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Beans, Some Like It Hot! "South Asian influenced beans with a kick. Great served over rice or in a tortilla as leftover burritos. Serve over rice (jasmine rice is my first choice). They come out really spicy, so add only as much spice as you're comfortable with." Directions Stir the coconut milk, ginger, garlic, and parsley into a deep skillet over medium heat. Season with salt, turmeric, cumin, chili powder, and curry paste. Bring to a slow boil. Then stir in black beans, kidney beans, and red and green bell peppers; simmer, stirring often, until about 1/3 of the liquid is evaporated and the sauce has thickened, about 30 to 45 minutes. Cover, and let cool for 5 to 10 minutes. Most Helpful Positive Review Nov 28, 2007 This sounded interesting so thought I'd try it... I reduced the ginger to 2 Tbsp. To round this into a full meal, I added a bit of onion, a package of thawed frozen spinach, some mushrooms, and paper-thin carrot slices. It would be good with other veggies as well. I needed all the juice, so simmered it covered, and served over jasmine rice. It was delicious! Not at all too spicy, but I do like spicy things! Most Helpful Critical Review Sep 21, 2011 I like this recipe, but, MAN it's salty! I've made this twice and both times found the salt overpowering (and I'm not one to shy away from the salt shaker). Good flavor, otherwise. I'd just recommend using half the salt the recipe calls for and adding more if necessary after tasting it. My husband and father-in-law (chile-heads) both loved this! It was a little hot for me, so the next I make it I'll take some of the coconut milk and pour it in a small saucepan and add half the hot ingredients to that pot so they can add the "hot sauce" to their taste and the main pot isn't too hot for me. And it reheats fabulously! This is an excellent vegan dish. I ended up also adding carrots, chiles, onion, squash and mushrooms to round it out and eliminate the need for a vegetable side dish. I also added to soft veggies (the mushrooms, squash, and bell pepper) very close to the end instead of at the beginning of the simmer. If you're the type who doesn't like super-soft and soggy vegetables, you should do this. It'll keep them a bit crunchy. I love you!!! This recipe is great! Finally, a veggie recipe that stands up to my fire-loving taste! I even added more chili powder than was called for, and it was wonderful! Will make again soon!! Thanks! I thought there was way too much chili powder. I cannot taste the coconut or curry at all because the chili powder completely overwhelms the other flavors. I had to add Tabasco to give it some heat and flavor. *Percent Daily Values are based on a 2,000 calorie diet. Your daily values may be higher or lower depending on your calorie needs. **Nutrient information is not available for all ingredients. Amount is based on available nutrient data. (-)Information is not currently available for this nutrient. If you are following a medically restrictive diet, please consult your doctor or registered dietitian before preparing this recipe for personal consumption.

In the United States alone, approximately 500,000 deaths will result from rupture of plaques considered "insignificant" on an angiographic evaluation. Available screening and diagnostic methods are insufficient to identify the victims before the event occurs. Therefore, there is a definite and urgent clinical need for an imaging technique that can identify and characterize the vulnerability of atherosclerotic plaques during coronary artery interventions. The overall goal of our research program is to develop an in-vivo imaging technology - intravascular photoacoustic imaging - capable of visualizing both structural and functional properties of atherosclerotic plaques. The underlying hypothesis of this project is that intravascular photoacoustic (IVPA) imaging combined with intravascular ultrasound (IVUS) imaging is possible and can be used to distinguish vulnerable plaques, thus assisting pre-intervention planning, the intervention itself, and improving the post-intervention outcome. Most importantly, the proposed photoacoustic imaging will not significantly change the current protocol of coronary artery intervention. A wide range of technical, scientific and clinical problems must be addressed to fully explore the capabilities of intravascular photoacoustic imaging in interventional cardiology. The central theme of the current project is to address the areas of known technical concerns so that the broader developmental efforts may proceed with minimal risk. The main objective of this R21 application is, therefore, to develop and initially test a prototype of the photoacoustic imaging system for intravascular applications. To achieve our objective, we will first design and build the intravascular photoacoustic imaging system based on a mechanically scanned, single element transducer IVUS cathetrer interfaced with a tunable laser source. We will also develop both theoretical and numerical foundations for photoacoustic and ultrasound imaging to optimize the performance of the system. Second, we will test the developed imaging system using tissue mimicking phantoms. Third, the developed imaging system will be tested using animal tissue samples where ultrasonic and photoacoustic images will be correlated with histological slides and biochemical analysis of tissue. Finally, based on the insights gathered during the project, we will outline the design and technical specifications of an intravascular photoacoustic imaging system. Atherosclerotic cardiovascular disease results in more than 19 million deaths annually, and coronary heart disease accounts for the majority of this toll. Despite major advances in treatment of coronary heart disease patients, a large number of victims of the disease who are apparently healthy die suddenly without prior symptoms. Available screening and diagnostic methods are insufficient to identify the victims before the event occurs - in the United States alone, approximately 500,000 deaths per year will result from rupture of plaques considered "insignificant" on an angiographic evaluation. Therefore, there is a definite and urgent clinical need for an imaging technique that can identify and characterize the vulnerability of atherosclerotic plaques during coronary artery interventions including percutaneous balloon angioplasty, endovascular stenting, ablation/vaporization and brachytherapy. [unreadable] [unreadable] [unreadable]

Complete genome sequence of a novel dsRNA mycovirus isolated from the phytopathogenic fungus Verticillium dahliae Kleb. A novel double-stranded RNA (dsRNA) mycovirus, designated Verticillium dahliae partitivirus 1 (VdPV1), was isolated from a strain of the fungus Verticillium dahliae. The VdPV1 genome has two dsRNA genome segments. The larger segment (1768 bp) has a single open reading frame (ORF) with a conserved RNA-dependent RNA polymerase (RdRP) domain. The smaller segment (1587 bp) contains a single ORF encoding a putative coat protein. Analysis of its genomic structure indicated that VdPV1 is a new member of the genus Partitivirus. We report the full-length sequence of this partitivirus that infects Verticillium dahliae, the causal agent of verticillium wilt of cotton.

Research Methodology Resourceshttp://www2.hcmuaf.edu.vn/data/quoctuan/Research%20Methodology%20-%20Methods%20and%20Techniques%202004.pdfhttp://www.is.cityu.edu.hk/staff/isrobert/phd/ch3.pdfhttp://www.londoninternational.ac.uk/sites/default/files/programme_resources/lse/lse_pdf/subject_guides/sc2145_ch1-3.pdfhttp://www.bl.uk/reshelp/findhelpsubject/socsci/topbib/methsocial/methodsresearch.pdfhttp://www.elib.tic.edu.vn:8080/dspace/bitstream/123456789/13168/1/7.pdf

Color is something that I’ve been thinking about a lot when it comes to his diet–the more colorful the better! As you might have expected, I enjoy making food for him at home, so I wanted to share a simple recipe that you could try, inspired by the deep and vibrant colors in the exhibition. Be sure to bring your little one on your next visit, then make some colorful food for him or her to enjoy at home–you’ll be feeding his body and his mind! If you’re brave, you might even let him paint his high chair tray–at least you’ll know the paint is safe to eat! Prepare the mango by cutting it around the skin, similar to how you would cut an avocado. Note that the pit can be a bit tricky, so do your best to remove it, separating the fruit into two halves. Using a knife, score the fruit up to the skin, being careful not to cut through it. Scoop out fruit pieces and juice, and add to saucepan set on medium-low heat. Add fresh or frozen berries to pan and lightly simmer for about 5 minutes, allowing the fruits to break down slightly and meld their flavors. Transfer fruit to the bowl of a baby food maker, small food processor, or large measuring bowl, if using an immersion blender. Puree into desired consistency for your baby. Divide puree into any portion size you’d like and freeze. I find that an ice cube tray works well for small portions that can be pulled out when needed and added to oatmeal, mixed with other fruits, or combined into a larger meal. Cooked fruit in the baby food maker Finished puree in ice trays Original recipe. And of course, be sure to always check with your pediatrician on the appropriate diet for your special little one.

With the help of this tool, you can choose to covert only some portions of the video and retain the rest. Its inbuilt features allow you to set the start time, end time as well as the length of the song you want to extract. You can further choose to extract just the audio or your video file. You can convert and save it into popular audio formats like MP3, WMA, MP2, AAC etc. It works at an extremely fast pace. Koyote Video Converter is an amazing application for downloading and converting FLV videos as well. All you need to do is simply cut, copy and paste the URL address of the video file format FLV or SWF on this downloader. It will automatically search for the video and download it at the brink of a moment. You can further search for latest and old videos on the interface of Koyote FLV converter. This downloaded will conduct search from the most popular sites like YouTube, Google Videos, DailyMotion, Spike, Metacafe, Veoh, iFilm, Yahoo, Broadcaster, Crackle, ZippyVideos, Revver, MySpace, LiveLeak, CollegeHumor, EyeSpot, SevenLoad, CrunchyRoll, Break, Blip.tv, archive.org, lulu.tv, TinyPic, Uncut AOL, EbaumsWorld, Guba, Tudou, Youku, Reuters, BBC News, and vh1.

Abbey Boland With Dr Tom Kolso Abbey Boland Your Happy Mouth™ Empowered! Do you know something else is possible with your teeth, mouth and body? Would you like to have the tools to change that? Add your details below for random insights into energetic dentistry. Subscribe to: Newsletter **Medical Disclaimer - The information on this site, classes and recordings are provided as an information resource only, and is not to be used or relied on for any diagnostic or treatment purposes. This information is not intended to be patient education, does not create any patient-dentist- relationship, and should not be used as a substitute for professional diagnosis and treatment. Please consult your dental health care provider, for an appointment, before making any dental decisions or for guidance about a specific dental condition. Happy Mouth™/Your Happy Mouth™/The Happy Mouth™ expressly disclaims responsibility, and shall have no liability, for any damages, loss, injury, or liability whatsoever suffered as a result of your reliance on the information contained in this site or in classes or recordings. Your Happy Mouth™

Q: How do I get Google search query string inside my content script? I'm trying to build a Chrome extension and clearly I'm a n00b. I want to display some links on the right side of Google's result page, based on the query the user has searched. But I'm just not able to get hold of the user query string!. I cannot depend on parsing URL since, the URL remains the same even though the user has made a second search. Let me clarify with a use case: User enters a search query "testing time" via omnibox and clicks on enter. URL has now become "https://www.google.co.in/search?q=testing+time" Now from within the results page, user changes the query to "testing again" and clicks on enter. The URL will remain what it was earlier, "https://www.google.co.in/search?q=testing+time". How then shall I get hold of the query string? A: For the case 2 mentioned by you, you should see #q=testing+again at the end of the URL. You can get it via location.hash.split("=").pop(); //you might have to unescape it OR alternatively you can read the new query from the text box itself. (I would prefer this method) document.getElementsByName("q")[0].value

Approximation of the functional kinematics of posterior stabilised total knee replacements using a two-dimensional sagittal plane patello-femoral model: comparing model approximation to in vivo measurement. Previous in vivo studies have observed that current designs of posterior stabilised (PS) total knee replacements (TKRs) may be ineffective in restoring normal kinematics in Late flexion. Computer-based models can prove a useful tool in improving PS knee replacement designs. This study investigates the accuracy of a two-dimensional (2D) sagittal plane model capable of predicting the functional sagittal plane kinematics of PS TKR implanted knees against direct in vivo measurement. Implant constraints are often used as determinants of anterior-posterior tibio-femoral positioning. This allowed the use of a patello-femoral modelling approach to determine the effect of implant constraints. The model was executed using motion simulation software which uses the constraint force algorithm to achieve a solution. A group of 10 patients implanted with Scorpio PS implants were recruited and underwent fluoroscopic imaging of their knees. The fluoroscopic images were used to determine relative implant orientation using a three-dimensional reconstruction method. The determined relative tibio-femoral orientations were then input to the model. The model calculated the patella tendon angles (PTAs) which were then compared with those measured from the in vivo fluoroscopic images. There were no significant differences between the measured and calculated PTAs. The average root mean square error between measured and modelled ranged from 1.17° to 2.10° over the flexion range. A sagittal plane patello-femoral model could conceivably be used to predict the functional 2D kinematics of an implanted knee joint. This may prove particularly useful in optimising PS designs.

Q: Creating a location wise search in Drupal 6 using Views and CCK How Can i create a search for the CCK fields in Drupal? Currently using a Finder Module is giving some error. If there is some other way kindly help me with it . Also .. is it possible to have a drop down for the Location Module fields which are visible on the Nodes? Since if I use use them for search then in the search the "ABC" and "abc" are treated as 2 separate locations. Also is there some way in which I can have the exposed filters as Drop Down? Kindly help Thanks A: I finally sorted the problem by simply using Views and and then exposing its filters. To ensure that i have a drop down in the search block i used the "Allowed Values" option while exposing the filter. To see it in action check. : http://naplesres.designbracket.com/ the Find Local Coupons Block on this page.

The many legal battles of Uber The ride-sharing company is notorious for entering markets without adhering to required legal procedures. Does this justify the convenience and comfort that it provides? Illustration by JL JAVIER Manila (CNN Philippines Life) — For a company that has been around for less than a decade, Uber has been embroiled in so many legal battles that it has become difficult to keep up. The most recent case takes place in our own backyard, with a month-long suspension by the LTFRB sparking outrage in the general public. This suspension was brought about by the company’s insistence to accept new applications despite the LTFRB’s order to stop doing so. For its consumers, Uber was a way of escaping the miserable and sometimes dangerous public transport options that we’re given. With traffic at its worst, an Uber could at least warrant us a fixed fare, a thoughtful driver, and a comfortable ride. But does the company’s track record justify the comfort that it provides? Uber is available in over 60 countries and more than 500 cities, and since the company’s boom, it has faced a myriad of bans and lawsuits in Europe and the United States. Many of these, similar to what’s happening here, are a result of the company operating without securing proper licenses for its drivers. While the pursuit for providing better public transportation is noble, the company’s brazen attitude and willful disobedience of the law puts it at risk of being a problematic and injurious vigilante. In 2014, UberPop, an Uber product similar to UberX and commonly used in Europe, was barred from operating in Germany for not providing licenses and insurance to its drivers. This marked the first nationwide ban for the company. Yet, a day later, drivers continued to pick up passengers. In 2016, UberPop came under fire again, this time in Paris, where the company had to pay €800,000 for not complying with the Thevenoud Law, which required all chauffeurs to hold professional licenses. Again, the company continued to operate despite warnings. Aside from operating illegally, Uber has also had to face questions of safety and ethics in the past years. In India, the company was banned from the capital and its screening process placed under major scrutiny as a woman was raped by a driver who had apparently been arrested for sexual assault 3 years prior. In San Francisco, an Uber driver was arrested after an accident resulting in the death of a 6-year old girl. Recently, the company has been struggling with the ethicality of its use of Greyball, a program that, though originally intended to keep competitors and shady individuals from misusing the app, has been helping Uber drivers dodge sting operations meant to catch those operating without proper licenses and permits. Meanwhile, internally, sexual harassment and discrimination claims have caused a major commotion, lending a hand in the stepping down of CEO Travis Kalanick. Conceived in 2008 by Garrett Camp and Travis Kalanick, Uber was seen as a way to solve the taxi problem in San Francisco. Back then, it was next to impossible to quickly score a taxi in the city. Eventually, the idea of providing premium black cars developed into a vision of making transportation cleaner, safer, and more accessible through ride-sharing. While the pursuit for providing better public transportation is noble, the company’s brazen attitude and willful disobedience of the law puts it at risk of being a problematic and injurious vigilante. For taxi drivers around the world, Uber is the company that is putting their livelihoods in jeopardy. Much of the commuting public find that it’s time for cabbies to go. This is especially true in the Philippines, where taxi drivers are notorious for their bad behavior, often found turning down passengers, tampering with the meter, and asking for dagdag. But the trouble with taxis goes much deeper than its drivers. It’s a messy combination of the daily boundary drivers must pay their operators and the heavy traffic that keeps them from actually reaching it. The boundary system also contributes to jeepney and bus drivers resorting to the reckless kaskasero-style driving just to get ahead of the competition. With traffic at its worst, an Uber could at least warrant us a fixed fare, a thoughtful driver, and a comfortable ride. But does the company’s track record justify the comfort that it provides? Even if the LTFRB can find a way to fix the boundary problem, there’s still the matter of congestion. In the US, one of Uber’s main tenets is to get more people into fewer cars. However, the reverse is happening for us here. Many opportunists use Uber to put up fleets of their own by purchasing vehicles and renting them out to drivers, much like how the local taxi system works. According to Yves Gonzalez, Uber Philippines government relations and public policy head, around 66,000 Uber cars travelled at least one trip in a year. In a metropolis where there are more vehicles than there are kilometers of road to accommodate them, it seems that the company that was supposed to save us is turning out to be a huge part of the problem. Uber is notorious for entering markets first and figuring out all the legal procedures later. But it seems that this time they have made a major oversight, stepping into the big mess of Metro Manila’s transportation system.

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Tuberculosis and HIV infection. How to safely treat both disorders concurrently. Progress has been made in screening, early recognition, prevention, and treatment of TB, but its coexistence with HIV infection continues to present a challenge. Healthcare professionals should be familiar with guidelines for treating HIV-infected patients with TB while concurrently administering highly active antiretroviral therapy. Primary care physicians are encouraged to consult specialists who are familiar with treatment of patients with such coexisting disease. Whenever feasible, directly observed therapy should be instituted in all cases of TB to promote compliance and reduce the incidence of drug resistance and treatment failure.

Friday, March 25, 2011 I told you I've been busy. LOL. Here's some stuff from the short films I've worked on. First is the teaser trailer for "Flappy Hands". I Costume Designed and ended up producing as well. Designers and producers generally don't get along...its usually "Hey I'd like to make this look awesome for you so can I get a bigger budget?" "No." I pretty much had to argue with myself and even hated myself at times. Never again. Just put me in the wardrobe trailer where I belong! Next, I was the makeup consultant for a piece that's currently untitled. I generally don't like to do makeup, but I'll do ghoulish things every once in a while: latex and acrylic. And finally, I designed costumes for a party scene that later turned into a blood bath. Rather than show you the soiled clothing, I'll just show you one of the "befores". Irma was a very thin, athletic girl. I changed that by putting her in elastic waisted acid wash jeans, horizontal striped tank, and an oversized 80's shirt. To insure that she didn't look like a hipster, I stuffed her pants to give her a gunt. What a busy week! I'm in the middle of designing THREE shows...on top of that, I styled a music video for Manika's new single "Just Can't Let You Go", featuring Lil Twist. I was particularly excited to be working with the legendary Travis Payne. In the short time I got to work with him, I have to say he's my new favorite director to work with. He had nothing but positive energy the entire time, was eager to take time and meet each crew member individually, and made sure to thank everyone at least three times on set. He knew exactly what shots he wanted, and expressed a clear vision from the very beginning for what kind of look he was going for. You can find out why I was so excited and why I consider him a legend, here. Music Videos are one of the most stressful and miserable sets to work on. The hours are at least 16 hours minimum, with a crappy rate. This one was definitely the exception. I won't get into the financial logisitics, but I will say that the actual shoot was about six hours--A NEW WORLD RECORD! Both of the performers were very very young and surprisingly sweet, particularly Lil Twist. He actually called me "ma'am". I just hope the fame doesn't warp their semi-innocent but very naive minds. I got those babies for the shoot from Barney's. They were a specific request and they were practically impossible to find. I think I went to like 8 different stores. Aren't they fab?! They're from John Varvatos for Converse. The shoe is a shiny beat up coated material with studded ankles...only $200!! I'm gonna take a second to share something one of the production assistants said to me on set. He said, "I'm pretty sure you're my favorite stylist I've ever worked with. Ever." Me: "For real? Cool. How come?" He replied, "You treat us like people, I mean please and thank you go a long way. You're not snobby at all, you don't act like you're the hot shit on set, you don't demand that we do everything for you. You're just cool". Wow. Please and thank you?? I've been around lots of other stylists and designers...and I have to admit I've witnessed plenty of diva-like behavior. If I can leave you with one thing, it is the reminder that EVERY crew member is equally important and deserves the same amount of respect as the director, the keys, and talent. I don't care who you are, you need to always thank who you're working with. Travis Payne is a prime example of that. He was loved and adored by everyone on set and that itself made the whole shoot roll smoothly. Saturday, March 19, 2011 Yesterday, I gave a wardrobe makeover to a hilarious young man. My client (whom I will refer to as Louie) started out with a 38" waist and an XL/XXL tshirt size. With the help of diet and exercise--NO EATING DISORDERS OR STUPID FASTS AND/OR PILLS, he has successfully shrunken down to a waist size between 34" and 36" and a MEDIUM tshirt size. I am so proud of him, especially for doing it the right way. Louie is a budding comedian and has been looking to change his look and get healthy. He contacted me and asked how much he would need to get a wardrobe makeover since nothing of his fit anymore. I told him $200 would be enough to start and that I was pretty good at staying on budget. Let me just say, that with that $200, we got: -2 pairs of shorts -5 tshirts -2 polos -3 dress shirts -1 cardigan -3 day shirts Everything was brand new, none of it was purchased second hand or via thrift. I know how to shop. I'm good at giving wardrobe makeovers. I stay on budget. If you need my services, contact me via my website: http://www.xtinakim.com. Sunday, March 6, 2011 First off, forgive me if the format is a bit off. As I mentioned before, we got rid of our Internet so updates are not as frequent. That being said, I just downloaded a new blogging app for my phone...testing it out tonight and the reviews for this app havent too positive. We shall see. So, the oscars were last week. I have to say, Colleen Atwood's acceptance speech made me not like her. She was dressed as the poor man's Stifler's mom and seemed extremely ungrateful. It's the same four women nominated every year for period pieces or a Tim Burton flick. That being said, I feel like Burlesque got shafted on costume nomination! Dude, you may not have cared for the story or anything else in that movie, but you cannot deny the incredible beauty and craftsmanship of those costumes. I feel like everyone who watched The Social Network in the theater has been completely brainwashed. What's up with all those nominations?? Congrats to Trent Reznor for his win, but that score was pretty mediocre. In fact, mediocre is my word for describing that movie. It's a celebration of lazy filmmaking and I'm quite offended that people are praising it this much. What was up with that wardrobe?! Gross! I get what they were going for, but there is a MUCH better way to achieve it. This industry is disappointing me a lot lately ...so is the audience. Cmon brothers and sisters. WE ARE BETTER THAN THIS

Q: Sequence field in django model without primary_key I need another sequence field in model this fild will start from 100000 and need to be incremented but django AutoField need to be primary_key, any way to do a sequence without be a PK ? thnkx. A: are these going to be unique as well? in what way are they different from the pk field? if all you need is for them to start at 100000, could you get away with using pk + 100000?

Q: How useful is image stabilisation below 200mm, really? Image stabilisation is all the rage, and hardly a new lens from Nikon or Canon is missing this "crucial" feature. To me this seems to be the new megapixel race (like when the manufacturers tried to overdo each other with higher resolution, they now try to do this with more (useless) features). Especially for wide angle lenses like the new Nikon 16-35 I can't really understand what the fuss with VR is about. As a rule of thumb you should use 1/mm as shutter-speed not to shake pictures, for 16-35 shutter times of 1/16s to 1/35s should be manageable without problems. At shutter speeds like 1/16s your subjects will blurred due be moving. Even more so if you really take advantage of the "4 more stops of light" VR might bring you. People will be blurred, because they are moving, talking. Leaves in a tree will be blurred because wind is moving them. Water will be blurred because of motion. For almost anything below 200mm the only situation where IS/VR would be useful is some kind of still-life photography, like architecture. But this kind is better shot using a tripod anyway for maximum image quality and to help create a deliberate composition. Of course IS/VR can (and probably should) be switched off when you don't need it, but why pay a premium for a stabilised lens when you can only use the advantage in very few situations? Why lug around the extra size and weight of an IS lens? Why tolerate the extra battery drain of the VR-system? The same applies for IS-systems which are integrated into the DSLR body. I owned and used the Pentax IS system for a few years, and found it pretty useless in almost any situation I encountered since something in the picture always was moving and therefore being subject to motion blur. Is there any real-world usage for IS below 200mm? Or is this mainly a marketing hype everybody is keen to attend? Of course you can (and will) create some exotic settings where the extra stop of light is helpful, but do these rare settings justify the downsides? A: I conducted a large number of accurate measurements on a 50 mm lens on a Pentax K7. The bottom line, Shake reduction/VR/IS (call it what you will) is very beneficial. A link to the full study is on www.scribd.com (pdf) The graph below shows the main results. Motion blur, in pixels, was used as a measure of image stabilisation. The tests show that motion blur was kept below 0.5 pixel down to a shutter speed of 1/8 sec, whereas without image stabilisation the motion blur was 5.9 pixel at 1/8 sec. See the full study for test details (pdf). A: As you say, the old adage, that you'd use the reciprocal of the focal length to avoid shaking (at full frame) still holds without VR: means 100mm = at maximum 1/100s ... or a tripod. Or 1/16 to 1/65 for your example. I can't say 4 stops, but my experience with my Nikkor 16-85 (APS-C) says two stops. That makes at least 1/4 to 1/20 out of these numbers ... ... and sometimes, blurred movement is part of the idea (I carry a ND8). ... and sometimes cranking up the ISO is not possible any more. If you want a deeper DOF and/or take photos at low light-conditions (night, an indoors party): unbearable without IS/tripod. ... and often people do not move that fast, 1/30 would suffice and comply with your ISO, but the 100mm focal lengths do dictate 1/100 for the nice portrait at the wedding-ceremony. (I do have a 17-50 2,8 for parties, but that makes another lens. Additionally: wedding-ceremonys of non-famous-people are better without a lot of flashes.) (did you seriously put up the measure to 200mm and thus way beyond the portrait-focal-lengths?) ... and very, very often tripods/monopods can't be used where you would like to. Be it due to local customs, the lost moment, local security, your own baggage-limits or that you simply do not want to lug around another kilo of a decent tripod everywhere. (My wife often bears the burden :) ) ... and sometimes you travel too and IS will certainly reduce this additional shake. See trains and ships and apply above ideas. A: Though there's no doubt that virtually anything can be a bullet point in the useless features race, I don't think IS/VR qualifies. While you're right that at wide angles you're not likely to need such a slow shutter speed that you can't handhold, there's a lot of room between 35mm and 200mm, and at many of those focal lengths you may have subjects that move sufficiently slowly that, say, a 1/60s shutter speed will pose no problems with motion blur, but if you're shooting at a 120 mm, without IS/VR you may get some shake. In a fast, wide-angle lens I don't think you're going to get any real benefit from IS/VR, but step up to middle focal lengths, especially with narrower apertures, and I think it often has value. Unless you always carry a tripod, I suppose -- and always have time to set it up. To me the bottom line is that it reduces the number of shots I miss, and the number that I have to accept a little less sharpness or a little narrower DOF than I really want.

For those who meet the criteria for access to confidential data, to request data, contact the first author <shelley.harris@cancercare.on.ca> or the data access committee at <datarequest@cancercare.on.ca> Introduction {#sec005} ============ The increased use of biological samples to measure biomarkers of internal dose, early biological effects, and genetic susceptibility or modifiers has improved methods of exposure assessment in case control studies. The type of biological sample collected depends on the exposures/markers of interest and typically reflects longer term exposures; for example saliva or blood samples for genetic mutations/variants or markers of DNA damage, serum for environmental contaminants or infection history, and hair or toenails for metals exposures. Urine samples may be collected, where excreted compounds typically reflect more recent exposures (i.e., phytoestrogens, phthalates). We and others have gained experience collecting urine and other biological samples in large prospective population-based cohort studies of healthy individuals \[[@pone.0127994.ref001]--[@pone.0127994.ref005]\]. However, many case control studies of cancer using biological samples have focused on genetic determinants, the bulk of our experience is with the collection of saliva and blood samples, including studies conducted in Ontario, Canada \[[@pone.0127994.ref006],[@pone.0127994.ref007]\]. In case control studies, it is important that response rates are maximized and that systematic bias in the provision of questionnaire information or biological samples does not occur. Thus, in the design phase of any study, an understanding of the expected response rates and how these might be affected by important confounding factors or subject inclusion criteria is needed. If confounding variables influence response rates or influence them differently by case control status, biased estimates of risk may result. In addition, if these factors influence response overall, certain group of individuals may be underrepresented in population based studies and this results in reduced generalizability. Overall response rates for the provision of biological samples in previous population-based cancer studies have been reasonable \[[@pone.0127994.ref008]--[@pone.0127994.ref012]\], but typically minimal information is reported on how these response or participation rates vary by demographic characteristics, case or control status, or the type of cancer or disease under investigation. In a review of 365 epidemiologic studies published during 2003, Morton et al., \[[@pone.0127994.ref013]\] reported that participation rates declined during the 2007 to 2003 study period for all study designs, and that rates were reported in only 44% of case control studies. Over time, more studies collected biological samples but participation with biological sample collection was only reported in 27% of the studies overall and in 13% of the case-control studies. The authors emphasized the need to consistently report participation rates in all studies. Furthermore, there are few published studies reporting how participation rates, and those specifically for biological sample collection, are affected by potential confounding variables such as age, ethnicity, socioeconomic status, etc. A cross-sectional study \[[@pone.0127994.ref014]\] was conducted in 2010 to assess phytoestrogen intake among breast cancer patients and to determine: 1) the proportion of breast cancer cases willing to provide biological samples (spot or 24 hour urine, saliva and blood samples), and/or contact information for friends or colleagues for future control recruitment, and 2) if these proportions varied by age group (\<45 and 45+) and other factors such as ethnicity, education, income, body mass index (BMI), smoking status and alcohol consumption. These objectives were of interest as a larger case control study of young women with breast cancer and exposures to emerging environmental contaminants was planned, and it is now underway (the Ontario Environment and Health Study, OEHS)\[[@pone.0127994.ref015]\]. In the OEHS, women under the age of 45 (used as a proxy for menopausal status) are asked to provide questionnaire information (dietary and environmental) and biological samples (urine and blood) for biomarker analyses. Methods {#sec006} ======= Cases were Ontario women 25--74 years of age identified through the population-based Ontario Cancer Registry (OCR) ePATH system (electronic data transmission) as having a pathology confirmed first primary diagnosis of breast cancer between April and May 2010. Cases were sent a letter from the OCR notifying them they would be contacted to request their participation and were given a toll-free number to call (within 4 weeks) if they wished to opt out. A self-administered questionnaire and cover letter were mailed to cases 2 months post-diagnosis, followed by post-card reminders and a second questionnaire package if necessary. The questionnaire included items to measure phytoestrogen food and supplement intake, treatment information and subject characteristics. Additional details on study design and methods are provided in Boucher et al. \[[@pone.0127994.ref014]\] A series of questions was asked on willingness to provide biological samples (blood, saliva and urine), and to provide names and contact information for female friends and/or colleagues of a similar age. The research was approved by the Research Ethics Board at the University of Toronto. Questionnaire data were analyzed using SAS, Version 9.1. Proportions and 95% exact (Clopper-Pearson) binomial confidence intervals (CI) were estimated and Χ^2^ analyses of contingency tables were conducted to evaluate associations with categorical variables (i.e., age group, education, ethnicity, marital status, income, BMI, smoking, alcohol consumption) and the willingness to provide biological samples or contact information for friends,. Odds ratios (OR) and the associated 95% Wald CI were estimated using older cases as the referent group. Results {#sec007} ======= Of the 462 eligible cases identified by the OCR, 45 opted out of participation in research following contact by the OCR, leaving 417 cases that we were able to contact to request consent and participation in the study. Of the 417 cases contacted, there were 52 under the age of 45 and 365 aged 45+; 67% of these cases returned questionnaires. Characteristics of the responding breast cancer cases are presented in [Table 1](#pone.0127994.t001){ref-type="table"}. The majority of cases were older than 50 years and most had graduated or had some college or university education. Of the total 278 cases, there were 33 cases (12%) under age of 45, and 245 (88%) who were 45 years of age and older. This age dichotomization was used in in the analyses reported in [Table 2](#pone.0127994.t002){ref-type="table"}, where a description of participant willingness to provide samples and contact information for their friends is presented overall and stratified by age group. Cases were quite willing to provide blood samples, by either visiting a clinic (62%) or by having a nurse or technician visit their home (61%). Participants indicated they were most willing to provide saliva samples (73%). When stratified by age group, the younger cases (≤45) were consistently more likely to provide any of the biological samples, but differences between the two age groups were not statistically significant except for the morning urine sample. Younger cases were 3.1 times more likely to report they would collect a morning urine sample and courier it to our laboratory (95% CI: 1.15--8.35). Although younger cases were equally likely to indicate they would send in a saliva sample (84%) this was not a significantly higher positive response when compared to older women (71%). 10.1371/journal.pone.0127994.t001 ###### Descriptive characteristics of study participants (N = 278). {#pone.0127994.t001g} Characteristic Subjects ------------------------------------------------------------------------------- ---------- ----- *Age (years)* [^*a*^](#t001fn001){ref-type="table-fn"} *N* *%*     31 to 40 15 5%     41 to 50 56 20%     51 to 60 106 38%     61 to 71 101 36% *Education completed*     Some high school 29 11%     Graduated high school 61 22%     Some college or university 55 20%     Graduated college or university 128 47%     *Annual Income*     \< \$ 40,000 41 15%     \$ 40,000--59,999 41 15%     \$ 60,000--99,999 61 22%     \$100,000+ 62 23%     Prefer not to answer 66 24% *Ethnicity*     *Caucasian* 227 82%     *Southeast Asians* [^*b*^](#t001fn002){ref-type="table-fn"} 20 7%     *Other* [^*c*^](#t001fn003){ref-type="table-fn"} 30 11% *BMI* [^*d*^](#t001fn004){ref-type="table-fn"} *(kg/m* ^*2*^ *) one year ago*     \<18.5 (Underweight) 9 3%     18.5--24.9 (Normal weight) 111 42%     25.0--29.9 (Overweight) 89 33%     30+ (Obese) 58 22% *Alcohol intake (drinks/week)* [^*e*^](#t001fn005){ref-type="table-fn"}     Never 116 49%     1--6 64 27%     ≥7 56 24% *Smoking status*     Current 27 10%     Ever 101 37%     Never 146 53% ^*a*^ *Of the 278 cases there were 33 (12%) under the age of 45 and 245 (88%) 45 years of age and older* ^*b*^ Southeast Asian includes Japanese, Chinese ^c^ Other includes South Asian (eg. East India, Pakistan) and Black ^*d*^ BMI = body mass index ^e^Total drinks based on beer or hard cider (12 oz/350mL, wine (4 oz/120 mL), and sake, sherry, port, spirits, liqueurs, brandy or liquor (1 oz/30 mL) 10.1371/journal.pone.0127994.t002 ###### Overall and age related distribution of breast cancer cases willing to provide biological samples and contact information of friends and work colleagues. {#pone.0127994.t002g} Question Age (years) ------------------------------------------------------------------------------ ------------- ----- ----------- ---- ----- ----------- ----- ----- ----------- ------------------- *Go to a local clinic to give a blood sample*     Yes 161 62% \[56-68\] 23 72% \[56-87\] 138 61% \[55-67\] 1.63 (0.72--3.68)     No 97 38% 9 28% 88 39% *Have a nurse or technician visit your home to take a blood sample*     Yes 161 61% \[55-67\] 20 63% \[46-79\] 141 61% \[55-67\] 1.06 (0.50--2.23)     No 102 39% 12 37% 90 39% *Provide a saliva sample and mail it back to the study laboratory*     Yes 190 73% \[67-78\] 27 84% \[72-97\] 163 71% \[65-77\] 2,22 (0.82--6.00)     No 72 27% 5 16% 67 29% *Collect a morning urine sample and courier it to our laboratory*     Yes 170 66% \[60-72\] 27 84% \[72-97\] 143 64% \[57-70\] 3.09 (1.15--8.35)     No 87 34% 5 16% 82 36% *Collect your urine throughout a whole day and courier it to our laboratory*     Yes 130 52% \[45-58\] 21 66% \[49-82\] 109 50% \[43-56\] 1.94 (0.90--4.22)     No 122 48% 11 34% 111 50% *Provide the names and contact information for women of a similar age*     Yes 69 26% \[21-32\] 11 35% \[19-52\] 58 25% \[20-30\] 1.64 (0.74--3.63)     No 193 74% 20 65% 173 75% ^*a*^ CI = exact binomial confidence interval Overall, only 26% of cases indicated they would be willing to provide contact information to approach friends or work colleagues to act as study controls. A slightly larger percentage of younger cases indicated they would provide this information (35% vs. 25% in 45+yrs). When age was assessed using 10 year age groups significant differences between groups were observed (Χ^2^ = 12.3, p = 0.007). Cases aged 41--50 years were most likely to agree to provide contact information for friends (43%). Younger and older cases were less likely to agree (range 17--20%). In addition to the effects of age, the influence of education, ethnicity, income, BMI, smoking, and alcohol consumption on willingness to provide samples and contact information was assessed. Significant differences were not observed by smoking status or ethnic categories, but the majority of the sample was white (82%), with only 7% Southeast Asian and 11% in the other category, so the comparison lacked power. Educated cases, who graduated or completed some university or college were more likely than those who graduated or completed some high school, to report they would accept a nurse or technician visit to collect a blood sample in their home (OR = 2.15, 95% CI: 1.26--3.67). However, these women did not consistently indicate they would be more willing to provide other types of samples (blood in clinic, urine samples or saliva samples collected at home) or information to contact friends/colleagues to act as controls. No relationship between willingness to provide samples and reported income was observed. However, cases who "preferred not to answer" the annual income question were less willing than those in other income categories to indicate they would go to a clinic (52% vs. 59--75%), have a nurse visit (49% vs. 61--70%) or provide saliva (60% vs. 71--87%) or urine samples (morning urine: 55% vs. 65--79%; 24-hr urine 40% vs. 54--57%). Most of these differences were not significant. None of the underweight cases (0%, n = 7 women) indicated they would go to a local clinic to give a blood sample. The percentage of normal weight, overweight, and obese cases who would attend a clinic was significantly higher (63--66%; p = 0.007) and a similar but non-significant pattern was observed for agreeing to have a nurse visit in the home (29% of underweight, 55--69% of normal, overweight and obese). Finally, cases who consumed alcohol were significantly more likely to agree that they would provide contact information for friends. Only 1% of non-drinkers would provide this information, while 35% of moderate drinkers (1--6 drinks/week) and 32% of cases drinking 7 or more drinks per week (p = 0.048) agreed. Discussion {#sec008} ========== Increasingly, biological samples are collected in health studies and analyzed to provide estimates of exposures or to measure indicators of susceptibility or effect. Our study was designed to evaluate the willingness to provide these samples in women recently diagnosed with breast cancer and to evaluate whether younger women were more or less likely to agree to provide these samples. Overall, the willingness to provide samples was very similar to the actual provision of blood that was observed in the past among breast cancer patients. At the Ontario site of the Cooperative Family Registry for Breast Cancer Studies (CFRBCS) 57% of normal risk and 63% of women diagnosed with breast cancer, who met criteria for increased genetic risk, provided in-clinic blood samples in 1996 \[[@pone.0127994.ref016]\]. Almost 15 years later in our study, 62% indicated they would agree to go to a local clinic to provide a blood sample. In studies conducted internationally, participation rates have been somewhat higher. In the Long Island Breast Cancer Study Project (LIBCSP) with cases recruited between 1996 and 1997, 73% of case and control subjects donated a blood sample after completing the questionnaire \[[@pone.0127994.ref010],[@pone.0127994.ref011]\]. In the Shanghai Women's Health Study (1996--2000) blood samples were obtained from 82% of cases and 84% of controls after completing an in-person interview \[[@pone.0127994.ref008],[@pone.0127994.ref017]\]. Younger cases were somewhat less likely to indicate they would have a nurse or technician visit their home to collect a blood sample (63%) as compared to attending a local clinic (72%) and this difference was not apparent for older cases. This could be an indication of the willingness of younger cases to have unknown visitors in the home, their ability to travel to a clinic, their actual willingness to provide the sample or more likely, a combination of these factors. Many cases in our study would also agree to provide a morning or a 24-hr urine sample and most would agree to provide saliva samples. These observations are consistent with what has been reported previously in Ontario. In one of our recent studies, 72% of 5000 breast cancer cases and population-based controls from Ontario provided saliva samples, and the response rates did not vary between case/control status \[[@pone.0127994.ref006],[@pone.0127994.ref007]\]. Higher response rates were observed in a population-based breast cancer case control study in Wisconsin (2004--2005), where 90% of both cases and controls returned urine samples following completion of an interview. Similarly, 93% of cases and 83% of controls donated a spot urine sample in LIBCSP \[[@pone.0127994.ref010],[@pone.0127994.ref011]\]. In our study, younger cases consistently indicated they were more likely to provide any type of biological sample, although these differences were generally not significant. They were significantly more likely to agree to provide a morning urine sample and ship it back to a laboratory than the older cases, but not whole day urine samples (24 hours) or saliva samples. We do not have an explanation for the increased willingness over older cases to provide a urine spot sample. We expected younger women to be less likely to agree due to time constraints which could include competing demands of children, aging parents, and full time employment during a cancer diagnosis. It is possible that younger women may be more motivated overall to provide biological samples in a search for the cause of their disease \[[@pone.0127994.ref010],[@pone.0127994.ref011]\]. Cases who were underweight were less likely to agree to provide biological samples. Since self-reported pre-diagnosis weight (one year ago) was used to calculate BMI, it is unlikely that the low BMI is an indicator of more advanced disease, which could in part explain a lower response rate. In the LIBCSP, investigators found that increasing age and past smoking decreased likelihood that a respondent would donate blood. Subjects who identified as "white" or "other" and those who used alcohol were more likely to provide blood samples \[[@pone.0127994.ref011]\]. Similarly, in the Ontario CFRBCS, non- whites were less likely to provide blood samples (35% vs. 60% in white women and men with breast cancer) \[[@pone.0127994.ref016]\]. In our study, cases who drank alcohol (moderate or heavier use) were more likely to agree that they would provide contact information of friends/colleagues but were not more likely to agree to provide biological samples. Overall, it is likely that female subjects enrolled in case-control studies of earlier onset breast cancer will agree to provide samples at slightly higher rates than those reported here. Our questions were hypothetical. In an etiologic study, following completion of dietary and other environmental questionnaires, subjects may be more interested and motivated to provide samples once an understanding of the study, its methods, and the investigators is gained. However, it is important to note that the potential participation/response rates were calculated using the "participants of the survey" as the denominator. Our actual response rate based on the population-based OCR would be lower since of the 462 eligible women identified by the OCR, 45 (9.7%) opted out and of the 417 remaining only 67% returned the completed questionnaires. Thus, if the total 462 eligible cases are used as the denominator (instead of 278), the overall response rates would be approximately half of those reported in [Table 2](#pone.0127994.t002){ref-type="table"}. For example, only 35% of the cases would "go to a local clinic to give a blood sample" if the total eligible sample is used. In case-control studies of cancer that collect biological samples, we would only invite those women who consent to participate in the research and also fully complete questionnaire information on risk factors and important confounders. Thus, our expectation for overall response rates for biological sample collection from eligible cases are lower than those reported in [Table 2](#pone.0127994.t002){ref-type="table"}. Finally, in earlier focus group work we conducted in young women free of cancer, all indicated they would enroll in a study if a friend or a work colleague asked them and they would provide blood and/or urine samples \[[@pone.0127994.ref017]\]. These results were encouraging and we proposed to evaluate this method in cases with breast cancer to determine the feasibility for future studies, particularly the OEHS. We did not expect to find such low percentages of women (26%) willing to provide contact information for potential controls. This did not vary by education, race or age, but did vary by alcohol consumption and resulted in a decision to select an alternate method for the OEHS. It is possible that cases view their diagnosis as private, may not want to burden their friends, or have friends who are unaware of their diagnosis since we contacted them within 4 weeks of receiving a pathology report. It is likely that alternate methods of control recruitment, such as using social networking sites, may be more feasible in these younger populations. In conclusion, the results of our study indicate that reasonable response rates for biological sample collection could be expected in future case-control studies of breast cancer in both younger and older women, but that other methods to select controls must be devised. The authors wish to thank the Study Coordinator, Ioan Curca. [^1]: **Competing Interests:**The authors have declared that no competing interests exist. [^2]: Conceived and designed the experiments: SH BB MC. Performed the experiments: SH BB MC. Analyzed the data: SH. Wrote the paper: SH BB MC.

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Introduction {#Sec1} ============ In this study, we consider a class of expanding channel flows in which the inflow is non-uniform. Expanding channels, known as diffusers, have the function of converting high-speed low-pressure flow to low-speed high-pressure flow. Diffusers have numerous applications, from turbines in aerospace to hydropower \[[@CR1]--[@CR3]\] to automotive design \[[@CR4]\]. There is a large body of literature on diffusers in the case where the inflow is uniform (see \[[@CR5]\]), but only a limited literature available for non-uniform inlet flows \[[@CR6]\]. In the case where the inflow is uniform, diffusers are usually designed to be straight sided, and the expansion angle is critical to performance \[[@CR5]\]. The optimal angle strikes a balance between not being too shallow, since thin channels have larger wall drag, and not being too wide, since wide expansion angles result in boundary layer separation and poor consequent pressure recovery \[[@CR7]\]. The optimum angle varies slightly, depending on the inflow boundary layer thickness, and whether the diffuser is two-dimensional or axisymmetric. In the case where the inflow is non-uniform, there have been some experimental studies which have investigated diffuser performance for specific inflow profiles. Horlock and Lewis \[[@CR8]\] studied an asymmetric shear flow and a symmetric wake flow in a linearly expanding two-dimensional diffuser using a simple inviscid model and experiments. They found that both of these non-uniform flow profiles became accentuated by the diffuser. The experiments of Wolf and Johnston \[[@CR9]\] studied several non-uniform inlet flows for a two-dimensional diffuser. They considered an asymmetric flow profile with uniform shear, an asymmetric step-shear profile, a symmetric jet profile, and a symmetric wake profile. For each case, they studied straight sided diffusers with linearly expanding walls, using several different expansion angles and non-dimensional lengths. They found that these non-uniform inflows resulted in poorer diffuser performance than for a uniform inflow. They attributed this to the early onset of diffuser stall observed for these non-uniform inflows due to the accentuation of the flow profile. Other experimental studies are given by \[[@CR10]--[@CR16]\]. As is shown by Wolf and Johnston \[[@CR9]\], the development of the non-uniform flow profile is strongly affected by the shape of the diffuser. An important feature in understanding non-uniform flows is the interplay between changes in the pressure and the kinetic energy flux factor, which is a normalised measure of how non-uniform a flow is \[[@CR5]\]. A decrease in kinetic energy flux factor corresponds to a more uniform flow, and a rise in pressure. As shown by \[[@CR8], [@CR9]\], diffusers with wide angles have the tendency to accentuate non-uniform flows and, in some extreme cases, create a jet-like outflow. In such cases, the outflow has a high-kinetic energy flux and, hence, a low-pressure recovery. On the other hand, diffusers with shallow angles have longer, narrower profiles, which create a lot of wall drag and consequently a larger drop in pressure. Optimal diffuser shapes, therefore, must strike a balance between mixing the flow in a narrow section and then widening the flow to decrease wall drag. In this paper, we identify the optimal diffuser shape which satisfies these criteria. In contrast to diffusers with uniform inflow, where the channel shape is only restricted due to boundary layer separation, diffusers with non-uniform inflow have a shape which is also restricted due to the effect of accentuating the non-uniform flow. We find that in some cases, the optimal diffuser angle for non-uniform flow is smaller than that typically used for diffusers with uniform inflow. Furthermore, we show that, unlike for uniform flow, optimal diffuser shapes for non-uniform flow may contain an initial straight section that helps mix the flow before diffusing. Therefore, from a design perspective, the effect of the inflow profile cannot be ignored. In our analysis, we show how to optimise diffuser design based on the nature of the non-uniform inflow. We investigate three different classes of non-uniform inflow, with the axial velocity varying across the width of the diffuser entrance. The first case has inner and outer streams of different speeds, with a velocity jump between them that evolves into a shear layer downstream, and the shear layer eventually interacts with the channel walls. The second case is the limit where the speeds of the streams are similar, creating a thin, slowly growing shear layer. In the third case, the inflow is a pure shear profile, with linear velocity variation between the centre and outer edge of the diffuser. These flow profiles are motivated by a low-head hydropower application, where the inner and outer streams are formed by a Venturi pipe which accelerates part of the flow in order to amplify the pressure drop across a turbine. For these non-uniform flows which we consider, the development of the flow profile, which is fundamental to pressure recovery, can be described using a simple model for turbulent shear layers in confining channels \[[@CR6]\]. The model assumes that the flow is composed of uniform streams separated by a linear shear layer. Wall drag is incorporated into the model with a friction factor, and the growth of the shear layers is modelled with a spreading parameter. As was shown by Benham et al. \[[@CR6]\], the model predictions have good agreement with both CFD and experimental work for a range of channel shapes and Reynolds numbers. We restrict our attention to slender diffuser shapes, since our model, which is based on integrated equations of mass and momentum, applies to long and thin domains which are slowly varying. In this way, we avoid situations where there is boundary layer separation, which is not included in our model. The effects of boundary layer separation have been described analytically in several recent studies \[[@CR17]--[@CR22]\]. Smith et al. \[[@CR20]\] used a streamfunction formulation and asymptotic analysis to study the complex boundary layer structures that arise for a breakaway separation, and they calculated the corresponding separation point. Furthermore, for such separated flows, the analytical results of Kluwick and Scheichl \[[@CR19]\] described how the velocity deficit between the outer flow and the flow in the boundary layer is related to the Reynolds shear stress. These studies are useful in determining the near-wall behaviour of the flow when there are strong adverse pressure gradients that cause separation. However, for the flows we consider in this study, we restrict our attention to diffuser shapes that are sufficiently slender that there is no risk of separation. Instead, we focus on the relationship between the diffuser shape and the development of the non-uniform bulk flow away from the walls. The simple model which we use to describe the flow, was applied by Benham et al. \[[@CR6]\] to investigate pressure recovery of a simple class of diffuser shapes by exhaustively searching a restricted design space. When we widen the parameter space and treat the diffuser shape as a continuous control, it is necessary to seek more complex tools to solve the problem. In this paper, we use the model as the basis for numerical optimisation of the diffuser shape, where the governing equations form the optimisation constraints. Such problems, as well as PDE-constrained optimisation problems, often arise in the field of flow control. With the advancement of computational power, these problems have become more feasible to solve. There are many different approaches to solving such problems which are discussed by Gunzburger \[[@CR23]\]. In our approach, we exploit the fact that the model is one-dimensional and, upon discretisation, there are relatively few decision variables. This, in combination with the use of automatic differentiation to calculate gradients, allows us to use an interior point Newton method with relatively low computational effort \[[@CR24]\]. In certain limiting cases, we solve the optimal control problem analytically using Pontragin's maximum principle \[[@CR25]\] and these analytical results aid interpretation of the results from the numerical optimisation. We show that some of the optimal diffuser shapes look approximately like they are composed of piecewise linear sections. This motivates a low-dimensional parameterisation of the diffuser shapes, for which we use more detailed and computationally intensive CFD models to search for optima under more realistic flow behaviours. The two CFD models we use are a *k*--$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\epsilon $$\end{document}$ \[[@CR26]\] and a *k*--$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega $$\end{document}$ Shear Stress Transport (SST) \[[@CR27]\] turbulence model. We find that the optimal diffuser shapes for both these CFD models are very similar to those found using our reduced model. Section [2](#Sec2){ref-type="sec"} outlines the model for the non-uniform flow profiles we consider and sets up the optimal control problem, discussing the choice of objective, the constraints, the number of parameters, and the optimisation approaches. In Sect. [3](#Sec8){ref-type="sec"}, we use a numerical optimisation approach to solve the optimal control problem and find optimal diffuser shapes in three different cases. In Sect. [4](#Sec12){ref-type="sec"}, we find analytical solutions to the optimal control problem in the last two of these cases. In Sect. [5](#Sec15){ref-type="sec"}, we present some CFD calculations and compare them to the results of the optimisation. Sect. [6](#Sec16){ref-type="sec"} summarises the results of the paper and discusses the dependence of the optimal shapes on parameter choices.Fig. 1Schematic diagram of the different flow cases. **a** *Developing shear layer case*, where the inflow has inner and outer streams of different speeds, with a velocity jump between them that develops into a shear layer. The channel length is sufficiently large such that the growing shear layer reaches across the channel. **b** *Small shear limit* case, which is the limiting case where the speeds of the streams are similar, such that the thin, slowly growing shear layer never reaches across the channel. **c** *Pure shear limit*, where the velocity varies linearly between the centre and the outer wall of the diffuser The model and optimal control problem {#Sec2} ===================================== Modelling turbulent shear layers in confining channels {#Sec3} ------------------------------------------------------ In this section, we describe the flow scenarios which we consider and outline the simple model, previously presented by Benham et al. \[[@CR6]\], which we use to describe these flows. This model is based on integrated conservation of mass and momentum equations in a long and thin geometry, as well as Bernoulli's equation, which govern an idealised time-averaged flow profile. A friction factor is used to parameterise the effect of wall drag, whilst a spreading parameter models the growth of shear layers. We restrict our attention to slender diffuser shapes with a small expansion angle, such that boundary layer separation is avoided. There are three different types of non-uniform channel flow we consider, all of which are symmetric about the channel centreline. In Fig. [1](#Fig1){ref-type="fig"}, we display each case, illustrating the axial velocity varying across the width of the diffuser. The first, which we call the *Developing shear layer case*, is an inflow composed of inner and outer streams of different speeds, with a velocity jump in between. In this case, a shear layer forms between the streams and grows downstream, eventually interacting with the channel walls. We restrict our attention to situations where the inner stream is slower than the outer stream. In other situations where the outer stream is slower than the inner stream, there is a greater risk of boundary layer separation, since the slowest region of flow is next to the wall \[[@CR5]\]. Furthermore, it is well known that asymmetric flow instabilities, such as the Coanda effect \[[@CR28]\], can occur in these situations, which we do not try to model here. The second case, called the *Small shear limit*, is similar to the first case, except the inner and outer streams have near-identical velocities, such that the shear between the flows is small and the thin shear layer grows slowly. In the third case, called the *Pure shear limit*, we consider a pure shear profile with linear velocity variation between the centre and outer edge of the diffuser. This corresponds to the first case in the downstream limit, where the shear layer has reached across the entire channel.Fig. 2Schematic diagram of symmetric flow in a half channel. We model the flow as plug flow regions separated by a linear turbulent shear layer. The model governs a reduced number of variables $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$U_1$$\end{document}$, $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$U_2$$\end{document}$, $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h_1$$\end{document}$, $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h_2$$\end{document}$, $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\delta $$\end{document}$, $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varepsilon _y$$\end{document}$ and *p*, which are all functions of *x*. The aspect ratio is exaggerated for illustration purposes The simple model, presented by Benham et al. \[[@CR6]\], is used to describe the idealised flow profiles for each of the three cases. The first two cases share the same formulation, whilst the third case is slightly different. Thus, we start by describing the governing equations for the first and second cases. Initially, we consider two-dimensional flow in a half channel $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0<y<h(x)$$\end{document}$ and, later, we extend the model to axisymmetric channels (see Fig. [1](#Fig1){ref-type="fig"}a, where we indicate our coordinate axes). The inflow for the first two cases is composed of a slower moving central stream with speed $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$U_2$$\end{document}$ and a faster outer stream with speed $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$U_1$$\end{document}$. A turbulent shear layer forms at the place where the parallel streams meet. We approximate the flow profile by decomposing it into two plug regions separated by a shear layer in which the velocity varies linearly between $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$U_1$$\end{document}$ and $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$U_2$$\end{document}$ (see Fig. [2](#Fig2){ref-type="fig"}). The approximate velocity profile is$$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} {u(x,y)={\left\{ \begin{array}{ll} U_{2} (x)&{}: 0<y<h_2(x),\\ U_2 (x)+\varepsilon _y (x) \left( y-h_2 (x)\right) &{}: h_2 (x)<y<h (x)-h_1 (x),\\ U_{1} (x) &{}: h (x)-h_1 (x)<y<h (x), \end{array}\right. }} \end{aligned}$$\end{document}$$where $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h_1$$\end{document}$ and $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h_2$$\end{document}$ are the widths of the two plug regions, $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\delta =h-h_1-h_2$$\end{document}$ is the width of the shear layer, and $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varepsilon _y = (U_1-U_2)/\delta $$\end{document}$ is the shear rate. In the small shear limit, the plug flow speeds $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$U_{1}$$\end{document}$ and $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$U_{2}$$\end{document}$ are similar, such that the shear layer grows slowly. Whilst in the developing shear layer case, the shear layer may grow and interact with the channel walls, in the small shear limit, the channel is chosen to be sufficiently short that the slowly growing shear layer remains thin. However, in both cases, the shear rate decays with *x* as the shear layer grows \[[@CR29]\]. We assume that the shear rate decays according to$$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \frac{U_1+U_2}{2}\frac{\mathrm{d} \varepsilon _y}{\mathrm{d}x}=-S\varepsilon _y^2, \end{aligned}$$\end{document}$$where *S* is a non-dimensional spreading parameter which must be determined from experiments or by comparison with CFD. Equation ([2](#Equ2){ref-type=""}) can be derived from an entrainment argument (see Appendix in \[[@CR6]\]), or by analogy with the growth of free shear layers. Assuming that the channel is long and thin, boundary layer theory \[[@CR29]\] indicates that, to good approximation, the pressure does not vary across the channel width $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p=p(x)$$\end{document}$. Averaged across the channel, conservation of mass and momentum equations are$$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned}&\int _0^h u\, \mathrm{d}y = Q, \end{aligned}$$\end{document}$$ $$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned}&\frac{\mathrm{d}}{\mathrm{d} x}\left( \int _0^h \rho u^2\, \mathrm{d}y \right) +h\frac{\mathrm{d} p}{\mathrm{d} x}=\tau _\mathrm{w}, \end{aligned}$$\end{document}$$where $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rho $$\end{document}$ is the density, *Q* is the constant flow rate (per unit depth), and $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau _\mathrm{w}$$\end{document}$ is the wall shear stress. We parameterise the wall stress term with a friction factor *f*, such that $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau _\mathrm{w}=-1/8f\rho U_1^2$$\end{document}$. We model the friction factor with the Blasius relationship, $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f=0.316Re^{-1/4}$$\end{document}$, for flow in smooth pipes \[[@CR30], [@CR31]\]. For all the examples we consider in this study, we use a finite value for the Reynolds number. For example, if $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Re=10^6$$\end{document}$, then $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f=0.01$$\end{document}$. Although this friction factor is small, over the long diffuser length scales we consider, the effect of wall drag on pressure variations is significant. Finally, we ignore viscous dissipation in the plug flow regions, since it is small compared to that at the walls and in the shear layer. Hence, in the plug regions, we assume Bernoulli's equation holds \[[@CR32]\]. In certain cases, especially when the diffuser angle is wide, the speed of the slower plug region $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$U_2$$\end{document}$ may decrease and reach zero. This has been observed in CFD simulations, which we display in Appendix A. In such cases, there is a portion of recirculating flow in the central part of the diffuser. We do not resolve the recirculation in these regions but since velocities are small, as observed in CFD, we treat the regions as stagnant zones with zero velocity (see Fig. [3](#Fig3){ref-type="fig"}). Bernoulli's equation in each plug region holds along streamlines, ignoring transverse velocity components since they are small, and is implemented in a complementarity format for convenience$$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned}&h_1\left( p-p(0)+\frac{1}{2}\rho (U_1^2- U_{1}(0)^2)\right) =0,\quad \mathrm {and}\quad h_1\ge 0, \end{aligned}$$\end{document}$$ $$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned}&U_2h_2\left( p-p(0)+\frac{1}{2}\rho (U_2^2- U_{2}(0)^2)\right) =0,\quad \mathrm {and}\quad h_2\ge 0, \quad U_2\ge 0. \end{aligned}$$\end{document}$$The complementarity format of Eqs. ([5](#Equ5){ref-type=""}) and ([6](#Equ6){ref-type=""}) ensures that when either of the plug regions disappears, or if the slower plug region stagnates, Bernoulli's equation ceases to hold in that region. We find good comparison between our model predictions of the stagnant region and CFD calculations, which we discuss in Appendix A.Fig. 3Schematic diagram of stagnated flow in a diffuser, where the slower plug region decelerates and reaches zero velocity. This can occur if the inflow is sufficiently non-uniform, or if the diffuser angle is sufficiently large To summarise the first and second cases, the simple model describes the evolution of the non-uniform velocity profile *u*(*x*, *y*), given by ([1](#Equ1){ref-type=""}), and pressure *p*(*x*) in a symmetric confining channel. Equations ([2](#Equ2){ref-type=""})--([6](#Equ6){ref-type=""}) govern the variables $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$U_1$$\end{document}$, $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$U_2$$\end{document}$, $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h_1$$\end{document}$, $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h_2$$\end{document}$, $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\delta $$\end{document}$, $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varepsilon _y$$\end{document}$ and *p*, which are all functions of *x*. These equations can be solved for all *x* given inflow conditions at $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x=0$$\end{document}$. Since the shear layer forms at $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x=0$$\end{document}$, the inflow conditions for $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\delta $$\end{document}$ and $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varepsilon _y$$\end{document}$ are $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\delta (0)=0$$\end{document}$ and $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varepsilon _y(0)=\infty $$\end{document}$. Pressure is measured with reference to the value at the inlet so we can take $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p(0)=0$$\end{document}$ without loss of generality. All other inflow conditions form part of the set of parameters which we discuss in Sect. [2.2](#Sec4){ref-type="sec"}. In the pure shear limit, the plug regions are non-existent, such that $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h_1=h_2=0$$\end{document}$ and $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\delta =h$$\end{document}$. Then the velocity profile takes the form$$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} u(x,y)=U_2(x)+\varepsilon _y(x)y. \end{aligned}$$\end{document}$$In this case, the governing equations of the model reduce to ([2](#Equ2){ref-type=""})--([4](#Equ4){ref-type=""}) and ([7](#Equ7){ref-type=""}), which govern the variables $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$U_1$$\end{document}$, $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$U_2$$\end{document}$, $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varepsilon _y$$\end{document}$ and *p*. We can extend the model to account for axisymmetric flows simply. For axisymmetric flow in a cylindrical channel $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0\le r\le h$$\end{document}$, we assume that that the velocity profile is identical to Eq. ([1](#Equ1){ref-type=""}) in the first two cases, and ([7](#Equ7){ref-type=""}) in the third case, except with *y* replaced by *r*. In the axisymmetric version of the model, Eqs. ([2](#Equ2){ref-type=""}) and ([5](#Equ5){ref-type=""})--([6](#Equ6){ref-type=""}) remain unchanged, but Eqs. ([3](#Equ3){ref-type=""}) and ([4](#Equ4){ref-type=""}) are altered to account for radial symmetry$$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned}&2 \pi \int _0^h u r\, \mathrm{d}r = Q, \end{aligned}$$\end{document}$$ $$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned}&2\pi \frac{\mathrm{d}}{\mathrm{d} x}\left( \int _0^h \rho u^2 r\, \mathrm{d}r \right) +\pi h^2 \frac{\mathrm{d} p}{\mathrm{d} x}=2\pi h\tau _\mathrm{w}. \end{aligned}$$\end{document}$$The results of the axisymmetric and two-dimensional cases are compared in Sect. [3](#Sec8){ref-type="sec"}. Formulation of the optimal control problem {#Sec4} ------------------------------------------ In this section, we describe the optimal control problem by choosing an optimisation objective and formulating the control variables and contstraints. Starting with the objective, we note that diffuser performance can be measured in a number of different ways, for example using a pressure recovery coefficient or a loss coefficient \[[@CR5]\]. The pressure recovery coefficient $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_p$$\end{document}$ is a measure of the pressure gain in the diffuser from inlet to outlet, relative to the kinetic energy flux at the inlet. The loss coefficient $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$K_l$$\end{document}$ is a measure of the total energy lost from inlet to outlet, relative to the kinetic energy flux at the inlet. For our optimal control problem, we could choose either of these coefficients as the objective. Maximising $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_p$$\end{document}$, for a given inflow, would produce the diffuser that converts the greatest amount of inflow kinetic energy into static pressure at the outflow. Minimising $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$K_l$$\end{document}$, for a given inflow, would produce the diffuser with the maximum amount of energy at the outflow. For this paper, we choose the pressure recovery coefficient as the objective. There are several ways to define the coefficient, but we shall use the so-called "mass-averaged" pressure recovery \[[@CR11]\], which is defined as$$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} C_p=\frac{\int _0^h u p \,\mathrm{d}y |_{x=L} - \int _0^h u p \,\mathrm{d}y |_{x=0}}{\int _0^h \frac{1}{2}\rho u^3 \,\mathrm{d}y |_{x=0} } \end{aligned}$$\end{document}$$for the two-dimensional case and$$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} C_p=\frac{\int _0^h u p r\,\mathrm{d}r |_{x=L} - \int _0^h u p r\,\mathrm{d}r |_{x=0}}{\int _0^h \frac{1}{2}\rho u^3 r \,\mathrm{d}r |_{x=0} } \end{aligned}$$\end{document}$$for the axisymmetric case. The pressure recovery coefficient can take values $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_p\in (-\infty ,1]$$\end{document}$, where $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_p=1$$\end{document}$ when all the kinetic energy of the inlet flow is converted into static pressure. For a given area ratio *h*(*L*) / *h*(0) and inflow, there is a maximum possible pressure recovery $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_{p_I}\le 1$$\end{document}$ \[[@CR5]\]. For uniform inviscid flow this ideal limit is $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_{p_I}=1-\left( h(0)/h(L)\right) ^2$$\end{document}$ in the two-dimensional case and $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_{p_I}=1-\left( h(0)/h(L)\right) ^4$$\end{document}$ in the axisymmetric case, but for non-uniform flow it is not known what the limit is. Now that we have chosen a suitable objective for the optimisation, we need to define a control. The diffuser shape is ultimately the control of the problem, but there are several different ways to formulate it. For example, we could use the shape function *h*(*x*) as the control, or we could use its derivative, or even the second derivative. To aid our choice of control, we consider the regularity requirements of the final shape. If the minimum requirement is that the shape be continuous, it will be convenient to choose the derivative of *h* as the control. If we also require smoothness (i.e. existence of the first derivative of *h*), then it will be convenient to choose the second derivative of *h* as the control. However, if no such requirements exist, then it is satisfactory to use *h* itself as the control. For this paper, we restrict ourselves to continuous but non-smooth shapes, and so we choose the shape derivative, or diffuser angle,$$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \alpha (x)=\frac{\mathrm{d}h}{\mathrm{d}x}, \end{aligned}$$\end{document}$$as the control for optimising the diffuser shape. In reality, sudden expansions and sharp corners, if severe enough, can cause flow separation which is detrimental to pressure recovery \[[@CR5]\]. Therefore, any such sharp corners must be rounded off with a suitable radius of curvature, upon construction. However, we neglect this concern from our mathematical analysis. An additional possible control of the problem is the channel length *L*. For now, we consider this fixed, but later we discuss the possibility of including *L* as a free parameter. After defining both the objective and the control of the optimisation, we now discuss the constraints. The most obvious constraints on the variables are the governing equations and inflow conditions. In addition, we may also want some constraints on the outflow. As mentioned earlier, constraining *h*(*L*) / *h*(0) gives us a fixed maximum value for the pressure recovery. If *h*(*L*) / *h*(0) is unconstrained, then the pressure recovery will be maximised with $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h(L)/h(0)=\infty $$\end{document}$ \[[@CR5]\]. However, this is impractical for construction and, due to Bernoulli's equation, we see that pressure recovery decays rapidly with *h* (like $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sim 1/h^2$$\end{document}$ for two-dimensional flows and like $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sim 1/h^4$$\end{document}$ for axisymmetric flows) so that a large majority of pressure is recovered for relatively small values of *h*(*L*) / *h*(0). For example, if $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h(L)/h(0)=3$$\end{document}$ in uniform inviscid axisymmetric flow, the pressure recovery is $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_{p_I}\approx 0.99$$\end{document}$. Therefore, for practical considerations, we constrain the channel width at the outflow$$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} h(L)=h_L. \end{aligned}$$\end{document}$$Another important constraint we need to consider is the boundedness of the control $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}$. In particular, we note that for large values of the diffuser angle, boundary layers at the channel walls have the tendency to separate \[[@CR7]\]. This phenomenon, which is often called 'diffuser stall', is not something that we attempt to capture with our model. However, it is known that diffuser stall has a detrimental effect on pressure recovery (because the flow does not slow down). Considering this, we give the control $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}$ an upper bound corresponding to the smallest diffuser angle which causes stall. The first appreciable stall of a straight walled diffuser is at $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha \approx \tan 7^\circ $$\end{document}$ for the two-dimensional case and $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha \approx \tan 3.5^\circ $$\end{document}$ for axisymmetric diffusers \[[@CR5]\]. Furthermore, due to engineering constraints, it might not always be possible to construct channel shapes which contract more than a certain angle. Therefore, a lower bound on the control may also be necessary. If we denote the upper and lower bounds $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha _\mathrm{max}$$\end{document}$ and $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha _\mathrm{min}$$\end{document}$, respectively, then $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}$ satisfies the box constraints$$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \alpha _\mathrm{min}\le \alpha \le \alpha _\mathrm{max}. \end{aligned}$$\end{document}$$It should be noted that, whilst Eq. ([14](#Equ14){ref-type=""}) applies, the optimal control might not necessarily attain these bounding values. In such cases, Eq. ([14](#Equ14){ref-type=""}) may be considered irrelevant. To summarise the formulation of the optimal control problem, we seek to maximise the pressure recovery by manipulating the control $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha (x)$$\end{document}$ within its bounds:$$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \max _{\alpha _\mathrm{min}\le \alpha (x)\le \alpha _\mathrm{max}} C_p, \end{aligned}$$\end{document}$$with the constraints that Eqs. ([2](#Equ2){ref-type=""})--([6](#Equ6){ref-type=""}) hold, together with inlet conditions for all variables at $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x=0$$\end{document}$, and the end constraint ([13](#Equ13){ref-type=""}). Before moving on to the optimisation approaches, we note that there are several parameters which affect the solution. We list these parameters in Table [1](#Tab1){ref-type="table"} and discuss them in more detail in Sect. [6](#Sec16){ref-type="sec"}.Table 1List of the parameters of the optimal control problem. We treat the first 5 of these parameters as problem-specific, whereas the last 2 parameters are considered fixed. We also make use of the shorthand $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h_0=h(0)$$\end{document}$ and $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$U_0=U_1(0)$$\end{document}$$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$U_2(0)/U_0$$\end{document}$Velocity ratio$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h_2(0)/h_0$$\end{document}$Plug width ratio$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h(L)/h_0$$\end{document}$Expansion ratio$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L/h_0$$\end{document}$Length ratio$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha _\mathrm{min},\, \alpha _\mathrm{max}$$\end{document}$Minimum/maximum angle*S*Spreading parameter*f*Friction factor Optimisation approaches {#Sec5} ----------------------- Here, we describe the two main approaches we use to solve the optimisation problem. The first is a numerical approach, and the second is an analytical approach which uses Pontryagin's maximum principle. In each case, we give a brief description of the background theory, without going into depth. For a more thorough discussion, the reader is directed to the references in the text. ### Numerical optimisation approach {#Sec6} For the numerical optimisation approach, we solve the optimisation problem ([15](#Equ15){ref-type=""}) by discretising space, introducing values of the variables $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$U_1$$\end{document}$, $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$U_2$$\end{document}$, $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h_1$$\end{document}$, $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h_2$$\end{document}$, $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\delta $$\end{document}$, $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varepsilon _y$$\end{document}$ and *p* at each spatial point, and treating each discretised value as a degree of freedom. We use an interior point Newton method \[[@CR24]\] (with the IpOpt library \[[@CR33]\]) for nonlinear-constrained optimisation problems. Gradients are calculated using automatic differentiation in the JuMP package \[[@CR34]\] of the Julia programming language \[[@CR35]\]. The equality constraints we need to impose are Eqs. ([2](#Equ2){ref-type=""})--([6](#Equ6){ref-type=""}), inlet conditions and the terminal condition ([13](#Equ13){ref-type=""}). There are also the inequality constraints ([14](#Equ14){ref-type=""}) and those listed in the complementarity condition ([5](#Equ5){ref-type=""})--([6](#Equ6){ref-type=""}). As is often done, we impose the equality constraints using the quadratic penalty method \[[@CR24]\], where we subtract their residual squared from the objective. For example, if our objective is to maximise the function *g*(*x*) subject to the equality constraint $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$c(x)=0$$\end{document}$, then we replace the objective with$$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \max _{x} \quad \left( g(x)-\mu c(x)^2\right) , \end{aligned}$$\end{document}$$where $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu $$\end{document}$ is a penalty parameter. The interpretation of ([16](#Equ16){ref-type=""}) is that by maximising $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$g-\mu c^2$$\end{document}$, we try to find the value of *x* that makes *g* as large as possible (to increase the objective value) and $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$c^2$$\end{document}$ as small as possible (to impose the constraint equation). The value of $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu $$\end{document}$ must be chosen to be sufficiently large that the constraint equation is imposed accurately, but not too large that the problem becomes numerically ill-conditioned. Our inequality constraints are simple box constraints. These are dealt with by the interior point method using logarithmic barrier functions. More details, including how to choose the penalty parameter $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu $$\end{document}$ and barrier functions, are discussed by Nocedal and Wright \[[@CR24]\]. It is not known whether this optimisation problem is convex so there may exist multiple solutions. In order to have confidence about the optimal solutions that are found, we use many different initial guesses to initialise the interior point method (although we have not yet found any multiple solutions). The governing equations of the model consist of the algebraic equations, which are ([3](#Equ3){ref-type=""}), ([5](#Equ5){ref-type=""})--([6](#Equ6){ref-type=""}) and inflow conditions, and the differential equations which are ([2](#Equ2){ref-type=""}) and ([4](#Equ4){ref-type=""}). We discretise space into *n* points and impose the algebraic equations exactly at every point. The differential equations are imposed using a second order backward finite difference scheme. It should be noted that whilst the complementarity conditions enforce a switch in the governing equations and may produce non-smooth behaviour in the solution, the equations themselves are smooth and can therefore be differentiated. Computation time is fast, owing to the use of automatic differentiation to calculate gradients (as opposed to finite differencing, for example). With 8 variables $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$U_1, U_2,h_1,h_2,\delta ,\varepsilon _y,p,h$$\end{document}$ and one control $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}$, the total number of degrees of freedom is 9*n*. For a discretisation of $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n=100$$\end{document}$ grid points, and therefore 900 degrees of freedom, computation time is of the order of less than 10 s on a laptop computer. ### Analytical optimisation approach {#Sec7} In the case of the small shear limit and the pure shear limit, we use an analytical optimisation approach. In this approach, we simplify the governing equations of our model (which are ([2](#Equ2){ref-type=""})--([6](#Equ6){ref-type=""}) for the small shear limit and ([2](#Equ2){ref-type=""})--([4](#Equ4){ref-type=""}), ([7](#Equ7){ref-type=""}) for the pure shear limit), and we solve the simplified optimal control problem using Pontryagin's maximum principle \[[@CR25], [@CR36]\]. Here, we briefly outline the mathematical details of Pontryagin's maximum principle which we will use later in Sects. [4.1](#Sec13){ref-type="sec"} and [4.2](#Sec14){ref-type="sec"}. For the purpose of this outline, we consider a simplified optimal control problem in which a variable *y*(*x*) is controlled by a control $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha (x)$$\end{document}$ and the domain is defined by $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0\le x\le L$$\end{document}$. We consider an objective functional$$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \max _{\alpha (x)}\,J\left( \alpha (x)\right) :=\int _0^L F\left( x,y(x),\alpha (x)\right) \,\mathrm{d}x+\varPhi \left( y(L)\right) , \end{aligned}$$\end{document}$$for some given functions *F* and $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varPhi $$\end{document}$, subject to the ordinary differential equation$$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \frac{\mathrm{d}y}{\mathrm{d}x}=G\left( x,y(x),\alpha (x)\right) , \end{aligned}$$\end{document}$$and initial/terminal conditions. We assume that the control $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha (x)$$\end{document}$ is piecewise continuous, *y*(*x*) is absolutely continuous and *F* and *G* are of class $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C^2$$\end{document}$ in *y* and $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}$, and piecewise continuous in *x* \[[@CR36]\]. The Hamiltonian is defined as$$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} H=F+\lambda G, \end{aligned}$$\end{document}$$where $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda (x)$$\end{document}$ is the adjoint variable (or Lagrange multiplier). The set of equations which govern the state variable *y*, the adjoint variable $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda $$\end{document}$ and the control $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}$, are known as Pontryagin's maximum principle, and these equations are$$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned}&\frac{\mathrm{d}y}{\mathrm{d}x} - \frac{\partial H}{\partial \lambda } =0, \end{aligned}$$\end{document}$$ $$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned}&\frac{\mathrm{d}\lambda }{\mathrm{d}x} +\frac{\partial H}{\partial y} =0,\end{aligned}$$\end{document}$$ $$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned}&\frac{\partial H}{\partial \alpha } =0, \end{aligned}$$\end{document}$$The governing equations ([20](#Equ20){ref-type=""})--([22](#Equ22){ref-type=""}) are accompanied by the boundary conditions$$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned}&\mathrm {either}\quad y(0)=y_0 \quad \mathrm {or}\quad \lambda (0)=0,\end{aligned}$$\end{document}$$ $$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned}&\mathrm {either}\quad y(L)=y_L \quad \mathrm {or}\quad \lambda (L)=\frac{\partial \varPhi }{\partial y}\left( y(L)\right) . \end{aligned}$$\end{document}$$where $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$y_0$$\end{document}$ and $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$y_L$$\end{document}$ are initial and terminal conditions on the state variable *y*, where appropriate. If we treat the length of the domain *L* as a control variable, as well as $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha (x)$$\end{document}$, then in addition to ([20](#Equ20){ref-type=""})--([24](#Equ24){ref-type=""}), there is the condition$$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} H(x=L)=0. \end{aligned}$$\end{document}$$For both the small shear limit and the pure shear limit in Sects. [4.1](#Sec13){ref-type="sec"} and [4.2](#Sec14){ref-type="sec"}, we find that $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$F=0$$\end{document}$ and both $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varPhi $$\end{document}$ and *G* are linear functions of the control $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}$. As described by Pitcher \[[@CR36]\] and McDanell and Powers \[[@CR37]\], if in addition to the problem being linear in $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}$, the control is also bounded above and below, as in ([15](#Equ15){ref-type=""}), then ([20](#Equ20){ref-type=""}) and ([21](#Equ21){ref-type=""}) are exactly as before but ([22](#Equ22){ref-type=""}) is replaced by$$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} {\alpha }(x)={\left\{ \begin{array}{ll} \alpha _\mathrm{min}\quad &{}\mathrm {if} \quad H_\alpha <0,\\ \alpha ^*(x) \in \left[ \alpha _\mathrm{min},\alpha _\mathrm{max}\right] \quad &{}\mathrm {if} \quad H_\alpha =0,\\ \alpha _\mathrm{max}\quad &{}\mathrm {if} \quad H_\alpha >0, \end{array}\right. } \end{aligned}$$\end{document}$$where we have introduced the shorthand notation $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H_\alpha =\partial H/\partial \alpha $$\end{document}$. When $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\alpha }(x)$$\end{document}$ only takes its extreme values, then the control is said to be "bang-bang". If $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\alpha }(x)=\alpha ^*(x)$$\end{document}$ satisfies $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H_\alpha =0$$\end{document}$ for a finite interval, then this is called a "singular arc". Robbins \[[@CR38]\] showed that during the singular arc, $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha ^*$$\end{document}$ is determined by solving$$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \frac{\mathrm{d}^q H_\alpha }{\mathrm{d}x^q}(x,y(x),\alpha ^*(x))=0, \end{aligned}$$\end{document}$$where *q* is the smallest even number for which $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{{d}}^q H_\alpha /\mathrm{{d}}x^q$$\end{document}$ is not independent of $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}$. Note that, if instead of a single-state variable *y* there are multiple state variables $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$y_i$$\end{document}$, as is the case in the examples in Sects. [4.1](#Sec13){ref-type="sec"} and [4.2](#Sec14){ref-type="sec"}, then the analysis of this section still applies but with a Hamiltonian defined as$$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} H=F+\sum _i \lambda _i G_i. \end{aligned}$$\end{document}$$Furthermore, ([20](#Equ20){ref-type=""}), ([21](#Equ21){ref-type=""}) and boundary conditions ([23](#Equ23){ref-type=""}), ([24](#Equ24){ref-type=""}) apply for each state variable and corresponding adjoint variable. Numerical optimisation {#Sec8} ====================== This section, in which we solve the optimal control problem numerically using the approach outlined in Sect. [2.3.1](#Sec6){ref-type="sec"} for several different cases, is divided into subsections for clarity. Firstly, we study the solution in the developing shear layer case (see Fig. [1](#Fig1){ref-type="fig"}a). In this case, we find that optimal diffuser shapes look approximately like they are composed of piecewise linear sections. This observation motivates us to introduce a low-dimensional parameterisation of the shapes that can be explored with contour plots, which is useful when comparing with CFD calculations later in Sect. [5](#Sec15){ref-type="sec"}. The small shear limit and the pure shear limit (see Fig. [1](#Fig1){ref-type="fig"}b, c) are discussed in Sects. [3.2](#Sec10){ref-type="sec"} and [3.3](#Sec11){ref-type="sec"}, respectively. The developing shear layer case {#Sec9} ------------------------------- Having discussed the optimisation routine in Sect. [2.3.1](#Sec6){ref-type="sec"}, we use it to optimise channel shapes in several different cases, starting with the developing shear layer case. For plotting purposes, we maintain all variables in non-dimensional form with reference to typical length scales and velocity scales. We use the initial channel half-width as a typical length scale $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h_0=h(0)$$\end{document}$ and the speed of the faster plug region at the inlet as a typical velocity scale $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$U_0=U_1(0)$$\end{document}$. In the developing shear layer case, we look at two-dimensional flow and choose parameter values $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$U_2(0)/U_0=0.3$$\end{document}$, $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h_2(0)/h_0=0.5$$\end{document}$, $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h(L)/h_0=1.5$$\end{document}$, $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L/h_0=30$$\end{document}$, $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha _\mathrm{min}=0^\circ $$\end{document}$ and $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha _\mathrm{max}=\tan 7^\circ $$\end{document}$. The other parameters are taken as $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S=0.11$$\end{document}$ (which we determine from comparison with CFD in Sect. [5](#Sec15){ref-type="sec"}) and $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f=0.01$$\end{document}$ (which corresponds to a Reynolds number of $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Re=10^6$$\end{document}$ and hydraulically smooth walls, using the Blasius relationship \[[@CR30], [@CR31]\]). The number of grid points for discretising the simple model is $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n=100$$\end{document}$. Simultaneously, we also investigate axisymmetric flow with the same parameter values, except with $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha _\mathrm{max}=\tan 3.5^\circ $$\end{document}$. We plot the optimal diffuser angle for the two-dimensional case in Fig. [4](#Fig4){ref-type="fig"}a, the corresponding optimal diffuser shape and velocity colour map in Fig. [4](#Fig4){ref-type="fig"}c, and pressure plot in Fig. [4](#Fig4){ref-type="fig"}g. The axisymmetric case is plotted in Fig. [4](#Fig4){ref-type="fig"}b, d, h.Fig. 4Optimal diffuser shape for the developing shear layer case, in two dimensions (**a**, **c**, **e**, **g**) and in the axisymmetric case (**b**, **d**, **f**, **h**). The optimal shapes found using 100 degrees of freedom (100 DOF) (**c**, **d**) can be well approximated by three constant-angle sections with divisions at $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x=x_1$$\end{document}$ and $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x=x_2$$\end{document}$ (2 DOF), as shown by comparisons of diffuser angle (**a**, **b**), velocity (**e**, **f**) and pressure (**g**, **h**). The parameter values used are given in the main text In both cases, we observe that the optimal shape looks approximately like a piecewise linear function, which is divided into a straight part, followed by a widening part, followed by another straight part. In the two-dimensional case, the length of the first straight section aligns with the length it takes for the shear layer to spread completely across the channel. This suggests that mixing the flow to a more uniform profile is advantageous for the widening part to perform well. This is as expected because, as mentioned earlier, diffusers tend to accentuate non-uniform flow, producing an outflow with large kinetic energy flux (and therefore a low-pressure recovery). However, as discussed earlier, long thin channels cause large loss in pressure due to wall drag. Therefore, the optimal shape must have a straight section which is sufficiently long that the shear layer reaches across the channel, making the flow more well mixed, but no longer than that because of wall drag. Interestingly, the widening part of the channel widens at a shallower angle than the maximum value (around $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tan 2.3 ^\circ $$\end{document}$ compared to $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tan 7^\circ $$\end{document}$). So the upper bound on $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}$ is not needed in this case. This behaviour is unexpected since diffusers are usually designed with a widening angle as close to $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tan 7^\circ $$\end{document}$ as possible, regardless of the inflow. These results suggest that there is an optimal widening angle which is determined by the non-uniform inflow, rather than the risk of boundary layer separation. Since we observe that the optimal shape in Fig. [4](#Fig4){ref-type="fig"}a--d looks approximately piecewise linear with three sections, we also try restricting the control $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}$ in this way to see if we can attain a near optimal solution with a piecewise linear shape. We parameterise $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}$ by splitting it into three parts: a straight part with $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha =0$$\end{document}$ for $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0\le x <x_1$$\end{document}$; a widening part with constant $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha >0$$\end{document}$ for $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x_1\le x <x_2$$\end{document}$, and a final straight part with $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha =0$$\end{document}$ for $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x_2\le x\le L$$\end{document}$. We treat $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x_1$$\end{document}$ and $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x_2$$\end{document}$ as control parameters and the value of $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}$ in the middle section is determined by the condition$$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \alpha =\frac{h_L-h_0}{x_2-x_1}. \end{aligned}$$\end{document}$$We optimise pressure recovery, using the same algorithm as before, but with $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}$ having only 2 degrees of freedom (DOF), the two parameters $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x_1$$\end{document}$ and $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x_2$$\end{document}$, instead of 100 DOF. We plot the optimal diffuser angle in Fig. [4](#Fig4){ref-type="fig"}a, which is nearly identical to that obtained with 100 DOF. Moreover, the velocity colour map and pressure plot displayed in Fig. [4](#Fig4){ref-type="fig"}e, g both show a very close match. The pressure recovery coefficient for 2 DOF is $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_p=0.5205$$\end{document}$, which is the same as for 100 DOF (up to 4 decimal places), suggesting that piecewise linear diffuser shapes are a very good approximation in this case. In Fig. [5](#Fig5){ref-type="fig"}a, we display a contour plot of $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_p$$\end{document}$ for all possible values of $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x_1$$\end{document}$ and $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x_2$$\end{document}$ (we cut out part of the contour plot corresponding to $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha >\tan 7^\circ $$\end{document}$). This indicates that there is a clear unique optimum at $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x_1/h_0=12.3$$\end{document}$ and $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x_2/h_0=24.3$$\end{document}$. Note that an unoptimised shape, say with $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x_1=0$$\end{document}$ and $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x_2=5$$\end{document}$, gives a value of $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_p=0.4254$$\end{document}$, which is $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$22\%$$\end{document}$ worse than the optimal shape.Fig. 5Contour plots of pressure recovery $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_p$$\end{document}$ ([10](#Equ10){ref-type=""}), ([11](#Equ11){ref-type=""}), using the low-dimensional parameterisation of the diffuser shapes, as shown in Fig. [4](#Fig4){ref-type="fig"}a, b, for all permissible values of $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x_1$$\end{document}$ and $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x_2$$\end{document}$, such that $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha \le \alpha _\mathrm{max}$$\end{document}$. **a** Two-dimensional case with $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha _\mathrm{max}=\tan 7^\circ $$\end{document}$. **b** Axisymmetric case with $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha _\mathrm{max}=\tan 3.5^\circ $$\end{document}$, indicating where the inner stream stagnates. The widening middle section has constant angle given by Eq. ([29](#Equ29){ref-type=""}) For the axisymmetric case, we find that the optimal shape has a similar structure and can also be well approximated by parameterisation with $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x_1$$\end{document}$ and $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x_2$$\end{document}$. We find that the optimal value of $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x_1/h_0=6.3$$\end{document}$ is a little bit shorter than the two-dimensional case. In fact, we can see in Fig. [4](#Fig4){ref-type="fig"}d, f that the shear layer has not reached all the way across the channel by $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x=x_1$$\end{document}$. Instead, $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x_1$$\end{document}$ corresponds to the point where the shear layer reaches the centre of the channel. It reaches the outer wall of the channel slightly further downstream, during the widening section. This could be explained by the fact that pressure gradients due to wall drag are stronger (per unit flux) in the axisymmetric case (e.g. Poiseuille flow \[[@CR32]\]), and therefore the optimal shape cannot afford a longer section of straight, narrow channel. Figure [4](#Fig4){ref-type="fig"}b, d, f, h shows a close comparison between the diffuser angle, velocity and pressure in the 2 DOF case and the 100 DOF case. The contour plot in Fig. [5](#Fig5){ref-type="fig"}b shows the optimal parameter values $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x_1/h_0=6.3$$\end{document}$ and $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x_2/h_0=19.8$$\end{document}$. The pressure recovery coefficient for 2 DOF is $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_p=0.6886$$\end{document}$ compared to $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_p=0.7018$$\end{document}$ for 100 DOF, suggesting that axisymmetric piecewise linear diffuser shapes are also a good approximation, but slightly less so than in the two-dimensional case. The contour plot in Fig. [5](#Fig5){ref-type="fig"}b has a steep gradient for small $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x_1/h_0$$\end{document}$, indicating that diffuser performance is poor in this case. This corresponds to situations in which the inner stream stagnates, and we model this with a zone which has zero velocity, as described earlier. We indicate all diffuser shapes where we do this by plotting a black line on top of the contours (there is no stagnation for the two dimensional case in Fig. [5](#Fig5){ref-type="fig"}a). The phenomenon of stagnation is particularly an issue when the inner stream is slow, and this analysis shows that the way to avoid such poor performance is to have a longer straight section in which the inner stream is accelerated before diffusing.Fig. 6Optimal diffuser shapes, velocity colour maps, pressure plots and diffuser angle plots for the small shear limit and the pure shear limit. **a**, **c**, **e** Two-dimensional flow where the plug regions have similar speeds $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$U_2(0)/U_0=0.8$$\end{document}$ and the channel length $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L/h_0=20$$\end{document}$ is sufficiently short such that the shear layer never reaches across the channel. **b**, **d**, **f** Two-dimensional flow where the shear layer has already reached across the channel at the inflow so that there are no plug regions. The inflow velocity ratio is $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$U_2(0)/U_0=0.35$$\end{document}$ Small shear limit {#Sec10} ----------------- For the small shear limit, we consider two-dimensional flow and choose parameter values $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$U_2(0)/U_0=0.8$$\end{document}$, $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h_2(0)/h_0=0.5$$\end{document}$, $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h(L)/h_0=2.3$$\end{document}$, $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L/h_0=20$$\end{document}$, $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha _\mathrm{min}=0$$\end{document}$ and $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha _\mathrm{max}=\tan 7^\circ $$\end{document}$. The other parameters *S* and *f* are taken at the same values as the previous cases. We display the optimal shape, velocity colour map and pressure plot in Fig. [6](#Fig6){ref-type="fig"}a, c, e. In this case, the optimal shape widens at the maximum angle $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha _\mathrm{max}$$\end{document}$ until it reaches the exit width *h*(*L*) and then stays straight. Since the shear is small and the flow is almost uniform, there is no risk of accentuating the flow profile drastically. Therefore, wide angles initially are not penalised much, allowing the control to take its maximum value. This design is typically what is built in the diffuser industry for uniform inflow \[[@CR5]\], where the maximum diffuser angle is set by the limit where boundary layer separation occurs. The optimal control only takes its extremal values, which is sometimes referred to as bang-bang control (see Sect. [2.3.2](#Sec7){ref-type="sec"}). In Sect. [4.1](#Sec13){ref-type="sec"}, we discuss analytical results for this limiting case and prove that the control must be bang-bang. Pure shear limit {#Sec11} ---------------- For the pure shear limit, we consider two-dimensional flow and choose parameter values $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$U_2(0)/U_0=0.35$$\end{document}$, $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h_L/h_0=2.3$$\end{document}$, $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L/h_0=40$$\end{document}$, $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha _\mathrm{min}=0^\circ $$\end{document}$ and $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha _\mathrm{max}=\tan 7^\circ $$\end{document}$. Parameters *S* and *f* are taken as the same as before. The optimal channel, velocity colour map, pressure and control are displayed in Fig. [6](#Fig6){ref-type="fig"}b, d, f. The optimal shape is similar to those in Fig. [4](#Fig4){ref-type="fig"}, with a natural decomposition into two straight sections separated by a widening section. The widening section has an angle that increases from $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha \approx \tan 2.5^\circ $$\end{document}$ to $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha \approx \tan 3^\circ $$\end{document}$ and is nowhere greater than $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tan 7^\circ $$\end{document}$, showing that the upper bound $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}$ was not needed in this case. The optimal shape, like in Fig. [4](#Fig4){ref-type="fig"}, exhibits the balance between the necessity of a straight section that is long enough to allow some mixing, but not too long that wall drag dominates. In this case, which does not involve any of the switching behaviour that occurs when plug regions reach the wall, we derive some analytical results (discussed in Sect. [4.2](#Sec14){ref-type="sec"}) which support and help interpret the numerical optimisation. In particular, we investigate the nature of the optimal widening angle which lies in the interval $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\alpha _\mathrm{min},\alpha _\mathrm{max})$$\end{document}$. This is of great interest because it indicates that the optimal design is unaffected by the conventional widening angle limit that exists due to boundary layer separation. Analytical results {#Sec12} ================== The numerical optimisation routine outlined in Sect. [2.3.1](#Sec6){ref-type="sec"} can be applied to find optimal shapes for any choice of the parameters listed in Table [1](#Tab1){ref-type="table"}. We have seen several examples of these in Figs. [4](#Fig4){ref-type="fig"} and [6](#Fig6){ref-type="fig"}. In this section, we show that in the two limiting cases displayed in Fig. [6](#Fig6){ref-type="fig"}, the small shear limit and the pure shear limit, it is possible to make some analytical progress which aids our understanding and interpretation of the optimal control. Furthermore, the results discussed in this section include simple relationships that may be of instructive use for the purpose of diffuser design in industry. In both cases, we derive a reduced set of equations describing the dynamics, that is amenable to optimal control analysis using Pontryagin's maximum principle \[[@CR25]\]. Small shear limit {#Sec13} ----------------- To start with, we consider a two-dimensional diffuser where the inflow, given by ([1](#Equ1){ref-type=""}), is almost uniform. We study this situation because it illustrates the limiting case of the earlier developing shear layer examples in Fig. [4](#Fig4){ref-type="fig"}, except where the inner and outer plug regions are of similar speeds. In such situations, the shear rate $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varepsilon _y$$\end{document}$ is small, such that the shear layer develops slowly between the plug flow regions (see Eq. ([2](#Equ2){ref-type=""})). Furthermore, we restrict our attention to situations where the channel is sufficiently short that the shear layer never reaches across the channel (see Fig. [1](#Fig1){ref-type="fig"}b). Therefore, we consider an inflow given by ([1](#Equ1){ref-type=""}) with small $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$U_1-U_2$$\end{document}$, which is a perturbation to a uniform velocity profile. Then, we asymptotically expand our governing equations ([1](#Equ1){ref-type=""})--([6](#Equ6){ref-type=""}) about the leading order uniform flow solution, resulting in a reduced set of equations which are amenable to analysis using Pontryagin's maximum principle. Hence, let us introduce the small parameter $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\epsilon \ll 1$$\end{document}$, which is defined by the difference in speed between the two plug regions at the inflow$$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \epsilon V=U_1(0)-U_2(0)=U_0-U_2(0), \end{aligned}$$\end{document}$$where *V* is a dimensional velocity scale. If the plug regions always exist, with positive width $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h_1>0$$\end{document}$, $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h_2>0$$\end{document}$, and we assume that the slower flow never stagnates $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$U_2>0$$\end{document}$, then we need not consider the complementarity format for Bernoulli's equation. Therefore, we replace Eqs. ([5](#Equ5){ref-type=""}) and ([6](#Equ6){ref-type=""}) with$$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} p+\frac{1}{2}\rho U_i^2=\frac{1}{2}\rho U_{i}(0)^2 \quad \mathrm {for}\quad i=1,2. \end{aligned}$$\end{document}$$We consider the distinguished limit where the friction factor *f* is small such that $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f=\epsilon S F $$\end{document}$, where $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$F=O(1)$$\end{document}$. Note that, whilst *f* is small, over the long diffuser length scales we consider, friction has a significant effect on the pressure variations. For a Reynolds number of $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Re=10^6$$\end{document}$ and hydraulically smooth walls, the friction factor is calculated as $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f=0.01$$\end{document}$, using the Blasius relationship \[[@CR30], [@CR31]\]. Therefore, if $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\epsilon = 0.1$$\end{document}$ and $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S=0.11$$\end{document}$, then $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$F=0.91$$\end{document}$. Choosing these parameter values and setting $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$V/U_0=2$$\end{document}$, we achieve the small shear limit example in Fig. [6](#Fig6){ref-type="fig"}a, c, e. By considering perturbations to uniform flow, we expand variables in powers of the small parameter $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\epsilon $$\end{document}$,$$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned}&U_1=U_{1_0}+\epsilon \hat{U}_1+\cdots , \end{aligned}$$\end{document}$$ $$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned}&U_2=U_{2_0}+\epsilon \hat{U}_2+\cdots ,\end{aligned}$$\end{document}$$ $$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned}&h_1=h_{1_0}+\epsilon \hat{h}_1+\cdots ,\end{aligned}$$\end{document}$$ $$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned}&h_2=h_{2_0}+\epsilon \hat{h}_2+\cdots ,\end{aligned}$$\end{document}$$ $$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned}&p=p_0+\epsilon \hat{p}+\cdots ,\end{aligned}$$\end{document}$$ $$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned}&\delta =\delta _0+\epsilon \hat{\delta }+\cdots ,\end{aligned}$$\end{document}$$ $$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned}&\varepsilon _y=\varepsilon _{y_0} +\epsilon \hat{\varepsilon }_y+\cdots . \end{aligned}$$\end{document}$$In the limit $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\epsilon \rightarrow 0$$\end{document}$, Eqs. ([2](#Equ2){ref-type=""})--([4](#Equ4){ref-type=""}) and ([31](#Equ31){ref-type=""}) are satisfied by$$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned}&U_{1_0}=U_{2_0}=\frac{U_0h_0}{h},\end{aligned}$$\end{document}$$ $$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned}&h_{2_0}=h-h_{1_0},\end{aligned}$$\end{document}$$ $$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned}&p_0=\frac{1}{2}\rho U_0^2\left( 1-\frac{h_0^2}{h^2}\right) ,\end{aligned}$$\end{document}$$ $$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned}&\delta _0=0,\end{aligned}$$\end{document}$$ $$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned}&\varepsilon _{y_0}=\frac{h_0U_0}{S\int _0^x h(\hat{x})\,\mathrm{d}\hat{x}}. \end{aligned}$$\end{document}$$The function $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h_{1_0}$$\end{document}$, which represents the location of the centre of the shear layer to leading order, is determined at order $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O(\epsilon )$$\end{document}$. Bernoulli's equation ([31](#Equ31){ref-type=""}) for each plug region, at order $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O(\epsilon )$$\end{document}$, is$$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \hat{p}+\rho \hat{U}_1 U_{1_0}&=0, \end{aligned}$$\end{document}$$ $$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \hat{p}+\rho \hat{U}_2 U_{1_0}&=-\rho U_0 V. \end{aligned}$$\end{document}$$From the relationship $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h_1+h_2+\delta =h$$\end{document}$ at order $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O(\epsilon )$$\end{document}$, we find that$$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \hat{h}_1 +\hat{h}_2 + \hat{\delta }=0. \end{aligned}$$\end{document}$$Thus, the conservation of mass equation ([3](#Equ3){ref-type=""}) is$$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \hat{U}_1h_{1_0} + \hat{U}_2 (h - h_{1_0}) = -V h_2(0), \end{aligned}$$\end{document}$$and the momentum equation ([4](#Equ4){ref-type=""}) is$$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} h\frac{d\hat{p}}{\mathrm{d}x}+\rho \frac{\mathrm{d}}{\mathrm{d}x}\left( 2 U_{1_0}\hat{U}_1 h_{1_0} +2 U_{1_0}\hat{U}_2 (h-h_{1_0}) \right) =-\frac{1}{8}SF\rho U_{1_0}^2. \end{aligned}$$\end{document}$$Thus, using Eqs. ([44](#Equ44){ref-type=""})--([46](#Equ46){ref-type=""}), we can simplify Eq. ([48](#Equ48){ref-type=""}) to an equation purely involving $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h_{1_0}$$\end{document}$ and *h*$$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} V h^2 \frac{\mathrm{d}h_{1_0}}{\mathrm{d}x} -V h h_{1_0} \frac{\mathrm{d}h}{\mathrm{d}x} =-\frac{1}{8}F Sh_0^2 U_0. \end{aligned}$$\end{document}$$Equation ([49](#Equ49){ref-type=""}) has solution$$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} h_{1_0}=h\left( \frac{h_1(0)}{h_0} -\int _0^x \frac{SFh_0^2U_0}{8V h(\hat{x})^3}\,\mathrm{d}\hat{x} \right) . \end{aligned}$$\end{document}$$Combining ([47](#Equ47){ref-type=""}) and ([48](#Equ48){ref-type=""}), we obtain a differential equation for the pressure correction $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hat{p}$$\end{document}$ in terms of the channel shape and its derivative $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha =h'(x)$$\end{document}$,$$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \frac{\mathrm{d}\hat{p}}{\mathrm{d}x}=-\frac{\rho U_0^2 h_0^2 }{h^{3}} \left( \frac{2 V}{U_0} \left( 1- \frac{h_1(0)}{h_0}\right) \alpha + \frac{S F}{8} \right) . \end{aligned}$$\end{document}$$We now solve the optimal control problem outlined in Sect. [2.2](#Sec4){ref-type="sec"}, using the approach outlined in Sect. [2.3.2](#Sec7){ref-type="sec"}. Since the inflow conditions are fixed and we take $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p(0)=0$$\end{document}$, maximising $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_p$$\end{document}$ is equivalent to maximising pressure at the outlet *p*(*L*). Furthermore, the constraint equations have been reduced to ([51](#Equ51){ref-type=""}). Therefore the optimal control problem, including terms up to and including order $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O(\epsilon )$$\end{document}$, and written as a system of first order differential equations, is as follows:$$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \max _{\alpha _\mathrm{min} \le \alpha (x)\le \alpha _\mathrm{max}}\quad \varPhi : = p(L), \end{aligned}$$\end{document}$$such that$$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned}&\frac{\mathrm{d}p}{\mathrm{d}x}=\frac{\rho U_0^2 h_0^2 }{h^{3}} \left( \left( 1- \epsilon \frac{2 V}{U_0} \left( 1- \frac{h_1(0)}{h_0}\right) \right) \alpha -\epsilon \frac{S F}{8} \right) , \end{aligned}$$\end{document}$$ $$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned}&\frac{\mathrm{d}h}{\mathrm{d}x}=\alpha ,\end{aligned}$$\end{document}$$ $$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned}&h(0)=h_0,\end{aligned}$$\end{document}$$ $$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned}&p(0)=0, \end{aligned}$$\end{document}$$ $$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned}&h(L)=h_L. \end{aligned}$$\end{document}$$We now solve this reduced problem using Pontryagin's maximum principle \[[@CR25]\], as outlined earlier. The Hamiltonian for this system is$$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} H=\lambda _p \frac{\mathrm{d}p}{\mathrm{d}x}+\lambda _h \frac{\mathrm{d}h}{\mathrm{d}x}, \end{aligned}$$\end{document}$$where $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda _p$$\end{document}$ and $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda _h$$\end{document}$ are the adjoint variables which satisfy the adjoint equations$$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \frac{\mathrm{d}\lambda _p}{\mathrm{d}x}&=-\frac{\partial H}{\partial p},\end{aligned}$$\end{document}$$ $$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \frac{\mathrm{d}\lambda _h}{\mathrm{d}x}&=-\frac{\partial H}{\partial h}. \end{aligned}$$\end{document}$$From ([24](#Equ24){ref-type=""}), since the objective function only depends on pressure at the outlet $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varPhi =p(L)$$\end{document}$, we have the natural boundary condition$$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \lambda _p(L)=\frac{\partial \varPhi }{\partial p}=1. \end{aligned}$$\end{document}$$Considering Eq. ([61](#Equ61){ref-type=""}) and the fact that there is no dependance of the Hamiltonian ([58](#Equ58){ref-type=""}) on the pressure *p*, Eq. ([59](#Equ59){ref-type=""}) tells us that $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda _p=1$$\end{document}$ for all values of *x*. There is no natural boundary condition for $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda _h$$\end{document}$ since we are enforcing a condition on *h* at the outlet $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x=L$$\end{document}$ (see ([24](#Equ24){ref-type=""})). The last condition from Pontryagin's maximum principle is the optimality condition, and since the Hamiltonian is linear in the control $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}$, this takes the form of Eq. ([26](#Equ26){ref-type=""}). Next we investigate whether the optimal control is bang-bang, or whether any singular arcs exist (see Sect. [2.3.2](#Sec7){ref-type="sec"}). Using ([58](#Equ58){ref-type=""}) with ([53](#Equ53){ref-type=""}), ([54](#Equ54){ref-type=""}) and ([60](#Equ60){ref-type=""}), and noting that $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda _p=1$$\end{document}$, we see that$$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \frac{\mathrm{d}H_\alpha }{\mathrm{d}x}=-\frac{3 \epsilon \rho S F U_0^2 h_0^2 }{8h^{4}}, \end{aligned}$$\end{document}$$which is negative for all values of *x*. Hence, it is impossible for singular arcs to exist in this case. Therefore the control is bang-bang with$$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \alpha (x)={\left\{ \begin{array}{ll} \alpha _\mathrm{max} &{} \mathrm {for} \quad x\in [0,\gamma ], \\ \alpha _\mathrm{min} &{} \mathrm {for} \quad x\in [\gamma ,L], \\ \end{array}\right. } \end{aligned}$$\end{document}$$where the switching point $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma $$\end{document}$ is given by$$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \gamma =\frac{h_L-h_0-\alpha _\mathrm{min} L}{\alpha _\mathrm{max} - \alpha _\mathrm{min} }. \end{aligned}$$\end{document}$$In Fig. [6](#Fig6){ref-type="fig"}c, e, we plot the solution to the optimal control problem found using the Hamiltonian approach on top of the solution found using the numerical optimisation routine outlined in Sect. [2.3.1](#Sec6){ref-type="sec"}. It is clear that the numerical optimisation routine has correctly found the bang-bang control which we have derived here, with $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma /h_0=10.59$$\end{document}$ (the small discrepancy is probably due to the finite value of $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\epsilon $$\end{document}$). It should be noted that the adjoint variable $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda _h$$\end{document}$ is only solved for up to a constant of integration *C* (from integrating Eq. ([60](#Equ60){ref-type=""})) since it has no boundary condition. Instead, *C* is determined by the condition that$$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} H_\alpha (x=\gamma )=0. \end{aligned}$$\end{document}$$In the case where we also allow the channel length *L* to be a control as well as $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}$, as described in Sect. [2.3.2](#Sec7){ref-type="sec"}, we have the additional constraint on the Hamiltonian at the final point ([25](#Equ25){ref-type=""}). By calculating *H* ([58](#Equ58){ref-type=""}), it is straightforward to show that ([65](#Equ65){ref-type=""}) and ([25](#Equ25){ref-type=""}) are inconsistent unless $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma =0$$\end{document}$ or $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma =L$$\end{document}$. For the case in Fig. [6](#Fig6){ref-type="fig"}a, c, e, it is clear that $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma =0$$\end{document}$ is impossible, so we conclude that the optimal diffuser length is $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L=\gamma $$\end{document}$. Therefore, including *L* as a control and taking $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha _\mathrm{min}=0^\circ $$\end{document}$, the optimal diffuser shape for the small shear limit is one which expands at the maximum angle until *h* reaches $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h_L$$\end{document}$, at which point the channel terminates (i.e. conventional diffuser design for uniform flow). Pure shear limit {#Sec14} ---------------- The next limiting case we investigate is the pure shear limit, in which the shear layer has already reached across the channel at the inflow, such that there are no plug regions (see Fig. [1](#Fig1){ref-type="fig"}c). The velocity profile is given by Eq. ([7](#Equ7){ref-type=""}). For this velocity profile, conservation of mass and momentum equations ([3](#Equ3){ref-type=""}), ([4](#Equ4){ref-type=""}) reduce to$$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned}&\frac{h}{2}(U_1+U_2)=Q,\end{aligned}$$\end{document}$$ $$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned}&h\frac{\mathrm{d}p}{\mathrm{d}x}+\frac{1}{3}\rho \frac{\mathrm{d}}{\mathrm{d}x}\left( h\left( U_1^2+U_1U_2+U_2^2\right) \right) =-\frac{1}{8}\rho f U_1^2. \end{aligned}$$\end{document}$$We now solve the optimal control problem outlined in Sect. [2.2](#Sec4){ref-type="sec"}. As in Sect. [4.1](#Sec13){ref-type="sec"}, we maximise pressure at the outlet *p*(*L*). Furthermore, it is convenient to introduce a new variable, the scaled velocity difference between maximum and minimum velocities $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tilde{U}=(U_1-U_2)/(U_1+U_2)$$\end{document}$. Using ([66](#Equ66){ref-type=""}) and this new variable we can simplify Eqs. ([2](#Equ2){ref-type=""}) and ([67](#Equ67){ref-type=""}), which are the reduced system of constraint equations. Therefore, the optimal control problem is as follows:$$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \max _{\alpha _\mathrm{min} \le \alpha (x) \le \alpha _\mathrm{max}} \quad \varPhi :=p(L), \end{aligned}$$\end{document}$$such that$$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned}&\frac{\mathrm{d}\tilde{U}}{\mathrm{d}x}=\frac{2\tilde{U}(\alpha -S\tilde{U})}{h},\end{aligned}$$\end{document}$$ $$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned}&\frac{\mathrm{d}p}{\mathrm{d}x}=\frac{\rho Q^2\left( 32 S \tilde{U}^3 -3 f (1 + \tilde{U})^2 + 24 \alpha (1 - \tilde{U}^2)\right) }{24 h^3}, \end{aligned}$$\end{document}$$ $$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned}&\frac{\mathrm{d}h}{\mathrm{d}x}=\alpha ,\end{aligned}$$\end{document}$$ $$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned}&\tilde{U}(0)=\tilde{U}_0,\end{aligned}$$\end{document}$$ $$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned}&p(0)=0,\end{aligned}$$\end{document}$$ $$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned}&h(0)=h_0,\end{aligned}$$\end{document}$$ $$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned}&h(L)=h_L, \end{aligned}$$\end{document}$$where $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tilde{U}_0=(1-U_2(0)/U_0)/(1+U_2(0)/U_0)$$\end{document}$. Similarly to Sect. [4.1](#Sec13){ref-type="sec"}, the Hamiltonian for the system is constructed as$$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} H=\lambda _{\tilde{U}} \frac{d\tilde{U}}{dx}+\lambda _p \frac{dp}{dx}+\lambda _h \frac{dh}{dx}, \end{aligned}$$\end{document}$$which is linear in the control $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}$. The adjoint equations are$$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned}&\frac{\mathrm{d}\lambda _{\tilde{U}}}{\mathrm{d}x}=-\frac{\partial H}{\partial {\tilde{U}}},\end{aligned}$$\end{document}$$ $$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned}&\frac{\mathrm{d}\lambda _p}{\mathrm{d}dx}=-\,\frac{\partial H}{\partial p},\end{aligned}$$\end{document}$$ $$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned}&\frac{\mathrm{d}\lambda _h}{\mathrm{d}x}=-\,\frac{\partial H}{\partial h}, \end{aligned}$$\end{document}$$which have the natural boundary conditions$$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \lambda _{\tilde{U}}(L)&=\frac{\partial \varPhi }{\partial \tilde{U}}=0, \end{aligned}$$\end{document}$$ $$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \lambda _p(L)&=\frac{\partial \varPhi }{\partial p}=1. \end{aligned}$$\end{document}$$There is no natural boundary condition for $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda _h$$\end{document}$ since *h* is already prescribed at $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x=L$$\end{document}$ (see ([24](#Equ24){ref-type=""})). Finally, as in Sect. [4.1](#Sec13){ref-type="sec"}, the optimality condition is ([26](#Equ26){ref-type=""}). As described in Sect. [2.3.2](#Sec7){ref-type="sec"}, in order for there to be a singular arc, we must have $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H_\alpha =0$$\end{document}$ and $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$dH_\alpha /dx=0$$\end{document}$ for a finite interval, where during this interval the value of the control is given by ([27](#Equ27){ref-type=""}). In this case, we find that $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q=2$$\end{document}$, such that ([27](#Equ27){ref-type=""}) becomes$$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \frac{\mathrm{d}^2H_\alpha }{\mathrm{d}x^2}(\alpha =\alpha ^*)=0. \end{aligned}$$\end{document}$$Setting $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H_\alpha =\mathrm{d}H_\alpha /\mathrm{d}x=0$$\end{document}$, and using Eq. ([82](#Equ82){ref-type=""}), we find that there will only be a singular arc when$$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \alpha ^*= \frac{2 S \tilde{U}^2 (8 S \tilde{U}^2 - f)}{ 3 f + f \tilde{U} + 8 S \tilde{U}^3} \quad \mathrm {for}\quad x \in [x_1,x_2], \end{aligned}$$\end{document}$$for some $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x_2>x_1$$\end{document}$. We can solve the coupled system ([26](#Equ26){ref-type=""}), ([69](#Equ69){ref-type=""})--([83](#Equ83){ref-type=""}) numerically for the optimal control and corresponding solution. There are, however, very special cases where the singular arc value $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha ^*$$\end{document}$ is constant, when we can find analytical solutions, which we discuss at the end of this section. In practice, these solutions appear to be close to the behaviour observed in normal conditions, as can be seen in Fig. [6](#Fig6){ref-type="fig"}f where $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}$ is approximately constant during the widening section of the diffuser. In Fig. [6](#Fig6){ref-type="fig"}b, d, f, we plot the solution to the optimal control problem found using the Hamiltonian approach over the solution found using the numerical optimisation routine outlined in Sect. [2.3.1](#Sec6){ref-type="sec"}. It is clear that both approaches have found the same solution, with the singular arc lying between $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x_1/h_0=2.9$$\end{document}$ and $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x_2/h_0=32.9$$\end{document}$. The singular arc represents the balance between mixing and widening effects in the diffuser. Mixing reduces the non-uniformity of the flow, whilst widening tends to accentuate the non-uniform profile, and such non-uniformity can produce a high-kinetic energy, low-pressure outlet. Therefore, the control initially takes its minimum value $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha =0^\circ $$\end{document}$ to create good mixing. However, a straight section which is too long is detrimental to pressure recovery because of wall drag. Hence, a widening section is required after a critical length. The optimal value of $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}$ in the widening section represents a balance between mixing and widening the flow. If $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}$ is too large, then the flow profile will become too non-uniform at the outlet. Conversely, if $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}$ is too shallow, wall drag losses are enhanced. The singular arc is interesting from both a mathematical point of view, but also from an engineering point of view. It clearly shows that diffuser designs for non-uniform inflow should take into account the nature of the non-uniform inflow profile. The optimal widening angle for manufacture is given by Eq. ([83](#Equ83){ref-type=""}). Calculating $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha ^*(x)$$\end{document}$ from ([83](#Equ83){ref-type=""}) is difficult in general ($\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tilde{U}$$\end{document}$ is a variable), but we find that for certain parameter values, it takes a simpler and more useful form. In general, during the singular arc $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha ^*(x)$$\end{document}$ is not constant, yet in certain cases, such as Fig. [5](#Fig5){ref-type="fig"}b, it does not vary much over the singular arc interval. This raises the question of whether it is possible to find constant $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha ^*$$\end{document}$ solutions. Noticing how the only variable in Eq. ([83](#Equ83){ref-type=""}) is $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tilde{U}$$\end{document}$, we seek solutions with constant $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tilde{U}$$\end{document}$. Furthermore, we restrict our attention to solutions which begin on the singular arc. From Eq. ([69](#Equ69){ref-type=""}), we see that constant $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha ^*$$\end{document}$ solutions only exist if$$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \alpha ^*=S\tilde{U}. \end{aligned}$$\end{document}$$Therefore, reconciling Eqs. ([83](#Equ83){ref-type=""}) and ([84](#Equ84){ref-type=""}), it can be shown that constant singular arc solutions exist for parameters which satisfy$$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} S \tilde{U} (8 S \tilde{U}^3 - 3 f(1+ \tilde{U} ) )=0. \end{aligned}$$\end{document}$$Excluding $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tilde{U}=0$$\end{document}$, and assuming that *f* and *S* are fixed, we are left with solving Eq. ([85](#Equ85){ref-type=""}) for $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tilde{U}$$\end{document}$. Substituting $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$U_2(0)$$\end{document}$ and $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$U_0$$\end{document}$ back into ([85](#Equ85){ref-type=""}), we rewrite the equation in terms of the inlet velocity ratio $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$U(0)=U_2(0)/U_0$$\end{document}$, so that we require the parameters to satisfy$$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} 4 S (U(0) -1 )^3 + 3 f (U(0)+ 1 )^2=0. \end{aligned}$$\end{document}$$Similarly, ([84](#Equ84){ref-type=""}) then indicates that$$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \alpha ^*=S\left( \frac{1-U(0)}{1+U(0)}\right) . \end{aligned}$$\end{document}$$For $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$U(0)=0.35$$\end{document}$, as in Fig. [6](#Fig6){ref-type="fig"}b, d, f, we find $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha ^*=\tan 2.76^\circ $$\end{document}$, which is very close to the solution from the numerical optimisation, indicating that ([87](#Equ87){ref-type=""}) is also a good approximation for non-constant singular arcs.Fig. 7Constant singular arc solution displaying velocity colour map and a plot of $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H_\alpha =\partial H/\partial \alpha $$\end{document}$, where the Hamiltonian *H* is given by ([76](#Equ76){ref-type=""}), for parameter values $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S=0.11$$\end{document}$ and $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f=0.01$$\end{document}$. The inflow velocity ratio $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$U(0)=0.471$$\end{document}$ is given by ([86](#Equ86){ref-type=""}) and the singular arc value $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha ^*=\tan 2.26^\circ $$\end{document}$ is given by ([87](#Equ87){ref-type=""}) Considering that in typical situations $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f/S\approx 0.1$$\end{document}$, and this is small, we expand ([86](#Equ86){ref-type=""}) and ([87](#Equ87){ref-type=""}) about *f* / *S* and ignore imaginary solutions, giving the approximate solution$$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned}&U(0)=1 - 3^{1/3}\left( \frac{f}{S}\right) ^{1/3}+ \frac{1}{3^{1/3}}\left( \frac{f}{S}\right) ^{2/3}+\cdots , \end{aligned}$$\end{document}$$ $$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned}&\frac{\alpha ^*}{S} = \frac{3^{1/3}}{2} \left( \frac{f}{S}\right) ^{1/3}+ \frac{1}{4 \cdot 3^{1/3}}\left( \frac{f}{S}\right) ^{2/3}+\cdots . \end{aligned}$$\end{document}$$ For the constant singular arc solution ([87](#Equ87){ref-type=""}), we can solve the system ([26](#Equ26){ref-type=""}), ([69](#Equ69){ref-type=""})--([83](#Equ83){ref-type=""}) analytically, though we do not include the details here. Note, we also need to ensure that both $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H_\alpha =0$$\end{document}$ and $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$dH_\alpha /dx=0$$\end{document}$ for all values of *x* during the singular arc. This will enforce a further constraint on the other parameters of the problem. We do not include the details of this here, but instead, we simply state the constraint, written in terms of the rescaled non-dimensional channel length $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L/(S h_0)$$\end{document}$, and both $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h_L/h_0$$\end{document}$ and *f* / *S*. Written in an asymptotic expansion in powers of *f* / *S* (similarly to before) this constraint takes the approximate form$$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \frac{L}{S h_0}= \left( 3^{-1/3}(1+2^{2/3}) \frac{h_L}{h_0} - 2\cdot 3^{-1/3}\right) \left( \frac{f}{S}\right) ^{-1/3} +\frac{1}{3} -\frac{1}{2}\frac{h_L}{h_0}+\cdots . \end{aligned}$$\end{document}$$As an example of such a constant singular arc solution, we choose parameter values $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S=0.11$$\end{document}$, $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f=0.01$$\end{document}$ and $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha _\mathrm{min}=0^\circ $$\end{document}$, from which, solving Eqs. ([86](#Equ86){ref-type=""}) and ([87](#Equ87){ref-type=""}), we have an inflow velocity ratio $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$U(0)=0.471$$\end{document}$ and a singular arc value of $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha ^*=\tan 2.26^\circ $$\end{document}$. Using ([90](#Equ90){ref-type=""}), we find that $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H_\alpha =0$$\end{document}$ and $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{{d}}H_\alpha /\mathrm{{d}}x=0$$\end{document}$ along the singular arc if we choose the remaining parameter values $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h_L/h_0=2$$\end{document}$ and $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L/h_0=40$$\end{document}$. In Fig. [7](#Fig7){ref-type="fig"}, we display the velocity colour map for this solution, together with a plot of $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H_\alpha $$\end{document}$. We see that the solution starts on the singular arc until the expansion ratio $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h_L/h_0=2$$\end{document}$ is reached, at which point $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H_\alpha $$\end{document}$ becomes negative, such that the remaining length of the diffuser has angle $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha _\mathrm{min}=0^\circ $$\end{document}$. It is of further interest to investigate how the singular arc depends on the model parameters *f* and *S*. We plot the relationship between the constant singular arc value $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha ^*$$\end{document}$ ([87](#Equ87){ref-type=""}) and these parameters in Fig. [8](#Fig8){ref-type="fig"}. It is clear that increasing the friction factor *f* results in a higher $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha ^*$$\end{document}$. This is to be expected, since larger wall drag will penalise smaller angles more. Increasing the spreading parameter *S* also increases $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha ^*$$\end{document}$. This is because higher spreading rates results in better mixing, and hence, wider angles are more affordable. Comparison with results from a *k*--$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\epsilon $$\end{document}$ model and a *k*--$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega $$\end{document}$ SST model {#Sec15} ============================================================================================================ In this section, we discuss comparisons between the optimal shapes found using the simple model in the previous sections to calculations from CFD. Benham et al. \[[@CR6]\] make comparisons between this model and a *k*--$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\epsilon $$\end{document}$ turbulence model \[[@CR26]\], as well as experimental data generated with Particle Image Velocimetry (PIV). Here, we use both a *k*--$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\epsilon $$\end{document}$ and a *k*--$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega $$\end{document}$ Shear Stress Transport (SST) model \[[@CR27]\] to compare with some of the simple model optimisation results. The *k*--$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\epsilon $$\end{document}$ model is one of the most popular computational turbulence models, whilst the *k*--$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega $$\end{document}$ SST model is particularly robust in situations with strong adverse pressure gradients \[[@CR27]\] (though for the small diffuser angles we consider in this study the adverse pressure gradients are not severe). Moreover, since a thorough comparison between the mathematical model and CFD has already been discussed in \[[@CR6]\], we do not perform comparisons for all of the optimisation results of Sect. [3](#Sec8){ref-type="sec"}. Instead, we look at the geometry in Fig. [4](#Fig4){ref-type="fig"}e as a single example.Fig. 8Parameter analysis for the constant $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha ^*$$\end{document}$ singular arc solution, given by ([87](#Equ87){ref-type=""}), which depends on the parameters *S* and *f* Consider the example in Fig.  [4](#Fig4){ref-type="fig"}e, as discussed in Sect. [3](#Sec8){ref-type="sec"}. In order to compare with the mathematical model, we use precisely the same inlet velocity profile in the CFD. Inlet conditions for the turbulence variables *k*, $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\epsilon $$\end{document}$ and $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega $$\end{document}$ are given by the free-stream boundary conditions \[[@CR29]\] $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k=I^2\times 3/2\left( u^2+v^2\right) $$\end{document}$, $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\epsilon =0.09 k^{3/2}/\ell $$\end{document}$ and $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega =\sqrt{k}/\ell $$\end{document}$, with turbulence intensity $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$I=10\%$$\end{document}$ and mixing length $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ell =0.1 h_0$$\end{document}$ ($\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$10\%$$\end{document}$ of the channel half-width). In both the CFD models, no slip boundary conditions are applied to the channel walls. Furthermore, we use all the standard turbulence parameter values, which are given by Launder and Spalding \[[@CR26]\] for the *k*--$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\epsilon $$\end{document}$ model and Menter \[[@CR27]\] for the *k*--$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega $$\end{document}$ SST model.Fig. 9Comparison between mathematical model and two computational turbulence models (*k*--$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\epsilon $$\end{document}$ and *k*--$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega $$\end{document}$ SST) for the optimal shape in Fig. [4](#Fig4){ref-type="fig"}c. **a** Velocity colour map calculated using the reduced model, with black dashed lines indicating the shear layer. **b** Corresponding velocity colour map calculated using the *k*--$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\epsilon $$\end{document}$ model. **c** Pressure, averaged across the channel width. **d** Velocity profiles at evenly spaced locations in the channel In Fig. [9](#Fig9){ref-type="fig"}a, b, we display colour plots of the time-averaged streamwise velocity *u* generated with both the simple model and the *k*--$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\epsilon $$\end{document}$ model. Figure [9](#Fig9){ref-type="fig"}d also compares velocity profiles at evenly spaced locations in the channel, for the simple model and both CFD models. There is good agreement between the models, with the simple model capturing the dominant features of the flow, such as maximum and minimum velocities, and the width of the shear layer. There is a slight discrepancy near the diffuser wall since our model does not resolve boundary layers, but instead parameterises their effect with a friction factor. However, we can see that our model accurately captures the effect of the boundary layers on the pressure by the close comparison between the models in Fig. [9](#Fig9){ref-type="fig"}c. In Sect. [3](#Sec8){ref-type="sec"}, we investigated reducing the dimension of the control $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}$ by splitting it into three piecewise constant sections divided by $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x_1$$\end{document}$ and $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x_2$$\end{document}$, which we treated as free parameters. Motivated by these piecewise linear shapes, here we make the same simplification, reducing the degrees of freedom of the control to 2. We explore the parameter space generated by $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x_1$$\end{document}$ and $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x_2$$\end{document}$, using both CFD models to calculate pressure recovery. Each calculation made by the CFD models is much more computationally expensive than that of the simple model, but because of the low dimension of the degrees of freedom, we can still feasibly explore the different possible combinations of $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x_1$$\end{document}$ and $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x_2$$\end{document}$. This would not be tractable, however, if we were to use 100 degrees of freedom, as we did with the simple model in Sect. [3](#Sec8){ref-type="sec"}. Hence, the numerical optimisation using the simple model is very useful for finding the general shape of the optimal channels, around which we can further search for optima using more realistic, yet more computationally intensive CFD models. In Fig. [10](#Fig10){ref-type="fig"}, we plot contours of pressure recovery $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_p$$\end{document}$, given by ([10](#Equ10){ref-type=""}), ([11](#Equ11){ref-type=""}), as a function of the two parameters $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x_1$$\end{document}$ and $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x_2$$\end{document}$, where $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_p$$\end{document}$ is calculated using the *k*--$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\epsilon $$\end{document}$ model instead of the simplified model, as in Fig. [5](#Fig5){ref-type="fig"}. Similarly to the contour plots in Fig. [5](#Fig5){ref-type="fig"}, we exclude values of $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x_1$$\end{document}$ and $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x_2$$\end{document}$ which result in a diffuser angle larger than $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tan 7^\circ $$\end{document}$ for the two-dimensional case and $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tan 3.5^\circ $$\end{document}$ for the axisymmetric case.Fig. 10Contour plots of pressure recovery $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_p$$\end{document}$, given by ([10](#Equ10){ref-type=""}), ([11](#Equ11){ref-type=""}), over all permissible values of $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x_1$$\end{document}$ and $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x_2$$\end{document}$, calculated using the *k*--$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\epsilon $$\end{document}$ model. Direct comparison is made with Fig. [5](#Fig5){ref-type="fig"}, where the same contour plots are calculated using the simple model. **a** Two-dimensional case. **b** Axisymmetric case Comparing Figs. [5](#Fig5){ref-type="fig"} and [10](#Fig10){ref-type="fig"}, we see that the optimal diffuser shape using both the simple model and the *k*--$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\epsilon $$\end{document}$ model, is characterised by similar values of $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x_1$$\end{document}$ and $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x_2$$\end{document}$. In the two-dimensional case, according to the *k*--$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\epsilon $$\end{document}$ model, the optimal diffuser shape has $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x_1/h_0=13$$\end{document}$ and $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x_2/h_0=25$$\end{document}$, with a pressure recovery of $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_p=0.5370$$\end{document}$. According to the simplified model, the optimal diffuser shape has $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x_1/h_0=12.3$$\end{document}$ and $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x_2/h_0=24.3$$\end{document}$, with a pressure recovery of $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_p=0.5205$$\end{document}$, which is very close to that obtained with the *k*--$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\epsilon $$\end{document}$ model. Similarly, for the axisymmetric case, the *k*--$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\epsilon $$\end{document}$ model suggests an optimal diffuser shape with $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x_1/h_0=7$$\end{document}$ and $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x_2/h_0=21$$\end{document}$, giving a pressure recovery of $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_p=0.7067$$\end{document}$, whereas the simplified model suggests $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x_1/h_0=6.3$$\end{document}$ and $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x_2/h_0=19.8$$\end{document}$, with a pressure recovery of $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_p=0.6886$$\end{document}$. Considering that the diffuser angle is given by Eq. ([29](#Equ29){ref-type=""}), it is clear that if the optimal values of $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x_1$$\end{document}$ and $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x_2$$\end{document}$ are similar, according to the simple model and the CFD, then the optimal diffuser angle is also similar. In fact, we can compare the value of $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_p$$\end{document}$ as a function of diffuser angle by looking at intersections of the contour plots (Figs. [5](#Fig5){ref-type="fig"}, [10](#Fig10){ref-type="fig"}) with the lines $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x_1-x_2=\mathrm {const}$$\end{document}$. We have also generated these pressure recovery data using the $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k-\omega $$\end{document}$ SST model, and we find the results very similar. The average discrepancy between the $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_p$$\end{document}$ values calculated using the *k*--$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega $$\end{document}$ SST model and the *k*--$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\epsilon $$\end{document}$ model is 0.004 for the two-dimensional case, and 0.003 for the axisymmetric case. These results indicate that the optimal shapes found using the numerical optimisation routine and the simplified model are similar to the optimal shapes that would be found if we were to use either of these computational turbulence models as a forward model. Hence, this gives us confidence that the optimal shapes generated using the simplified model are close to true optimal shapes in reality. Discussion and conclusion {#Sec16} ========================= The effect of parameter values on the optimal shape {#Sec17} --------------------------------------------------- Although we have investigated optimal diffuser shapes in a number of specific cases, we have not yet explored the various parameters of the model thoroughly, which are listed in Table [1](#Tab1){ref-type="table"}. We now briefly discuss the effect that each of these parameters has on the optimal shapes. However, since there are many parameters, we do not provide plots for the analysis of every single parameter. One of the most important parameters is the velocity ratio $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$U_2(0)/U_0$$\end{document}$ of the inflow. To explore this parameter, we investigate optimal diffuser shapes for a fixed inflow with $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h_2(0)/h_0 = 0.5$$\end{document}$, an expansion ratio $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h_L/h_0 = 2.3$$\end{document}$ and a length ratio $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L/h_0 = 40$$\end{document}$, and we vary the velocity ratio. The results of the optimisation are displayed in Fig. [11](#Fig11){ref-type="fig"}, for $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$U_2(0)/U_0=0.3$$\end{document}$ and $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$U_2(0)/U_0=0.7$$\end{document}$. We see that the effect of a velocity ratio which is closer to 1 is that an initial widening section becomes favourable. This is because when the inflow is more uniform, wider angles penalise pressure recovery less. Therefore, the balance is tipped in favour of reducing wall drag by expanding the channel a little. In the extreme case where $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$U_2(0)/U_0$$\end{document}$ becomes close to unity, we have seen in Sect. [4.1](#Sec13){ref-type="sec"} that this initial widening section dominates throughout, such that the optimal control is purely bang-bang, with no singular arc. Notice how in the case of $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$U_2(0)/U_0=0.7$$\end{document}$ the shape can no longer be approximated with the parameterisation of $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x_1$$\end{document}$ and $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x_2$$\end{document}$.Fig. 11Investigation of the dependence of optimal diffuser shapes on the inflow velocity ratio in the two-dimensional case, showing velocity colour maps (**a**, **b**) and plots of the control $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}$ (**c**, **d**). In both cases, we choose an inflow with $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h_2(0)/h_0= 0.5$$\end{document}$, an expansion ratio $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h_L/h_0 = 2.3$$\end{document}$ and a length ratio $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L/h_0 = 40$$\end{document}$. The lower limit for the diffuser angle in both cases is $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha _\mathrm{min}=0^\circ $$\end{document}$. The upper limit is $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha _\mathrm{max}= \tan 7^\circ $$\end{document}$ The effect of increasing or decreasing the ratio of the size of the plug regions from $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h_2(0)/h_0=0.5$$\end{document}$ is that the distance it takes for one of the plug regions to disappear becomes smaller. If the velocity ratio is small then, as described earlier, this distance is critical because it marks the point where the flow is sufficiently mixed that it is acceptable to expand thereafter at a wider angle. Hence, the effect of increasing or decreasing $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h_2(0)/h_0$$\end{document}$ is that this critical distance becomes smaller. The effects of varying the diffuser expansion ratio $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h_L/h_0$$\end{document}$ and length ratio $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L/h_0$$\end{document}$ are more obvious and less interesting. Neither of them affect the optimal widening angle, but instead simply make the diffuser continue to expand wider and longer respectively. This is because they don't affect the crucial balance between wall drag and mixing effects. Varying the upper and lower bounds on the diffuser angle, $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha _\mathrm{max}$$\end{document}$ and $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha _\mathrm{min}$$\end{document}$, only affects the optimal solution if the diffuser angle touches the bounds over an interval. For example, in Fig. [11](#Fig11){ref-type="fig"}a, c, we see that $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}$ never touches $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha _\mathrm{max}$$\end{document}$. Therefore, in this case, raising $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha _\mathrm{max}$$\end{document}$ would have no effect on the solution. However, $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}$ clearly lies on the lower-bound $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha _\mathrm{min}$$\end{document}$ over an interval at the beginning and near the end of the domain. Therefore, varying $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha _\mathrm{min}$$\end{document}$ here moves the optimal control along with it. Throughout this manuscript, we have used a constant value of the spreading parameter $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S=0.11$$\end{document}$. In Sect. [5](#Sec15){ref-type="sec"}, we showed that this parameter value is consistent with both a *k*--$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\epsilon $$\end{document}$ and a *k*--$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega $$\end{document}$ SST computational turbulence model using all standard turbulence parameter values \[[@CR26], [@CR27]\]. In earlier work \[[@CR6]\], we compared our simple model to PIV experiments in a three-dimensional geometry and found $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S=0.18$$\end{document}$. The equivalent spreading parameter for free shear layers \[[@CR39]\] has been reported to take a range of values for different experiments and CFD calculations. Since the spreading parameter *S* is associated with shear layer growth rate, for larger *S*, the shear layer will entrain the plug regions over a shorter distance. Similar to varying $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h_2(0)/h_0$$\end{document}$, this decreases the critical distance after which expansion occurs. We have already discussed the effect of *S* on the singular arc in Sect. [4.2](#Sec14){ref-type="sec"}. For rougher channels with a larger friction factor *f*, thinner channels and smaller angles will be penalised more. In such cases, the optimal widening angle is larger. Furthermore, if *f* is sufficiently large, it becomes more advantageous to have an initial widening section, similar to situations where the velocity ratio $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$U_2(0)/U_0$$\end{document}$ is close to 1. In the extreme case where wall drag dominates, the control becomes bang-bang because the penalty of worsening the non-uniform flow is eclipsed by the effect of wall drag. For very small wall drag, the optimal diffuser shape appears to prioritise mixing over widening the flow. In these cases, thin channels and small diffuser angles are not penalised very much, such that the critical distance after which expansion occurs is precisely the point where the shear layer has reached across the entire channel. At this point, the flow is sufficiently mixed and can afford expansion. Conclusions {#Sec18} ----------- We have developed a numerical optimisation routine to find the diffuser shape which maximises pressure recovery for given non-uniform inflow, in both two-dimensional and axisymmetric cases. The optimisation uses a simplified mathematical model for the development of turbulent shear layers in confining channels. We find that some of the optimal diffuser shapes are well approximated by shapes which are composed of two straight sections separated by a widening section with a constant widening angle. This is in contrast to diffuser design for uniform flow, where diffusers do not typically have an initial straight section. Furthermore, we show that the optimal widening angle is less than the angle at which boundary layer separation typically occurs, which is usually the diffuser angle chosen for uniform flow. Therefore, we have shown that the effects of non-uniform inflow are critical to diffuser performance, and should not be ignored when it comes to diffuser design. In two limiting cases, we use analytical techniques to interpret the optimal diffuser shapes found with the numerical optimisation. The first of these cases is the small shear limit, where the inflow is almost uniform, in which case the optimal control is bang-bang, such that the diffuser widens at the maximum possible angle until it reaches the desired cross-sectional area, and then remains at that area. The second case is the pure shear limit, where the inflow is a purely sheared flow with no plug regions. In this case, the optimal control may have a singular arc where, on an interval, the diffuser angle takes values between its upper and lower bounds. We show that in certain cases, the singular arc corresponds to a constant angle, and this angle depends on the friction factor *f* and the spreading parameter *S*. We compare some of the numerical optimisation results with CFD simulations using both a *k*--$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\epsilon $$\end{document}$ and a *k*--$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega $$\end{document}$ SST turbulence model (using all standard turbulence parameter values), and the comparion showed good agreement. In the case where we approximate the diffuser shape with piecewise linear sections, we show that both the simplified model and the CFD share almost identical optimal shapes. This suggests that the optimal shapes found using the numerical optimisation and the simplified model are indeed close to the true optimal shapes in reality. Appendix A: Diffuser stagnation {#Sec19} =============================== We have discussed how diffusers have the tendency to accentuate non-uniform flow. In extreme cases, where the diffuser angle is too large, it is possible for regions of the flow to slow to zero velocity and recirculate. Let us now consider diffusers which have a non-uniform inflow velocity given by ([1](#Equ1){ref-type=""}). In our mathematical model, outlined in Sect. [2.1](#Sec3){ref-type="sec"}, we account for the possibility of a stagnated region by introducing the velocity of the slower plug region $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$U_2$$\end{document}$ into Bernoulli's equation ([6](#Equ6){ref-type=""}) in the form of a complementarity condition. In this way, if the slower central plug region reaches zero velocity, we model this as a region of dead water and maintain it at zero velocity. In reality, these regions have relatively slow recirculation. We do not resolve the recirculation, but instead we resolve the size of the regions and treat them as having average streamwise velocity $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$u=0$$\end{document}$. In order to justify this model assumption, we compare it with CFD calculations for a diffuser with a stagnated region.Fig. 12Comparison between our simple model and a *k*--$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\epsilon $$\end{document}$ CFD model for a two-dimensional diffuser with a stagnation region in the centre. **a** Velocity colour map calculated using the reduced model, with black dashed lines indicating the shear layer, and a solid black contour indicating the stagnated zone. **b** Corresponding velocity colour map calculated using the *k*--$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\epsilon $$\end{document}$ model. **c** Streamlines calculated from the *k*--$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\epsilon $$\end{document}$ model. **d** Pressure profile averaged across the width of the channel. An alternative colour scheme is used in the colour maps for the purposes of illustrating regions of zero velocity clearly To make the comparison, we choose an invelocity with $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$U_2(0)/U_0=0.75$$\end{document}$ and $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h_2(0)/h_0=0.5$$\end{document}$. We choose a value of $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$U_2(0)/U_0$$\end{document}$ fairly close to 1 to show that stagnation can occur for even moderately non-uniform inflow conditions. The diffuser that we select has constant widening angle $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha =\tan 11^\circ $$\end{document}$ and has non-dimensional length $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L/h_0=30$$\end{document}$. For the CFD, we use the same *k*--$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\epsilon $$\end{document}$ turbulence model as in Sect. [5](#Sec15){ref-type="sec"}. In Fig. [12](#Fig12){ref-type="fig"}, we compare the results of the model and the CFD. Time-averaged velocity colour maps are compared in Fig. [12](#Fig12){ref-type="fig"}a, b, where we indicate the stagnated region in our model (a) with a black contour. The comparison is good, with the model capturing the dominant flow features, such as the width of the shear layer. In Fig. [12](#Fig12){ref-type="fig"}c, we display streamlines calculated using CFD. These indicate that there is indeed a stagnated region with recirculation in the centre of the diffuser. This region is located in approximately the same position, and has approximately the same size as the prediction from the mathematical model. The time-averaged pressure profile, averaged across the channel width is plotted in Fig. [12](#Fig12){ref-type="fig"}d and, again, it shows good agreement between the CFD and our model, suggesting that our model accurately captures the general behaviour of the diffuser when it has a stagnated region. This publication is based on the work supported by the EPSRC Centre for Doctoral Training in Industrially Focused Mathematical Modelling (EP/L015803/1) in collaboration with VerdErg Renewable Energy Limited and inspired by their novel Venturi-Enhanced Turbine Technology for low-head hydropower.

Final date of releases availablility Due to some technical delays we will get Ambivalence and Black Forest CDs from the plant in next two weeks.All booklets for Thorns of the Carrion, Ambivalence and Black Forest will arrive to us in next few days. We will start to send the Thorns of the Carrion packages (which has been ordered without Ambivalence or Black Forest) on the next week. Thanks for comprehension

{"widgetClass":"VariantMatrixWidget","backorderMessage":"Backordered","backorderMessageSingleVariant":"This item is backordered.","orderedSelection":true,"productVariantId":0,"variantIdField":"product114362_VariantId","backorderToMessageSingleVariant":"This item is backordered and is expected by {0}.","lowPrice":9999.0,"attributeIndexes":[],"productId":114362,"priceVariance":true,"backorderToMessage":"Backordered to {0}","updateLastSelector":true,"highPrice":-9999.0,"fireStatusEvents":true} Rated 5 out of 5 by Betina from The dress is perfectNice dress wearing it was a hit in my party I got a lot of compliments Date published: 2017-04-02 Rated 5 out of 5 by Jeana from Just LovelyFits well, shoulder pads are larger than the online photo but it gives the dress a great look. Date published: 2016-12-26 Rated 4 out of 5 by Bebelover0123 from Pretty dress minus the shoulder padsI bought the light pink colour of this dress in stores on sale so I got a good deal on it. I was hesitant about trying it in because of the style and the shoulder pads however I was pleasantly surprised. The style and colour is great, I'm definitely doing to wear it to a wedding or something in the spring/summer. The shoulder pads are horrendous and didn't work for me but luckily I just cut them off. I'm 5'1, 92lbs and got it in a 0 and the fit was good, the inside lining did scrunch up a bit but it wasn't a deal breaker. Date published: 2016-12-25 Rated 5 out of 5 by Valy from ElegantIt is a glamorous, elegant dress. I love the delicate tissue. It gives a perfect body shape. Date published: 2016-10-22 Rated 5 out of 5 by Loveddress from Perfect!I absolutely love this dress! I went shopping looking for a dress I could wear to a wedding. Saw this dress and tried it on and I loved the way it looked and got. Exactly what I was looking for. I got so many compliments when I was at the wedding. I am wearing it again for another dress in January and also for a military awards dinner. Date published: 2016-10-13 Rated 2 out of 5 by Angel9 from Too fittedI did not like the way it fit on my arms and shoulders. It didn't feel comfortable. Date published: 2016-09-18 Rated 1 out of 5 by Yiyilabella from DesillusiinedI already bought baby clothes but this time the results were not pleasant, 3 garments buy 2 of them I did not like anything, nor height, nor dress fabric is rough and uncomfortable Date published: 2016-09-16 Rated 5 out of 5 by Mauri from Very pretty !this dress is beautiful , I bought it in red and am wearing it for a wedding in October. Very Well made , great martial , and fits perfect ! I'm about 125 and 5'4 and ordered a size 4. I did cut out the shoulder pads incase anybody is hesitant on those ( they weren't flattering for me ) . I do think the color is darker in person , i thought it would have been more of a bright red. But I still think it's a beautiful color and will be perfect for a fall wedding .

The present invention relates to an image forming apparatus adapted to enable a sheet or the like stuck in a carrier path to be removed by opening the carrier path between a feeding unit for feeding such a sheet to an image forming unit and a discharge unit for discharging the sheet carried from the image forming unit to the outside. Digital technology has recently found its fields of application in copying machines, and attempts are being made to improve image quality through the use of laser recording. The digital copying machines are now capable of producing an image output from data transmitted from devices other than a scanner unit in a copying machine, such as a personal computer and a facsimile machine, connected through an interface. A need arises here to produce image outputs in the same order as the associated image data inputs are received from another device or apparatus. xe2x80x9cFace-downxe2x80x9d types are currently popular; those types discharge sheet sequentially from the discharge unit so that the side of the sheet on which an image is formed looks down. The face-down type is equipped with a carrier path through which, sheet is fed sheet by sheet from a feeding unit, such as a sheet feeding unit, situated below an image forming unit and also sheet, after an image is formed thereon, is discharged face-down from a discharge unit situated above the image forming unit. Along the carrier path extending upright between the feeding unit and the discharge unit are there provided a pair of carrier rollers, transfer device, peeler device, fixing device, and other devices, which overall complicates the structure of the apparatus. Miniaturization of the image forming apparatus is another trend recently being pursued; if moving sheet gets stuck in the carrier path as a result of a problem in the image forming apparatus, removing the stuck sheet is a troublesome task. Japanese Patent Publication No. 8-18724 discloses an image forming apparatus having a main body which is separable into two parts with respect to the carrier path extending upright between the feeding unit and the discharge unit, one of the parts being a static body including an image forming unit, the other part being a movable body which, near the bottom thereof, is engaged rotatably to the static body via a supporting axis and which can thereby swing with respect to the static body, wherein if moving sheet gets stuck in the carrier path, the carrier path can be opened by swinging the movable body around the supporting axis, allowing the sheet to be removed from the carrier path. In the conventional image forming apparatus, the movable body in the main body is engaged rotatably with the static body, and the movable body is swung around the supporting axis. The structure allows the carrier path to be wide open on the side opposite to the swing center, but not on the side of the swing center. Therefore, it is difficult to remove sheet stuck near the entrance of the carrier path (near the feeding unit). Further, the entire movable body swings around the supporting axis, tracing an arc; therefore the transfer device, the carrier rollers, and other components which forms the carrier path in the movable body move tracing a curve, rather than a straight line. This makes it difficult to accurately position the aforementioned components of the carrier path mounted to the movable body and the image forming unit and the components of the carrier path, such as the carrier rollers and the fixing device, mounted to the static body. The movable body swings especially violently on the side far from the swing center, in other words, the exit of the carrier path, tracing a large arc, and requires high accuracy in relative positioning with respect to the static body. If accurate positioning of the components of the carrier path fails, problems are likely to develop with moving sheet in the carrier path. Besides, when the movable body is swung around the supporting axis, the movable body experiences a relatively large impact. Possible impact could be taken care of, by providing strength compensation to the supporting axis and associated parts and impact alleviation by means of a hydraulic dumper or another mechanism. However, this will add to the total weight of the image forming apparatus and result in increased load in swinging the movable body, which undesirably degrades operability of the movable body. To make the entrance of the carrier path (a part near the feeding unit) wide open, the supporting axis and the static body need be separated by a relatively great distance. This however adds to the size of the image forming apparatus and requires increased room for installation including free space to swing the movable body. It therefore becomes difficult to install the apparatus in limited space. If the movable body is provided with a switchback carrier path and a cover body which can swing so as to open the switchback carrier path, the movable body is swung first, and the cover body needs be also swung with respect to the already swung movable body, which adds to difficulty to the removing of sheet. An object of the invention is to provide an image forming apparatus having a carrier path which can be wide open along the entire length thereof without adding to the size owing to such a configuration that enables a movable body in a main body to slide and optionally a sub-carrier path, being connected to the carrier path at the midpoint thereof, which can be wide open together with the carrier path. Another object of the invention is to provide an image forming apparatus that can maintain good positional relationship among components forming a carrier path between a static body and a movable body in a main body and also that can position, relative to the image forming unit, an auxiliary device, such as a transfer device, mounted to the movable body with increased accuracy when the movable body is slid closed, owing to a configuration in which the static body or the movable body has a guide member for guiding the slide movement of the movable body. A further object of the invention is to provide an image forming apparatus which satisfactorily prevents a sheet stuck in the carrier path from falling when the carrier path is opened, owing to a configuration in which either the static body or the movable body has a pair of carrier rollers carrying the sheet. Yet another object of the invention is to provide an image forming apparatus that can position the auxiliary device, such as the transfer device, relatively to the image forming unit with increased accuracy when the movable body is slid closed, owing to a configuration in which the auxiliary device is provided swingingly to the movable body. An image forming apparatus in accordance with a first aspect includes: an image forming unit for forming an image on a sheet; a feeding unit for feeding the sheet toward the image forming unit; a discharge unit for discharging the sheet carried from the image forming unit to the outside thereof, and a main body separable into a static body and a movable body along a carrier path extending from the feeding unit to the discharge unit, the static body being provided with the image forming unit, and is adapted so that the movable body is slidable with respect to the static body. According to the first aspect, the carrier path extending from the feeding unit to the discharge unit can be wide open along the entire length thereof by sliding open the movable body; therefore, sheet stuck in the carrier path, especially, in winding and other parts where sheet is likely to get stuck, can be readily spotted and easily removed. The image forming apparatus thus delivers good operability in sheet removal. The movable body slides and experiences a relatively small impact when slid open; therefore, the movable body no longer needs a complicated supporting mechanism. The image forming apparatus weighs less and requires less installation space. An image forming apparatus in accordance with a second aspect is such that the feeding unit is provided in plurality and that the main body is separable into the static body and the movable body along the carrier path extending from the plurality of feeding units to the discharge unit. An image forming apparatus in accordance with a third aspect is such that the carrier path of one of the plurality of feeding units which is located relatively near the image forming unit is connected to the carrier path formed by one of the plurality of feeding units which is located relatively far from the image forming unit. According to the second and third aspects, the carrier path extending from the plurality of feeding units to the discharge unit can be wide open along the entire length thereof by sliding open the movable body; therefore, sheet stuck near any feeding unit can be easily removed. The image forming apparatus thus delivers good operability in sheet removal. An image forming apparatus in accordance with a fourth aspect is such that the movable body has guide units for guiding the sheet on which an image is formed by the image forming unit along the carrier path. According to the fourth aspect, when the movable body is slid closed, the carrier path extending from the image forming unit to the discharge unit can be positioned to a predetermined state by means of a simple configuration; therefore, problems are less likely to occur at junctions of the static body and the movable body in the carrier path. An image forming apparatus in accordance with a fifth aspect includes: an image forming unit for forming an image on a sheet; a feeding unit, provided below the image forming unit, for feeding the sheet toward the image forming unit; a discharge unit, provided above the image forming unit, for discharging the sheet carried from the image forming unit to the outside; a carrier path extending from the feeding unit to the discharge unit; a sub-carrier path, being connected to the carrier path near an exit thereof, for carrying the sheet carried from the image forming unit in a direction moving away from the discharge unit; and a main body separable into a static body and a movable body along the carrier path, the static body being provided with the image forming unit, and is adapted so that the sub-carrier path extends flatly sideways and that the movable body is slidable with respect to the static body along the sub-carrier path. With the fifth aspect, all the advantages of the first aspect are available. Further, the sub-carrier path can be wide open, and sheet stuck in the sub-carrier path can be easily removed. An image forming apparatus in accordance with a sixth aspect is such that the sub-carrier path is shorter than the carrier path. According to the sixth aspect, the carrier path and the sub-carrier path can be wide open along the entire lengths thereof by sliding the movable body a distance, L+xcex1, which is equal to a sum of the length L of the sub-carrier path and a suitable distance xcex1. Therefore, the movable body needs to be slid a shorter distance, requiring less space to install the image forming apparatus. An image forming apparatus in accordance with a seventh aspect is such that the sub-carrier path, near an entrance thereof, overlaps the carrier path and from the entrance to an exit thereof, extends flatly in a direction moving away from the discharge unit and that the movable body is slidable along the sub-carrier path. According to the seventh aspect, the sub-carrier path extending flatly in a direction moving away from the discharge unit, near an entrance thereof, overlaps the carrier path; therefore, the movable body needs to be slid an even shorter distance, requiring even less space to install the image forming apparatus. An image forming apparatus in accordance with an eighth aspect is such that the sub-carrier path is an entrance of a switchback carrier path for carrying the sheet carried from the image forming unit to an entrance of the carrier path. According to the eighth aspect, the switchback carrier path can be wide open near the entrance thereof, that is, the exit of the carrier path, which is the most difficult part to carry sheet in the carrier path; therefore, sheet stuck in the carrier path can be readily spotted and easily removed. An image forming apparatus in accordance with a ninth aspect includes a pair of carrier rollers, mounted to either the static body or the movable body, for carrying the sheet along the carrier path while holding the sheet in between at a position facing the carrier path. According to the ninth aspect, when the movable body is slid open to open the carrier path, the pair of carrier rollers mounted to the movable body continue holding the sheet in between. Those areas surrounding the carrier path and the user""s hands can be thereby prevented from being smeared with an unfixed toner image on sheet which droops or falls from the carrier path. The sheet stuck in the carrier path can be readily spotted. The image forming apparatus thus again delivers good operability in sheet removal. An image forming apparatus in accordance with a tenth aspect is such that the static body includes: a control roller for controlling a timing to carry the sheet to the image forming unit; and a guide body for guiding the sheet to the control roller, the control roller and the guide body both being provided between the feeding unit and the image forming unit at a position facing the carrier path. According to the tenth aspect, even if the carrier path is opened, the control roller for controlling a timing to carry the sheet to the image forming unit is positioned unchanged with respect to the guide body for guiding the sheet to the control roller, for better resist precision. The image is therefore formed on the sheet at an ideal position. An image forming apparatus in accordance with an eleventh aspect includes: an image forming unit for forming an image on a sheet; a feeding unit for feeding the sheet toward the image forming unit; a discharge unit for discharging the sheet carried from the image forming unit to the outside; a sub-carrier path, being connected to an exit side of a carrier path between the feeding unit and the discharge unit, for carrying the sheet having passed through the image forming unit in a direction different from the discharge unit; and a main body separable into a static body and a movable body along the carrier path, the static body being provided with the image forming unit, and is adapted so that the movable body is slidable with respect to the static body and has a guide unit for guiding the sheet along the sub-carrier path. With the eleventh aspect, all the advantages of the first aspect are available. Further, the sheet in the carrier path can be carried to the sub-carrier path along the guide unit of the movable body; therefore, by sliding open the movable body, the sub-carrier path can be wide open, facilitating the removal of sheet stuck in the sub-carrier path. An image forming apparatus in accordance with a twelfth aspect includes: an image forming unit for forming an image on a sheet; a feeding unit for feeding the sheet toward the image forming unit; a discharge unit for discharging the sheet carried from the image forming unit to the outside; a switchback carrier path, being connected to an entrance side and an exit side of a carrier path between the feeding unit and the discharge unit, for carrying the sheet carried from the image forming unit toward the feeding unit; and a main body separable into a static body and a movable body along the carrier path, the static body being provided with the image forming unit, and is adapted so that the feeding unit is provided in plurality and that the movable body has a guide unit, provided below a connection portion where the switchback carrier path is connected to the exit side of the carrier path, for guiding along the carrier path the sheet carried from one of the plurality of feeding units which is located relatively far from the image forming unit to the carrier path formed by one of the plurality of feeding units which is located relatively near the image forming unit. With the twelfth aspect, all the advantages of the first aspect are available. Further, when the movable body is slid closed, the carrier path connected to the plurality of feeding units can be positioned to a predetermined state by means of a simple configuration; therefore, problems are less likely to occur at junctions of the static body and the movable body in the carrier path. An image forming apparatus in accordance with a thirteenth aspect is such that the movable body has a guide unit for guiding along the carrier path the sheet carried from the switchback carrier path to the carrier path. According to the thirteenth aspect, when the movable body is slid closed, a part of the carrier path which is connected to the switching carrier path near the exit thereof can be positioned to a predetermined state by means of a simple configuration; therefore, problems are less likely to occur at junctions of the static body and the movable body in the carrier path. An image forming apparatus in accordance with a fourteenth aspect includes: a carrier switching body for carrying the sheet carried from the image forming unit by switching between the discharge unit and the sub-carrier path; and a holding body, mounted swingingly to the movable body, for holding the carrier switching body. According to the fourteenth aspect, the holding body for holding the carrier switching body is mounted swingingly to the movable body; therefore, when the movable body is slid closed, the carrier switching body can be accurately positioned with respect to the carrier path and the sub-carrier path, thereby improving the quality of the image output produced on the sheet. The sheet can be carried in a satisfactory manner in the sub-carrier path in which eet passes after the fixing and tends to be carried only in an unstable manner. An image forming apparatus in accordance with a fifteenth aspect is such that either the static body or the movable body has multiple guide members for guiding the slide movement of the movable body, and the movable body has an auxiliary device, located among the guide members, for assisting image formation on the sheet in the image forming unit. According to the fifteenth aspect, the auxiliary device, for example, a transfer device, is mounted to the movable body, among the guide members. Therefore, when the movable body is slid closed, the auxiliary device can be moved toward the image forming unit, while keeping a substantially correct positional relationship. The auxiliary device can thereby be accurately positioned with respect to the image forming unit, which improves the quality of the image formed on the sheet. An image forming apparatus in accordance with a sixteenth aspect is such that the guide members are disposed on both sides of the carrier path in terms of width thereof and on an entrance side and an exit side of the carrier path. According to the sixteenth aspect, the auxiliary device is mounted to the movable body in an area formed by the guide members disposed in the back and those disposed in the front as viewed with the image forming apparatus installed in a suitable place; therefore, when the movable body is slid closed, the auxiliary device can be moved straightly toward the image forming unit in a stable condition. The auxiliary device can be thereby accurately positioned with respect to the image forming unit, improving the quality of the image formed on the sheet. An image forming apparatus in accordance with a seventeenth aspect is such that the auxiliary device is disposed at the central position among the guide members. According to the seventeenth aspect, the auxiliary device is mounted to the movable body substantially at the center of an area formed by the multiple guide members; therefore, when the movable body is slid closed, the auxiliary device can be moved straightly toward the image forming unit in a stable condition. The auxiliary device can be thereby accurately positioned with respect to the image forming unit, improving the quality of the image formed on the sheet. An image forming apparatus in accordance with an eighteenth aspect is such that either the static body or the movable body has: a guide member for guiding the slide movement of the movable body; and prevention means for preventing the slide movement of the movable body, and there is provided an auxiliary device, located between the guide member and the prevention means, for assisting image formation on the sheet in the image forming unit. According to the eighteenth aspect, the auxiliary device is mounted to the movable body between the guide member and the prevention means; therefore, when the movable body is slid closed, the auxiliary device can be moved straightly toward the image forming unit in a stable condition, and the movable body can be surely kept closed. The auxiliary device can be thereby accurately positioned with respect to the image forming unit, and the relative position is surely maintained, improving the quality of the image formed on the sheet. An image forming apparatus in accordance with a nineteenth aspect is such that either the static body or the movable body has guide members, located near an entrance and exit of the carrier path, for guiding the slide movement of the movable body, and there are provided among the guide members: an auxiliary device for assisting image formation on the sheet in the image forming unit; and prevention means for preventing the slide movement of the movable body. According to the nineteenth aspect, the guide members are disposed near the top and an bottom of the main body, and sheet stuck in the carrier path can be readily removed, with none of the guide members obstructing the removing action. Besides, the auxiliary device and the prevention means are disposed among the guide members for sliding the movable body; therefore, when the movable body is slid closed, the auxiliary device can be moved straightly toward the image forming unit, while keeping a substantially correct positional relationship. The auxiliary device can thereby be accurately positioned with respect to the image forming unit. In addition, the movable body can be slid smoothly and experiences less deformation in the slide movement; as a result, the movable body can be slid straightly. An image forming apparatus in accordance with a twentieth aspect includes: guide members, disposed on both sides of the carrier path in terms of width thereof, for guiding the slide movement of the movable body; and an auxiliary device, located near the guide members, for assisting image formation on the sheet in the image forming unit. According to the twentieth aspect, the auxiliary device is located among the guide members disposed on both sides of the carrier path in terms of width thereof, therefore, when the movable body is slid closed, the auxiliary device can be moved straightly toward the image forming unit, while keeping a substantially correct positional relationship. The auxiliary device can thereby be accurately positioned with respect to the image forming unit, improving the quality of the image formed on the sheet. An image forming apparatus in accordance with a twenty-first aspect is such that there are more guide members on one side of the carrier path in terms of width thereof than on the other side. According to the twenty-first aspect, there can be less guide members in the front than in the back as viewed with the image forming apparatus installed in a suitable place; therefore, sheet stuck in the carrier path can be readily spotted. Moreover, the guide members present less obstruction to sheet removing action. The image forming apparatus thus delivers good operability in sheet removal. An image forming apparatus in accordance with a twenty-second aspect is such that one side of the auxiliary device is supported between the guide members on one side and the other side thereof is supported near the guide members on the other side. According to the twenty-second aspect, the auxiliary device is mounted to the movable body with one of sides of the auxiliary device located near the guide members on the other side and with the other side located between the guide members on the one side; therefore, when the movable body is slid closed, the auxiliary device can be moved straightly toward the image forming unit, while keeping a substantially correct positional relationship. The auxiliary device can thereby be accurately positioned with respect to the image forming unit, improving the quality of the image formed on the sheet. An image forming apparatus in accordance with a twenty-third aspect is such that the auxiliary device is a transfer device of a contact type which contacts the image forming unit, and the transfer device is disposed near the prevention means. According to the twenty-third aspect, a good positional relationship is always ensured between the sheet and the transfer device, and the prevention means reduces variations in the relationship between the sheet and the rotated transfer device to a minimum. The transfer device can thereby be accurately positioned with respect to the image forming unit, improving the quality of the image formed on the sheet. An image forming apparatus in accordance with a twenty-fourth aspect is such that the guide members on the other side of the carrier path in terms width thereof are located far from a contact portion where a side of the sheet contacts in the carrier path. An image forming apparatus in accordance with a twenty-fifth aspect is such that the contact portion is a winding part, a connection portion where the sub-carrier path is connected, or a connection portion where a switchback carrier path is connected. According to the twenty-forth or twenty-fifth aspect, those guide members in the front as viewed with the image forming apparatus installed in a suitable place can be disposed a distance away from parts of a carrier path where problems are likely to develop with moving sheet. The guide members therefore present less obstruction in removing sheet stuck in the carrier path. The image forming apparatus thus delivers improved operability in sheet removal. An image forming apparatus in accordance with a twenty-sixth aspect is such that the auxiliary device is disposed swingingly. According to the twenty-sixth aspect, the auxiliary device is mounted swingingly to the movably body; therefore, when the movable body is slid closed, the auxiliary device can thereby be accurately positioned with respect to the surface of the image forming unit, improving the quality of the image formed on the sheet. Further, since the auxiliary device can thereby be accurately positioned with respect to the surface of the image forming unit, no highly precise sliding means is required to slide the movable body. Costs are saved and the movable body can be slid smoothly. An image forming apparatus in accordance with a twenty-seventh aspect is such that the auxiliary device is a transfer device for transferring the image formed by the image forming unit onto the sheet. According to the twenty-seventh aspect, when the movable body, which is slidable by the benefit of the guide members, is slid closed, the transfer device can be positioned with respect to the image forming unit mounted to the static body in a suitable condition. Thus, the quality of the image formed on the sheet is ensured. An image forming apparatus in accordance with a twenty-eighth aspect is such that the auxiliary device is a transfer device of a contact type which contacts the image forming unit. According to the twenty-eighth aspect, the transfer device of a contact type is mounted to the movable body which is slidable; therefore, when the movable body is slid closed, the transfer device of a contact type can be positioned with respect to the image forming unit in a predetermined positional relationship, and the quality of the image formed on the sheet is improved. An image forming apparatus in accordance with a twenty-ninth aspect is such that the transfer device has a connection terminal connected to and disconnected from a power source terminal provided to the static body. According to the twenty-ninth aspect, the connection terminal is provided to the transfer device which can be accurately positioned with respect to the image forming unit; therefore, when the movable body is slid closed, the connection terminal provided to the transfer device can be surely connected to the power source terminal provided to the static body, which ensures image formation on the sheet. Further, the connection terminal can be surely connected to the power source terminal; therefore, faulty operations due to damage or improper connection of the power source terminal and the connection terminal can be avoided. The above and further objects and features of the invention will more fully be apparent from the following detailed description with accompanying drawings. FIG. 1 is a cross-sectional view of an image forming apparatus in accordance with the invention, showing an open carrier path; FIG. 2 is a cross-sectional view of major components of an image forming apparatus in accordance with the invention, showing an open carrier path; FIG. 3 is a cross-sectional view of an image forming apparatus having a single feeding unit in accordance with the invention, showing a closed carrier path; FIG. 4 is an enlarged cross-sectional view of the entrance and vicinity of a carrier path in an image forming apparatus in accordance with the invention; FIGS. 5A-5C are enlarged cross-sectional views of the exit and vicinity of a carrier path in an image forming apparatus in accordance with the invention; FIG. 6 is a cross-sectional view of a second embodiment of the image forming apparatus in accordance with the invention, showing an open carrier path; FIG. 7 is a perspective view of a fourth embodiment of the image forming apparatus in accordance with the invention, showing an open carrier path; FIG. 8 is a perspective view of a fifth embodiment of the image forming apparatus in accordance with the invention, showing an open carrier path; FIG. 9 is a perspective view of a sixth embodiment of the image forming apparatus in accordance with the invention, showing an open carrier path; FIG. 10 is a perspective view of the sixth embodiment of the image forming apparatus in accordance with the invention, showing an open carrier path; and FIG. 11 is a cross-sectional view of major components of an image forming apparatus in accordance with the invention, showing an open carrier path.

1. Field of the Invention The present invention relates generally to asphalt cements and to asphalt or bituminous concrete paving compositions. More specifically, the present invention is concerned with the provision of novel reinforcing filler compositions for use in asphalt cements, which reinforcing filler compositions impart desirable properties to asphalt cements, per se, and to asphalt concretes formed therewith. 2. The Prior Art In the 1962 Proceedings of the Australian Road Research Board, Vol. 1, Part 2, there appear separate reports by K. G. Martin (pages 895 ff) and A. G. Aliotti (pages 912 ff). The major premise upon which these reports are based resides in the authors' respective conceptualizations of benefits to be enjoyed by the use of rubber reinforcing grades of carbon black as additives in asphalt cements and concretes. Unfortunately, the experimental results of Martin's work, wherein there were employed rubber-grade carbon black pellets, led this author to the conclusion that the benefits he originally projected were either not forthcoming or existed to such a minor degree as to be of minor significance. Martin further concluded that the optimal amounts of carbon black to be employed were about 3 weight parts of carbon black on 100 weight parts of the asphalt cement. Attempts by Martin to use higher amounts of carbon black and to add higher amounts of fluxing oil separate from the carbon black resulted in the conclusion that "if an aromatic oil is used to facilitate dispersion, the fluxing effect of the oil on the bitumen more than offsets any advantages conferred by the carbon black." The Aliotti report merely provides a condensed review of the history, techniques of manufacture and properties of carbon black, the author speculating that incorporation of carbon black into asphalt cements should have some beneficial effects. However, Aliotti does not teach or suggest as to how to achieve the beneficial results; he merely submits that work should be encouraged by responsible authorities to conduct practical field tests. In accordance with the present invention, there are now provided carbon black based reinforcing filler compositions which compositions impart profound and beneficial improvements in the properties of asphalt cements and in bituminous or asphalt concrete paving compositions formed therewith.

Expanded Metal To Innovate With Epicor ERP AUSTIN, Texas and LONDON, April 02, 2014 Unlike Other Solutions, Epicor Showed It had Manufacturing in Its DNA Epicor Software Corporation, a global leader in business software solutions for manufacturing, distribution, retail and services organisations, today announced that The Expanded Metal Company Limited, part of the Gibraltar Industries Inc. group, and a global manufacturer of expanded mesh products to a wide range of industries, has selected the Epicor next-generation enterprise resource planning (ERP) solution to replace its existing ERP software and support its international operations. Expanded Metal has been manufacturing mesh-based metal products for more than 120 years at its site in Hartlepool, and also has a state-of-the-art production facility in Hannover, Germany. Unlike many companies in its industry, Expanded Metal has used an ERP system to manage its full quote-to-cash cycle for over 20-years. As ERP software evolved, the product it was using has become out-of-date and is now a risk to the business, as the complexity of its products demand more than its feature-set can support. “The solution we currently use is no longer supported by the software vendor and has not been updated for some time,” said John Charlton, Finance Director and project lead for Expanded Metal. “It became time for us to look at a system that would allow us to deal with the value-add manufacturing services that we offer, as we move away from being a commodity business, and used more advanced production scheduling techniques.” The new solution needed to provide sales, finance, production, CRM, manufacturing and supply chain support for the company, on a single consistent platform, while ensuring adherence to all local financial regulations. Expanded Metal started by reviewing the top tier ERP solution used by its parent company, but didn't feel it could meet its needs cost effectively. Following a review of the wider market, Epicor ERP was selected because of its ease of use and versatile manufacturing features which were available out-of-the-box. “We've become a business that provides complex products to demanding markets such as the automotive and architectural industries,” added Charlton. “They require efficient manufacturing and supply chain processes, as well as particular attention to quality control and traceability. Epicor will give us all of these features, and has manufacturing in its DNA - we didn't get that feeling from the other products we reviewed.” “Companies need to have the right technology in place, not just for today, but for tomorrow - it must react and evolve with the company's needs,” said Steve Winder, regional vice president for Epicor in the UK and Ireland. “Technology-led change is an essential part of allowing companies to innovate, and that has been the finding of our recent Inspired to Make It research. Technology innovation was seen as critical to the future of manufacturing success, with 98% saying change had to happen, and 57% saying high levels of innovation were required. Technology such as Epicor ERP plays a key role in enabling and inspiring that innovation if embraced across a company's operations.” About Epicor Software Corporation Epicor Software Corporation is a global leader delivering inspired business software solutions to the manufacturing, distribution, retail and services industries. With over 40 years of experience serving small, midmarket and larger enterprises, Epicor has more than 20,000 customers in over 150 countries. Epicor enterprise resource planning (ERP), retail management software, supply chain management (SCM), and human capital management (HCM) enable companies to drive increased efficiency and improve profitability. With a history of innovation, industry expertise and passion for excellence, Epicor provides the single point of accountability that local, regional and global businesses demand. The Company's headquarters are located in Austin, Texas, with offices and affiliates worldwide. For more information, visit www.epicor.com. Epicor and the Epicor logo are trademarks of Epicor Software Corporation, registered in the United States and other countries. Other trademarks referenced are the property of their respective owners. The product and service offerings depicted in this document are produced by Epicor Software Corporation. Cookies are important to the proper functioning of a site. To improve your experience, Epicor uses cookies to remember log-in details and provide secure log-in, collect statistics to optimize site functionality, and deliver content tailored to your interests. Click ‘agree and proceed’ to accept cookies and go directly to the site, or click on our terms of use and privacy policy for more information.

Andrew Webster Andrew Webster may refer to: Andrew Webster (cricketer) (born 1959), English cricketer Andrew Webster (footballer, born 1947), English footballer Andrew Webster (footballer, born 1982), Scottish footballer Andrew Webster (rugby league) (born 1982), Australian rugby league player and coach

Art on the Lagoon A Surgeon's-Eye View This is a still from Yuri Ancarani’s video called “Da Vinci”, possibly the most striking piece from the Arsenale group exhibition curated by the New Museum’s Massimiliano Gioni. All the video gives us, more or less, is a fiber-optic, surgeon’s-eye view of the inside of someone’s gut, as it undergoes a laparoscopic operation. We watch, from inside and among folds of offal, as the surgeon’s tiny robotic tools push their way in, cut things up, burn things off then sew up what’s left. I’m afraid that the “magic” performed by the operating room’s Da Vinci Si model robot, and the real work that it does in the world, makes the best of art’s meager efforts seem almost impotent. This, you could say, is the true issue at the heart of Gioni’s ambitious curating … but you’ll have to wait for my upcoming Newsweek review to get all the – gory – details.

1. Field of the Invention This invention relates to surface heating means for cooking purposes, and particularly to a combined reflector pan and trim ring that supports the heating unit. 2. Description of the Prior Art In the past, most if not all reflector pans were separate from the decorative trim ring which surrounds the heating unit. Most trim rings are made integral with the heating unit as is shown in the Dills U.S. Pat. No. 3,258,580. Some trim rings are made independent of both the heating unit and the reflector pan. All trim rings are made with a highly reflective surface such as chromium plating to present a decorative appearance. Most reflector pans are made with highly reflective surface to direct the heat energy in an upwardly direction for improved heat transfer efficiency with respect to a utensil supported on the heating unit. It is well to maintain both the reflector pan and the trim ring clean of food soil for both appearance and operational purposes. Many electric ranges are furnished with pyrolytic self-cleaning ovens which utilize a high temperature cycle between about 750.degree. F. and 950.degree. F. for an extended period of time for automatically decomposing the food soil and grease spatter lodged on the walls of the oven liner and the oven door. It is advantageous to be able to clean the reflector pans and trim rings in the self-cleaning oven. Aluminum reflector pans have been widely used and later cleaned in a self-cleaning oven. One disadvantage is that the aluminum tends to soften at heat cleaning temperatures. It is important not to place anything on top of an inverted reflector pan during the pyrolytic cleaning cycle in order to prevent distortion of the pan once the aluminum softens during cleaning. After a few cleaning cycles, an aluminum pan loses its strength completely and it can be distorted even when handling very carefully. Chromium plated reflector pans and trim rings cannot be cleaned in a self-cleaning oven because they cannot withstand the high temperatures without discoloring badly. Porcelain enamelled steel reflector pans have been used with surface heating units and cleaned in self-cleaning ovens but there still remains the problem with cleaning and discoloration of the trim rings, and reflecting the heat energy in an upward direction. The principal object of the present invention is to provide a combined reflector pan and trim ring of sheet material which will not deteriorate when subjected to the temperatures encountered in a pyrolytic self-cleaning oven. A further object of the present invention is to provide a combined reflector pan and trim ring of the class described formed of composite sheet material with an aluminum top layer reinforced steel layer that is corrosion resistant. A further object of the present invention is to provide a combined reflector pan and trim ring of the class described of corrosion resistant steel which supports and reinforces an integral aluminum trim ring.

Recently, application of rice flour to fermented bakery products and noodles has been highlighted because rice is highly recognized as a healthy food. There are many suggestions for the process for producing unpolished- or polished-rice flour, which is favorable for producing bakery products and noodles as an substitute of wheat flour, using unpolished- or polished-rice as a material. Unpolished rice flour is generally produced by the steps of roasting unpolished rice grains without polishing, and milling the resultant into flour. For example, a process for producing unpolished rice flour, comprising the steps of allowing to expand unpolished rice grains by heating and pressurizing, and drying and milling the resultant, was proposed as disclosed in Japanese Patent Kokai No. 22155/88. Also, as disclosed in Japanese Patent Kokai No. 45130/2002, a process for producing unpolished rice flour, comprising the steps of steaming unpolished rice grains, and drying and milling the resultant, has been proposed. While, polished rice flour is generally produced by the steps of polishing unpolished rice by applying to a polisher for shaving bran, soaking the polished rice in water, and drying and milling the resultant by using various milling methods such as roll-type milling, impact-type milling, stamp-milling, and grinding with water. “JOSHINKO”, a kind of polished rice flour produced by roll-type milling, and “JOYOKO”, a kind of polished rice flour produced by stamp-milling are well known. Recently, there have been proposed several processes for producing polished rice flour, for example, a process comprising the steps of soaking rice grains in a solution comprising pectinase, dehydrating the resulting rice grains, milling the dehydrated rice grains to a fine rice flour, drying the flour to give a moisture content of about 15% (w/w) (hereinafter, “% (w/w)” is simply abbreviated as “%” in this specification), and baking the resulting flour at about 150° C. as disclosed in Japanese Patent Kokai No. 287,652/92; a process comprising the steps of soaking a material rice grains in a solution comprising enzymes such as hemicellulase, pectinase, and pectin esterase, drying the resulting rice grains, and milling the dried rice grains as disclosed in Japanese Patent Kokai No. 68,468/93; and a process comprising the steps of soaking rice grains in a solution comprising salts of organic acids and those with pectinase, dehydrating and drying the soaked rice rice grains, and milling the dried rice grains as disclosed in Japanese Patent Kokai No. 175,636/2000. As described above, the processes for producing rice flour (throughout the specification, both unpolished- and polished-rice flours may be simply called as “rice flour”) are different depending on which unpolished-rice or polished-rice is used as a material, because the properties of those rice grain are different. Therefore, in the case of producing both unpolished- and polished-rice flours, there are disadvantages of requiring specific hardwares and processes, which are suitable therefor, and high costs for producing them. While, a method for producing rice flour from both unpolished- and polished-rice using a single process as above has been also proposed. For example, a process for producing rice flour, comprising the steps of soaking raw rice grains including unpolished rice into water which contains an amylase; freezing the soaked rice; and drying and milling the resultant, was disclosed in Japanese Patent No. 3,075,556. However, the process has disadvantages of requiring a process of freezing rice and a relatively high cost for the production. The present invention was accomplished to solve the above various disadvantages of conventional processes for producing rice flour. The first object of the present invention is to provide a process for producing rice flour, which enables to prepare unpolished- and polished-rice into rice flours in an single method on an industrial scale and inexpensively. The second object of the present invention is to provide rice flour produced by the process and uses thereof for producing bakery products and noodles.

Q: COUNT() and Left Join not working I'm having trouble at query which displays the Employee Number, First Name, Last Name and the number of orders of each employee. Make sure that the Number of orders column name should be “OrderCount”. Order By the OrderCount then by employee ID. Null is allowed. employee_data containing columns: Emp_ID, F_Name, L_Name order_data containing columns: O_ID,Emp_ID, OrderNumber Here's my query: Select order_data.Emp_ID, F_Name, L_Name, COUNT(employee_data.Emp_ID) as OrderCount FROM order_data LEFT JOIN employee_data ON employee_data.Emp_ID = order_data.Emp_ID GROUP BY order_data.Emp_ID ORDER BY OrderCount These are my tables: employee_data order_data And the output should be: But it is giving me this wrong input. A: Aggregate functions cannot be used along with other fields in a query. You can use it in a sub-query, as follows: Select order_data.Emp_ID, F_Name, L_Name, (select COUNT(employee_data.Emp_ID) from employee_data) as OrderCount FROM order_data LEFT JOIN employee_data ON employee_data.Emp_ID = order_data.Emp_ID GROUP BY order_data.Emp_ID ORDER BY OrderCount Hope it helps .. :) A: Try this: SELECT od.Emp_ID, ed.F_Name, ed.L_Name, COUNT(DISTINCT od.O_ID) AS OrderCount FROM order_data od LEFT JOIN employee_data ed ON ed.Emp_ID = od.Emp_ID GROUP BY od.Emp_ID ORDER BY OrderCount

Q: Padding text in listbox var a1 = "HEL"; var a2 = "HELLO"; var a3 = "LLO"; var length = a2.Length+5; listbox.Items.Add(a1.PadRight(length) +"End"); listbox.Items.Add(a2.PadRight(length) + "End"); listbox.Items.Add(a3.PadRight(length) + "End"); I have code like this to obviously pad all text so that the word End lines up. The problem is I have to change the font from the wpf listbox from Segoe UI to Courier New to have this work. The rest of my app uses Segoe UI, so I think it looks weird here. Is there any way to achieve the result with Segoe UI or maybe a similar font with correct spacing I could use, or maybe someone has some other smart solution i haven't even thought of? :-) Thanks edit at the end of the day I want this to display to related items like this: ITEM A -> ITEM B ITEM X -> ITEM Y ITEM C -> ITEM E dont want to use gridview. A: Feed the ListBox the two pieces of data separately, and use a data template. Here's how. First, create a little class to represent each item you want to insert: public class WordPair { public string First { get; set; } public string Second { get; set; } } (You probably already have a suitable class and/or collection in your application -- I assume those pairs of strings are coming from somewhere!) Second, set your ListBox.ItemsSource to a collection of these things: listBox.ItemsSource = new List<WordPair> { new WordPair { First = "ITEM A", Second = "ITEM B" }, new WordPair { First = "ITEM X", Second = "ITEM Y" }, }; Again, this collection may already exist in your app. Third, create a DataTemplate specifying the desired layout, and assign it to your ListBox.ItemTemplate: <!-- in your Window.Resources section --> <DataTemplate x:Key="AlignedPairs"> <Grid> <Grid.ColumnDefinitions> <ColumnDefinition Width="*" /> <ColumnDefinition Width="Auto" /> <ColumnDefinition Width="*" /> </Grid.ColumnDefinitions> <TextBlock Text="{Binding First}" Grid.Column="0" /> <TextBlock Text="->" TextAlignment="Center" Grid.Column="1" /> <TextBlock Text="{Binding Second}" TextAlignment="Right" Grid.Column="2" /> </Grid> </DataTemplate> <ListBox Name="listBox" ItemTemplate="{StaticResource AlignedPairs}"> <ListBox.ItemContainerStyle> <Style TargetType="ListBoxItem"> <Setter Property="HorizontalContentAlignment" Value="Stretch" /> </Style> </ListBox.ItemContainerStyle> </ListBox> (I've guessed at the exact alignment you want for the items, but you can obviously tweak it.) Note that you also need to set the HorizontalContentAlignment of the ListBoxItems to Stretch using ListBox.ItemContainerStyle. Otherwise each ListBoxItem will take up only the space it needs, resulting in all the Grid columns being minimal size and looking like a straight concatenation. Stretch makes each ListBoxItem fill the full width so the Grid columns are forced to grow accordingly.

import random from mmf.common.sample import Sample from mmf.datasets.builders.coco import COCODataset class MaskedCOCODataset(COCODataset): def __init__(self, config, dataset_type, imdb_file_index, *args, **kwargs): super().__init__(config, dataset_type, imdb_file_index, *args, **kwargs) self.dataset_name = "masked_coco" self._two_sentence = config.get("two_sentence", True) self._false_caption = config.get("false_caption", True) self._two_sentence_probability = config.get("two_sentence_probability", 0.5) self._false_caption_probability = config.get("false_caption_probability", 0.5) def load_item(self, idx): sample_info = self.annotation_db[idx] current_sample = Sample() if self._use_features: features = self.features_db[idx] if hasattr(self, "transformer_bbox_processor"): features["image_info_0"] = self.transformer_bbox_processor( features["image_info_0"] ) if self.config.get("use_image_feature_masks", False): current_sample.update( { "image_labels": self.masked_region_processor( features["image_feature_0"] ) } ) current_sample.update(features) else: image_path = str(sample_info["image_name"]) + ".jpg" current_sample.image = self.image_db.from_path(image_path)["images"][0] current_sample = self._add_masked_caption(sample_info, current_sample) return current_sample def _add_masked_caption(self, sample_info, current_sample): captions = sample_info["captions"] image_id = sample_info["image_id"] num_captions = len(captions) selected_caption_index = random.randint(0, num_captions - 1) other_caption_indices = [ i for i in range(num_captions) if i != selected_caption_index ] selected_caption = captions[selected_caption_index] other_caption = None is_correct = -1 if self._dataset_type == "train": if self._two_sentence: if random.random() > self._two_sentence_probability: other_caption = self._get_mismatching_caption(image_id) is_correct = False else: other_caption = captions[random.choice(other_caption_indices)] is_correct = True elif self._false_caption: if random.random() < self._false_caption_probability: selected_caption = self._get_mismatching_caption(image_id) is_correct = False else: is_correct = True processed = self.masked_token_processor( { "text_a": selected_caption, "text_b": other_caption, "is_correct": is_correct, } ) processed.pop("tokens") current_sample.update(processed) return current_sample def _get_mismatching_caption(self, image_id): other_item = self.annotation_db[random.randint(0, len(self.annotation_db) - 1)] while other_item["image_id"] == image_id: other_item = self.annotation_db[ random.randint(0, len(self.annotation_db) - 1) ] other_caption = other_item["captions"][ random.randint(0, len(other_item["captions"]) - 1) ] return other_caption

Q: Индексация БД Подскажите, как правильно и стоит ли создавать индекс для таблиц? A: обычно индексы создаются для ускорения выборки из таблички.. Индексируется, чаще всего, поле таблицы, по которому происходит выборка.. Как создать индекс в mysql можно поитать тут. (не стоит забвать что индексы увеличивают время инсертов и апдейтов)

Q: C++ Headers & Undefined Reference So I'm just getting to grips with C++ and progressing onto using header files. Thing is, I'm totally confused. I've read a documentation but none to make me understand it well enough. I'm just making a silly 'game' which is interactive, it will probably be discarded and thought I could practice use on header files. This is my file structure: terminal_test ├── core.cpp └── game ├── game.cpp └── game.h Now, here is my core.cpp: #include <iostream> #include <stdio.h> #include <unistd.h> #include "game/game.h" using namespace std; void mainMenu(); void rootInterface() { cout << "root@system:~# "; } int main() { system("clear"); usleep(2000); mainMenu(); return 0; } void mainMenu() { int menuChoice = 0; cout << "[1] - Start Game"; cout << "[2] - How To Play"; cout << endl; rootInterface(); cin >> menuChoice; if ( menuChoice == 1 ) { startGame(); } else if ( menuChoice == 2 ) { cout << "This worked."; } } Everything else works fine but startGame(); under my menu choice. When I compile using g++ core.cpp game/game.cpp it bounces back with this error: undefined reference to startGame();. I firstly did some troubleshooting to see if it was properly finding game.h by changing the #include "game/game.h" to something like #include "game.h" without the directory listed inside and it gave me a game.h could not be found so I know it's recognising it, just not compiling at all. Here is my game.h: #ifndef GAME_H // Making sure not to include the header multiple times #define GAME_H #include "game.h" void startGame(); #endif game.cpp: #include <iostream> #include <stdio.h> #include "game.h" int main(int argc, char const *argv[]) { void startGame() { cout << "It worked."; } return 0; } My file structure isn't named properly either, I just threw it in because it was something to just get to grips with header files in C++. So, here are my questions: 1) - What is this error specifically saying and what should I do to fix it? 2) - How do header files communicate and work with other files and is there clear documentation/guides out there that can help? A: Local function definitions are not what you want here: #include <iostream> #include <stdio.h> #include "game.h" int main(int argc, char const *argv[]) { // an attempt to define startGame() inside of main() void startGame() { cout << "It worked."; } return 0; } main is not needed in your game.cpp file. You should define startGame() outside of main, like this: #include <iostream> #include <stdio.h> #include "game.h" // definition of startGame void startGame() { cout << "It worked."; }

YOUR FACE WILL HURT FROM SMILING SO MUCH! WORLD CLASS TERRAIN PERSONALITIES FOR DAYS COME HOME SAFE avalanche saftey training lv. 1 $295 PER PERSON SKI TOURING & BACKCOUNTRY SPLITBOARDING $250 PER PERSON Ally Gandy, Vancouver, BC I’ve taken a few courses with G and have kept coming back because of his knowledge and flexibility. He taught our AST1 course at a backcountry hut. He even customized our AST2 course with extra field days and evening classroom days to maximize time in the mountains. Alex Marangoni, Guelph, ON I can attest to the extensive local knowledge, the very high technical level of instruction, the constant attention to safety and the never-ending energy and enthusiasm. The boys learned some real backcountry skills while having a lot of fun in a very positive environment. We take you to iconic locations, show you things that you wouldn't see on your own, and offer a local's perspective on recreation. Our guests will share genuine mountain memories and a quiet pride of achievement. There was a Whistler here before the condos, lifts and shops...we take you there!

Modulation of bovine platelet function by C-reactive protein. The addition of C-reactive protein (CRP) to bovine platelets suspended in homologous plasma consistently produced a reversible aggregation response following stimulation with either platelet activating factor or adenosine diphosphate while untreated control samples exhibited irreversible aggregation. This deaggregation response was independent of the amount of CRP incorporated into the platelet aggregates but did appear to be mediated through a component either present in bovine plasma or loosely bound to the exterior platelet membrane. The aggregation response of bovine platelets, separated from plasma by gel-filtration, was not affected by the addition of CRP to the platelet suspensions. It is proposed that one of the physiological actions of bovine CRP is to modulate platelet function.

Computing For six decades, women across Britain have tuned into BBC Radio 4'S Woman's Hour, a much-loved national institution that has played a major role in defining female identity. Arguably, it's a sign of how beleaguered men feel as more and more women take on the top jobs and leave stay-at-home husbands to take care of the children that another BBC radio station has seen the need to introduce Men's Hour. From mid-July this year, Radio 5 Live has been airing Men's Hour on Sunday evenings. "It's about capturing the spirit of when good mates sit around nowadays - amidst all the banter you can actually open up about what's on your mind without being ripped apart. We're celebrating modern man's mix of swagger and neurosis," said Tim Samuels, the programme's host and creator. Woman's Hour has built up a hugely loyal following, eager for its intelligent discussion of the gamut of women's issues, from cohabitation to menopause. It is chaired by long-serving presenter Jenni Murray, an established feminist, who has been awarded an Order of the British Empire for her services to broadcasting. Special guests have included former Prime Minister Gordon Brown in the run-up to this year's general election - as he campaigned, not successfully enough given that he was not re-elected, for support from women voters. So far men and women of the media have been unconvinced men have any need for their own radio hour. Critics have questioned whether the whole idea is misguided. Running the risk of gender stereotyping, some argued that what most men like best when they sit around as "good mates" is bloke-ish humour rather than meaningful debate. A studio discussion about men being genetically predisposed to infidelity resulted in "the sound of five men staring at their shoes filling the airwaves," wrote Sarah Vine in 'The Times' newspaper. "The reason Woman's Hour works is because women love talking stuff through. Men on the whole don't." Journalist and campaigner Rosie Boycott, who founded feminist magazine, 'Spare Rib' in 1972, had different reasons for disagreeing with the concept. "I'm not sure it's healthy. Woman's Hour started very much because women weren't being listened to. This implies that men aren't being listened to," she has been quoted as saying. Back in 1946, when Woman's Hour was first aired, women struggled to be heard to the extent that the radio programme especially for them was presented by a man, who addressed housewives as they went about their household chores. Now roughly 213,000 UK men stay at home while their wives carve out careers, according to government statistics for the first quarter of the year, although they pale by comparison with the roughly two million women who decide not to go out to work. Britain's 'Guardian' newspaper imagined how a dialogue between the Men's Hour presenter and a caller might proceed. "This is the most idiotic concept imaginable. A programme for men? What is Radio 5 Live, if not an entire station for blokes?" the imagined caller asked. Some 70 per cent of the roughly 6.5 million-per-week audience of Radio 5 Live is men, with an average age of 47. They are lured by an output with a high content of sports programmes, including coverage of the football World Cup, which stoked laddishness across Britain in June and early July. A BBC spokesman argued Men's Hour had a relatively subtle appeal. "It's a kind of a mix of the light-hearted and the thoughtful," he said. "It's not lads culture. It's interesting and entertaining as well." A BBC statement went further, promising the show would "delve into uncharted emotional territory for men - bringing real candour to the challenges of relationships and life, alongside irreverent manly chatter". "Less about leering at ladies and more concerned with how to maintain monogamy, this is the men's magazine women have been waiting for," it said. Britain's 'Independent' newspaper asked a man and a woman to review the first edition of Men's Hour and, while unanimous in their dismissal, they agreed it was not laddish.

Herbert Kirschner Herbert Kirschner (7 April 1925 – 9 August 2010) was a German sprint canoer who competed in the late 1950s. Competing for the United Team of Germany at the 1956 Summer Olympics in Melbourne, he was eliminated in the heats of the C-2 1000 m event. References Category:1925 births Category:2010 deaths Category:Canoeists at the 1956 Summer Olympics Category:German male canoeists Category:Olympic canoeists of the United Team of Germany

Hypomethylation-mediated activation of cancer/testis antigen KK-LC-1 facilitates hepatocellular carcinoma progression through activating the Notch1/Hes1 signalling. Kita-Kyushu lung cancer antigen-1 (KK-LC-1) is a cancer/testis antigen reactivated in several human malignancies. So far, the major focus of studies on KK-LC-1 has been on its potential as diagnostic biomarker and immunotherapy target. However, its biological functions and molecular mechanisms in cancer progression remain unknown. Expression of KK-LC-1 in HCC was analysed using RT-qPCR, Western blot and immunohistochemistry. The roles of KK-LC-1 on HCC progression were examined by loss-of-function and gain-of-function approaches. Pathway inhibitor DAPT was employed to confirm the regulatory effect of KK-LC-1 on the downstream Notch signalling. The interaction of KK-LC-1 with presenilin-1 was determined by co-immunoprecipitation. The association of CpG island methylation status with KK-LC-1 reactivation was evaluated by methylation-specific PCR, bisulphite sequencing PCR and 5-Aza-dC treatment. We identified that HCC tissues exhibited increased levels of KK-LC-1. High KK-LC-1 level independently predicted poor survival outcome. KK-LC-1 promoted cell growth, migration, invasion and epithelial-mesenchymal transition in vitro and in vivo. KK-LC-1 modulated the Notch1/Hes1 pathway to exacerbate HCC progression through physically interacting with presenilin-1. Upregulation of KK-LC-1 in HCC was attributed to hypomethylated CpG islands. This study identified that hypomethylation-induced KK-LC-1 overexpression played an important role in HCC progression and independently predicted poor survival. We defined the KK-LC-1/presenilin-1/Notch1/Hes1 as a novel signalling pathway that was involved in the growth and metastasis of HCC.

Thursday, May 01, 2008 Raspberry-Lime Petit Fours I've been to tea parties before, but lately I've had a strong craving to host my own. The boyo thinks I'm silly, but I've a tea set that's yet to be used and a desire to bake lots of little edibles. In fact, when I saw Jen's petit four post from Use Real Butter, I couldn't wait any longer. Raspberries were on sale and I had a couple of days off from work -- it was perfect timing. I'm just considering it practice! Jen's recipe is for higher altitudes, but since I'm at sea level and already having various problems adapting my baking to the climate, I decided to piece together some well-known recipes for my own version. I was expecting to have ~30 petit fours, but I ended up with over 100. Luckily, the boyo's coworkers were gratifyingly appreciative so there weren't leftovers to worry about, but you should scale the recipe accordingly if you're not feeding a small army. Preheat oven to 400F. Line the bottom of a jelly-roll pan (I just used a cookie sheet with sides) with parchment so that the paper overhangs the pan at 2 opposite ends. Heat milk with butter in small saucepan until butter melts. Reduce heat to low, and keep hot, but do not simmer. Sift flour with baking powder twice. Return to sifter and set aside. In large heatproof bowl, combine sugar, whole eggs, egg yolks and vanilla. Set the bowl in a pan of barely simmering water and whisk occasionally, until lukewarm to the touch. Now take off heat, and beat at high speed until mixture has cooled, tripled in volume, and has the consistency of thick whipped cream. Sift one-third of flour mixture over batter, and fold in gently by hand, using the largest spatula you have. Fold in half of remaining flour; then fold in the remainder. Pour the hot milk and butter into batter and fold well, scraping the bottom each time and bringing the batter up the sides of the bowl until you can no longer see traces of liquid. Turn batter into prepared pan. Bake for about 10 minutes. The cake will have browned on top, and started to shrink from the sides of the pan. Combine egg whites and sugar in a stand mixer. Whisk constantly over a bain marie until 140F is reached. Place on mixer witha whisk and whip until stiff. Turn down whip speed to 3rd and whip until cool to the touch -- this will take a while, should be cooler than your hand. Change to a paddle and gradually add soft butter by tablespoons. Mix to emulsify. Once desired consistency has been reached, add lime juice and zest. Combine the sugar, water, corn syrup and flavorings in a double boiler over medium heat. Stir until smooth, then add the cream, butter, and white chocolate. Stir until incorporated, watching that it doesn't burn. Add coloring to preference. AssemblyMake the sponge and cool completely. Slice into quarters and freeze, placing wax paper liners between sections. When frozen thoroughly, using a long serrated knife (a bread knife is ideal) slice each quarter horizontally. Return to the freezer until jam, buttercream and syrup are finished. Heat jam until liquid (I did this in small batches). Using one quarter of the sponge, brush the bottom half with the lime syrup then spread the jam over the syrup. Spread the buttercream on the bottom of the top half of the sponge, and place over the jam (sandwich style). Brush the top of the sponge quarter with the syrup again, and refreeze. Repeat with the rest of the sponge. Once the sponge sections have been sandwiched and completely refrozen, slice into 1"x1" squares (you may need to clean your knife several times during this process). Return to the freezer while you make the fondant. Place a wire cooling rack over a cookie sheet and arrange the cake cubes about 1 inch apart from each other. The following process works best if the fondant is very warm and liquid. Using a ladle, pour the fondant over each cube, using a toothpick to smooth out any gaps. Garnish with raspberries before fondant cools. Allow petit fours to sit for a few minutes and fondant to harden. Using a sharp paring knife, free the base of the petit four from the rack and place into a cupcake liner. The leftover fondant from the cookie sheet/rack can be reheated and reused - just make sure it's free of cake crumbs. Keep finished petit fours refrigerated until ready to serve.

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Physiological and pharmacological interventions in radionuclide imaging of the tubular gastrointestinal tract. Radionuclide studies of the gastrointestinal tract (GI) are used to measure GI function and to detect anatomic lesions such as Meckel's diverticuli. A variety of physiological and pharmacological interventions have been applied to both types of studies to gain a better understanding of GI function and to improve detection of disease. This article will review interventions useful in imaging the tubular GI tract. Discussed are the measurement of GI motility and function by gastric emptying and imaging studies for GI bleeding including the Meckel's scan. Interventions involving the hepatobiliary system are covered elsewhere in this issue.

Campaign Finance Reform 2001-01-25T00:05:58-05:00https://images.c-span.org/Files/014/20010125000631002_hd.jpgFollowing a meeting with President Bush to discuss campaign finance reform, Senator McCain spoke to the reporters and answered question about how he would proceed in the Senate. Following a meeting with President Bush to discuss campaign finance reform, Senator McCain spoke to the reporters and answered question about how he would proceed in the Senate.

T. nigra T. nigra may refer to: Tandonia nigra, an air-breathing land slug species Tarucus nigra, a small butterfly species found in India Tetraponera nigra, an ant species Trithemis nigra, a dragonfly species See also Nigra (disambiguation)

Unloaded is a unified yet diverse visual engagement of a disquieting piece of Americana UNLOADED In SPACE Gallery's exhibition Unloaded, 23 artists evaluate gun culture and our enduring crisis of gun violence. In the exhibition essays, curator Susanne Slavick writes, while the show "reflects a number of perspectives, ... none endorse the gun as a means to an end." Still, sweeping through and counting more than 100 images of guns, a viewer finds that a majority of the work leverages the gun's visual power quite directly, with the artists reworking this cultural symbol (and its affiliated iconography of crosshairs, bullets, bullet holes) in varying media and sensibilities. In "Cross for the Unforgiven," Mel Chin welded together eight AK-47s, resulting in an intimidating Maltese cross. By sealing their barrel tips in a perpendicular pattern, however, the artist removes the assault rifles' intended utility so that they instead function benevolently, as decoration. Dark thought I can't shake, given this model's notoriety in illicit trade: What would be the body count if they were not rendered impotent? Gun-neutering is also possible by shrinking and covering firearms in fur or glitter, as in Don Porcella's bag of mini "GUNS," as written on the disproportionately large label in block handwriting. And well-placed near the men's room is Jim Duesing's dude-spoofing animation, "Dog," depicting a bouncy wiener in sunglasses, looped in animated infinity, twirling the revolver between its legs. High on machismo, he's content (toothy smile intact) "doing his thing" ad nauseum. Differently, Chin, Porcella and Duesing subtract gun's visual potency through disfiguration. The photo snapshot "Destiny Fulfilled" shows artist Brander looking confident with, but dwarfed by, a rifle she's showing off. In her other hand is a practice target riddled with bullet holes. ("I'm a good shot," it tells us.) Immersed and participating in a gun enclave, Brander's persona imparts brash reflexive irony either as staged photography or as performance piece. Syjuco appropriates the standard-issue Smith & Wesson image into a crochet design, then capitalizes on audience participation by sharing the instructions online. But when she's contacted by a gun enthusiast (an exchange captured in an email from a woman assuming similar kinship), roles, in a humorous twist, turn upside-down: Syjuco becomes an unintentional producer of gun-culture commodities, while the enthusiast, by materializing the subversive design, becomes an oblivious performer of Syjuco's critique. And speaking of mix-ups, there are the Tumblr-based photography/video/performance projects of Dadpranks, a collective that trades in clever pictorial tropes combining consumer lifestyle junk with irresistible snark. Distilled is a punny feminist-aware goal regurgitating popular media. Their contribution here sniffs out the oddly marketed association between gun culture and hominess in a photo: a gun-shaped coffee mug from Cabela's (the outdoors megastore, known for gaudy taxidermied game displays and "Redneck Gift Ideas") with a steeping bag of Echinacea tea. Punchline in title: "Echinacea Plus Cold Defense." "Unloaded" is also reasonably pensive, some artists forgoing innuendo for straightforward approaches. Conceptual artist Adrian Piper, with characteristic blue-chip gravity, has us gaze squarely into a framed target. Faintly beneath is the now-iconic portrait of the be-hoodied Trayvon Martin, the bull's-eye aligned between his eyes, red text reading: "Imagine what it's like to be me." click to enlarge A still from "Ungun" (2013), a video by Jessica Fenlon Stripped of industrial harshness, the gun reveals itself like an enduring visual archetype, as seen in two ersatz gun collections: Jennifer Nagle Myers' found gun-like sticks ("A City Without Guns") and Anthony Cervino's minimalist rod forms ("Pieces"). Each object echoes barrel and handle; split pieces of bark become triggers and hammers, our minds easily connected to weapons. Finally, Vanessa German's creative vitality raises awareness on race and violence in her community-activism-as-art-approach with two projects: her "Stop Shooting We Love You" signs (now displayed throughout Pittsburgh) and the ARThouse, in Homewood, which turns her home into an art workshop for children. German's aim is wide and clear, while her impact is real, the proverbial boots on the ground. Cogent essays that accompany this exhibition are mindfully goal-oriented toward gun-control; but these propositions, in their overall lecture-to-the-faculty decisiveness, might not go too far, especially when considering gun control's history of frustratingly ex post facto legislation.Unloaded works as a unified and diverse visual engagement of a disquieting piece of Americana, but leaves us with a bigger, although critical, picture of just how much power guns have.

Calhoun Index to Deeds By GRANTEE June 1, 1951 - October 15, 1962 M - R Click on a link below to download the .pdf file. Publications in PDF can only be viewed and printed using the Adobe Acrobat Reader version 4.0 or higher. The downloadable Acrobat Reader software is available at NO CHARGE from the Adobe Systems website. For more information on other files viewers go to our Accessibility page. The following documents will open in a new window. (Note: The index files are large. Please be patient while they load.) ************************************************ Online Services MyFloridaCounty.com is a service of Florida's Clerks of Court. The website provides several online services that are fast, convenient and secure. Click on the links below to access the services which are also available en español. Official Records are documents required or authorized to be recorded in one general series called "Official Records". Search thousands of records across counties, all in one place. Frequently ordering records? Create an account for streamlined checkout. Records can also be purchased online. Non-custodial parents and employers can pay online with a credit card or direct debit from a bank account. Inquiry on a case’s payment history is also available online. Avoid the hassle of sending checks each month and pay online. Use MyFloridaRemit.com for all child support payments made using the electronic check (e-check) payment method. The services are also available en español. Other Clerk of Court Services State of Florida ePortal Site The Florida ePortal web site provides eFiling and eRecording capability to users with a single statewide login. Users may utilize the ePortal web interface to submit documents to Clerks and Recorders. Find information about the Courts, public records, research how to file a small claims case or find an official record. The Clerk's office performs nearly 1,000 different constitutional and statutory functions or duties, representing the broadest and most diverse mantle of responsibility of any locally elected official. Find out more about the many things we do and the many ways we can help you at MyFloridaClerks.com

/* * Copyright (c) 2008-2011 Atheros Communications Inc. * * Permission to use, copy, modify, and/or distribute this software for any * purpose with or without fee is hereby granted, provided that the above * copyright notice and this permission notice appear in all copies. * * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. */ #ifndef EEPROM_H #define EEPROM_H #define AR_EEPROM_MODAL_SPURS 5 #include "../ath.h" #include <net/cfg80211.h> #include "ar9003_eeprom.h" /* helpers to swap EEPROM fields, which are stored as __le16 or __le32. Since * we are 100% sure about it we __force these to u16/u32 for the swab calls to * silence the sparse checks. These macros are used when we have a Big Endian * EEPROM (according to AR5416_EEPMISC_BIG_ENDIAN) and need to convert the * fields to __le16/__le32. */ #define EEPROM_FIELD_SWAB16(field) \ (field = (__force __le16)swab16((__force u16)field)) #define EEPROM_FIELD_SWAB32(field) \ (field = (__force __le32)swab32((__force u32)field)) #ifdef __BIG_ENDIAN #define AR5416_EEPROM_MAGIC 0x5aa5 #else #define AR5416_EEPROM_MAGIC 0xa55a #endif #define CTRY_DEBUG 0x1ff #define CTRY_DEFAULT 0 #define AR_EEPROM_EEPCAP_COMPRESS_DIS 0x0001 #define AR_EEPROM_EEPCAP_AES_DIS 0x0002 #define AR_EEPROM_EEPCAP_FASTFRAME_DIS 0x0004 #define AR_EEPROM_EEPCAP_BURST_DIS 0x0008 #define AR_EEPROM_EEPCAP_MAXQCU 0x01F0 #define AR_EEPROM_EEPCAP_MAXQCU_S 4 #define AR_EEPROM_EEPCAP_HEAVY_CLIP_EN 0x0200 #define AR_EEPROM_EEPCAP_KC_ENTRIES 0xF000 #define AR_EEPROM_EEPCAP_KC_ENTRIES_S 12 #define AR_EEPROM_EEREGCAP_EN_FCC_MIDBAND 0x0040 #define AR_EEPROM_EEREGCAP_EN_KK_U1_EVEN 0x0080 #define AR_EEPROM_EEREGCAP_EN_KK_U2 0x0100 #define AR_EEPROM_EEREGCAP_EN_KK_MIDBAND 0x0200 #define AR_EEPROM_EEREGCAP_EN_KK_U1_ODD 0x0400 #define AR_EEPROM_EEREGCAP_EN_KK_NEW_11A 0x0800 #define AR_EEPROM_EEREGCAP_EN_KK_U1_ODD_PRE4_0 0x4000 #define AR_EEPROM_EEREGCAP_EN_KK_NEW_11A_PRE4_0 0x8000 #define AR5416_EEPROM_MAGIC_OFFSET 0x0 #define AR5416_EEPROM_S 2 #define AR5416_EEPROM_OFFSET 0x2000 #define AR5416_EEPROM_MAX 0xae0 #define AR5416_EEPROM_START_ADDR \ (AR_SREV_9100(ah)) ? 0x1fff1000 : 0x503f1200 #define SD_NO_CTL 0xE0 #define NO_CTL 0xff #define CTL_MODE_M 0xf #define CTL_11A 0 #define CTL_11B 1 #define CTL_11G 2 #define CTL_2GHT20 5 #define CTL_5GHT20 6 #define CTL_2GHT40 7 #define CTL_5GHT40 8 #define EXT_ADDITIVE (0x8000) #define CTL_11A_EXT (CTL_11A | EXT_ADDITIVE) #define CTL_11G_EXT (CTL_11G | EXT_ADDITIVE) #define CTL_11B_EXT (CTL_11B | EXT_ADDITIVE) #define SUB_NUM_CTL_MODES_AT_5G_40 2 #define SUB_NUM_CTL_MODES_AT_2G_40 3 #define POWER_CORRECTION_FOR_TWO_CHAIN 6 /* 10*log10(2)*2 */ #define POWER_CORRECTION_FOR_THREE_CHAIN 10 /* 10*log10(3)*2 */ /* * For AR9285 and later chipsets, the following bits are not being programmed * in EEPROM and so need to be enabled always. * * Bit 0: en_fcc_mid * Bit 1: en_jap_mid * Bit 2: en_fcc_dfs_ht40 * Bit 3: en_jap_ht40 * Bit 4: en_jap_dfs_ht40 */ #define AR9285_RDEXT_DEFAULT 0x1F #define ATH9K_POW_SM(_r, _s) (((_r) & 0x3f) << (_s)) #define FREQ2FBIN(x, y) (u8)((y) ? ((x) - 2300) : (((x) - 4800) / 5)) #define FBIN2FREQ(x, y) ((y) ? (2300 + x) : (4800 + 5 * x)) #define ath9k_hw_use_flash(_ah) (!(_ah->ah_flags & AH_USE_EEPROM)) #define OLC_FOR_AR9280_20_LATER (AR_SREV_9280_20_OR_LATER(ah) && \ ah->eep_ops->get_eeprom(ah, EEP_OL_PWRCTRL)) #define OLC_FOR_AR9287_10_LATER (AR_SREV_9287_11_OR_LATER(ah) && \ ah->eep_ops->get_eeprom(ah, EEP_OL_PWRCTRL)) #define EEP_RFSILENT_ENABLED 0x0001 #define EEP_RFSILENT_ENABLED_S 0 #define EEP_RFSILENT_POLARITY 0x0002 #define EEP_RFSILENT_POLARITY_S 1 #define EEP_RFSILENT_GPIO_SEL ((AR_SREV_9462(ah) || AR_SREV_9565(ah)) ? 0x00fc : 0x001c) #define EEP_RFSILENT_GPIO_SEL_S 2 #define AR5416_OPFLAGS_11A 0x01 #define AR5416_OPFLAGS_11G 0x02 #define AR5416_OPFLAGS_N_5G_HT40 0x04 #define AR5416_OPFLAGS_N_2G_HT40 0x08 #define AR5416_OPFLAGS_N_5G_HT20 0x10 #define AR5416_OPFLAGS_N_2G_HT20 0x20 #define AR5416_EEP_NO_BACK_VER 0x1 #define AR5416_EEP_VER 0xE #define AR5416_EEP_VER_MAJOR_SHIFT 12 #define AR5416_EEP_VER_MAJOR_MASK 0xF000 #define AR5416_EEP_VER_MINOR_MASK 0x0FFF #define AR5416_EEP_MINOR_VER_2 0x2 #define AR5416_EEP_MINOR_VER_3 0x3 #define AR5416_EEP_MINOR_VER_7 0x7 #define AR5416_EEP_MINOR_VER_9 0x9 #define AR5416_EEP_MINOR_VER_16 0x10 #define AR5416_EEP_MINOR_VER_17 0x11 #define AR5416_EEP_MINOR_VER_19 0x13 #define AR5416_EEP_MINOR_VER_20 0x14 #define AR5416_EEP_MINOR_VER_21 0x15 #define AR5416_EEP_MINOR_VER_22 0x16 #define AR5416_NUM_5G_CAL_PIERS 8 #define AR5416_NUM_2G_CAL_PIERS 4 #define AR5416_NUM_5G_20_TARGET_POWERS 8 #define AR5416_NUM_5G_40_TARGET_POWERS 8 #define AR5416_NUM_2G_CCK_TARGET_POWERS 3 #define AR5416_NUM_2G_20_TARGET_POWERS 4 #define AR5416_NUM_2G_40_TARGET_POWERS 4 #define AR5416_NUM_CTLS 24 #define AR5416_NUM_BAND_EDGES 8 #define AR5416_NUM_PD_GAINS 4 #define AR5416_PD_GAINS_IN_MASK 4 #define AR5416_PD_GAIN_ICEPTS 5 #define AR5416_NUM_PDADC_VALUES 128 #define AR5416_BCHAN_UNUSED 0xFF #define AR5416_MAX_PWR_RANGE_IN_HALF_DB 64 #define AR5416_MAX_CHAINS 3 #define AR9300_MAX_CHAINS 3 #define AR5416_PWR_TABLE_OFFSET_DB -5 /* Rx gain type values */ #define AR5416_EEP_RXGAIN_23DB_BACKOFF 0 #define AR5416_EEP_RXGAIN_13DB_BACKOFF 1 #define AR5416_EEP_RXGAIN_ORIG 2 /* Tx gain type values */ #define AR5416_EEP_TXGAIN_ORIGINAL 0 #define AR5416_EEP_TXGAIN_HIGH_POWER 1 /* Endianness of EEPROM content */ #define AR5416_EEPMISC_BIG_ENDIAN 0x01 #define AR5416_EEP4K_START_LOC 64 #define AR5416_EEP4K_NUM_2G_CAL_PIERS 3 #define AR5416_EEP4K_NUM_2G_CCK_TARGET_POWERS 3 #define AR5416_EEP4K_NUM_2G_20_TARGET_POWERS 3 #define AR5416_EEP4K_NUM_2G_40_TARGET_POWERS 3 #define AR5416_EEP4K_NUM_CTLS 12 #define AR5416_EEP4K_NUM_BAND_EDGES 4 #define AR5416_EEP4K_NUM_PD_GAINS 2 #define AR5416_EEP4K_MAX_CHAINS 1 #define AR9280_TX_GAIN_TABLE_SIZE 22 #define AR9287_EEP_VER 0xE #define AR9287_EEP_MINOR_VER_1 0x1 #define AR9287_EEP_MINOR_VER_2 0x2 #define AR9287_EEP_MINOR_VER_3 0x3 #define AR9287_EEP_MINOR_VER AR9287_EEP_MINOR_VER_3 #define AR9287_EEP_MINOR_VER_b AR9287_EEP_MINOR_VER #define AR9287_EEP_NO_BACK_VER AR9287_EEP_MINOR_VER_1 #define AR9287_EEP_START_LOC 128 #define AR9287_HTC_EEP_START_LOC 256 #define AR9287_NUM_2G_CAL_PIERS 3 #define AR9287_NUM_2G_CCK_TARGET_POWERS 3 #define AR9287_NUM_2G_20_TARGET_POWERS 3 #define AR9287_NUM_2G_40_TARGET_POWERS 3 #define AR9287_NUM_CTLS 12 #define AR9287_NUM_BAND_EDGES 4 #define AR9287_PD_GAIN_ICEPTS 1 #define AR9287_EEPMISC_WOW 0x02 #define AR9287_MAX_CHAINS 2 #define AR9287_ANT_16S 32 #define AR9287_DATA_SZ 32 #define AR9287_PWR_TABLE_OFFSET_DB -5 #define AR9287_CHECKSUM_LOCATION (AR9287_EEP_START_LOC + 1) #define CTL_EDGE_TPOWER(_ctl) ((_ctl) & 0x3f) #define CTL_EDGE_FLAGS(_ctl) (((_ctl) >> 6) & 0x03) #define LNA_CTL_BUF_MODE BIT(0) #define LNA_CTL_ISEL_LO BIT(1) #define LNA_CTL_ISEL_HI BIT(2) #define LNA_CTL_BUF_IN BIT(3) #define LNA_CTL_FEM_BAND BIT(4) #define LNA_CTL_LOCAL_BIAS BIT(5) #define LNA_CTL_FORCE_XPA BIT(6) #define LNA_CTL_USE_ANT1 BIT(7) enum eeprom_param { EEP_NFTHRESH_5, EEP_NFTHRESH_2, EEP_MAC_MSW, EEP_MAC_MID, EEP_MAC_LSW, EEP_REG_0, EEP_OP_CAP, EEP_OP_MODE, EEP_RF_SILENT, EEP_OB_5, EEP_DB_5, EEP_OB_2, EEP_DB_2, EEP_TX_MASK, EEP_RX_MASK, EEP_FSTCLK_5G, EEP_RXGAIN_TYPE, EEP_OL_PWRCTRL, EEP_TXGAIN_TYPE, EEP_RC_CHAIN_MASK, EEP_DAC_HPWR_5G, EEP_FRAC_N_5G, EEP_DEV_TYPE, EEP_TEMPSENSE_SLOPE, EEP_TEMPSENSE_SLOPE_PAL_ON, EEP_PWR_TABLE_OFFSET, EEP_PAPRD, EEP_MODAL_VER, EEP_ANT_DIV_CTL1, EEP_CHAIN_MASK_REDUCE, EEP_ANTENNA_GAIN_2G, EEP_ANTENNA_GAIN_5G, }; enum ar5416_rates { rate6mb, rate9mb, rate12mb, rate18mb, rate24mb, rate36mb, rate48mb, rate54mb, rate1l, rate2l, rate2s, rate5_5l, rate5_5s, rate11l, rate11s, rateXr, rateHt20_0, rateHt20_1, rateHt20_2, rateHt20_3, rateHt20_4, rateHt20_5, rateHt20_6, rateHt20_7, rateHt40_0, rateHt40_1, rateHt40_2, rateHt40_3, rateHt40_4, rateHt40_5, rateHt40_6, rateHt40_7, rateDupCck, rateDupOfdm, rateExtCck, rateExtOfdm, Ar5416RateSize }; enum ath9k_hal_freq_band { ATH9K_HAL_FREQ_BAND_5GHZ = 0, ATH9K_HAL_FREQ_BAND_2GHZ = 1 }; struct base_eep_header { __le16 length; __le16 checksum; __le16 version; u8 opCapFlags; u8 eepMisc; __le16 regDmn[2]; u8 macAddr[6]; u8 rxMask; u8 txMask; __le16 rfSilent; __le16 blueToothOptions; __le16 deviceCap; __le32 binBuildNumber; u8 deviceType; u8 pwdclkind; u8 fastClk5g; u8 divChain; u8 rxGainType; u8 dacHiPwrMode_5G; u8 openLoopPwrCntl; u8 dacLpMode; u8 txGainType; u8 rcChainMask; u8 desiredScaleCCK; u8 pwr_table_offset; u8 frac_n_5g; u8 futureBase_3[21]; } __packed; struct base_eep_header_4k { __le16 length; __le16 checksum; __le16 version; u8 opCapFlags; u8 eepMisc; __le16 regDmn[2]; u8 macAddr[6]; u8 rxMask; u8 txMask; __le16 rfSilent; __le16 blueToothOptions; __le16 deviceCap; __le32 binBuildNumber; u8 deviceType; u8 txGainType; } __packed; struct spur_chan { __le16 spurChan; u8 spurRangeLow; u8 spurRangeHigh; } __packed; struct modal_eep_header { __le32 antCtrlChain[AR5416_MAX_CHAINS]; __le32 antCtrlCommon; u8 antennaGainCh[AR5416_MAX_CHAINS]; u8 switchSettling; u8 txRxAttenCh[AR5416_MAX_CHAINS]; u8 rxTxMarginCh[AR5416_MAX_CHAINS]; u8 adcDesiredSize; u8 pgaDesiredSize; u8 xlnaGainCh[AR5416_MAX_CHAINS]; u8 txEndToXpaOff; u8 txEndToRxOn; u8 txFrameToXpaOn; u8 thresh62; u8 noiseFloorThreshCh[AR5416_MAX_CHAINS]; u8 xpdGain; u8 xpd; u8 iqCalICh[AR5416_MAX_CHAINS]; u8 iqCalQCh[AR5416_MAX_CHAINS]; u8 pdGainOverlap; u8 ob; u8 db; u8 xpaBiasLvl; u8 pwrDecreaseFor2Chain; u8 pwrDecreaseFor3Chain; u8 txFrameToDataStart; u8 txFrameToPaOn; u8 ht40PowerIncForPdadc; u8 bswAtten[AR5416_MAX_CHAINS]; u8 bswMargin[AR5416_MAX_CHAINS]; u8 swSettleHt40; u8 xatten2Db[AR5416_MAX_CHAINS]; u8 xatten2Margin[AR5416_MAX_CHAINS]; u8 ob_ch1; u8 db_ch1; u8 lna_ctl; u8 miscBits; __le16 xpaBiasLvlFreq[3]; u8 futureModal[6]; struct spur_chan spurChans[AR_EEPROM_MODAL_SPURS]; } __packed; struct calDataPerFreqOpLoop { u8 pwrPdg[2][5]; u8 vpdPdg[2][5]; u8 pcdac[2][5]; u8 empty[2][5]; } __packed; struct modal_eep_4k_header { __le32 antCtrlChain[AR5416_EEP4K_MAX_CHAINS]; __le32 antCtrlCommon; u8 antennaGainCh[AR5416_EEP4K_MAX_CHAINS]; u8 switchSettling; u8 txRxAttenCh[AR5416_EEP4K_MAX_CHAINS]; u8 rxTxMarginCh[AR5416_EEP4K_MAX_CHAINS]; u8 adcDesiredSize; u8 pgaDesiredSize; u8 xlnaGainCh[AR5416_EEP4K_MAX_CHAINS]; u8 txEndToXpaOff; u8 txEndToRxOn; u8 txFrameToXpaOn; u8 thresh62; u8 noiseFloorThreshCh[AR5416_EEP4K_MAX_CHAINS]; u8 xpdGain; u8 xpd; u8 iqCalICh[AR5416_EEP4K_MAX_CHAINS]; u8 iqCalQCh[AR5416_EEP4K_MAX_CHAINS]; u8 pdGainOverlap; #ifdef __BIG_ENDIAN_BITFIELD u8 ob_1:4, ob_0:4; u8 db1_1:4, db1_0:4; #else u8 ob_0:4, ob_1:4; u8 db1_0:4, db1_1:4; #endif u8 xpaBiasLvl; u8 txFrameToDataStart; u8 txFrameToPaOn; u8 ht40PowerIncForPdadc; u8 bswAtten[AR5416_EEP4K_MAX_CHAINS]; u8 bswMargin[AR5416_EEP4K_MAX_CHAINS]; u8 swSettleHt40; u8 xatten2Db[AR5416_EEP4K_MAX_CHAINS]; u8 xatten2Margin[AR5416_EEP4K_MAX_CHAINS]; #ifdef __BIG_ENDIAN_BITFIELD u8 db2_1:4, db2_0:4; #else u8 db2_0:4, db2_1:4; #endif u8 version; #ifdef __BIG_ENDIAN_BITFIELD u8 ob_3:4, ob_2:4; u8 antdiv_ctl1:4, ob_4:4; u8 db1_3:4, db1_2:4; u8 antdiv_ctl2:4, db1_4:4; u8 db2_2:4, db2_3:4; u8 reserved:4, db2_4:4; #else u8 ob_2:4, ob_3:4; u8 ob_4:4, antdiv_ctl1:4; u8 db1_2:4, db1_3:4; u8 db1_4:4, antdiv_ctl2:4; u8 db2_2:4, db2_3:4; u8 db2_4:4, reserved:4; #endif u8 tx_diversity; u8 flc_pwr_thresh; u8 bb_scale_smrt_antenna; #define EEP_4K_BB_DESIRED_SCALE_MASK 0x1f u8 futureModal[1]; struct spur_chan spurChans[AR_EEPROM_MODAL_SPURS]; } __packed; struct base_eep_ar9287_header { __le16 length; __le16 checksum; __le16 version; u8 opCapFlags; u8 eepMisc; __le16 regDmn[2]; u8 macAddr[6]; u8 rxMask; u8 txMask; __le16 rfSilent; __le16 blueToothOptions; __le16 deviceCap; __le32 binBuildNumber; u8 deviceType; u8 openLoopPwrCntl; int8_t pwrTableOffset; int8_t tempSensSlope; int8_t tempSensSlopePalOn; u8 futureBase[29]; } __packed; struct modal_eep_ar9287_header { __le32 antCtrlChain[AR9287_MAX_CHAINS]; __le32 antCtrlCommon; int8_t antennaGainCh[AR9287_MAX_CHAINS]; u8 switchSettling; u8 txRxAttenCh[AR9287_MAX_CHAINS]; u8 rxTxMarginCh[AR9287_MAX_CHAINS]; int8_t adcDesiredSize; u8 txEndToXpaOff; u8 txEndToRxOn; u8 txFrameToXpaOn; u8 thresh62; int8_t noiseFloorThreshCh[AR9287_MAX_CHAINS]; u8 xpdGain; u8 xpd; int8_t iqCalICh[AR9287_MAX_CHAINS]; int8_t iqCalQCh[AR9287_MAX_CHAINS]; u8 pdGainOverlap; u8 xpaBiasLvl; u8 txFrameToDataStart; u8 txFrameToPaOn; u8 ht40PowerIncForPdadc; u8 bswAtten[AR9287_MAX_CHAINS]; u8 bswMargin[AR9287_MAX_CHAINS]; u8 swSettleHt40; u8 version; u8 db1; u8 db2; u8 ob_cck; u8 ob_psk; u8 ob_qam; u8 ob_pal_off; u8 futureModal[30]; struct spur_chan spurChans[AR_EEPROM_MODAL_SPURS]; } __packed; struct cal_data_per_freq { u8 pwrPdg[AR5416_NUM_PD_GAINS][AR5416_PD_GAIN_ICEPTS]; u8 vpdPdg[AR5416_NUM_PD_GAINS][AR5416_PD_GAIN_ICEPTS]; } __packed; struct cal_data_per_freq_4k { u8 pwrPdg[AR5416_EEP4K_NUM_PD_GAINS][AR5416_PD_GAIN_ICEPTS]; u8 vpdPdg[AR5416_EEP4K_NUM_PD_GAINS][AR5416_PD_GAIN_ICEPTS]; } __packed; struct cal_target_power_leg { u8 bChannel; u8 tPow2x[4]; } __packed; struct cal_target_power_ht { u8 bChannel; u8 tPow2x[8]; } __packed; struct cal_ctl_edges { u8 bChannel; u8 ctl; } __packed; struct cal_data_op_loop_ar9287 { u8 pwrPdg[2][5]; u8 vpdPdg[2][5]; u8 pcdac[2][5]; u8 empty[2][5]; } __packed; struct cal_data_per_freq_ar9287 { u8 pwrPdg[AR5416_NUM_PD_GAINS][AR9287_PD_GAIN_ICEPTS]; u8 vpdPdg[AR5416_NUM_PD_GAINS][AR9287_PD_GAIN_ICEPTS]; } __packed; union cal_data_per_freq_ar9287_u { struct cal_data_op_loop_ar9287 calDataOpen; struct cal_data_per_freq_ar9287 calDataClose; } __packed; struct cal_ctl_data_ar9287 { struct cal_ctl_edges ctlEdges[AR9287_MAX_CHAINS][AR9287_NUM_BAND_EDGES]; } __packed; struct cal_ctl_data { struct cal_ctl_edges ctlEdges[AR5416_MAX_CHAINS][AR5416_NUM_BAND_EDGES]; } __packed; struct cal_ctl_data_4k { struct cal_ctl_edges ctlEdges[AR5416_EEP4K_MAX_CHAINS][AR5416_EEP4K_NUM_BAND_EDGES]; } __packed; struct ar5416_eeprom_def { struct base_eep_header baseEepHeader; u8 custData[64]; struct modal_eep_header modalHeader[2]; u8 calFreqPier5G[AR5416_NUM_5G_CAL_PIERS]; u8 calFreqPier2G[AR5416_NUM_2G_CAL_PIERS]; struct cal_data_per_freq calPierData5G[AR5416_MAX_CHAINS][AR5416_NUM_5G_CAL_PIERS]; struct cal_data_per_freq calPierData2G[AR5416_MAX_CHAINS][AR5416_NUM_2G_CAL_PIERS]; struct cal_target_power_leg calTargetPower5G[AR5416_NUM_5G_20_TARGET_POWERS]; struct cal_target_power_ht calTargetPower5GHT20[AR5416_NUM_5G_20_TARGET_POWERS]; struct cal_target_power_ht calTargetPower5GHT40[AR5416_NUM_5G_40_TARGET_POWERS]; struct cal_target_power_leg calTargetPowerCck[AR5416_NUM_2G_CCK_TARGET_POWERS]; struct cal_target_power_leg calTargetPower2G[AR5416_NUM_2G_20_TARGET_POWERS]; struct cal_target_power_ht calTargetPower2GHT20[AR5416_NUM_2G_20_TARGET_POWERS]; struct cal_target_power_ht calTargetPower2GHT40[AR5416_NUM_2G_40_TARGET_POWERS]; u8 ctlIndex[AR5416_NUM_CTLS]; struct cal_ctl_data ctlData[AR5416_NUM_CTLS]; u8 padding; } __packed; struct ar5416_eeprom_4k { struct base_eep_header_4k baseEepHeader; u8 custData[20]; struct modal_eep_4k_header modalHeader; u8 calFreqPier2G[AR5416_EEP4K_NUM_2G_CAL_PIERS]; struct cal_data_per_freq_4k calPierData2G[AR5416_EEP4K_MAX_CHAINS][AR5416_EEP4K_NUM_2G_CAL_PIERS]; struct cal_target_power_leg calTargetPowerCck[AR5416_EEP4K_NUM_2G_CCK_TARGET_POWERS]; struct cal_target_power_leg calTargetPower2G[AR5416_EEP4K_NUM_2G_20_TARGET_POWERS]; struct cal_target_power_ht calTargetPower2GHT20[AR5416_EEP4K_NUM_2G_20_TARGET_POWERS]; struct cal_target_power_ht calTargetPower2GHT40[AR5416_EEP4K_NUM_2G_40_TARGET_POWERS]; u8 ctlIndex[AR5416_EEP4K_NUM_CTLS]; struct cal_ctl_data_4k ctlData[AR5416_EEP4K_NUM_CTLS]; u8 padding; } __packed; struct ar9287_eeprom { struct base_eep_ar9287_header baseEepHeader; u8 custData[AR9287_DATA_SZ]; struct modal_eep_ar9287_header modalHeader; u8 calFreqPier2G[AR9287_NUM_2G_CAL_PIERS]; union cal_data_per_freq_ar9287_u calPierData2G[AR9287_MAX_CHAINS][AR9287_NUM_2G_CAL_PIERS]; struct cal_target_power_leg calTargetPowerCck[AR9287_NUM_2G_CCK_TARGET_POWERS]; struct cal_target_power_leg calTargetPower2G[AR9287_NUM_2G_20_TARGET_POWERS]; struct cal_target_power_ht calTargetPower2GHT20[AR9287_NUM_2G_20_TARGET_POWERS]; struct cal_target_power_ht calTargetPower2GHT40[AR9287_NUM_2G_40_TARGET_POWERS]; u8 ctlIndex[AR9287_NUM_CTLS]; struct cal_ctl_data_ar9287 ctlData[AR9287_NUM_CTLS]; u8 padding; } __packed; enum reg_ext_bitmap { REG_EXT_FCC_MIDBAND = 0, REG_EXT_JAPAN_MIDBAND = 1, REG_EXT_FCC_DFS_HT40 = 2, REG_EXT_JAPAN_NONDFS_HT40 = 3, REG_EXT_JAPAN_DFS_HT40 = 4 }; struct ath9k_country_entry { u16 countryCode; u16 regDmnEnum; u16 regDmn5G; u16 regDmn2G; u8 isMultidomain; u8 iso[3]; }; struct eeprom_ops { int (*check_eeprom)(struct ath_hw *hw); u32 (*get_eeprom)(struct ath_hw *hw, enum eeprom_param param); bool (*fill_eeprom)(struct ath_hw *hw); u32 (*dump_eeprom)(struct ath_hw *hw, bool dump_base_hdr, u8 *buf, u32 len, u32 size); int (*get_eeprom_ver)(struct ath_hw *hw); int (*get_eeprom_rev)(struct ath_hw *hw); void (*set_board_values)(struct ath_hw *hw, struct ath9k_channel *chan); void (*set_addac)(struct ath_hw *hw, struct ath9k_channel *chan); void (*set_txpower)(struct ath_hw *hw, struct ath9k_channel *chan, u16 cfgCtl, u8 twiceAntennaReduction, u8 powerLimit, bool test); u16 (*get_spur_channel)(struct ath_hw *ah, u16 i, bool is2GHz); u8 (*get_eepmisc)(struct ath_hw *ah); }; void ath9k_hw_analog_shift_regwrite(struct ath_hw *ah, u32 reg, u32 val); void ath9k_hw_analog_shift_rmw(struct ath_hw *ah, u32 reg, u32 mask, u32 shift, u32 val); int16_t ath9k_hw_interpolate(u16 target, u16 srcLeft, u16 srcRight, int16_t targetLeft, int16_t targetRight); bool ath9k_hw_get_lower_upper_index(u8 target, u8 *pList, u16 listSize, u16 *indexL, u16 *indexR); bool ath9k_hw_nvram_read(struct ath_hw *ah, u32 off, u16 *data); int ath9k_hw_nvram_swap_data(struct ath_hw *ah, bool *swap_needed, int size); bool ath9k_hw_nvram_validate_checksum(struct ath_hw *ah, int size); bool ath9k_hw_nvram_check_version(struct ath_hw *ah, int version, int minrev); void ath9k_hw_usb_gen_fill_eeprom(struct ath_hw *ah, u16 *eep_data, int eep_start_loc, int size); void ath9k_hw_fill_vpd_table(u8 pwrMin, u8 pwrMax, u8 *pPwrList, u8 *pVpdList, u16 numIntercepts, u8 *pRetVpdList); void ath9k_hw_get_legacy_target_powers(struct ath_hw *ah, struct ath9k_channel *chan, struct cal_target_power_leg *powInfo, u16 numChannels, struct cal_target_power_leg *pNewPower, u16 numRates, bool isExtTarget); void ath9k_hw_get_target_powers(struct ath_hw *ah, struct ath9k_channel *chan, struct cal_target_power_ht *powInfo, u16 numChannels, struct cal_target_power_ht *pNewPower, u16 numRates, bool isHt40Target); u16 ath9k_hw_get_max_edge_power(u16 freq, struct cal_ctl_edges *pRdEdgesPower, bool is2GHz, int num_band_edges); u16 ath9k_hw_get_scaled_power(struct ath_hw *ah, u16 power_limit, u8 antenna_reduction); void ath9k_hw_update_regulatory_maxpower(struct ath_hw *ah); int ath9k_hw_eeprom_init(struct ath_hw *ah); void ath9k_hw_get_gain_boundaries_pdadcs(struct ath_hw *ah, struct ath9k_channel *chan, void *pRawDataSet, u8 *bChans, u16 availPiers, u16 tPdGainOverlap, u16 *pPdGainBoundaries, u8 *pPDADCValues, u16 numXpdGains); static inline u16 ath9k_hw_fbin2freq(u8 fbin, bool is2GHz) { if (fbin == AR5416_BCHAN_UNUSED) return fbin; return (u16) ((is2GHz) ? (2300 + fbin) : (4800 + 5 * fbin)); } #define ar5416_get_ntxchains(_txchainmask) \ (((_txchainmask >> 2) & 1) + \ ((_txchainmask >> 1) & 1) + (_txchainmask & 1)) extern const struct eeprom_ops eep_def_ops; extern const struct eeprom_ops eep_4k_ops; extern const struct eeprom_ops eep_ar9287_ops; extern const struct eeprom_ops eep_ar9287_ops; extern const struct eeprom_ops eep_ar9300_ops; #endif /* EEPROM_H */

Q: Get term_id for each instance of custom taxonomy I am building a custom image slider. I have a custom post type called 'slide' with an associated custom taxonomy called 'slideshows'. When you create a new 'slideshow' it add to a custom table in the DB called wp_slideshowsmeta with columns for "meta_id, slideshows_id, meta_key, and meta_value". Each slideshow has its own settings page using 'slideshows_add_form_fields' and 'slideshows_edit_form_fields'. To call a slideshow I created a function ( 'gps_slider()' ) that is placed in the template file where you want the slideshow to appear. It has one parameter which is the slideshow name. Everything works great... it loads the appropriate slideshow and functions. BUT, all the slideshows use the first one's settings. I need to pass the slideshow name to my function that uses 'wp_localize_script' to pass the settings to the javascript. I'm guessing it's likely a foreach loop, but can't seem to see how to construct it. Any help is greatly appreciated. Bryce A: The structure of this is kind of weird. But your main issue is that the wp_enqueue_scripts action runs before any calls to gps_slider() can possibly happen. Hook your script localization to the wp_footer action instead, so the slideshow data in the page already exists and has been output. Additionally you'll have to make your slideshow data an array of arrays so you can pass the settings for each individually. $data = array(); $data[$name] = array( 'gpsslidermode' => $slider_mode, 'gpssliderspeed' => $slider_speed ); wp_localize_script('gps-slider_script', 'gpsslidersettings', $data); Also, why not just use the options table for your slideshow data, keyed to the slideshow ID? You don't seem to be doing anything with your custom table that couldn't be replicated with a built in core table, except creating more work for yourself. At the very least just save all of your slideshow meta in a single row in a serialized array, and cut 8 database queries from each slideshow load. EDIT- function gps_slider( $slideshow = '' ) { include('lib/gps-slider-output.php'); global $slideshows; $slideshows[$slideshow] = array( // fetch and insert your settings data here 'gpsslidermode' => $slider_mode, 'gpssliderspeed' => $slider_speed, // etc.. ); } function gps_slider_localize(){ global $slideshows; wp_localize_script('gps-slider_script', 'gpsslidersettings', $slideshows); } add_action( 'wp_footer', 'gps_slider_localize' );

58 F.Supp.2d 907 (1999) Linda GULO, Plaintiff, v. Kenneth S. APFEL, Commissioner of Social Security, Defendant No. 97 C 6239. United States District Court, N.D. Illinois, Eastern Division. July 28, 1999. Barry A. Schultz, Evanston, for Plaintiff. Samuel D. Brooks, Assistant United States Attorney, Leslye E. Jones, Assistant Regional Counsel, Chicago, for Defendant. MEMORANDUM OPINION AND ORDER DENLOW, United States Magistrate Judge. The Seventh Circuit Court of Appeals affirmed in part and remanded in part this Court's decision approving the denial of Social Security disability benefits to Plaintiff, Linda Gulo. Gulo v. Apfel, 175 F.3d 1020 (7th Cir.1999) (unpublished order). *908 The case is now before the Court on Plaintiff's petition for attorney's fees and costs pursuant to the Equal Access to Justice Act ("EAJA"), 28 U.S.C. § 2412(d). The principal issue presented is whether the Commissioner of Social Security ("Commissioner"), was substantially justified in its legal and factual positions. Because the Commissioner's positions throughout this proceeding had a reasonable basis in law and fact, the Plaintiff's petition for attorney's fees and costs is denied. I. BACKGROUND FACTS Plaintiff applied for disability insurance benefits ("DIB") in April, 1994, alleging an inability to work because of a variety of physical ailments, including arthritis and tendinitis in her hands, a severe hearing impairment, pain in her back, shoulders, feet and under her arms, and swelling in her legs. She also experiences some vertigo and sleeping difficulty. Plaintiff was denied DIB by the Social Security Administration and challenged the denial at a hearing before an Administrative Law Judge ("ALJ"). Plaintiff raised three principal arguments before the ALJ: first, that Plaintiff's maladies constitute a severe impairment under the Social Security Act, second, that Plaintiff could not touch objects with her hands and was therefore disabled, or alternatively, that the condition of her hands rendered her unable to engage in any substantial gainful employment. The ALJ found against Plaintiff on all three issues, and in particular, found that Plaintiff was not disabled because she could perform assembler and inspector/checker jobs. Subsequently, Plaintiff sought judicial review in this Court. This Court granted the Commissioner's motion for summary judgment and affirmed the ALJ's decision. Plaintiff then sought review by the Seventh Circuit. On appeal, Plaintiff raised three issues. First, Plaintiff challenged the ALJ's determination that she is capable of performing assembler and inspector/checker jobs. The Seventh Circuit remanded this issue to the ALJ to clarify her finding because of an apparent inconsistency between the ALJ's finding that Plaintiff could not perform activities requiring repetitive fingering and her finding that Plaintiff was capable of performing the assembler and inspector/checker jobs. The Seventh Circuit was uncertain as to whether the ALJ meant to find that Gulo's fingering limitation affected one hand or both. On the second issue, the Seventh Circuit affirmed this Court's determination that substantial evidence existed to support the ALJ's finding that Gulo could touch objects. Finally, the Seventh Circuit held that Plaintiff waived her third argument regarding whether the ALJ should have assessed her case under Rule 202.13. II. STANDARD FOR FEE AWARDS UNDER EAJA EAJA directs a court to award attorney fees and other expenses to private parties who prevail in litigation against the United States if, among other conditions, the Government's position was not "substantially justified." 28 U.S.C. § 2412(d)(1)(A) (1994). The position of the United States includes both its position during litigation and its position during the administrative proceedings. 28 U.S.C. § 2412(d)(2)(D) (1994). To meet its burden of proof the government must establish that its position had a reasonable basis in law and fact. Cummings v. Sullivan, 950 F.2d 492, 495 (7th Cir.1991). The standard of "substantially justified" is satisfied if there is a genuine dispute, or if reasonable people could differ as to the appropriateness of the contested action. Pierce v. Underwood, 487 U.S. 552, 565, 108 S.Ct. 2541, 2550, 101 L.Ed.2d 490 (1988). "While the parties' postures on individual matters may be more or less justified, the EAJA — like other fee-shifting statutes — favors treating a case as an inclusive whole, rather than as atomized line items." Commissioner, INS v. Jean, 496 U.S. 154, 161-162, 110 S.Ct. 2316, 2320-2321, 110 L.Ed.2d 134 (1990). *909 "The test for substantial justification is whether the agency had a rational ground for thinking it had a rational ground for its action." Kolman v. Shalala, 39 F.3d 173, 177 (7th Cir.1994). The Government's success on the merits is relevant to the "substantial justification" determination. In Pierce, the Supreme Court observed: Conceivably, the Government could take a position that is not substantially justified, yet win; even more likely, it could take a position that is substantially justified, yet lose. Nevertheless, a string of losses can be indicative; and even more so a string of successes. Pierce, 487 U.S. at 568, 108 S.Ct. at 2551. In addition, an innocent clerical error in the administrative law judge's conclusions does not make the government's position unreasonable. See Cummings, 950 F.2d at 499. In Cummings, the Appeals Council failed to review certain evidence apparently due to a clerical failure to file those reports in the case file. Id. "We will not treat this clerical error, which was not shown or suggested to have been deliberate, as actual proof that the government acted unreasonably." Id. III. THE COMMISSIONER'S POSITION WAS SUBSTANTIALLY JUSTIFIED The Commissioner had a rational ground for its actions. There were three issues raised by Plaintiff on appeal. The Seventh Circuit sustained the Commissioner's position on two of the three issues. With respect to these two issues, it is clear the Commissioner had a reasonable basis in law and in fact. The crux of this case revolves around the third issue. Was it reasonable for the Commissioner to fight to uphold the ALJ's determination regarding Plaintiff's ability to perform assembler and inspector/checker positions? Did the ALJ's finding that Plaintiff could not perform activities regarding repetitive fingering make it unreasonable for the Commissioner to support the ALJ's conclusion that Plaintiff could perform either an assembler or inspector/checker position? The Commissioner contends that it was justified in seeking to uphold the ALJ's decision. The Commissioner argues: 1) there is some evidence that suggests that the ALJ failed to specify that the repetitive fingering limitation applied only to plaintiff's right hand in her findings and this was an inadvertent omission or clerical error. This argument finds support in the ALJ's questioning of the vocational expert in which the expert was asked to assume the Plaintiff "[c]an't do repetitive fingering with her dominant right hand." (R. at 64.) (emphasis supplied); 2) The medical evidence did not support a conclusion that plaintiff was unable to perform repetitive fingering with both hands. The Commissioner pointed to medical evidence showing plaintiff had a normal range of motion in her wrist (R. at 146), unremarkable x-rays of both wrists (R. at 148) as examples of supporting evidence; 3) Finally, the Commissioner argues that the vocational experts' testimony was not inconsistent with the ALJ's finding. The Commissioner asserts that although Plaintiff could not perform repetitive fingering, she could still perform light assembler and inspector/checker positions. It was not unreasonable for the Commissioner to pursue these positions before the Appeals Council, this Court or the Seventh Circuit. For these reasons, Plaintiff is not entitled to any attorney's fees or costs under EAJA. IV. CONCLUSION The Commissioner has met its burden of demonstrating a reasonable basis in law and fact for its conduct. As a result, Plaintiff's petition for an award of fees and costs pursuant to the Equal Access to Justice Act is denied.

I actually watched it when it was on FOX back in the day, but that was back in the days before DVRs and when FOX began screwing around with the order the shows were played, making it more and more difficult to follow the plotlines, I admit I gave up. A nephew who had a DVD set kept raving about how great it was, and then I saw Serenity in the theatre and immediately went out and bought the set myself. Mind-blowing characters and story, and as a Trekkie fan, I was totally intrigued at the concept of a "rebel faction" in their equivalent of Trek's "United Federation of Planets". Got me to thinking that what if all the star systems Kirk, Picard and Janeway visited didn't WANT to join the Federation? Imposing civilization and order, as the government did in the grittier Serenity universe, rather than in the sanitized Trek 'verse, was not something that outworld settlers wanted. Whedon's brilliance is that he showed what the future will probably be - ordinary people, struggling and sometime having to steal to exist. Well, as i'm sure he'd be the first to admit, Joss was far from the first to depict a gritty, borderline dystopic future (not in film/TV and certainly not in sci-fi in general - i'd recommend Allen Steele's 'rude astronauts' books for a great depiction of ordinary working people in space, much nearer future than 'Firefly' though) but he certainly did a great job of it. There were several Trek episodes featuring non-Federation worlds (because they were too primitive to be allowed to join) sometimes even showcasing the damage caused when a very advanced culture meets one that's less so though I can't recall any where a world was asked and refused, that would've been interesting. 'Deep Space 9' developed into the least sanitised Trek incarnation, certainly later on with the introduction of Section 31 (more or less a sort of secret police that would probably have found a use for someone like The Operative) and by showing us how the Federation might be forced to change if it was ever caught up in a long term "hot" war. I like both types personally, the (probably more realistic) grit and hand-to-mouth struggle of the 'Firefly' style and the grand optimism of the Roddenberry vision, wouldn't be without either. (and I guess that's the sole point of interest for 'Firefly' still being on TV - new fans can see it and become smitten) Riverine, I second Saje's suggestion on Deep Space 9...in it, Bajor eventually DID refuse admission into the Federation. It was actually a pretty major plot point. Sisko was sent there to help Bajor into the Federation, and the early episodes feature a lot of trying to push the application through. When they are accepted, they are advised to not join (it's a really interesting story arc, so I won't spoil it, despite the show being very old). Man, I loved DS9. There are lots of complex characters (Sisko, Dukat and surprisingly Nog come to mind. And, of course Garak!) and plots subverting almost everything you take for granted about Star Trek. If you watch one episode, "In The Pale Moonlight" is absolutely not to be missed. Back on topic, Firefly and DS9 compliment each other well in lots of ways. Too bad Firefly didn't get another 6 seasons :-( ...Bajor eventually DID refuse admission into the Federation. It was actually a pretty major plot point. I'd totally forgotten about that, good catch narse. (though it's not quite what we were talking about since - Google reminds me ;) - Bajor asked to join and Sisko advised them against it for their own sake whereas the idea mentioned - and AFAIK unseen on Trek - was the Federation approaching a world, offering them a place and the world refusing) And yep, "In the Pale Moonlight", great ep. And before that we'd had 'Rocks and Shoals', 'Favour the Bold/Sacrifice of Angels' and one of my favourite episodes of sci-fi ever, 'Far Beyond the Stars'. Was season 6 the best ? Hard to say but it's surely up there. Without violating the Non Disclosure Agreement I signed when I joined the company, I know that Discovery Science is a pay-for add-on for Bell TV in Canada. Discovery Channel period is an add-on as well, but through a different subscription option. oooh, "Far Beyond The Stars", good call! I'm also very fond of season seven's "Siege of AR-558" and "It's Only A Paper Moon". And you are right, Bajor did try to join, and only pulled out after they were accepted. Perhaps a stronger Firefly parallel would be the Maquis, though they weren't strictly anti-Federation, just pissed that they were sold out to the Cardassians. Our Friend Wikipedia has a great quote from "For the Cause": "Everybody should want to be in the Federation. Nobody leaves paradise. In some ways, youíre even worse than the Borg. At least they tell you about their plans for assimilation. You assimilate people and they donít even know it." Fantastic promo. Also, I am onboard for the DS9 love, which became the best Trek by far over the course of the series. Episodes like "Far Beyond the Stars" are exactly why. Brililant television. Makes me all the more sad we didn't get a couple more seasons of Captain Tightpants and co. When marketing and creative really get what something is about, and unite to promote it properly... ahhh, beautiful thing. An excellent recent example is the "Friday Death Slot" promo Fox did when Fringe moved. It made me realize you can't slag Fox for improper promotion all the time -- sometimes they totally nail it. Just like Discovery Science nails it here. If you look down at the bottom of the discoverychannel.ca page (under "CTV Network") you'll see a link to Discovery Science, which is the channel running 'Firefly' (in the US Discovery Science is just called the Science Channel). (which isn't to say it'll necessarily air in Canada/elsewhere BTW - it's the same channel but with slightly different content in different places. The UK Discovery Channel still shows 'Mythbusters' for instance but with an English narrator)

Salluard Route (6a+ 260m ) on Pointe Adolphe Rey (Mont Blanc du Tacul massif) is nice multipitch route on good cracks and corners. But the place is impressive. A heavy recommended route for warm up and acclimatization. Granite is excellent here :). Also, you have here sun by almost all day. Grade: 6a+ Lenght: 260 m, 8 pitches Time: 3-4 h Localization: Pointe Adolphe Rey / Mont Blanc du Tacul / Chamonix Character: corners, cracks, slabs First ascent: 1951, 6 September - Toni Busi and Franco Salluard View from The route Approach You have two options: From Aiguille du Midi (1,5h) From Refuge Torino (1h) From Rifugio Torino (3375m) traverse west towards Col des Flambeaux. From here continue beneath the cable car and descend towards the obvious Pic Adolphe Rey rocky outcrop Prepare that later you must approach this same way to Torino (uphill) :-). Route 1. pitch 4a, 30 m. Climb rotten rocks to a corner-crack and go to belay on the ledge Tomek Reinfuss on first pitch - very nice crack :) 2. pitch 6a, 25 m. Go to the small overhang above the belay. This is the crux of the route and place is technical and physical, but quite ok. Tomasz Reinfuss on the crux pitch 3. pitch 5c, 25 m. Climb a crack (and corners) on the left side of the ridge. 4. pitch 5b, 30m. Go to big groove and later go on a big ledge, where you will be below a big chimney. 5. pitch 5c, 35m Climb the chimney (nice cracks inside) and then go to the left to another corner. Pass belay and go to the left and climb the cracked slab above for 10 meters. You will find belay on a ledge. 6. pitch 5a, 35m go to a big ledge and climb cracks to belay - which is 5m from the left of the arete. Last pitch 7. pitch 5b, 30m. Go to corner system on the left (nice cracks) and direct to V-shaped col. The belay will be on a big ledge. Bartek Szeliga on last pitch 8. pitch 5c, 40m. Climb directly from the belay on the cracks and flakes. The last belay is on the summit ridge of the Pointe Adolphe Rey. Usually climbers descent from this point, but you can continue to the summit. Reaching the summit of Everest is on every climber’s to-do list, and if it’s not, it should be. That said, it’s not exactly the wild ride it used to be, and you’re more likely to see the likes of Damien and Willie Benegas cleaning up the litter left by hundreds of climbers than empty rock faces. To get away from all that, head to the glaciers of Iceland. The Icelandic tourist scene is still developing, so while you’ll see some tours around, die-hard climbers will be able to get their fix of uninterrupted, uncrowded, unspoiled climbing amid awe-inspiring natural formations. And don’t let a potential lack of guides or hooks put you off. Or that rumor that there is no ice in Iceland. With a bit of preparation and bravado, even ice climbing beginners can have a memorable trip. And on that note, let’s have a look at some of the top places apart from the obvious (the active volcano and highest peak, Hvannadalshnúkur) to go for an extraordinary climb. A good site for ice climbers to make their debut is the Sólheimajökull glacier. It’s a quick and easy journey from Reykjavik, home to most native ice climbers, to the car park closest to the glacier. But first, you’ll have to walk for about 15 minutes to get to the foot of the ice wall. True novices in the world of ice climbing should be aware that glacier hiking isn’t necessarily a walk in the park — be prepared for some uneasiness and ice crunches underfoot. To make the hike slightly less disconcerting, donning crampons for this part helps a lot. The beginner wall at the glacier lives up to its name: there are quite a few handholds that have been formed by other people’s axes and crampons icing over so while you’ll still have to work at getting your axes anchored in, your feet will have a bit of help. Kaldakinn in Skjálfanda, which is in the northeast of the country, would undoubtedly be much more popular if it wasn’t so far away — you’re looking at a six-hour drive or internal flight from the capital. But is it worth it? That depends. Are you looking for up to 200 meters of clean ice? About 20 stretches of which have probably never been climbed before? For anyone looking to get a real adrenaline rush or to build on previous experience, Kaldakinn is well worth a visit. And for seasoned ice climbers, those who have done all the “easy” climbs and are looking for a real challenge, Glymsgil is the place to head toward. It’s just an hour away from Reykjavik and therefore much more accessible. At the opening of the canyon, there are several easier climbs, but as you move further in, you’ll have to contend with a river that doesn’t freeze completely. Rappelling down is easy, but once you’re there, the only way to get out is by going up. The routes are long and it’s an arduous climb. Be prepared and make sure your equipment is in good shape because these routes aren’t frequently climbed, so do everything in your power to ensure you don’t get stranded. The Icelandic Alpine Club has more information about the routes at Glymsgil (in Icelandic), including the best ways to get there by car. Iceland is, as of now, an untouched paradise for climbing, with only the locals getting into it. Our advice is to head there sooner rather than later before it becomes as commercial as other spots. After all, where’s the fun of conquering an ice face that has been done by thousands before you? The Cosmiques Ridge (in french Arête des Cosmiques) is one of the most classic climbs in Mont Blanc Massif. This ridge on the Aiguille du Midi need minimal approach and is easily accessible from the cable car. Give easy grade (french PD/PD+), nice views and you know why Cosmiques are so popular. This is also a good way for acclimatization for harder routes, and for a relative beginning climbers great alpine goal. Technical Information: Arête des Cosmiques offers climbing on rock, ice, and snow. It is possible to do this route in every season. It is not difficult for climbers, but you must be prepared for mixed conditions which depend from the time of the year. You will descent to the glacier and climb up granite slabs & crack. Area of Aiguille du Midi is known for a good place for acclimatization. Typically you take a cable car to the top (~3800 m), do some route and quickly go to Chamonix (~1000 m). That was our tactic for climbing on north face of Grandes Jorasses. Cosmiques are very popular (especially in high season (from June to September) then be prepared for a lot of people on the ridge. A good option is to start early (first cable car). Also, be prepared if there is a strong wind. Approach From Chamonix take a cable car to the top of Aiguille du Midi (ticket up/down cost ~60 euro…) and go to the ice tunnel. Descent the steep snow ridge and traverse below the South Face of the Midi (outstanding summer climbing in orange granite). Go near of the Simond Hut. Descending from Aiguille du Midi The Cosmiques Ridge The Ridge start on easy mixed terrain, which leads to a small summit. At this part of the climb, you will go on the right side of the “ridge”. Take direction to the first gendarme (~3731 m ), climb the inclined slabs (4b). Go on the ridge to the second subsidiary summit. Do a descending traverse (or abseil). View to crux of the route {loadposition position-14} Next, go to the first tower and abseil 30 m (bolted belays). Move on the right on the base of the first tower. Climb a small chimney (4a) and go up to ridge (here go also the Cosmiques Couloir). On big ledge go right around the second tower. Author on crux pitch. Photo Tomasz Klimczak Before you are crux section. 5 meters of terrain 4c (slab with cracks). The slab is quite easy because you have drilled (sic!) holes for your front points of crampons. Traverse right above the slab, go to the narrow ledge. From there go to the big terrace and cross the ridge to NW face. Outstanding view! Descent and go right to couloir chimney (2 pitches 3c and 4a). On the ridge go to the metal ladder and access to the terrace of Midi station and to cable car, back to Chamonix. Desmaison (Gousseault) on the north face of Grandes Jorasses is described as one of the finest mixed climbs in The french Alps. On 11-14 of October 2017 we do this route and here you have a description of Desmaison. Like they say in the guidebook: “Go for it, before you become an old fart”... ;-). "When I think of the Grandes Jorasses, I think real classWhen I think of good conditions on the north face, I think those who are not there are missing outWhen I think of all those routese, I think I still have loads to doWhen I think of the Desmaison, I think- Go for it, before you become an old fart...." Climbing on the north face of Grandes Jorasses isn’t easy. This is one of the wildest places in Mont Blanc massif. After you climb north face you have complicated (and dangerous) descent on the south side of Grandes Jorasses. Lescheaux hut. Photo Damian Granowski Approach The best way is to train to Montenvers (from Chamonix). You go to Mer de Glace and approach ~4 hours to mountain hut Leschaux, where is good to stay for a night. From there you have 3-4 hours to the base of the north face of Grandes Jorasses. Approach to the base of the north face. Photo Tomasz Klimczak Climbing Best time for climbing this route is autumn, winter, and early spring. You can do this route in any conditions, but… I recommended that do this route in good conditions :). On route, you will find a lot of rotten rock, and a few big boulders, which can fall with you (especially if they will be not frozen).Best is if easy terrain on Ramps is covered in consolidated snow and ice. Perfect conditions were for that purpose were in 2014 (very rare) and some teams do Desmaison in 2 days. We have poor conditions (but good weather) and need 4 days to complete Desmaison. The hardest pitches were this easiest :-). Sometimes you can find a rotten rock, covered by snow. A lot of time takes in this conditions to find holds and solid place for protection. In good conditions, you probably run at this “easy” places.Another problem was bivi places, which are VERY poor if there is not so many snow. All our bivouacs were in sitting position. Check fresh foto of the wall and search for ice on ramps :-). Hardest pitches (with M-grade) are usually possible to climb even if they are dry. We don’t have problems with them. Desmaison (Gousseault) has some start variation:Originally (1971 and 1973 year) Desmaison started on an overhanging wall between the gully of The Shroud and Ramp I. Now you can start also: October 2000 start (250 m by The Schrund and go to the top of Ramp I), January 2000 (Start at gully on the right of The Shroud and go to chimney), Colton-Smith (most logical if the start of this route is covered in ice). All the starts to the Desmaison lead to the top of Ramp I. After reconnaissance, we choose January 2000 start.We climb ~60 meters in quite good ice. Next, we climb mixt M5 pitch which ends at the base of the chimney M5+. Prepare for war if there is no conditions in chimney :-]. Tomek at the beginning of chimney pitch After chimney pitch move to the right to the easier-angled mixed ground to the foot of a rock step (top of Ramp I). On this step, you will find 2 pitches. First is 5c/M6, with traverse (old poor fixed ropes) to a small flake. Secon M5 to the top of Ramp I. M6 pitch to the top of Ramp I. Photo Tomasz Klimczak Second pitch. Photo Tomasz Klimczak In this area (2-3 easier pitches) we have the first bivouac. Morning of second day After that, you go to start of Ramp II. From here you climb 50 m rock wall (right to the chimney and after to the left). Next 80 meters of easier terrain (M4, 80°. We have some nice ice and later poor rotten rock covered in snow), which ends at the base of Ramp III. You will find there 60 meters of 6a/M7 mixed terrain (or A1). Tomek aid last part and move out to “excellent bivvy site”, which was not so excellent :-). But in better conditions should be better. From here you have 300 meters of easier climbing in ice (section 80-85° thin ice). If there will be not so many ice then prepare for battle in corners with loose rock. Ramp III goes to the foot of headwall, where are connections to other routes. At the base of headwall we have another bivvy site, but if you have time, then try one more pitch of headwall and you probably find a better place, with a sun at dawn :-). III Ramp. Photo Damian Granowski At the base of headwall. Photo Tomasz Klimczak Headwall consists some nice mixt pitches. First is 50 m of climbing in cracks at grade M5. Second is M5+, which goes diagonally (to the right) in solid red rock to the base of the chimney.We climb 40m in - not so good - rock, climb chimney (M5, some old fixed ropes - abandoned during a Korean attempt. After you climb chimney go to the right (poor rock, and loose blocks) below monolithic step.Crux pitch (M6 or 5c A1) of headwall is before you. Climb the wide crack (hand traverse) and after this go to left (don’t go to pegged crack on the right!). Climb to the corner (maybe you must take off gloves) and go to ice smear. Hand traverse on the headwall crux pitch. Photo Tomasz Klimczak After this pitch, you have 4-5 pitches of Exit Ramp (200m, M4, 75°). Nice 1000 meter exposure :-). Photo Damian Granowski It depends from the conditions. We have some “hard” climbing in not consolidate snow. On the last part go to corners from the right side. It should be the easiest way to the top. Tomek on exit ramp. Photo Damian Granowski Good morning Mont Blanc! Photo Damian Granowski Descent (4-5 hours) from the Grandes Jorasses is one of the hardest and complicated in Mont Blanc massif. Some sections are exposed to seracs, stone fall or avalanche… In the night or poor weather can be difficult to find the route. It's a good idea to have map, compass, and GPS with coordinates of crucial points.The best way from Pte Walker is “normal” route. From the summit head down (slightly leftwards) to S rock ridge. The descent on the crest (rock&ice) to glacial plateau. Traverse west across the glacier (be quick! Above you are a line of seracs) to get to the Rochers Whymper (base of S spur of Pte Whymper).You will find here some Rappels (in good conditions you can descent without them) which lead you to Gl. des Grandes Jorasses. Traverse this glacier to the west to the top of Rocher du Reposoir. Go down the crest of this ridge (poor rocks). After few hundred meters go to left side of the crest. Last part you can climb down or use two 30 m abseils. Descent on Rocher du Reposoir. Photo Damian Granowski We use abseils and after that don’t go down (hard slabs and bergschrund), but traverse to the west to easier part of the glacier.Head down on the glacier (but take the left side of Glacier de Planpincieux. Near of Rognon de la Bouteille). Move off the glacier onto a rocky plateau. Continue down rocky rib to Boccalatte hut (fixed ropes). The hut cannot be seen until the last minute.From Boccalatte hut go down by patch to village Planpincieux (2-3 hours). Desmaison 11-14 October 2017, Damian Granowski and Tomasz Klimczak. 3 bivvy at the wall and one of the peak of Grande Jorasses. 1200 m, M6+, WI4, A1. In April 2017 we check new destination on worlds climbing map – Leonidio in Greece. Almost two weeks in this quite new sector was a good time. In this article, you will find some tips for climbing and accommodate here. Getting there Leonidio (~6000 residents) is placed in a valley on the east coast of the Peloponnese peninsula (210 kilometers from Athens). It is surrounded by big limestone crags, and from city to Sea is 3 kilometers. The best way to getting there is to buy a fly ticket directly to Athens. From there you have a 4-hour drive (you can rent a car from airport) to Leonidio (highway and later express road near of Mediterain Sea. Climbing in hot rock. Photo. Damian Granowski Another option is going there by bus: By Bus:From Athens International Airport take Bus X93 to Kifissou Bus station (in greek: Κηφισού). It is the final station of the line, ca. 1h drive, 5€.At the bus terminal buy your ticket at the counter "Leonidio" (in greek: ΛΕΩΝΙΔΙΟ or Λεωνίδιο). Accommodation & Food Leonidio – The traditional town offers a lot of places to accommodation. There is the big touristic base for summer, when a lot of people go there for holidays (sea and beach). But out the season lot of them is free (and probably cheaper). Here you have link to possible places. The traditional town still offers a pleasant way of life and is a good place to choose for a relaxing and/or active vacation! Many of you have visited our beautiful village and have experienced the stunning cliffs surrounding Leonidio. Currently, there are more than 1000 routes across a wide range of grades, and there is still potential for much more. In Leonidio, you have 2 small supermarkets. But you also have a lot of bakeries, small shops (fruit & vegetables). For long evenings you have a tavern and pizza restaurants. Local taverns have a lot of vegetarian and vegan dishes. Guidebook? There is „Leonidio Climbing Guidebook” (edition 2016, also in English). Almost 1000 routes in 50 sectors. More than 40 intro pages. It cost ~30 euro. It was produced by the climber from Panjika cooperative in Leonidio. They have in Leonidio bar, climbing shop, the restaurant in one ;). Przemek Patelka on Tufa Tango 6c, Sector Mars Best season for climbing Climbing conditions in Leonidio are best in autumn, winter, and spring. Best period for climbing is from October to April, with the climate being typically Mediterranean. Some crags can be climbable even on hot spring and summer days. We have been there on the beginning of May and there was a lot of crags where you can climb. But in many cases, we tried to climb in shade, For example, after 1 am there was shadow on sector Mars. Main sectors (above Leonidio) like Hot Rock are best in winter when the sun is your friend :-). Daniel Wdowiak on Metallica 5c+ A lot of climbers is there at the beginning of November, when is Leonidio Climbing Festival (in this year 2-5 November). {loadposition position-14} The rock In Leonidio is limestone. Usually red/orange in overhangs. The vast majority of climbing routes in Leonidio are relatively new. Many still require thorough cleaning of loose rock and traffic to improve. Pieces still break off, so helmets are strongly recommended. Ania Kołodziej in Sector Red Rock In general quality of rock is good. You will find crimps, pockets (not so many), tufas. Climbing on slabs, vertical, overhanging rock. Mateusz Kołodziej climbing 6b in Sector Mars Routes Near of Leonidio, there are close to a thousand climbing routes ( the state from 2016), most of them are quite new. The majority are single pitch routes, but you will find some multi-pitch climbing (up to 200 m) on the main cliff above the city. All the climbs are sensibly bolted (no clipstic required). It is recommended to take an 80m rope since some of the routes are up to 40m high and required as many as 20 quickdraws (I hear that on some harder and long (~50m) routes you need 25). However, it is possible to get away with a 70 m rope and still climb the majority of the routes. Even 60 m rope should be ok, for a lot of routes (For example sector Mars). For sports multi-pitch climbing you need 80 m single rope (rappels are 40 m long) or 50-60 double rope. The double rope should be better on traditional routes. Daniel Wdowiak and Krzysiek Sadnicki on multipitch route Mira 6b Almost every climber will find something for them. From french 5a to 9a. But this area is not for very beginners climber. It is ok if you do 6a grade (OS or quick RP). There are not many routes at 4 and 5 grade. A lot of routes have soft grade and are good for Onsight. It depends from the area. There where are routes bolted by German and Czech climbers will be more thoughtful. One more time I repeat - A helmet is highly recommended, especially on vertical/long routes. Best crags Approach to the crack is usually short and well-signposted. Some sectors are 20-40 minutes from parking. And there you drive 5-20 minutes from Leonidio. Sectors like Red Rock, Hot Rock, Mars are available 20-30 minutes of walk from Leonidio. If you prefer you can hire bicycle or scooter in the town. I don’t recommend Pillar of Fire. Its ugly trad (with some bolts) - better take only quickdraws and go for fully bolted routes :-). Second pitch on Mira 6b Take necessary gear + water, adequate clothes, and headlight. Best way to go down is rappeling by this same route or go to dedicated rappeling route on the right side of the wall (rappels have 40 m and are marked by red dots). Other options for rest - Mountain bike- Diving in Sea- visit monasteries of Elona. One hour from Leonidio is Mycenae and Tiryns Topo There are a lot of climbing sectors in Leonidio. You can find more information and topos here:http://climbing-leonidio.com/en.htmlhttp://climbgreece.com/leonidio/http://www.climbinleonidio.com/https://27crags.com/areas/leonidio Today I write about something special. Eliteclimb Raptor - lightweight ice axes from carbon fibers. I had the honor to test one of the first prototypes of this tools and some of my ideas are in new Raptors. In this text, I will write something about this ice tools and answer the question: Is this Raptor for You? JW: Company has roots in mountains. The idea was born in the middle of Kazalnica (famous polish winter wall in Tatras) at 2013. Near of our team was climbing team Wojtek Ryczer and Piotr Xięski. Wojtek saw hammer from Kevlar and give the idea of ice tools from that same material. With his help after half of the year, Salamandras axes go with Artur Małek on the expedition to K2. What was first product? Of course first was hammer ;). After that were 3 Salamandra tools. Their lucky owners are Artur, Wojtek and me. In the meantime, I work on a snow shovel. Some prototype goes to polish expedition K2 & Broad Peak Middle in 2014. Another project was ice tool Czarny Łabędź (Black Swan) for Ice World Cup. Tester was Olga Kosek, but the project now is closed, because UIAA changes limit box for Ice tools. After K2 we create Kruk (Raven) and in this year we have the last version of Raptors. Great thanks for Artur Małek. His experience in high mountains and lot of winter climbing allows creating great products for mountain terrain. Say something about technology In production, we use hybrid carbon and Kevlar composite. Combination of this two materials results in high strength and low weight. Everything is prepared manually. New Raptor? Raptor is next step. Before it was Salamandra. Raptor is designed to technical mixt climbing (ice & rock) and dry tooling. It takes 2 years from idea to product. In the first version, geometry was not so good. Ice tool was also too flexible. We change the shape of shaft and picks. The purpose was: light weight, great swing, stiff shaft and good to place in ice. I think that now Raptor is good. What are next products? We have some ideas. People ask for a combination of ice tool and shovel. Others ask for a typical ice axe.Interesting can be trekking pools. I have some project in my mind. How is going on the international market? Eliteclimbs are recognized in many countries. Salamandras and shovels were used in Romania, Pakistan, USA, UK, Norway, and Switzerland. A big success was Ouray Ice Festival, where we have been the first polish company. We have some new contacts in America. Below short movie about production Eliteclimb {youtube}_8DPe2ZhtrQ{/youtube} Abour Raptors To 2017 you can buy Kruk and Salamandra. This last one was technical ice tool with a shape like in Petzl Quark and was dedicated to alpine climbing. There wasn’t ice tool like Petzl Nomic or BD Fusion. This empty space fills Raptor.Raptor is technical ice tool (dedicated to ice and mixt technical climbing) with rounded shape and grip for your hand. It weighs 430 gram. Construction Construction is “easy”. We have kevlar and tendon coal, also steel pick.The pick is universal. For rock and ice - in this second terrain we can place steel plates from Nomic to give more weight to our ice tool (better swing). Pick also has a minimal hammer. At the top of ice tool, we have the hole for carabiners (we can place our tools to harness).Shaft and grip are from hybrid carbon and Kevlar composite. Everything is profiled for best rigid. At the bottom is an aluminum blade (adze). One Raptor cost 1300 zł (~270 euro) How did they perform? My favorite tools for winter climbing are Petzl Nomics (version 2), which are great construction. So in many cases in this article, I will compare Nomics with Raptors. Raptors First about what you think is weight. First time in my hands I had a feeling that this is plastic :). After some time you get used to but tools are very light.In total, you have two ice tools with weight 900 grams. In comparison Nomics weight 1270 gram. It is almost 400 grams of difference! Attack angle Raptor is designed for mixt and ice climbing in vertical or overhanging terrain. Of course, it will be good also in slab terrain and at roofs.The shape is similar like in Petzl Nomic or Black Diamond Fusion. But Raptors are a little bit bigger "Feeling" In hard mixt climbing (especially dry tooling) is important to have “feeeling” of your tools. When you put your weight on small crimps you “feel” if your tool catch hold. Another detail is jamming of your tools. For example, Nomic has a little bit flexible shafts. When you hang on the roof (especially on figure 4 or 9) Nomic can increase his length and return when you lighten. Sometimes in this situation grip of Nomic can jam. From opposite is Fusion Black Diamond, where a shaft is very rigid. How is with Raptors? The shaft is also flexible. Maybe smaller than in Nomics, but there is something. But you know - They are built not from an alloy of metal but from hybrid carbon and Kevlar composite. SomethingRaptor is leashless, but it has a small hole for something - BD Fusion weight 672 gram and Raptor 430 gram. Another important point is a grip on your tools. Good ergonomic handle is treasure, which gives us huge benefit on overhanging routesGrip in Raptors is ok, but not so good like in Petzl Nomics or Cassin X-dream. The shaft in Raptor is covered with special abrasive paint for better grip. But soon (if you climb in overhang routes) or later (if you climb in alpine terrain) this paint go away and friction will be not so good.At this point, I feel a difference in dry tooling (big overhangs and roofs). Not so bad but Fusion, Nomic and Cassin X-dream have better grip. The solution can be grip tape on the shaft and… training ;). The shape of the grip for me is too thick (better is in Nomic and X-dream).Carbon and kevlar grip is better in alpine terrain. This material is warm for your hands and snow did not glue to your shaft. {loadposition position-14} Griprests Raptor has 3 grip rest. First at the bottom of the handle is quite big and protect our hand from hitting ice&rock. He has a serrated blade which gives us the opportunity to put ice tool in snow (easy terrain).The second grip rest is at the top of the handle. Third in the middle of the shaft (which is good in easy alpine terrain or in overhang dry tooling routes). Leash Raptor is leashless, but it has a small hole to put cord there. Durability I use Raptor 2 winter seasons. Two pairs (prototype and new - actual - version). Last part quite often. I’m curious how strong will be a tool from carbon fibers. Carbon and Kevlar don’t brake suddenly (like a shaft in Nomics a ). First, we hear cracking sound. Maybe in hard dry tooling after years of using you have the chance for that. But in alpine/mixt/ice climbing I doubt. There is not so many force to break your shaft. Another point is picks They weigh ~140 gram (almost like in Petzl Nomics). The profile is for ice and mixt climbing in vertical and overhanging terrain. There is only one picks profile (some producents have picks for ice and mixt).Picks have wide 4mm on the tip. An alloy of picks for me is a little bit softer than in picks from original Nomics. Maybe in this season picks will be harder. One pair of picks cost 25 euro (in Poland). Dry tooling I climb with Raptors a lot. Usually in terrain harder than M6. To grade M7+ they are excellent. Good “feeling” of tools and light weight is quite good for this type of dry tooling.I climb with them in harder terrain - big overhanging routes (also roofs). “Feeling” of your tools is also good.Problem is with grip. It is not so good like in Nomics or X-dreams. We must use more force of our arms. Maybe a solution is to stretch grip tape on shaft and grip. Dry tooling on Zakrzówek (Kraków, Poland) Mixt climbing I use them usually in Tatras. In rock, they are similar like in dry tooling. Placing your tools in ice, consolidated snow and frozen grass without problems. Their great advantage is weight :-). On approach and descent, we have almost ~400 grams less in our backpack. Photo Bartek Szeliga Climbing in ice Artur Małek says that Raptors are born for ice :). I didn't climb with them in hard ice (WI5+ and harder) then I don’t have the comparison with Nomic.I use Raptors more in rock than ice. But I do several hundred meters on icefalls (about 150 of grade WI5+) and they were ok. I climb without pick weights and I think that Nomic is a little bit better on ice.Unfortunately, I didn’t test with one Raptor and Nomic at one icefall. Who should use? Good question. Buying a new pair of ice tools is a big investment in climbing gear. Raptors are specialized tools for:winter mountaineering, steep technical alpine climbing. Everywhere where we don’t have long routes in overhanging and roofs. Every cent will return on approach and descents.Big mountain expeditions where weight is crucial.The light person, where a weight of ice tools is important. For example, girls which weight is under 55 kg.Climbing on long icefall in water ice.Climbing in snow/ice couloirs.For climbers, who prefers climbing in big overhangs and roofs, Raptors will be not so good. The good climber will climb with them, but you will need more grip strength. Conclusion Raptors from Eliteclimb are interesting ice tools. If you are rather Mountaineer (to M8) than dry tooling monkey then you should consider this purchase. But if you go too long mountain expedition then buy them ;). Poland is mostly flat but we have some mountains and rock climbing. I cannot describe all of them (~200), so just I write about best spots where you can do rock climbing. Lucky this locations are very close to big cities like Kraków, Katowice or Wrocław. In a different article, I write about mountaineering in Tatras (the highest polish mountains) - check if you want. Very quick - like I say. Poland is mostly flat, but on the south side, you have almost 200 climbing areas and probably 15000-20000 routes! You will find in Poland typical rock: limestone, granite, sandstone. Routes have to 30 meters, from 3+ to 9a. You will find sport and trad routes. Generally, all that you need ;). We have also mountaineering, dry tooling, bouldering but I will don’t write here about this. Just only rock climbing. Rock climbing near of Kraków (Łabajowa Rock in Będkowska Valley) Below practical info and later bigger description of areas. Practical info Poland is a big country with long history. There is a lot of things to see. Good idea is to connect climbing with touring or hiking. Of course, we are climbers then first I will tell you about climbing. At the end of the article, you will find some ideas for a rest day. Trad climbing on Wronia Baszta (Kobylańska Valley near of Kraków) Getting there? Poland has good airplane connections with almost every country in Europe. To Kraków, Katowice and Wrocław fly cheap airlines like Wizzair, Ryanair. At this places, you can rent a Car, but airports have good public transport. From Kraków and Wrocław you can go to crags by public transport! From Katowice, You have a good connection to Kraków, Wrocław, and Częstochowa.The most comfortable will be traveling motorway by car. Be prepared that polish roads are not so good like in Germany ;). In every bigger climbing area, you will find camping or guest houses.Be careful and parking only in designated places (the best way to avoid conflicts with locals). Usually, the best places to parking you will find in guidebooks. Good option to check a status of the crag is on website naszeskaly.pl (Our Crags). Something like American Acces Fund. On naszeskaly.pl you will find info and status of different cragsApproach to crags depends from the area - on Jura it should not take more than 30 minutes (rare is 40-60 minutes), on Sokoliki 25-45 minutes. Granite climbing in Sokoliki Accommodation and food Accommodation opportunities depend from a place. But almost everywhere you will find private rooms and in most popular crag areas will be campsite or hostel.In the most cases sleeping in the woods is not allowed. There are some places like Kobylańska Valley (free campsite in the Valley) or in Podlesice, but the better option will be to use (cheap) campsites (2-3 euro for tent, 5-7 euro for a bed in the house).On my climbing school website, I wrote two articles about accommodation near of Kraków and Sokoliki. Articles are in Polish… but you can use Google Translator and Google Maps ;).Accommodation and eating near of KrakówAccommodation and eating near of Sokoliki Generally in every place is no problem with finding grocery shops. In bigger cities (even villages) will be a market.Popular crags areas are places where is a lot of people, then you will find there some restaurant (check my articles about Kraków and Sokoliki). View from Krzywa Turnia (Sokoliki) Guidebooks Almost every crag in Poland is in the guidebook and descriptions are quite good :-). We don’t have guidebooks in English, but I think that every climber with a quarter of the brain will know how to use books :). In guidebooks, you will find maps, GPS locations (crag and parking), approach patches and short notifications “How to Use the Guide” in English.The most popular (and very actually) are: Another option is Big Brother Google. A lot of crags topo is available online. Highly recommended are websites like: wspinanie.pl, goryonline.com, toprope.pl, drytooling.com.pl (my website with topo of multipitch climbing in Tatras). But the best website is Portalgorski with its topo base of polish crags! You also have dedicated App ;).Last but not least - Watch out! Advertise ;). If you want help then write an email to Me. I will try to advise you the best option for classic climbs in Poland.You can also hire me to be your Climbing Guide or Instructor. Check my offer on this page: Climbing Courses in Poland. Trad climbing on Malinowa Rock (Rudawy Janowickie Best season for climbing In Poland, you can climb all year, but for Rock Climbing best season is from April to September. One important thing - Our climate doesn't have something like “long period of stable weather”. It is mostly random and I can just tell you that some months probably will be ok, but you never know ;). Generally is ok, last long period with big rains was in 2009 (almost one month of rain and floods) ;). Usually 1-3 days of rain (Mostly light rain). January-February-March: We have winter. Sometimes you can climb, when are better periods of good weather. These periods are very random and temperatures are from 0-10°C (mostly below zero). But this is a good time for dry tooling.April-May: There is spring but weather can be random. Usually, the temperature will be from 10-30°C but can be also 0-10°C in some days. Spring in Poland has good weather, not so many rainy days (usually storms) and temperatures are quite good for hard climbing. In this time Jura is very beautiful with fresh green grass and trees.June-July(and two weeks of August): The hottest (20-35°C) and most wet (storms) time of the year. But like I say before, usually, it is a storm, then you can climb very quickly after rain. But shit happens and you can have 2-4 days of heavy rain. But mostly you must search for crags in shadow because Sun is too hot.The second part of August-September: Probably best time for climbing in Poland (if you are a serious climber). A few rainy days, good temperature (10-25°C), rare storms and autumn in our country is wonderful.October: For hard climbing is very good (5-20°C). Not so many rainy days (but happens that 2-3 days of rain). Days are shorter and sometimes crags in deep Valleys (like near of Kraków) can be wet (morning fog).November-December: For rock climbing not recommended time: a lot of rainy days, low temperatures, short days. But a good time for dry tooling ;). Sukiennice in Sokolikie. One of the best crags in Poland Climbing in Poland You will find here almost 200 hundred crag areas with 15-20k routes (mostly sport, but you will find also nice trad routes). Difficulties between 3 and 9a (even 9a/a+). We have three main type of rock: limestone (Jura), granite (Sokoliki and Rudawy) and sandstone (Podkarpacie and Hejszowina).Routes are to 30 meters high, but average high is 15-25 meters. We have almost rock formation what climber need to live. There are some higher crags like Sokolica, Łysina or Żabi Koń where you have multipitch climb (usually well bolted). Polish limestone has challenging routes on tiny holds with worse friction than the one found in most of the climbing spots in the Western Europe. Jura has a lot of small pockets (worse than on Frankenjura) and on harder routes, this pockets will be your footholds. Watch your fingers! I promise that after climbing trip to Poland your strength in fingers and footwork will improve ;).Typical Polish route (at grade 6b-7b, ~20m) in white limestone is vertical with small crimps, pockets, small footholds and endurance climbing. We don’t have many overhanging routes like in Spain, but there is some climbing in roofs. Don’t dream about climbing on tufas in Poland ;). Granite in Sudety (Sokoliki) are roughly and they have a lot of crimps and cracks. Cracks are not like in Yosemite where you have only cracks... and jamming is mandatory. In Sokoliki lot of (not every) routes have cracks, crimps, jugs and other holds. Usually, grades have been given in the Kurtyka Scale. Below is a table with the comparison. Routes are equipment in rings. Belay stances are from 2 rings and chain. Nowadays is very rare to have a route with old protection (especially bolts in limestone).There is some outstanding trad climbing - most of them in Sokoliki, Hejszowina (sandstone) and Tatras (multipitch). But some of them are on Jura and this limestone trad climb is mode demanding (irregular crack, then you must use nuts and hexes). Limestone climbing in Bolechowice Valley (near of Kraków) What gear do you need? Standard rope in Poland is single 60m. 13-15 quickdraws should be enough. On polish limestone, the best are climbing shoes with a hard sole and sharp tip (a lot of small pockets). The standard for belays are 2 ring + chain and routes are well equipment. For trad climbing gear rack: - set of cam (to #4 Camalot Black Diamond) on harder trad routes set of microfriends.- set of nuts- set of slings- some alpine quickdraws On Jura (limestone) better than cams are hexes (irregular cracks). Jura The most popular area for climbers in Poland is the Kraków-Częstochowa Upland (in Polish: Jura Krakowsko Częstochowska). These limestone crags are located between Kraków and Częstochowa. Very good access from Kraków (airport) and Katowice (airport).For climbers, Jura has 3 sections: South (10-40 from Kraków), Middle (50-60 km from Kraków and Katowice) and North (50-100 from Kraków and Katowice). Every area has almost the same type of limestone ( the difference is usually with the size of pockets and… slippery). A lot of crags are hidden in the forest, but many are on hills with an outstanding view! North JuraThere are more crags on hills. Rock has more pockets than on South Jura.Olsztyn, Mirów, Rzędkowice, Łutowiec, Góra Zborów, Góra Kołoczek, Biblioteka, Jastrzębnik, Okiennik Skarżycki, Góra Birów Kobylańska Valley (near of Kraków) SokolikiGóry Sokole is the north-west edge of Rudawy Janowickie, but is often regarded as a distinct location. The rocks here are also granite, and the area is subdivided into three regions: Krzyżna Góra, Rejon Sokolika and Rejon Sukiennic, all of which are also a part of Rudawy Landscape Park.This small mountain range offers best granite climbing in Poland (I don’t include multipitch climbing in Tatras). On this area is ~1000 sport and trad routes (also multipitch climbing to 60 meters). Rudawy JanowickieRudawy Janowickie is a mountain range in the Western Sudetes, fairly close to the border with the Czech Republic and Germany. It’s located about 100 kilometres west of Wrocław and is enclosed by Rudawy Landscape Park (Rudawski Park Krajobrazowy). The mountain range is commonly divided into four regions: Rejon Zamku Bolczów, Grupa Fajki, Grupa Skalnego Mostu and Starościńskie Skały, each of which offers numerous granite rocks, higher than the limestone peaks in Jura. Lot of climbing in Rudawy are on trad. Also area is bigger than Sokoliki - You will have longer approach to crags. Granite slabs in Rudawy Janowickie (Starościńskie Skały) Best crags in Rudawy JanowickieStarościńskie Skały, Malinowa, Fajka Other placesIn Poland you will find more (small) crag area. I will mention about most popular and recommended to climb. Sandstone areasProbably best sectors are: Rożnów (close to Nowy Sącz), Kamień Leski (near of Sanok) and Czarnorzeki (close to Rzeszów). This second should be better (more routes).On the Lower Silesia (border between Poland and Czech Republic) is Hejszowina, where are big sandstone walls. But protection is from rings (long distance between them) and knots :). Like in Czech: Ardspach and Teplice. I hope that this article was helpful for you. If you have any question then contact with me. Also I'm climbing instructor then if you want I can be your guide on polish crags or you can take part in my climbing courses near of Kraków or Sokoliki. Check there for more information: Climbing Courses in Poland. Winter in Ireland is a very fleeting mistress with a sudden drop in the ambient air temperature and an even swifter rise in temperature, Winter conditions in the Irish mountains can come and go in a single day. It is when a period of extended cold weather hits the Emerald Isle, it is then that its mountains are transformed into a true winter wonderland. The online winter climbing guide is found at uniqueascent.ie. At the northern end of The Derryveagh Mountains in County Donegal lives a huge flat topped mountain called Muckish named from the Irish, Mucais or an Mhucais, meaning the pig's back. The south face of the mountain holds the easiest and most popular route to it’s huge flat topped summit. The north face of Muckish is a completely different beast as the entire face is dominated by a huge steep sided corrie. This corrie holds the remains of the ancient mining works used long ago to extract the high grade quartz sand from the mountain, the sand was then used to produce high quality glass. {youtube}u-aIgKu-Q_s{/youtube} Looking for Donegal Ice The old miners track into the corrie provides an excellent and easy summer navigation route into the corrie and up onto the summit of the mountain. When winter hits county Donegal this corrie is transformed into an outstanding winter mountaineering venue. The steep normally wet sides of the corrie freeze and are plastered with snow. With a few freeze/ thaw cycles this snow soon consolidates and is quickly transformed into superb neve. This neve provides outstanding underfoot conditions for winter walking into this magnificent corrie. The miners track is quite steep in places and a single walking axe and crampons are recommended as the track weaves it’s way up and through several amazing but steep gullies to the huge summit plateau. Unclimbed Winter Ground From the summit of Muckish Mountain the views are vast, uninterrupted and breathtaking as far as the eye can see towards the Slievetooey massif to the South, the Inishowen Peninsula to the North and the surrounding Derryveagh mountains. Poisoned Glen climbing Poisoned Glen in the Derryveagh Mountains is by far the most outstanding winter climbing venue in Donegal and a contender for the best in Ireland. This wall of north-facing cliff stretches for over a kilometre and reaches a height of 400m at its highest point on The Bearnas Buttress. The cliff is seamed with deep wet gullies and hidden vertical water courses and given the correct winter conditions it will provide many lifetimes of icy climbing potential. Alas when the glen comes into excellent condition it is prone to temperature inversion which can allow for good conditions for the walk in but means an early start to avoid the midday thaw on the high faces. Errigal Topo Errigal Mountain is Donegal’s highest point. Its south ridge route is climbed by thousands of walkers on an annual basis. Under winter conditions this mountain provides exceptional winter mountaineering routes on its exposed north, west and east faces. The climbing is mainly mixed climbing on faces and arêtes with the north face providing the excellent 200m long, grade III Tower Ridge. Slieve Snaght Summit The North face of Mac Uchta, Errigal’s next door neighbour provides a collection of steep snow gullies all in the lower grade in a spectacular and lonely setting. The north face of Maumlack high above the shores of Lough Croloughan provides an easy accessed venue with a reliable collection of water ice routes. The huge, remote and mildly intimidating north face of Slieve Snaght in the Derryveagh Mountains, provides a selection of excellent low grade winter climbs in a superb and atmospheric location. Maumlack Topo The Horseshoe Coire is a huge steep sided corrie immediately to the northwest of Lough Barra in the Derryveagh mountains and provides many steep water courses and falls. The potential for further winter routes here is enormous alas it is south-facing and requires a prolonged deep freeze. Square Cut Gully The above locations are just a small sample of the winter climbing available when conditions allow, with many more less reliable venues scattered throughout the county’s mountain ranges. Iain Miller is a rock climber living working and playing on the sea cliffs, sea stacks, uninhabited islands and mountain ranges of County Donegal in the Republic of Ireland. The climbers guide to Donegal is http://uniqueascent.ie/undiscovered_donegal. The rear heel clip features a micro-adjustment system for a secure fit Dual-density ABS plates keeps snow from sticking to the bottom of these crampons Ideal for steep ice and mixed climbing Item #BLD0483 Tech Specs Material: steel Boot Compatibility step-in Front Points dual Number of Points: 12 Anti-balling plates: yes Claimed Weight[pair]: 1120 gram Recommended Use: ice/mixed climbing, mountaineering Manufacturer Warranty1 year Mixed climbing (on ski tour boots) in Tatras.. Fot. Cezary Klus {loadposition position-14} Climbing Review Cyborgs are crampons dedicated to ice/mixed climbing and mountaineering. We have choice to use in them mono or dual point, which is great advantage for different type of climbing. In fact you have 3 different types of crampons! If you want a single crampon that can climb in three different modes and you don’t mind a little extra weight, the Cyborg should be your type. Personally I prefer mono point (especially in Tatra mountains). Dual point usually I used on snow type climbing routes. I prefer monopoint system, then I cut hole in antibot plates to better set single point. Unfortunately it was difficult to proper cut this hole. After 1-2 hours (and involves a hacksaw) of working I achieved success… But in crampons for 200 bucks producent should prepare something better. You can place single point without cutting hole in your snow plate, but it will be more demanding for your calf to stay on small footholds and holes in ice. Front of my Cyborg before retiring ;-). Photo Damian Granowski In general if You climb usually on mono point, then maybe better choice will be to buy Black Diamond Stinger Crampons (960 gram pair). Cyborg has heel clip features a micro-adjustment system for a secure fit, but after 3 years of using I have problem with them. Steel wire “jump” in plastic hole when I placed crampons on my boot. After that it was loose on my heel. I solved this problem with climbing tape, but… you know… crampons for 200 $... Photo Damian Granowski Strap are quite long, then you can cut them for your shoes. I climb in them routes to M10 and WI6. They stay well on foot and small crimps, penetrate ice and frozen grass. What else you need :-)? Ice climbing in Tatras. Photo Bartłomiej Szeliga Weight of Cyborg (pair) Monopoint – no antibot – 940 gram Dual Point – no antibot – 1000 gram Dual Point – with antibot – 1120 gram If you want a single crampon that can climb in three different modes and you don’t mind a little extra weight, the Cyborg might be the your choice. Especially on steep ice and winter mixed climbing. There are routes which every alpine climber want to do. One of them is Heckmair Route on North Face of Eiger, biggest wall in The Alps. Wall with history – before the first ascent in 1938, there died some climbers and wall has new nickname „Mordwand”. Today Heckmair Route is hard classic alpine route and usually teams needs 2 days of climbing. But speed record is below 3 hours… We (Michał Dorocicz and Damian Granowski) climb North Face of Eiger in 2016 (22-23 March). Below you have description and topo of Heckmair Route. Original article (in polish) you will find here: drytooling.com.pl. These days the most popular time for climbing on North Face of Eiger is late autumn, winter, and early spring. In summer – due to global warming – conditions are not good. A lot of loose rock (which in winter are frozen) and falling stones. Here you have some tips: Heckmair Route isn’t extreme alpine route but rather “hard alpine classic” but don’t disrespect difficulties.- In general, the route is hard, rock is rotten with demanding protection. You will find old pitons, some bolts. On harder pitches protection is better.- falling stones. In summer much more- There are some fixed lines but be careful. Some of them are not in good shape ;)- Do proper acclimatization. In higher parts of the route, you must be quick. Maybe tray something easy and quick (like Breithorn).- Go when conditions are ok.- Almost half of the route you do on simul-climbing. Take good partner... {loadposition position-14} To Grindenwald go by your own car (40 euros for a vignette on a highway). There you will find accommodation on campings (10-15 euro) or apartments (from 60 franks). Grindelwald lay on 1000 m a.s.l.. The base of Eiger North Face on 2160 m a.s.l.. The best option is to go by small historic train. You go to Kleinescheidegg (2000 m) and after that to station Eigergletscher.From there we go to base of the wall (short traverse). Fototopo of Heckmair Route. Credits: Damian Granowski The first part of the route (about 800 meters) is “easy” and in good conditions, you can go to Difficult Crack almost free solo.We start on the right side of First Pillar (about 200 meters) and follow the easiest line. There are many variations, but all are quite easy (with some short rock sections). After 150 meters (at the Shattered Pillar height) we go to the right and soon to the left. Traverse on snow ledges and when you will be on snowfield (with overhang wall above) then you go 50 meters to right.There will be Difficult Crack (Belay pegs, old slings). Difficult Crack is… well Difficult, even if has V- (M5+). One pitch and we are on Belay. From there you go to the left to small rock Dihedral. After that, you have easy snow terrain which leads you to Hinterstoisser Traverse. Climbing after the Difficult Crack. Photo: Michał Dorocicz Travers is very hard for mixed climbing. Almost without steps and holds. After 30 seconds I decided to aid this :-). There are 60 meters of fixed lines (traverse and small chimney). Pitch end on belay on beginning First Icefield. On The Hinterstoisser Traverse. Photo: Michał Dorocicz We go 100 meters (snow/ice to 55 degrees) to the upper right, where is Ice Hose. 20 meters of Icefall (if you have good conditions something about WI3-4). 30 m above Icefall you will find “good” belay on the big boulder. Now we are on Second Ice Field. We go straight ahead to rocks. After that run to the left, across the icefield to the upper left corner. There climb chimney, groove and easy terrain to the Death Bivvy. Michał Dorocicz on the Second Ice Field On the Death Bivvy, you will find a place (snow ledge) for 4 persons. Clean rock and lot of old pegs and bolts. At the 18.00 pm, there will be sun ;-).The Death Bivvy is probably the best place to spend a night, but if you are here very early (14-15.00) then try to push The Ramp and spend a night on Traverse of Gods. From the Death Bivvy, we traverse to a big ramp. There are 4-5 pitches (circa 150 m) of climbing. Including Ice Chimney (M7 in good conditions, a lot of pitons). In the middle of The Ramp is Spanish Bivvy, but is weak… Begining of the Ramp Above the Ice chimney is one small wall – hard and demanding. After that is easy climbing in snow and ice. We go to the start of Brittle Ledges (possibly bivy). Traverse them to start of the Brittle Crack – one V+ pitch with quite good rock (especially after The Brittle Ledges). Climbin above the Ice Chimney. Photo: Michał Dorocicz After the Brittle Crack, you will find a flat place for a bivy (one team). I'm not sure, but place probably is windy. And then you have The Traverse of the Gods. 150 meters to The White Spider. Quite exposed but easy (max IV). The Traverse of the Gods You reach The White Spider, Snow/Ice field in the upper part of the wall. From there retreat was difficult. Climb 150 m to the right (big Gully). Be careful not to go to left, big corner with ice – but hard.Once more 150 meters of climbing in a gully and you will be at the base of The Quartz Crack. Difficult (IV+. SIC!?) chimney.After that you traverse to the left and climb a small crack to the big pulpit. Here you will find fixed lines which lead you to the Exit Chimneys. The Exit Chimneys can be pretty hard (but only IV) in weak conditions. Climb them 3-4 pitches (circa 150 m) to the easier terrain which leads you to snow / ice field. Above them will be a ridge. Ridge is easy and in good conditions you won’t need rope. To summit, you need 15-20 minutes of climbing. {loadposition position-14} If you want more mountaineering topo articles in future, then click to like funpage WinterClimb.com :)

Q: WordNetLemmatizer not returning the right lemma unless POS is explicit - Python NLTK I'm lemmatizing the Ted Dataset Transcript. There's something strange I notice: Not all words are being lemmatized. To say, selected -> select Which is right. However, involved !-> involve and horsing !-> horse unless I explicitly input the 'v' (Verb) attribute. On the python terminal, I get the right output but not in my code: >>> from nltk.stem import WordNetLemmatizer >>> from nltk.corpus import wordnet >>> lem = WordNetLemmatizer() >>> lem.lemmatize('involved','v') u'involve' >>> lem.lemmatize('horsing','v') u'horse' The relevant section of the code is this: for l in LDA_Row[0].split('+'): w=str(l.split('*')[1]) word=lmtzr.lemmatize(w) wordv=lmtzr.lemmatize(w,'v') print wordv, word # if word is not wordv: # print word, wordv The whole code is here. What is the problem? A: The lemmatizer requires the correct POS tag to be accurate, if you use the default settings of the WordNetLemmatizer.lemmatize(), the default tag is noun, see https://github.com/nltk/nltk/blob/develop/nltk/stem/wordnet.py#L39 To resolve the problem, always POS-tag your data before lemmatizing, e.g. >>> from nltk.stem import WordNetLemmatizer >>> from nltk import pos_tag, word_tokenize >>> wnl = WordNetLemmatizer() >>> sent = 'This is a foo bar sentence' >>> pos_tag(word_tokenize(sent)) [('This', 'DT'), ('is', 'VBZ'), ('a', 'DT'), ('foo', 'NN'), ('bar', 'NN'), ('sentence', 'NN')] >>> for word, tag in pos_tag(word_tokenize(sent)): ... wntag = tag[0].lower() ... wntag = wntag if wntag in ['a', 'r', 'n', 'v'] else None ... if not wntag: ... lemma = word ... else: ... lemma = wnl.lemmatize(word, wntag) ... print lemma ... This be a foo bar sentence Note that 'is -> be', i.e. >>> wnl.lemmatize('is') 'is' >>> wnl.lemmatize('is', 'v') u'be' To answer the question with words from your examples: >>> sent = 'These sentences involves some horsing around' >>> for word, tag in pos_tag(word_tokenize(sent)): ... wntag = tag[0].lower() ... wntag = wntag if wntag in ['a', 'r', 'n', 'v'] else None ... lemma = wnl.lemmatize(word, wntag) if wntag else word ... print lemma ... These sentence involve some horse around Note that there are some quirks with WordNetLemmatizer: wordnet lemmatization and pos tagging in python Python NLTK Lemmatization of the word 'further' with wordnet Also NLTK's default POS tagger is under-going some major changes to improve accuracy: Python NLTK pos_tag not returning the correct part-of-speech tag https://github.com/nltk/nltk/issues/1110 https://github.com/nltk/nltk/pull/1143 And for an out-of-the-box / off-the-shelf solution to lemmatizer, you can take a look at https://github.com/alvations/pywsd and how I've made some try-excepts to catch words that are not in WordNet, see https://github.com/alvations/pywsd/blob/master/pywsd/utils.py#L66

Basil, tea tree and clove essential oils as analgesics and anaesthetics in Amphiprion clarkii (Bennett, 1830)CorreiaA. M.PedrazzaniA. S.MendonçaR. C.MassucattoA.OzórioR. A.TsuzukiM. Y.2017<div><p>Abstract In this study were evaluated the anaesthesia and analgesic effects of clove Eugenia caryophyllata, tea tree Melaleuca alternifolia and basil Ocimum basilicum essential oils (EO) during handling of yellowtail clownfish Amphiprion clarkii. Juveniles (3.70 ± 0.75 cm and 1.03 ± 0.50 g; mean ± standard deviation) were submitted to concentrations of 40, 50, 60, 70 and 80 µl L-1 of clove, 150, 200, 250, 300 and 350 µl L-1 of basil and 200, 300, 400, 500 and 600 µl L-1 of tea tree oils (n=10/concentration), previously defined in pilot tests. Individually and only once, fish from each treatment were placed in a glass recipient containing 1 L of seawater at a temperature of 25 °C, salinity of 35 g L-1 and the specific concentration of diluted EO (stock solution). Control (only seawater) and blank (seawater and ethanol at the highest concentration used to dilute the oils) treatments were also conducted. After reaching the stage of surgical anaesthesia, fish were submitted to biometry and a sensibility test. After that, they were transferred to clean seawater for anaesthesia recovery. The times of induction needed to reach each anaesthesia stage and anaesthesia recovery were recorded. Animals were observed for 72 hours after the procedures. All the EO provoked anaesthesia and analgesic effects in A. clarkii, but basil oil is not recommended because it caused involuntary muscle contractions and mortality in 100% and 12% of fish, respectively. The lower concentrations that promote suitable induction and recovery times are 50 µl L-1 of clove oil and 500 µl L-1 of tea tree oil. However, due to its complementary high analgesic efficiency, clove oil is recommended as the ideal anaesthetic for A. clarkii.</p></div>

const UserText = { USER_INFO_LABEL_NAME: '用户名称', USER_INFO_LABEL_EMAIL: '用户邮件', USER_INFO_LABEL_PASSWORD: '密码', USER_INFO_LABEL_CONFIRM_PASSWORD: '确认密码', USER_INFO_PLACEHOLDER_NAME: '请输入用户名称', USER_INFO_PLACEHOLDER_EMAIL: '请输入邮箱地址', USER_INFO_PLACEHOLDER_PASSWORD: '请输入密码', USER_INFO_PLACEHOLDER_CONFIRM_PASSWORD: '请再次输入密码确认', USER_INFO_BTN_SUBMIT: '确认', } export default UserText

--- abstract: 'Very recently the Dark Energy Survey (DES) Collaboration has released their second group of Dwarf spheroidal (dSph) galaxy candidates. With the publicly-available Pass 8 data of Fermi-LAT we search for $\gamma-$ray emissions from the directions of these eight newly discovered dSph galaxy candidates. No statistically significant $\gamma-$ray signal has been found in the combined analysis of these sources. With the empirically estimated J-factors of these sources, the constraint on the annihilation channel of $\chi\chi \rightarrow \tau^{+}\tau^{-}$ is comparable to the bound set by the joint analysis of fifteen previously known dSphs with kinematically constrained J-factors for the dark matter mass $m_\chi>250$ GeV. In the direction of Tucana III (DES J2356-5935), one of the nearest dSph galaxy candidates that is $\sim 25$ kpc away, there is a weak $\gamma-$ray signal and its peak test statistic (TS) value for the dark matter annihilation channel $\chi\chi\rightarrow \tau^{+}\tau^{-1}$ is $\approx 6.7$ at $m_\chi \sim 15$ GeV. The significance of the possible signal likely increases with time. More data is highly needed to pin down the physical origin of such a GeV excess.' author: - Shang Li - 'Yun-Feng Liang' - 'Kai-Kai Duan' - 'Zhao-Qiang Shen' - 'Xiaoyuan Huang$^\ast$' - 'Xiang Li$^\ast$' - 'Yi-Zhong Fan$^\ast$' - 'Neng-Hui Liao' - Lei Feng - Jin Chang bibliography: - 'refs.bib' title: 'Search for gamma-ray emission from eight dwarf spheroidal galaxy candidates discovered in Year Two of Dark Energy Survey with Fermi-LAT data' --- Introduction ============ The nature of dark matter particles is still unknown and among various speculated particles weakly interacting massive particles (WIMPs) are the most popular candidates [@Jungman:1995df; @Bertone:2004pz; @Hooper:2007qk; @Feng:2010gw]. WIMPs may annihilate or decay and then produce stable high-energy particle pairs such as electrons/positrons, protons/antiprotons, neutrinos/anti-neutrinos, $\gamma-$rays and so on. The main goal of the so-called indirect detection experiments is to identify cosmic rays or $\gamma-$rays with a dark matter origin [@Jungman:1995df; @Bertone:2004pz; @Hooper:2007qk; @Feng:2010gw]. The charged cosmic rays are deflected by the magnetic fields and their energy spectra would also be (significantly) modified during their propagation. As a result, the dark-matter origin of some cosmic ray anomalies$-$for example, the well-known electron/positron excesses [@Chang:2008aa; @Adriani:2008zr; @Adriani:2011xv; @FermiLAT:2011ab; @Aguilar:2013qda; @Aguilar:2014fea] $-$ is hard to reliably establish. The morphology of prompt $\gamma-$rays from annihilation or decay, instead, directly traces the dark matter spatial distribution and is therefore possible to choose regions in the sky with high dark matter density to investigate the dark matter properties. The annihilation signal is expected to be the brightest in the Galactic center but the astrophysical backgrounds are very complicated there [@Bertone:2004pz; @Hooper:2007qk]. That is why the dark matter annihilation origin of the GeV excess in the inner Galaxy [@Goodenough:2009gk; @2009arXiv0912.3828V; @Hooper:2010mq; @Hooper:2010im; @Abazajian:2012pn; @Gordon:2013vta; @Hooper:2013rwa] has not been widely accepted yet though its significance has been claimed to be as high as $\sim 40 \sigma$ [@Daylan:2014rsa] and this excess is found to be robust across a variety of models for the diffuse galactic $\gamma-$ray emission [@Zhou:2014lva; @Calore:2014xka; @Huang:2015rlu; @TheFermi-LAT:2015kwa]. The dwarf Spheroidal (dSph) galaxies are widely believed to be favorable targets with high signal-to-noise ratio [@Lake:1990du; @Baltz:2004bb; @Strigari:2013iaa], because on the one hand these objects are very nearby and on the other hand they are far away from complicated emission regions. Several searches for gamma-ray emissions from dwarf galaxies detected by Sloan Digital Sky Survey (SDSS), which covers the northern-hemisphere [@Simon:2007dq], and earlier experiments [@York:2000gk; @McConnachie:2012vd] have been performed using Fermi-LAT data, and none of them reported a significant detection [@Ackermann:2011wa; @GeringerSameth:2011iw; @Tsai:2012cs; @Mazziotta:2012ux; @2012PhRvD..86b3528C; @Ackermann:2013yva; @Ackermann:2015zua; @2015PhRvD..91h3535G; @2015arXiv151000389B]. The ongoing Dark Energy Survey (DES) [@Abbott:2005bi; @2016arXiv160100329D] is instead a southern-hemisphere optical survey and in early 2015 the DES Collaboration released their first group of dSph galaxy candidates [@Bechtol:2015cbp; @Koposov:2015cua]. Shortly after that, another dSph galaxy candidate (Triangulum II) was discovered with the data from the Panoramic Survey Telescope and Rapid Response System (Pan-STARRS) [@Laevens:2015una] and a few additional candidates were reported by other collaborations [@martin15_hydra; @kim15_pegasus; @kim15_horologium; @laevens15_3dsph]. Though a reliable J-factor is not available for most newly-discovered sources, the velocity dispersion measurements strongly suggest that some sources (e.g. Triangulum II, Horologium II) are indeed dark matter-dominated dSphs [@kim15_horologium; @kirby15_tri2]. The analysis of the publicly-available Fermi-LAT Pass 7 Reprocessed data found moderate evidence for $\gamma-$ray emission from Reticulum 2 [@Geringer-Sameth:2015lua; @Hooper:2015ula] and the signal was found to be consistent with the Galactic GeV excess reported in [@Hooper:2010mq; @Hooper:2010im; @Abazajian:2012pn; @Gordon:2013vta; @Hooper:2013rwa; @Daylan:2014rsa; @Zhou:2014lva; @Calore:2014xka; @Huang:2015rlu; @TheFermi-LAT:2015kwa]. Interestingly, later, the J-factor of Reticulum 2 is found to be among the largest of Milky Way dSphs [@2015ApJ...808L..36B]. The analysis of the Fermi-LAT Pass 8 data in the direction of Reticulum 2, however, just found a $\gamma-$ray signal with a largest local significance of $\sim 2.4\sigma$ for any of the dark matter masses and annihilation channels [@Drlica-Wagner:2015xua]. Very recently the DES Collaboration has released their second group of new dSph galaxy candidates [@Drlica-Wagner:2015ufc]. In this work we search for possible $\gamma-$ray emission from the directions of these very recently-discovered dSph galaxy candidates by the DES collaboration (hereafter we call them the DES Y2 dSph galaxy candidates). Data analysis ============= In this paper, we used the newly released Pass 8 data to search for gamma-ray emission from these DES Y2 dSph galaxy candidates. The Pass 8 data benefit from an improved energy reach (changing from the range of $0.1-300$ GeV to $60~{\rm MeV}-500~{\rm GeV}$), effective area in particular in the low energy range, and the point-spread function [@Atwood:2013rka]. Thanks to such improvements, the differential point-source sensitivity improves by 30-50% in P8R2\_SOURCE\_V6 data relative to P7REP\_SOURCE\_V15 data [@Drlica-Wagner:2015xua], which make it more sensitive to faint sources like dSph galaxies. We used the Fermi-LAT data collected from 2008 August 4 to 2015 August 4 that have passed the P8R2 SOURCE event class selections from 500 MeV to 500 GeV. To suppress the effect of the Earth’s limb, the $\gamma-$ray events with zenith angles greater than $100^{\circ}$ were rejected. We use the updated standard Fermi Science Tools package with version v10r0p5 to analyze Fermi-LAT data. The regions of interest (ROI) are selected as regions centered at the position of each DES Y2 dSph galaxy candidate. The selected data using criterion described above were divided into 100$\times$100 spatial bins with 0.1$^{\circ}$ bin size. Following Fermi team’s recommendation, we adopted a diffuse emission model based on the Pass 7 Reprocessed model for Galactic diffuse emission but has been scaled to account for differences in energy dispersion between Pass 7 reprocessed data and Pass 8 data [^1]. We took the approach developed in [@Tsai:2012cs; @Ackermann:2013yva; @Ackermann:2015zua] to analyze the gamma-ray emission for each dSph candidate, we refer readers to these literature for details of the approach we used. First, we carried out a standard binned likelihood fit over the entire energy range with 24 logarithmically spaced energy bins to determine the background sources using [*[gtlike]{}*]{} tool in Fermi Science Tools. All point-like sources from 3FGL [@Acero:2015hja] within $15^{\circ}$ of the center of each dSph galaxy were included and new excesses in TS map with ${\rm TS}\geq 25$ were identified as new sources and then included in the fit. The normalization of point sources within $5^{\circ}$ and the two diffuse backgrounds (Galactic diffuse emission and an isotropic components) were set free, while other parameters were fixed at the 3FGL values. No component associate with dSph was included in this step. Next, we adopted a bin-by-bin analysis as [@Tsai:2012cs; @Ackermann:2013yva; @Ackermann:2015zua]. For each ROI, a point source is added to the best fitting model in last step in the position of each dSph galaxy to consider the signal from the given direction. We modeled these dSph galaxy candidates as point-like sources rather than spatially extended sources due to the lack of the information of the spatial extension of dark matter halos of these newly-discovered objects. Likelihood profile, which is a curve of how likelihood varying as the flux of the newly added putative point source, are generated for everyone of 24 logarithmically evenly spaced energy bins. Within each energy bin, we fixed all the model parameters but the normalization of the newly added dSph point source, and use a power-law spectral model ($dN/dE \propto E^{-\Gamma}$) with spectral index of $\Gamma=2$ to fit the putative dwarf galaxy source. We scanned the likelihood as a function of the flux normalization of the assumed dark matter signal independently by varying the flux normalization to derive the profile. These likelihood profile will be used in later analysis in section \[sec2\_1\]. Using these profiles, we can also derive bin-by-bin energy-flux upper limits at 95% confidence level for each dSph candidate, which are shown in Figure 1. ---------------- ----------------- ---------------------- ------------------------------------- Name $(l,b)^{\rm a}$ ${\rm Distance^{b}}$ $\log_{10}{{\rm (Est. J)}^{\rm c}}$ (deg) (kpc) $\log10{\rm (GeV^{2}cm^{-5})}$ DES J2204-4626 (351.15,-51.94) $53\pm 5$ 18.8 DES J2356-5935 (315.38,-56.19) $25\pm 2$ 19.5 DES J0531-2801 (231.62,-28.88) $182\pm 18$ 17.8 DES J0002-6051 (313.29,-55.29) $48\pm 4$ 18.9 DES J0345-6026 (273.88,-45.65) $92\pm 13$ 18.3 DES J2337-6316 (316.31,-51.89) $55\pm 9$ 18.8 DES J2038-4609 (353.99,-37.40) $214\pm 16$ 17.6 DES J0117-1725 (156.48,-78.53) $30\pm 3$ 19.3 ---------------- ----------------- ---------------------- ------------------------------------- $^{\rm a}$ Galactic longitudes and latitudes are adopted from [@Drlica-Wagner:2015ufc]. $^{\rm b}$ The distances are taken from [@Drlica-Wagner:2015ufc]. $^{\rm c}$ J-factors are estimated with the empirical relation $J(d)\approx 10^{18.3\pm 0.1}(d/100~{\rm kpc})^{-2}$ [@Drlica-Wagner:2015xua]. {width="100.00000%"} Combined constraint on the dark matter physical properties with the newly discovered eight dwarf galaxies {#sec2_1} --------------------------------------------------------------------------------------------------------- The dSph galaxies are known to be dominated by dark matter. The ${\gamma}-$ray flux expected from annihilation of dark matter particles in a dSph galaxy is given by [@Jungman:1995df; @Bertone:2004pz; @Hooper:2007qk; @Feng:2010gw] $${\Phi}(E)={\frac{<{\sigma}v>}{8{\pi}m_{\chi}^{2}}\times \frac{dN_{\gamma}}{dE_{\gamma}}\times J},$$ where ${m_{\chi}}$ is the rest mass of the dark matter particle, ${<{\sigma}v>}$ is the thermal average annihilation cross section, $dN_{\gamma}/dE_{\gamma}$ is the spectrum of prompt ${\gamma}-$rays resulting in dark matter particle annihilation and $J={\int}dld{\Omega}{\rho}(l)^{2}$ is the line-of-sight integral of the square of the dark matter density (i.e., the so-called J-factor). {width="45.00000%"} {width="45.00000%"} {width="45.00000%"} {width="45.00000%"} Utilizing the likelihood profile derived above, we reconstructed a broadband likelihood function by multiplying the bin-by-bin likelihood functions evaluated at the predicted fluxes for a given dark matter model. Then we combined the eight DES Y2 dSph candidates’ broad-band likelihood functions and added an extra J-factor likelihood term for each dSph candidate to take into account the J-factor’s statistical uncertainties. The J-factor likelihood term for each dwarf galaxy is given by $$L_{\rm J}(J_{\rm obs,i},{\sigma}_{\rm i})={1 \over \ln(10)J_{\rm obs,i}\sqrt{2\pi}{\sigma}_{\rm i}} \exp^{-[\log_{10}(J_{\rm i})-\log_{10}(J_{\rm obs,i})]^{2}/{2\sigma_{\rm i}^2}},$$ where $i$ represent different target, $J_{\rm i}$ is the J-factor’s “real" value and the $J_{\rm obs,i}$ is the J-factor’s empirically-estimated value with an error of ${\sigma}_{\rm i}$ [@Ackermann:2015zua]. After combining the J-factor likelihood term and the broad-band likelihood functions, the likelihood function for target $i$ reads ${\widetilde L_{\rm i}}(\boldsymbol{\mu},\boldsymbol{\theta}_{\rm i}={\lbrace}\boldsymbol{\alpha}_{\rm i},J_{\rm i}{\rbrace}{\vert}D_{\rm i})=L_{\rm i}(\boldsymbol{\mu},\boldsymbol{\theta}_{\rm i}{\vert}D_{\rm i}){L_{\rm J}(J_{\rm obs,i},{\sigma}_{\rm i})}$, where $\boldsymbol{\mu}$, $\boldsymbol{\alpha}_{\rm i}$, ${J_{\rm i}}$ and $D_{\rm i}$ represent the parameters of the dark matter model, the parameters of astrophysical background, the dSph J-factor and the gamma-ray data, respectively; and $\boldsymbol{\theta}_{\rm i}$ incorporates $\boldsymbol{\alpha}_{\rm i}$ and ${J_{\rm i}}$ [@Ackermann:2015zua]. To reduce the uncertainty on the direction of gamma-rays, we took into account four PSF event types (PSF0, PSF1, PSF2 and PSF3) when constructing the likelihood function, for which the broadband likelihood function for target $i$ is given by $L_{\rm i}(\boldsymbol{\mu},\boldsymbol{\theta}_{\rm i}{\vert}D_{\rm i})={\prod\limits_{\rm j}}L_{\rm i}(\boldsymbol{\mu},{\boldsymbol\theta}_{\rm i}{\vert}D_{\rm i,j})$, where $j$ represents the different PSF event type [@Ackermann:2015zua]. ![The TS value of the possible dark matter annihilation signal in the combined $\gamma-$ray data in the directions of seven “nearby" dSph galaxies (candidates), including Segue I, Segue II, Ursa Major II, Reticulum II, Tucana III, Cetus II and Willman I. The dark matter annihilation channels are labeled in the plot.[]{data-label="Fig.4"}](f4.eps){width="50.00000%"} So far the reliable J-factors for these eight DES Y2 dSph galaxy candidates are unavailable. An empirical relation between the heliocentric distances and J-factors of ultra-faint and classical dwarf galaxies is suggested to be $J(d)\approx 10^{18.3\pm 0.1}(d/100~{\rm kpc})^{-2}$ in [@Drlica-Wagner:2015xua], where $d$ is the distance of the object to the Sun and a symmetric logarithmic uncertainty on the J-factor of $\pm0.4$ dex for each DES dSph galaxy candidate is assumed [@Drlica-Wagner:2015xua]. The estimated values of J-factors of the eight DES Y2 dSph galaxy candidates are presented in Table 1. The individual and combined constraints on the dark matter annihilation channels of $\chi\chi \rightarrow b\bar{b}$ or $\tau^{+}\tau^{-}$ with these sources are presented in Figure 2. If the real J-factors are similar to our estimates, we can rule out the thermal relic cross section for WIMP with $m_\chi \lesssim 25$ GeV annihilating into either $b\bar{b}$ or $\tau^{+}\tau^{-}$. We have also analyzed all the 16 dSph candidates reported in [@Bechtol:2015cbp; @Koposov:2015cua; @Drlica-Wagner:2015ufc] and found out that the combined constraints on the dark matter models are similar to that set by the DES Y2 data. Hence we do not present them in this work. $\gamma-$ray emission in the direction of Tucana III ---------------------------------------------------- At a distance of 25 kpc, Tucana III (also known as DES J2356-5935) is one of the nearest dSph galaxy candidates locating at a high latitude that is suitable for dark matter indirect detection. We first used a global binned likelihood fit in the energy range from 500MeV to 500GeV with a power-law spectral model (i.e., $\frac{dN}{dE} {\propto}E^{-2}$) for this dSph candidate. Interestingly we found a weak “excess" of gamma-ray in the direction of Tucana III with ${\rm TS}\approx6.0$ after adding a possible weak point source (${\rm ra \approx 0.74^{\circ},~dec \approx -59.72^{\circ}}$) that is about 0.8 degree away. In addition, we used bin-by-bin method to make a further analysis of Tucana III. In Figure 3 we present TS values of $\gamma-$ray signal in the direction of Tucana III for various annihilation channels and dark matter masses. Note that Fig.3a is for the 7 year LAT data (i.e., from 2008 August 4 to 2015 August 4), in which one can find that in each channel the significance of the signal peaks above $2\sigma$. Particularly, in the case of $\chi\chi\rightarrow \tau^{+}\tau^{-}$, the TS value of the fit peaks about 6.7 at $m_\chi \sim 15$ GeV. For the adopted empirical J-factor, a $\langle \sigma v\rangle_{\chi\chi\rightarrow \tau^{+}\tau^{-}}\sim 5\times 10^{-27}~{\rm cm^{3}~s^{-1}}$ is needed to reproduce the signal. In the case of $\chi\chi\rightarrow b\bar{b}$, the TS value of the fit peaks about 6 at $m_\chi \sim 66$ GeV. With the adopted empirical J-factor, a $\langle \sigma v\rangle_{\chi\chi\rightarrow b\bar{b}}\sim 2\times 10^{-26}~{\rm cm^{3}~s^{-1}}$ is needed to account for the signal. Such $m_\chi$ and $\langle \sigma v\rangle$ are similar to that “preferred" by the Galactic GeV excess data as well as the possible gamma-ray signal in the direction of Reticulum 2 [@Hooper:2010mq; @Hooper:2010im; @Abazajian:2012pn; @Gordon:2013vta; @Hooper:2013rwa; @Daylan:2014rsa; @Zhou:2014lva; @Calore:2014xka; @Huang:2015rlu; @TheFermi-LAT:2015kwa; @Geringer-Sameth:2015lua; @Hooper:2015ula]. In view of the similar though weak signals in the directions of Reticulum 2 [@Geringer-Sameth:2015lua; @Hooper:2015ula; @Drlica-Wagner:2015xua] and Tucana III, following the same data analysis approach we make a combined analysis for these two nearby dSph candidates. The TS values for a dark matter annihilation signal (for the representative channels $\chi\chi \rightarrow b\bar{b}$, $\tau^{+}\tau^{-}$ and $\mu^{+}\mu^{-}$) are evaluated. Interestingly, the TS values of this GeV-excess like signal increase sizeably and in the case of $\chi\chi\rightarrow \tau^{+}\tau^{-}$ we have the largest ${\rm TS}\approx 14$ for $m_{\chi} \approx 16$ GeV. This corresponds to a local significance of $\sim3.7\sigma$, which decreases to $\sim2.3\sigma$ if we take into account the so-called trail-factor correction since here we have just chosen two sources from in total 16 DES dSph candidates. We have also analyzed the gamma-ray emission in the directions of dSph galaxies (candidates) within a distance $\leq 40$ kpc from the sun, including Segue I, Segue II, Ursa Major II, Reticulum II, Tucana III, Cetus II and Willman I but excluding Sagittarius and Canis Major since they are close to the Galactic plane. In the case of $\chi\chi\rightarrow \tau^{+}\tau^{-}$ we have the largest ${\rm TS}\approx 9.2$ at $m_{\chi} \approx 16$ GeV (see Figure 4). Now we briefly examine the possible astrophysical origin of the weak $\gamma-$ray signal in the direction of Tucana III. The “signal" is too weak to directly get the variability information. Instead, we calculate the TS values of the potential ‘GeV excess’ component in another time interval from 2008 August 4 to 2012 February 4 (i.e., the 3.5 year Fermi-LAT data) and the results are presented in Fig.3b. Interestingly the TS values of the annihilation channels shown in Fig.3a are larger than those in Fig.3b, implying that the significance is indeed increasing. Such an increase is expected in the models of dark matter annihilation or alternatively a steady astrophysical source. It is well known that radio loud active galactic nuclei (RLAGNs) could be possible counterparts because of the high galactic latitude of the possible $\gamma-$ray signal. We note that there is a radio source PMN J2355-5948 about $\rm 0.3^{\circ}$ away from the optical position of Tucana III. It is included in the Parkes-MIT-NRAO (PMN) surveys [@1994ApJS...91..111W] and Sydney University Molonglo Sky Survey (SUMSS) [@Mauch:2003zh] and the fluxes at 4.85 GHz and 843 MHz are $55\pm8$ mJy and $259\pm8$ mJy, respectively. Assuming its radio emission follows a power-law distribution, the radio spectrum index can be estimated as $\alpha_{\rm r}\simeq 0.9$ (note that we refer to a spectral index $\alpha$ as the energy index such that $F_{\nu}\propto\nu^{-\alpha}$). Since blazars characterized by the flat radio spectrum ($|\alpha_{\rm r}|\leq$ 0.5) are dominated the extragalactic $\gamma$-ray sky and $\gamma-$ray emissions from only a handful of steep radio spectrum RLAGNs have been detected [@Ackermann:2015yfk; @Liao:2015jfj], it is less likely that PMN J2355-5948 is capable to produce significant $\gamma-$ray emission. Discussion and conclusion ========================= Dwarf spheroidal galaxies are one of the best targets for the indirect detection of dark matter annihilation signal. However, the reliable identification of dwarf spheroidal galaxies in optical is a hard job. Before 2015, just 25 dSphs have been reported [@Simon:2007dq; @York:2000gk; @McConnachie:2012vd] and the $\gamma-$ray data analysis of these sources have imposed very stringent constraints on parameters for dark matter annihilation [@Ackermann:2011wa; @GeringerSameth:2011iw; @Tsai:2012cs; @Mazziotta:2012ux; @Ackermann:2013yva; @Ackermann:2015zua]. In 2015, with the optical imaging data from Dark Energy Survey, 16 new dwarf spheroidal galaxy candidates, including a few “nearby" sources at distances of $20-30$ kpc, have been released [@Bechtol:2015cbp; @Koposov:2015cua; @Drlica-Wagner:2015ufc]. The sample of dSphs thus increased significantly and quickly. Although the reliable estimates of J-factors of most of these new dSph candidates are still unavailable, it is the time to carry out the $\gamma-$ray data analysis to check whether there are some interesting signals or not. The $\gamma-$ray search for the first group DES dSph candidates have been reported in [@Drlica-Wagner:2015xua]. No significant gamma-ray emission signal has been identified and strong constraints on the dark matter annihilation channels have been provided by adopting an empirical relation between the J-factor of the dSph and its distance to us [@Drlica-Wagner:2015xua]. A very weak signal resembling the Galactic GeV excess, however, may present in the direction of Reticulum 2 [@Geringer-Sameth:2015lua; @Hooper:2015ula; @Drlica-Wagner:2015xua]. In this work we have analyzed the publicly-available Pass 8 data of Fermi-LAT in the directions of eight new dSph galaxy candidates discovered in Year Two of Dark Energy Survey (see Fig.\[Fig.1\]). No statistically significant $\gamma-$ray signal has been found in the combined analysis of these new sources. With the empirically estimated J-factors of these sources, the constraint on the annihilation channel of $\chi\chi \rightarrow \tau^{+}\tau^{-}$ is found comparable to the bound set by the joint analysis of fifteen previously known dSphs with kinematically constrained J-factors for $m_\chi>250$ GeV (see Fig.\[Fig.2\]). Interestingly, in the direction of Tucana III, a dSph galaxy candidates that is $\sim 25$ kpc away, there is a very weak GeV-excess like $\gamma-$ray signal. We have a ${\rm TS}\approx 6.7$ for the annihilation channel $\chi\chi\rightarrow \tau^{+}\tau^{-1}$ and $m_\chi \approx 15$ GeV. The significance of the possible signal increases with time (see Fig.\[Fig.3\] for the comparison of the results for the 7 year and 3.5 year Fermi-LAT data), as expected in the models of dark matter annihilation or alternatively a steady astrophysical source. To further check the significance of the possible gamma-ray signal, we have also analyzed the Fermi-LAT Pass 8 data in the directions of seven “nearby" dSphs, including Segue I, Segue II, Ursa Major II, Reticulum II, Tucana III, Cetus II and Willman I. In the case of $\chi\chi\rightarrow \tau^{+}\tau^{-}$ we have the largest ${\rm TS}\approx 9.2$ at $m_{\chi} \approx 16$ GeV for the combined $\gamma-$ray data set (see Fig.\[Fig.4\]). Interestingly, the corresponding mass and annihilation cross section of dark matter for the weak gamma-ray signal are consistent with those needed for the dark matter interpretation of GeV excess. The origin of GeV excess from Galaxy inner region is still in heavy debate [@Cirelli:2015gux] and additional support to the dark matter interpretation could be from dSph galaxies that do not suffer from the contamination caused by the complicated background emission. Though our current results seems encouraging, we would like to remind that the astrophysical origin or even a statistical fluctuation origin of the very weak signal is still possible. More data is highly needed to draw a more formal conclusion. We thank the anonymous referee for helpful comments/suggestions. This work was supported in part by 973 Program of China under grant 2013CB837000, by NSFC under grants 11525313 (i.e., the National Natural Fund for Distinguished Young Scholars), 10925315, 11361140349 and 11103084, by Foundation for Distinguished Young Scholars of Jiangsu Province, China (No. BK2012047), and by the Strategic Priority Research Program (No. XDA04075500). $^\ast$Corresponding authors (huangxiaoyuan@gmail.com, xiangli@pmo.ac.cn, yzfan@pmo.ac.cn). [^1]: http://fermi.gsfc.nasa.gov/ssc/data/access/lat/BackgroundModels.html

Q: If I start a new StarCraft 2 campaign can I still watch the movies from my completed campaign? I've completed the campaign and would like to be able to periodically re-watch some of the movies. Is there a way to do so if I start a new campaign? A: Just save in different file and just load your old save file to watch the movies. Or search in youtube :P

Paralysed Woman 'Locked In' Her Body Can Communicate Again After Brain Implant This is astonishing... A brain implant has helped a woman with ‘locked-in’ syndrome to communicate again despite her severe paralysis. In 2008, Hanneke de Bruijne from the Netherlands, was diagnosed with Amyotrophic lateral sclerosis, also known as Lou Gehrig’s disease, which the NHS says affects approximately 2 in every 100,000 people in the UK. umcutrecht The 58-year-old now has very late-stage ALS, characterised by loss of voluntary muscle control in her arms, legs and fingers, but has retained normal cognition. Options for communication have been limited to blinking and using an eye-tracking device to answer closed-ended questions. But now the new technology has allowed de Bruijne to independently control a computer-typing program just 28 weeks after the electrodes were inserted on her motor cortex and thorax. The implant system works on the basis of localised activation: meaning that attempts to move limbs and communicate prompts specific signals in corresponding regions of the brain. The computer interface is then able to decipher these signals and produce communication that can be understood by others. Spelling was accomplished by the selection, with brain clicks, of individual or grouped letters that were highlighted automatically and sequentially. Published in the New England Journal Of Medicine, the successful trial has so far allowed the patient to compose entire sentences directly from her brain, at the rate of two words per minute. Nick Ramsey, professor of neuroscience, told CNN: “It’s a fully implantable system that works at home without need for any experts to make it work.”

Differences in functional activity and antigen expression of granulocytes primed in vivo with filgrastim, lenograstim, or pegfilgrastim. Granulocyte-colony-stimulating factor (G-CSF) is known to affect functional activity and antigen expression of neutrophil granulocytes. Beside nonglycosylated filgrastim and glycosylated lenograstim, pegylated filgrastim (pegfilgrastim) has recently been introduced for single administration into clinical use. Here, granulocytes from 27 patients with nonmyeloid malignancies were compared functionally (migration, reactive oxygen species production, and G-CSF serum levels) and phenotypically (cell surface antigen expression) before and after G-CSF administration. After exposure to G-CSF, chemotaxis was reduced significantly in the filgrastim group. Immunophenotypically, in vivo G-CSF-primed granulocytes were more mature in the lenograstim than in the filgrastim and to lesser extent in the pegfilgrastim groups as shown by the expression profile for CD11b, CD14, and CD16. Of note, G-CSF serum levels were similar among the groups. Our data suggest that granulocytes exposed to glycosylated G-CSF in vivo seem to resemble more closely their steady-state phenotype than after treatment with nonglycosylated and to lesser extent pegylated G-CSF.

WILLITS, CHRISTOPHER & RYUICHI SAKAMOTO "Ancient Future is the second collaboration between composer and visionary pianist Ryuichi Sakamoto and electronic pioneer Christopher Willits. Built around a series of piano pieces that Sakamoto sent to Willits after the release of the duo's first record together, ... more »

Fil de Cassons Fil de Cassons (also known as Cassonsgrat) is a mountain in the Glarus Alps, located near Flims in the canton of Graubünden, Switzerland. The southern face is referred to as "Flimserstein", dominating the appearance of the town of Flims. In its east lies Bargis from where a valley leads to its north face, while to its western face the sliding surface tears off of the biggest visible landslide in the world, Flims Rockslide. Piz Dolf is lying to the north across the Bargis valley, and to its west Piz Segnas, both showing the tectonic line of the Glarus thrust in its upper part, a now UNESCO world heritage. The easiest access to Fil de Cassons is an aerial cableway from Flims to this ridge, that actually allows also walks and an alpine experience from the cablecar for people that would not dare to walk a steep mountain path. Walking on top you will easily identify the tectonic line under your feet, as rocks turn from greenish to bright light grey on top of the wide ridge. For hikers aiming for more than a walk, several routes reach the high plateau and the very wide ridge, among them a historic Via Ferrata called Pinut. One hiking route uses the ascent via Val Bargis and Scala Mola, the path that the cows are being sent up to graze in summer. If you stay at the base of the valley of Bargis, you will hike on a path leading more or less around Fil de Cassons from east to northwest before reaching its top. Being a ridge, there is very often hardly snow, allowing walks even in winter along at least one mile on Fil de Cassons. See also List of mountains of Switzerland accessible by public transport References External links Cassons – experiencing Nature myswitzerland.com Category:Mountains of the Alps Category:Mountains of Switzerland Category:Tourist attractions in Switzerland Category:Flims Category:Mountains of Graubünden Category:Tourist attractions in Graubünden Category:Two-thousanders of Switzerland

Melphalan and prednisone plus thalidomide or placebo in elderly patients with multiple myeloma. In this double-blind, placebo-controlled study, 363 patients with untreated multiple myeloma were randomized to receive either melphalan-prednisone and thalidomide (MPT) or melphalan-prednisone and placebo (MP). The dose of melphalan was 0.25 mg/kg and prednisone was 100 mg given daily for 4 days every 6 weeks until plateau phase. The dose of thalidomide/placebo was escalated to 400 mg daily until plateau phase and thereafter reduced to 200 mg daily until progression. A total of 357 patients were analyzed. Partial response was 34% and 33%, and very good partial response or better was 23% and 7% in the MPT and MP arms, respectively (P < .001). There was no significant difference in progression-free or overall survival, with median survival being 29 months in the MPT arm and 32 months in the MP arm. Most quality of life outcomes improved equally in both arms, apart from constipation, which was markedly increased in the MPT arm. Constipation, neuropathy, nonneuropathy neurologic toxicity, and skin reactions were significantly more frequent in the MPT arm. The number of thromboembolic events was equal in the 2 treatment arms. In conclusion, MPT had a significant antimyeloma effect, but this did not translate into improved survival. This trial was registered at www.clinicaltrials.gov as #NCT00218855.

The natural history of acute confusional migraine. Children with migraine, or, less commonly, with no previous history of migraine, may have agitated confusion lasting from several minutes to hours. There is a tendency for the confusional attacks to recur, but they are eventually replaced by typical migraine. The natural history of this syndrome with 1 1/2 to 5 years' follow-up in five children is reported. The mechanism is believed to be cerebral ischemia of one or both hemispheres.

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Q: R shiny isolate reactive data.frame I am struggling to understand how isolate() and reactive() should be used in R Shiny. I want to achieve the following: Whenever the "Refresh" action button is clicked: Perform a subset on a data.frame and, Feed this into my function to recalculate values. The subset depends on a group of checkboxes that the user has ticked, of which there are approximately 40. I cannot have these checkboxes "fully reactive" because the function takes about 1.5 sec to execute. Instead, I want to give the user a chance to select multiple boxes and only afterwards click a button to (a) subset and (b) call the function again. To do so, I load the data.frame in the server.R function: df1 <- readRDS("D:/././df1.RData") Then I have my main shinyServer function: shinyServer(function(input, output) { data_output <- reactive({ df1 <- df1[,df1$Students %in% input$students_selected] #Here I want to isolate the "students_selected" so that this is only #executed once the button is clicked }) output$SAT <- renderTable({ myFunction(df1) }) } A: How about something like data_output <- eventReactive(input$button, { df1[,df1$Students %in% input$students_selected] }) Here is my minimal example. library(shiny) ui <- list(sliderInput("num", "rowUpto", min= 1, max = 10, value = 5), actionButton("btn", "update"), tableOutput("tbl")) server <- function(input, output) { data_output <- eventReactive(input$btn, { data.frame(id = 1:10, x = 11:20)[seq(input$num), ] }) output$tbl <- renderTable({ data_output()}) } runApp(list(ui = ui, server = server)) Edit Another implementation, a bit more concise. renderTable by default inspects the changes in all reactive elements within the function (in this case, input$num and input$button). But, you want it to react only to the button. Hence you need to put the elements to be ignored within the isolate function. If you omit the isolate function, then the table is updated as soon as the slider is moved. library(shiny) ui <- list(sliderInput("num", "rowUpto", min= 1, max = 10, value = 5), actionButton("btn", "update"), tableOutput("tbl")) server <- function(input, output) { output$tbl <- renderTable({ input$btn data.frame(id = 1:10, x = 11:20)[seq(isolate(input$num)), ] }) } runApp(list(ui = ui, server = server))

Agh! Pretty blah episode for the big Top 20 announcement in Vegas. Here’s the 20-second recap: Most of Thursday’s guys were unmemorable and/or bad, and it was painfully obvious due to the judges’ scripted comments who’d been pre-selected to go through. Randy is still looking for “moments,” Nicki Minaj knows what everyone who “wants to make it out of the hood” FEELS LIKE, and Mariah Carey wants every contestant to know SHE has loved them from the very beginning. And now for the longer version…. ELIMINATED Bryant Tadeo – Why this stranger-‘til-now, a Hawaiian department store employee, was shown the door is still a mystery. The crowd loved him, he seemed like a genuinely nice guy, and he lent a beautiful tone to “New York State of Mind.” Nicki Minaj graciously took some time off from her busy schedule of throwing grotesque side-eyes to tell Bryant “Babe. Ummmm. I loved that last note you did… I didn’t like anything else,” and Randy volunteered that the song “never quite went there for me.” Mariah attempted to explain the crowd’s enthusiasm: “I think what people responded to is the fact that you sounded professional – the tonality of your voice.” And?! Shouldn’t that be a good thing? Sorry Bryant! Next time try living somewhere near a hurricane. David Willis – The judges immediately ganged up on David for his song choice, a sped-up, bluesy rendition of Peggy Lee’s “Fever.” After Nicki learned David was married, she bleated an aggressively over-it “HI, WIFE” and suggested David sounded like a kid who’d just received a guitar for Christmas, playing poorly in front of his family. Just, no. Rude! I wasn’t blown away, but I hadn’t remembered David from any other point in the season, and I thought the uptempo cover was pretty cool considering we rarely see anything like it on Idol. The overall effect reminded me of the True Blood opening credits, jangly and dark but also fun. I was into it! Farewell, David! How dare you even try. After all, a Black Guy With Guitar could be even more potentially deadly than the white version!

Q: Making fonts in Illustrator/Photoshop, exporting them to .ttf/.otf Is there a way to export photoshop/Illustrator files to .ttf or .otf files? I know there is no option for it in these programs themselves, but perhaps there is a third party program which can import them? Are programs like Glyphs or something the only way to make fonts? And how do professionals make them? Hope you can help A: FontLab (commercial app) can import Illustrator paths: http://www.fontlab.com/contact-and-support/faq/faq-fontlab-typetool-mdash-glyph-drawing/ . FontForge (FOSS) can as well, and apparently some other vector formats: http://fontforge.org/importexample.html As for the second part of your question: most professionals use tools such as FontLab, Glyphs, RoboFont, etc. and draw directly in the font-making applications. In many cases they will work from a template/background of some sort, such as a scan of hand-drawings, or perhaps outlines of a different weight of the same design, etc. A: If you are looking to make an Icon as a font then this guide will help. The easiest way is to use a great free online app called IcoMoon, by Keyamoon, which takes away all of the hassle of converting symbols into a web font. Click RED button on top "ICO Moon App" and just go with the flow. For Step by Step guide for doing the conversion you can follow the below link: http://www.webdesignerdepot.com/2013/04/how-to-turn-your-icons-into-a-web-font/

--- abstract: 'We examine the energetics of Coronal Mass Ejections (CMEs) with data from the LASCO coronagraphs on SOHO. The LASCO observations provide fairly direct measurements of the mass, velocity and dimensions of CMEs. Using these basic measurements, we determine the potential and kinetic energies and their evolution for several CMEs that exhibit a flux-rope morphology. Assuming flux conservation, we use observations of the magnetic flux in a variety of magnetic clouds near the Earth to determine the magnetic flux and magnetic energy in CMEs near the Sun. We find that the potential and kinetic energies increase at the expense of the magnetic energy as the CME moves out, keeping the total energy roughly constant. This demonstrates that flux rope CMEs are magnetically driven. Furthermore, since their total energy is constant, the flux rope parts of the CMEs can be considered to be a closed system above $\sim$ 2 $R_{\sun}$.' author: - 'A. Vourlidas, P. Subramanian' - 'K. P. Dere, R. A. Howard' title: LASCO Measurements of the Energetics of Coronal Mass Ejections --- Introduction ============ Material ejections are a common phenomenon of the solar corona. Since the first observation on 14 December 1971 [@tousey73], several thousands of CMEs have been seen [@howard85; @kahler92; @webb92; @hund97; @gos97]. Nevertheless, the mechanisms that cause a CME and the forces acting on it during its subsequent propagation through the corona are largely unknown. Of these two issues, the issue of CME propagation through the corona is by far more amenable. Past observations have provided insufficient coverage of the CME development for several reasons: restricted field of view of the coronagraphs, frequent orbital nights and low sensitivity of the instruments. Consequently, past studies were largely focused on either the phenomenological description and classification of CMEs or the measurement of average values for the physical properties of the events such as speed, mass, kinetic energy [@jackson78; @howard85]. The study of the CME energetics, in particular, was necessarily restricted to a handful of well observed events [@rust80; @webb80]. Their analysis revealed the importance of the (elusive) magnetic energy and established that the potential energy dominates the kinetic energy. It was also found that the energy residing in shocks, radio continua and other forms of radiation was insignificant in comparison to the mechanical energy of the ejected material. The lessons learned from the past resulted in a greatly improved set of instruments; the LASCO coronagraphs [@bru95], aboard the SOHO spacecraft [@dom95]. The location of the spacecraft at the L1 point permits the continuous monitoring of the Sun while the combination of the three LASCO coronagraphs provides an unprecedented field of view from 1.1 $R_\odot$ to 30 $R_\odot$. The replacement of videcons with CCD detectors and the very low stray light levels of the coronagraphs have led to a vast sensitivity improvement. It is now possible to routinely follow the dynamical evolution of a CME. Here, we compute basic quantities; mass, velocity and geometry and derive quantities such as the potential, kinetic and magnetic energies of CMEs as they progress through the outer corona into the heliosphere. To our knowledge, this is the first time that detailed observations of the dynamical evolution of these quantities has been presented. These measurements are expected to provide concrete observationally-based constraints on the driving forces in CME models. For this study, we focus on a group of CMEs that share a common characteristic; namely, they resemble a helical flux rope in the C2 and C3 coronagraph images. We choose these events for three reasons: (i) the area of a CME that corresponds to the flux rope is usually easily identifiable in the coronagraph images, (ii) their appearance can be related to the flux rope structures measured in-situ from Earth-orbiting spacecraft, and (iii) there has been extensive theoretical and observational interest for this class of CMEs. Several CMEs observed with the LASCO instrument exhibit a helical structure like that of a flux rope [@chen97; @dere99; @wood99]. The theoretical basis for flux rope configurations in solar and interplanetary plasmas is well established [e.g., @gold63; @gold83; @chen93; @low96; @kumar96; @guo96; @wu97]. These treatments envisage the helical flux rope as a magnetic structure that resides in the lower corona and erupts to form a CME. There is some debate about whether the flux rope is formed before the eruption, or whether it is formed as a consequence of reconnection processes that lead to the eruption. These arguments are related to those which consider whether the reconnection occurs above the sheared arcade which presumably forms the flux rope, or below it [@spyro99]. Neither the physical mechanisms of the initial driving impulse, nor the conditions in the corona which determine the subsequent propagation of the flux rope are very well known from observations. Theoretical models often rely on educated guesses to model both the initiation of the CME as well as its propagation through the corona. Statements about the energetics, or driving forces behind CMEs are made on these bases; for instance, @chen96 and @wu97_2 show plots of the variation of kinetic, potential and magnetic energies of CMEs as calculated from their models. The measurements we present in this paper are expected to yield some clues about the validity of the assumptions made in these models. It may be emphasized that our measurements are made only in the outer corona (2.5 $R_{\odot}$ - 30 $R_{\odot}$). They are therefore not expected to shed much light on the energetics of the flux rope CMEs immediately following initiation, or on the initiation process itself. Our estimates of the magnetic energy of flux-rope CMEs are made on the basis of in-situ measurements of magnetic clouds near the earth. This is because flux-rope CMEs ejected from the Sun are often expected to evolve into magnetic clouds [@rust94; @kumar96; @chen97; @gopal98]. Conversely, in-situ measurements of magnetic clouds near the earth suggest that their magnetic field configuration resembles a flux rope [@burlaga88; @lep90; @farrugia95; @marubashi97]. Radio observations of moving Type-IV bursts can also probe the magnetic field in CMEs [@steward85; @rust80] but they are so rare that near-Earth measurements are the most reliable estimates of the magnetic flux. It should be borne in mind, however, that the precise relationship between CMEs and magnetic clouds and the manner in which CMEs evolve into magnetic clouds is not very well understood [@dryer96; @gopal98]. The main reason for this situation is the simple observational fact that while CMEs are best observed off the solar limb, magnetic clouds are measured near the Earth. This issue will hopefully be addressed in the near future by the next generation of space-borne instruments. The rest of the paper is organized as follows: We describe our methods of measuring the mass and position of a CME and of calculating the different forms of energy associated with it in § 2. § 3 presents the results of our measurements. We discuss caveats that accompany these results in § 4 and draw conclusions in § 5. Data Analysis ============= {width="16cm"} ![ *Solid line:* Thomson scattering calculation of the angular dependence of the total brightness of a single electron at a heliocentric distance of 10 R$_\odot$. The curve is normalized to the brightness at $0^\circ$. *Dash-dot line:* Ratio of the observed relative to the actual mass of a simulated CME, centered on the plane of the sky, as a function of its angular width (see text). \[siml\]](f2.ps){width="6cm"} Mass calculations ----------------- White light coronagraphs detect the photospheric light scattered by the coronal electrons and therefore provide a means to measure coronal density. Transient phenomena, such as CMEs, appear as intensity (hence, density) enhancements in a sequence of coronagraph images. We compute the mass for a CME in a manner similar to that described by @poland81. After the coronagraph images are calibrated in units of solar brightness, a suitable pre-event image is subtracted from the frames containing the CME. The excess number of electrons is simply the ratio of the excess observed brightness, $B_{obs}$, over the brightness, $B_e(\theta)$, of a single electron at some angle, $\theta$, (usually assumed to be 0) from the plane of the sky. $B_e(\theta)$ is computed from the Thomson scattering function [@bill66]. The mass, $m$, is then calculated assuming that the ejected material comprises a mix of completely ionized hydrogen and 10% helium. Namely, $$m = {B_{obs}\over B_e(\theta)}\cdot 1.97\times10^{-24} {\rm gr}$$ After the mass image is obtained, we delineate the flux rope by visual inspection, as shown in Figure \[cartoon\]. We attempt to circumscribe the cross section of the helical flux rope as seen in the plane of the sky. The cavity seen in the white light/mass images is taken to be the interior of the flux rope, bounded by the helical magnetic field (Figure \[cartoon\]). The mass contained in the flux rope is computed by summing the masses in the pixels encompassed by the flux rope. The accuracy of the mass calculations depends on three factors: the CME depth and density distribution along the line of sight and the angular distance of the CME from the plane of the sky. All three factors are unknown since the white light observations represent only the projection of the CME on the plane of the sky. Some additional information can be obtained from pB measurements, but these are only occasionally available. Therefore, to convert the observed brightness to a mass measurement we have to make an assumption. Namely, we assume that all the mass in the CME is concentrated in the plane of the sky. Since CMEs are three-dimensional structures, our calculations will tend to underestimate the actual mass. To quantify the errors arising from our assumption, we performed two brightness calculations shown in Figure \[siml\]. The solid line shows the angular dependence of the quantity $B_e(\theta)$ in equation (1) normalized to its value at $0^\circ$. We see that our assumption that the ejected mass is always in the sky plane ($\theta=0^\circ$) underestimates the mass by about a factor of 2 at angles $\sim 50-60^\circ$. We expect that the CMEs in our sample are relatively close to the plane of the sky ($\theta<50^\circ$) since their flux rope morphology is clearly visible. Next, we investigate the effect of the finite width of a CME. We simulate a CME with constant density per angular bin along the line of sight, centered in the plane of the sky at a heliocentric distance of 10 R$_{\sun}$. Using equation (1) we calculate the observed mass, $m_{obs}$, for various widths and compare it to the actual mass, $m_{cme}$ for the same widths. The dashed line in Figure \[siml\] shows the dependence of this ratio, $m_{obs}/m_{cme}$ on the width of the CME. For angular widths similar to those of the CMEs in our sample ($\lesssim60^\circ$) the mass would be underestimated by about $\sim15\%$. Finally, we estimate the noise in the LASCO mass images from histograms of empty sky regions. The statistics in these areas show a gaussian distribution centered at zero, as expected. We define the noise level as one standard deviation or about $5\times10^8$ gr in the C2 frames and $3\times10^{10}$ gr in the C3 frames. The average C2 pixel signal in the measured CMEs is 10 times the noise and the C2 pixel signal-to-noise ratio in the mass measurements is between 10-100. The CMEs get fainter as they propagate farther from the sun. Therefore, the pixel signal-to-noise ratio in the C3 images drops to about 3-4. These figures refer to single pixel statistics and demonstrate the quality of the LASCO coronagraphs. Our measurements are based on statistics of hundreds or thousands of pixels for each image. Therefore, the “mass” noise in our images is insignificant compared to the systematic errors involved in the calculation of a CME mass as discussed previously. In summary, these calculations suggest that the LASCO measurements tend to underestimate the CME mass by about 50%, for realistic widths and propagation angles. A more detailed analysis of CME mass calculations will appear elsewhere. CME Energy calculations ----------------------- In this analysis we consider only three forms of energy — potential, kinetic, and magnetic energy. These energies can be estimated from quantities measured directly in the LASCO images like CME area, mass and speed. Two of the many other forms of energy that can exist in the CME/corona system can be estimated based on some assumptions and educated guesses: the CME enthalpy $U$ and the thermal energy $E_T$. We will show in § 4 that the thermal energy $E_T$ is insignificant. There are several uncertainties involved in calculating the enthalpy of a CME. Firstly, the temperature structure of a CME is far from known. It is conceivable that is composed of multithermal material. In situ measurements of magnetic clouds near the earth reveal a temperature range of $10^4-10^5$ K. Furthermore, it is not clear if the gas in the CMEs in the outer corona is in local thermodynamic equilibrium. Nonetheless, if we assume the CME to be a perfect gas in local thermodynamic equilibrium with equal electron and ion temperatures, the enthalpy $U$ can be as large as $5E_T\,= 5nkT$. If we assume a temperature of a million degrees K and a mass of $10^{15}$ gr, this yields $U\approx 3\times10^{29}$ ergs. As will be seen later, even this upper limit for the enthalpy $U$ is lower than the kinetic and potential energies by at least one order of magnitude, except in the lower corona where it can be comparable to the kinetic energy. Furthermore, the enthalpy is directly proportional to the mass, which, as will be seen later, remains approximately constant as the CME propagates outwards. We therefore conclude that the enthalpy is a small, constant magnitude correction which can be safely neglected without affecting the overall conclusions regarding CME energetics. #### Potential Energy We define the potential energy of the flux rope as the amount of energy required to lift its mass from the solar surface. The gravitational potential energy is calculated using $$E_P = { \sum_{{\rm flux}\,{\rm rope}}} \, \int^{R}_{R_{\odot}} \, \frac{G\, M_{\odot} \, m_{i}}{r_{i}^{2}} \, dr_{i} \, ,$$ where $m_{i}$ and $r_{i}$ denote the mass and distance from sun-center respectively, of each pixel, $M_{\odot}$ is the mass of the sun, $R_{\odot}$ is the solar radius and $G$ is the gravitational constant. The summation is taken over the pixels comprising the flux rope (Figure \[cartoon\]). #### Kinetic Energy We use the center of mass of the flux rope to describe its movement. The location of the center of mass relative to the sun center is given by $$\vec{r}_{CM} = \frac{{\sum_{{\rm flux}\,{\rm rope}}}\,m_{i}\,\vec{r_{i}}}{{\sum_{{\rm flux}\,{\rm rope}}}\,m_{i}} \, ,$$ where $\vec{r}_{CM}$ is the radius vector of the center of mass and $\vec{r_{i}}$ is the radius vector for each pixel. The summation, as before, is taken over the pixels comprising the flux rope. We calculate $\vec{r}_{CM}$ for each CME frame as it progresses through the LASCO field of view. In other words, we compile a table of center-of-mass locations versus time, ($\vec{r}_{CM}\, , t$). By fitting a second degree polynomial to ($\vec{r}_{CM}\, , t$) we obtain the center of mass velocity, $\vec{v}_{CM}$ and acceleration $\vec{a}_{CM}$. The calculation of the speed and acceleration as described above has the advantage of involving only the measurement of the CME center of mass. Once the flux rope is delineated, its mass, speed and energetics follow. The kinetic energy is simply $$E_K = \frac{1}{2}\, \sum_{{\rm flux}\,{\rm rope}} \, m_{i} \, v_{CM}^{2} \, .$$ Note that these measurements are based on the plane of the sky location of the center of mass. The speed used in the calculations is therefore a projected quantity and not the true radial speed. It follows that the derived kinetic energies are lower limits. The same applies for all of our observed and derived quantities which facilitates the comparison among the different events. #### Magnetic Energy The calculations of the potential and kinetic energies of flux rope CMEs are made directly from the mass images. On the other hand, the values we use for the magnetic energy of these CMEs are only estimates because the magnetic field strength in a CME is unknown. In-situ measurements by spacecraft like WIND yield the magnetic field contained in magnetic clouds observed near the earth. As mentioned in § 1, helical flux-rope CMEs are thought to evolve into magnetic clouds similar to those observed at the earth. Therefore, measurements of the magnetic flux contained in such magnetic clouds are expected to be fairly representative of that carried by flux rope CMEs. The magnetic energy carried by a flux rope CME is defined by $$E_M = \frac{1}{8\,\pi} \int_{{\rm flux}\,{\rm rope}} B^{2} dV\, ,$$ where $B$ is the magnetic field carried by the flux rope, and the integration is carried out over the volume of the flux rope. For a highly conducting medium such as the heliosphere, the magnetic flux, $\int B dA$, is frozen into the CME as it evolves to form a magnetic cloud. The magnetic flux measured in-situ is therefore taken to be the same as that contained in the CME as it passes through the LASCO field of view. We use this frozen flux assumption since we feel that it is a simple, physically motivated one. Another assumption which gives very similar results is conservation of magnetic helicity [@kumar96]. The volume integral in equation (5) contains another unknown; the volume occupied by the flux rope. Assuming a cylindrical flux rope with constant magnetic field, equation (5) is approximated as $$E_M \sim \frac{1}{8\,\pi}\, \frac{l}{A} \, (B\cdot A)^2 ,$$ where $A$ is the area of flux rope as measured in the LASCO images and $l$ is the length of flux rope. The quantity $B\cdot A$ is the magnetic flux frozen into the flux rope and is conserved. For our purposes, we need, in equation (6), a representative value for the magnetic flux of a flux rope. We obtain such an estimate from model fits [@lep90] to several magnetic clouds observed by WIND between 1995–1998 available at <http://lepmfi.gsfc.nasa.gov/mfi/mag_cloud_pub1p.html>. We only consider clouds that occurred at the same time interval as the LASCO CMEs (1997-98). From this sample we get the average magnetic flux, $<B\cdot A> = 1.3\pm1.1 \times10^{21}$ G cm$^2$ which we put in equation (6). The resulting magnetic energy uncertainty is then $(1.1/1.3)^2 \approx 70\%$. To calculate the magnetic energy, we also need the length $l$ of the rope along the line of sight. Since the true length of the rope cannot be obtained observationally, we assume that the flux rope is expanding in a self-similar manner, with its length being proportional to its heliocentric height; namely, $l\sim r_{CM}$. [ccccc]{} 970223 & 02:55 & 89 & 63 & 920\ 970413 & 16:12 & 260 & 42 & 520\ 970430 & 04:50 & 83 & 70 & 330\ 970813 & 08:26 & 272 & 36 & 350\ 971019 & 04:42 & 90 & 77 & 263\ 971030 & 18:21 & 85 & 50 & 215\ 971031 & 09:30 & 260 & 54 & 476\ 981101 & 20:11 & 272 & 57 & 264\ 980204 & 17:02 & 284 & 43 & 420\ 980224 & 07:55 & 88 & 32 & 490\ 980602 & 09:37 & 246 & 47 & 600\ Finally, we emphasize that the magnetic cloud data used here are only representative. They are not measurements from the same LASCO events we analyzed. Also the magnetic flux in individual events can differ from the average value we adopted. Furthermore, the magnetic field values we use refer to the total (toroidal + poloidal) magnetic field contained in the flux rope. The definition of $B\cdot A$, however, refers only to the toroidal component of the magnetic field which is normal to the cross-sectional area of the flux rope. For these reasons, it is difficult to ascribe errors to our magnetic energy calculations of individual events. Therefore, we decided to use the statistical uncertainty in the average flux to compute the error in the magnetic energy which is about 70% as shown above. It is unfortunate that the magnetic energy measurements are so uncertain and they will continue to be so until direct observations of the coronal magnetic field become available. Results ======= {width="15cm"} {width="15cm"} {width="15cm"} {width="15cm"} For our analysis, we searched the LASCO database for CMEs with clear flux rope morphologies. We picked 11 events for which we compiled the evolution of the mass and velocity of the center of mass and the potential, kinetic and magnetic energies as the CME progressed through the LASCO C2 and C3 fields of view. For reference purposes we present a list of the events in Table 1. The information for the 1997 CMEs is taken from the LASCO CME list compiled by Chris St. Cyr (<http://lasco-www.nrl.navy.mil/cmelist.html>) except for the final speeds in the last column that refer to the center of mass of the fluxropes and were calculated by us. Further information on source regions and associated photospheric/low corona emissions for some of these events can be found in the references noted in the table. Our measurements are shown in Figures \[res1\] – \[res4\]. The horizontal axis denotes heliocentric height in solar radii. Each row is a separate CME event, labeled by its date of observation by the LASCO/C2 coronagraph. The left panels show the evolution of the potential, kinetic, magnetic and total energy in the CME. The total energy is the sum of the potential, kinetic and magnetic energies. The right panels show the evolution of the flux rope mass and the center-of-mass speed. As discussed in § 2, a second degree fit to ($\vec{r}_{CM}\, , t$) yields the acceleration of the center of mass $\vec{a}_{CM}$. The radial component of $\vec{a}_{CM}$ is also shown in this panel. The dash-dot line, visible in some plots, marks the escape speed from the Sun as a function of height. An inspection of the plots leads to the following overall conclusions that hold for most of the events: - The total energy (curves marked with +) is relatively constant, to within a factor of 2, for the majority of the events despite the substantial variation seen in the individual energies. This suggests that, for radii between approximately $3 R_{\odot}$ and $30 R_{\odot}$, the flux rope part of these CMEs can be considered as an isolated system; i.e., there is no additional “driving energy” other than the energies we have already taken into account (potential and kinetic energies of the flux rope, and magnetic energy associated with the magnetic field inside the flux rope). - We see that the kinetic and, (to a lesser degree) potential energies increase at the expense of the magnetic energy, keeping the total energy fairly constant. The decrease in magnetic energy is a direct consequence of the expansion of the CME. It could imply that the untwisting of the flux rope might be providing the necessary energy for the outward propagation of the CME in a steady-state situation. - The center of mass accelerates for most of the events, and the CMEs achieve escape velocity at heights of around 8-10 $R_{\sun}$, well within the LASCO/C3 field of view. - The mass in the flux rope remains fairly constant for some events (e.g., 97/08/13 or 97/10/30) while other events (e.g., 97/11/01 or 98/02/04) exhibit a significant mass increase in lower heights and tend to a constant value in the outer corona, above about $10-15$ R$_{\sun}$. This observation raises the question: why is pile up of preexisting material observed only in some flux rope CMEs? We plan to investigate this effect further in the future. It would also be interesting to examine how the mass increase close to the Sun relates to interplanetary “snowplowing” observations [@webb96]. The only notable exception is the event of 98/06/02 which is also the most massive and its total energy increases with distance from the center of the sun. This CME is associated with an exceptionally bright prominence which may affect the measurements. A detailed analysis of this event is presented in @plunk99. Discussion ========== The conclusions of the previous section are based on a set of broadband white light coronagraph observations. The accuracy of the measurement of any structure (i.e., CME) in such images is inherently restricted by three unknowns: the amount and distribution of the material and the extent of the structure along the line of sight. We addressed the first two problems in § 2 where we showed that for the case of a uniformly filled CME extending $\pm 80$ degrees out of the plane of the sky, we will measure about 65% of its mass. Since the potential and kinetic energies are directly proportional to the mass, our measurements in Figures \[res1\] - \[res4\] could be higher by as much as 35%. The spatial distribution of the material will also affect the visibility of the structures we are trying to measure. Because we delineate the area of the flux rope by visual inspection, we might not be following the same cross section as the structure evolves. This might account for some of the variability of the energy curves. However, we chose the CMEs based on their clear flux rope signatures. The measurements involve hundreds or even thousands of pixels per image and therefore we don’t expect that the trends seen in the data are affected by the slight changes in the visibility of the structure. The widths along the line of sight of the observed CMEs are difficult to quantify. There is no way to measure this quantity with any instrumentation in existence today. Only the magnetic energy depends on the width of the flux rope. In § 2.2, we assumed that the width of the flux rope is equal to the height of its center of mass which implies that its preeruption length is about a solar radius. Prominences and loop arcades of this length are not uncommon features on the solar surface. {width="12cm"} As described in § 1, flux rope CMEs are expected to evolve into magnetic clouds near the earth. This is the basis on which we use in-situ data to estimate the magnetic energy carried by the flux rope CMEs (§ 2). In § 2, we also estimated that the overall normalization of the magnetic energy curve is uncertain by about 70%. In summary, none of the above errors can affect the trends of the curves for a given event. Only the magnitudes of the various energies could change. Finally, some of the variability of the measured quantities could be attributed to the intrinsic variability of the corona and/or of the CME structure itself and cannot be removed without affecting the photometry. For this reason, it is rather difficult to associate an error estimate to individual measurements. Therefore, we decided not to include any error bars in our figures. The analysis of the CME dynamics in Figures \[res1\]-\[res4\] reveals an interesting trend; namely, the total energy remains constant. It appears that the flux rope part of a CME propagates as a self-contained system where the magnetic energy decrease drives the dynamical evolution of the system. All the necessary energy for the propagation of the CME must be injected in the erupting structures during the initial stages of the event. The notions that these CMEs are indeed magnetically driven and that the thermal energy contribution can be ignored are further reinforced by the magnitude of the plasma $\beta$ parameter (Fig. \[beta\]). The calculations were performed with the assumption that the CME material is at a coronal temperature of $10^6$ K. We see that the CMEs have a very small $\beta$ (except the events on 98/02/04 and 98/06/02) which increases slightly outwards. It appears to tend towards a constant value. Such a behavior for the plasma $\beta$ parameter was predicted in the flux rope model of @kumar96. We also find that the potential energy is larger than the kinetic energy. These results confirm the conclusions from earlier Skylab measurements (see @rust80 for details). The relation between the helical structures seen in the coronagraph images and eruptive prominences is still unclear. In our sample, only half of the CMEs have clear associations with eruptive prominences (e.g., 97/02/23). No helical structures are visible in pre-eruption EIT 195Å images, in agreement with past work [@dere99]. On the other hand, the flux rope of the event on 98/06/02 is very clearly located above the erupting prominence and there is strong evidence that it was formed before the eruption [@plunk99]. It seems, therefore, likely that the process of the formation of the flux rope is completed during the early stages of the eruption at heights below the C2 field of view ($<2$ R$_{\sun}$). Such an investigation, however, is beyond the scope of this paper. {width="12cm"} Finally, we turn our attention to the evolution of the flux rope shape as a function of height. We proceed by comparing the velocity of the CME front to its center of mass velocity. Because the visual identification of points along the front can be influenced by visibility changes as the CME evolves, it is susceptible to error. A better method is to use a statistical measure for the location of the front such as the center of mass. Hence, the location of the front is defined as the center of mass of the pixels that lie within 0.1 $R_{\sun}$ of the front of the flux rope and within $\pm 25^\circ$ of the radial line that connects the sun center with the center of mass. The velocity of the front, $v_{f}$ is calculated in the same manner as $v_{CM}$ (§ 2.2). The comparison of the two velocity profiles for some representative events is shown in Figure \[front\]. Six of the eleven CMEs have profiles similar to 97/08/13 (self-similar expansion) or 97/10/30 (no expansion), while five show a progressive flattening such as 97/04/13 or 97/11/01, similar to that found in @wood99. Some theoretical flux rope models also predict flattening of the flux rope as it propagates outwards [@chen97; @wood99]. Conclusions =========== We have examined, for the first time, the energetics of 11 flux rope CMEs as they progress through the outer corona into the heliosphere. The kinetic and potential energies are computed directly from calibrated LASCO C2 and C3 images, while the magnetic energy is based on estimates from near-Earth in-situ measurements of magnetic clouds. These results are expected to provide constraints on flux rope models of CMEs and shed light on the mechanisms that drive such CMEs. These measurements provide no information about the initial phases of the CME (at radii below $\sim 2 R_{\odot}$). All the measurements and conclusions hold for heights in the C2 and C3 fields of view; between 3 and $30 R_{\odot}$. The salient conclusions from an examination of 11 CMEs with a flux rope morphology are: - For relatively slow CMEs, which constitute the majority of events, - The potential energy is greater than the kinetic energy. - The magnetic energy advected by the flux rope is given up to the potential and kinetic energies, keeping the total energy roughly constant. In this sense, these events are magnetically driven. - For the relatively fast CMEs with velocities $\geq$ 600 km/s (97/02/23, 98/06/02), - The kinetic energy exceeds the potential energy by the time they reach the outer corona (above $\sim 15 R_{\sun}$). - The magnetic energy carried by flux rope is significantly below the potential and kinetic energies. We thank D. Spicer for the initial discussions that led to this paper and the referee for his/her constructive comments. SOHO is an international collaboration between NASA and ESA and is part of the International Solar Terrestrial Physics Program. LASCO was constructed by a consortium of institutions: the Naval Research Laboratory (Washington, DC, USA), the University of Birmingham (Birmingham, UK), the Max-Planck-Institut für Aeronomie (Katlenburg-Lindau, Germany) and the Laboratoire d’Astronomie Spatiale (Marseille, France). Andrews, M. D., & Howard, R. A. 1999, in AIP Conf. Proc. 471, Solar Wind Nine, eds. S.R. Habbal et al. (Woodbury: AIP), 629 Antiochos, S. K., Devore, C. R., & Klimchuk, J. A. 1999, , 510, 485 Billings, D. E. 1966, a Guide to the Solar Corona, (New York: Academic Press) Brueckner, G. E., et al. 1995, , 162, 291 Burlaga, L. F. 1988, , 93, 7217 Chen, J., & Garren, D. A. 1993, , 20, 2319 Chen, J. 1996, , 101, 27499 Chen, J. et al. 1997, , 490, L191 Dere, K. P. et al. 1999, , 516, 465 Domingo, V., Fleck, B., and Poland, A. I. 1995, , 162, 1 Dryer M. 1996, , 169, 421 Farrugia, C. J., Osherovich, V. A., and Burlaga, L. F., 1995, , 100, 12293 Gold, T. 1963, Proc. Pontificial Acad. of Sciences, Vatican 25, 431 Goldstein, H. 1983, in NASA Conf. Publ. 2280, Solar Wind Five, ed. M. Neugebauer, NASA CP-2280, 731 Gopalswamy, N. et al. 1998, , 25, 2485 Gosling, J. T. 1997, in AGU Geophys. Monograph 99, Coronal Mass Ejections, ed. N. Crooker, J. A. Joselyn & J. Feynman (Washington, D.C.: AGU), 9 Guo, W. P., Wu, S. T., & Tandberg-Hanssen, E., 1996, , 469, 944 Howard, R. A., Sheeley, N. R., Koomen, M., J., Michels, D. J. 1985, , 90, 8173 Hundhausen, A. G. 1997, in Cosmic Winds and the Heliosphere, eds. J. R. Jokipi, C. P. Sonett, & M. S. Giampapa (Tucson: Univ. of Arizona Press) Jackson, B. V., & Hildner, E. 1978, , 60, 155 Kahler, S. 1992, , 30, 113 Lepping, R. P., Jones, J. A., & Burlaga, L. F. 1990, , 95, 11957 Low, B. C. 1996, , 167, 217 Kumar, A., & Rust, D. M. 1996, , 101, 15667 Marubashi, K. 1997, in AGU Geophys. Monograph 99, Coronal Mass Ejections, ed. N. Crooker, J. A. Joselyn & J. Feynman (Washington, D.C.: AGU), 147 Poland, A. I. et al., 1981, , 69, 169 Plunkett, S. P., Vourlidas, A., & Simberova, S. 2000, , in print Rust, D. M. et al. 1980 in Solar Flares: A Monograph from Skylab Solar Workshop II, ed. P. A. Sturrock (Boulder: Colorado Univ. Press), 273 Rust, D. M., & Kumar, A. 1994, , 155, 69 Stewart, R. T. 1985 in Solar Radiophysics, eds. D. J. McLean & N. R. Labrum (Cambridge: Cambridge Univ. Press), 361 Tousey, R. 1973 in Space Research XIII, eds. M. J. Rycroft & S. K. Runcorn (Berlin: Akademie-Verlag), 713 Webb, D. F. et al. 1980 in Solar Flares: A Monograph from Skylab Solar Workshop II, ed. P. A. Sturrock (Boulder: Colorado Univ. Press), 471 Webb, D. F. 1992, in Eruptive Solar Flares, eds. Z. Svestka, B.V. Jackson & M. Machado (New York: Springer-Verlag), 234 Webb, D. F., Howard, R. A., & Jackson, B. V. 1996, in Proceedings of the Eighth Solar Wind Conf., ed. D. Winterhalter et al. (New York: AIP), 540 Wood, B. E. et al. 1999, , 512, 484 Wu, S. T., Guo, W. P., & Dryer, M., 1997, , 170, 265 Wu, S. T. et al. 1997, , 175, 719

Q: Restart all activities in task I'm implementing a setting to my app that allows the user to switch themes, the user will be in the settings activity when he switches the theme, and above it in the task will be the main screen. I want the current activity to restart after the theme change, but I also want the main screen to restart, so when the user hits back from the settings page, he'll see the main screen with the new activity. Restarting the current activity is easy, but how do I force the previous activities in the current task to restart as well? I've tried adding FLAG_ACTIVITY_CLEAR_TOP / FLAG_ACTIVITY_CLEAR_TASK to the intent, but it'll remove those activities from the task, so when I hit back from settings, I'm returned to the home screen and not to my app main screen. Thanks. A: One possible way would be to restart the main activity when the user returns to it. If you open your Preferences activity with startActivityForResult, then, when finishing that activity, you can use setResult to tell the main activity whether or not it needs to be restarted. Finally, in the main activity's onActivityResult you can look at the passed result and restart the main activity if necessary.

[Chemical constituents from Lagotis brevituba]. To study on the chemical consitituents of Lagotis brevituba. The chemical consitituents were isolated by silica gel column chromatography, polyamide column chromatography and semi-preparative HPLC, and their structures were identified by spectroscopic methods. Eight compounds were isolated and they were identified as beta-sitosterol (1), succinic acid (2), luteolin-7-O-beta-D-glucoside (3), uracil (4), apigenin (5), chrysoeriol (6), chrysoeriol-7-O-beta-D-glucoside (7), and apigenin-7-O-beta-D-glucoside (8). Compound 4-8 were isolated from L. brevituba for the first time, and among them, compound 7 and 8 were isolated from genus Lagotis for the first time.

ommon divisor of 46 and 782? 46 Calculate the greatest common divisor of 360 and 300. 60 What is the highest common factor of 460 and 1035? 115 What is the greatest common factor of 11604 and 60? 12 Calculate the highest common divisor of 33 and 42. 3 Calculate the highest common divisor of 16 and 1264. 16 Calculate the highest common factor of 88 and 200. 8 Calculate the highest common divisor of 40 and 35. 5 Calculate the highest common divisor of 1541 and 23. 23 Calculate the greatest common factor of 6 and 842. 2 What is the greatest common divisor of 41 and 48913? 41 Calculate the greatest common factor of 8924 and 1940. 388 Calculate the highest common divisor of 91 and 897. 13 What is the highest common factor of 118 and 1534? 118 Calculate the greatest common factor of 1 and 41. 1 What is the greatest common divisor of 4150 and 50? 50 What is the highest common factor of 516 and 3354? 258 What is the highest common factor of 10 and 4910? 10 Calculate the greatest common divisor of 56 and 126. 14 Calculate the greatest common divisor of 14 and 497. 7 What is the greatest common factor of 1293 and 3? 3 Calculate the highest common divisor of 28 and 5782. 14 Calculate the highest common divisor of 27029 and 604. 151 Calculate the greatest common factor of 99 and 477. 9 Calculate the greatest common divisor of 288 and 464. 16 Calculate the highest common divisor of 51 and 357. 51 What is the greatest common factor of 92 and 138? 46 What is the highest common factor of 377 and 39? 13 What is the highest common divisor of 98 and 126? 14 What is the highest common divisor of 1062 and 18? 18 What is the greatest common divisor of 3238 and 2? 2 Calculate the highest common factor of 4 and 36. 4 What is the highest common divisor of 147 and 7301? 49 What is the highest common divisor of 275 and 14905? 55 What is the greatest common factor of 2 and 49? 1 What is the highest common divisor of 574 and 10086? 82 Calculate the greatest common divisor of 32 and 208. 16 What is the highest common factor of 119 and 1393? 7 Calculate the greatest common factor of 11704 and 56. 56 Calculate the greatest common divisor of 6 and 669. 3 Calculate the greatest common divisor of 550 and 800. 50 Calculate the highest common divisor of 636 and 12. 12 Calculate the greatest common divisor of 10712 and 104. 104 Calculate the greatest common divisor of 12610 and 30. 10 Calculate the highest common factor of 1204 and 1582. 14 Calculate the greatest common divisor of 14972 and 19. 19 What is the greatest common divisor of 860 and 40? 20 Calculate the greatest common factor of 1121 and 57. 19 What is the highest common factor of 276 and 736? 92 What is the greatest common divisor of 21 and 63? 21 Calculate the highest common factor of 4 and 106. 2 Calculate the greatest common divisor of 288 and 5856. 96 Calculate the highest common factor of 14 and 1652. 14 Calculate the highest common factor of 11 and 77759. 11 Calculate the highest common divisor of 12 and 90504. 12 Calculate the highest common factor of 513 and 108. 27 Calculate the greatest common factor of 404 and 303. 101 What is the highest common factor of 144 and 912? 48 What is the greatest common divisor of 100 and 175? 25 Calculate the highest common divisor of 448 and 25312. 224 Calculate the greatest common factor of 1150 and 5. 5 Calculate the greatest common divisor of 385 and 6545. 385 What is the greatest common factor of 581 and 83? 83 Calculate the highest common factor of 245 and 15. 5 What is the greatest common factor of 364 and 520? 52 What is the highest common factor of 143 and 26? 13 What is the greatest common factor of 69 and 3? 3 What is the greatest common factor of 8588 and 76? 76 Calculate the highest common divisor of 10 and 530. 10 Calculate the greatest common divisor of 338 and 754. 26 Calculate the greatest common factor of 609 and 21. 21 What is the greatest common divisor of 483 and 69? 69 What is the greatest common factor of 6 and 102? 6 Calculate the highest common factor of 2201 and 1136. 71 What is the highest common factor of 1778 and 28? 14 Calculate the greatest common factor of 58 and 7917. 29 What is the greatest common divisor of 6 and 129? 3 Calculate the greatest common divisor of 1008 and 3906. 126 What is the greatest common factor of 1001 and 11? 11 What is the highest common factor of 11528 and 264? 88 Calculate the highest common divisor of 2054 and 494. 26 What is the highest common divisor of 114 and 6042? 114 Calculate the highest common factor of 46 and 7360. 46 Calculate the greatest common factor of 25 and 425. 25 What is the greatest common divisor of 60 and 285? 15 Calculate the highest common divisor of 2624 and 1804. 164 Calculate the greatest common divisor of 63 and 45. 9 Calculate the greatest common divisor of 30 and 290. 10 What is the highest common divisor of 1310 and 393? 131 Calculate the greatest common divisor of 656 and 1744. 16 Calculate the greatest common factor of 1665 and 13653. 333 Calculate the highest common factor of 64 and 1888. 32 Calculate the highest common factor of 42 and 1106. 14 Calculate the highest common factor of 2 and 284. 2 What is the highest common divisor of 6 and 54? 6 Calculate the highest common factor of 1974 and 434. 14 What is the greatest common divisor of 44 and 33? 11 Calculate the highest common factor of 4 and 81. 1 What is the greatest common divisor of 1 and 447? 1 Calculate the greatest common factor of 87 and 9483. 87 What is the highest common factor of 160 and 1256? 8 What is the highest common factor of 69 and 7613? 23 What is the greatest common divisor of 40 and 55? 5 Calculate the greatest common divisor of 245 and 35. 35 What is the highest common divisor of 366 and 12? 6 Calculate the highest common factor of 108 and 8. 4 Calculate the greatest common factor of 24 and 21. 3 Calculate the greatest common factor of 56 and 252. 28 What is the highest common divisor of 126 and 294? 42 Calculate the highest common factor of 6596 and 68. 68 What is the greatest common divisor of 2 and 361? 1 Calculate the greatest common divisor of 7 and 84. 7 What is the highest common divisor of 196 and 1813? 49 Calculate the highest common factor of 18 and 5274. 18 What is the greatest common factor of 27 and 1422? 9 What is the greatest common divisor of 33 and 363? 33 What is the greatest common factor of 2208 and 1056? 96 Calculate the greatest common divisor of 972 and 48. 12 Calculate the greatest common divisor of 686 and 14. 14 Calculate the highest common factor of 903 and 387. 129 Calculate the greatest common factor of 1688 and 56. 8 What is the greatest common factor of 912 and 48? 48 What is the greatest common divisor of 12 and 1004? 4 What is the greatest common divisor of 169 and 143? 13 What is the greatest common divisor of 17861 and 53? 53 What is the greatest common factor of 1287 and 234? 117 What is the highest common factor of 11 and 913? 11 What is the highest common divisor of 804 and 7437? 201 Calculate the greatest common divisor of 36 and 15354. 18 What is the highest common factor of 13 and 1807? 13 Calculate the greatest common divisor of 3854 and 287. 41 Calculate the highest common factor of 78 and 78. 78 What is the highest common factor of 30371 and 121? 121 Calculate the highest common divisor of 72 and 120. 24 What is the greatest common divisor of 235 and 2209? 47 What is the highest common divisor of 14 and 406? 14 What is the highest common factor of 257 and 38293? 257 Calculate the highest common divisor of 250 and 7050. 50 Calculate the greatest common divisor of 292 and 4. 4 What is the greatest common factor of 68 and 10132? 68 What is the greatest common factor of 99 and 18? 9 What is the highest common factor of 7500 and 60? 60 What is the greatest common divisor of 15 and 5? 5 Calculate the greatest common factor of 30 and 48. 6 What is the greatest common factor of 104 and 664? 8 Calculate the greatest common factor of 333 and 629. 37 What is the greatest common factor of 256 and 48? 16 Calculate the highest common divisor of 440 and 110. 110 What is the highest common factor of 117 and 3991? 13 Calculate the highest common divisor of 63 and 1897. 7 Calculate

Cellulose 1,4-beta-cellobiosidase (reducing end) Cellulose 1,4-beta-cellobiosidase (reducing end) (, CelS, CelSS, endoglucanase SS, cellulase SS, cellobiohydrolase CelS, Cel48A) is an enzyme with systematic name 4-beta-D-glucan cellobiohydrolase (reducing end). This enzyme catalyses the following chemical reaction Hydrolysis of (1->4)-beta-D-glucosidic linkages in cellulose and similar substrates, releasing cellobiose from the reducing ends of the chains. The CelS enzyme from Clostridium thermocellum is the most abundant subunit of the cellulosome formed by the organism. References External links Category:EC 3.2.1

Q: CodeIgniter and Joomla - session data lost I am facing a really weird issue here. I have two websites: **A** and **B** **A** is the landing page (a micro website). **A** is running Joomla. **B** - payment pages. Coded with CodeIgniter. Uses session library and stores session data in a database. ================= Scenario: a user visits a landing page (website A), chooses a service package and clicks buy. Then he is taken to the payment page (website B) and starts filling in his application form. Once he is done, he is taken to a payment gateway (provided by SecureTrading) and makes a payment. After a successful payment, a user is taken back to website B, where he has to finish the last bit of his application. Problems: After a successful payment, user is redirected back to website B, but for some reason all session data is lost. When does this happen: Session data is lost only when a user is coming from the landing page (A). If i start filling the application form without visiting the landing page at first, everything works just fine. Why is this happening? How do i fix this? A: Make sure in your application/config.php file you have the following setting set to this value: $config['cookie_domain'] = ".mysite.com"; Take note of the leading . which denotes that the cookie domain is site-wide. This will make sure the cookie can be accessed from all sub-domains. Here is more information on how cookie domains work. You should always setup this config option as it defaults to empty and will thus use the default cookie setting which in most setups is not what the developer will want.

AGON Online AGON Online was a social gaming platform for the iPhone. It supports leaderboards, location-aware scoring, and friends lists. It was similar to OpenFeint, Plus+, and Scoreloop. On March 30, 2011, AGON Online announced due to the competition from OpenFeint, Plus+ and Apple Game Center, it would shut down on June 30, 2011 and delete all user data. References External links Official website Category:Defunct iOS software

/**************************************************************************** Copyright (c) 2010-2012 cocos2d-x.org Copyright (c) 2013-2014 Chukong Technologies Inc. http://www.cocos2d-x.org Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. ****************************************************************************/ #include "platform/CCCommon.h" #include "CCStdC.h" NS_CC_BEGIN #define MAX_LEN (cocos2d::kMaxLogLen + 1) void MessageBox(const char * pszMsg, const char * pszTitle) { MessageBoxA(NULL, pszMsg, pszTitle, MB_OK); } void LuaLog(const char *pszMsg) { int bufflen = MultiByteToWideChar(CP_UTF8, 0, pszMsg, -1, NULL, 0); WCHAR* widebuff = new WCHAR[bufflen + 1]; memset(widebuff, 0, sizeof(WCHAR) * (bufflen + 1)); MultiByteToWideChar(CP_UTF8, 0, pszMsg, -1, widebuff, bufflen); OutputDebugStringW(widebuff); OutputDebugStringA("\n"); bufflen = WideCharToMultiByte(CP_ACP, 0, widebuff, -1, NULL, 0, NULL, NULL); char* buff = new char[bufflen + 1]; memset(buff, 0, sizeof(char) * (bufflen + 1)); WideCharToMultiByte(CP_ACP, 0, widebuff, -1, buff, bufflen, NULL, NULL); puts(buff); delete[] widebuff; delete[] buff; } NS_CC_END

The economics of physical activity: societal trends and rationales for interventions. What are Americans doing with their time and their money and what has changed in recent decades? Do changes suggest interventions that will lead to healthier lifestyles? This paper analyzes several different data sets that reveal some surprising (and some less surprising) insights. The big growth areas, both in terms of expenditure and time allocation, have been leisure time and travel/transportation. Leisure-time industries outpace gross-domestic-product growth for both "active" (sporting goods, dance studios, gyms) and "sedentary" industries (spectator sports, cable TV), although industries associated with more sedentary lifestyles grow the fastest. Overall time spent in productive activities, whether at home or work, has declined by several hours each week for both men and women compared to 40 years ago. Reduced physical activity by itself is not a reason for intervening, as many changes improved overall quality of life (even if not necessarily health-related quality of life). But other trends are more likely to reflect poorly functioning markets, leading to worse economic and health outcomes. Market failures that lead to less physical activity or unhealthy nutrition justify interventions, both from an economic and a public health perspective.

Changing seasons require changing your approach to cooking. What is best served in the summer, is not best served in the winter. Pumpkins are associated with Autumn and for good reason. Learn how to utilise the naturally occurring seasons. There is no way of changing the seasons, so the good Cookman adapts to the natural world.

Uncharted developer Naughty Dog has given its opinion on Wii U in an interview with NowGamer, and the studio isn't sold on Nintendo's innovation this time around. Game director Justin Richmond from Sony-owned Naughty Dog said the console looks interesting but is nothing that couldn't be done on Sony consoles: To be...

The present invention relates to a microwaveable packaged good article, and more particularly, it relates to an overcap for a microwaveable packaged good article. Consumers have responded favorably to a variety of packaged foods provided as microwaveable packaged good articles. In particular, consumers have shown a strong preference for ready-to-eat packaged good articles that can be quickly and conveniently heated in a microwave oven. Some particularly popular packaged good articles include lunch or dinner entrees such as soups, chilies, stews, and pasta meals (e.g., spaghetti and ravioli) provided in sealed containers that are suitable for microwave heating. In general, a microwaveable packaged good article includes a container containing a consumable item, an optional removable lid to sealingly preserve the consumable item within the container prior to preparation/consumption, and an overcap. To prepare the consumable item, the consumer typically first removes the overcap from the container for access to the removable lid. The removable lid is then separated from the container to expose the consumable item within the container. The overcap is then replaced on the container to form a covered cooking vessel. In this manner, the assembled container/overcap is readied for subsequent microwave heating of the consumable item. During microwave heating, the consumable item is preferably heated to its boiling point. When the consumable item boils, steam is generated. In this regard, the overcap typically includes at least one vent to permit an equalization of pressure within the container. That is to say, the heated steam exits the container through the vent to alleviate a build-up of pressure inside the container. Boiling of the consumable item inevitably results in bubbling or splashing within the container, resulting in liquid accumulation along an inside surface of the overcap. Frequently, the bubbling/splashing consumable item will seep between the overcap and a lip of the container, dripping or flowing onto an exterior of the container. For example, one known overcap for a microwaveable packaged good article includes a top panel provided with vent holes and a skirt descending from the top panel. A series of spaced reinforcing ribs is provided on the interior of the overcap, extending between an interior surface of the top panel and an interior side of the skirt. Upon final assembly, the ribs rest against a top of the container, with a portion of the skirt extending along an exterior of the container. Unfortunately, during microwave heating, the boiling consumable item within the container can accumulate between the reinforcing ribs and subsequently seep or drip between the skirt and the exterior of the container. These drips are unsightly, may soil the microwave (or other surface that the container is subsequently placed on), and may lead to user handling inconveniences. In addition, the known overcap can deform when a large axial force is applied to the top panel. For example, during distribution and merchandising, several packaged good articles are commonly stacked vertically one on top of another. To this end, mass distribution normally entails grouping a number of individual packaged good articles within a tray or box, and then stacking multiple ones of the so-formed trays on a pallet. In this manner, a large axial loading is directed onto the top panel of the bottommost packaged good article present on a distributor's pallet or even a merchant's shelf. By way of reference, the skirt/ribs of the known microwaveable container overcap are sized to position the top panel well above a top portion of the container to ensure adequate spacing during boiling. Thus, the overcap is supported relative to the container primarily by the ribs, which in turn are supported by the skirt. In the presence of axial loadings of greater than forty pounds, the known overcap exhibits structural failure in the form of the ribs deflecting or deforming, leading to non-reversible deformation of the skirt. These deformations create an unattractive merchandizing unit at the point of sale, reduce viability of the overcap during subsequent microwave heating and have the potential to damage the contained item by rupturing the removable lid. In any regard, the known overcap insufficiently resists deformation from axial loadings that are oftentimes encountered during normal distribution and merchandizing. Consumers continue to show strong demand for microwaveable packaged good articles. Unfortunately, the standard overcap for microwaveable packaged good articles can lead to the boiling consumable item exiting the container and soiling the container's exterior and/or inside of the microwave. In addition, the known overcap employed with microwaveable packaged good articles can radially deform under common distribution and merchandizing loads, thus threatening the integrity of the packaged good article. The typical radial deformation of known overcaps presents addition challenges in designing a microwaveable packaged good article. In particular, in order to maintain the overcap coupled to the container during microwave heating and radial deformation, the microwaveable packaged good article typically employs a rather robust coupling mechanism or means. However, the robust coupling mechanisms oftentimes require significant amounts of force applied in specific locations of the overcap to remove the overcap from the container. The amount of force required is even higher when the overcap has recovered from deformation or has not yet been heated to radially deform. The requirement of relatively high forces to remove the overcap decreases the ease of usability of the microwaveable packaged good article. In particular, individuals in general and especially individuals having relatively low strength or dexterity may have difficulties in removing the overcap from the container to access the consumable item contained therein. Attempts to address this problem have included addition of a release mechanism (e.g., pull tab) as part of the overcap design (e.g., formed during molding). Unfortunately, this approach entails significant additional costs and may not provide a consistent, easy-to-use product to the consumer. Therefore, a need exists for an overcap for a microwaveable packaged good article that resists radial deformation and prevents boiling contents from exiting the container. A need also exists for an overcap that maintains overcap coupled to the container during use and expansion while still providing a container that is relatively easy to open when desired.

William Heymann William Heymann (26 October 1885 — 27 November 1969) was an English cricketer. He was a right-handed batsman and a left-arm medium pace bowler who played for Nottinghamshire. He was born in Nottingham and died in Long Clawson. Heymann made a single first-class appearance, during the 1905 season, against Middlesex. As a lower order batsman, Heymann did not bat during the match, the team declaring their only innings after centuries from Arthur Jones and George Gunn. He bowled 23 overs during the match, taking two wickets. External links William Heymann at Cricket Archive Category:1885 births Category:1969 deaths Category:English cricketers Category:Nottinghamshire cricketers Category:Sportspeople from Nottingham Category:People educated at Haileybury and Imperial Service College

Status: AVAILABLE A Book Description : Frontier Fictions Shaping The Iranian Nation 1804 1946 in frontier fictions firoozeh kashani sabet looks at the efforts of iranians to defend if not expand their borders in the nineteenth and early twentieth

Correlation of conventional thrombelastography and rapid thrombelastography in trauma. Conventional thrombelastography has been in use for over 6 decades and provides a functional assay of coagulation. Rapid thrombelastography was developed to provide more rapid comprehensive analysis of coagulation status in an emergency setting. The purpose of this study was to determine the correlation of rapid thrombelastographic values with conventional thrombelastographic values in trauma patients. We performed a prospective study on trauma patients at a university level 1 trauma center. Conventional thrombelastography and rapid thrombelastography were performed on 190 consecutive major trauma patients upon admission between 2010 and 2012. Conventional thrombelastographic and rapid thrombelastographic parameters were analyzed using bivariate analysis with Pearson correlation. Group comparisons were performed using the Mann-Whitney U test. Patients were predominantly male (71.6%, P < .05) with a median Injury Severity Score of 17 (range 10 to 29) and a median age of 43 years (range 29 to 53 years). There were significantly more patients with blunt trauma than penetrating trauma (72% vs 28%, P < .05). There was a strong correlation between the rapid thrombelastographic and conventional thrombelastographic maximal amplitude value, which represents platelet function (r = .80). There was a moderate correlation between the G (overall clot strength, r = .70), k (speed of clot formation, r = .66), and α-angle (r = .38), which reflects the degree of fibrin cross-linking. Lysis at 30 minutes correlated poorly (r = .19). Overall, there is a strong correlation between rapid thrombelastography and conventional thrombelastography in terms of overall clot strength and platelet function. There is a moderate correlation in assessing the degree of fibrin cross-linking and a poor correlation in evaluating thrombolysis. These correlations should be considered when evaluating coagulation status using rapid thrombelastography.

A Complete laboratory for functional analysis of the athlete Through integrated motion capture technology, BTS SPORTLAB provides complete and objective information to sports medical staff which can be used for the functional analysis of the athletes’ musculoskeletal state and motor strategies and sports performance. Sports teams, clubs and Olympic committees worldwide use BTS SPORTLAB to recruit talents, to fine-tune training programs, to prevent injuries and to maintain the optimal physical condition of athletes. Customize and maximize each training BTS SPORTLAB allows physicians to plan customized training programs based on in-depth knowledge of the athlete’s actual potential and physical condition, thus avoiding over-training risks and performance downturns. The integrated functional assessment resulting from the use of this technology is based on 4 key factors: posture, movement, muscle activity and force. SMART-DX 7000 High precision optoelectronic systems for motion analysis FREEEMG Electromyography device with wireless probes for the dynamic analysis of muscle activity INFINI-T The first digital sensory floor for motion analysis VIXTA Cameras for the analysis from different viewing perspectives 0 infrared cameras 0 sensorized platforms 0 EMG Channels Total freedom of movement BTS SPORTLAB facilitates integral motion analysis of athletic movements promoting the natural performance of the task. The total absence of wires, the miniaturization of the device and the removal of restrictions during the ground contact phase, contribute to the absence of interference by the measuring tools on the movement itself, resulting in an accurate reconstruction of motor behavior. A ready to use laboratory, which can be also used outdoors BTS SPORTLAB allows athletes to undergo quick and accurate exams obtaining periodical follow ups of their sports performance. The system natively integrates advanced tools for kinematic, dynamic and EMG analysis and it can also be operated outdoors (playing fields, running tracks, etc.) and in poorly lit environments (gyms, sports centers, etc.), without experiencing any loss of accuracy. A wide library of protocols BTS SPORTLAB includes a wide library of the main scientifically validated protocols:

DiversifYA: Tristina Wright Tristina Wright is a blue-haired bisexual with anxiety and opinions. She writes super epic queer YA SFF, and I can’t wait for her books to hit shelves someday, so you can all experience her amazing words too. <3 Until then, you can find her on Tumblr, her website, and Twitter. 1. How do you identify yourself? Bisexual/Biromantic 2. What did it feel like growing up bisexual? In a word, confusing. I didn’t even know the word bisexual existed until I was in college. I grew up in a very conservative atmosphere where anything not-straight was wrong and a damnable offense. It was confusing and terrifying for me when I developed a crush on my best friend in high school or imagined kissing her. I knew I still liked boys. I liked them a lot, but I also thought she was very pretty. I found myself admiring other girls in my class the same way I’d admire a boy. “I bet her hair is really soft.” “Gosh, I could stare at her eyes forever.” “Please laugh again; that’s the best sound.” I thought I was broken. I thought you were supposed to pick one and, as I’d been taught, there was a right one and a wrong one. So I dated boys and never pursued girls and basically pined quietly, convinced that I was wrong to want such things and I needed to just be content with boys. College was eye-opening for me. I insisted on going to a non-conservative school and, while the academic experience wasn’t the best for me, the social side became a pivotal point for me and my identity. I kissed girls and I didn’t get struck by lightning! The ground didn’t open up and swallow me into hell! It was amazing. It wasn’t perfect, mind you. The word bisexual comes with its own mountain of stereotypes and cliches and biases, which is difficult to navigate when you’re trying to figure out who you are. “Well, I don’t want to be known as easy or always down for a threesome or a cheater or or or… so maybe that’s not the right word for me.” It’s actually very damaging for a young person to think that the only reason someone hangs out with you is because they think you’re easy. It puts the sole focus of the entire identity on sex, which is so unhealthy. It took years for me to finally unpack the word down to its basic meanings and find people like me who embraced it and fought hard against the stereotypes. 3. What are the biggest challenges? Conversely, what are the quirks/perks? The biggest challenges are definitely the stereotypes, as I touched on above. People think bisexual means you’re down for whatever, whenever. They think it means you’re easy and always up for sex. They think you’re automatically okay with threesomes (or more). They don’t think you’re capable of being monogamous. They think bisexuals cheat because we’re always looking at other genders. There’s a sense of implied competition. A girl I know in college told me she’d been told by a gay friend of hers that he’d never date a bi man because he was certain the man would leave him for a girl. And sadly, it’s a common perception. “I won’t date a bi girl because a penis has been there.” “I won’t date a bi man because he’ll leave me for a girl.” It’s this horrible, broad paintbrush that gets whipped across all of us before we even open our mouths. That isn’t to say there aren’t bisexuals out there who aren’t down for whatever, whenever. Or bisexuals who love threesomes. Or bisexuals who don’t ever want to be in a long-term relationship. But those are all individual decisions and should be acknowledged as such — not used as examples to hold up the evil sex-crazed bisexual stereotype. It’s damaging and horribly offensive to those who do enjoy lots of sex. It tells them that they’re doing it wrong. In the end, it’s no one’s business. Another common stereotype is the assumption that we’re gay or straight now when we do get married or enter into any type of long-term relationship. As if bisexuality is only a label that can be applied to single people. I might be married to a man, but that does not mean I still don’t tilt my head and whisper damn when I see a hot woman! Does that mean I’m going to leave my husband and pursue that hot woman? No. It just means I find her attractive. It’s no different from my husband admiring a favorite actress. It’s biology and too many people are way to consumed with policing biology. Perks? So many pretty people! ::whale noises:: Like seriously, there are so many beautiful people of all genders on this planet, and I could stare at them all day long. I honestly sometimes feel sorry for my husband that he’s straight. He’s missing out on so many gorgeous people out there, it’s truly heartbreaking. I weep. 4. What do you wish people knew about being bisexual? Oh gosh, so much. I guess the biggest thing I wish people knew is that there is no right way to be bisexual. There’s this pervading notion that you have to qualify in order to use the label. It comes from the 50-50 stereotype, I think. The idea that you have to be attracted to men and women equally to be bisexual, which is just false. Or that you have to have slept with the same amount of multiple genders in order to be bisexual, which is also false. Virgins declare themselves gay or lesbian and yet we don’t tell they can’t be until they’ve had sex, do we? We apply straightness to babies constantly: “He’ll be such a ladies man!” “Oh better get a shotgun for all the boys knocking down her door!” So why this idea that you can’t be bisexual unless you satisfy some sexual measurement? Truth time. I’ve only ever had serious relationships with men. I have kissed and slept with other genders, but I’ve only ever had serious relationships with men. I have never officially dated another gender. Does that make me less bisexual? No. Definitely not. Even if I’d only ever slept with men and never touched another gender, I’d still be bisexual. Period. You’ll hear people insist bi means two. Well, gay means happy and lesbian means from the Isle of Lesbos. Language evolves. Obviously. People will use this definition to insist that bisexuality is exclusionary. That we don’t include trans or non-binary individuals in our attraction. And that’s….that’s so not true. Bisexual, at its heart, means attraction to two or more genders. You’ll also hear same and different genders, which also perfectly acceptable; however, keep in mind there are bisexuals who are not attracted to their own gender. You may meet female bisexuals not attracted to men. You may meet male bisexuals not attracted to women. There are all different types and there’s no right or wrong way to be bisexual. Two or more. That’s it. That’s all there is to it. It’s multi-gender attraction. Period. There’s no sex requirement. There’s no marriage requirement. There are no rules or restrictions or qualifying checkboxes, and if anyone tries to tell you there are, then rub this definition all over their face. My favorite definition of bisexual is from Robyn Ochs: I call myself bisexual because I acknowledge that I have in myself the potential to be attracted – romantically and/or sexually – to people of more than one sex and/or gender, not necessarily at the same time, not necessarily in the same way, and not necessarily to the same degree. I can’t count the number of conversations I’ve had with people who basically say, “I’m afraid of saying I’m bi because I’ve only ever been with X gender. It doesn’t feel like I count.” And that’s years and years of 50-50 and bi means 2 stereotyping talking. Of gatekeepers insisting on requirements and regulations. It’s ingrained in us and it’s so hard to break away from. You do count. You do. 5. What are the biggest cliches/stereotypes you’ve seen? I’ve sort of answered this one already but the biggest? Threesomes, probably. That’s the one I run into the most often. People wink wink nudge nudge at my husband when they find out I’m bi. Because if I’m bi that means I’ll sleep with whoever, right? Again, the vast majority of stereotypes and cliches reduce bisexuality down to who we have in bed with us. It makes it all about the sex as if it’s a hobby instead of who we are as people. It’s not taken seriously, which is so sad and incredibly frustrating. It’s as if bisexuality is the immature party child of the more grown up serious gay, lesbian, or straight labels. BONUS: What is your advice for writers writing diverse characters? You’ll see this advice everywhere and that’s because, I think, it’s the most important piece of advice if you’re writing diversely: Read and listen. Read books and poems and essays and blogs and tweets by diverse people. Listen to what people are saying. I learn so much when I spend a few hours on social media just reading and not speaking. The world is so diverse and you’re doing yourself a huge disservice by not including that in your writing. But to do it as well as you’re able, you need to listen and learn. Diversity is not a monolith. Even as a bisexual, when I write bisexual characters, I have other bisexuals read them and offer critiques. My experience with bisexuality is not yours or theirs or hers or his. It’s mine and that’s it. You’ll hear differing and even opposing viewpoints on how certain things should be portrayed. People are individual. As much as the media would like you to think there is a baseline individual (straight, white, abled, cis, usually male), there isn’t. And there are countless ways to portray people. You have to learn and listen and do your research. You will mess something up. Accept that and write anyway. Do the best you can, listen to criticism, learn, and write more. I know that no matter how much I read and talk to people, I will get something wrong. I’m not free of ingrained prejudice. I come from a place of privilege. I grew up in an environment where the other was scary and not to be trusted. It’s taken me years to undo that, and I’m still not completely free of it. I do not experience the same microagressions as someone not me. I will mess up, and you will too. That doesn’t mean you don’t try. That doesn’t mean you give up after being told you messed something up. You learn. You apologize. You apply that to your next project. You grow. Accept that you will never be perfect. You will always be learning and unpacking and shedding preconceptions. Writing diversely is a constant state of evolution. 2 Responses to DiversifYA: Tristina Wright What a fantastic post! Thank you so much for writing on this topic! I wrote a bisexual character in my series, and it wasn’t much different than writing any of the other characters except he found both men and women attractive. It was wonderful to have him along for the ride. Kentaro turned out to be one of my all-time favorite characters. <3

Solid propellants (fuels) are widely used in missile engines. The burning of the fuels generates a huge thrust so that a missile can be quickly launched. The main chemical compositions of solid fuels include nitrate (NO2), carbon (C) and sulfur (S). Such fuels are usually stored in the back portion of the missile for effectively generating the thrust. During the long storage process of the missile (e.g., years), the compositions of the fuels can change due to the slow chemical reaction processes among different components of the fuels as well as the reactions of the fuels with the outside atmosphere (e.g., O2). Thus, to ensure a successful and safe launch of the missile, it is critical to be able to monitor the status of the fuels and ensure a proper fuel composition ratio at the time of use.

Q: System.NullReferenceException: Object reference not set to an instance of an object iframe src I received this error while passing src value of an iframe through ASP.NET C#. Here isrc is a string variable: Line 26: HtmlControl ifm = (HtmlControl)this.FindControl("ifm"); Line 27: if (cover_id != null) Line 28: ifm.Attributes["src"] = isrc; Line 29: //Response.Redirect("Default2.aspx") Line 30: } \Default2.aspx.cs Line: 28 Source File: c:\Users\arsha\Documents\Visual Studio 2008\WebSites\hajcover\Default2.aspx.cs Line: 28 Stack Trace: [NullReferenceException: Object reference not set to an instance of an object.] Default2.btn1_Click(Object sender, EventArgs e) in c:\Users\arsha\Documents\Visual Studio 2008\WebSites\hajcover\Default2.aspx.cs:28 System.Web.UI.WebControls.Button.OnClick(EventArgs e) +111 System.Web.UI.WebControls.Button.RaisePostBackEvent(String eventArgument) +110 System.Web.UI.WebControls.Button.System.Web.UI.IPostBackEventHandler.RaisePostBackEvent(String eventArgument) +10 System.Web.UI.Page.RaisePostBackEvent(IPostBackEventHandler sourceControl, String eventArgument) +13 System.Web.UI.Page.RaisePostBackEvent(NameValueCollection postData) +36 System.Web.UI.Page.ProcessRequestMain(Boolean includeStagesBeforeAsyncPoint, Boolean includeStagesAfterAsyncPoint) +1565 Version Information: Microsoft .NET Framework Version:2.0.50727.4984; ASP.NET Version:2.0.50727.4971 A: To access a control on the server side, it needs to be tagged runat="server". Change your iframe to; <iframe name="ifm" id='ifm' width="100%" height="680" runat="server" style="background-color:#FFFFFF; border:solid #999999 1px"> </iframe> then change your code to just access the control right away; // Next line is not needed, control is automatically available with runat="server" // HtmlControl ifm = (HtmlControl)this.FindControl("ifm"); if (cover_id != null) ifm.Attributes["src"] = isrc; ...and you should be set.

Battle of the Göhrde The battle of the Göhrde was a battle of the War of the Sixth Coalition on 18 September 1813 between French and Coalition troops at Göhrde in Germany. The French troops were defeated and withdrew to Hamburg. Site It occurred near what is now the site of the Göhrde State Forest (Staatsforst Göhrde), near Dannenberg, near Lüneburg. At that time this area belonged to the electorate of Braunschweig-Lüneburg (Hanover), which had been occupied by the French since 1803. The battlefield lies on the border between the modern-day districts of Lüneburg and Lüchow-Dannenberg, between Oldendorf an der Göhrde and Göhrde. Context In spring 1813, Russian troops under Friedrich Karl von Tettenborn forced the French out of Hamburg and some northern areas of Hanover. In the wake of Prussia's reentry into the war against France, the eastern areas of Hanover also rose against Napoleon. Wallmoden then received overall command of all the Allied troops on the Lower Elbe: troops from Prussia, Russia, the United Kingdom, Hanover, Hamburg, Mecklenburg and Sweden, including the Russian German legion, the Lützow Free Corps, the Hanseatic Legion and a part of the King's German Legion, under the overall command of Generalleutnant Ludwig von Wallmoden-Gimborn. Part of the British contingent was the newly formed Rocket Brigade under Capt Richard Bogue. On 7 September Bogue marched with half his brigade to join the main Army of the North, near Wittenburg. The other half of the brigade, under Lieut Thomas Fox Strangways, joined the 4th Cavalry Division of General von Dornberg under General Wallmoden. The Free Corps such as that from Lützow again and again attacked French supply lines and bases in the area around Mecklenburg, south of the Elbe. The XIII Corps there, under marshal Davout, had up to this point behaved quite passively, restricting itself to holding Wallmoden's corps in check. As an anti-skirmishes measure, in September Davout sent general Pécheux on the western Elbufer with a brigade of 50th infantry division and moved on Lüneburg with 3,000 troops. After completing his mission, Pécheux was ordered to rejoin the French troops in Magdeburg. Wallmoden's corps advanced on Dömitz on 15 September with 12,300 men, crossed the Elbe, marched toward the Frenchmen and set up camp in Dannenberg. Course The French division under Pécheux decided to attack the allies. On the early afternoon of 18 September 1813, it reached the Steinker Höhen (Steinker Heights) in Nahrendorf and gave battle. Whilst Wallmoden's infantry attacked the centre, Dornberg with the KGL cavalry and artillery attacked the enemy's left. However, Dornberg brought the guns and rockets into action at too great a range; their fire was ineffective and General Lyon's infantry attack was held up. The French began to retire, formed in squares, and Strangways advanced to bring the rockets into action “close under the fire of the enemy’s infantry”. The 3rd KGL Hussars broke two squares and the rockets spread such terror through the retiring ranks that order could no longer be preserved, and breaking, the French fled in all directions. Results The battle was the first victory over the French troops garrisoning Germany, and interrupted the link between XIII Corps under marshal Davout (with its headquarters in Hamburg) and Napoleon's main army (then in Saxony) and the French armies' supply-lines across Hanover from France to Magdeburg and Berlin. This result was critical for the outcome of the Battle of Leipzig soon afterwards. This was the first battle in which the newly developed Congreve Rocket had been successfully deployed in action. At the Battle of Leipzig, The Rocket Brigade, under Bogue and Strangways, would make a significant attack whilst attached to the Swedish Corps of Crown Prince Bernadotte. Commemorations A large stone monument stands as a memorial to the battle in 1839, at a site now north of Bundesstraße 216 about 2 km behind Oldendorf in Richtung Dannenberg. 1000 dead soldiers from both sides were buried in a mass grave in the forest, 100m from where the memorial is sited. This grave was rediscovered in 1985. Rudolf von Bennigsen's father Karl von Bennigsen fought in this battle (as a lieutenant), as did the famous freedom fighter Eleonore Prochaska. She had disguised herself as a man and joined the Lützow Free Corps. During the battle she was wounded and soon afterwards succumbed to her injuries in the hospital at Dannenberg. A reconstruction of the battle occurs every two years at Dahlenburg. At the Heimatmuseum in the town a diorama of the battle is on permanent display, with 1500 tin soldiers. References External links hamburg1813.de Examination of the battlefield Course of the battle Category:Battles of the Napoleonic Wars Category:Battles of the War of the Sixth Coalition Category:Battles involving France Category:Battles involving Prussia Category:Battles involving Russia Category:Battles involving the United Kingdom Category:King's German Legion Category:1813 in France Category:1813 in Germany Category:Conflicts in 1813 Category:September 1813 events Category:Battles in Lower Saxony

Ask Lisa Thompson what really makes her angry, and she will say: "Snoop Dogg and Hugh Hefner and Bling Bling Barbie Dolls." When the gangster rapper appeared in an Orbit chewing gum TV commercial, Thompson vowed never to buy the brand. "They're all part of the example of how American culture is accepting the commodification of women and girls," she said. If Thompson is sensitive about the cheapening of women, it's because she spends working days-and nights-tracking the worldwide spread of the problem. In Sri Lanka, a huge billboard advertises a shop reading simply "Bling." In rural Sierra Leone, Thompson spied a village elder wearing a 50 Cent shirt, what she calls "the almost transcendence and omnipresence of pimp subculture in the world." And that's just the tame stuff. "People get so shocked that there could be sex trafficking and sex slaves but not bat an eyelash when Snoop Dogg and [former Chrysler chairman] Lee Iacocca do a commercial together," said Thompson, 36, who heads a Salvation Army campaign to abolish sex trafficking. We see you’ve been enjoying the content on our exclusive member website. Ready to get unlimited access to all of WORLD’s member content? Get your risk-free, 30-Day FREE Trial Membership right now.(Don’t worry. It only takes a sec—and you don’t have to give us payment information right now.) Eight years ago Thompson hardly knew what sex trafficking was. But the plight of stolen, kidnapped, and abused women grabbed her attention while working for the National Association of Evangelicals; now, the former grant writer, Beijing English teacher, and private-eye office manager says the work is "what I was born to do." Thompson wants to cauterize a modern slave trade that sells women and girls into forced prostitution. In the faith-based community, Thompson is the face many associate with turning trafficking into a burning social issue. It's the kind of job where many either "burn out very quickly or go crazy," said retired Major Marilyn White, a longtime colleague of Thompson's. Thompson confesses that the job duties and the travel stretch her into a "human crepe." But the horrors only make her work harder. The latest State Department report on trafficking estimates that 600,000 to 800,000 people are trafficked across international borders each year. About 80 percent are women and girls and up to 50 percent are minors. The 2006 report, released last June, shows an alarming trend-spurred in part by economic globalization-of trafficking persons for purposes of slave labor, too. After being immersed in those statistics for over six years now, little shocks Thompson. When something comes along to rattle her, as it did last summer when she first heard of a West African practice called "breast ironing," she is quick to mobilize advocates and speak out against it. With breast ironing, mothers try to flatten their pubescent daughters' budding breasts so they will seem less attractive to boys and men. One common method is to heat a wooden pestle in the kitchen and roll and hammer a girl's breasts. The pain is agonizing, and a recent survey in Cameroon showed a quarter of girls enduring it there. Sometimes the tissue damage is so extensive, the breasts disappear altogether. Or it haunts a woman in other ways: One woman, the Reuters news service reported, had trouble producing breast milk as a new mother, and her baby almost died as a result. "Tragically, in far too many parts of the world women's bodies are viewed as bad and the 'source' of immorality," Thompson said. "It never ceases to amaze me how women's bodies are tortured with a view toward either preventing immorality, or on the other hand, stoking desire [or] attraction." Thompson's passion can spill over into social gatherings, friends say, where she freely discusses sex trade details in mixed company. "When you ask Lisa how work's going, it's not just a matter of how some people say, 'Oh, it's fine,' or 'It's stressful,'" said Megan Lee, a high-school teacher and long-time friend. "I've seen her become very emotional." Earlier this year, Thompson broke down in tears when she saw photographs of Bangladeshi women who were victims of sulfuric or hydrochloric acid attacks. The women, who have horrendously disfigured faces, are often attacked by angry husbands or boyfriends, or become the object of anger in dowry disputes. Thompson's dedication also has caught the attention of groups on the left. The American Prospect blamed her and other activists for a shift in U.S. policy, where groups lobbying for legalized prostitution no longer could receive federal funding. The magazine said the "most prominent figures include right-wing policy-makers, a Jewish 'moral entrepreneur,' [human rights advocate Michael Horowitz] and evangelical leaders, whom critics call overzealous and moralistic. Together, the 'abolitionists' have formed a potent political force." So potent, the article quoted one official, that for Thompson and others, "Horowitz is the Charlie to their Angels." Hyperbole aside, Thompson has not only irritated traditional foes but influenced them: feminists who believed faith-based programs did more moralizing than good on prostitution. "When you first meet her, it's easy to underestimate her," said Donna Hughes, a 20-year anti-trafficking warrior. "She's a thin, attractive young woman. Only when you get to know her [do you see] she has a compassionate personality and a will of steel." Faith and family help an abolitionist cope with the job's strains, and for the single Thompson, that comes from her Wesleyan church and her Kentucky home. Thompson grew up in a close-knit family, on the same country road as both sets of her grandparents. She remembers their farming days, when she would ride a tractor-pulled hay wagon or hang tobacco leaves to barn-dry. Ask her how she is, and she might still say, "Fine as frog fur." At Thompson's office at the Salvation Army's National Headquarters in Alexandria, Va., family photos surround her desk. On it is a copy of the Falmouth Outlook, from the closest town to where she grew up in Kentucky, carrying a story about a local beauty queen who had once dated her cousin and now wants to combat sex trafficking. Also on the desk are encouraging cards sent by her grandmother's country church, and Prostitution, Trafficking and Traumatic Stress, a book fringed with neon-pink stickies for bookmarks. Artifacts of her work and travel are arrayed on bookcases: a set of four African wooden elephants; a sculpture of Christ with a crown of thorns from Ecuador; a chance picture of her with defense secretary Donald Rumsfeld; a framed invitation to U.S. Ambassador John Miller's swearing-in. Miller is head of the State Department's Trafficking in Persons office. As part of her work now, Thompson trundles through dozens of sex-trafficking articles a day, then sends the choicest stories to a hundreds-strong e-mail list. She signs off every one with, "Abolition! Lisa." The practice inspired Miller to start speaking of "abolishing" trafficking. Recipients sometimes complain that Thompson's mailings overwhelm them, but she sends only a fraction of what she runs across. Breast ironing is only one horror Thompson handles almost daily. Other abuses are better known, such as female genital mutilation, or FGM, practiced in parts of eastern and northern Africa. The goal is to reduce a woman's sexual pleasure, and therefore make her less likely to seek illicit sex, by removing part or all of her genitalia. The operations are often done with a blunt instrument and without anesthetic. Severe FGM can lead to obstetric fistula, where days-long obstructed childbirth causes the soft tissue between the vagina and bladder or rectum to die, creating a hole. Not only does the baby die, but the infant's mother is left incontinent, unable to control leaking urine or feces. Communities often ostracize fistula sufferers, leaving them to fend for themselves. With all these flashpoints, Thompson knows abolition is a consuming battle. Sometimes she despairs at all the work that needs doing to help abused women. But she falls back on her trust in God: "At the end of the day, it's not my fight, and He loves these people more than I could ever conceive of."

import { Dropoff } from "./Dropoff"; import { GameMap } from "./GameMap"; import { Logging } from "./Logging"; import { Player } from "./Player"; import { Position } from "./Position"; import { ServerCommunication } from "./ServerCommunicaion"; import { Ship } from "./Ship"; import { Shipyard } from "./Shipyard"; export class Game { public turnNumber = 0; public server: ServerCommunication = new ServerCommunication(); public myId = 0; public players = new Map<number, Player>(); public me?: Player; public gameMap?: GameMap; /** * Initialize a game object collecting all the start-state * instances for pre-game. Also sets up a log file in * "bot-<bot_id>.log". * @returns The initialized gameMap and me so we don't have to check if undefined. */ public async initialize(): Promise<[GameMap, Player]> { const serverData = await this.server.getInitialData(); this.myId = serverData.myId; Logging.setup(`bot-${this.myId}.log`); serverData.players.forEach((playerData) => { const player = new Player(playerData.id, new Shipyard(playerData.id, -1, new Position(playerData.x, playerData.y))); this.players.set(player.id, player); }); this.me = this.players.get(this.myId); this.gameMap = new GameMap(serverData.cells); return [this.gameMap as GameMap, this.me as Player]; // We cast here because we have just initialized } /** * Updates the game object's state. */ public async updateFrame() { const data = await this.server.getUpdateData(this.players.size); this.turnNumber = data.turn; Logging.info(`================ TURN ${this.turnNumber.toString().padStart(3, "0")} ================`); data.players.forEach((playerData) => { const player = this.players.get(playerData.id) as Player; player.haliteAmount = playerData.halite; // Process ships const newShipsData = playerData.ships .filter((shipData) => !player.hasShip(shipData.id)); newShipsData.forEach((newShipData) => player.addShip(new Ship(player.id, newShipData.id, new Position(newShipData.x, newShipData.y), newShipData.halite))); const lostShips = player.getShips() .filter((ship) => !playerData.ships.some((shipData) => shipData.id === ship.id)); lostShips.forEach((ship) => player.loseShip(ship.id)); player.getShips().forEach((ship) => { const updatedShipData = playerData.ships .find((shipData) => ship.id === shipData.id); if (updatedShipData) { [ship.haliteAmount, ship.position.x, ship.position.y] = [updatedShipData.halite, updatedShipData.x, updatedShipData.y]; } }); // Process dropoffs const newDropoffsData = playerData.dropoffs .filter((dropoffData) => !player.dropoffs.has(dropoffData.id)); newDropoffsData.forEach((newDropoffData: { id: number, x: number, y: number }) => player.dropoffs.set(newDropoffData.id, new Dropoff(player.id, newDropoffData.id, new Position(newDropoffData.x, newDropoffData.y)))); const lostDropoffs = Array.from(player.dropoffs.values()) .filter((dropoff) => !playerData.dropoffs.some((dropoffData) => dropoffData.id === dropoff.id)); lostDropoffs.forEach((lostDropoff) => { player.dropoffs.delete(lostDropoff.id); player.lostDropoffs.set(lostDropoff.id, lostDropoff); }); }); const gameMap = this.gameMap as GameMap; // Mark all cells as safe gameMap.cells.forEach((row) => row.forEach((cell) => cell.markSafe())); // Update cells data.cells.forEach((cell) => gameMap.get(new Position(cell.x, cell.y)).haliteAmount = cell.halite); // Mark cells with ships as unsafe for navigation, mark sturctures for (const player of this.players.values()) { player.getShips() .forEach((ship) => gameMap.get(ship.position).markUnsafe(ship)); player.getDropoffs() .forEach((dropoff) => gameMap.get(dropoff.position).structure = dropoff); } } /** * Indicate that your bot is ready to play by sending the bot name. */ public async ready(botName: string) { await this.server.sendCommands([botName]); } /** * Send all commands to the game engine, effectively ending your * turn. */ public async endTurn(commands: string[]) { await this.server.sendCommands(commands); } }

Q: substrings length This is kind of a beginner's question but the code I am looking at is in production and I don't want to break anything. So, just in case: isn't text.Substring(index, length).Length is equivalent to just length? (Except for the potential ArgumentOutOfRangeException.) A: Yes, it will be exactly the same.

<?php /* * This file is part of Twig. * * (c) 2009 Fabien Potencier * * For the full copyright and license information, please view the LICENSE * file that was distributed with this source code. */ /** * Imports macros. * * <pre> * {% import 'forms.html' as forms %} * </pre> */ class Twig_TokenParser_Import extends Twig_TokenParser { /** * Parses a token and returns a node. * * @param Twig_Token $token A Twig_Token instance * * @return Twig_NodeInterface A Twig_NodeInterface instance */ public function parse(Twig_Token $token) { $macro = $this->parser->getExpressionParser()->parseExpression(); $this->parser->getStream()->expect('as'); $var = new Twig_Node_Expression_AssignName($this->parser->getStream()->expect(Twig_Token::NAME_TYPE)->getValue(), $token->getLine()); $this->parser->getStream()->expect(Twig_Token::BLOCK_END_TYPE); $this->parser->addImportedSymbol('template', $var->getAttribute('name')); return new Twig_Node_Import($macro, $var, $token->getLine(), $this->getTag()); } /** * Gets the tag name associated with this token parser. * * @return string The tag name */ public function getTag() { return 'import'; } }

Gruta Olhos d'Água Gruta Olhos d'Água (MG-0288) is a 9,100 meter-long cave located in the municipality of Itacarambi, State of Minas Gerais, Brazil. It is considered the fourth longest in Brazil and contains many limestone formations reaching up to 1 km long. The cave is 1180 m wide in its main axis and is formed by rocks of the pre-cambrian age, belonging to the Açungui Group of caverns frequently used for extraction of marble, limestone, talc, lead and iron. Its fauna consists of bats and spiders as well as depigmented crickets. See also List of caves in Brazil References External links Base de Dados do Ministerio do Meio Hambiente Governo Federal - ICMBIO Official Website Category:Caves of Minas Gerais Category:Wild caves

The list of command line arguments passed to a Python script. argv[0] is the script name (it is operating system dependent whether this is a full pathname or not). If the command was executed using the -c command line option to the interpreter, argv[0] is set to the string '-c'. If no script name was passed to the Python interpreter, argv[0] is the empty string. To loop over the standard input, or the list of files given on the command line, see the fileinput module. Set during Python startup, before site.py is run, to the same value as exec_prefix. If not running in a virtual environment, the values will stay the same; if site.py finds that a virtual environment is in use, the values of prefix and exec_prefix will be changed to point to the virtual environment, whereas base_prefix and base_exec_prefix will remain pointing to the base Python installation (the one which the virtual environment was created from). Set during Python startup, before site.py is run, to the same value as prefix. If not running in a virtual environment, the values will stay the same; if site.py finds that a virtual environment is in use, the values of prefix and exec_prefix will be changed to point to the virtual environment, whereas base_prefix and base_exec_prefix will remain pointing to the base Python installation (the one which the virtual environment was created from). A tuple of strings giving the names of all modules that are compiled into this Python interpreter. (This information is not available in any other way — modules.keys() only lists the imported modules.) Return a dictionary mapping each thread’s identifier to the topmost stack frame currently active in that thread at the time the function is called. Note that functions in the traceback module can build the call stack given such a frame. This is most useful for debugging deadlock: this function does not require the deadlocked threads’ cooperation, and such threads’ call stacks are frozen for as long as they remain deadlocked. The frame returned for a non-deadlocked thread may bear no relationship to that thread’s current activity by the time calling code examines the frame. This function should be used for internal and specialized purposes only. This hook function is called by built-in breakpoint(). By default, it drops you into the pdb debugger, but it can be set to any other function so that you can choose which debugger gets used. The signature of this function is dependent on what it calls. For example, the default binding (e.g. pdb.set_trace()) expects no arguments, but you might bind it to a function that expects additional arguments (positional and/or keyword). The built-in breakpoint() function passes its *args and **kws straight through. Whatever breakpointhooks() returns is returned from breakpoint(). The default implementation first consults the environment variable PYTHONBREAKPOINT. If that is set to "0" then this function returns immediately; i.e. it is a no-op. If the environment variable is not set, or is set to the empty string, pdb.set_trace() is called. Otherwise this variable should name a function to run, using Python’s dotted-import nomenclature, e.g. package.subpackage.module.function. In this case, package.subpackage.module would be imported and the resulting module must have a callable named function(). This is run, passing in *args and **kws, and whatever function() returns, sys.breakpointhook() returns to the built-in breakpoint() function. If value is not None, this function prints repr(value) to sys.stdout, and saves value in builtins._. If repr(value) is not encodable to sys.stdout.encoding with sys.stdout.errors error handler (which is probably 'strict'), encode it to sys.stdout.encoding with 'backslashreplace' error handler. sys.displayhook is called on the result of evaluating an expression entered in an interactive Python session. The display of these values can be customized by assigning another one-argument function to sys.displayhook. Pseudo-code: defdisplayhook(value):ifvalueisNone:return# Set '_' to None to avoid recursionbuiltins._=Nonetext=repr(value)try:sys.stdout.write(text)exceptUnicodeEncodeError:bytes=text.encode(sys.stdout.encoding,'backslashreplace')ifhasattr(sys.stdout,'buffer'):sys.stdout.buffer.write(bytes)else:text=bytes.decode(sys.stdout.encoding,'strict')sys.stdout.write(text)sys.stdout.write("\n")builtins._=value If this is true, Python won’t try to write .pyc files on the import of source modules. This value is initially set to True or False depending on the -B command line option and the PYTHONDONTWRITEBYTECODE environment variable, but you can set it yourself to control bytecode file generation. This function prints out a given traceback and exception to sys.stderr. When an exception is raised and uncaught, the interpreter calls sys.excepthook with three arguments, the exception class, exception instance, and a traceback object. In an interactive session this happens just before control is returned to the prompt; in a Python program this happens just before the program exits. The handling of such top-level exceptions can be customized by assigning another three-argument function to sys.excepthook. These objects contain the original values of breakpointhook, displayhook, and excepthook at the start of the program. They are saved so that breakpointhook, displayhook and excepthook can be restored in case they happen to get replaced with broken or alternative objects. This function returns a tuple of three values that give information about the exception that is currently being handled. The information returned is specific both to the current thread and to the current stack frame. If the current stack frame is not handling an exception, the information is taken from the calling stack frame, or its caller, and so on until a stack frame is found that is handling an exception. Here, “handling an exception” is defined as “executing an except clause.” For any stack frame, only information about the exception being currently handled is accessible. If no exception is being handled anywhere on the stack, a tuple containing three None values is returned. Otherwise, the values returned are (type,value,traceback). Their meaning is: type gets the type of the exception being handled (a subclass of BaseException); value gets the exception instance (an instance of the exception type); traceback gets a traceback object (see the Reference Manual) which encapsulates the call stack at the point where the exception originally occurred. A string giving the site-specific directory prefix where the platform-dependent Python files are installed; by default, this is also '/usr/local'. This can be set at build time with the --exec-prefix argument to the configure script. Specifically, all configuration files (e.g. the pyconfig.h header file) are installed in the directory exec_prefix/lib/pythonX.Y/config, and shared library modules are installed in exec_prefix/lib/pythonX.Y/lib-dynload, where X.Y is the version number of Python, for example 3.2. Note If a virtual environment is in effect, this value will be changed in site.py to point to the virtual environment. The value for the Python installation will still be available, via base_exec_prefix. A string giving the absolute path of the executable binary for the Python interpreter, on systems where this makes sense. If Python is unable to retrieve the real path to its executable, sys.executable will be an empty string or None. Exit from Python. This is implemented by raising the SystemExit exception, so cleanup actions specified by finally clauses of try statements are honored, and it is possible to intercept the exit attempt at an outer level. The optional argument arg can be an integer giving the exit status (defaulting to zero), or another type of object. If it is an integer, zero is considered “successful termination” and any nonzero value is considered “abnormal termination” by shells and the like. Most systems require it to be in the range 0–127, and produce undefined results otherwise. Some systems have a convention for assigning specific meanings to specific exit codes, but these are generally underdeveloped; Unix programs generally use 2 for command line syntax errors and 1 for all other kind of errors. If another type of object is passed, None is equivalent to passing zero, and any other object is printed to stderr and results in an exit code of 1. In particular, sys.exit("someerrormessage") is a quick way to exit a program when an error occurs. Since exit() ultimately “only” raises an exception, it will only exit the process when called from the main thread, and the exception is not intercepted. Changed in version 3.6: If an error occurs in the cleanup after the Python interpreter has caught SystemExit (such as an error flushing buffered data in the standard streams), the exit status is changed to 120. A struct sequence holding information about the float type. It contains low level information about the precision and internal representation. The values correspond to the various floating-point constants defined in the standard header file float.h for the ‘C’ programming language; see section 5.2.4.2.2 of the 1999 ISO/IEC C standard [C99], ‘Characteristics of floating types’, for details. attribute float.h macro explanation epsilon DBL_EPSILON difference between 1 and the least value greater than 1 that is representable as a float dig DBL_DIG maximum number of decimal digits that can be faithfully represented in a float; see below mant_dig DBL_MANT_DIG float precision: the number of base-radix digits in the significand of a float integer constant representing the rounding mode used for arithmetic operations. This reflects the value of the system FLT_ROUNDS macro at interpreter startup time. See section 5.2.4.2.2 of the C99 standard for an explanation of the possible values and their meanings. The attribute sys.float_info.dig needs further explanation. If s is any string representing a decimal number with at most sys.float_info.dig significant digits, then converting s to a float and back again will recover a string representing the same decimal value: A string indicating how the repr() function behaves for floats. If the string has value 'short' then for a finite float x, repr(x) aims to produce a short string with the property that float(repr(x))==x. This is the usual behaviour in Python 3.1 and later. Otherwise, float_repr_style has value 'legacy' and repr(x) behaves in the same way as it did in versions of Python prior to 3.1. Return the number of memory blocks currently allocated by the interpreter, regardless of their size. This function is mainly useful for tracking and debugging memory leaks. Because of the interpreter’s internal caches, the result can vary from call to call; you may have to call _clear_type_cache() and gc.collect() to get more predictable results. If a Python build or implementation cannot reasonably compute this information, getallocatedblocks() is allowed to return 0 instead. Return the name of the encoding used to convert between Unicode filenames and bytes filenames. For best compatibility, str should be used for filenames in all cases, although representing filenames as bytes is also supported. Functions accepting or returning filenames should support either str or bytes and internally convert to the system’s preferred representation. Return the current value of the recursion limit, the maximum depth of the Python interpreter stack. This limit prevents infinite recursion from causing an overflow of the C stack and crashing Python. It can be set by setrecursionlimit(). Return the size of an object in bytes. The object can be any type of object. All built-in objects will return correct results, but this does not have to hold true for third-party extensions as it is implementation specific. Only the memory consumption directly attributed to the object is accounted for, not the memory consumption of objects it refers to. If given, default will be returned if the object does not provide means to retrieve the size. Otherwise a TypeError will be raised. getsizeof() calls the object’s __sizeof__ method and adds an additional garbage collector overhead if the object is managed by the garbage collector. Return a frame object from the call stack. If optional integer depth is given, return the frame object that many calls below the top of the stack. If that is deeper than the call stack, ValueError is raised. The default for depth is zero, returning the frame at the top of the call stack. CPython implementation detail: This function should be used for internal and specialized purposes only. It is not guaranteed to exist in all implementations of Python. CPython implementation detail: The gettrace() function is intended only for implementing debuggers, profilers, coverage tools and the like. Its behavior is part of the implementation platform, rather than part of the language definition, and thus may not be available in all Python implementations. Return a named tuple describing the Windows version currently running. The named elements are major, minor, build, platform, service_pack, service_pack_minor, service_pack_major, suite_mask, product_type and platform_version. service_pack contains a string, platform_version a 3-tuple and all other values are integers. The components can also be accessed by name, so sys.getwindowsversion()[0] is equivalent to sys.getwindowsversion().major. For compatibility with prior versions, only the first 5 elements are retrievable by indexing. platform will be 2(VER_PLATFORM_WIN32_NT). product_type may be one of the following values: Constant Meaning 1(VER_NT_WORKSTATION) The system is a workstation. 2(VER_NT_DOMAIN_CONTROLLER) The system is a domain controller. 3(VER_NT_SERVER) The system is a server, but not a domain controller. This function wraps the Win32 GetVersionEx() function; see the Microsoft documentation on OSVERSIONINFOEX() for more information about these fields. platform_version returns the accurate major version, minor version and build number of the current operating system, rather than the version that is being emulated for the process. It is intended for use in logging rather than for feature detection. Returns an asyncgen_hooks object, which is similar to a namedtuple of the form (firstiter, finalizer), where firstiter and finalizer are expected to be either None or functions which take an asynchronous generator iterator as an argument, and are used to schedule finalization of an asynchronous generator by an event loop. The version number encoded as a single integer. This is guaranteed to increase with each version, including proper support for non-production releases. For example, to test that the Python interpreter is at least version 1.5.2, use: ifsys.hexversion>=0x010502F0:# use some advanced feature...else:# use an alternative implementation or warn the user... This is called hexversion since it only really looks meaningful when viewed as the result of passing it to the built-in hex() function. The struct sequencesys.version_info may be used for a more human-friendly encoding of the same information. An object containing information about the implementation of the currently running Python interpreter. The following attributes are required to exist in all Python implementations. name is the implementation’s identifier, e.g. 'cpython'. The actual string is defined by the Python implementation, but it is guaranteed to be lower case. version is a named tuple, in the same format as sys.version_info. It represents the version of the Python implementation. This has a distinct meaning from the specific version of the Python language to which the currently running interpreter conforms, which sys.version_info represents. For example, for PyPy 1.8 sys.implementation.version might be sys.version_info(1,8,0,'final',0), whereas sys.version_info would be sys.version_info(2,7,2,'final',0). For CPython they are the same value, since it is the reference implementation. hexversion is the implementation version in hexadecimal format, like sys.hexversion. cache_tag is the tag used by the import machinery in the filenames of cached modules. By convention, it would be a composite of the implementation’s name and version, like 'cpython-33'. However, a Python implementation may use some other value if appropriate. If cache_tag is set to None, it indicates that module caching should be disabled. sys.implementation may contain additional attributes specific to the Python implementation. These non-standard attributes must start with an underscore, and are not described here. Regardless of its contents, sys.implementation will not change during a run of the interpreter, nor between implementation versions. (It may change between Python language versions, however.) See PEP 421 for more information. When this attribute exists, its value is automatically called (with no arguments) when the interpreter is launched in interactive mode. This is done after the PYTHONSTARTUP file is read, so that you can set this hook there. The site module sets this. Enter string in the table of “interned” strings and return the interned string – which is string itself or a copy. Interning strings is useful to gain a little performance on dictionary lookup – if the keys in a dictionary are interned, and the lookup key is interned, the key comparisons (after hashing) can be done by a pointer compare instead of a string compare. Normally, the names used in Python programs are automatically interned, and the dictionaries used to hold module, class or instance attributes have interned keys. Interned strings are not immortal; you must keep a reference to the return value of intern() around to benefit from it. These three variables are not always defined; they are set when an exception is not handled and the interpreter prints an error message and a stack traceback. Their intended use is to allow an interactive user to import a debugger module and engage in post-mortem debugging without having to re-execute the command that caused the error. (Typical use is importpdb;pdb.pm() to enter the post-mortem debugger; see pdb module for more information.) The meaning of the variables is the same as that of the return values from exc_info() above. An integer giving the value of the largest Unicode code point, i.e. 1114111 (0x10FFFF in hexadecimal). Changed in version 3.3: Before PEP 393, sys.maxunicode used to be either 0xFFFF or 0x10FFFF, depending on the configuration option that specified whether Unicode characters were stored as UCS-2 or UCS-4. A list of meta path finder objects that have their find_spec() methods called to see if one of the objects can find the module to be imported. The find_spec() method is called with at least the absolute name of the module being imported. If the module to be imported is contained in a package, then the parent package’s __path__ attribute is passed in as a second argument. The method returns a module spec, or None if the module cannot be found. This is a dictionary that maps module names to modules which have already been loaded. This can be manipulated to force reloading of modules and other tricks. However, replacing the dictionary will not necessarily work as expected and deleting essential items from the dictionary may cause Python to fail. A list of strings that specifies the search path for modules. Initialized from the environment variable PYTHONPATH, plus an installation-dependent default. As initialized upon program startup, the first item of this list, path[0], is the directory containing the script that was used to invoke the Python interpreter. If the script directory is not available (e.g. if the interpreter is invoked interactively or if the script is read from standard input), path[0] is the empty string, which directs Python to search modules in the current directory first. Notice that the script directory is inserted before the entries inserted as a result of PYTHONPATH. A program is free to modify this list for its own purposes. Only strings and bytes should be added to sys.path; all other data types are ignored during import. A dictionary acting as a cache for finder objects. The keys are paths that have been passed to sys.path_hooks and the values are the finders that are found. If a path is a valid file system path but no finder is found on sys.path_hooks then None is stored. This string contains a platform identifier that can be used to append platform-specific components to sys.path, for instance. For Unix systems, except on Linux, this is the lowercased OS name as returned by uname-s with the first part of the version as returned by uname-r appended, e.g. 'sunos5' or 'freebsd8', at the time when Python was built. Unless you want to test for a specific system version, it is therefore recommended to use the following idiom: Changed in version 3.3: On Linux, sys.platform doesn’t contain the major version anymore. It is always 'linux', instead of 'linux2' or 'linux3'. Since older Python versions include the version number, it is recommended to always use the startswith idiom presented above. See also os.name has a coarser granularity. os.uname() gives system-dependent version information. The platform module provides detailed checks for the system’s identity. A string giving the site-specific directory prefix where the platform independent Python files are installed; by default, this is the string '/usr/local'. This can be set at build time with the --prefix argument to the configure script. The main collection of Python library modules is installed in the directory prefix/lib/pythonX.Y while the platform independent header files (all except pyconfig.h) are stored in prefix/include/pythonX.Y, where X.Y is the version number of Python, for example 3.2. Note If a virtual environment is in effect, this value will be changed in site.py to point to the virtual environment. The value for the Python installation will still be available, via base_prefix. Strings specifying the primary and secondary prompt of the interpreter. These are only defined if the interpreter is in interactive mode. Their initial values in this case are '>>>' and '...'. If a non-string object is assigned to either variable, its str() is re-evaluated each time the interpreter prepares to read a new interactive command; this can be used to implement a dynamic prompt. Set the interpreter’s “check interval”. This integer value determines how often the interpreter checks for periodic things such as thread switches and signal handlers. The default is 100, meaning the check is performed every 100 Python virtual instructions. Setting it to a larger value may increase performance for programs using threads. Setting it to a value <= 0 checks every virtual instruction, maximizing responsiveness as well as overhead. Deprecated since version 3.2: This function doesn’t have an effect anymore, as the internal logic for thread switching and asynchronous tasks has been rewritten. Use setswitchinterval() instead. Set the flags used by the interpreter for dlopen() calls, such as when the interpreter loads extension modules. Among other things, this will enable a lazy resolving of symbols when importing a module, if called as sys.setdlopenflags(0). To share symbols across extension modules, call as sys.setdlopenflags(os.RTLD_GLOBAL). Symbolic names for the flag values can be found in the os module (RTLD_xxx constants, e.g. os.RTLD_LAZY). Set the system’s profile function, which allows you to implement a Python source code profiler in Python. See chapter The Python Profilers for more information on the Python profiler. The system’s profile function is called similarly to the system’s trace function (see settrace()), but it is called with different events, for example it isn’t called for each executed line of code (only on call and return, but the return event is reported even when an exception has been set). The function is thread-specific, but there is no way for the profiler to know about context switches between threads, so it does not make sense to use this in the presence of multiple threads. Also, its return value is not used, so it can simply return None. Error in the profile function will cause itself unset. Profile functions should have three arguments: frame, event, and arg. frame is the current stack frame. event is a string: 'call', 'return', 'c_call', 'c_return', or 'c_exception'. arg depends on the event type. The events have the following meaning: 'call' A function is called (or some other code block entered). The profile function is called; arg is None. 'return' A function (or other code block) is about to return. The profile function is called; arg is the value that will be returned, or None if the event is caused by an exception being raised. 'c_call' A C function is about to be called. This may be an extension function or a built-in. arg is the C function object. Set the maximum depth of the Python interpreter stack to limit. This limit prevents infinite recursion from causing an overflow of the C stack and crashing Python. The highest possible limit is platform-dependent. A user may need to set the limit higher when they have a program that requires deep recursion and a platform that supports a higher limit. This should be done with care, because a too-high limit can lead to a crash. If the new limit is too low at the current recursion depth, a RecursionError exception is raised. Changed in version 3.5.1: A RecursionError exception is now raised if the new limit is too low at the current recursion depth. Set the interpreter’s thread switch interval (in seconds). This floating-point value determines the ideal duration of the “timeslices” allocated to concurrently running Python threads. Please note that the actual value can be higher, especially if long-running internal functions or methods are used. Also, which thread becomes scheduled at the end of the interval is the operating system’s decision. The interpreter doesn’t have its own scheduler. Set the system’s trace function, which allows you to implement a Python source code debugger in Python. The function is thread-specific; for a debugger to support multiple threads, it must be registered using settrace() for each thread being debugged. Trace functions should have three arguments: frame, event, and arg. frame is the current stack frame. event is a string: 'call', 'line', 'return', 'exception' or 'opcode'. arg depends on the event type. The trace function is invoked (with event set to 'call') whenever a new local scope is entered; it should return a reference to a local trace function to be used that scope, or None if the scope shouldn’t be traced. The local trace function should return a reference to itself (or to another function for further tracing in that scope), or None to turn off tracing in that scope. If there is any error occurred in the trace function, it will be unset, just like settrace(None) is called. The events have the following meaning: 'call' A function is called (or some other code block entered). The global trace function is called; arg is None; the return value specifies the local trace function. 'line' The interpreter is about to execute a new line of code or re-execute the condition of a loop. The local trace function is called; arg is None; the return value specifies the new local trace function. See Objects/lnotab_notes.txt for a detailed explanation of how this works. Per-line events may be disabled for a frame by setting f_trace_lines to False on that frame. 'return' A function (or other code block) is about to return. The local trace function is called; arg is the value that will be returned, or None if the event is caused by an exception being raised. The trace function’s return value is ignored. 'exception' An exception has occurred. The local trace function is called; arg is a tuple (exception,value,traceback); the return value specifies the new local trace function. 'opcode' The interpreter is about to execute a new opcode (see dis for opcode details). The local trace function is called; arg is None; the return value specifies the new local trace function. Per-opcode events are not emitted by default: they must be explicitly requested by setting f_trace_opcodes to True on the frame. Note that as an exception is propagated down the chain of callers, an 'exception' event is generated at each level. CPython implementation detail: The settrace() function is intended only for implementing debuggers, profilers, coverage tools and the like. Its behavior is part of the implementation platform, rather than part of the language definition, and thus may not be available in all Python implementations. Accepts two optional keyword arguments which are callables that accept an asynchronous generator iterator as an argument. The firstiter callable will be called when an asynchronous generator is iterated for the first time. The finalizer will be called when an asynchronous generator is about to be garbage collected. New in version 3.6: See PEP 525 for more details, and for a reference example of a finalizer method see the implementation of asyncio.Loop.shutdown_asyncgens in Lib/asyncio/base_events.py Note This function has been added on a provisional basis (see PEP 411 for details.) Allows enabling or disabling coroutine origin tracking. When enabled, the cr_origin attribute on coroutine objects will contain a tuple of (filename, line number, function name) tuples describing the traceback where the coroutine object was created, with the most recent call first. When disabled, cr_origin will be None. To enable, pass a depth value greater than zero; this sets the number of frames whose information will be captured. To disable, pass set depth to zero. This setting is thread-specific. New in version 3.7. Note This function has been added on a provisional basis (see PEP 411 for details.) Use it only for debugging purposes. If called twice, the new wrapper replaces the previous one. The function is thread-specific. The wrapper callable cannot define new coroutines directly or indirectly: defwrapper(coro):asyncdefwrap(coro):returnawaitcororeturnwrap(coro)sys.set_coroutine_wrapper(wrapper)asyncdeffoo():pass# The following line will fail with a RuntimeError, because# ``wrapper`` creates a ``wrap(coro)`` coroutine:foo() On Windows, UTF-8 is used for the console device. Non-character devices such as disk files and pipes use the system locale encoding (i.e. the ANSI codepage). Non-console character devices such as NUL (i.e. where isatty() returns True) use the value of the console input and output codepages at startup, respectively for stdin and stdout/stderr. This defaults to the system locale encoding if the process is not initially attached to a console. The special behaviour of the console can be overridden by setting the environment variable PYTHONLEGACYWINDOWSSTDIO before starting Python. In that case, the console codepages are used as for any other character device. Under all platforms, you can override the character encoding by setting the PYTHONIOENCODING environment variable before starting Python or by using the new -Xutf8 command line option and PYTHONUTF8 environment variable. However, for the Windows console, this only applies when PYTHONLEGACYWINDOWSSTDIO is also set. When interactive, stdout and stderr streams are line-buffered. Otherwise, they are block-buffered like regular text files. You can override this value with the -u command-line option. Note To write or read binary data from/to the standard streams, use the underlying binary buffer object. For example, to write bytes to stdout, use sys.stdout.buffer.write(b'abc'). However, if you are writing a library (and do not control in which context its code will be executed), be aware that the standard streams may be replaced with file-like objects like io.StringIO which do not support the buffer attribute. These objects contain the original values of stdin, stderr and stdout at the start of the program. They are used during finalization, and could be useful to print to the actual standard stream no matter if the sys.std* object has been redirected. It can also be used to restore the actual files to known working file objects in case they have been overwritten with a broken object. However, the preferred way to do this is to explicitly save the previous stream before replacing it, and restore the saved object. Note Under some conditions stdin, stdout and stderr as well as the original values __stdin__, __stdout__ and __stderr__ can be None. It is usually the case for Windows GUI apps that aren’t connected to a console and Python apps started with pythonw. When this variable is set to an integer value, it determines the maximum number of levels of traceback information printed when an unhandled exception occurs. The default is 1000. When set to 0 or less, all traceback information is suppressed and only the exception type and value are printed. A string containing the version number of the Python interpreter plus additional information on the build number and compiler used. This string is displayed when the interactive interpreter is started. Do not extract version information out of it, rather, use version_info and the functions provided by the platform module. A tuple containing the five components of the version number: major, minor, micro, releaselevel, and serial. All values except releaselevel are integers; the release level is 'alpha', 'beta', 'candidate', or 'final'. The version_info value corresponding to the Python version 2.0 is (2,0,0,'final',0). The components can also be accessed by name, so sys.version_info[0] is equivalent to sys.version_info.major and so on. The version number used to form registry keys on Windows platforms. This is stored as string resource 1000 in the Python DLL. The value is normally the first three characters of version. It is provided in the sys module for informational purposes; modifying this value has no effect on the registry keys used by Python.

The pregnant antithrombin III deficient patient: management without antithrombin III concentrate. Pregnant patients with antithrombin III (AT III) deficiency have an unacceptably high risk of venous thromboembolism (VTE). Antithrombotic therapy is therefore recommended. The reported clinical experience of such prophylaxis is limited. Some authors have recommended the use of AT III concentrate in addition to heparin in the management of these patients. We report successful management with heparin alone during pregnancy and the postpartum period in two patients with AT III deficiency. Both patients had experienced VTE during a prior pregnancy; one also experienced VTE during the reported pregnancy. Both patients were therefore at particularly high risk of further VTE. Based on the good results in these two patients, and a review of previously reported cases, we propose that heparin alone, in a dose to maintain the APTT in a therapeutic range, provides adequate prophylaxis and treatment for VTE during pregnancy and delivery in many AT III deficient subjects.

Q: How can I search and replace in Firefox? I am moderator on a site with lots of structured content and regularly edit posts for poor formatting (in particular Markdown and LaTeX). Many of those tasks are tedious and could easily be performed by a search & replace function which, sadly, my browser of choice Firefox lacks. I could not find a suitable plugin (although I admittedly did not check all >900 results) which is surprising; this seems to easy and useful a feature to not have a plugin! Copying posts into a text editor is a nice workaround in some cases, but not in all. Some text editors don't have search ^ replace (e.g. gedit, default editor for many GTK based Linux distributions), and I might not be able to install one on every machine I use SE on (university, friends, ...). Is there a way to bring search & replace to Firefox, preferably with regexp support? My OS is GNU/Linux, more specifically Ubuntu. A: You can use FoxReplace which should do what you want. This extension allows you to replace text fragments (strings) in a page by other text fragments. The system is based on substitutions, where each substitution has an input text which has to be replaced (the "Replace" field) and an output text by which the first has to be replaced (the "With" field). When a substitution is applied it's over the whole content of a page (you can't do partial substitutions at the moment). Substitutions can be case-sensitive or insensitive. The use of regular expressions is also supported.

Accounting for Mathematicians This visual guide is part of a collection of documents created by the One Student One ERP (OSOE) project in collaboration with Institut Mines Telecom, Telecom Bretagne, Dresden University of Technology and the South Westfalia University of Applied Sciences. It can be used to teach modern ERP theory and practice to undergraduate students or professionals. Copyright: You are free to copy, distribute, display, and perform the work under the following conditions: you must attribute the work in the manner specified by the author or licensor; you may not use this work for any commercial purposes including training, consulting, advertising, self-advertising, publishing, etc.; you may not alter, transform, or build upon this work. For any reuse or distribution, you must make clear to others the license terms of this work. Any of these conditions can be waived if you get permission from the copyright holder through a commercial license or an educational license. For more information, contact info@nexedi.com Agenda Account Space Legislation Space Currency Space & Exchange Transactions and Journals Invariants Reports Profits The goal of this lesson is to teach accounting in a way which will be valid in the next 100 years or more. For that purpose, we introduce in the lesson the concepts of accounting using a set theory formalism. We believe that too much fashion, too many fuzzy words are used in the current approaches of accounting education. Students learn about the so-called general accounting, which is not general at all and which is usually presented in a way which is specific to each legislation. Students learn about the so-called cost accounting, which has no relation to costs. Students learn about analytical accounting, with a singular, instead of learning about accounting analytics, with a plural. Students learn about activity based accounting, which is just one example of accounting analytics. We hope, through this lesson, to exhibit the concept of universal accounting in such a way that students can learn a model which is useful to understand and explain all the types of accounting which exist or will be created in the near or distant future, based on the ever evolving fashion in corporate management. The Account Space: A The first concept in accounting is the Account. An account is a point in an arbitrary N-dimensional discrete space. Some people like to give names to those dimensions, names which will likely become irrelevant in a century. Dimension 1 is called “General Account”. It represents the economic nature of the account: income, expense, inventory, etc. Dimension 2, the “Party”, represents a supplier, a client, a business unit or any 3rd party. Dimension 3, the “Project”, represents a project in a company which does project management. Dimension 4, the “Activity”, represents activities such as gardening. More dimensions could be used to provide more powerful accounting analytics. Legislation: L Governments, especially in countries of Civil Law, like to define an official space of accounts, called L. This space of account contains usually a few thousand standard account names which are required to be used to produce legislation dependent tax reports and exchange data. This space of account can evolve. Many accountants believe that Dimension 1 of the space of accounts is the space of accounts provided by the government. This creates a lot of troubles each time the legislation changes or whenever a company has subsidiaries in different countries. To solve all these problems, we define here a Legislation L as a mapping between the space of Accounts A and a single dimension discrete space which represents one possible legislation. Thanks to this approach, called indirection, our space of accounts no longer depends on political fashion, as long as A is a superset of L. In countries, especially in countries of Common Law, governments prefer to define accounting principles through quite ambiguous rules. Those rules are then interpreted by chartered accountants who use their legal expertise to create their own space of account. It is like the Legislation L is provided here by chartered accountants instead of being provided by the government. The Currency Space: C Accounting lives in a world of currencies. We introduce a space of currencies: C. C is a single dimension discrete space. A currency exchange function E is also introduced, whether currencies can be really exchanged or not. The currency exchange space is required because most tax reports must be produced using a single currency, the currency of the country, although most companies use multiple currencies. The currency exchange function E provides for a given currency c in C an exchange rate expressed in a universal currency. Note: this currency exchange model is a simplified symmetrical model for currency exchange. Reality is more complex and is based on asymmetric currency to currency exchange rates. However, introducing a more complex model for currency exchange would not help for the education purpose of this lesson. Accounting Transactions: T An accounting transaction is a finite series of sextuples. Each item is a finite series is called a transaction line. Each sextuple is made of 3 couples The first couple represents the account of the transaction at the source and the amount in the currency of the source. The second couple represents the account of the transaction at the destination and the amount of the transaction in the currency of the destination. The third tuple represents the currency and the amount in that currency of the transaction. Let us give an example to explain. If the source represents the supplier and if the destination represents the client. If the supplier sells a product to a client with a price expressed in USD. If the supplier is a company in Germany which operates in EUR and the client is a company in Japan which operates in JPY, the amount of the invoice is expressed in USD. The supplier registers the invoice in its accounting using for example an “Income” or a “Receivable” account and expresses the amount in EUR. The client registers the invoice in its accounting using for example an “Expense” or a “Payable” account and expresses the amount in JPY. We have just described the simplest universal model of an accounting transaction. In our example, the accounting transaction has 2 lines. One line with Income at the source and Expense at the destination. One line with Receivable at the source and Payable at the destination. Transaction Journal: J Account Transactions form a finite series called the Journal J. Each item of the Journal defines a date t and a transaction T. Debit & Credit Invariance: a Myth Every transaction in traditional accounting should meet the “debit and credit” invariant principle. Technically, it is quite simple. The total of amounts at the source is zero. The total of amounts at the destination is zero. The total of trade amounts converted in universal currency is zero. However, in “real world accounting”, accountants call a positive value a debit. They call a negative value a credit. This way, they do not need to display any negative signs in their reports. Assets, a positive value, are displayed as a debit. Debts, a negative value, are displayed as credit. Moreover, they consider that sales income are future profits, that profits are debts to the owner of the company, and that income should thus be considered as a negative value, just like debts. Just the same way, expenses are future losses, which will reduce the capital of the company, i.e. reduce a debt to the owner of the company, and should thus be considered positive values. It is a bit weird at first but consistent. Income, a negative value, is displayed as credit. Expense, a positive value, is displayed as debit. Now, where does this debit and credit invariant comes from? The sad truth is that this debit and credit invariant has no well defined rationale. Many companies in the world do accounting without following this invariant, even if accountants in countries of Civil Law hate to hear that. The only rationale of the debit and credit invariant is to help making sure that every transaction can be partitioned in 2 subsets of opposite total, consistently with the partitioning of accounts introduced later. However, it is not the only way to reach that goal. Supplier & Client Invariant The supplier and client invariant is a real and universal invariant which most accountants are not aware of. It relates to the principles of chemistry “nothing is created, nothing disappears, everything is transformed”. What this invariant says is that whenever a supplier has an income, its client has an expense of equivalent amount, consistently with the exchange rate of the transaction currency. This invariant applies to many situations, even in situations where the same company acts as supplier and as client. For example, amortization of an asset, could be represented with a single transaction line with same company in Dimension 2 of the space of accounts on both sides. The company at the source acts as a supplier and provides a share of machine which reduces the Immobilisation amount (an asset). The company at the destination acts as a client which consumes a share of machine, just like it would rent the machine, which is represented as an Expense. No other line is required since no cash is transferred and nothing would anyway appear at consolidation time. Another common example is the case of currency transfer, which is represented much more efficiently with a single transaction with same company at both ends. Last but not least, some companies prefer to enter only a single for every sales they make and then, at the end of the month, gather all sales transactions into a single receivable. In short: the invariance of Debit & Credit is a myth, the supplier and client invariance is universal. Tax Report Tax reports are made by calculating the total of transaction amounts expressed in the national currency of a single organisation for a subset of the space of accounts. Both source and destination amounts should be taken into account since the organisation for which the tax report is calculated could appear on both side. The report space R is a subset of the space of accounts A. Consolidated Tax Report Consolidated Tax reports are made by calculating the total of transaction amounts expressed in the national currency of a single organisation for a subset of the space of accounts, as long one side of the transaction has an account which is not part of the report space R. Auxiliary Tax Report Consolidated Tax reports are made by calculating the total of transaction amounts expressed in the national currency of a single organisation for two subsets of the space of accounts : R1 and R2. R1 represents all accounts (ex. payable) of a given organisation A. R2 represents all accounts (ex. Receivable) of another organisation B. The auxiliary report will produce in this example the amount of payable from B to A which has been accounted by A as receivable and by B as payable. Weighted Tax Report Weighted Tax reports consists of using a weight function W instead of using mere set membership, which is just a simple case of weight with values in 0 and 1. Trade Report in €: R Trade reports consist of making reports using a given currency and using the trade amount of the transaction. Legislation Report Legislation reports consist are tax reports which define the subset of accounts on which the total should be made through membership tests on the Legislation function L. An Example of Account Partition Accountants like to create partitions. First, they make a difference between accounts of “our” company, called here Aacme and other accounts. Inside Aacme, they make a difference between accounts called Asset, Liability, Income and Expense. Those accounts represent traditional ways of creating accounts based on legal principles, which are rather universal. Yet, in some countries, Capital is considered as a 5th partition item whereas in others Capital is part of Liabilities. This is just a matter of Habit and Law. Other ways of partitioning could be introduces of course. Profit Accounts then define words, based on the partitioning. Profit is for example of the sum of transactions lines amounts for accounts which are either Income or Expense. Remember here that Expense is a negative value and Income a positive value, since we do not use Debit or Credit. Asset Assets are defined by summing transaction amounts which account is in Asset. Liability The same goes for Liability. Asset and Liability Invariance And, by magic, general principles such as : asset + liability + profit = 0 can be exhibited. This sounds like magic, but it just means that by summing transactions which lines implement the invariance of Debit and Credit, and by making a partition of the account of space, the total is obviously always zero. Things would of course be different if the invariance of Debit and Credit was not respected. And this is probably where the rationale of this invariance comes from. By partitioning the space of accounts, certain accounting principles can be introduced. For example, it is usual to consider that every Income (ex. sales) must have an equal counterpart in the form of an Asset (this is of course simplified). Every Expense must have an equal counterpart in the form of Liability. Whenever Debit & Credit invariance is not respected at the level of a transaction, it is certain that such principles can not be fulfilled. Debit & Credit invariance is thus only a simple way, a kind of hack, to help accountants reduce input mistakes which would else break general reporting principles related to the partitioning of the space of Accounts. IFRS Accounting IFRS is a tentative of creating international accounting standards in the 21st century. It will likely fail because it is based on fuzzy principles which rely on the interpretation of chartered accounts and which are sensitive to fashion. In practice, it is yet another legislation, which can call here Lifrs. However, one key principle of IFRS, the economic value, is interesting in our model. IFRS requires accountant to consider the economic value of every asset. This means that whenever a transaction is recorded for a given receivable asset, even if its formal value is 100, it should be recorded by taking into account its real value, i.e. the formal value multiplied by the estimated probability of payment. This would be a major change in the accounting model, and possibly a useful change. Either by adding new items to the transactions in order to categorize transaction lines, or by adding new dimensions to transaction lines and hold various estimators, it is possible to extend the universal model of accounting to support fine grained evaluation of the economic value of each transaction. Combined with data mining to build estimates from transaction history, this would be a way to introduce more science in the work of chartered accounts for who, IFRS, is mostly nowadays a way to add unpredictable transactions with little rationale to the formal input of the accountant and maximize the assets of a company for the great benefit of the stockholder.

Having Daniella stay in our home was a lovely and unforgettable gift to our family! She is kind and warm and lights up the place with her bright and gentle presence. I hope she will stay with us again in the future but either way we know we have made a new, true friend. Thank you Daniella!

smartphone menu rubriken Reconciliation with Ulterior Motives Muammar al-Gaddafi has made an art out of embarrassing his European hosts in public, and he was certainly on form during his recent state visit to Italy, where he unsubtly reminded Italy of its colonial past as he stepped off the plane. Bernhard Schmid reports The Libyan leader's recent state visit to Italy was meant to mark a new beginning in relations between Italy and its former colony following the signing of an agreement between the two countries in August 2008 ​​Officially, the Libyan head of state and "revolutionary leader" Muammar al-Gaddafi has not been regarded by the international community as a rogue since December 2003. That was when the leadership in Tripoli declared formally to the USA and Great Britain that it would no longer seek to develop nuclear weapons. All the same, his hosts prefer to see the general with the sunglasses and the pithy comments leaving than arriving. That's a view which the Italian prime minister, Silvio Berlusconi, has probably come to share with the French president, Nicolas Sarkozy following Gaddafi's most recent visit to Italy. Back in December 2007, Gaddafi paid a highly controversial official visit to France which lasted a whole week. During the visit, Gaddafi contradicted Sarkozy in front of the cameras when Sarkozy said that "human rights had also been a topic" at the bilateral talks. Now, from June 10th to 13th, Gaddafi was Berlusconi's guest in Rome. The Italian apology Gaddafi was returning a short official visit which Berlusconi made on August 30th last year to Benghazi in Eastern Libya. During that visit Berlusconi caused a small sensation: in spite of the fact that his cabinet includes members of far-right parties, he publicly acknowledged the crimes committed during the period when Italy was the colonial power in Libya, between 1911 and 1942/3. Political scandal: after having been made to wait several hours for Gaddafi to arrive at an official engagement, representatives of the Italian parliament cancelled a meeting with Libya's revolutionary leader on the final day of his visit ​​In spite of this gesture of reconciliation, Gaddafi snubbed his hosts several times during his return visit. For example, he was due to make a speech before several hundred members of parliament and other prominent guests. He kept them waiting for two hours and when he had still not turned up and had not sent an apology, the president of the Italian parliament, Gianfranco Fini, eventually cancelled the meeting altogether – to the applause of part of the assembly. The Libyan embassy said later that Gaddafi had been held up "by Friday prayers". It's more likely, however, that he'd found out what was in the speech that Fini planned to deliver. Informed sources say that Fini, who's on the right of Italian politics, had included criticism of Gaddafi. The purest cynicism He intended to point to something Gaddafi had said on the second day of his visit and accuse him of comparing the US attacks on Libya in 1986 with later terror attacks by Al Qaeda. He also wanted to call on Gaddafi to open up the holding camps – which Libya has set up on its own soil for potentially unwanted immigrants to Europe – to inspection by an Italian parliamentary delegation, so that they could "assure themselves that human rights are being observed in these camps." Human rights groups criticised the agreement to deport refugees who illegally try to enter Italy after crossing the Mediterranean from Libya ​​Seen objectively, these planned criticisms are the purest cynicism. In reality, the inmates of the camps are subject to an absolute tyranny in a country which does not acknowledge the existence of a right to asylum in its laws. Bearing in mind the way the country treats its unwanted black African migrants, it would be more appropriate to ban the deportation of potential immigrants to Libya. But that by no means is current Italian policy. Since early May, two boats carrying refugees near the southern coast of Italy have been forced to turn back and hand over their passengers to the Libyan authorities, instead of checking whether any of the refugees might be entitled to rights in Italy such as the right to apply for asylum. Five hundred people were thus handed over to Libya. A crafty tactician Gaddafi is not just vain. He knows that Europe has an enormous interest in the huge oil and gas reserves in his country. And he's a crafty tactician, with enough experience to prevent the leaders of European democracies from meddling in his affairs while still managing to make them look like fools. When he arrived in Italy, Gaddafi demonstratively wore on his uniform a photo of the legendary Libyan revolutionary fighter Omar Mukhtar (<i>centre</i>), who was hung by Italian colonialists in 1931 ​​Another of Gaddafi's snubs was more justified. On his arrival at Rome Airport, he was wearing a large photo of Omar al-Mokhtar, the leader of a Libyan uprising in 1931, on the lapel of his uniform. With the photo, he was bringing a generally repressed episode in Italian colonial history to the attention of those Italians who were following the visit in the media. Libya had already been conquered by Italy in 1911, but it suffered serious oppression during the period of the fascist dictator Benito Mussolini from 1922 to 1943. Historians estimate that 20,000 Libyans were killed for resisting the colonial regime, and 100,000 were deported to camps in the desert. Half of those died of their privations, or from epidemics and executions, including al-Mokhtar. You scratch my back, I'll scratch yours A temporary marriage of convenience: in the friendship agreement concluded by the two nations, Italy undertakes to pay Libya $5 billion in compensation for the period of Italian occupation; in return, it is hoping for closer ties in the energy sector ​​When Berlusconi made his "national apology" in 2008, it was agreed that Italy would pay Libya five billion dollars (currently 3.4 million euros) over the next 25 years in reparations. In concrete terms, Italy was to invest 200 million dollars a year in Libyan infrastructure, such as an East-West motorway along the coast from the Tunisian to the Egyptian border, or "a large number" of social housing units. Rome also promised to grant scholarships to Libyan students and to pay an invalidity pension to victims of the mines laid by the Italians. What made the deal particularly attractive for Berlusconi was what Libya was to give in return. During his recent visit, Gaddafi assured him that "Italian enterprises" would in future "enjoy priority status" in his country. Italian is Libya's main business partner, both for imports and exports. And the treatment of the migrants the EU doesn't want – whatever the human rights situation – is also part of the political deal between the two governments. This is "the other side of the coin" – the bitterest aspect of the reconciliation between the two countries. Compensation for Italian Colonial PolicyA Double Deal with Tripoli "We'll have fewer illegal immigrants and more oil" – these were the words with which the Italian prime minister, Silvio Berlusconi, praised his latest political deal with the Libyan revolutionary leader, Muammar Ghaddafi. Bernhard Schmid explains the background to the new Libyan-Italian "friendship agreement" Political Reforms in LibyaRevolutionary Rhetoric or Radical Change? Last year, Colonel Gaddafi announced his intention to modernise the Libyan "state of the masses". At the recent General People's Congress, however, some of his decisions were rescinded, leaving widespread confusion among Libyans and experts alike. Beat Stauffer has the details Migrants in LibyaGate-Money for the Desert State An estimated two million migrants live in Libya, most of which want to move on to Europe. But after the rapprochement with Europe, the EU, in part, supports Gaddafi's refugee and deportation policy. By Charlotte Wiedemann Facebook, Twitter, Google+ In submitting this comment, the reader accepts the following terms and conditions: Qantara.de reserves the right to edit or delete comments or not to publish them. This applies in particular to defamatory, racist, personal, or irrelevant comments or comments written in dialects or languages other than English. Comments submitted by readers using fantasy names or intentionally false names will not be published. Qantara.de will not provide information on the telephone. Readers' comments can be found by Google and other search engines. Partner Organizations Facebook Most Recent Photo Essay Nowruz is one of the oldest celebrations in the world. It has been a fixture on the cultural calendar in many regions for more than 2,500 years. It marks the beginning of spring and also the change of seasons in the Iranian solar calendar. Sharam Ahad offers his impressions of the celebrations.

Bioenergetics in the aging Fischer 344 rat: effects of exercise and food restriction. The capacity for energy production was evaluated in male, Fischer 344 rats as they advanced from adulthood through senescence. At 10 months of age, the animals were divided into three groups: sedentary, fed ad libitum (S); exercised by treadmill running, fed ad libitum (E); and sedentary, caloric restricted by alternate day feeding (R). Activities of selected enzymes, ADP-stimulated respiration and levels of cytochromes, were determined in homogenates of liver and gastrocnemius muscle prepared from young controls (10-month old S) and 18-, 24-, and 30-month old animals. In liver, age-linked decrements were found in the activities of 3-hydroxyacyl-CoA dehydrogenase (S, E, and R) and citrate synthase (S), and in cytochrome c content (S and E), whereas substrate-catalysed oxidations were unaffected. In the gastrocnemius muscle (S, E, and R), respiration, activities of enzymes of the Krebs cycle and glycolysis, and cytochrome content were decreased after the age of 18 months. Oxidative capacity was increased in muscle through exercise (about 40%) and in liver by food restriction (about 20%). Body and soleus muscle mass declined similarly in all groups (about 14% from 30 to 18 months of age), whereas the loss of weight in the gastrocnemius muscle was much greater (34%). The data indicate that energy metabolism in the senescent animal is competent to meet its needs and age-related declines in energy metabolism are secondary to the aging process.

Introduction ============ Crops are generally grown at high planting density in the field. For better yield and resistance against lodging, cereal crops, such as rice, with semi-dwarf and/or erect leaf phenotypes are strongly desired ([@B31]; [@B26]). A rice leaf is composed of a leaf sheath, leaf blade, and a lamina joint (area between leaf blade and sheath, also called the collar) with auricles and ligule ([@B13]). In particular, leaf angle (the degree of bending between the leaf blade and leaf sheath) is one of the key agronomic traits that affects crop architecture and grain yields ([@B28]). Crops with erect leaves capture more light for photosynthesis and are also desirable for dense planting, all of which increase yields ([@B26]). Previously, it was shown that both phytohormone and non-hormone-related genes are involved in controlling the lamina inclination. The brassinosteroid (BR)-deficient mutant *dwarf4-1, ebisu dwarf* (*d2*), and *dwarf1* (*brd1*), the BR signaling mutant *d61-7*, and plants with suppressed expression of *OsBRASSINAZOLE-RESISTANT 1* (*OsBZR1*) encoding a transcription factor involved in the BR signaling cascade display erect leaves ([@B11], [@B12]; [@B26]; [@B3]) while overexpression of BR biosynthesis genes or signaling components resulted in large leaf inclination ([@B36]; [@B3]). For example, transgenic rice plants overexpressing sterol C-22 hydroxylase (a rate-limiting enzyme in BR biosynthesis) showed increased lamina angles ([@B34]). In addition to BR, other phytohormones are also involved in controlling the lamina inclination of rice. Ethylene participates in the response of BR-induced lamina joint inclination, and auxin (IAA) influences the lamina joint inclination at high concentrations and has a synergistic interaction with BR ([@B5]; [@B25]). Reduced expression of *SPINDLY*, a negative regulator of gibberellin (GA) signaling, also causes increased lamina inclination ([@B27]). In addition, transgenic rice plants with overexpression of *LAX PANICLE (LAX)* ([@B20]), *OsILI-BINDING HLH1* (*OsIBH1*) ([@B37]) and T-DNA insertion mutants of *OsWRKY11* ([@B32]), *OsLIGULELESS1* (*OsLG1*) encoding a *SQUAMOSA* promoter binding domain protein ([@B22]) exhibited erect leaves, whereas the double stranded RNA interference (dsRNAi) transgenic lines for rice MADS-box genes belonging to the SHORT VEGETATIVE PHASE (SVP) group such as O*sMADS22, OsMADS47*, and *OsMADS55* showed increased lamina angles ([@B23]). Decreased expression of *OsLIC* encoding a CCCH-type zinc-finger protein also results in increased lamina inclination through regulating BR signaling ([@B33]). It was also reported that *LC2* encoding a VERNALIZATION INSENSITIVE 3 (VIN3)-like protein acts as a repressor of cell division for regulation of collar development and the *lc2* mutation caused increased leaf angles ([@B40]). A recent report showed that an activation tagging line of rice, *slender grain Dominant* (*slg-D*), with enhanced expression of a gene encoding BAHD acyltransferase-like protein, produced slender grains with enlarged leaf angles ([@B7]), and a gain-of-function epiallele of rice *RELATED TO ABSCISIC ACID INSENSITIVE3* (*ABI3*)*/VIVIPAROUS1* (*VP1*) 6 (*RAV6*) encoding a B3 DNA-binding domain-containing protein caused larger lamina inclination but smaller grain size by modulating BR homeostasis ([@B38]). Moreover, induced expression of genes encoding atypical Helix-Loop-Helix (HLH) proteins such as *BRASSINISTEROID UPREGULATED1* (*BU1*; [@B29]), *Oryza sativa BU1 like 1* (*OsBUL1*; [@B14]), *INCREASED LAMININAR INCLINATION* (*ILI*; [@B37]) and *POSITIVE REGULATOR OF GRAIN LENGTH 1* (*PGL1*; [@B10]) or basic HLH (bHLH) proteins including *OsBUL1 Complex1* (*OsBC1*; [@B14]) conferred rice plants higher lamina angle degree with increased grain size. In this work, transcriptomes in collars and panicles of *OsBUL1* null mutants and WT plants were analyzed and *OsBUL1 DOWNSTREAM GENE1* (*OsBDG1*) was identified as a putative downstream gene of *OsBUL1*. It encodes a small leucine rich repeat (LRR) protein possessing cell elongation activity. Sequentially, *OsAP2* and *OsWRKY24* are identified as putative downstream genes of *OsBDG1*, and functional activities are assessed with respect to rice lamina inclination and grain size. Both genes are able to increase lamina inclination and grain size under the control of *OsBUL1* promoter. We, therefore, provide a sequential flow of acting genes from *OsBUL1* for positive effects on rice lamina joint inclination and grain size likely through cell elongation. Materials and Methods {#s1} ===================== Plant Materials and Growth Conditions ------------------------------------- The activation tagging line of *OsBDG1*, PFG_1B_05536 is in Dongjin background ([@B17]). Transgenic rice plants were produced with Tainung67 (TNG67) japonica rice cultivar. Rice plants (*Oryza sativa*) were grown in the field under natural long days or in the greenhouse with 28°C day/25°C night cycles. To assess the leaf angles of mature rice plants in the paddy field, leaves were numbered from top to bottom. Lamina angles were measured between a stem and a leaf blade at the second or the third leaf from eight to twelve individual plants per line when panicles come out of flag-leaf sheaths. Transgenic plants used for analyses in this work are all T3 or T4 independent lines. Lamina Joint Inclination Bioassay --------------------------------- Sterilized seeds were germinated and grown for 10 days in a dark chamber. Lamina joint inclination bioassays were performed as previously described ([@B18]). Seedlings were sampled by excising approximately 2 cm segments that contained lamina joints at the same position from each plant under dim light condition. They were floated on distilled water containing various concentrations of BL. After incubation in a dark chamber at 28°C for 2 days, the angle induced between the lamina and the sheath was measured. Vector Construction and Transformation -------------------------------------- Each open reading frame (ORF) of *OsBDG1, OsAP2*, and *OsWRKY24* was cloned into pGA3426 ([@B19]) or its derivatives for overexpression and/or dsRNAi purposes in rice. For expression by *OsBUL1* promoter, the ubiquitin promoter of pGA3426 was replaced with the 2.2 kb-*OsBUL1* promoter ([@B14]). Constructed plasmids were individually transformed into embryonic calli of TNG67 rice cultivars by *Agrobacterium*-LBA4404 mediation as described previously ([@B16]). Hormone Treatment ----------------- Ten-day-old rice (*O*. *sativa* cv. TNG67) seedlings grown in the growth chamber were treated with brassinolide (1 μM, BL from Sigma--Aldrich) or GA (100 μM GA3 from Sigma--Aldrich). Whole parts above the roots were harvested for RNA extraction at 24 h time point after treatment. Total RNA Isolation and Quantitative RT-PCR Analysis ---------------------------------------------------- Total RNAs of all the materials harvested were isolated using RNeasy plant mini kit (Qiagen) or Trizol solution (Invitrogen) according to the manufacturer's instructions. RNAs after DNase treatment were subjected to reverse transcriptase reactions using oligo(dT) primer and Superscript III reverse transcriptase (Invitrogen) according to the manufacturer's protocol. Subsequent PCR was conducted with the first-strand cDNA mixture and EX-Taq polymerase (Takara Bio). Quantitative PCR (qPCR) was carried out by a CFX96TM real-time system (Bio-Rad) using Maxima SYBR Green qPCR Master Mix (Thermo). For PCR, each sample was analyzed in triplicate. The run protocol was: denaturation at 95°C for 10 min and annealing/extension repeated 45 times (95°C for 15 s and 60°C for 30 s, data acquisition was performed). Housekeeping genes such as *OsUBQ* ([@B21]) and *OsAct* ([@B4]) were included in the reactions as internal controls for normalizing the variations in the amount of cDNA used ([@B8]). The threshold cycle (C~T~) was automatically determined for each reaction by the system set with default parameters. The specificity of the qRT-PCR was determined by curve analysis of the amplified products using the standard method installed in the system. Information on primers used is presented in **Supplementary Table [S1](#SM7){ref-type="supplementary-material"}**. Microarray Analyses ------------------- Collars of 80-day-old rice plants and young panicles less than 10 cm in length were harvested for RNA extraction for microarray. We used the Rice Whole Genome OneArray v1.1 (Phalanx Biotech Group, Taiwan) containing 22,003 DNA oligonucleotide probes. Each probe is a 60-mer designed in the sense direction. Among the probes, 21,179 probes corresponded to the annotated genes in the RGAP v.6.1 and BGI database. Additionally, we included 824 control probes. The detailed descriptions of the gene array list are available from <http://www.phalanx.com.tw/products/RiOA_Probe.php>. Fluorescent antisense RNA targets were prepared from 1 μg total RNA samples with the OneArray Amino Allyl aRNA Amplification Kit (Phalanx Biotech Group, Taiwan) and Cy5 dyes (Amersham Pharmacia, United States). Fluorescent targets were hybridized to the Rice OneArray with Phalanx hybridization buffer using Phalanx Hybridization System. After hybridization for 16 h at 50°C, non-specific binding targets were washed away by three washing steps (Washing I, 42°C 5 min; Washing II, 42°C, 5 min; 25°C, 5 min; Washing III, rinse 20 times), and the slides were dried by centrifugation and scanned by an Agilent G2505C scanner (Agilent Technologies, United States). The Cy5 fluorescent intensities of each spot were analyzed by GenePix 4.1 software (Molecular Devices). The signal intensity of each spot was introduced into Rosetta Resolver System (Rosetta Bio-software) to process data analysis. The error model of the Rosetta Resolver System could remove both systematic and random errors from the data. We filtered out the spots whose flag was less than 0. Spots that passed the criteria were normalized by 50% media scaling normalization method. The technical repeat data was tested by Pearson correlation coefficient calculation to check the reproducibility (*R*-value \> 0.975). Normalized spot intensities were transformed to gene expression log~2~ ratios between the control and treatment groups. The interest spots which show significant differences were selected by log~2~ ratio ≥ 1 or log~2~ ratio ≤-1 and *P* \< 0.05. Two independent biological replicates of hybridizations were performed. Histological Analyses --------------------- Lamina joint samples were fixed by 4% paraformaldehyde in 0.1 [M]{.smallcaps} sodium phosphate buffer, dehydrated through a series of graded ethanol baths, replaced with xylene, and embedded in Paraplast plus (Sigma--Aldrich). Paraffin sections (12 μm) were cut and stained with filtered 1% toluidine blue. The sections were photographed under a light microscope (Olympus BX51). Subcellular Localization of Proteins ------------------------------------ For cellular localization of OsBC1, OsBDG1, OsBUL1, OsAP2.2, and OsWRKY24 in rice, either yellow florescence protein (YFP):gateway (GW) or cyan fluorescent protein (CFP):GW vector was used for the florescence fusion as described previously ([@B15]). Isolation and transfection of rice protoplasts were followed as described by [@B39] and images of cells with fluorescence were taken by confocal microscopy (LSM 510 META NLO DuoScan, Carl Zeiss). Scanning Electron Microscopy ---------------------------- To observe epidermal cells of lemma in rice grains by scanning electron microscopy (SEM), whole grains were coated with gold by the ion sputter machine (E-1010, Hitachi) and examined with SEM (Quanta 250, FEI, Hillsboro, OR, United States). Results ======= *OsBDG1* May Act Downstream of *OsBUL1* --------------------------------------- To identify the downstream genes of *OsBUL1* in the expressional hierarchy, comparison of transcriptomes of collars and panicles between WT and *osbul1* plants was conducted using rice 22k-oligo microarrays^[1](#fn01){ref-type="fn"}^. The *osbul1* is a mRNA null mutant caused by a T-DNA insertion in the first exon of *OsBUL1* gene ([@B14]). Fourteen genes were upregulated, while 221 genes were downregulated in both collars and panicles of *osbul1* plants (**Figure [1A](#F1){ref-type="fig"}**). Among candidate genes, *OsBUL1 DOWNSTREAM GENE* (*OsBDG1*) was selected for further study since expression level of *OsBDG1* was reduced both in collars and panicles of *osbul1* plants (**Figure [1B](#F1){ref-type="fig"}**), and *OsBDG1* encodes a novel small protein containing a conserved LRR N-terminal domain (LRRNT) at the N-terminal part and three leucin-rich-repeat (LRR) domains toward its carboxyl terminus. In addition, its expression is known to be induced in transgenic rice plants overexpressing *Arabidopsis CYP90B1* which encodes for a sterol C-22 hydroxylase active in BR biosynthesis ([@B34]). To verify the microarray results, we performed expressional analyses on *OsBDG1* in collars and panicles of *osbul1* and WT plants, and found similar expression patterns to the microarray results (**Figure [1C](#F1){ref-type="fig"}**). On the contrary, the level of *OsBDG1* expression was higher in *OsBUL1*-overexpressing rice plants compared to the WT control (**Figure [1D](#F1){ref-type="fig"}**) indicating *OsBUL1* may act upstream of *OsBDG1*. Transgenic rice plants harboring p*Ubi*:*OsBDG1* show increased lamina inclination with elongated cells in the lamina joint and grain size (**Figures [2A](#F2){ref-type="fig"}--[C](#F2){ref-type="fig"}**) whereas reduced expression of *OsBDG1* results in erect leaves with reduced cell length in lamina joint and smaller grains (**Figures [2D](#F2){ref-type="fig"}--[F](#F2){ref-type="fig"}**). Phenotypes of overexpressors and dsRNAi lines for *OsBDG1* are similar to those of rice plants with increased *OsBUL1* expression and *osbul1*, respectively, supporting the expressional relationship between *OsBUL1* and *OsBDG1.* ![*OsBDG1* is a putative downstream gene of *OsBUL1* in expression. **(A)** Venn diagrams for upregulated and downregulated genes in the panicle and collar of *osbul1*. **(B)** A heat map based on microarray hybridization results shows that *OsBDG1* expression is reduced in *osbul1*. Color scale represents log signal values and Os10g30190 is a control showing similar signal values in the microarray hybridization between WT and *osbul1*. **(C)** Quantitative RT-PCR confirmed the reduced expression of *OsBDG1* in *osbul1* in collars and panicles. Conversely, expression level of *OsBDG1* is higher in an *OsBUL1* activation tagging line, *OsBUL1D* ([@B14]) and *OsBUL1* overexpressors (ox) than in the WT **(D)**. Data are the average of three or four independent experiments and normalized by *OsUBQ*. Error bars indicate SD.](fpls-08-01253-g001){#F1} ![Transgenic rice plants with p*Ubi*:*OsBDG1* and *OsBDG1*-dsRNAi constructs. **(A--C)** Overexpression of *OsBDG1* driven by *ubiquitin* promoter caused increase of leaf angles with cell length in the lamina joint and grain size. Longitudinal sections of the second leaf lamina joint are shown in **(A)** with measured cell length. Values are means ± SD (μm, *n* \> 20) as instructed by [@B37]. (^∗^*P* \< 0.01, Student's *t*-test). Bar = 20 μm. Semi-quantitative RT-PCR was conducted for *OsBDG1* expression in transgenic rice plants together with WT. Twenty-four PCR cycles for both *OsBDG1* and *OsUBQ* were applied. Values of grain size and leaf angles are presented as means ± SD in **(B)** (*n* = 35; ^∗^*P* \< 0.01, Student's *t*-test) and **(C)** (*n* \> 10; ^∗^*P* \< 0.01, Student's *t*-test), respectively. **(D--F)** Reduced expression of *OsBDG1* by dsRNAi-*OsBDG1* approaches resulted in erect leaves with shorter cells in lamina joint and smaller grains. The 384 bp-fragment of *OsBDG1* amplified by primers 5′ ATGGGGGCTCATTCTGCAGCGGCAGCTC 3′ and 5′ GTGCCACTCAGTGAATTCTTCTGAAGCTC 3′ was used for the dsRNAi construct. Semi-quantitative RT-PCR was conducted for *OsBDG1* expression in transgenic rice plants together with vector control (VC). Thirty-five and 24 PCR cycles were used for *OsBDG1* and *OsUBQ*, respectively. Longitudinal sections of the second leaf lamina joint are shown in **(D)** with measured cell length (μm, *n* \> 20; ^∗^*P* \< 0.01, Student's *t*-test). Bar = 20 μm. Values of grain size and leaf angles are presented in **(E)** (*n* \> 25; ^∗^*P* \< 0.01; ^∗∗^*P* \< 0.05, Student's *t*-test) and **(F)** (*n* \> 8; ^∗^*P* \< 0.01, Student's *t*-test), respectively.](fpls-08-01253-g002){#F2} Identification of an Activation Tagging Line for *OsBDG1* --------------------------------------------------------- A putative activation tagging line for *OsBDG1*, PFG_1B_05536 has been identified through the rice T-DNA database^[2](#fn02){ref-type="fn"}^ ([@B1]). Phenotypic analysis of the heterozygous population displayed a 3:1 ratio of *OsBDG1D* mutant phenotype to wild-type indicating *OsBDG1D* is a dominant mutant. T-DNA flanking sequence of the mutant was confirmed by PCR and comparison of the sequence through blastn search showed that the T-DNA was inserted in the 4.1 Kb downstream of Os11g31530 near Os11g31520 on chromosome 11 (**Figure [3A](#F3){ref-type="fig"}**). The expression of Os11g31530 was obviously influenced whereas the expression level of other genes located near the insertion position was not significantly affected (**Figure [3B](#F3){ref-type="fig"}**). The lamina angle increased more than two-fold in the activation tagging line with an increase of grain size (**Figures [3C](#F3){ref-type="fig"}--[E](#F3){ref-type="fig"}**), which is similar to *OsBDG1* overexpressors. {#F3} Expression of *OsBDG1* under the Control of *OsBUL1* Promoter ------------------------------------------------------------- To confirm the expression cascade of *OsBUL1* and *OsBDG1*, we made a construct for expression of *OsBDG1* under the control of the 2.2 kb-*OsBUL1* promoter (**Figure [4A](#F4){ref-type="fig"}**) preferentially active in lamina joints and panicles of rice ([@B14]). Transgenic rice containing the construct exhibited a dramatic increase in lamina inclination and grain size (**Figures [4B](#F4){ref-type="fig"}--[E](#F4){ref-type="fig"}**), which was similar to the lamina inclination and grain phenotypes of the *OsBDG1* activation tagging line, PFG_1B_05536 and *OsBDG1*-overexpressing lines driven by *ubiquitin* promoter. Thus, expression of *OsBDG1* under the control of *OsBUL1* promoter phenocopies *OsBUL1* overexpression by *ubiquitin* promoter or activation tagging systems ([@B14]) suggesting that *OsBDG1* may act downstream of *OsBUL1*. {#F4} *OsAP2* and *OsWRKY24* Are Upregulated by *OsBDG1* in Lamina Joints ------------------------------------------------------------------- To identify candidate genes affected by *OsBDG1* in the lamina joint and also likely responsible for the increased lamina inclination, we compared transcriptomes of collars among two independent homozygous transgenic lines of p*OsBUL1*:*OsBDG1*, \#13-2-2 and \#20-1-5, and wild-type plants by microarray hybridization^[3](#fn03){ref-type="fn"}^. Since the expression level of *OsBDG1* in the collar of a \#13-2-2 plant is lower than that of a \#20-1-5 plant (**Figure [4C](#F4){ref-type="fig"}**), we selected genes that showed the same increasing or decreasing patterns in the order of WT, \#13-2-2 and \#20-1-5. Five genes were identified as being upregulated by *OsBDG1* in the lamina joint (**Figures [5A,B](#F5){ref-type="fig"}**) but no candidate was found to be downregulated in the comparison. Also, no significant difference in *OsBUL1* expression was detected among WT, \#13-2-2 and \#20-1-5 lines (GEO accession no. GSE93817 for microarray results). We confirmed the expression patterns of each gene by qRT-PCR (**Figure [5C](#F5){ref-type="fig"}**). The Os10g41330 (*OsAP2*) produced two transcripts, Os10g41330.1 and Os10g41330.2 by alternative splicing (**Supplementary Figure [S1](#SM1){ref-type="supplementary-material"}**) and both transcripts showed similar accumulation patterns. Based on the increased expression level of each gene in the transgenic plants, we focused on two genes, Os10g41330 (*OsAP2*) and Os01g61080 (*OsWRKY24*) encoding putative transcription factors containing an AP2 domain and WRKY domain, respectively. Conversely, in collars of *OsBDG1* dsRNAi lines, the expression of *OsAP2.2* and *OsWRKY24* is reduced without altered expression level of *OsBUL1* supporting the notion that the two genes are downstream of *OsBDG1* in expression (**Supplementary Figure [S2](#SM2){ref-type="supplementary-material"}**). However, the expression of *OsBUL1* and *OsBDG1* was positively affected by p*OsBUL1*:*OsAP2* and/or p*OsBUL1*:*OsWRKY24* (**Supplementary Figure [S3](#SM3){ref-type="supplementary-material"}**). {ref-type="fig"}**. **(B)** A heat map generated by microarray hybridization shows expression level of the five candidate genes identified as being gradually increased by *OsBDG1* expression. Color scale represents log signal values. **(C)** Verification of the expression level on each candidate gene in the collar of WT and transgenic lines, \#13-2-2 and \#20-1-5 by quantitative RT-PCR. Os10g41330 is known to produce two putative transcripts, Os10g41330.1 and Os10g41330.2 by alternative splicing (**Supplementary Figure [S1](#SM1){ref-type="supplementary-material"}**). Data are the average of three or four independent experiments and normalized by *OsUBQ*. Error bars indicate SD.](fpls-08-01253-g005){#F5} Molecular Characterization of *OsBDG1, OsAP2*, and *OsWRKY24* ------------------------------------------------------------- Spatiotemporal expression of *OsBDG1, OsAP2*, and *OsWRKY24* also overlapped in collars and growing panicles (**Supplementary Figure [S4A](#SM4){ref-type="supplementary-material"}**). Interestingly, the expression of the three genes was upregulated by phytohormones such as GA3 and BL, which affect cell elongation (**Supplementary Figure [S4B](#SM4){ref-type="supplementary-material"}**). Indeed, *OsBDG1* dsRNAi lines exhibited reduced, but transgenic rice containing p*OsBUL1*:*OsBDG1* showed increased sensitivity in BR response through lamina bending assays (**Supplementary Figure [S4C](#SM4){ref-type="supplementary-material"}**). The OsBDG1 protein containing a short LRR motif was localized in the cytoplasm as well as the nucleus similar to OsBUL1 ([@B14]; **Supplementary Figure [S5](#SM5){ref-type="supplementary-material"}**). However, OsAP2.2 and OsWRKY24 proteins are localized in the nucleus and each protein shows a transcriptional activation activity in the yeast system (**Supplementary Figures [S5](#SM5){ref-type="supplementary-material"}, [S6C](#SM6){ref-type="supplementary-material"}**). Increased Lamina Inclination and Grain Size Phenotypes Are Observed in p*OsBUL1*:*OsAP2* and p*OsBUL1*:*OsWRKY24* Plants ------------------------------------------------------------------------------------------------------------------------ Transgenic rice plants containing p*OsBUL1*:*OsAP2.2*, a short transcript of Os10g41330 and p*OsBUL1*:genomic *OsAP2* were generated for phenotypic analyses of lamina angles and grain size (**Figure [6](#F6){ref-type="fig"}** and **Supplementary Figure [S1](#SM1){ref-type="supplementary-material"}**). Compared with the wild-type control, transgenic rice plants showed increased lamina inclination with increased amounts of *OsAP2.2* transcripts (**Figures [6A,B](#F6){ref-type="fig"}**). However, we could not detect the long form of the transcript, *OsAP2.1* in the transgenic plants containing p*OsBUL1*:genomic *OsAP2*. Transgenic rice for p*OsBUL1*:*OsWRKY24* also exhibited a significant increase in lamina angles (**Figure [6C](#F6){ref-type="fig"}**) indicating both *OsAP2.2* and *OsWRKY24* are likely affected by *OsBDG1* in the lamina joint. Of note, reduced expression level of both *OsAP2.2* and *OsWRKY24* was observed in panicles and lamina joints of *osbul1* plants (**Supplementary Figure [S2](#SM2){ref-type="supplementary-material"}**). Additionally, panicle morphology of transgenic rice was affected by the two transgenes: panicle branches were spread and grain size was also increased (**Supplementary Figure [S3C](#SM3){ref-type="supplementary-material"}**). Elongated epidermal cells of lemma were also observed with higher expression level of genes involved in cell elongation such as *OsExpansin* (*OsEXP*) genes, *OsXyloglucan endotransglucosylase/hydrolase1* (*OsXTH1*) and *Osxyloglucan endotransglycosylase related1* (*OsXTR1*) in spikelets of transgenic rice plants (**Supplementary Figure [S6](#SM6){ref-type="supplementary-material"}**; [@B6]; [@B30]; [@B9]). {#F6} Discussion ========== Controlling leaf angle and grain size of crop plants occupies a key position in the generation of elite lines with desirable agronomic traits in crop breeding programs. However, the mechanisms regulating the traits remain largely unknown. In this work, we identified putative genes acting downstream of *OsBUL1* for a positive effect on lamina inclination and grain size. First, with a view to investigating the downstream genes of *OsBUL1*, collection and comparison of transcriptomes of collars and panicles from WT and *osbul1* were conducted through microarray hybridization and, *OsBDG1* was selected as a putative downstream gene of *OsBUL1*. The expression of *OsBDG1* was reduced both in collars and panicles of *osbul1* and conversely increased in overexpressing plants and gain-of-function mutant of *OsBUL1*. Previously, *OsBDG1* was shown to be upregulated in transgenic rice ectopically expressing a sterol C-22 hydroxylase that controls BR levels in plants ([@B34]). Also, *OsBDG1* encodes a novel small protein with a rare structural feature; an LRR N-terminal domain (LRRNT) at the N-terminal part and three LRRs toward its carboxyl terminus. In this study, *OsBDG1* transcripts were shown to accumulate in response to BL and transgenic rice plants with overexpression and reduced expression of *OsBDG1* exhibited higher and lower sensitivities to BL, respectively, in lamina joint inclination bioassays (**Supplementary Figure [S4](#SM4){ref-type="supplementary-material"}**). Transgenic rice plants with increased expression of *OsBDG1* driven by *ubiquitin* promoter or *OsBUL1* promoter had phenotypes similar to those of rice plants including gain-of-function mutants of *OsBDG1, OsBUL1* and *OsBUL1* overexpressors ([@B14]) whereas *OsBDG1*-dsRNAi lines displayed similar phenotypes to *osbul1* in lamina inclination and grain size implying correlation between the expression and functional cascade between the two genes, although we cannot exclude the possibility of their having parallel genetic pathways. Sequentially, two genes encoding nuclear proteins, *OsAP2* and *OsWARKY24* were identified as being downstream of *OsBDG1* in the lamina joint based on expression analyses of p*OsBUL1*:*OsBDG1* plants. Moreover, the expression level of the two genes was lower in *osbul1* as well as *OsBDG1* knockdown lines demonstrating an expression cascade among *OsBUL1, OsBDG1, OsAP2*, and *OsWRKY24* genes (**Supplementary Figures [S2](#SM2){ref-type="supplementary-material"}**). Recently, it was reported that *SMALL ORGAN SIZE1* (*SMOS1*) encoding an AP2-type transcriptional factor acts as an auxin-dependent regulator for cell expansion during organ size control ([@B2]) and SHOEBOX (SHB), another AP2/ERF transcription factor directly activates transcription of the GA biosynthesis gene *KS1* for the elongation of meristem cells in a developmental stage-specific manner ([@B24]). Moreover, [@B32] reported that OsWRKY11, a WRKY transcription factor, also regulates leaf inclination by analyzing a leaf angle mutant *large leaf angles* (*lla*), a T-DNA insertion mutant of *OsWRKY11*. Intriguingly, both *OsAP2.2* and *OsWARKY24* genes are upregulated by GA3 and slightly by BL and each protein exhibits transcriptional activation activity indicating that OsAP2.2 and OsWRKY24 may act as transcriptional activators to regulate the expression of downstream genes by phytohormones such as GA3 and/or BL. Functional characterization of the two genes by analyzing transgenic rice plants expressing each gene in the place where *OsBUL1* is expressed also suggests that they influence cell elongation in a positive manner. Thus, we found expressional and putative functional relationships of genes involved in the promotion of cell elongation for increased lamina inclination and grain size of rice although it remains unknown whether direct regulation is available among these genes (**Figure [6D](#F6){ref-type="fig"}**). It would be of value to examine transcripts affected by the two transcription factors, OsAP2.2 and OsWRKY24 in the lamina joint of rice. The next challenge is to produce rice plants with erect leaves and larger grain size. A trial for reduced expression of genes such as *OsBUL1* and/or *OsBDG1* under the control of *OsBC1* promoter ([@B14]) is worth conducting to test whether rice plants can exhibit an erect leaf trait without compromising on the grain size. Conclusion ========== We have identified a series of novel rice genes related to increased lamina inclination and grain size based on exploitation of their expressional relationships and evaluated their functional roles by molecular genetic approaches. These results indicate that they are good candidates that may be further studied or used together with proper promoters for improving crop productivity through desirable plant architecture in the future. Accession Numbers ================= Genes in this article can be found in the GenBank/EMBL or RiceGE databases under the following accession numbers: *OsAP2* ([Os10g41330](Os10g41330)), *OsBDG1* ([Os11g31530](Os11g31530)), *OsBUL1* ([Os02g51320](Os02g51320)), *OsEXPA1* ([Os04g15840](Os04g15840)), *OsEXPA2* ([Os01g60770](Os01g60770)), *OsEXPA3* ([Os05g19570](Os05g19570)), *OsEXPA4* ([Os05g39990](Os05g39990)), *OsWRKY24* ([Os01g61080](Os01g61080)), *OsXTH1* ([Os04g51460](Os04g51460)), *OsXTR1* ([Os11g33270](Os11g33270)). GEO accession number for microarray data in this study is [GSE93817](GSE93817). Author Contributions ==================== SJ designed the experiments. SJ and H-YL performed the experiments, analyzed the data. SJ wrote the article. Conflict of Interest Statement ============================== The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. **Funding.** This research was supported by a core grant from the Biotechnology Center in Southern Taiwan (BCST) of the Agricultural Biotechnology Research Center (ABRC), Academia Sinica, Taiwan to SJ. We thank Dr. Gynheung An (Crop Biotech Institute, Kyung Hee University) for providing the *OsBDG1* activation tagging mutant. We thank Ms. Pei-Chun Liao for rice transformation, Ms. Ching-Han Wang for lamina bending assays and Ms. Mei-Lin Kuo for analyses of microarray data. We also thank members of core facility laboratories of Academia Sinica for microscopy and DNA sequencing and Ms. Miranda Loney for help with English editing. <http://www.phalanxbiotech.com> <http://signal.salk.edu/cgi-bin/RiceGE> <http://www.phalanxbiotech.com> Supplementary Material ====================== The Supplementary Material for this article can be found online at: <http://journal.frontiersin.org/article/10.3389/fpls.2017.01253/full#supplementary-material> ###### Sequence of *OsAP2* genomic clone used for construction of p*OsBUL1*:genomic *OsAP2*. The long transcript of *OsAP2* (*OsAP2.1*) is marked with uppercase and the yellow block is for *OsAP2.2*, a short transcript. Introns are shown in lowercase. Underlined sequences are quantitative PCR primers for *OsAP2.1* and double underlined sequences are for *OsAP2.2*. Start and stop codons are presented with red color. ###### Click here for additional data file. ###### Click here for additional data file. ###### Expression of *OsAP2* and *OsWRKY24* is reduced in *osbul1* plants. **(A)** A heat map showing that the expression level of *OsAP2* and *OsWRKY24* as well as *OsBDG1* is reduced in *osbul1* plants. Color scale represents log signal values. **(B,C)** Experimental confirmation of the expression level of *OsAP2.2* and *OsWRKY24* compared with microarray data in **(A)**. The expression of *OsAP2.2* and *OsWRKY24* is reduced in collars **(D)** and panicles **(E)** of *OsBDG1*-dsRNAi lines without significant alteration of *OsBUL1* expression **(F)**. Data are the average of two or three independent experiments and normalized by *OsUBQ*. Error bars indicate SD. ###### Click here for additional data file. ###### Click here for additional data file. ###### Expression of *OsBUL1* and *OsBDG1* is affected by p*OsBUL1*:*OsWRKY24* and/or p*OsBUL1*:*OsAP2*. **(A)** *OsBUL1* expression is increased by p*OsBUL1*:*OsWRKY24* and p*OsBUL1*:*OsAP2.2* in panicles while *OsBDG1* transcripts **(B)** are accumulated only in p*OsBUL1*:*OsAP2.2* plants. Data are the average of three independent experiments and normalized by *OsUBQ*. Error bars indicate SD. **(C)** Panicle branches exhibit increased angles in p*OsBUL1*:*OsAP2.2* and p*OsBUL1*:*OsWRKY24* transgenic rice plants. Arrowheads indicate nodes for panicles. Bar = 5 cm. Length of grains from the transgenic lines also show a significant increase. (mm; *n* \> 25). (^∗^*P* \< 0.01, Student's *t-*test). ###### Click here for additional data file. ###### Click here for additional data file. ###### Expression pattern of *OsBDG1, OsAP2.2* and *OsWRKY24* analyzed by quantitative RT-PCR and lamina inclination of p*OsBUL1*:*OsBDG1* and *OsBDG1*-dsRNAi plants in lamina bending assays. **(A)** Spatiotemporal expression patterns of genes studied. Error bars indicate SD of three technical repeats. **(B)** Expression analyses of genes with treatment of GA3 and BL at 24 h time points after treatment. Data are the average of three or four independent experiments and normalized by *OsUBQ* or *OsAct*. Error bars indicate SD of three biological replicates. Differences between the mock and hormone treated samples are highlighted with ^∗^*P* \< 0.01; ^∗∗^*P* \< 0.05 with Student's *t-*test. **(C)** Lamina joint inclination bioassays with various concentrations of BL. ###### Click here for additional data file. ###### Click here for additional data file. ###### Subcellular localization of proteins. **(A)** YFP:OsBDG1 and CFP:OsBC1 were co-transformed into rice protoplasts. OsBDG1 is localized in the cytoplasm as well as the nucleus while OsBC1 ([@B14]) is only found in the nucleus. **(B)** CFP:OsBDG1 and YFP:OsBUL1 were co-transformed into rice protoplasts. OsBDG1 and OsBUL1 are co-localized in the cell. **(C,D)** CFP:OsAP2.2 and CFP:OsWRKY24 are localized in the nucleus. Bar = 5 μm. ###### Click here for additional data file. ###### Click here for additional data file. ###### Morphological alteration of epidermal cells of lemma from p*OsBUL1*:*OsAP2.2* and p*OsBUL1*:*OsWRKY24* and expression pattern of genes involved in cell elongation. **(A)** Elongated epidermal cells of lemma from p*OsBUL1*:*OsAP2.2* and p*OsBUL1*:*OsWRKY24* transgenic plants compared to those of WT. Bar = 100 μm. **(B)** Expression of genes involved in cell elongation in spikelets of transgenic lines. Data are the average of three independent experiments and normalized by *OsAct*. Error bars indicate SD. **(C)** Transcriptional activation activity analyses of OsAP2.2 and OsWRKY24. Unlike BD-OsBDG1, both BD-OsAP2.2 and BD-OsWARK24 fusion proteins displayed a transcriptional activation activity in the yeast system described by [@B15]. ###### Click here for additional data file. ###### Click here for additional data file. ###### Primers used for expression analyses in this study. ###### Click here for additional data file. ###### Click here for additional data file. [^1]: Edited by: *Hiroshi Takatsuji, National Agriculture and Food Research Organization (NARO), Japan* [^2]: Reviewed by: *Eiji Nambara, University of Toronto, Canada; Robert Henry, The University of Queensland, Australia; Yukihiro Ito, Tohoku University, Japan* [^3]: This article was submitted to Plant Genetics and Genomics, a section of the journal Frontiers in Plant Science

538 F.2d 313 Ramirezv.People to People Health Foundation, Inc. No. 75-7567, 75-7595 United States Court of Appeals, Second Circuit 4/2/76 1 S.D.N.Y. 2 AFFIRMED* * Oral opinion delivered in open court in the belief that no jurisprudential purpose would be served by a written opinion. An oral opinion or a summary order is not citable as precedent. Local Rule Sec. 0.23

Jeff McLane, Inquirer Staff Writer Safety Nate Allen did not practice Friday because of a left hamstring injury he suffered the day before. If he can't play Monday night against the Saints, David Sims will start in his place, Eagles coach Andy Reid said. Allen said that he injured his hamstring during Thursday's practice. He injured his other hamstring in the fourth quarter of the overtime loss to the Lions on Oct. 14 and was replaced by Colt Anderson. Allen returned two weeks later, after the bye, and played the entire game against the Falcons. Allen has three days to get ready for Monday night's game against the Saints. The Eagles practice again on Saturday, have a walk-through on Sunday and then fly to New Orleans immediately afterward. Anderson had several issues in short relief of Allen against the Detroit, so Sims is now ahead of him on the depth chart. Guard Danny Watkins (ankle) and wide receiver Mardy Gilyard (hamstring) were the only other Eagles to not practice on Friday. Defensive tackle Cullen Jenkins (knee) returned after sitting out a day and defensive tackle Mike Patterson continues to make progress toward a return after January brain surgery. We encourage respectful comments but reserve the right to delete anything that doesn't contribute to an engaging dialogue. Help us moderate this thread by flagging comments that violate our guidelines. Comment policy: Philly.com comments are intended to be civil, friendly conversations. Please treat other participants with respect and in a way that you would want to be treated. You are responsible for what you say. And please, stay on topic. If you see an objectionable post, please report it to us using the "Report Abuse" option. Please note that comments are monitored by Philly.com staff. We reserve the right at all times to remove any information or materials that are unlawful, threatening, abusive, libelous, defamatory, obscene, vulgar, pornographic, profane, indecent or otherwise objectionable. Personal attacks, especially on other participants, are not permitted. We reserve the right to permanently block any user who violates these terms and conditions. Additionally comments that are long, have multiple paragraph breaks, include code, or include hyperlinks may not be posted.