloped areas would make them ideal settlers for the annexed eastern territories.", "\n\nOn 27 October 1941 Roosevelt stated in a speech \"I have in my possession a secret map, made in Germany by Hitler's government, by planners of the new world order. ", "It is a map of South America and part of Central America as Hitler proposes to organize it\" into five countries under German domination. ", "The speech amazed both the United States and Germany; the latter claimed the map was a forgery. ", "While British Security Coordination indeed forged the map and arranged for discovery by the Federal Bureau of Investigation, it likely was based in part on a real, public map of boundary changes German agents used to persuade South American countries to join the New Order.", "\n\nFuture wars against Asia\n\nAlthough pursuing an alliance based on Realpolitik with Imperial Japan in the battle against the \"Western Plutocracies\" and Soviet Bolshevism, the Nazi leadership ultimately considered this cooperation only temporary in nature. ", "The racial ideology of Nazism predicted that the fate of human civilization depended on the ultimate triumph of the Germanic-Nordic peoples, and in fact the populous Asian continent was seen as the greatest threat to hegemony of the white race. ", "The Japanese people were characterized as 'culture-bearers', meaning they could make use of the technological and civilizational achievements of the Aryan race and by so doing maintain an advanced society, but could not truly create 'culture' themselves. ", "Gerhard Weinberg asserts that the historical evidence points to the conclusion that Hitler, like he had done with the Soviets in the 1939–1941 period, employed a tactic of conceding to the Japanese whatever they desired until they in turn could be defeated in a subsequent war. ", "In early 1942, Hitler is quoted saying to Ribbentrop: \"We have to think in terms of centuries. ", "Sooner or later there will have to be a showdown between the white and the yellow races.\"", "\n\nIn July 1941, as plans were being laid out for post-Barbarossa military operations, the Wehrmacht's naval top-level command, the Oberkommando der Marine was not ready to exclude the possibility of a war between Germany and Japan. ", "In 1942, NSDAP official Erhard Wetzel (Reich Ministry for the Occupied Eastern Territories) predicted that \"the self-determination of the numerically strong Asian peoples after this war\" would challenge German-controlled Europe with Japanese instigation, and stated that \"a Greater Asia and an independent India are formations that dispose over hundreds of millions of inhabitants. ", "A German world power with 80 or 85 million Germans by contrast is numerically too weak\". ", "Wetzel further pondered on Germany's choices on the population policies in occupied Russia: if the Russians were restricted to having as few children as possible in the interest of German colonization, this would further \"weaken the white race in view of the dangers of Asia\".", "\n\nAs the Japanese were conquering one European colonial territory after another in Asia and Oceania, and seemingly poised to take over Australia and New Zealand as well, Hitler further believed that the white race would disappear altogether from these regions, which he viewed as a turning point in history. ", "He was relieved that Japan had entered the war on Germany's side, however, as he had long hoped to use that country as a strategic counterweight against the United States, but also because Japanese hegemony in East Asia and the Pacific would guarantee both countries' security against other powers. ", "Looking into the future, he remarked that \"There's one thing Japan and Germany have in common; both of us need fifty to a hundred years for purposes of digestion: we for Russia, they for the Far East\".", "\n\nDuring his speech at the meeting of SS major-Generals at Posen on 4 October 1943, Heinrich Himmler commented on the future conflicts between Nazi-controlled Europe and Asia:\n\nHimmler addressed this apocalyptic vision in an earlier speech given to SS generals at the University of Kharkiv, Ukraine in April 1943. ", "He first spoke on the necessity of the war against the Soviets and Jewry:\n\nEnd of the New Order project\n\nAfter the decisive German defeat at the Battle of Stalingrad on 2 February 1943, Germany was forced onto the defensive and was no longer able to actively pursue implementation of the New Order in the Soviet Union, although the genocide against Jews, Romani, and other minorities continued. ", "Following the subsequent failure of the 1943 summer offensive to regain the territories lost to the Soviets earlier that year, the Wehrmacht was no longer able to mount an effective large-scale counter-attack on the Eastern Front. ", "In a discussion with Joseph Goebbels on 26 October 1943 Hitler opined that Germany should conclude a temporary armistice with the Soviet Union and return to its 1941 border in the east. ", "This would then give Germany the opportunity to defeat the British forces in the west first (no mention was made of the United States's part in the Allied alliance) before resuming a new war for Lebensraum against the Soviet Union at a later point in time. ", "Hitler thought that his future successor might have to carry out this later war, as he believed himself to be too old by then.", "\n\nLate in the war, after the failure of the final Ardennes offensive and the Allied crossing of the Rhine into Germany itself, Hitler hoped that a decisive victory on the Eastern Front might still preserve the Nazi regime, resulting in Operation Spring Awakening. ", "He believed that, with the conclusion of a separate peace-treaty with the Soviet Union, a division of Poland might still be realized and leave Hungary and Croatia (the former still under German occupation at the time, the latter a Croatian fascist puppet-state) under German control. ", "Hitler only acknowledged Germany's imminent defeat mere days prior to his suicide.", "\n\nSee also\n\n Areas annexed by Nazi Germany\n Greater Germanic Reich, the domain which the Nazis tried to create by merging all the Germanic-populated countries in Europe into one state.", "\n Greater East Asia Co-Prosperity Sphere, the envisioned Japanese economic equivalent of the New Order and the Greater Germanic Reich.", "\n A-A line\n Jewish settlement in the Japanese Empire\n SS State of Burgundy\n The Ural Mountains in Nazi planning\n Wehrbauer\n Imperial Italy (fascist), the Fascist Italian project for securing dominion over the Mediterranean area.", "\n Axis power negotiations on the division of Asia during World War II\n Grossdeutschland\n Drang nach Osten (\"The Drive Eastward\")\n Lebensraum\n Generalplan Ost\n Lebensborn\n Final solution\n The Holocaust\n European theater of World War II\n German-occupied Europe\n New world order (international relations theory)\n Posen speeches – In two notable speeches given in October 1943, Himmler details the tasks of the SS in implementing the New Order.", "\n Hegemony\n Hypothetical Axis victory in World War II\n\nCitations\n\nReferences\n\nFurther reading\n Evans, Richard J. The Third Reich at War (2009) pp 321–402\n \n Fritz, Stephen G. Ostkrieg: Hitler's War of Extermination in the East (2011)\n Longerich, Peter. ", "Heinrich Himmler: A Life (2012)\n Lund, Joachim. \"", "Denmark and the 'European New Order', 1940-1942,\" Contemporary European History, (2004) 13#3 pp 305–321,\n Mazower, Mark. ", "Hitler's Empire: How the Nazis Ruled Europe (2009)\n Mazower, Mark. \"", "Hitler's New Order, 1939-45,\" Diplomacy and Statecraft (1996) 3#1 pp 29–53,\n Snyder, Timothy. ", "Bloodlands: Europe Between Hitler and Stalin'' (2010)\n\nCategory:Nazism\nCategory:Nazi Germany\nCategory:Politics of World War II\nCategory:1941 in Germany\nCategory:Axis powers" ]

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[ "About Us\n\nOur Story\n\nSmall Beginnings\n\nVictorious Life Christian Church began as a small charismatic house church of about a dozen people in 1981. ", "The group was a Troy offshoot of what was then known as Albany Christian Community located in Glenmont, New York. ", "Sensing God's call to a greater commitment to His purposes and to one another, we incorporated as a local church in 1983 with the name, Troy Christian Community. ", "Meeting in homes and various places, we continued to grow as we worshipped the Lord and sought His will for our lives. ", "Many local college students and Capital Region families joined our congregation during this early season of growth. ", "In 1986, Pastor Anthony Germano was ordained as senior pastor of the church.", "\n\nA Home Grown Church\n\nIn 1987 we leased our first public place of worship in a downtown Troy storefront on River Street. ", "During this time we developed outreaches to Rensselaer Polytechnic Institute and Sage College as well as a heart for urban evangelism and ministry. ", "Believing in house church ministry as a scriptural model for discipleship and growth, we continued to establish our home groups to accommodate our growing congregation. ", "Our young families also grew with many children causing us to establish a children's ministry to accommodate our children during our Sunday service.", "\n\nA New Home and a New Name\n\nIn 1988 we affiliated with a network of like-minded local churches which helped establish our youthful, home grown congregation. ", "With a firm commitment to team ministry, we ordained Dominick Brignola and Brian Barker as elders during this time. ", "Without space to grow in our storefront, we sought a larger place to meet. ", "In 1991 we purchased the former St. John's Lutheran Church in downtown Troy, an 11,000 square foot facility with a seating capacity of 300 for the bargain price of $90,000. ", "At this time we changed our name to Victorious Life Christian Church, committing to being an urban congregation with a viable mission to its community.", "\n\nAn Established Vision\n\nWith this next season came building renovations, training our deaconate, and seeking to clarify our urban vision in a time when many churches were forsaking the cities and the poor. ", "Believing that the gospel of Jesus Christ is truly the hope of every community we decided to remain based in the city making Troy our home. ", "This decision came in 1996, perhaps one of Troy's bleakest years. ", "At this time, Troy was on the brink of bankruptcy and was required to be financially regulated by the State. ", "Troy City Hall was put up for sale and Troy was among the most distressed cities in New York State.", "\n\nIn 1997, Pastor Tony answered the call to trans-local ministry, at which time Pastor Dominick Brignola was ordained as senior pastor. ", "Pastor Dominick brought strong conviction and vision to our urban vision and established Arise and Build Community Ministries, a not-for-profit Christian ministry dedicated to serving the needs of the inner-city. ", "Alight Care Center was established, as well as Provisions Community Food and Storehouse. ", "Victorious Life is currently governed by a bi-vocational eldership team and continues to grow in this vision. ", "Philip Smith was ordained and joined the eldership team in 2002. ", "Joseph Rice and Lindsay Todd were ordained and joined the eldership team in 2010. ", "Now a congregation of about 200, we are seeking to expand our leadership team and continue to find creative ways to reach our community with the gospel.", "\n\nWe Have a Future and a Hope\n\nWe have had much joy seeing Victorious Life become established in the last thirty years. ", "We have impacted the lives of thousands of households through our many community outreaches and have genuinely experienced God's grace upon us as we have grown. ", "However, for Victorious Life, we believe the best years are yet to come. ", "Troy's economy and outlook has improved greatly since 1996 and the Capital Region is preparing for considerable economic growth.", "\n\nThrough every season of our journey, Victorious Life has remained a strong, growing local church with an exceptional vision and a deep devotion to our Lord and Savior, Jesus Christ. ", "Together with Him, we are becoming a prevailing, multi-generational local church with growing influence in the city of Troy, the Capital Region and beyond. ", "We invite you to partner with us in this unfolding story of God's love and redemption." ]

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[ "[Amendment to the law governing the professional activities of physicians in general practice].", "\nThe amendment to the law governing the activities of physicians in general free practice, which came into force on 1st January 2007, has brought a large number of changes. ", "The age limit has been abolished, partial licences to practice and the formation of professional communities covering more than one district are permitted and new employment possibilities for physicians have been created. ", "With these new regulations, many traditional principles of this law have been fundamentally changed. ", "The purpose of the amendment is to make the health service more flexible and increase competition among providers of medical services." ]

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[ "Christine Gentry grew up in a house in Texas where there was one important rule above all others. ", "It came from her dad: we have loaded guns in the house, and even though I’ve taught you how to shoot them, no one can ever touch them without me being there. ", "As far as anyone in the family knew the kids grew up obeying that rule. ", "Until this past December when Christine confesses to the one time when — as a teenager — that she broke the rule. (", "10 minutes)" ]

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[ "Q:\n\nRegarding questions and the relevance of tags to the actual content\n\nI originally titled this as \"How much coverage over the question's content should your tag choice revolve around?\", ", "and similar variants, all of which could be very confusing so I went with a less inquisitive title. ", "I did look at the FAQ, but my particular concern was not addressed.", "\nIt is recommended that you use as many applicable tags as you can in order to increase the chances of people actually looking at your question. ", "Sometimes, though, there are tags which are very much applicable, but only to certain portions of the question. ", "I then think to myself whether I should add the tag, especially if it is a tag which seems to reduce the number of views.", "\nSKIP TO THE BOTTOM IF YOU'D PREFER, IT IS A LENGTHY DISCOURSE FOR JUST AN EXAMPLE\nI'll use an example question which I once pondered, but I never asked because I figured out that my currently implemented algorithm was as optimized as possible.", "\n\nI need to remove a certain value from a delimited string. ", "However, the string input will also include the delimiter at the beginning and end of the string. ", "For example, I might have to remove 3;#Delta from the string ;#1;#Alpha;#2;#Beta;#3;#Delta;#. ", "The algorithm would be different if the input string was at the beginning, end, or middle of the string. ", "Can I optimize the following algorithm?", "\n~CODE WOULD BE HERE~\n\nThe obvious tags would be [c#] and [string-manipulation], maybe also [optimization] and [delimiter]. ", "I could also include [sharepoint], because the whole ;# delimiter included both at the start and end is because I am using SharePoint. ", "However, the actual question has nothing to do with SharePoint. ", "It can be understood and answered quite correctly without any knowledge that SharePoint was in the situation. ", "SharePoint is merely the environment that enforces why I am in the situation in the first place. ", "So while [sharepoint] does have relevance to the situation and content of the question, it doesn't really apply to the essence of the question.", "\nBut maybe when I write the question, I might state \"SharePoint\" in order to just explain why I'm in the situation, but note that it is more specifically a C# question than even a C# and SharePoint question. ", "Or maybe someone posts a comment asking \"Why are you using such a stupid delimiter scheme?\", ", "and I would explain that it was because of SharePoint. ", "If I include the [sharepoint] tag, then maybe I wouldn't have to answer that comment because it would be implied. ", "I use a [sharepoint] example specifically because as far as I see, its presence does tend to reduce the number of people who look at the question. ", "Perhaps it is because SharePoint has an equivalence between how evil it is and how useful it can be once you use it right, and maybe it might be because the people who address those questions are elsewhere. ", "The reason is largely irrelevant because the example question is only marginally related to SharePoint. ", "The tag would provide information as to the origin of the question, but it has little to do with the core of the code and the solution.", "\nESSENCE OF THIS META QUESTION IS DOWN HERE\nI write too much. ", "I'm aware of that at times. ", "But it feels wasteful to erase. ", "Maybe I'm daft.", "\nBut even though I use a [sharepoint] example, I ponder about tag choice in general for all situations. ", "Often times, you do have a very specific question that you'll be pounding your head against the 5 tag limit. ", "But sometimes you aren't finding yourself at the 5 tag limit, and there are some tags which could apply to your question, but should they be used? ", "Should you base your tag choice to hit all reaches of your question, no matter how remote? ", "At what point does search coverage overtake the relevance of the tag? ", "Should tags primarily be focused on the core of the question?", "\nI'm not asking for a change in how people tag. ", "I'm more curious as to people who have stumbled upon thinking what to tag their questions, if they run into this kind of situation, or people who do have some insight or recommendations to these things.", "\n\nA:\n\nThis is a really subjective topic since tags applied to a question are completely dependent on the question itself.", "\nGenerally speaking, however, I'll tag a question by starting with a list of tags (not limited to 5), generated like so:\n\nClassification/context tag(s), in descending order of importance. ", "These are the most important tags that, if omitted or wrongly included, don't give the wanted solution. ", "I.e., tagging with [perl] instead of [c#] when a C# solution is wanted is not going to end well.", "\nDirect subject tag(s), in descending order of importance. ", "These tags identify the actual thing needing help, or being talked about. ", "I.e., [string] means \"I need help with how a string works\" (usually accompanied by the [c++] tag), or \"how do I use strings to solve problem XYZ?\" ", "These are normally tags that could be omitted and still allow someone to give an answer. ", "For example, if someone wants to know the syntax of a for loop, they will still get a good answer as long as the correct language tag is on the question, even if [for-loop] is omitted.", "\n\nUsually 5 tags is enough to give all that information. ", "If I end up with more than 5, I'll start paring down the list by removing the least important tags from either (1) or (2) which has the most tags in the list, depending on the question context, of course. ", "If a tag is specific to the situation (usually a subject tag), it should almost always be left in, possibly even at the expense of the least-significant context tag.", "\nI've never run into a situation where either the context or subject couldn't be well described in 4 tags, leaving at least 1 tag to describe the other.", "\nMeta-tags, like [sharepoint] in your example, should be removed, as they don't add any information, context, or value to the question. ", "The question can be answered without any knowledge of SharePoint. ", "It really isn't relevant, since if you changed the delimiter in your sample to something more normal, the point is completely moot.", "\nThat being said, if you feel the need to explain why something is the way it is (\"I denormalized those 25 tables on purpose. ", "Really!\"), ", "go ahead and mention what you need to in the question body, probably in an addendum at the end of the post which shouldn't be required reading for anyone to give an answer.", "\n\n" ]

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[ "4.6K shares Save\n\nShare\n\nTweet\n\nReddit\n\nEmail\n\nSeriously, this crusty, rustic, no knead bread is THE easiest bread I think you can make. ", "I used to be terrified of making bread, it always goes back to this one time a couple of years ago that I tried to make an Italian loaf and it turned out like a skinny rubber snake. ", "An experience like that can scar you into just buying bread because store bought loafs won’t give you nightmares.", "\n\nI came across this no knead bread recipe on Pinterest here, and she found it on a couple of other sites, but as far as I can figure out it originated from Le Creuset. ", "Makes sense seeing as it bakes in a Dutch oven.", "\n\nNo Knead Bread Origin Update:\n\nHayley messaged me with the actual originator of this recipe. ", "It’s Jim Lahey and his recipe was featured in The New York Time’s Minimalist column here. ", "It’s definitely worth a read because there are some tips and tricks for working with the loaf that I hadn’t seen on the Pinterest versions. ", "Great find Hayley, so thank you! ", "And thank you to Jim Lahey, my husband is now your biggest fan!", "\n\nNow Back The The No Knead Bread Recipe Making!", "\n\nI was a little nervous as first. ", "It seemed too simple, you know? ", "But the pictures looked amazing and seeing as it was only going to use up 5 minutes of my time, I figured I’d be an idiot not to try.", "\n\nYes. ", "You read that correctly.", "\n\nThis will only take 5 minutes of hands on time to make.", "\n\nAnd there’s no kneading.", "\n\nSeriously, it’s like magic or something.", "\n\nThrow your flour, salt, and yeast in a large bowl. ", "I really like glass bowls for rising dough, easier to gauge what’s going on.", "\n\nWhisk it up.", "\n\nAdd the water (use room temperature water, you’re aiming for warm, but not hot).", "\n\nMix it up with a wooden spoon or spatula.", "\n\nCover it tightly with plastic wrap and let it rise. ", "Now, directions say to let it rise for 12 to 18 hours. ", "That doesn’t work for me who wants to prep it in the morning and eat it with dinner. ", "I put this in the oven, with the oven light on. ", "It works perfectly and rises in about 6 hours. ", "Then just take it out and let it finish on the counter until you’re ready to bake it.", "\n\nBeautifully risen dough.", "\n\nThis is the moment I started believing it was actually going to turn out.", "\n\nThrow a bunch of flour down on your counter, put the dough on it, then put more flour on top of the dough.", "\n\nQuickly shape it into a ball. ", "This takes 1 minute. ", "That’s it. ", "At this stage, if you wanted too, you could mix some stuff in. ", "Looking for ideas: rosemary, grated cheese (I’d go with an old cheddar), some roasted garlic, a combination of them, or anything else you can think of.", "\n\nCover loosely with plastic wrap and leave for 30 minutes. ", "While this is resting put your Dutch oven, lid and all, into the pre-heated oven for the 30 minutes.", "\n\nPut the ball of dough into the pre-heated Dutch oven, put the lid on it, and put it in the oven. ", "I sprinkled some sea salt on top first. ", "I suggest you do the same. ", "Side note: this is one of the worst pictures I’ve taking in a long time, so sorry for the blur. ", "I had a dog playing between my legs and was cooking dinner at the time too so no chance for a re-take.", "\n\nAfter 30 minutes take off the lid; this is what the bread will look like at this point. ", "Continue cooking for 15 more minutes. ", "I’m new to the bread game, so I worry about the inside being done. ", "There are two ways to gage this: first, when you knock on the loaf it should sound hollow. ", "While a nice fact, I don’t trust myself to accurately gage “hollow”. ", "I stick an instant read thermometer into the side of the loaf, if it registers 190ºF – 200ºF we’re good to go.", "\n\nAnd this, my dears, is what I ended up with. ", "I was just as amazed as you are. ", "This is like, the perfect loaf of rustic artisan bread, only it’s a no knead bread. ", "I didn’t know before this moment that could be possible! ", "It was great too, a nice chewy interior and a super crisp exterior. ", "Bo was in absolute heaven and his only comment: I wouldn’t be upset if you made this every night. ", "On that note, I’ve got one rising in the oven for tonight as I type.", "\n\nWant More Delicious Bread Recipes?", "\n\nThis Cheesecake Factory Bread copycat recipe is the most popular recipe on my blog, and one of the ones I’m most proud of! ", "It’s definitely a couple notches up from this no knead bread, but you won’t regret giving it a shot (I mean, if you’ve eaten at the Cheesecake Factory before you understand that the bread is the best part of the meal!).", "\n\nHere’s the printable:\n\nServings 1 loaf Crusty, Rustic, No Knead Bread (aka the easiest bread you’ll ever make) 5 minPrep Time 45 minCook Time PT8-18H50MTotal Time Save Recipe Save Recipe Print Recipe My Recipes My Lists My Calendar Ingredients 3 cups all-purpose flour\n\n1½ tsp salt\n\n½ tsp yeast\n\n1½ cups warm water (not hot, think room temperature) Instructions In a large glass bowl whisk together the flour, salt, and yeast. ", "Stir in the water with a wooden spoon until a shaggy looking ball forms. ", "Cover tightly with plastic wrap and let rise for 12-18 hours. ", "Alternatively, you can place the bowl in the oven with only the light turned on. ", "The dough should rise in about 6 to 8 hours like this. ", "Pre-heat your oven to 450ºF with a rack in the middle position. ", "Turn the dough out onto a well floured counter. ", "Add additional flour to the top of the dough and quickly form into a ball. ", "Cover loosely with plastic wrap and let rest for 30 minutes.", "While the dough is resting, place a large Dutch oven, with the lid on, into the pre-heated oven to warm for 30 minutes. ", "You can also use any large, lidded cast iron or pyrex dish, so long as it can handle 450ºF. Place the dough ball into the heated Dutch oven, put the lid on, and bake for 30 minutes. ", "Remove the lid and return to the oven for an additional 15 minutes, until the loaf is golden brown, sounds hollow when knocked on, and an instant-read thermometer registers between 190ºF and 200ºF. Let cool on a wire rack before cutting. ", "7.8.1.2 107 https://www.kitchentrials.com/2012/04/03/crusty-rustic-no-knead-bread-aka-the-easiest-bread-youll-ever-make/ Copyright Kitchen Trials 2017" ]

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[ "Russian troops surrounded a village in 2000 during the second chechan war and killed all of the 75 prisoners using torture tactics." ]

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[ 0 ]

[ "---\nabstract: 'Partial words are sequences over a finite alphabet that may contain wildcard symbols, called holes, which match or are compatible with all letters; partial words without holes are said to be full words (or simply words). ", "Given an infinite partial word $w$, the number of distinct full words over the alphabet that are compatible with factors of $w$ of length $n$, called subwords of $w$, refers to a measure of complexity of infinite partial words so-called subword complexity. ", "This measure is of particular interest because we can construct partial words with subword complexities not achievable by full words. ", "In this paper, we consider the notion of recurrence over infinite partial words, that is, we study whether all of the finite subwords of a given infinite partial word appear infinitely often, and we establish connections between subword complexity and recurrence in this more general framework.'", "\nauthor:\n- 'Francine Blanchet-Sadri'\n- Aleksandar Chakarov\n- Lucas Manuelli\n- Jarett Schwartz\n- Slater Stich\nbibliography:\n- 'bibliography.bib'\ntitle: 'Recurrent Partial Words[^1]'\n---\n\nIntroduction {#sec:introduction}\n============\n\nLet $w$ be a (right) infinite word over a finite alphabet $A$. ", "A subword of $w$ is a block of consecutive letters of $w$. The [*subword complexity*]{} function, $p_w(n)$, counts the number of distinct subwords of length $n$ in $w$. Subword complexity is a well-studied topic and relates to dynamical systems, ergodic theory, theoretical computer science, etc. [", "@All; @DBLP:books/daglib/0025558; @Cas97; @DBLP:journals/dm/Ferenczi99; @Ghe]. ", "Another topic of interest on infinite words is the one of [*recurrence*]{}. ", "An infinite word is said to be recurrent if every subword appears infinitely many times. ", "In 1938, Morse and Hedlund introduced many concepts dealing with recurrence [@MoHe38]. ", "Rauzy in [@Rau] surveys subword complexity and recurrence in infinite words, while Cassaigne in [@DBLP:conf/stacs/Cassaigne01] surveys some results and problems related to recurrence.", "\n\nPartial words are sequences over a finite alphabet that may contain wildcard symbols, called holes, which match, or are compatible with, all letters in the alphabet (full words are those partial words without holes). ", "Combinatorics on partial words is a relatively new subject [@DBLP:journals/tcs/BerstelB99; @BSbook]; oftentimes the basic tools have not yet been developed. ", "In [@DBLP:conf/tamc/Blanchet-SadriSSW10], Blanchet-Sadri et al. ", "investigated finite partial words of maximal subword complexity where the subword complexity function of a partial word $w$ over a finite alphabet $A$ assigns to each positive integer, $n$, the number, $p_w(n)$, of distinct full words over $A$ that are compatible with factors of length $n$ of $w$. In [@DBLP:conf/lata/ManeaT10], Manea and Tiseanu showed that computing subword complexity in the context of partial words is a “hard” problem.", "\n\nIn [@BSChMaScSt_1], with the help of our so-called hole functions, we constructed infinite partial words $w$ such that $p_w(n)=\\Theta(n^\\alpha)$ for any real number $\\alpha > 1$. In addition, these partial words have the property that there exist infinitely many non-negative integers $m$ satisfying $p_w(m+1)-p_w(m) \\geq m^{\\alpha}$. Combining these results with earlier ones on full words, we showed that this represents a class of subword complexity functions not achievable by full words. ", "We also constructed infinite partial words with intermediate subword complexity, that is between polynomial and exponential.", "\n\nIn this paper, we introduce recurrent infinite partial words and show that they have several nice properties. ", "Some of the properties that we present deal with connections between recurrence and subword complexity. ", "Besides reviewing some basics in Section \\[sec:preliminaries\\] and concluding with some remarks in Section \\[sec:conclusion\\], our paper can roughly be divided into two parts: Among other things, Section \\[sec:recurrent\\_partial\\_words\\] extends well-known results on recurrent infinite full words to infinite partial words. ", "Section \\[sec:completions\\] uses the results obtained previously to prove new results. ", "There, we study the relationship between the subword complexity of an infinite partial word $w$ and that of its various completions; here a completion is a “filling in” of the holes of $w$ with letters from the alphabet. ", "In particular we ask when can a completion achieve maximal, or nearly maximal, complexity? ", "It turns out that this is intimately related to the notion of recurrence.", "\n\nPreliminaries {#sec:preliminaries}\n=============\n\nFor more information on basics of partial words, we refer the reader to [@BSbook]. ", "Unless explicitly stated, $A$ is a finite alphabet that contains at least two distinct letters. ", "We denote the set of all words over $A$ by $A^*$, which under the concatenation operation forms a free monoid whose identity is the empty word $\\varepsilon$.\n\nA *finite partial word* of length $n$ over $A$ is a function $w:\\{0,\\ldots,n-1\\}\\rightarrow A\\cup \\{{{\\ensuremath{\\diamond}}}\\}$, where ${{\\ensuremath{\\diamond}}}\\not \\in A$. ", "The union set $A\\cup \\{{{\\ensuremath{\\diamond}}}\\}$ is denoted by $A_{{{\\ensuremath{\\diamond}}}}$ and the length of $w$ by $|w|$. A *right infinite partial word* or *infinite partial word* over $A$ is a function $w:\\mathbb{N}\\rightarrow A_{{{\\ensuremath{\\diamond}}}}$. In both the finite and infinite cases, the symbol at position $i$ in $w$ is denoted by $w(i)$. If $w(i) \\in A$, then $i$ is defined in $w$, and if $w(i) = {{\\ensuremath{\\diamond}}}$, then $i$ is a hole in $w$. If $w$ has no holes, then $w$ is a *full word*. ", "A *completion* $\\hat{w}$ is a “filling in” of the holes of $w$ with letters from $A$. ", "Two partial words $u$ and $v$ are compatible, denoted $u\\uparrow v$, if there exist completions $\\hat{u}$ and $\\hat{v}$ such that $\\hat{u} = \\hat{v}$.\n\nA finite partial word $w$ over $A$ is said to be $p$-*periodic*, if $p$ is a positive integer such that $w(i) = w(j)$ whenever $i$ and $j$ are defined in $w$ and satisfy $i \\equiv j \\bmod {p}$. We say that $w$ is *periodic* if it is $p$-periodic for some $p$. An infinite partial word $w$ over $A$ is called *periodic* if there exists a positive integer $p$ (called a *period* of $w$) and letters $a_0, a_1, \\ldots, a_{p-1} \\in A$ such that for all $i \\in \\mathbb{N}$ and $j \\in \\{0,\\ldots, p-1\\}$, $i \\equiv j \\bmod{p}$ implies $w(i) \\uparrow a_j$. If $w$ is an infinite partial word, then we define the [*shift*]{} $\\sigma_p(w)$ by $\\sigma_p(w)(i) = w(i+p)$. The infinite partial word $w$ is called *ultimately periodic* if there exist a finite partial word $u$ and an infinite periodic partial word $v$ (both over $A$) such that $w = uv$. If $w$ is a full ultimately periodic word, then $w=xy^{\\omega}=xyyy\\cdots$ for some finite words $x, y$ with $y \\not = \\varepsilon$ called a [*period*]{} of $w$ (we also call the length $|y|$ a period). ", "If $|x|$ and $|y|$ are as small as possible, then $y$ is called the [*minimal period*]{} of $w$.\n\nGiven a partial word $w$ over $A$, a finite partial word $u$ is a *factor* of $w$ if there exists some $i \\in \\mathbb{N}$ such that $u = w(i)\\cdots w(i+|u|-1)$. We adopt the following notations for factors: $w(i..j)$ (resp., ", "$w[i..j)$, $w(i..j]$, $w[i..j]$) denotes $w(i+1) \\cdots w(j-1)$ (resp., ", "$w(i)\\cdots w(j-1)$, $w(i+1)\\cdots w(j)$, $w(i)\\cdots w(j)$). ", "On the other hand, a finite full word $u$ is a *subword* of $w$, denoted $u\\lhd w$, if there exists some $i \\in \\mathbb{N}$ such that $u\\uparrow w[i..i+|u|)$. In the context of this paper, subwords are always finite and full. ", "We denote by ${\\mbox{\\hspace{.01in}Sub}}_w(n)$ the set of all subwords of $w$ of length $n$, and by ${\\mbox{\\hspace{.01in}Sub}}(w) = \\bigcup_{n\\geq0}{\\mbox{\\hspace{.01in}Sub}}_w(n)$ the set of all subwords of $w$. Note that $p_w(n)$ is precisely the cardinality of ${\\mbox{\\hspace{.01in}Sub}}_w(n)$. Furthermore, if $\\hat{w}$ is a completion of $w$, then $p_{\\hat{w}}(n) \\leq p_w(n)$, since ${\\mbox{\\hspace{.01in}Sub}}_{\\hat{w}}(n) \\subset {\\mbox{\\hspace{.01in}Sub}}_{w}(n)$.\n\nThe following result extends well-known necessary conditions for a function to be the subword complexity function of an infinite full word [@DBLP:journals/dm/Ferenczi99].", "\n\n\\[thm:Fer\\] The following are necessary conditions for a function $p_w$ from $\\mathbb{N}$ to $\\mathbb{N}$ to be the subword complexity function of an infinite partial word $w$ over a finite alphabet $A$:\n\n1. ", " $p_w$ is non-decreasing;\n\n2. ", " $p_w(m+n) \\leq p_w(m) p_w(n)$ for all $m,n$;\n\n3. ", " whenever $p_w(n) \\leq n$ or $p_w(n+1) = p_w(n)$ for some $n$, then $p_w$ is bounded;\n\n4. ", " if $A$ has $k$ letters, then $p_w(n) \\leq k^n$ for all n; if $p_w(n_0) < k^{n_0}$ for some $n_0$, then there exists a real number $\\kappa < k$ such that $p_w(n) \\leq \\kappa^n$ for all $n$ sufficiently large.", "\n\nRecurrent Partial Words {#sec:recurrent_partial_words}\n=======================\n\nRecurrence is a well-studied topic in combinatorics on infinite full words. ", "We turn our attention to the study of infinite recurrent partial words. ", "We call an infinite partial word $w$ *recurrent* if every $u \\in {\\mbox{\\hspace{.01in}Sub}}_w(n)$ occurs infinitely often in $w$; that is, there are infinitely many $j$’s such that $w(j+i) \\uparrow u(i)$ for $i \\in \\{0, \\ldots, n-1\\}$. We call an infinite partial word $w$ *uniformly recurrent*, if for every $u \\in {\\mbox{\\hspace{.01in}Sub}}_w(n)$, there exists $m \\in \\mathbb{N}$ such that every factor of length $m$ of $w$ has $u$ as a subword, that is, $u \\lhd w[0..m-1]$, $u \\lhd w[1..m]$, …. ", "Clearly, a uniformly recurrent partial word is recurrent. ", "The following proposition gives a few equivalent formulations of recurrence.", "\n\n\\[pro:recurrence\\] Let $w$ be an infinite partial word. ", "The following are equivalent:\n\n1. ", " The partial word $w$ is recurrent;\n\n2. ", " Every subword compatible with a finite prefix of $w$ occurs at least twice;\n\n3. ", " Every subword of $w$ occurs at least twice.", "\n\nIt is clear that $(1)$ implies both $(2)$ and $(3)$, whereas $(3)$ implies $(2)$ since any subword compatible with a finite prefix of $w$ is itself a subword of $w$. To show that $(2)$ implies $(1)$, for the sake of contradiction suppose some word $v\\in {\\mbox{\\hspace{.01in}Sub}}_w(n)$ appeared only finitely many times in $w$. Suppose the last occurrence of $v$ starts at position $i$. Then for all $j>i$, $v$ is not compatible with $w[j..j+n)$. Now let $\\hat{u}$ be a completion of the prefix of length $i+n$ of $w$ such that $\\hat{u}[i..i+n) = v$. Then by $(2)$, $\\hat{u}$ must appear at least twice in $w$. In particular, there exists some position $j>0$ such that $\\hat{u} \\uparrow w[j..j+i+n)$. But then $v \\uparrow w[j+i..j+i+n)$, contradicting the fact that the last occurrence of $v$ started at position $i$. Hence, every subword of $w$ must appear infinitely many times.", "\n\n\\[thm:rec\\_up\\] If $w$ is an infinite recurrent partial word with a positive but finite number of holes, then $w$ is not ultimately periodic.", "\n\nFor the sake of contradiction, suppose $w$ is ultimately periodic. ", "Then we can write $w = xyyy\\cdots$ where $y$ is a finite full word such that $|y|$ is the minimal period of $w$. Let $j$ be the position of the last hole in $x$. Let $z = a x[j+1..|x|)y^n = a v y^n$ where $n \\geq |y|$ and the letter $a$ is chosen so that $a \\neq y(j')$, where $j' = |y|-1-|v|\\bmod{|y|}$. Since $w$ is recurrent and $z$ is a subword of $w$, $z$ occurs infinitely many times in $w$. In particular, it occurs somewhere in $u = y^\\omega$, where $|y|$ is the minimal period of $u$. Thus, there exists $i \\in \\{0,\\ldots,|y|-1\\}$ such that $u(i)\\cdots u(i+|z|-1) = z$. Since $y(i)=a \\neq y(j')$, we have $i \\neq j'$.\n\nSet $i' = (i + |v| + 1)\\bmod{|y|}$, $y_1=y(0)\\cdots y(i'-1)$, and $y_2=y(i')\\cdots y(|y|-1)$. We get $y=y_1y_2=y_2y_1$, and so $y_1$ and $y_2$ are powers of a common word $y'$. Thus $y^{|y'|} = (y')^{|y|}$. However, $1 \\leq |y'| < |y|$. Then $u = y^\\omega = (y^{|y'|})^\\omega = ((y')^{|y|})^\\omega = (y')^\\omega$ is $|y'|$-periodic, which contradicts the minimality of period $|y|$.\n\nTo extend the above theorem to the case where $w$ has infinitely many holes we must introduce some additional restrictions. ", "We would like to impose some constraints on the number of holes and their distribution inside $w$. The motivation for these is the fact that any infinite partial word with a large number of holes exhibits a behavior similar to the one of the trivial partial word $w={{\\ensuremath{\\diamond}}}^\\omega$, which is recurrent and periodic.", "\n\nNext we define the gap function which quantifies the spacing between consecutive appearances of the hole symbol in a partial word. ", "Let $H(n)-1$ be the position of the $n$th hole in an infinite partial word $w$ (we also say that $H(n)$ is the *hole function* of $w$). ", "Then let $h(n)=H(n)-H(n-1)$, for $n\\geq2$, be defined as the *gap function* of $w$. For example, the infinite partial word $${{\\ensuremath{\\diamond}}}{{\\ensuremath{\\diamond}}}a{{\\ensuremath{\\diamond}}}a {{\\ensuremath{\\diamond}}}aaa {{\\ensuremath{\\diamond}}}aaaaa {{\\ensuremath{\\diamond}}}aaaaaaaaaaa {{\\ensuremath{\\diamond}}}aaaaaaaaaaaaaaaaaaaa {{\\ensuremath{\\diamond}}}\\cdots$$ has holes at positions $H(n)-1 = \\lceil 2^{4(n-1)/5}\\rceil -1$ and the distance between the 5th and 6th holes is $h(6)=H(6)-H(5)=16-10=6$. This is actually an example of an infinite partial word (regarded as a partial word over the alphabet $\\{a, b\\}$) having a complexity function not achievable by any full word.", "\n\n\\[cor:rec\\_up\\] Let $w$ be a recurrent partial word with infinitely many holes for which there exists $N>0$ such that $h(n)<h(n+1)$ for all $n\\geq N$. Then $w$ is not ultimately periodic.", "\n\nFor the sake of contradiction, suppose $w$ is ultimately periodic. ", "Then we can write $w=xy_1y_2\\cdots$, where for all $i,j>0$, $y_i$ and $y_j$ are compatible factors of length $p$ with $p$ being the minimal period. ", "We will refer to $y_1, y_2, \\ldots$ as the $y$ factors. ", "By choosing sufficiently large $n\\geq3$, we can ensure that $h(n)>3p$. Thus, there exists $j>p$ such that both $y_j$ and $y_{j+1}$ are full words. ", "Let $v=xy_1y_2\\cdots y_{j-1}$. Then $v$ contains at least two holes. ", "Without loss of generality, assume that $v(l)=v(l')={{\\ensuremath{\\diamond}}}$, for some $l<l'$.\n\nLet $i_l = (p-|v|+l)\\bmod{p}$ and $i_{l'} = (p-|v|+l')\\bmod{p}$. Then choose a completion $\\hat{v}$ of $v$ such that $\\hat{v}(l)\\neq y_j(i_l)$ and $\\hat{v}(l')\\neq y_j(i_{l'})$. Let $u=\\hat{v}y_jy_{j+1}$ and $m$ be sufficiently large so that $h(m)>2|u|$. Since $w$ is recurrent, the subword $u$ must occur at some position to the right of $H(m)-1$. So suppose it occurs at position $i$. Then if we let $z=w[i..i+|u|)$ then $z$ contains at most one hole. ", "By the choice of $i_l$ and $i_{l'}$, at least one of $\\hat{v}(l)$ or $\\hat{v}(l')$ is incompatible with the corresponding symbol in $z$. Thus the $y$ factors in $u$ cannot align with the $y$ factors in $z$. Also, at least one of the $y$ factors in $z$ is full. ", "Analogous to the proof of Theorem \\[thm:rec\\_up\\], we conclude that $y_j\\cdots y_{j+p-1}$ is periodic with period $p'<p$, where $p'$ is the length of the offset. ", "This contradicts the minimality of $p$ and, therefore, no ultimately periodic words with the desired property exist.", "\n\nLet $w$ be an infinite partial word. ", "We define $R_w(n)$, the *recurrence function* of $w$, to be the smallest integer $m$ such that every factor of length $m$ of $w$ contains at least one occurrence of every subword of length $n$ of $w$. The following theorem extends a well-known result on full words to partial words (see [@DBLP:books/daglib/0025558]).", "\n\n\\[thm:theorem4\\] Let $w$ be a uniformly recurrent infinite partial word. ", "Then the following hold:\n\n1. ", " $R_w(n+1)>R_w(n)$ for all $n\\geq 0$;\n\n2. ", " If for each $n > 0$ there exists an index $i$ such that $w[i..i+n)$ is a full word then $R_w(n) \\geq p_w(n)+n-1$ for all $n\\geq 0$;\n\n3. ", " If $w$ has a positive finite number of holes or an eventually increasing gap function, then $R_w(n)\\geq 2n$ for all $n \\geq 0$.\n\nThe proof of $(1)$ is identical to that for full words. ", "For $(2)$, let $n\\geq 0$ and set $m=R_w(n)$. Then there exists an index $i$ such that $v= w[i..i+m)$ is a full word. ", "Since $|v|=m$, $v$ contains every subword of $w$ of length $n$. But any full word of length $m$ contains at most $m-n+1$ distinct subwords of length $n$. Hence, $p_w(n)\\leq m-n+1$. Therefore, $R_w(n) \\geq p_w(n)+n-1$ for all $n\\geq 0$. For $(3)$, note that the conditions on $w$ together with Theorem \\[thm:rec\\_up\\] and Corollary \\[cor:rec\\_up\\] imply that $w$ is not ultimately periodic. ", "Thus by Theorem \\[thm:Fer\\](3), $p_w(n)\\geq n+1$ for all $n\\geq 0$. Since $(3)$ implies $(2)$, we get $R_w(n) \\geq p_w(n)+n-1 \\geq 2n$ for all $n\\geq 0$.\n\nThe following theorem captures the fact that a uniformly recurrent word cannot achieve maximal complexity.", "\n\n\\[cannotachieve\\] Let $w$ be a uniformly recurrent infinite word. ", "Then there exists $N$ such that $p_w(n)<k^n$ for all $n\\geq N$, where $k$ is the alphabet size.", "\n\nBy Theorem \\[thm:Fer\\](4), we only need to show that $p_w(n)<k^n$ for some $n$. We split the proof into two cases. ", "If $p_w(1)<k$ then we are done. ", "Thus suppose $p_w(1)=k$. Then let $t=R_w(1)$. For the sake of contradiction, suppose $w$ achieves maximal complexity, that is, $p_w(n)=k^n$ for all $n\\geq 0$. Then $w$ contains the subword $a^t$, where $a\\in A$. ", "Hence, $|a^t|=t=R_w(1)$ implies $b\\lhd a^t$ for some $b \\in A, b \\neq a$, which is a contradiction.", "\n\nIt is natural to extend the above theorem to partial words with finitely many holes.", "\n\n\\[cor:recurrence\\_complexity\\] Let $w$ be a uniformly recurrent infinite partial word with finitely many holes. ", "Then there exists $N$ such that $p_w(n)<k^n$ for all $n\\geq N$, where $k$ is the alphabet size.", "\n\nChoose $N$ such that $j\\geq N$ implies $w(j)\\neq {{\\ensuremath{\\diamond}}}$. Then let $v=\\sigma_N(w)$. Then uniform recurrence implies that ${\\mbox{\\hspace{.01in}Sub}}(w)={\\mbox{\\hspace{.01in}Sub}}(v)$. Hence, $p_w(n)=p_v(n)$ and thus Theorem \\[cannotachieve\\] gives us the result.", "\n\nTo extend the result to partial words with infinitely many holes we must introduce some additional restrictions. ", "In essence too many holes still allows us to achieve maximal complexity. ", "A trivial example is $w={{\\ensuremath{\\diamond}}}^{\\omega}$.\n\n\\[cor:recurrence\\_complexity2\\] Let $w$ be a uniformly recurrent infinite partial word for which there exists $n_0$ such that $n\\geq n_0$ implies $h(n)\\leq h(n+1)$ and $\\lim_{n \\to \\infty}h(n+1)-h(n) = \\infty$. Then there exists $N>0$ such that $p_w(n)<k^n$ for all $n \\geq N$, where $k$ is the alphabet size.", "\n\nThe proof is very similar to that of Theorem \\[cannotachieve\\].", "\n\nThe following result illustrates the relationship between a recurrent partial word and its completions.", "\n\n\\[pro:prop2\\] Let $w$ be an infinite partial word having a finite number of holes or an eventually increasing gap function. ", "Then $w$ is recurrent if and only if every completion $\\hat{w}$ is recurrent.", "\n\nFirst suppose $w$ is recurrent. ", "Let $\\hat{w}$ be any completion of $w$. Proposition \\[pro:recurrence\\] implies that we only need to show that each subword of $\\hat{w}$ appears at least twice. ", "Choose $u \\in {\\mbox{\\hspace{.01in}Sub}}_{\\hat{w}}(n)$. Suppose $w$ has a finite number of holes. ", "Then there exists $N>0$ such that $j\\geq N$ implies $w(j)\\neq {{\\ensuremath{\\diamond}}}$. Since $w$ is recurrent, $u$ appears starting at some position $i\\geq N$, that is, $u = w[i..i+n)$. But note that $\\hat{w}[i..i+n) = w[i..i+n)$. Hence, the subword $u$ occurs twice in $\\hat{w}(i)\\hat{w}(i+1)\\cdots$ and thus $\\hat{w}$ is recurrent.", "\n\nNow suppose $w$ has an eventually increasing gap function. ", "Since $w$ is recurrent, we see that there exists a word $v$ such that $uvu\\in {\\mbox{\\hspace{.01in}Sub}}(w)$. Let $m=|uvu|$ and choose $N$ such that for all $j\\geq N$ we have $h(j)>m$. Recurrence implies that $uvu$ appears starting at some position $i$ greater than $H(N)$. Suppose $uvu\\uparrow z$ where $z=w[i..i+m)$. Then $z$ contains at most one hole. ", "Hence, at least one of $u = w[i..i+n)$ or $u = w[i+m-n..i+m)$ holds. ", "Since $w$ is recurrent, $uvu$ has to appear again in $w$, and so $u$ must appear one more time in a factor of $w$ that contains no holes. ", "Without loss of generality, assume that $w[i'..i'+n)$ is the desired full word. ", "Then $w[i'..i'+n) = \\hat{w}[i'..i'+n)$. Hence $u = \\hat{w}[i'..i'+n)$ so that $u$ appears at least twice in $\\hat{w}$. Hence, $\\hat{w}$ is recurrent.", "\n\nNow suppose every completion is recurrent. ", "Choose $u\\in {\\mbox{\\hspace{.01in}Sub}}(w)$. Then there exists a completion $\\hat{w}$ such that $u \\in {\\mbox{\\hspace{.01in}Sub}}(\\hat{w})$. Since $\\hat{w}$ is recurrent $u$ occurs again at an index different from where it appeared initially in $w$. Suppose $u = \\hat{w}[i..i+|u|)$. Since $\\hat{w}$ is a completion of $w$ we see that $\\hat{w}[i..i+|u|) \\uparrow w[i..i+|u|)$. Hence $u$ occurs twice in $w$ so that $w$ is recurrent.", "\n\nCompletions of Infinite Partial Words {#sec:completions}\n=====================================\n\nWe investigate the relationship between the complexity of an infinite partial word $w$ and the complexity achievable by a given completion $\\hat{w}$. Our main question is given an infinite partial word $w$ how much complexity can be preserved while passing to a completion?", "\n\n\\[partialEquiv\\] Let $w$ be an infinite recurrent partial word. ", "Then there exists a completion of $w$, $\\hat{w}$, such that ${\\mbox{\\hspace{.01in}Sub}}(w) = {\\mbox{\\hspace{.01in}Sub}}(\\hat{w})$.\n\nThe set ${\\mbox{\\hspace{.01in}Sub}}(w)$ is countable, so choose some enumeration of its elements $x_0, x_1, x_2, \\ldots$. Choose $n_0$ so that $x_0 \\lhd w[0..n_0]$. Since $x_1$ occurs infinitely often in $w$, we can find some $n_1>n_0$ so that $x_1 \\lhd w(n_0..n_1]$. Similarly we can find some $n_2 > n_1$ so that $x_2 \\lhd w(n_1..n_2]$ and so on for each $x_i$. Now we complete $w[0..n_0]$ so that it contains $x_0$ as a subword, $w(n_0..n_1]$ so that it contains $x_1$, and so on to get $\\hat{w}$. By construction ${\\mbox{\\hspace{.01in}Sub}}(w) \\subset {\\mbox{\\hspace{.01in}Sub}}(\\hat{w})$ and we have ${\\mbox{\\hspace{.01in}Sub}}(\\hat{w}) \\subset {\\mbox{\\hspace{.01in}Sub}}(w)$.\n\nAnother question is to ask when a completion with maximal complexity exists. ", "We know by Theorem \\[partialEquiv\\] that it is sufficient that the original partial word $w$ be recurrent. ", "In the case where $w$ has infinitely many holes, this turns out to be necessary as well.", "\n\n\\[thm:completion\\] Let $w$ be a partial word with infinitely many holes. ", "Then $w$ is recurrent if and only if there exists a completion $\\hat{w}$ such that ${\\mbox{\\hspace{.01in}Sub}}(w) = {\\mbox{\\hspace{.01in}Sub}}(\\hat{w})$.\n\nThe forward implication is simply a consequence of Theorem \\[partialEquiv\\]. ", "For the backward implication, suppose there exists a completion $\\hat{w}$ such that ${\\mbox{\\hspace{.01in}Sub}}(w) = {\\mbox{\\hspace{.01in}Sub}}(\\hat{w})$. We show that the prefix of length $H(n)-1$ of $\\hat{w}$ occurs twice for every $n\\geq 1$. Choose $a\\in A$ such that $a \\neq \\hat{w}(H(n)-1)$. Then $v= \\hat{w}[0..H(n)-1)a \\in {\\mbox{\\hspace{.01in}Sub}}(w) = {\\mbox{\\hspace{.01in}Sub}}(\\hat{w})$. Hence $v$ must occur somewhere in $\\hat{w}$. But it cannot occur as a prefix since $a \\neq \\hat{w}(H(n)-1)$. Thus there exists $i> 0$ such that $\\hat{w}[i..i+H(n)) = v$. But then $\\hat{w}[i..i+H(n)-1) = \\hat{w}[0..H(n)-1)$ so that $\\hat{w}[0..H(n)-1)$ appears twice. ", "Thus every prefix of $\\hat{w}$ occurs twice and thus $\\hat{w}$ is recurrent and since ${\\mbox{\\hspace{.01in}Sub}}(w) = {\\mbox{\\hspace{.01in}Sub}}(\\hat{w})$, $w$ is recurrent as well.", "\n\nThe proof really relies on the fact that $w$ has infinitely many holes. ", "The theorem is not true in the case of finitely many holes. ", "For example, choose $w = {{{\\ensuremath{\\diamond}}}} a^\\omega$ and $\\hat{w} = ba^\\omega$. Then ${\\mbox{\\hspace{.01in}Sub}}(w) = {\\mbox{\\hspace{.01in}Sub}}(\\hat{w})$ but $w$ is not recurrent since $b$ occurs only once. ", "However, we note that $\\sigma(w)$ is recurrent. ", "This fact actually holds more generally. ", "First we call an infinite partial word $w$ [*ultimately recurrent*]{} if there exists an integer $p \\geq 0$ such that $\\sigma_p(w)$ is recurrent. ", "With this definition in hand we can extend Theorem \\[thm:completion\\] to the case when we may not have infinitely many holes.", "\n\n\\[cor:unlabelled1\\] Let $w$ be an infinite partial word with at least one hole. ", "If there exists a completion $\\hat{w}$ of $w$ such that ${\\mbox{\\hspace{.01in}Sub}}(w) = {\\mbox{\\hspace{.01in}Sub}}(\\hat{w})$, then $w$ is ultimately recurrent. ", "In fact $\\sigma_{H(1)}(w)$ is recurrent, where $H(n)$ is the hole function.", "\n\nWe claim that if $H(1)-1$ is the position of the first hole and $p = H(1)$ then $\\sigma_p(w)$ is recurrent. ", "Let $v = \\sigma_p(w)$. By Proposition \\[pro:recurrence\\], it suffices to show that every finite prefix of any completion of $v$ occurs twice in $v$. Thus suppose $z$ is a full word such that $z \\uparrow v[0..n)$. Choose a completion $u$ of $w[0..n+p)$ so that $z = u[p..n+p)$. In addition, we require that the hole at position $H(1)-1$ be filled in such a way that $u(H(1)-1) \\neq \\hat{w}(H(1)-1)$. Then $u \\in {\\mbox{\\hspace{.01in}Sub}}(\\hat{w})$. However, we see that the way we filled in the hole at $H(1)-1$ prohibits $u$ from occuring as a prefix of $\\hat{w}$. Thus there exists an index $i > 0$ such that $u = \\hat{w}[i..i+n+p)$. But then $z = u[p..n+p) =\\hat{w}[i+p..i+n+p) \\uparrow v[i..i+n)$ so that $z$ appears twice in $v$. Hence $v$ is recurrent. ", "Thus $w$ is ultimately recurrent.", "\n\nLet ${\\mbox{\\hspace{.01in}RSub}}_w(n)$ denote the set of recurrent subwords of length $n$ of a finite or infinite partial word $w$. Let ${\\mbox{\\hspace{.01in}RSub}}(w) = \\bigcup_{n\\geq 1} {\\mbox{\\hspace{.01in}RSub}}_w(n)$. Let $r_w(n) = |{\\mbox{\\hspace{.01in}RSub}}_w(n)|$ and $d_w(n) = p_w(n) - r_w(n)$. In other words, $d_w(n)$ counts the number of non-recurrent subwords of length $n$. Note that $d_w(n)$ is non-decreasing. ", "The following proposition captures the fact that in an ultimately recurrent partial word with finitely many holes almost every subword is recurrent.", "\n\n\\[pro:bounded\\] Let $w$ be an infinite partial word with finitely many holes. ", "Then $w$ is ultimately recurrent if and only if $d_w(n)$ is bounded.", "\n\nSuppose $w$ is ultimately recurrent. ", "Then there exists $p$ such that $\\sigma_p(w)$ is recurrent. ", "We claim that $d_w(n) \\leq p$. Note that any subword beginning at an index $\\geq p$ must be recurrent. ", "Thus any non-recurrent subword must appear starting at a position less than $p$. Each position $i$ with $0\\leq i < p$ contributes finitely many distinct subwords of length $n$.\n\nNow suppose $d_w(n)$ is bounded. ", "Since $d_w(n)$ is non-decreasing, there exist a constant $C$ and an integer $n$ such that $C = d_w(n) = d_w(m)$ for all $m\\geq n$. Since there are only $C$ non-recurrent subwords of length $n$ and each appears only finitely many times in $w$, there exists an $N$ such that none of these non-recurrent subwords appear starting at positions $i \\geq N$. We claim that $w' = \\sigma_N(w)$ is recurrent. ", "For the sake of contradiction, suppose $w'$ is not. ", "Then there must exist a non-recurrent word $v$ in ${\\mbox{\\hspace{.01in}Sub}}(w')$. Assume without loss of generality that $|v| = m \\geq n$. Now we break the proof into two cases. ", "If the prefix of length $n$ of $v$ was a non-recurrent subword of $w$, then this would contradict the choice of $N$. So suppose that the prefix of length $n$ of $v$ is not a non-recurrent subword of $w$. Note that each length $n$ non-recurrent subword contributes at least one distinct length $m$ non-recurrent subword. ", "In addition $v$ is distinct from each of these since the prefixes of length $n$ do not match. ", "Thus $d_w(m) > d_w(n)$, a contradiction.", "\n\nThe case when $w$ has infinitely many holes is markedly different. ", "In particular $d_w(n)$ cannot be positive and bounded. ", "This is captured in the following proposition.", "\n\n\\[pro:prop4\\] Let $w$ be a partial word with infinitely many holes. ", "Then $d_w(n)$ is either identically zero or unbounded.", "\n\nFor the sake of contradiction, suppose there exists a constant $C$ such that $1\\leq d_w(n) \\leq C$ for all $n>0$. Then there exists an $n$ and a $v$ such that $v \\in {\\mbox{\\hspace{.01in}Sub}}_w(n) \\backslash {\\mbox{\\hspace{.01in}RSub}}_w(n)$. Since $v\\in {\\mbox{\\hspace{.01in}Sub}}(w)$ there exists an index $i$ such that $v \\uparrow w[i..i+n)$. Since $w$ has infinitely many holes, there exists an $m$ such that $w[n..m]$ has at least $h$ holes where $k^h > C$. ", "Since $v$ is not recurrent, each of the completions of $vw[n..m]$ is non-recurrent. ", "Hence if we let $j = |vw[n..m]|$ we see that $d_w(j) = p_w(j) - r_w(j) \\geq k^h > C$, a contradiction.", "\n\nThe infinite partial word $w$ being ultimately recurrent does not imply anything about the growth of $d_w(n)$ by itself. ", "However, we can relate the growth of $p_w(n)$ and $r_w(n)$. Intuitively we can think of $w$ being ultimately recurrent as capturing the fact that $w$ has a large proportion of recurrent subwords. ", "We would expect that $r_w(n)$ is a good approximation of $p_w(n)$. In fact, it turns out that $p_w(n) = \\Theta(r_w(n))$.\n\n\\[pro:prop5\\] Let $w$ be an ultimately recurrent infinite partial word. ", "Then there exists a constant $C$ such that $r_w(n) \\leq p_w(n) \\leq C r_w(n)$ for all $n$ sufficiently large. ", "In other words, $p_w(n) = \\Theta(r_w(n))$.\n\nSuppose $N$ is such that $\\sigma_N(w)$ is recurrent. ", "Consider $d_w(n)$ for $n > N$. Then every non-recurrent subword of length $n$ must start at some position $i$, $0\\leq i < N$, and must be compatible with a factor of the form $w[i..i+n)$. We can break the factor into two parts: $w[i..N)$ which may have a non-recurrent completion, and $w[N..i+n)$ where every completion is recurrent. ", "If there are $h$ holes in $w[i..N)$, there are at most $k^h$ completions of $w[i..N)$. Any completion of $w[N..i+n)$ must be recurrent, each has length at most $n$, so there are at most $r_w(n)$ such completions. ", "Hence there are at most $k^h r_w(n)$ distinct non-receurrent subwords of length $n$ starting at position $i$. Since there are exactly $N$ possible starting positions for non-recurrent subwords, we see that $d_w(n) \\leq N k^h r_w(n)$. Since $p_w(n) = r_w(n) + d_w(n)$, the result follows.", "\n\nOne might expect that if $w$ has a large proportion of recurrent subwords then it might be ultimately recurrent. ", "However, this is not true in general. ", "Consider the word $w$ that is all $a$’s except for $b$’s at positions $H(n)-1 = n^2-1$. Then it is easy to check that $p_w(n)$ is linear. ", "Also, it is clear that every subword containing at most one $b$ is recurrent. ", "There are $n+1$ such length $n$ words. ", "Hence both $r_w(n)$ and $p_w(n)$ are linear. ", "However, $w$ is not ultimately recurrent since any subword with at least two $b$’s occurs exactly once. ", "Thus the requirement that a word be ultimately recurrent is too restrictive. ", "In fact we can also find a partial word with infinitely many holes such that the same property holds. ", "All that is required is to let the hole function be $H(n) = \\lceil \\alpha^n \\rceil$ with $\\alpha >2$ being a real number, and then notice that $p_w(n)$ is asymptotically linear. ", "Then as before every word with at most one $b$ is recurrent so that $r_w(n) = n+1$. Hence $p_w(n) \\leq C r_w(n)$ for a suitable constant $C \\in \\mathbb{R}$.\n\nThe above proposition has an easy corollary. ", "We know that we can always find a completion that contains all the recurrent subwords. ", "Thus if $w$ is ultimately recurrent then there exists a completion $\\hat{w}$ whose complexity function is of the same order of growth as that of $w$.\n\nLet $w$ be an ultimately recurrent infinite partial word. ", "Then there exists a completion $\\hat{w}$ such that $p_w(n) = \\Theta(p_{\\hat{w}}(n))$.\n\nIntuitively, the “closest” that a complexity function can be to another is to be within a constant of that function. ", "Thus, if we could not attain maximal complexity with a completion, the best we could hope for is “off by a constant” complexity. ", "The following proposition shows that this is not possible in general.", "\n\n\\[pro:close\\] Let $w$ be a partial word with infinitely many holes. ", "If $\\hat{w}$ is a completion of $w$ such that $p_w(n) \\leq p_{\\hat{w}}(n) + C$ for all $n>0$ and some constant $C$, then ${\\mbox{\\hspace{.01in}Sub}}(w) = {\\mbox{\\hspace{.01in}Sub}}(\\hat{w})$ and thus $p_w(n) = p_{\\hat{w}}(n)$.\n\nFor the sake of contradiction, assume there existed $v \\in {\\mbox{\\hspace{.01in}Sub}}_w(n)$ with $v \\not\\in {\\mbox{\\hspace{.01in}Sub}}_{\\hat{w}}(n)$. Then $v \\uparrow w[i..i+n)$ for some $i$. Now using the fact that $w$ contains infinitely many holes, we can chose an index $m$ such that $w_n \\cdots w_m$ has at least $h$ holes where $k^h > C$. ", "Then there are at least $k^h$ completions of $vw_n \\cdots w_m$. Since $p_w(n) - p_{\\hat{w}}(n) \\leq C$ at least one of these completions, call it $u$, must also be a subword of $\\hat{w}$. But then since $v$ is a prefix of $u$ we would necessarily have $v \\in {\\mbox{\\hspace{.01in}Sub}}({\\hat{w}})$, a contradiction.", "\n\nThus a completion $\\hat{w}$ must satisfy either $p_w(n) = p_{\\hat{w}}(n)$ or the function $f(n) = p_w(n) - p_{\\hat{w}}(n)$ must be unbounded. ", "The above result actually holds more generally. ", "What allows us to prove the above proposition is that we are able to use the holes to create “enough” subwords to overcome the constant $C$. ", "Thus if we have $p_w(n) \\leq p_{\\hat{w}}(n) + \\varphi(n)$ for some increasing function $\\varphi$, then as long as the holes are spaced close enough together we must have $p_w(n) = p_{\\hat{w}}(n)$. Thus the closer spaced the holes become, the farther away a non-maximal completion must be in terms of complexity.", "\n\n\\[pro:varphi\\] Let $w$ be an infinite partial word with hole function $H(m)$. If $\\hat{w}$ is a completion of $w$ such that $p_w(n) \\leq p_{\\hat{w}}(n) + \\varphi(n)$ for all $n > 0$ and some increasing function $\\varphi$ satisfying $\\lim_{n \\rightarrow \\infty} \\frac{\\varphi(H(n))}{k^n} = 0$, then $p_w(n) = p_{\\hat{w}}(n)$.\n\nThe proof follows the same general strategy as that of Proposition \\[pro:close\\]. ", "For the sake of contradiction, suppose there existed $v \\in {\\mbox{\\hspace{.01in}Sub}}_w(n)$ such that $v \\not\\in {\\mbox{\\hspace{.01in}Sub}}_{\\hat{w}}(n)$. Then $v \\uparrow w[i..i+n)$ for some $i$. Let $j$ be the smallest integer such that $H(j) \\geq i+n$. Then choose $m>j$ such that $k^{m-j} > \\varphi(H(m))$. Then there are at least $k^{m-j}$ distinct completions of $vw[i+n..H(m))$. Since they have length less than $\\varphi(H(m))$ and $\\varphi$ is increasing we see that at least one of them, call it $u$, must be contained in ${\\mbox{\\hspace{.01in}Sub}}(\\hat{w})$. But since $v$ is a prefix of $u$ we see that $v \\in {\\mbox{\\hspace{.01in}Sub}}(\\hat{w})$, a contradiction.", "\n\nThe situation is different for infinite partial words with finitely many holes. ", "If $w$ has finitely many holes then for each completion there exists a constant $C$ such that $p_w(n) \\leq p_{\\hat{w}}(n) + C$. ", "However, if $C$ is small enough then it turns out that $w$ is actually ultimately recurrent.", "\n\n\\[pro:prop8\\] Let $w$ be an infinite partial word with exactly $h$ holes where $1 \\leq h < \\infty$. If there exists a completion $\\hat{w}$ of $w$ such that $p_w(n) \\leq p_{\\hat{w}}(n) + C$ for all $n>0$ and some constant $C$ satisfying $C \\leq k^h - 2$, then $w$ is ultimately recurrent.", "\n\nWe show that $v = \\sigma_{H(h)}(w)$ is recurrent. ", "We show that every finite prefix of $v$ occurs at least twice. ", "Consider $v[0..n)$. Then there are $k^h$ distinct completions of $w[0..H(h))v[0..n)$. Since $C \\leq k^h - 2$ at least two of these completions must be subwords of $\\hat{w}$. Thus at least one is not compatible with a prefix of $\\hat{w}$. Let $u$ be this subword. ", "Then there must exist some $i>0$ such that $u = \\hat{w}[i..i+|u|)$. Since $v[0..n)$ is a suffix of $u$ this implies that there exists $j>0$ such that $v[0..n) = v[j..j+n)$ so that every finite prefix of $v$ occurs twice.", "\n\nThe following is a strengthening of Theorem \\[thm:completion\\].", "\n\n\\[thm:recurrence\\_completion3\\] Let $w$ be a partial word with infinitely many holes. ", "Then $w$ is recurrent if and only if there exists a completion $\\hat{w}$ and constant $C$ such that $p_w(n) \\leq p_{\\hat{w}}(n) + C$ for all $n > 0$.\n\nThe forward implication is a direct consequence of Theorem \\[thm:completion\\]. ", "For the backward implication, if $p_w(n) \\leq p_{\\hat{w}}(n) + C$ then Proposition \\[pro:close\\] implies that ${\\mbox{\\hspace{.01in}Sub}}(w) = {\\mbox{\\hspace{.01in}Sub}}(\\hat{w})$. Then Theorem \\[thm:completion\\] implies that $w$ is recurrent.", "\n\nIntuitively Theorem \\[thm:recurrence\\_completion3\\] shows us that we cannot get too close (i.e off by a constant) to the complexity of $w$ with a completion unless $w$ is recurrent. ", "In fact the conditions in the previous theorems are actually stronger than what is needed. ", "In order to show recurrence of $w$ we only need to be able to find completions $\\hat{w}$ that stay close to $p_w(n)$ for arbitrarily large $n$. This is made precise in the following lemma.", "\n\n\\[lem:recurrence\\_almost\\_maximal\\] Let $w$ be a partial word with infinitely many holes. ", "Suppose that for each $N > 0$ there exists a completion $\\hat{w}$ such that $p_w(n) = p_{\\hat{w}}(n)$ for all $n \\leq N$. Then $w$ is recurrent.", "\n\nBy Proposition \\[pro:recurrence\\] it suffices to show that each subword appears at least twice. ", "We argue by contradiction. ", "Suppose there exists a subword $v \\in {\\mbox{\\hspace{.01in}Sub}}_w(n)$ that appears only once. ", "Say $v \\uparrow w[i..i+n)$. Since $w$ has infinitely many holes there exists a smallest index $j \\geq i+n$ such that $w(j) = {{\\ensuremath{\\diamond}}}$. Now choose a completion $\\hat{w}$ such that $p_w(m) = p_{\\hat{w}}(m)$ for all $m \\leq j+1$. Choose $a \\in A$ such that $a \\neq \\hat{w}_j$. Then consider $u = v w[i+n..j) a$. Then $|u| \\leq j+1$ so that $u$ is a subword of $\\hat{w}$. Thus $u$ must appear somewhere in $\\hat{w}$. But it cannot appear starting at position $i$. Thus there must exist another position $i'$ such that $u = \\hat{w}[i'..i'+|u|)$. But then $v \\uparrow w[i'..i'+n)$ so that $v$ appears twice in $w$, a contradiction.", "\n\nWe can now use the above lemma to prove a stronger version of Theorem \\[thm:recurrence\\_completion3\\].", "\n\n\\[cor:unlabelled2\\] Let $w$ be a partial word with infinitely many holes. ", "Suppose there exists a constant $C$ such that for each $N > 0$ there exists a completion $\\hat{w}$ such that $p_w(n) \\leq p_{\\hat{w}}(n) + C$ for all $n \\leq N$. Then $w$ is recurrent.", "\n\nWe reduce the proof to an application of Lemma \\[lem:recurrence\\_almost\\_maximal\\]. ", "For each $n >0$, we find a completion $\\hat{w}$ such that $p_w(n) = p_{\\hat{w}}(n)$ which allows us to apply the lemma. ", "Fix $n$. Now choose $N$ such that all subwords of $w$ of length $n$ appear in $w[0..N)$. Now choose $M$ such that $w[N..M)$ has at least $h$ holes where $k^h > C$. ", "Then choose $\\hat{w}$ such that $p_w(m) \\leq p_{\\hat{w}}(m) + C$ for all $m \\leq M$. Now we claim that $p_w(n) = p_{\\hat{w}}(n)$. Choose $v\\in {\\mbox{\\hspace{.01in}Sub}}_w(n)$. Now complete $w[0..N)$ such that $v$ appears as a subword. ", "Call this completed subword $u$. Then there are at least $k^h > C$ completions of $uw[N..M)$. Hence since $p_w(n) \\leq p_{\\hat{w}}(n) + C$ at least one completion must be a subword of $\\hat{w}$. Since $v$ is a prefix of $u$ this implies $v \\in {\\mbox{\\hspace{.01in}Sub}}(\\hat{w})$. Thus ${\\mbox{\\hspace{.01in}Sub}}_w(n) = {\\mbox{\\hspace{.01in}Sub}}_{\\hat{w}}(n)$ and hence $p_w(n) = p_{\\hat{w}}(n)$. All that remains is to apply the lemma to conclude that $w$ is recurrent.", "\n\nA similar argument provides a generalization of Proposition \\[pro:varphi\\].", "\n\n\\[pro\\] Let $w$ be an infinite partial word with hole function $H(m)$ and let $\\varphi$ be an increasing function. ", "If for each $N>0$ there exists a completion $\\hat{w}$ such that $p_w(n) \\leq p_{\\hat{w}}(n) + \\varphi(n)$ for all $n \\leq N$ and $\\lim_{n \\rightarrow \\infty} \\frac{\\varphi(H(n))}{k^n} = 0$, then $p_w(n) = p_{\\hat{w}}(n)$ and $w$ is recurrent.", "\n\nAnother question that one may ask is how the complexity of a completion $p_{\\hat{w}}(n)$ relates to the recurrence function $r_w(n)$ for the original partial word $w$. If the complexity of all completions is bounded by $r_w(n)$ (up to a constant) then it turns out that $w$ is actually ultimately recurrent. ", "The following theorem states this rigorously.", "\n\n\\[thm:ultimate\\_recurrence\\] Let $w$ be an infinite partial word. ", "Then $w$ is ultimately recurrent if and only if for each completion $\\hat{w}$ there exists a constant $C$ such that $p_{\\hat{w}}(n) \\leq r_w(n) + C$ for all $n > 0$.\n\nSuppose $w$ is ultimately recurrent. ", "Then there exists $C$ such that $\\sigma_C(w)$ is recurrent. ", "Then consider any completion $\\hat{w}$. Any subword starting at an index $i \\geq C$ is contained in ${\\mbox{\\hspace{.01in}RSub}}(w)$. Thus the only possible subwords in ${\\mbox{\\hspace{.01in}Sub}}(\\hat{w}) \\backslash {\\mbox{\\hspace{.01in}RSub}}(w)$ must occur starting at positions $0 \\leq i < C$. ", "There are at most $C$ such subwords. ", "Thus $p_{\\hat{w}}(n) \\leq r_w(n) + C$. ", "Now suppose for each completion $\\hat{w}$ there exists a constant $C$ such that $p_{\\hat{w}}(n) \\leq r_w(n) + C$ for all $n > 0$. The intuition of the proof is as follows. ", "If $w$ is not ultimately recurrent we can find as many non-recurrent subwords as we like. ", "This allows us to find a completion $\\hat{w}$ that contains all the recurrent subwords and have $p_w(n) - r_w(n)$ be unbounded.", "\n\nFor the sake of contradiction, assume $w$ is not ultimately recurrent. ", "Then let $\\{ w_n \\}$ be an enumeration of the elements of ${\\mbox{\\hspace{.01in}RSub}}(w)$. Since $w$ is not ultimately recurrent we can choose a non-recurrent subword $v_0$. Let $i_0$ be an index such that $v_0$ is not a subword of $\\sigma_{i_0}(w)$. Complete $w[0..i_0)$ so that it contains $v_0$ as a subword. ", "Now choose $j_0$ such that $w_0$ is a subword of $w[i_0..j_0)$. Complete $w[i_0..j_0)$ so that $w_0$ is a subword. ", "Now since $w$ is not ultimately recurrent there exists a non-recurrent subword $v_1$ appearing in $\\sigma_{j_0}(w)$ with $|v_1| \\geq |v_0|$. Choose $i_1$ such that $v_1$ is not a subword of $\\sigma_{i_1}(w)$. Complete $w[j_0..i_1)$ such that $v_1$ appears as a subword. ", "Now choose $j_1$ such that $w_1$ is a subword of $w[i_1..j_1)$ and complete it so that $w_1$ appears as a subword. ", "Continuing on in this way we see that $\\hat{w}$ contains all the recurrent subwords and infinitely many non-recurrent subwords. ", "Now fix a $C$. ", "Choose $m = |v_C|$. Then each $v_i$ for $0\\leq i \\leq C$ contributes (by extending to the right) a length $m$ subword. ", "In addition each of these is non-recurrent. ", "Also they are all distinct since otherwise they would have to have matching prefixes, a contradiction. ", "Hence $p_{\\hat{w}}(m) \\geq C + 1 + r_w(m)$. Thus for this completion there exists no constant $C$ such that $p_{\\hat{w}}(n) \\leq r_w(n) + C$ for all $n>0$, a contradiction.", "\n\nWe can actually strengthen the above theorem. ", "The proof above shows that if $w$ is ultimately recurrent then the same $C$ works for all completions $\\hat{w}$. In other words the bound is uniform across completions. ", "We state this in a corollary.", "\n\nLet $w$ be an infinite partial word. ", "If $w$ is ultimately recurrent, then there exists a constant $C$ such that $p_{\\hat{w}}(n) \\leq r_w(n) + C$ for all $n>0$ and all completions $\\hat{w}$ of $w$.\n\nOftentimes if every completion of an infinite partial word $w$ has a certain property, then $w$ has it as well. ", "In particular this property holds with respect to ultimate recurrence.", "\n\n\\[pro:prop10\\] Let $w$ be an infinite partial word. ", "Then $w$ is ultimately recurrent if every completion $\\hat{w}$ is ultimately recurrent.", "\n\nIf $w$ is not ultimately recurrent, then the completion constructed in the proof of Theorem \\[thm:ultimate\\_recurrence\\] is not ultimately recurrent.", "\n\nWe now introduce the notion of a [*most complex completion*]{}. ", "The motivation is that this concept helps us understand the role of recurrent subwords in completions. ", "Let $w$ be an infinite partial word. ", "We say that $\\hat{w}$ is a most complex completion of $w$ if for all completions $\\bar{w}$ of $w$ and all $n>0$ we have $p_{\\bar{w}}(n) \\leq p_{\\hat{w}}(n)$. In general a most complex completion of an infinite partial word may not exist. ", "However, assuming that $w$ possesses such a completion we have the following result which states that a most complex completion must contain all the recurrent subwords. ", "The intuition here is straightforward. ", "In a rough sense one gets the recurrent subwords of $w$ for free. ", "We can delay putting them in the completion for arbitrarily long, and they still occur after that for us to capture. ", "Thus it is not difficult to construct a completion of higher complexity if this is not the case.", "\n\n\\[pro:prop11\\] Let $w$ be an infinite partial word. ", "If $\\hat{w}$ is a most complex completion, then ${\\mbox{\\hspace{.01in}RSub}}(w) \\subset {\\mbox{\\hspace{.01in}Sub}}(\\hat{w})$.\n\nConclusion {#sec:conclusion}\n==========\n\nIntuitively all the above work culminates to show that completions can achieve complexities equal (or “close”) to that of the original partial word if and only if the word is recurrent or ultimately recurrent. ", "Another interesting avenue of research would be to investigate whether a relation exists between the growth of $r_w(n)$ and that of $p_w(n)$. Although it would be nice, the answer seems to be no. ", "Given any constant $\\delta < 1$ we can find a partial word with infinitely many holes such that $\\frac{r_w(n)}{p_w(n)} \\rightarrow \\delta$. Also, even if we impose the restriction that $r_w(n)$ be linear then we still have a fair bit of freedom with the complexity of $p_w(n)$. In particular we can make it so that asymptotically $p_w(n)$ attains any polynomial complexity. ", "We can also attain some intermediate complexities, i.e. functions of the form $2^{\\sqrt{n}}$. The construction of these examples is actually quite simple. ", "You just have a word that is all $a$’s with holes at positions $H(n)-1$. Since the hole functions in all of our constructions are eventually increasing we see that any word with at least two $b$’s is not recurrent. ", "Since there are exactly $n+1$ words of length $n$ with at most one $b$ we see that $r_w(n) = n+1$. By controlling the growth of $H(n)$ we can control the growth of $p_w(n)$. The slower $H(n)$ grows the faster $p_w(n)$ grows.", "\n\n[^1]: This material is based upon work supported by the National Science Foundation under Grant No. ", "DMS–0754154. ", "The Department of Defense is also gratefully acknowledged.", "\n" ]

{ "pile_set_name": "ArXiv" }

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[ "Q:\n\nID for a newly saved backbone.js model\n\nBackbone.js makes a POST request when a new model is created and saved, but it doesn't consider the model to be saved (i.e, further saves result in PUTs not POSTs) until the model has an id.. how should the server return the ID of a newly created model so that backbone.js can set it (i.e, how should it respond to the initial POST)?", "\nIf backbone.js doesn't handle that, I assume the best way to do it is using the success handler to set the ID?", "\n\nA:\n\nYou have two options. ", " The first is to return the same JSON structure for a POST request as you would a GET request for the show action (returning a single item.) ", " This uses a single request.", "\nFrom the documentation:\n\nSet a hash of model attributes, and sync the model to the server. ", "If the server returns an attributes hash that differs, the model's state will be set again.", "\n\nThe other option is to trigger a fetch on your collection after you save. ", " This will take more than 1 request though and will always be less efficient.", "\n\n" ]

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[ "The address for Amelia Superior Hotel is Albena Resort, Albena 9620\n\nBased on recent averages, the price for tonight can start at 73.", "\n\nBased on recent averages, the room rate for this weekend can be as low as 73 per night." ]

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[ "1. ", "Field of the Invention\nThe present invention relates to systems and methods for analyzing computer-mediated communications, including computer generated communications and other communications that have been digitized and fed into a computer.", "\n2. ", "Description of the Prior Art\nPsychological profiling algorithms have been developed based upon the work of Walter Weintraub. ", "Weintraub has identified 14 critical speech categories, as listed in FIG. ", "1, which are believed by psychologists to reflect the operation of psychological coping mechanisms or defenses. ", "Weintraub's opinion is that the distribution of these variables indicates the distribution of defenses in an individual and provides insight into the individual's psychological state or personality. ", "Weintraub's and his colleague's original research dates from 1964.", "\nThis original research demonstrated differences in the distribution of these categories of speech as used by normal persons and persons with different forms of psycho-pathology, including depression, impulsiveness, delusions and compulsiveness. ", "Weintraub profiled and compared political leaders, such as participants in the Watergate matter in 1981. ", "In 1989, he extended his methodology for leadership profiling to the assessment and comparison of United States Presidents, including Eisenhower, Kennedy, Johnson, Nixon, Ford, Carter and Reagan.", "\nOver the past 35 years, Weintraub's algorithms have also been used to analyze the speech and written products of leaders, to develop in-depth psychological profiles of these individuals and comparisons between them. ", "Weintraub has also discussed the possibility of providing computerized portions of his algorithms to expedite the analytical process, but he never did so.", "\nHowever, Weintraub's algorithms are not known by the public to have been applied to the evaluations of changes in an individual's psychological state over time, to the communications of normal employees in the workplace, to computer-mediated communications, e.g. email and chat, to generating a warning of a potentially dangerous change in an individual's psychological state, to self-monitoring of a person's psychological state, to assessment of the emotional tone of computer-mediated communications or media coverage, or to personnel selection.", "\nThe Weintraub algorithms quantify the number of words and relevant events in the speech categories of FIG. ", "1. ", "The total word count for each category may be multiplied by a corrective figure, which is obtained by dividing 1,000 by the number of words in the sample and rounding off to three decimal places, to provide a normalized basis for comparison.", "\nThe Weintraub algorithms may be used to profile the following psychological states:\n1. ", "Indicators of Anger—\nIncreases in the number of: words personal references negatives evaluators statements of feeling direct references rhetorical questions interruptions I We \nDecreases in the number of: qualifiers retractors \n2. ", "Indicators of Anxiety—\nIncreases in the number of: retractors qualifiers expressions of feeling negatives explainers \n3. ", "Indicators of Depression— decreased number of words increased I increased me increased negative key words increased direct references increased expressions of feeling increased evaluators increased adverbial intensifiers \n4. ", "Indicators of Emotional withdrawal— decreased number of words decreased number of communications decreased I score decreased personal references decreased expressions of feelings decreased evaluators \n5. ", "Indicators of Rigidity or lack of flexibility— decreased number of qualifiers decreased number of retractors decreased we's increased I's decreased explainers increased evaluators increased adverbial intensifiers \n6. ", "Indicators of Impulsiveness— increased retractors increased expressions of feeling \n7. ", "Indicators of Emotional instability— increased I-to-We ratio increased adverbial intensifiers increased direct references increased expression of feelings increased evaluators \nScore Interpretations of Weintraub's psychological profiling algorithms have been suggested as follows:\n1. ", "I scores— high I score—self-preoccupied moderate I—healthy ability to commit self in thought and action while maintaining degree of autonomy low I—avoidance of candor, intimacy, commitment \n2. ", "We scores— moderate score—healthy capacity to recognize and collaborate with others high we+low I—avoidance of intimacy and commitment \n3. ", "Me— high use reflects dependence and passivity \n4. ", "Negatives— high scores associated with stubbornness, oppositionality, anger, use of denial as defense mechanism \n5. ", "Qualifiers— low score—dogmatism—over-certainty, rigidity high score—lack of decisiveness, avoidance of commitment very high score—anxiety \n6. ", "Retractors— high score—difficulty adhering to previous decisions, impulsiveness moderate—mature capacity to reconsider, flexibility, openness to new possibility very low—dogmatism, rigidity \n7. ", "Direct References— high scores—difficulty with correspondence or conversation, seeking to distract or manipulate low or absent—shyness, aloofness, anxiety \n8. ", "Explainers— high—use of rationalization low or absent—dogmatism, rigidity \n9. ", "Expressions of Feeling— low score—aloofness, hesitant to share feelings, trust high score—insincere, histrionic \n10. ", "Evaluators— high scores—severe or troubled conscience, psychopathology, anger, dogmatism, rigidity Low scores—fear of intimacy, lack of commitment \n11. ", "Adverbial Intensifiers— high scores indicate histrionic personality, exaggeration, rigidity, judgmental \n12. ", "Rhetorical Questions— increase anger and an effort to control the dialogue \n13. ", "Interruptions— increased anger and an effort to dominate \nThe specialized composite scores with relevance for personal relationships, organizational behavior and leadership remain unpublished but include: emotionally controlled—low anxiety and depression scores sensitivity to criticism—high negatives+high explainers+high I+me accommodating versus rivalrous—low to moderate negatives and moderate to high retractors oppositional—high negatives score. ", " controlling in relationships—low score on negatives, feelings, evaluators, and qualifiers passive vs. active—high me score planner vs. reactor—high I+we to me ratio decisiveness—low to moderate qualifiers unrealistic—high negatives high need for others—high we high need for achievement—high I+We, low me, low qualifiers dependent—high me plus high evaluators, negatives, feelings well organized—high I+we, low me, low qualifiers, low evaluators, low feelings, low negatives narcissistic—high negatives+high explainers+high evaluators, high I, low qualifiers obsessive—high evaluators+high negatives+low retractors, low me, low qualifiers, low feelings paranoid—high negatives, high explainers, low retractors loner vs. team player—high I, low we or Ito We \nHowever, Weintraubs algorithms have not been tested or validated for use with computer-mediated communications, media communications, or self-monitoring or in personnel selection. ", "They have not been used to monitor and evaluate changes in emotional state over time, nor have they been applied to the detection and warning of at-risk states. ", "This validation work will be required for a reliable and valid operational system. ", "The current invention also adds multiple variables to the Weintraub categories (e.g. negative and positive feelings, negative and positive evaluators) and uses an original computerized dictionary—presently containing over 1400 words coded for emotional tone. ", "This dictionary is continually updated as data is collected from subject samples.", "\nBeginning in the late 1950's, Gottschalk demonstrated that the arousal associated with psychological events plays an important role in the occurrence of epileptic seizures in children and later (1955) in adults. ", "While working at the National Institute of Mental Health, Gottschalk and his colleagues explored differences in the effects of different forms of stimulation on speech variables, such as rate, frequency, duration of pauses, grammatical categories and parts of speech (Gottschalk and Hambridge, 1955). ", "Later, Gottschalk and his colleagues examined differences in speech between psychotic and non-psychotic patients (Gottschalk, Glessner and Hambridge, 1957). ", "In 1958, Gottschalk conducted a time series analysis of the verbal behavior of a single psychoanalytic patient to determine any possible effects of the therapy (Hambridge and Gottschalk, 1958).", "\nIn the 1960's, Gottschalk worked with Dr. Golding Glenser at the University of Cincinnati. ", "This work identified variations in the use of parts of speech by normal individuals according to gender and intelligence (for example, Gleser, Gottschalk and John 1959; Gottschalk and Gleser, 1964). ", "Gottshalk and Gleser (1960) also used their content analysis method to distinguish genuine from pseudo-suicide notes. ", "By the end of the 1960's, Gotschalk and his colleagues added new complexity to their content analysis method by moving from the analysis of individual words to more complex phrases. ", "In 1969, Gottshalk and Gleser described a method for determining an individual's psychological state (anxiety, hostility, alienation, and disorganization) from brief samples of speech (Gottshalk and Gleser 1969). ", "Gottschalk, Wingate and Glesner (1969), have described their content analysis scales in a scoring manual. ", "Since 1969, Gottschalk and colleagues have applied their methods to the study of medical conditions, medications, treatment, and psychological conditions on children, adolescents and adults. ", "This work has been summarized in Gottschalk (1995).", "\nGottshalk and his colleagues have computerized their content analytical scales in order to make them more efficient and more widely available to other researchers. ", "These efforts are also described in Gottschalk (1995, pgs. ", "157-160).", "\nGottschalk and his colleagues have produced a content analytical system that can detect emotional states and changes in emotional states in individuals as a result of a wide range of psychological and medical conditions and treatments. ", "The have also measured changes in these states in individuals over time and designed a computerized version of the system.", "\nHowever, Gottschalk and his colleagues have not utilized their algorithms regarding communications by normal employees in the workplace, computer-mediated communications, e.g. email and chat, the generation of a warning of a potentially dangerous change in an individual's psychological state, or self-monitoring of a psychological state. ", "Nor have they utilized their approach for the assessment of media images or personnel selection or screening.", "\nMargaret Hermann, over the last 25 years, has used content analysis for psychological profiling. ", "In 1977, Herman (with Thomas Milburn) edited an academic collection entitled “A Psychological Examination of Political Leaders”, (New York Free Press 1977). ", "This text brought together the work of psychologists and political scientists interested in the remote assessment of leadership characteristics utilizing content analysis of the leader's speech and writings. ", "It also contains chapters by political-psychological profilers on the history and different approaches to political psychological content analysis, including Value Analysis (White 1951), Evaluation Assertion Analysis (Osgood 1959), the Psychologic (Shneidman 1961, 1963), General Inquirer (Stone, Dunphy, Smith and Ogilvie 1966), and Mode of Imagery (Winter 1973). ", "Hermann, in 1977, in a chapter entitled, “Vocal Behavior of Negotiators in Periods of High and Low Stress: the 1965-1966 New York City Transit Negotiations,” described a content analytical system that analyzed the psychological state of political leaders involved over time and in different stress states. ", "The collection of content analytical measures drew on the previous work of psychologists, political scientists and others interested in the assessment of emotional states and their changes over time. ", "In another chapter in the same text, she described three content analysis systems designed to assess a leader's beliefs, motives, decision-making and interpersonal style as it might affect their attitude toward foreign aid. ", "These personal characteristics included optimism, cognitive complexity, and humanitarian ideology. ", "The results of the study related variations in these characteristics to the policy positions taken by the leaders examined. ", "Both Herman and her colleagues have refined and expanded the number of personal characteristics derived from content analysis of a leader's speeches or interviews and detailed their effects on a leader's foreign policy orientation and likely political behavior. ", "The personal characteristics of nationalism, belief in one's ability to control events, need for power, need for affiliation, conceptual complexity, self-confidence, distrust of others, and task orientation have been applied to over 100 domestic and foreign political leaders, including heads of states and leaders of revolutionary and terrorist organizations.", "\nHermann uses scores obtained on a leader for each of the aforementioned eight personal characteristics to classify the leader in terms of six possible foreign policy orientations, including expansionist, active independent, influential, opportunist, mediator and developmental. ", "Each of the orientation types can be expected to differ in world view, political style, decision-making process, manner of dealing with political rivals, and view of foreign policy.", "\nHermann has designed computerized approaches to her content analytical system. ", "However, complexity of coding required to produce measures for many of the characteristics has limited validity and reliability of the resultant automated process.", "\nIn summary, Hermann has designed a content analysis system to assess the motives, beliefs, decision-making and interpersonal style of political leaders. ", "She has applied this system to the in-depth profiling of subjects, comparison with other leaders, and the assessment of the dynamics of leadership groups determined by member differences. ", "She has also used the system to analyze a leader's reaction to distress.", "\nHowever, Herman has not applied her system to the communications of normal employees in the workplace, to computer-mediated communications, e.g. email and chat, to media communications, to generating a warning of a potentially dangerous change in an individual's psychological state; to self-monitoring of a psychological state or assessment of media images or to management of computer-mediated communications or personnel selection issues.", "\nAnother measure of psychological state is described in Mehrabian and Wiener (1966) which is identified herein as “Psychological Distance”. ", "Psychological distance is an emotional state expressed by the speaker toward a target, individual or group. ", "Because the speaker normally unconsciously selects the semantic structures used to calculate psychological distance, it is an excellent measure of “covert” attitude. ", "When a speaker's covert attitude, as measured by psychological distances, is compared with overt content of a speaker's remarks (the number of negative, positive or neutral words associated with the name of an individual or group), it becomes a reliable measure of deception or bluffing. ", "For example, if the overt attitude toward the person or group is positive and the covert attitude is negative, this is an indicator of deception. ", "If the covert attitude towards the group or individual is more positive than the overt attitude, this is an indicator of bluffing.", "\nPsychological distance is scored according to the following guidelines. ", "First, each reference by the speaker to the target is identified. ", "Second, the word structures around the reference to the target are evaluated for the presence or absence of each of the nine conditions below. ", "Third, for each time one of these nine conditions is present, a single score is received. ", "Fourth, for each communication, an average psychological distance score is constructed by taking the number of references to the target divided by the number of points received in the communication across all references to the target. ", "This score is usually between one and nine with the higher score indicating the presence of greater hostility or psychological distance.", "\nPsychological Distance Coding Guideline\n1. ", "Spatial: the communicator refers to the object of communication using demonstrative pronouns such as “that” or “those.” ", "E.g. “those people need help” versus “these people need help.”", "\n2. ", "Temporal: the communicator's relationship with the object of communication is either temporally past or future. ", "E.g., “X has been showing me his house” versus “X is showing me his house.”", "\n3. ", "Passivity: the relationship between the communicator and the object of communication is imposed on either or both of them. ", "E.g., “I have to see X” versus “I want to see X.”\n4. ", "Unilaterally: the relationship between communicator and the object of communication is not mutually determined. ", "E.g., “I am dancing with X” versus “X and I are dancing.”", "\n5. ", "Possibility: the relationship between the communicator and the object of communication is possible rather than actual. ", "E.g., “I could see X” versus “I want to see X.”\n6. ", "Part (of Communicator): only a part, aspect, or characteristic of the communicator is involved in the relationship with the object of communication. ", "E.g., “My thoughts are about X” versus “I am thinking of X.”\n7. ", "Object (Part of Object): only a part, aspect, or characteristic of the object of communication is involved in the relationship with the communicator. ", "E.g., “I am concerned about X's future” versus “I am concerned about X.”\n8. ", "Class (of Communicator): a group of people who include the communicator is related to the object of communication. ", "E.g., “X came to visit us” versus “X came to visit me.”", "\n9. ", "Class (of Object): the object of communication is related to as a group of objects, which includes the object of communication, e.g., “I visited X and his wife” versus “I visited X.”\nHowever, Mehrabian and Wiener never computerized their system or applied their measure of psychological distance to computer-generated communications, detecting changes in employee groups over time, self-monitoring, assessment of media coverage, or personnel selection issues.", "\nIn December 1999, at pages 43-44, in Security Management, it was stated: “The [inventor's] firm, has developed psycho-linguistic measures sensitive to changes in an employee's psychological state indicative of increased risk. ", "In the case of the employee who abruptly changes tone in his email messages, post hoc use of these measures detected both the employee's initial disgruntlement and the contrast between his overt and covert activities. ", "Had these automated measures been monitored by security, this incident might have been prevented”. ", " \nFIGS. ", "2-5 illustrate slides presented by the present inventor at conferences on May 12, 1999, Jun. 17, 1999, Jul. 28, 1999, and Oct. 20, 1999 to persons involved with the security industry. ", "The slides illustrate analysis of the electronic mail messages of an actual perpetrator of a computer crime which occurred several months after the e-mail messages were generated. ", "The mean prior values of the number of “negatives”, as illustrated in FIG. ", "2, the number of “evaluators” as illustrated in FIG. ", "3, the “number of words per email”, as illustrated in FIG. ", "4, and the “number of alert phrases” as illustrated in FIG. ", "5 were compared to the values obtained from analysis of an electronic mail message prior to and associated with the crime in question. ", "The increase over the mean values was discussed as indicating the risk of the criminal activity in question. ", "The slides of FIGS. ", "2-5 represent the inventor's analysis after the crime occurred of emails of the perpetrator of the crime in question and were not produced at the time of the crime and were not produced by the present invention. ", "As noted above, the categories of evaluators and alert phrases have been modified and expanded since this presentation.", "\nFIG. ", "6 illustrates a slide presented by the present inventor at the aforementioned conferences analyzing continued covert hostility versus psychological distance over time. ", "As time passed, the criminal whose activities are analyzed above in FIGS. ", "2-5 deceived his supervisor with “charming pleasantries” as the attack was prepared. ", "Prior art email screening techniques would also have been deceived by the activities of the criminal. ", "As is shown in FIG. ", "6, a continued high degree of psychological distance was exhibited in emails after the plan of the attack was occurring. ", "This graph was produced by the analysis of the inventor, was not produced by an analysis of the criminal's activity as events unfolded, and was not produced with the present invention.", "\nFIG. ", "7 illustrates another slide provided by the present inventor at the aforementioned conferences illustrating indicators of psychological distance versus overt attitude consistent with deception. ", "Again, as is seen, the aforementioned conduct of the prior art of FIGS. ", "2-6 shows a drop in overt hostility from three months to two weeks prior to the crime which deceived the criminal's supervisor, while the analysis, as depicted in FIG. ", "6, shows a more or less constant continued covert hostility. ", "The graph of FIG. ", "7 was produced by the present inventor's analysis and was not produced with the present invention.", "\nEmail-monitoring software for the securities industry has been developed as a result of a United States Securities and Exchange Commission order that brokerage houses monitor their sales force for illegal sales practices. ", "This software detects key words indicative of potential trading sales violations.", "\nAs a result of increased employee use of information technology, non-psychological systems of employee monitoring have emerged which are designed to protect companies from employee misuse or other threats. ", "These systems are operated by companies to monitor employee use of information technology to detect patterns involving unauthorized visits to internet sites, errors in the use of software requiring additional training, and visits by email or other communications to or from unauthorized sites within and external to the organization.", "\nIn addition, systems exist to detect occurrence of “keywords” indicative of possible violations of law (the above-referenced security industries practice) and regulations or the existence of possible security violations.", "\nOther systems screen incoming and outgoing communications for the existence of dangerous viruses and/or other destructive content. ", "However, none of these systems currently assesses the psychological tone of computerized communications, the characteristics of authors of these communications, or the psychological state of an employee to generate an indicator of risk, or use these results for the purpose of improved management of communications and relationships. ", "Nor are these systems utilized to evaluate the psychological content of media coverage or as an aid in personnel selection.", "\nIn 1984 Jarol Manheim and Robert Albritton published an article in the American Political Science Review entitled “Changing National Images: International Public Relations and Media Agenda Setting.” ", "In the article the authors proposed the assessment of the media image of a nation according to several criteria, including mean insertions per month (the number of times the nation is mentioned in the media) and the percent of all insertions which were positive (page 654). ", "This scheme was used to determine the impact of the efforts of public relations firms on the media image of target nations by tracking the number of insertions and the percent of insertions which were positive before and after the public relations firm's efforts.", "\nThe current invention utilizes a related scheme to measure the quantity and emotional tone of communications. ", "However, in addition to the number of communications, the current invention utilizes the length, frequency per time period and other characteristics of the communications. ", "In addition to the percent of insertions which are positive, the current invention initially examines the percent which are positive and negative. ", "Instead of coding the percent positive by observation and hand, the current invention automatically codes the content of the communications in a more complex fashion utilizing psychological content analysis categories such as negative and positive feelings, negative and positive evaluators and negatives. ", "The user can then examine the actual content associated with this coding to determine the content associated with the emotional tone. ", "In addition, the authors never applied their scheme to the computerized communications of individuals, changes in the emotional tone of these communications over time, support for managing these media- and computer-based relationships, monitoring and assessing potential risk from an individual's psychological state, or personnel selection processes." ]

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[ "2-Aminothiazoles: a new class of agonist allosteric enhancers of A(1) adenosine receptors.", "\nThis report describes the synthesis and structure-activity relationships of a new class of A(1) adenosine receptor agonist allosteric enhancers, 2-aminothiazolium salts. ", "The EC(50) of compounds 6a, 6b, 7, and 8 were 0.3, 4.5, 3.8, and 1.2 microM, substantially lower than that of the 'Gold Standard' 2-amino-3-benzoyl thiophene (PD 81,723), which has an EC(50) of 38 microM." ]

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[ "Grazia Verasani\n\nGrazia Verasani (born July 8, 1964, Bologna, Italy) is an Italian writer and singer-songwriter. ", "The author of novels, plays, and screenplays she is a musician who composes, performs, and records.", "\n\nShe graduated from the Accademia Nazionale di Arte Drammatica Silvio D'Amico in Rome at the age of twenty. ", "After some work with the Teatro Stabile d'Abruzzo and with the Teatro Stabile di Torino, she began writing, while continuing her work as an actor.", "\n\nShe has written five crime novels featuring the PI Giorgia Cantini, a private investigator in Bologna. ", "The first, published in 2004, Quo Vadis, Baby? ", "was made into a film the following year by Oscar-winning film maker Gabriele Salvatores. ", "A TV series soon followed. ", "This novel was translated into English as Quo Vadis, Baby? ", "in 2017 and is published by Italica Press. ", "The series also includes: Velocemente da nessuna parte (2006), Di tutti e di nessuno (2009), Cosa sai della notte (2012), and Senza ragione apparente (2015).", "\n\nIn 2011, Verasani won the National Dramatic Art Festival of Pesaro award for best author for her play Maternity Blues (From Medea), which was later made into a film that won the 2012 Tonino Guerra Prize for best screenplay. ", "In 2016 Verasani published the epistolary novel. ", "Her most recent novel (2017) is La vita com'è. ", "Storia di bar, piccioni, cimiteri e giovani scrittori.", "\n\nWorks \n L'amore è un bar sempre aperto, 1999, Fernandel.", "\n Fuck me mon amour, 2001, Fernandel.", "\n Tracce del tuo passaggio, 2002, Fernandel.", "\n From Medea, 2004, Sironi.", "\n Quo vadis, baby?, ", "2004 Oscar, Arnoldo Mondadori Editore. [", "http://www.italicapress.com/index488.html Quo Vadis, Baby?] (", "English Translation) 2017, Italica Press.", "\n Velocemente da nessuna parte, 2006, Feltrinelli.", "\n Tutto il freddo che ho preso, 2008, Feltrinelli.", "\n Di tutti e di nessuno, 2009, Kowalsi/Feltrinelli. ", "\n Vuoto d'aria, collana inaudita, 2010, transeuropa edizioni.", "\n Cosa sai della notte, collana Foxcrime 2012, Feltrinelli, pp. ", "223.", "\n Accordi minori, 2013, Gallucci.", "\n Mare d'inverno, 2014, Giunti Narrativa, Collana Italiana.", "\n Senza ragione apparente, 2015, Feltrinelli.", "\n Lettera a Dina, 2016, Giunti.", "\n La Vita com'e', 2017, La Nave di Teseo.", "\n\nReferences\n\nCategory:1964 births\nCategory:20th-century Italian novelists\nCategory:Living people\nCategory:Italian women novelists\nCategory:20th-century Italian women writers" ]

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[ "The horizontal line represents the person’s life.1731 - born1785 - “A Treatise on ancient Armour and Weapons”; “A Classical Dictionary of the Vulgar Tongue”1785 - “A Treatise on ancient Armour and Weapons”; “A Classical Dictionary of the Vulgar Tongue”1786 - “Military\nAntiquities being a History of the English Army from the\nConquest to the present Time”; “The History of Dover Castle, by the rev. ", "William.", "\nDarell”1786 - “Military\nAntiquities being a History of the English Army from the\nConquest to the present Time”; “The History of Dover Castle, by the rev. ", "William.", "\nDarell”1788 - “A Provincial Glossary, with a\nCollection of local Proverbs and popular Superstitions”; “Rules for drawing Caricatures”1788 - “A Provincial Glossary, with a\nCollection of local Proverbs and popular Superstitions”; “Rules for drawing Caricatures”1789 - “Supplement to the Treatise on ancient Armour and Weapons”1769 - died\n\nGrose, Francis\n\n, an eminent English antiquary, was\nthe son of Mr. Francis Grose, of Richmond, jeweller, who\ndied in 1769. ", "He was born in 1731, and having a taste\nfor heraldry and antiquities, his father procured him a place\nin the college of arms, which, however, he resigned in\n1763. ", "By his father he was left an independent fortune,\nwhich he was not of a disposition to add to, or even to -reserve. ", "He early entered into the Surrey militia, of which\nhe became adjutant and paymaster; but so much had dissipation taken possession of him, that in a situation which\nabove all others required attention, he was so careless as\nto have for some time (as he used pleasantly to tell) only\ntwo books of accounts, viz. ", "his right and left hand pockets.", "\nIn the one he received, and from the other paid; and this\ntoo with a want of circumspection which may be readily\nsupposed from such a mode of book keeping. ", "His losses\non this occasion roused his latent talents: with a good\nclassical education he united a fine taste for drawing, which\nhe now began again to cultivate; and encouraged by his\nfriends, he undertook the work from which be derived both\nprofit and reputation: his Views of Antiquities in England\nand Wales, which he first began to publish in numbers in\n1773, and finished in 1776. ", "The next year he added two\nmore volumes to his English views, in which he included\nthe islands of Guernsey and Jersey, which were completed\nin 1787. ", "This work, which was executed with accuracy\nand elegance, soon became a favourite with the public at\nlarge, as well as with professed antiquaries, from the neatness of the embellishments, and the succinct manner in\nwhich he conveyed his information, and therefore answered\nhis most sanguine expectations; and, from the time he began it to the end of his life, he continued without intermission to publish various works, generally to the advantage\nof his literary reputation, and almost always to the benefit\nof his finances. ", "His wit and good-humour were the abundant source of satisfaction to himself and entertainment to\nhis friends. ", "He visited almost every part of the kingdom,\nand was a welcome guest wherever he went. ", "In the summer of 1789 he set out on a tour in Scotland the result\nof which he began to communicate to the public in 1790,\nin numbers. ", "Before he had concluded this work, he proceeded to Ireland, intending to furnish that kingdom with\nviews and descriptions of her antiquities, in the same manner he had executed those of Great Britain; but soon after\n| his arrival in Dublin, being at the house of Mr. Hone\nthere, he suddenly was seized at table with an apoplecticfit, on the 6th May 1791, and died immediately. ", "He was\ninterred in Dublin.", "\n\n“His literary history,” says a friend, “respectable as\nit is, was exceeded by his good-humour, conviviality, and\nfriendship. ", "Living much abroad, and in the best company\nat home, he had the easiest habits of adapting himself to\nall tempers; and, being a man of general knowledge, perpetually drew out some conversation that was either useful\nto himself, or agreeable to the party. ", "He could observe\nupon most things with precision and judgment; but his natural tendency was to humour, in which he excelled both\nby the selection of anecdotes and his manner of telling\nthem: it may be said too, that his figure rather assisted\nhim, which was in fact the very title-page to a joke. ", "He\nhad neither the pride nor malignity of authorship: he felt\nthe independency of his own talents, and was satisfied with\nthem, without degrading others. ", "His friendships were of\nthe same cast; constant and sincere, overlooking some\nfaults, and seeking out greater virtues.”", "\n\nGrose, to a stranger, says Mr. Noble, might have been\nsupposed not a surname, but one selected as significant of\nhis figure: which was more of the form of Sancho Panca\nthan Falstaff; but he partook of the properties of both.", "\nHe was as low, squat, and rotund as the former, and not\nless a sloven; equalled him too in his love of sleep, and\nnearly so in his proverbs. ", "In his wit he was a Falstaff. ", "He\nwas the butt for other men to shoot at, but it always rebounded with a double force. ", "He could eat with Sancho,\nand drink with the knight. ", "In simplicity, probity, and a\ncompassionate heart, he was wholly of the Panca breed;\nhis jocularity could have pleased a prince. ", "In the “St.\nJames’s Evening Post,” the following was proposed as an\nepitaph for him:\n\nMr. Grose married Catherine, daughter of Mr. Jordan,\nof Canterbury, by whom he had two sons and five daughters;\n1. ", "Francis Grose, of Croydon-Crook in Surrey, esq. ", "a colonel in the army, governor in 1790 of New South Wales;\n2. ", "Onslow Grose, esq. ", "captain of the pioneer corps on the\n| Madras establishment, who died very lately in India; and\nfour daughters, one of whom married to Anketel Singleton,\nesq. ", "lieutenant-governor of Landguard-Fort, in Essex.", "\n\nHis works are, 1. “", "The Antiquities of England and\nWales,” 8 vols. ", "4to and 8vo. ", "2. “", "The Antiquities of\nScotland,” 2 vols. ", "4to and 8vo. ", "3. “", "The Antiquities of\nIreland,” 2 vols. ", "4to and 8vo, a posthumous work, edited\nby Mr. Ledwich, 1794. ", "4. “", "A Treatise on ancient Armour and Weapons,” 1785, 4to. ", "5. “", "A Classical Dictionary of the Vulgar Tongue,” 1785, 8vo. ", "6. “", "Military\nAntiquities being a History of the English Army from the\nConquest to the present Time,” 1786, 1788, 2 vols. ", "4to.", "\n7. “", "The History of Dover Castle, by the rev. ", "William.", "\nDarell,” 1786, 4to. ", "8. “", "A Provincial Glossary, with a\nCollection of local Proverbs and popular Superstitions,”\n1788, 8vo. ", "9. “", "Rules for drawing Caricatures,” 1788,\n8vo. ", "10. “", "Supplement to the Treatise on ancient Armour and Weapons,” 1789, 4to. ", "11. “", "A guide to Health,\nBeauty, Honour, and Riches,” being a collection of humorous advertisements, pointing out the means to obtain\nthose blessings with a suitable introductory preface, 8vo.", "\n12. “", "The Olio, a collection of Essays,” jests, small pieces\nof poetry, all highly characteristic of Mr. Grose, but the\ncollection was not made by him, and we suspect all the\ncontents are not from his pen; 1793, 8vo. ", "1\n\nThis text has been generated using commercial OCR software,\nand there are still many problems; it is slowly getting better\nover time.", "\nThe text was scanned and OCRd several times, and\na majority version of each line of text was chosen.", "\nPlease don't reuse the content\n(e.g. do not post to wikipedia)\nwithout asking liam\nat holoweb dot net first (mention the colour of your socks in the mail),\nbecause I am still working on fixing errors.", "\nThanks!" ]

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