title: Xena: Warrior Princess

text: Other major antagonists of the show include Caesar and Alti, a Roman official and shamaness respectively. Caesar's first appearance was in the second-season episode "Destiny." He is introduced as a young Roman patrician brimming with arrogance - so much so, that when he is captured by Xena and her pirates he is not afraid. When threatened by Xena he tells her """I know what I'm fated to do with my life.""" He pretends to let Xena seduce him, when in reality she is the one being seduced. This ultimately leads to her capture and crucifixion at his hands, and he orders his men to break her legs - an extremely painful memory that is often revisited during the series. Caesar's betrayal fills her with rage, and is the catalyst for her transition from pirate to warlord.


title: Xena: Warrior Princess

text: Alti is an evil shamaness from the Northern Amazon tribes of Siberia, who had been driven out of her tribe because of her hunger for power. She is one of the most influential people encountered by Xena in her dark days, and possesses a wealth of spiritual powers, including travelling to the spiritual realm. Alti is probably best known for her trademark "stare", which brings up pain and suffering from the target's life and unleashes the torment once again (in the form of both pain and physical symptoms). When she "stares" at Xena, Xena often feels the pain of her legs being broken, her back being snapped, and a crippling barrage of attacks from her worst enemies. As Alti grows in power during the series, she can also conjure up pain and suffering from a person's future, and from their future lives. This power backfires early in Season 4, when she shows Xena a vision from her future, of her and Gabrielle being crucified on Mount Amarro. Xena realizes that Gabrielle must still be alive, and this gives her the strength to defeat Alti.


title: Xena: Warrior Princess

text: Over the course of the series, viewers were also introduced to family members of both Xena and Gabrielle, but most notably featured their children. Xena gave her first child, a son named Solan, to a group of centaurs after the death of his father, Borias, who was killed in combat against a warrior in Xena's employ. Solan never knew that Xena was his mother, however knowing Xena for a long time. While aiding Xena and Boudica to defend Britannia against Caesar, comes into contact with an evil cult that tricks her into killing one of its priestesses, Meridian. Using her, the dark god impregnates Gabrielle just as Xena rescues her. Over the next few days the child grows inside Gabrielle, and she eventually (and quite dramatically) gives birth to a girl, naming her Hope. Even though she is the seed of an evil deity, Gabrielle tells Xena that she is also a part of her and that there must be some good in her as well. Being the daughter of Dahak, she quickly developed supernatural powers, and kills within hours of being born, proving to Xena that there was no chance of saving her. Hope aged amazingly fast, and, mere months after being drifted down a river by her mother, she appeared to be about 9 years old. Despite Gabrielle's hopes that she would "be good", Hope killed Xena's son Solan before being poisoned by Gabrielle herself.


title: Xena: Warrior Princess

text: During the episode "", at the end of season 4, Xena and Gabrielle were crucified by the Romans, as Caesar is betrayed and killed by Brutus. They are later revived by a mystic named Eli with the spiritual aid of Callisto, who by that time had become an angel; Callisto also engineers a plan to have Xena conceive a daughter after the resurrection, and this child is prophesied to bring about the Twilight of the Olympian gods; this girl was named Eve. To escape the gods' persecution, Xena and Gabrielle fake their deaths, but their plan goes awry when Ares buries them in an ice cave where they sleep for 25 years; during that time, Eve is adopted by the Roman nobleman Octavius and grows up to become Livia, the Champion of Rome, and a ruthless persecutor of Eli's followers. After her return, Xena is able to turn Livia to repentance, and Livia takes back the name Eve and becomes the Messenger of Eli. After Eve's cleansing by baptism, Xena is granted the power to kill gods as long as her daughter lives. In a final confrontation, the Twilight comes to pass when Xena kills most of the gods on Olympus to save her daughter, and is herself saved by Ares when he gives up his immortality to heal the badly injured and dying Eve and Gabrielle.


title: Xena: Warrior Princess

text: The vast majority of locations in the series are fictional. However, a few locations in the plot are centered on real Ancient Greek towns, including:


title: Xena: Warrior Princess

text: Xena – the main character of the show – was born in the city of Amphipolis in northern Greece. Xena and her best friend, Gabrielle, frequently visited there over the course of the series and it was referenced often. Xena described Amphipolis as "full of life", although several times it was full of death: for instance, the city became a breeding ground for demons after Xena and Gabrielle returned from their twenty-five-year sleep. Mephistopheles, the King of Hell, had captured the soul of Xena's mother Cyrene and imprisoned her in Hell.


title: Xena: Warrior Princess

text: In the backstory of the show, ten years ago Xena had set out to become a warrior to protect Amphipolis from attacks by a warlord called Cortese.


title: Xena: Warrior Princess

text: This was the journey that turned her into a fierce fighter with an evil reputation. When she was inspired to fight for good, she returned to Amphipolis, seeking a reunion with her mother. Along the way, she met Gabrielle in Potidaea.


title: Xena: Warrior Princess

text: In a fictionalized conversation between Julius Caesar and Xena in the "Destiny" episode in , Xena tells him Stageira "is the ancient enemy of my homeland, Amphipolis."


title: Xena: Warrior Princess

text: was born in Potidaea in Chalkidiki, Greece, which features many times as a rural village, which should have been portrayed as a fishing village. Many pivotal episodes are based here, including the series premiere, "Sins of The Past", and "A Family Affair".


title: Xena: Warrior Princess

text: Joxer was brought up in the city of Athens, capital of Greece, and it is often mentioned in passing. Xena and Gabrielle rarely pass through it, but it was the main setting for the clip show "Athens City Academy of the Performing Bards", and was nearly visited in "One Against an Army" and "Blind Faith".


title: Xena: Warrior Princess

text: Callisto is from Cirra in Phocis, central Greece. Xena's army torched the village when Callisto was a child, killing most of her family. Xena and Gabrielle only visit Cirra once, although it is mentioned often.


title: Xena: Warrior Princess

text: In addition to Greece, Xena and Gabrielle visit many countries during their travels, including Italy (usually referred to by its capital, Rome), China, (called Chin), Japan (known as Jappa, only seen in the finale, and mentioned in passing in "Who's Gurkhan"), Great Britain (known as Brittania), India, Siberia, Egypt (called 'The Land of the Pharaohs'), Sahara, Morocco (in "Who's Gurkhan" and "Legacy") and several Scandinavian countries (called 'Norseland').


title: Xena: Warrior Princess

text: To remain in keeping with the ancient world, and to avoid using modern names, the script often removed the last letter of a country's name, changing China to Chin, and Japan to Jappa.


title: Xena: Warrior Princess

text: There have been numerous "Xena" spin-offs into various media, including films, books, comics and video games.


title: Xena: Warrior Princess

text: "", a direct-to-video animated movie, was released in January 1998. The film features the voices of actors from both "" and "Xena: Warrior Princess" – including Lucy Lawless, Kevin Sorbo, Michael Hurst and Renee O'Connor. The plot involves Hercules' mother being kidnapped by Zeus and the release of the Titans. Xena and Gabrielle have supporting roles in the movie.


title: Xena: Warrior Princess

text: Since the end of the series, rumors have circulated that a feature-length movie was in the works. In 2003, screenwriter Katherine Fugate was approached for the project, and was quoted saying that she expected the start of production to be three to five years away, which suggested a release sometime between 2006 and 2009. Actress Lucy Lawless was quoted in several interviews saying she would be interested in participating in a "Xena" film as well.


title: Xena: Warrior Princess

text: In April 2009, Robert Tapert stated there was no intention of a live-action "Xena" feature film. "It's something that just won't happen...In twenty years or ten years, in some amount of years, like "McGyver", like "Charlie's Angels", it [could] happen like that [with other actresses]."


title: Xena: Warrior Princess

text: Following the continued online popularity of the show, a global campaign to directly bombard Universal Pictures with requests for a "Xena" movie was launched in April 2013. Over a few days, hundreds of thousands of messages were sent showing support for the production of a "Xena" film starring the original cast. After receiving acknowledgement from Universal Studios' offices in Australia, Finland, and Spain, campaign efforts were rewarded in May 2013 when Lucy Lawless stated on her Twitter account that she had been contacted by a "chap who wants to re-invigorate the #Xena brand", while warning fans that "there's a lot of red tape around #XWP so don't get your knickers in a twist. It may come back in a different form". Since then, Lucy Lawless has appeared on multiple televised interviews showing her support of a potential revival of the "Xena" franchise, stating that talks are currently underway to resolve legal issues impeding the progress of a potential "Xena" movie project.


title: Xena: Warrior Princess

text: Many books have been released as tie-ins, including "The Official Guide to the Xenaverse" by Robert Weisbrot. This includes a detailed episode guide for the first two seasons, a look behind the scenes, the story of the origin of the show, biographies of cast and crew, and trivia about the show. After the sixth and final season, "Xena Warrior Princess: Complete Illustrated Companion" was published.


title: Xena: Warrior Princess

text: In 1998, "XENA: All I Need to Know I Learned From the Warrior Princess", was published, allegedly written by Gabrielle, Bard of Potidaea and "translated" by Josepha Sherman. In it, Gabrielle writes enthusiastically about many of the lessons that she learned. For example, in a chapter entitled "Anything can be a weapon- Anything!", she instructs the reader on fighting with unconventional weapons; in another, "Nobody Likes a Winer", she bemoans the perils of alcohol.


title: Xena: Warrior Princess

text: There have been a number of novelizations by authors such as Martin H. Greenberg, and fiction such as "The Empty Throne", "The Huntress and The Sphinx", "The Thief of Hermes", and "Prophecy of Darkness." The series has also figured in many doctoral theses, including a thesis by French/American scholar, Dr. Anne Sweet, "Girl Power Interrogated in Xena Warrior Princess and Charmed, Social and Economic Issues at Play in the Politics of Gender".


title: Xena: Warrior Princess

text: There have been a number of . The earliest ones were released by Topps Comics and Dark Horse Comics (written by Ian Edginton and John Wagner). More recently the license has moved to Dynamite Entertainment.


title: Xena: Warrior Princess

text: Anchor Bay Entertainment released all 6 seasons of "Xena: Warrior Princess" on DVD in Region 1 between 2003 and 2005, with a wide range of extras. As of 2010, these releases have been discontinued.


title: Xena: Warrior Princess

text: On January 12, 2010, Universal Studios Home Entertainment announced plans to re-release "Xena: Warrior Princess" on DVD. They have subsequently re-released all six seasons. A complete series set was released on May 17, 2016.


title: Xena: Warrior Princess

text: In Region 2 & 4, Universal Pictures released the entire series on DVD. In addition, a complete series collection was released on DVD in Region 2 on October 8, 2007.


title: Xena: Warrior Princess

text: On Rotten Tomatoes, the first season has a rating of 89%, based on 9 reviews, with an average rating of 8/10. The site's critical consensus reads, "Lucy Lawless exudes steely charisma in "Xena: Warrior Princess", a swashbuckling actioner that transcends its origin as a spinoff and becomes a fully realized saga in its own right." Ken Tucker of "Entertainment Weekly", giving the season a B+: "Xena is Wonder Woman on steroids, and Lawless — with her dark bangs, moon face, light blue eyes, and small, grim smiles — plays the warrior princess with barely concealed delight."


title: Xena: Warrior Princess

text: "Xena" has enjoyed a particular cult status in the lesbian community. Some of the lesbian fan base see Xena and Gabrielle as a couple and have embraced them as role models and lesbian icons. A group called The Marching Xenas has participated in many gay and lesbian Pride parades. Xena's popularity was successfully utilized by Subaru when trying to establish a healthy base of lesbian customers: one ad had a car with the license plate "XENA LVR" (Xena lover).


title: Xena: Warrior Princess

text: A subject of much interest and debate among viewers is the question of whether Xena and Gabrielle are lovers. The issue is left deliberately ambiguous by the writers. Jokes, innuendo, and other subtle evidence of a romantic relationship between Xena and Gabrielle is referred to as "lesbian subtext" or simply "subtext" by fans. The issue of the true nature of the Xena/Gabrielle relationship caused intense "shipping" debates in "Xena" fandom, which turned especially impassioned due to spillover from real-life debates about same-sex sexuality and gay rights.


title: Xena: Warrior Princess

text: Many fans felt that the sexual nature of Xena and Gabrielle's relationship was cemented by an interview given by Lucy Lawless to "Lesbian News" magazine in 2003. Lawless stated that after the series finale, where Gabrielle revives Xena with a mouth-to-mouth water transfer filmed to look like a full kiss, she had come to believe that Xena and Gabrielle's relationship was "definitely gay". "There was always a, 'Well, she might be or she might not be' but when there was that drip of water passing between their lips in the very final scene, that cemented it for me. Now it wasn't just that Xena was bisexual and kinda liked her gal pal and they kind of fooled around sometimes, it was 'Nope, they're married, man'."


title: Xena: Warrior Princess

text: The "Xena" fandom also popularized the term altfic (from "alternative fiction") to refer to same-sex romantic fan fiction.


title: Xena: Warrior Princess

text: In 2006, Lucy Lawless donated her personal Xena costume to the National Museum of American History. In an interview the same year with "Smithsonian" magazine, she was asked the question "Was the Warrior Princess outfit comfortable?" and responded:


title: Xena: Warrior Princess

text: Uberfic is a variety of fan fiction in which the characters live in an alternate universe. The characters and events are true to the original canon, but usually in a different time period, often as the ancestors, descendants, or reincarnations of canon characters. The term originated in "Xena" fandom. Uber was employed several times in the series, beginning with the second-season episode "The Xena Scrolls", in which the descendants of Xena, Gabrielle and Joxer meet up at an archeological dig in 1940 and unwittingly release Ares from his tomb.


title: Xena: Warrior Princess

text: On July 20, 2015, it was reported that NBC was developing a "Xena" reboot series, with Raimi and Tapert returning as executive producers, with the show's debut sometime in 2016. Insiders also requested that Lawless return to the series as Xena, as well as take up a role in the show's production. A day later, Lawless tweeted that the reboot was a rumor. On August 13, 2015, NBC Entertainment chairman Bob Greenblatt confirmed the reboot was in development. "Entertainment Weekly" announced that Javier Grillo-Marxuach would serve as writer and producer for the reboot.


title: Xena: Warrior Princess

text: In a post on Tumblr, Grillo-Marxuach stated that they would be "fully exploring a relationship that could only be shown subtextually in first-run syndication in the 1990s," which several websites such as "The Guardian" and "Newsweek" took to mean "Xena will be an out and proud lesbian." These articles resulted in frustration from fans regarding the apparent erasure of Xena's bisexuality, but Grillo-Marxuach answered "it feels like - from a few sentences - everyone has already made up their mind about what it is I am doing. I would prefer people be surprised by the story." In April 2017, Grillo-Marxuach announced that he had left the project because of "insurmountable creative differences."


title: Xena: Warrior Princess

text: On August 21, 2017, NBC announced that it had cancelled its plans for the reboot. NBC Entertainment president Jennifer Salke said, "I'd never say never on that one because it's such a beloved title but the current incarnation of it is dead."


title: Galicia (Eastern Europe)

text: Galicia () ( ; ; ) is a historical and geographic region spanning what is now southeastern Poland and western Ukraine, long part of the Polish–Lithuanian Commonwealth. It covers much of such historic regions as Red Ruthenia (centered on Lviv) and Lesser Poland (centered on Kraków).


title: Galicia (Eastern Europe)

text: The name of the region derives from the medieval city of Halych, and was first mentioned in Hungarian historical chronicles in the year 1206 as "Galiciæ". The eastern part of the region was controlled by the medieval Kingdom of Galicia and Volhynia. In 1253, Prince Daniel of Galicia was crowned the King of Rus () or King of Ruthenia following the Mongol invasion of Kievan Rus'. In 1352, the Kingdom of Poland annexed the Kingdom of Galicia and Volhynia as the Ruthenian Voivodeship (). During the partitions of Poland, it was incorporated into a crown land of the Austrian Empire – the Kingdom of Galicia and Lodomeria.


title: Galicia (Eastern Europe)

text: The nucleus of historic Galicia lies within the modern regions of western Ukraine: the Lviv, Ternopil, and Ivano-Frankivsk oblasts near Halych. In the 18th century, territories that later became part of the modern Polish regions of the Lesser Poland Voivodeship, Subcarpathian Voivodeship, and Silesian Voivodeship were added to Galicia after the collapse of the Polish-Lithuanian Commonwealth.


title: Galicia (Eastern Europe)

text: Eastern Galicia became contested ground between Poland and Ruthenia in medieval times and was fought over by Poland and Ukraine in the 20th century. In the 10th century, several cities were founded there, such as Volodymyr and Jaroslaw, whose names mark their connections with the Grand Princes of Kiev. There is considerable overlap between Galicia and Podolia (to the east) as well as between Galicia and south-west Ruthenia, especially in a cross-border region (centred on Carpathian Ruthenia) inhabited by various nationalities and religious groups.


title: Galicia (Eastern Europe)

text: Halych-Volhynia had cut a swathe as a mighty principality under the rule of Prince Roman the Great (Roman Mstislavich), a member of the Rurik dynasty from 1170 to 1205. Andrew II, King of Hungary from 1205 to 1235, claimed the title " ("King of Galicia and Lodomeria") – a Latinised version of the Slavic names Halych and Volodymyr, the major cities of the principality of Halych-Volhynia, which the Hungarians ruled from 1214 to 1221. After the expulsion of the Hungarians in 1221, Ruthenians took back rule of the area. Roman's son Daniel of Galicia (Prince of Galicia until 1255) was crowned king of Halych-Volhynia in 1253. About 1247 Daniel of Galicia founded Lviv (), named in honour of his son Leo I, who later moved the capital northwestwards from Halych to Lviv in 1272.


title: Galicia (Eastern Europe)

text: The Ukrainian name ' () (' in Polish, in Russian, ' in Latin) comes from the Khwalis or Kaliz who occupied the area from the time of the Magyars. They were also called ' in Greek, and " () in Ukrainian. Some historians speculated that the name had to do with a group of people of Thracian origin (i.e. Getae) who during the Iron Age moved into the area after the Roman conquest of Dacia in 106 CE and may have formed the Lypytsia culture with the Venedi people who moved into the region at the end of Le Tène period (La Tène culture). The Lypytsia culture supposedly replaced the existing Thracian Hallstatt (see Thraco-Cimmerian) and Vysotske cultures. Connection with Celtic peoples supposedly explains the relation of the name "Galicia" to many similar place names found across Europe and Asia Minor, such as ancient or Gaul (modern France, Belgium, and northern Italy), Galatia (in Asia Minor), the Iberian Peninsula's Galicia, and Romanian .Some other scholars assert that the name "Halych" has Slavic origins – from "halytsa", meaning "a naked (unwooded) hill", or from "halka" which means "jackdaw".


title: Galicia (Eastern Europe)

text: The name, however, predates the coat of arms, which may represent canting or simply folk etymology). Although Ruthenians drove out the Hungarians from Halych-Volhynia by 1221, Hungarian kings continued to add "" to their official titles.


title: Galicia (Eastern Europe)

text: In 1349, in the course of the Galicia–Volhynia Wars, King Casimir III the Great of Poland conquered the major part of Galicia and put an end to the independence of this territory. Upon the conquest Casimir adopted the following title: Casimir by the grace of God king of Poland and Rus (Ruthenia), lord and heir of the land of Kraków, Sandomierz, Sieradz, Łęczyca, Kuyavia, Pomerania (Pomerelia). . Following the death of Casimir in 1370, Poland entered into a personal union with Hungary (1370–1382) and Ruthenia (Galicia) came under the rule of a Ruthenian lord, Vladislaus II of Opole, appointed by the King of Hungary. Later Galicia was ruled for a short time by various Hungarian voivodes of Ruthenia.


title: Galicia (Eastern Europe)

text: Under the Jagiellonian dynasty (Kings of Poland from 1386 to 1572), the Kingdom of Poland revived and reconstituted its territories. In place of historic Galicia there appeared the Ruthenian Voivodeship.


title: Galicia (Eastern Europe)

text: In 1526, after the death of Louis II of Hungary, the Habsburgs inherited the Hungarian claims to the titles of the Kingship of Galicia and Lodomeria, together with the Hungarian crown. In 1772 the Habsburg Empress Maria Theresa, Archduchess of Austria and Queen of Hungary, used those historical claims to justify her participation in the First Partition of Poland. In fact, the territories acquired by Austria did not correspond exactly to those of former Halych-Volhynia – the Russian Empire took control of Volhynia to the north-east, including the city of Volodymyr-Volynskyi () – after which Lodomeria was named. On the other hand, much of Lesser Poland – and (1772–1918), (1772–1809), (1795–1809), and (1846–1918) – became part of Austrian Galicia. Moreover, despite the fact that Austria's claim derived from the historical Hungarian crown, "Galicia and Lodomeria" were not officially assigned to Hungary, and after the of 1867, the territory found itself in Cisleithania, or the Austrian-administered part of Austria-Hungary.


title: Galicia (Eastern Europe)

text: The full official name of the new Austrian territory was the Kingdom of Galicia and Lodomeria with the Duchies of and Zator. After the incorporation of the Free City of Kraków in 1846, it was extended to "Kingdom of Galicia and Lodomeria, and the Grand Duchy of Kraków with the Duchies of Auschwitz and Zator" ().


title: Galicia (Eastern Europe)

text: Each of those entities was formally separate; they were listed as such in the Austrian emperor's titles, each had its distinct coat-of-arms and flag. For administrative purposes, however, they formed a single province. The duchies of Auschwitz () and Zator were small historical principalities west of , on the border with Prussian Silesia. Lodomeria, under the name Volhynia, remained under the rule of the Russian Empire – see Volhynian Governorate.


title: Galicia (Eastern Europe)

text: In Roman times, the region was populated by various tribes of Celto-Germanic admixture, including Celtic-based tribes – like the "Galice" or "Gaulics" and "Bolihinii" or "Volhynians" – the Lugians and Cotini of Celtic, Vandals and Goths of Germanic origins (the Przeworsk and Púchov cultures). During the Great Migration period of Europe (coinciding with the fall of the Roman Empire), a variety of nomadic groups invaded the area, but overall, the East Slavic tribes White Croats and Tivertsi dominated the area since the 6th century until were annexed to Kievan Rus' in the 10th century.


title: Galicia (Eastern Europe)

text: In the 12th century, a Rurikid Principality of Halych (Halicz, Halics, Galich, Galic) formed there, which merged at the end of the century with the neighbouring Volhynia into the Kingdom of Ruthenia. Galicia and Volhynia had originally been two separate Rurikid principalities, assigned on a rotating basis to younger members of the Kievan dynasty. The line of Prince Roman the Great of Vladimir-in-Volhynia had held the principality of Volhynia, while the line of Yaroslav Osmomysl held the Principality of Halych (later adopted as Galicia). Galicia–Volhynia was created following the death in 1198 or 1199 (and without a recognised heir in the paternal line) of the last Prince of Galicia, Vladimir II Yaroslavich; Roman acquired the Principality of Galicia and united his lands into one state. Roman's successors would mostly use Halych (Galicia) as the designation of their combined kingdom. In Roman's time Galicia–Volhynia's principal cities were Halych and Volodymyr-in-Volhynia. In 1204, Roman captured Kiev, while being in alliance with Poland, he signed a peace treaty with Hungary and established diplomatic relations with the Byzantine Empire.


title: Galicia (Eastern Europe)

text: In 1205, Roman turned against his Polish allies, leading to a conflict with Leszek the White and Konrad of Masovia. Roman was subsequently killed in the Battle of Zawichost (1205), and his dominion entered a period of rebellion and chaos. Thus weakened, Galicia–Volhynia became an arena of rivalry between Poland and Hungary. King Andrew II of Hungary styled himself "", Latin for "king of Galicia and Vladimir [in-Volhynia]", a title that later was adopted in the House of Habsburg. In a compromise agreement made in 1214 between Hungary and Poland, the throne of Galicia–Volhynia was given to Andrew's son, Coloman of Lodomeria.


title: Galicia (Eastern Europe)

text: In 1352, when the principality was divided between the Polish Kingdom and the Grand Duchy of Lithuania, the territory became subject to the Polish Crown. With the Union of Lublin in 1569 Poland and Lithuania merged to form the Polish–Lithuanian Commonwealth, which lasted for 200 years until conquered and divided up by Russia, Prussia, and Austria.


title: Galicia (Eastern Europe)

text: In 1772 with the partition of the Polish–Lithuanian Commonwealth, the south-eastern part of the former Polish–Lithuanian Commonwealth was awarded to the Habsburg Empress Maria-Theresa, whose bureaucrats named it the Kingdom of Galicia and Lodomeria, after one of the titles of the princes of Hungary, although its borders coincided but roughly with those of the former medieval principality. Known informally as Galicia, it became the largest, most populous, and northernmost province of the Austrian Empire, while after 1867 part of the Austrian half of Austria-Hungary, until the dissolution of the monarchy at the end of World War I in 1918, when it ceased to exist as a geographic entity.


title: Galicia (Eastern Europe)

text: During the First World War, Galicia saw heavy fighting between the forces of Russia and the Central Powers. The Russian forces overran most of the region in 1914 after defeating the Austro-Hungarian army in a chaotic frontier battle in the opening months of the war. They were in turn pushed out in the spring and summer of 1915 by a combined German and Austro-Hungarian offensive.


title: Galicia (Eastern Europe)

text: In 1918, Western Galicia became a part of the restored Republic of Poland, which absorbed the Lemko-Rusyn Republic. The local Ukrainian population briefly declared the independence of Eastern Galicia as the "West Ukrainian People's Republic". During the Polish-Soviet War the Soviets tried to establish the puppet-state of the Galician SSR in East Galicia, the government of which after a couple of months was liquidated.


title: Galicia (Eastern Europe)

text: The fate of Galicia was settled by the Peace of Riga on 18 March 1921, attributing Galicia to the Second Polish Republic. Although never accepted as legitimate by some Ukrainians, it was decided by the Conference of Ambassadors on 14 March 1923 and internationally recognized on 15 May 1923.


title: Galicia (Eastern Europe)

text: The Ukrainians of the former eastern Galicia and the neighbouring province of Volhynia made up about 12% of the Second Polish Republic population, and were its largest minority. As Polish government policies were unfriendly towards minorities, tensions between the Polish government and the Ukrainian population grew, eventually giving rise to the militant underground Organization of Ukrainian Nationalists.


title: Galicia (Eastern Europe)

text: In 1773, Galicia had about 2.6 million inhabitants in 280 cities and market towns and approximately 5,500 villages. There were nearly 19,000 noble families, with 95,000 members (about 3% of the population). The serfs accounted for 1.86 million, more than 70% of the population. A small number were full-time farmers, but by far the overwhelming number (84%) had only smallholdings or no possessions.


title: Galicia (Eastern Europe)

text: Galicia had arguably the most ethnically diverse population of all the countries in the Austrian monarchy, consisting mainly of Poles and "Ruthenians"; the peoples known later as Ukrainians and Rusyns, as well as ethnic Jews, Germans, Armenians, Czechs, Slovaks, Hungarians, Roma and others. In Galicia as a whole, the population in 1910 was estimated to be 45.4% Polish, 42.9% Ruthenian, 10.9% Jewish, and 0.8% German. This population was not evenly distributed. The Poles lived mainly in the west, with the Ruthenians predominant in the eastern region ("Ruthenia"). At the turn of the twentieth century, Poles constituted 88% of the whole population of Western Galicia and Jews 7.5%. The respective data for Eastern Galicia show the following numbers: Ruthenians 64.5%, Poles 22.0%, Jews 12%. Of the 44 administrative divisions of Austrian eastern Galicia, Lviv (, ) was the only one in which Poles made up a majority of the population. Anthropologist Marianna Dushar has argued that this diversity led to a development of a distinctive food culture in the region.


title: Galicia (Eastern Europe)

text: Linguistically, the Polish language was predominant in Galicia. According to the 1910 census 58.6% of the combined population of both western and eastern Galicia spoke Polish as its mother tongue compared to 40.2% who spoke a Ruthenian language. The number of Polish-speakers may have been inflated because Jews were not given the option of listing Yiddish as their language. Eastern Galicia was the most diverse part of the region, and one of the most diverse areas in Europe at the time. In 1910, Eastern Galicia had 5.3 million inhabitants, with 39.8% being Polish and 58.9% Ruthenian.


title: Galicia (Eastern Europe)

text: The Jews of Galicia had immigrated in the Middle Ages from Germany. German-speaking people were more commonly referred to by the region of Germany where they originated (such as Saxony or Swabia).


title: Galicia (Eastern Europe)

text: For inhabitants who spoke different native languages, e.g. Poles and Ruthenians, identification was less problematic, but widespread multilingualism blurred the ethnic divisions again.


title: Galicia (Eastern Europe)

text: Religiously, Galicia was predominantly Christian. Catholicism was practiced in two rites. Poles were Roman Catholic, while Ukrainians belonged to the Greek Catholic Church. Judaism represented the third largest religious group, and notably, Galicia was the center of Hasidism.


title: Galicia (Eastern Europe)

text: The new state borders cut Galicia off from many of its traditional trade routes and markets of the Polish sphere, resulting in stagnation of economic life and decline of Galician towns. Lviv lost its status as a significant trade centre. After a short period of limited investments, the Austrian government started the fiscal exploitation of Galicia and drained the region of manpower through conscription to the imperial army. The Austrians decided that Galicia should not develop industrially but remain an agricultural area that would serve as a supplier of food products and raw materials to other Habsburg provinces. New taxes were instituted, investments were discouraged, and cities and towns were neglected. The result was significant poverty in Austrian Galicia. Galicia was the poorest province of Austro-Hungary, and according to Norman Davies, could be considered "the poorest province in Europe".


title: Galicia (Eastern Europe)

text: Near Drohobych and Boryslav in Galicia, significant oil reserves were discovered and developed during the mid 19th and early 20th centuries. The first European attempt to drill for oil was in Bóbrka in western Galicia in 1854. By 1867, a well at Kleczany, in Western Galicia, was drilled using steam to about 200 meters. On 31 December 1872, a railway line linking Borysław (now Boryslav) with the nearby city of Drohobycz (now Drohobych) was opened. British engineer John Simeon Bergheim and Canadian William Henry McGarvey came to Galicia in 1882. In 1883, their company bored holes of 700 to 1,000 meters and found large oil deposits. In 1885, they renamed their oil developing enterprise the Galician-Karpathian Petroleum Company (), headquartered in Vienna, with McGarvey as the chief administrator and Bergheim as a field engineer, and built a huge refinery at Maryampole near Gorlice, south of Tarnow. Considered the biggest, most efficient enterprise in Austro-Hungary, Maryampole was built in six months and employed 1,000 men. Subsequently, investors from Britain, Belgium, and Germany established companies to develop the oil and natural gas industries in Galicia. This influx of capital caused the number of petroleum enterprises to shrink from 900 to 484 by 1884, and to 285 companies manned by 3,700 workers by 1890. However, the number of oil refineries increased from thirty-one in 1880 to fifty-four in 1904. By 1904, there were thirty boreholes in Borysław of over 1,000 meters. Production increased by 50% between 1905 and 1906 and then trebled between 1906 and 1909 because of unexpected discoveries of vast oil reserves of which many were gushers. By 1909, production reached its peak at 2,076,000 tons or 4% of worldwide production. Often called the "Polish Baku", the oil fields of Borysław and nearby Tustanowice accounted for over 90% of the national oil output of the Austro-Hungarian Empire. From 500 residents in the 1860s, Borysław had swollen to 12,000 by 1898. At the turn of the century, Galicia was ranked fourth in the world as an oil producer. This significant increase in oil production also caused a slump in oil prices. A very rapid decrease in oil production in Galicia occurred just before the Balkan Wars of 1912–1913.


title: Leopold and Loeb

text: Nathan Freudenthal Leopold Jr. (November 19, 1904 – August 29, 1971) and Richard Albert Loeb (; June 11, 1905 – January 28, 1936), usually referred to collectively as Leopold and Loeb, were two wealthy students at the University of Chicago who kidnapped and murdered 14-year-old Bobby Franks in Chicago, Illinois, United States, in May 1924. They committed the murder – characterized at the time as "the crime of the century" – hoping to demonstrate superior intellect, which they believed enabled and entitled them to carry out a "perfect crime" without consequences.


title: Leopold and Loeb

text: After the two men were arrested, Loeb's family retained Clarence Darrow as lead counsel for their defense. Darrow's twelve-hour summation at their sentencing hearing is noted for its influential criticism of capital punishment as retributive rather than transformative justice. Both young men were sentenced to life imprisonment plus 99 years. Loeb was murdered by a fellow prisoner in 1936; Leopold was released on parole in 1958. The case has since served as the inspiration for several dramatic works.


title: Leopold and Loeb

text: Nathan Leopold was born on November 19, 1904, in Chicago, Illinois, the son of Florence (née Foreman) and Nathan Leopold, a wealthy German-Jewish immigrant family. A child prodigy, Leopold claimed to have spoken his first words at the age of four months. At the time of the murder, he had completed an undergraduate degree at the University of Chicago with Phi Beta Kappa honors and planned to begin studies at Harvard Law School after a trip to Europe. Leopold had reportedly studied fifteen languages, claimed to speak five fluently, and had achieved a measure of national recognition as an ornithologist. Leopold and several other ornithologists identified the Kirtland's warbler and made astute observations about the parasitic nesting behavior of brown-headed cowbirds, which threatened the warblers. (He evidently maintained his interest in birds after his crime, writing to the Field Museum from his prison cell regarding specimens he had donated.)


title: Leopold and Loeb

text: Richard Loeb was born on June 11, 1905, in Chicago, to the family of Anna Henrietta (née Bohnen) and Albert Henry Loeb, a wealthy lawyer and retired vice president of Sears, Roebuck & Company. His father was Jewish and his mother was Catholic. Like Leopold, Loeb was exceptionally intelligent. With the encouragement of his governess, he skipped several grades in school and became the University of Michigan's youngest graduate at age 17. Loeb was a student at the University of Chicago Law School and was especially interested in doing graduate work in history at the time of the murder.


title: Leopold and Loeb

text: Compared to Leopold, Loeb was not as strictly intellectual; he often socialized, played tennis, and read detective novels.


title: Leopold and Loeb

text: The two young men grew up with their respective families in the affluent Kenwood neighborhood on Chicago's South Side. The Loebs owned a summer estate (now called Castle Farms) in Charlevoix, Michigan, as well as a mansion in Kenwood, two blocks from the Leopold home.


title: Leopold and Loeb

text: Though Leopold and Loeb knew each other casually while growing up, they began to see more of each other in mid-1920, and their relationship flourished at the University of Chicago, particularly after they discovered a mutual interest in crime. Leopold was particularly fascinated by Friedrich Nietzsche's concept of "supermen" ("Übermenschen"), interpreting them as transcendent individuals possessing extraordinary and unusual capabilities, whose superior intellects allowed them to rise above the laws and rules that bound the unimportant, average populace. Leopold believed that he and Loeb were such individuals, and as such, by his interpretation of Nietzsche's doctrines, they were not bound by any of society's normal ethics or rules. In a letter to Loeb, he wrote, "A superman ... is, on account of certain superior qualities inherent in him, exempted from the ordinary laws which govern men. He is not liable for anything he may do." There is considerable evidence, including a letter found during the police raid on Nathan Leopold’s home following the murder of Bobby Franks, that Leopold and Loeb were engaged in a homosexual romantic relationship. Historian Simon Baatz claims “there was an arrangement that Richard would agree to have sex with Nathan, if Nathan accompanied Richard when he did his crimes.”


title: Leopold and Loeb

text: The pair began asserting their perceived immunity from normal restrictions with acts of petty theft and vandalism. Breaking into a fraternity house at the University of Michigan, they stole penknives, a camera, and a typewriter that they later used to type their ransom note. Emboldened, they progressed to a series of more serious crimes, including arson, but no one seemed to notice. Disappointed with the absence of media coverage of their crimes, they decided to plan and execute a sensational "perfect crime" that would garner public attention and confirm their self-perceived status as "supermen".


title: Leopold and Loeb

text: Leopold and Loeb (who were 19 and 18, respectively, at the time) settled on kidnapping and murdering a younger adolescent as their perfect crime. They spent seven months planning everything, from the method of abduction to disposal of the body. To obfuscate the actual nature of their crime and motive, they decided to make a ransom demand, and devised an intricate plan for collecting it involving a long series of complex instructions to be communicated, one set at a time, by phone. They typed the final set of instructions involving the actual money drop in the form of a ransom note, using the typewriter stolen from the fraternity house. A chisel was selected as the murder weapon and purchased.


title: Leopold and Loeb

text: After a lengthy search for a suitable victim, mostly on the grounds of the Harvard School for Boys in the Kenwood area, where Leopold had been educated, the pair decided upon Robert "Bobby" Franks, the 14-year-old son of wealthy Chicago watch manufacturer Jacob Franks. Bobby Franks was Loeb's second cousin and an across-the-street neighbor who had played tennis at the Loeb residence several times.


title: Leopold and Loeb

text: Leopold and Loeb put their plan in motion on the afternoon of May 21, 1924. Using an automobile that Leopold rented under the name Morton D. Ballard, they offered Franks a ride as he walked home from school. The boy initially refused, because his destination was less than two blocks away, but Loeb persuaded him to enter the car to discuss a tennis racket that he had been using. The precise sequence of the events that followed remains in dispute, but a preponderance of opinion placed Leopold behind the wheel of the car while Loeb sat in the back seat with the chisel. Loeb struck Franks, who was sitting in front of him in the passenger seat, several times in the head with the chisel, then dragged him into the back seat and gagged him, where he died.


title: Leopold and Loeb

text: With the body on the floorboard, out of view, the men drove to their predetermined dumping spot near Wolf Lake in Hammond, Indiana, south of Chicago. After nightfall, they removed and discarded Franks' clothes, then concealed the body in a culvert along the Pennsylvania Railroad tracks north of the lake. To obscure the body's identity, they poured hydrochloric acid on the face and genitals to disguise the fact that he had been circumcised.


title: Leopold and Loeb

text: By the time the two men returned to Chicago, word had already spread that Franks was missing. Leopold called Franks's mother, identifying himself as "George Johnson", and told her that Franks had been kidnapped; instructions for delivering the ransom would follow. After mailing the typed ransom note and burning their blood-stained clothing, then cleaning the blood stains from the rented vehicle's upholstery, they spent the remainder of the evening playing cards.


title: Leopold and Loeb

text: Once the Franks family received the ransom note on the following morning, Leopold called a second time and dictated the first set of instructions for the ransom payment. The intricate plan stalled almost immediately when a nervous family member forgot the address of the store where he was supposed to receive the next set of directions, and it was abandoned entirely when word came that Franks's body had been found. Leopold and Loeb destroyed the typewriter and burned a car robe (lap blanket) they had used to move the body. They then went about their lives as usual.


title: Leopold and Loeb

text: Chicago police launched an intensive investigation; rewards were offered for information. While Loeb went about his daily routine quietly, Leopold spoke freely to police and reporters, offering theories to anyone who would listen. He even told one detective, "If I were to murder anybody, it would be just such a cocky little son of a bitch as Bobby Franks."


title: Leopold and Loeb

text: Police found a pair of eyeglasses near Franks's body. Although common in prescription and frame, they were fitted with an unusual hinge purchased by only three customers in Chicago, one of whom was Leopold. When questioned, Leopold offered the possibility that his glasses might have dropped out of his pocket during a bird-watching trip the previous weekend.


title: Leopold and Loeb

text: Leopold and Loeb were summoned for formal questioning on May 29. They asserted that on the night of the murder, they had picked up two women in Chicago using Leopold's car, then dropped them off some time later near a golf course without learning their last names. Their alibi was exposed as a fabrication when Leopold's chauffeur told police that he was repairing Leopold's car while the men claimed to be using it. The chauffeur's wife confirmed that the car was parked in the Leopold garage on the night of the murder. The destroyed typewriter was recovered from the Jackson Park Lagoon on June 7.


title: Leopold and Loeb

text: Loeb was the first to confess. He asserted that Leopold had planned everything and had killed Franks in the back seat of the car while Loeb drove. Leopold's confession followed swiftly thereafter, but he insisted that he was the driver and Loeb the murderer. Their confessions otherwise corroborated most of the evidence in the case. Both confessions were announced by the state's attorney on May 31. Leopold later claimed (long after Loeb was dead) that he pleaded in vain with Loeb to admit to killing Franks. "Mompsie feels less terrible than she might, thinking you did it", he quotes Loeb as saying, "and I'm not going to take that shred of comfort away from her." While most observers believed that Loeb did indeed strike the fatal blows, some circumstantial evidence – including testimony from eyewitness Carl Ulvigh, who said he saw Loeb driving and Leopold in the back seat minutes before the kidnapping – suggested that Leopold could have been the killer.


title: Leopold and Loeb

text: Both Leopold and Loeb admitted that they were driven by their thrill-seeking, "Übermenschen" (supermen) delusions, and their aspiration to commit a "perfect crime". Neither claimed to have looked forward to the killing, but Leopold admitted interest in learning what it would feel like to be a murderer. He was disappointed to note that he felt the same as ever.


title: Leopold and Loeb

text: The trial of Leopold and Loeb at Chicago's Cook County Criminal Court became a media spectacle and the third – after those of Harry Thaw and Sacco and Vanzetti – to be labeled "the trial of the century." Loeb's family hired the renowned criminal defense attorney Clarence Darrow to lead the defense team. It was rumored that Darrow was paid $1 million for his services, but he was actually paid $70,000 (). Darrow took the case because he was a staunch opponent of capital punishment.


title: Leopold and Loeb

text: While it was generally assumed that the men's defense would be based on a plea of not guilty by reason of insanity, Darrow concluded that a jury trial would almost certainly end in conviction and the death penalty. Thus, he elected to enter a plea of guilty, hoping to convince Cook County Circuit Court Judge John R. Caverly to impose sentences of life imprisonment.


title: Leopold and Loeb

text: The trial (technically an extended sentencing, as their guilty pleas had already been accepted) ran for thirty-two days. The state's attorney, Robert E. Crowe, presented over 100 witnesses, documenting details of the crime. The defense presented extensive psychiatric testimony in an effort to establish mitigating circumstances, including childhood neglect in the form of absent parenting, and in Leopold's case, sexual abuse by a governess. One piece of evidence was a letter written by Leopold claiming that he and Loeb were having a homosexual affair. Both the prosecution and the defense interpreted this information as supportive of their own position. Darrow called a series of expert witnesses, who offered a catalog of Leopold's and Loeb's abnormalities. One witness testified to their dysfunctional endocrine glands, another to the delusions that had led to their crime.


title: Leopold and Loeb

text: Darrow's impassioned, twelve-hour-long "masterful plea" at the conclusion of the hearing has been called the finest speech of his career. Its principal arguments were that the methods and punishments of the American justice system were inhumane, and the youth and immaturity of the accused:


title: Leopold and Loeb

text: The judge was persuaded, but he explained in his ruling that his decision was based primarily on precedent and the youth of the accused. On September 10, 1924, he sentenced both Leopold and Loeb to life imprisonment for the murder, and an additional 99 years for the kidnapping. A little over a month later, Loeb's father died of heart failure.


title: Leopold and Loeb

text: Leopold and Loeb initially were held at Joliet Prison. Although they were kept apart as much as possible, the two managed to maintain their friendship. Leopold was transferred to Stateville Penitentiary in 1931, and Loeb was later transferred there as well. Once reunited, the two expanded the prison school system, adding a high school and junior college curriculum.


title: Leopold and Loeb

text: On January 28, 1936, Loeb was attacked by fellow inmate James Day with a straight razor in a shower room; he died soon after in the prison hospital. Day claimed that Loeb had sexually assaulted him, but he was unharmed while Loeb sustained more than fifty wounds, including defensive wounds on his arms and hands. His throat had been slashed from behind. News accounts suggested Loeb had propositioned Day; the authorities, perhaps embarrassed by alleged same-sex behavior in the prison, ruled that Day was defending himself.


title: Leopold and Loeb

text: A sexual motive for the killing was suggested. While some sources state that newsman Ed Lahey began his story in the "Chicago Daily News" with the lead, "Richard Loeb, despite his erudition, today ended his sentence with a proposition" – no evidence has been found that this lead was ever published, and actual copy from that date reads otherwise. On February 19, 1936, in a column printed in the "Syracuse Journal", Mark Hellinger wrote, "I must tell you of the line that came to me from an unknown correspondent in Chicago. This anonymous contributor said he had the absolute low-down on the recent slaying of Dickie Loeb. Seems that Loeb made a slight mistake in grammar. He ended a sentence in a proposition..." Other newspapers at the time appeared to praise Day, who was later tried and acquitted of Loeb's murder.


title: Leopold and Loeb

text: There is no evidence that Loeb was a sexual predator while in prison, but Day was later caught at least once in a sexual act with a fellow inmate. In his autobiography, "Life Plus 99 Years", Leopold ridiculed Day's claim that Loeb had attempted to sexually assault him. This was echoed by the prison's Catholic chaplain, a confidant of Loeb's, who said that it was more likely that Day attacked Loeb after Loeb rebuffed his advances.


title: Leopold and Loeb

text: Leopold continued with his work after Loeb's death. Despite suffering from depression, he became a model prisoner and made many significant contributions to improving conditions at Stateville Penitentiary. These included reorganizing the prison library, revamping the schooling system and teaching its students, and volunteer work in the prison hospital. In 1944, Leopold volunteered for the Stateville Penitentiary Malaria Study; he was deliberately inoculated with malaria pathogens and then subjected to several experimental malaria treatments. He later wrote that all his good work in prison and after his release was an effort to compensate for his crime.


title: Leopold and Loeb

text: In the early 1950s, author Meyer Levin, a classmate at the University of Chicago, requested Leopold's cooperation in writing a novel based on the Franks murder. Leopold responded that he did not wish his story told in fictionalized form, but offered Levin a chance to contribute to his own memoir, which was in progress. Levin, unhappy with that suggestion, went ahead with his book alone, despite Leopold's express objections. The novel, titled Compulsion, was published in 1956. Levin portrayed Leopold (under the pseudonym Judd Steiner) as a brilliant but deeply disturbed teenager, psychologically driven to kill because of his troubled childhood and an obsession with Loeb. Leopold later wrote that reading Levin's book made him "physically sick... More than once I had to lay the book down and wait for the nausea to subside. I felt as I suppose a man would feel if he were exposed stark-naked under a strong spotlight before a large audience."


title: Leopold and Loeb

text: Leopold's autobiography, "Life Plus 99 Years", was published in 1958 as part of his campaign to win parole. In beginning his account with the immediate aftermath of the crime, he engendered widespread criticism for his deliberate refusal (expressly stated in the book) to recount his childhood or to describe any details of the murder. He also was accused of writing the book solely as a means of rehabilitating his public image by ignoring the dark side of his past.


title: Leopold and Loeb

text: After thirty-three years and numerous unsuccessful petitions, Leopold was paroled in March 1958. The Brethren Service Commission, a Church of the Brethren-affiliated program, accepted him as a medical technician at its hospital in Puerto Rico. He expressed his appreciation in an article: "To me the Brethren Service Commission offered the job, the home, and the sponsorship without which a man cannot be paroled. But it gave me so much more than thatthe companionship, the acceptance, the love which would have rendered a violation of parole almost impossible." He was known as "Nate" to neighbors and to co-workers at Castañer General Hospital in Adjuntas, where he worked as a laboratory and X-ray assistant.


title: Leopold and Loeb

text: Later in 1958, Leopold attempted to set up the Leopold Foundation, to be funded by royalties from "Life Plus 99 Years", "to aid emotionally disturbed, retarded, or delinquent youths." The State of Illinois voided his charter, however, on grounds that it violated the terms of his parole.


title: Leopold and Loeb

text: In 1959, Leopold sought to block production of the film version of "Compulsion" on the grounds that Levin's book had invaded his privacy, defamed him, profited from his life story, and "intermingled fact and fiction to such an extent that they were indistinguishable." Eventually the Illinois Supreme Court ruled against him, holding that Leopold, as the confessed perpetrator of the "crime of the century", could not reasonably argue that any book had injured his reputation.


title: Leopold and Loeb

text: Subsequently, Leopold moved to Santurce and married a widowed florist. He earned a master's degree at the University of Puerto Rico, then taught classes there; became a researcher in the social service program of Puerto Rico's department of health; worked for an urban renewal and housing agency; and did research on leprosy at the University of Puerto Rico School of Medicine. Leopold was also active in the Natural History Society of Puerto Rico, traveling throughout the island to observe its birdlife. In 1963, he published "Checklist of Birds of Puerto Rico and the Virgin Islands". While he spoke of his intention to write a book titled "Reach for a Halo" about his life following prison, he never did.


title: Leopold and Loeb

text: The Franks murder has inspired works of film, theatre, and fiction, including the 1929 play "Rope" by Patrick Hamilton, performed on BBC television in 1939, and Alfred Hitchcock's film of the same name in 1948. A fictionalized version of the events formed the basis of Meyer Levin's 1956 novel "Compulsion" and its 1959 film adaptation. In 1957, two more fictionalized novels were released: "Nothing but the Night" by James Yaffe and "Little Brother Fate" by Mary-Carter Roberts. "Never the Sinner", John Logan's 1985 play, was based on contemporary newspaper accounts of the case, and included an explicit portrayal of Leopold and Loeb's sexual relationship. In 2019, the story was fictionally retold again in the third season of "The Sinner".


title: Leopold and Loeb

text: In his book "Murder Most Queer" (2014), theater scholar Jordan Schildcrout examines changing attitudes toward homosexuality in various theatrical and cinematic representations of the Leopold and Loeb case.


title: Leopold and Loeb

text: Other works said to be influenced by the case include Richard Wright's 1940 novel "Native Son", the "Matlock" episode “The Sisters”, the "Columbo" episode "Columbo Goes To College" (1990), Tom Kalin's 1992 film "Swoon", Michael Haneke's 1997 Austrian film "Funny Games" and the 2008 International remake, Barbet Schroeder's "Murder by Numbers" (2002), Daniel Clowes's 2005 graphic novel "Ice Haven", Stephen Dolginoff's 2005 off-Broadway musical "Thrill Me: The Leopold and Loeb Story",


title: Catatonia

text: Catatonia is a complex neuropsychiatric behavioral syndrome that is characterized by abnormal movements, immobility, abnormal behaviors, and withdrawal. The onset of catatonia can be acute or subtle and symptoms can wax, wane, or change during episodes. There are several subtypes of catatonia: akinetic catatonia, excited catatonia, malignant catatonia, delirious mania, and self-injurious behaviors in autism.


title: Catatonia

text: Although catatonia has historically been related to schizophrenia (catatonic schizophrenia), catatonia is most often seen in mood disorders. It is now known that catatonic symptoms are nonspecific and may be observed in other mental, neurological, and medical conditions. Catatonia is not a stand-alone diagnosis (although some experts disagree), and the term is used to describe a feature of the underlying disorder.


title: Catatonia

text: Recognizing and treating catatonia is very important as failure to do so can lead to poor outcomes and can be potentially fatal. Treatment with benzodiazepines or ECT can lead to remission of catatonia. There is growing evidence of the effectiveness of the NMDA receptor antagonists amantadine and memantine for benzodiazepine-resistant catatonia. Antipsychotics are sometimes employed, but they can worsen symptoms and have serious adverse effects.


title: Catatonia

text: The presentation of a patient with catatonia varies greatly depending on the subtype, underlying cause and it can be acute or subtle.


title: Catatonia

text: Because most patients with catatonia have an underlying psychiatric illness, the majority will present with worsening depression, mania, or psychosis followed by catatonia symptoms. Catatonia presents as a motor disturbance in which patients will display marked reduction in movement, marked agitation, or a mixture of both despite having the physical capacity to move normally. These patients may be unable to start an action or stop one. Movements and mannerisms may be repetitive, or purposeless.


title: Catatonia

text: The most common signs of catatonia are immobility, mutism, withdrawal and refusal to eat, staring, negativism, posturing (rigidity), rigidity, waxy flexibility/catalepsy, stereotypy (purposeless, repetitive movements), echolalia or echopraxia, verbigeration (repeat meaningless phrases). It should not be assumed that patients presenting with catatonia are unaware of their surroundings as some patients can recall in detail their catatonic state and their actions.


title: Catatonia

text: There are several subtypes of catatonia and they are characterized by the specific movement disturbance and associated features. Although catatonia can be divided into various subtypes, the natural history of catatonia is often fluctuant and different states can exist within the same individual.


title: Catatonia

text: Withdrawn Catatonia: This form of catatonia is characterized by decreased response to external stimuli, immobility or inhibited movement, mutism, staring, posturing, and negativism. Patients may sit or stand in the same position for hours, may hold odd positions, and may resist movement of their extremities.


title: Catatonia

text: Excited Catatonia: Excited catatonia is characterized by odd mannerisms/gestures, performing purposeless or inappropriate actions, excessive motor activity, restlessness, stereotypy, impulsivity, agitation, and combativeness. Speech and actions may be repetitive or mimic another person's. People in this state are extremely hyperactive and may have delusions and hallucinations. Catatonic excitement is commonly cited as one of the most dangerous mental states in psychiatry.


title: Catatonia

text: Malignant Catatonia: Malignant catatonia is a life-threatening condition that may progress rapidly within a few days. It is characterized by fever, abnormalities in blood pressure, heart rate, respiratory rate, diaphoresis (sweating), and delirium. Certain lab findings are common with this presentation; however, they are nonspecific, which means that they are also present in other conditions and do not diagnose catatonia. These lab findings include: leukocytosis, elevated creatine kinase, low serum iron. The signs and symptoms of malignant catatonia overlap significantly with neuroleptic malignant syndrome (NMS) and so a careful history, review of medications, and physical exam are critical to properly differentiate these conditions. For example, if the patient has waxy flexibility and holds a position against gravity when passively moved into that position, then it is likely catatonia. If the patient has a "lead-pipe rigidity" then NMS should be the prime suspect.


title: Catatonia

text: Patients may experience several complications from being in a catatonic state. The nature of these complications will depend on the type of catatonia being experienced by the patient. For example, patients presenting with retarded catatonia may have refusal to eat which will in turn lead to malnutrition and dehydration. Furthermore, if immobility is a symptom the patient is presenting with, then they may develop pressure ulcers, muscle contractions, and are at risk of developing deep vein thrombosis (DVT) and pulmonary embolus (PE). Patients with excited catatonia may be aggressive and violent, and physical trauma may result from this. Catatonia may progress to the malignant type which will present with autonomic instability and may be life-threatening. Other complications also include the development of pneumonia and neuroleptic malignant syndrome.


title: Catatonia

text: Catatonia is almost always secondary to another underlying illness, often a psychiatric disorder. Mood disorders such as a bipolar disorder and depression are the most common etiologies to progress to catatonia. Other psychiatric associations include schizophrenia and other primary psychotic disorders. It also is related to autism spectrum disorders.


title: Catatonia

text: Catatonia is also seen in many medical disorders, including infections (such as encephalitis), autoimmune disorders, meningitis, focal neurological lesions (including strokes), alcohol withdrawal, abrupt or overly rapid benzodiazepine withdrawal, cerebrovascular disease, neoplasms, head injury, and some metabolic conditions (homocystinuria, diabetic ketoacidosis, hepatic encephalopathy, and hypercalcaemia).


title: Catatonia

text: The pathophysiology that leads to catatonia is still poorly understood and a definite mechanism remains unknown. Neurologic studies have implicated several pathways; however, it remains unclear whether these findings are the cause or the consequence of the disorder.


title: Catatonia

text: Abnormalities in GABA, glutamate signaling, serotonin, and dopamine transmission are believed to be implicated in catatonia.


title: Catatonia

text: Furthermore, it has also been hypothesized that pathways that connect the basal ganglia with the cortex and thalamus is involved in the development of catatonia.


title: Catatonia

text: There is not yet a definitive consensus regarding diagnostic criteria of catatonia. In the American Diagnostic and Statistical Manual of Mental Disorders, Fifth Edition (DSM-5) and the World Health Organization's eleventh edition of the International Classification of Disease (ICD-11) the classification is more homogeneous than in earlier editions. Prominent researchers in the field have other suggestions for diagnostic criteria.


title: Catatonia

text: The DSM-5 does not classify catatonia as an independent disorder, but rather it classifies it as catatonia associated with another mental disorder, due to another medical condition, or as unspecified catatonia. Catatonia is diagnosed by the presence of three or more of the following 12 psychomotor symptoms in association with a mental disorder, medical condition, or unspecified:


title: Catatonia

text: Other disorders (additional code 293.89 [F06.1] to indicate the presence of the co-morbid catatonia):


title: Catatonia

text: If catatonic symptoms are present but do not form the catatonic syndrome, a medication- or substance-induced aetiology should first be considered.


title: Catatonia

text: In ICD-11 catatonia is defined as a syndrome of primarily psychomotor disturbances that is characterized by the simultaneous occurrence of several symptoms such as stupor; catalepsy; waxy flexibility; mutism; negativism; posturing; mannerisms; stereotypies; psychomotor agitation; grimacing; echolalia and echopraxia. Catatonia may occur in the context of specific mental disorders, including mood disorders, schizophrenia or other primary psychotic disorders, and Neurodevelopmental disorders, and may be induced by psychoactive substances, including medications. Catatonia may also be caused by a medical condition not classified under mental, behavioral, or neurodevelopmental disorders.


title: Catatonia

text: Catatonia is often overlooked and under-diagnosed. Patients with catatonia most commonly have an underlying psychiatric disorder, for this reason, physicians may overlook signs of catatonia due to the severity of the psychosis the patient is presenting with. Furthermore, the patient may not be presenting with the common signs of catatonia such as mutism and posturing. Additionally, the motor abnormalities seen in catatonia are also present in psychiatric disorders. For example, a patient with mania will show increased motor activity that may progress to exciting catatonia. One way in which physicians can differentiate between the two is to observe the motor abnormality. Patients with mania present with increased goal-directed activity. On the other hand, the increased activity in catatonia is not goal-directed and often repetitive.


title: Catatonia

text: Catatonia is a clinical diagnosis and there is no specific laboratory test to diagnose it. However, certain testing can help determine what is causing the catatonia. An EEG will likely show diffuse slowing. If seizure activity is driving the syndrome, then an EEG would also be helpful in detecting this. CT or MRI will not show catatonia; however, they might reveal abnormalities that might be leading to the syndrome. Metabolic screens, inflammatory markers, or autoantibodies may reveal reversible medical causes of catatonia.


title: Catatonia

text: Vital signs should be frequently monitored as catatonia can progress to malignant catatonia which is life-threatening. Malignant catatonia is characterized by fever, hypertension, tachycardia, and tachypnea.


title: Catatonia

text: Various rating scales for catatonia have been developed, however, their utility for clinical care has not been well established. The most commonly used scale is the Bush-Francis Catatonia Rating Scale (BFCRS) (external link is provided below). The scale is composed of 23 items with the first 14 items being used as the screening tool. If 2 of the 14 are positive, this prompts for further evaluation and completion of the remaining 9 items.


title: Catatonia

text: A diagnosis can be supported by the lorazepam challenge or the zolpidem challenge. While proven useful in the past, barbiturates are no longer commonly used in psychiatry; thus the option of either benzodiazepines or ECT.


title: Catatonia

text: The differential diagnosis of catatonia is extensive as signs and symptoms of catatonia may overlap significantly with those of other conditions. Therefore, a careful and detailed history, medication review, and physical exam are key to diagnosing catatonia and differentiating it from other conditions. Furthermore, some of these conditions can themselves lead to catatonia. The differential diagnosis is as follows:


title: Catatonia

text: The initial treatment of catatonia is to stop medication that could be potentially leading to the syndrome. These may include steroids, stimulants, anticonvulsants, neuroleptics, dopamine blockers, etc. The next step is to provide a "lorazepam challenge," in which patients are given 2 mg of IV lorazepam (or another benzodiazepine). Most patients with catatonia will respond significantly to this within the first 15–30 minutes. If no change is observed during the first dose, then a second dose is given and the patient is re-examined. If the patient responds to the lorazepam challenge, then lorazepam can be scheduled at interval doses until the catatonia resolves. The lorazepam must be tapered slowly, otherwise, the catatonia symptoms may return. The underlying cause of the catatonia should also be treated during this time. If within a week the catatonia is not resolved, then ECT can be used to reverse the symptoms. ECT in combination with benzodiazepines is used to treat malignant catatonia. In France, zolpidem has also been used in diagnosis, and response may occur within the same time period. Ultimately the underlying cause needs to be treated.


title: Catatonia

text: Electroconvulsive therapy (ECT) is an effective treatment for catatonia that is well acknowledged. ECT has also shown favorable outcomes in patients with chronic catatonia. However, it has been pointed out that further high quality randomized controlled trials are needed to evaluate the efficacy, tolerance, and protocols of ECT in catatonia.


title: Catatonia

text: Antipsychotics should be used with care as they can worsen catatonia and are the cause of neuroleptic malignant syndrome, a dangerous condition that can mimic catatonia and requires immediate discontinuation of the antipsychotic.


title: Catatonia

text: There is evidence clozapine works better than other antipsychotics to treat catatonia, following a recent systematic review.


title: Catatonia

text: Excessive glutamate activity is believed to be involved in catatonia; when first-line treatment options fail, NMDA antagonists such as amantadine or memantine may be used. Amantadine may have an increased incidence of tolerance with prolonged use and can cause psychosis, due to its additional effects on the dopamine system. Memantine has a more targeted pharmacological profile for the glutamate system, reduced incidence of psychosis and may therefore be preferred for individuals who cannot tolerate amantadine. Topiramate is another treatment option for resistant catatonia; it produces its therapeutic effects by producing glutamate antagonism via modulation of AMPA receptors.


title: Catatonia

text: Patients who experience an episode of catatonia are more likely to recur. Treatment response for patients with catatonia is 50–70% and these patients have a good prognosis. However, failure to respond to medication is a very poor prognosis. Many of these patients will require long-term and continuous mental health care. For patients with catatonia with underlying schizophrenia, the prognosis is much poorer.


title: Catatonia

text: Catatonia has been mostly studied in acutely ill psychiatric patients. Catatonia frequently goes unrecognized, leading to the belief that the syndrome is rare; however, this is not true and prevalence has been reported to be as high as 10% in patients with acute psychiatric illnesses. One large population estimate has suggested that the incidence of catatonia is 10.6 episodes per 100 000 person-years. It occurs in males and females in approximately equal numbers. 21-46% of all catatonia cases can be attributed to a general medical condition.


title: Jewish population by country

text: As of 2020, the world's "core" Jewish population (those identifying as Jews above all else) was estimated at 14.8 million, 0.19% of the 7.95 billion worldwide population. This number rises to 18 million with the addition of the "connected" Jewish population, including those who say they are partly Jewish or that have Jewish backgrounds from at least one Jewish parent, and rises again to 21 million with the addition of the "enlarged" Jewish population, including those who say they have Jewish backgrounds but no Jewish parents and all non-Jewish household members who live with Jews. Counting all those who are eligible for Israeli citizenship under Israel's Law of Return, in addition to Israeli Jews, raised the total to 23.8 million.


title: Jewish population by country

text: Two countries account for 81% of those recognised as Jews or of sufficient Jewish ancestry to be eligible for citizenship in Israel under its Law of Return: the United States with 51% and Israel with 30% (including the West Bank with 2%). An additional 16% is split between France (3%), Canada (3%), Russia (3%), the United Kingdom (2%), Argentina (1%), Germany (1%), Ukraine (1%), Brazil (1%), Australia (1%), and Hungary (1%), while the remaining 3% are spread around approximately 98 other countries and territories with less than 0.5% each. With nearly 6.8 million Jews, Israel is the only Jewish-majority country and the only .


title: Jewish population by country

text: In 1939, the core Jewish population reached its historical peak of 17 million. Due to the Holocaust, this number was reduced to 11 million by 1945. The population grew to around 13 million by the 1970s and then recorded almost no growth until around 2005, due to low fertility rates and assimilation of Jews. From 2005 to 2018, the world's Jewish population grew 0.63% annually on average, while world population grew 1.1% annually in the same period. This increase primarily reflected the rapid growth of Haredi and some Orthodox sectors, who remain a growing proportion of Jews.


title: Jewish population by country

text: Recent Jewish population dynamics are characterized by continued steady increase in the Israeli Jewish population and flat or declining numbers in other countries (the diaspora). The Jewish population of Israel increased from 630,000 at the country's inception in 1948 to 6,135,000 in 2014, while the population of the diaspora has dropped from 10.5 to 8.1 million over the same period. Current Israeli Jewish demographics are characterized by a relatively high fertility rate of 3 children per woman and a stable age distribution. The overall growth rate of Jews in Israel is 1.7% annually. The diaspora countries, by contrast, have low Jewish birth rates, an increasingly elderly age composition, and a negative balance of people leaving Judaism versus those joining.


title: Jewish population by country

text: Immigration trends also favour Israel ahead of diaspora countries. The Jewish state has a positive immigration balance (called aliyah in Hebrew). Israel saw its Jewish numbers significantly buoyed by a million-strong wave of Jewish immigrants from the former Soviet Union in the 1990s, and immigration growth has been steady (in the low tens of thousands) since then. In the rest of the world, only the United States, Canada, Australia, and Germany have had a positive recent Jewish migration balance outside of Israel. In general, the modern English-speaking world has seen an increase in its share of the diaspora since the Holocaust and the foundation of Israel, while historic diaspora Jewish populations in Eastern Europe, North Africa, and the Middle East have significantly declined or disappeared.


title: Jewish population by country

text: France continues to be home to the world's third largest Jewish community, at around 500,000, but has shown an increasingly negative trend. As a long term tend, intermarriage has reduced its "core" Jewish population and increased its "connected" and "enlarged" Jewish populations. More recently, migration loss to Israel amongst French Jews reached the tens of thousands between 2014 and 2017, following a wave of anti-Semitic attacks.


title: Jewish population by country

text: According to a 2017 Pew Research Center survey, between 2010 and 2015 "an estimated one million babies were born to Jewish mothers and roughly 600,000 Jewish died, meaning that the natural increase in the Jewish population – i.e., the number of births minus the number of deaths – was 500,000 over this period". According to the same study, over the next four decades the number of Jews around the world is expected to increase from 14.2 million in 2015 to 20.3 million in 2060.


title: Jewish population by country

text: The number of Jews in the United States has been the subject of much debate because of questions over counting methodology. In 2012, Sheskin and Dashefsky put forward a figure of 6.72 million based on a mixture of local surveys, informed local estimates, and US census data. They qualified their estimate with a concern over double counting and suggested the real figure may lie between 6 and 6.4 million. Drawing on their work, the Steinhardt Social Research Institute released their own estimate of 6.8 million Jews in the United States in 2013. These figures are in contrast to Israeli demographer Sergio Della Pergola's number of 5,425,000, also in 2012. He has called high estimates “implausible” and “unreliable” although he revised the United States Jewish number upward to 5.7 million in subsequent years. This controversy followed a similar debate in 2001 when the National Jewish Population Survey released a United States Jewish estimate as low as 5.2 million only to have serious methodological errors suggested in their survey. In sum, a confidence interval of a million or more people is likely to persist in reporting on the number of Jewish Americans.


title: Jewish population by country

text: Below is a list of Jewish populations in the world by country. All data below, except the last column, are from the Berman Jewish DataBank at Stanford University in the World Jewish Population (2020) report coordinated by Sergio DellaPergola at the Hebrew University of Jerusalem. The Jewish DataBank figures are primarily based on national censuses combined with trend analysis.


title: Jewish population by country

text: The above table represents Jews that number at least a few dozen per country. Reports exist of Jewish communities remaining in other territories in the low single digits that are on the verge of disappearing, particularly in the Muslim world, as their reaction to the birth of Israel in 1948 was the persecution of Jews in nearly all Muslim lands; these are often of historical interest as they represent the remnant of much larger Jewish populations. For example, Egypt had a Jewish community of 80,000 in the early 20th century that numbered fewer than 40 as of 2014, mainly because of the forced expulsion movements to Israel and other countries at that time. Despite a 2,000 year history of Jewish presence, there are no longer any known Jews living in Afghanistan, as its last Jewish resident Zablon Simintov fled the country in September 2021. In Syria, another ancient Jewish community saw mass exodus at the end of the 20th century and numbered fewer than 20 in the midst of the Syrian Civil War. The size of the Jewish community in Indonesia has been variously given as 65, 100, or 18 at most over the last 50 years. In Yemen due to the ongoing civil war, the Yemenite Jews have faced persecution by the Houthis, who've demanded they convert to Islam or face mandatory expulsion from the country. The Israeli military has conducted operations evacuating the population and moving them to Israel. On 28 March 2021, 13 Jews were forced by the Houthis to leave Yemen, leaving the last four elderly Jews in Yemen. According to one report there are six Jews left in Yemen: one woman; her brother; 3 others, and Levi Salem Marahbi (who had been imprisoned for helping smuggle a Torah scroll out of Yemen).


title: Navier–Stokes equations

text: In physics, the Navier–Stokes equations ( ) are partial differential equations which describe the motion of viscous fluid substances, named after French engineer and physicist Claude-Louis Navier and Anglo-Irish physicist and mathematician George Gabriel Stokes. They were developed over several decades of progressively building the theories, from 1822 (Navier) to 1842–1850 (Stokes).


title: Navier–Stokes equations

text: The Navier–Stokes equations mathematically express conservation of momentum and conservation of mass for Newtonian fluids. They are sometimes accompanied by an equation of state relating pressure, temperature and density. They arise from applying Isaac Newton's second law to fluid motion, together with the assumption that the stress in the fluid is the sum of a diffusing viscous term (proportional to the gradient of velocity) and a pressure term—hence describing "viscous flow". The difference between them and the closely related Euler equations is that Navier–Stokes equations take viscosity into account while the Euler equations model only inviscid flow. As a result, the Navier–Stokes are a parabolic equation and therefore have better analytic properties, at the expense of having less mathematical structure (e.g. they are never completely integrable).


title: Navier–Stokes equations

text: The Navier–Stokes equations are useful because they describe the physics of many phenomena of scientific and engineering interest. They may be used to model the weather, ocean currents, water flow in a pipe and air flow around a wing. The Navier–Stokes equations, in their full and simplified forms, help with the design of aircraft and cars, the study of blood flow, the design of power stations, the analysis of pollution, and many other things. Coupled with Maxwell's equations, they can be used to model and study magnetohydrodynamics.


title: Navier–Stokes equations

text: The Navier–Stokes equations are also of great interest in a purely mathematical sense. Despite their wide range of practical uses, it has not yet been proven whether smooth solutions always exist in three dimensions—i.e., whether they are infinitely differentiable (or even just bounded) at all points in the domain. This is called the Navier–Stokes existence and smoothness problem. The Clay Mathematics Institute has called this one of the seven most important open problems in mathematics and has offered a US$1 million prize for a solution or a counterexample.


title: Navier–Stokes equations

text: The solution of the equations is a flow velocity. It is a vector field—to every point in a fluid, at any moment in a time interval, it gives a vector whose direction and magnitude are those of the velocity of the fluid at that point in space and at that moment in time. It is usually studied in three spatial dimensions and one time dimension, although two (spatial) dimensional and steady-state cases are often used as models, and higher-dimensional analogues are studied in both pure and applied mathematics. Once the velocity field is calculated, other quantities of interest such as pressure or temperature may be found using dynamical equations and relations. This is different from what one normally sees in classical mechanics, where solutions are typically trajectories of position of a particle or deflection of a continuum. Studying velocity instead of position makes more sense for a fluid, although for visualization purposes one can compute various trajectories. In particular, the streamlines of a vector field, interpreted as flow velocity, are the paths along which a massless fluid particle would travel. These paths are the integral curves whose derivative at each point is equal to the vector field, and they can represent visually the behavior of the vector field at a point in time.


title: Navier–Stokes equations

text: The Navier–Stokes momentum equation can be derived as a particular form of the Cauchy momentum equation, whose general convective form is


title: Navier–Stokes equations

text: By setting the Cauchy stress tensor to be the sum of a viscosity term (the deviatoric stress) and a pressure term (volumetric stress), we arrive at


title: Navier–Stokes equations

text: In this form, it is apparent that in the assumption of an inviscid fluid – no deviatoric stress – Cauchy equations reduce to the Euler equations.


title: Navier–Stokes equations

text: Assuming conservation of mass we can use the mass continuity equation (or simply continuity equation),


title: Navier–Stokes equations

text: The left side of the equation describes acceleration, and may be composed of time-dependent and convective components (also the effects of non-inertial coordinates if present). The right side of the equation is in effect a summation of hydrostatic effects, the divergence of deviatoric stress and body forces (such as gravity).


title: Navier–Stokes equations

text: All non-relativistic balance equations, such as the Navier–Stokes equations, can be derived by beginning with the Cauchy equations and specifying the stress tensor through a constitutive relation. By expressing the deviatoric (shear) stress tensor in terms of viscosity and the fluid velocity gradient, and assuming constant viscosity, the above Cauchy equations will lead to the Navier–Stokes equations below.


title: Navier–Stokes equations

text: A significant feature of the Cauchy equation and consequently all other continuum equations (including Euler and Navier–Stokes) is the presence of convective acceleration: the effect of acceleration of a flow with respect to space. While individual fluid particles indeed experience time-dependent acceleration, the convective acceleration of the flow field is a spatial effect, one example being fluid speeding up in a nozzle.


title: Navier–Stokes equations

text: Remark: here, the Cauchy stress tensor is denoted formula_4 (instead of formula_5 as it was in the general continuum equations and in the incompressible flow section).


title: Navier–Stokes equations

text: The compressible momentum Navier–Stokes equation results from the following assumptions on the Cauchy stress tensor:


title: Navier–Stokes equations

text: So by alternatively decomposing the stress tensor into isotropic and deviatoric parts, as usual in fluid dynamics:


title: Navier–Stokes equations

text: Both second viscosity ζ and dynamic viscosity need not be constant – in general, they depend on two thermodynamics variables if the fluid contains a single chemical species, say for example, pressure and temperature. Any equation that makes explicit one of these transport coefficient in the conservation variables is called an equation of state.


title: Navier–Stokes equations

text: Apart from its dependence of pressure and temperature, the second viscosity coefficient also depends on the process, that is to say, the second viscosity coefficient is not just a material property. For instance, in the case of a sound wave with a definitive frequency that alternatively compresses and expands a fluid element, the second viscosity coefficient depends on the frequency of the wave. This dependence is called the "dispersion". In some cases, the second viscosity can be assumed to be constant in which case, the effect of the volume viscosity is that the mechanical pressure is not equivalent to the thermodynamic pressure: as demonstrated below.


title: Navier–Stokes equations

text: However, this difference is usually neglected most of the time (that is whenever we are not dealing with processes such as sound absorption and attenuation of shock waves, where second viscosity coefficient becomes important) by explicitly assuming formula_12. The assumption of setting formula_12 is called as the Stokes hypothesis. The validity of Stokes hypothesis can be demonstrated for monoatomic gas both experimentally and from the kinetic theory,; for other gases and liquids, Stokes hypothesis is generally incorrect. With the Stokes hypothesis, the Navier–Stokes equations become


title: Navier–Stokes equations

text: If the dynamic viscosity is also assumed to be constant, the equations can be simplified further. By computing the divergence of the stress tensor, since the divergence of tensor formula_14 is formula_15 and the divergence of tensor formula_16 is formula_17, one finally arrives to the compressible (most general) Navier–Stokes momentum equation:


title: Navier–Stokes equations

text: where formula_18 is the material derivative. The left-hand side changes in the conservation form of the Navier–Stokes momentum equation:


title: Navier–Stokes equations

text: Bulk viscosity is assumed to be constant, otherwise it should not be taken out of the last derivative. The convective acceleration term can also be written as


title: Navier–Stokes equations

text: For the special case of an incompressible flow, the pressure constrains the flow so that the volume of fluid elements is constant: isochoric flow resulting in a solenoidal velocity field with formula_21.


title: Navier–Stokes equations

text: The incompressible momentum Navier–Stokes equation results from the following assumptions on the Cauchy stress tensor:


title: Navier–Stokes equations

text: Dynamic viscosity need not be constant – in incompressible flows it can depend on density and on pressure. Any equation that makes explicit one of these transport coefficient in the conservative variables is called an equation of state.


title: Navier–Stokes equations

text: Incompressibility rules out density and pressure waves like sound or shock waves, so this simplification is not useful if these phenomena are of interest. The incompressible flow assumption typically holds well with all fluids at low Mach numbers (say up to about Mach 0.3), such as for modelling air winds at normal temperatures. the incompressible Navier–Stokes equations are best visualised by dividing for the density:


title: Navier–Stokes equations

text: If the density is constant throughout the fluid domain, or, in other words, if all fluid elements have the same density, formula_24, then we have


title: Navier–Stokes equations

text: The higher-order term, namely the shear stress divergence , has simply reduced to the vector Laplacian term . This Laplacian term can be interpreted as the difference between the velocity at a point and the mean velocity in a small surrounding volume. This implies that – for a Newtonian fluid – viscosity operates as a "diffusion of momentum", in much the same way as the heat conduction. In fact neglecting the convection term, incompressible Navier–Stokes equations lead to a vector diffusion equation (namely Stokes equations), but in general the convection term is present, so incompressible Navier–Stokes equations belong to the class of convection–diffusion equations.


title: Navier–Stokes equations

text: one can finally condense the whole source in one term, arriving to the incompressible Navier–Stokes equation with conservative external field:


title: Navier–Stokes equations

text: The incompressible Navier–Stokes equations with conservative external field is the fundamental equation of hydraulics. The domain for these equations is commonly a 3 or less dimensional Euclidean space, for which an orthogonal coordinate reference frame is usually set to explicit the system of scalar partial differential equations to be solved. In 3-dimensional orthogonal coordinate systems are 3: Cartesian, cylindrical, and spherical. Expressing the Navier–Stokes vector equation in Cartesian coordinates is quite straightforward and not much influenced by the number of dimensions of the euclidean space employed, and this is the case also for the first-order terms (like the variation and convection ones) also in non-cartesian orthogonal coordinate systems. But for the higher order terms (the two coming from the divergence of the deviatoric stress that distinguish Navier–Stokes equations from Euler equations) some tensor calculus is required for deducing an expression in non-cartesian orthogonal coordinate systems.


title: Navier–Stokes equations

text: where and are solenoidal and irrotational projection operators satisfying and and are the non-conservative and conservative parts of the body force. This result follows from the Helmholtz theorem (also known as the fundamental theorem of vector calculus). The first equation is a pressureless governing equation for the velocity, while the second equation for the pressure is a functional of the velocity and is related to the pressure Poisson equation.


title: Navier–Stokes equations

text: with a similar structure in 2D. Thus the governing equation is an integro-differential equation similar to Coulomb and Biot–Savart law, not convenient for numerical computation.


title: Navier–Stokes equations

text: An equivalent weak or variational form of the equation, proved to produce the same velocity solution as the Navier–Stokes equation, is given by,


title: Navier–Stokes equations

text: for divergence-free test functions satisfying appropriate boundary conditions. Here, the projections are accomplished by the orthogonality of the solenoidal and irrotational function spaces. The discrete form of this is eminently suited to finite element computation of divergence-free flow, as we shall see in the next section. There one will be able to address the question "How does one specify pressure-driven (Poiseuille) problems with a pressureless governing equation?".


title: Navier–Stokes equations

text: The absence of pressure forces from the governing velocity equation demonstrates that the equation is not a dynamic one, but rather a kinematic equation where the divergence-free condition serves the role of a conservation equation. This all would seem to refute the frequent statements that the incompressible pressure enforces the divergence-free condition.


title: Navier–Stokes equations

text: Consider the incompressible Navier–Stokes equations for a Newtonian fluid of constant density in a domain


title: Navier–Stokes equations

text: being and portions of the boundary where respectively a Dirichlet and a Neumann boundary condition is applied ():


title: Navier–Stokes equations

text: Let be the dynamic viscosity of the fluid, the second-order identity tensor and the strain-rate tensor defined as:


title: Navier–Stokes equations

text: The functions and are given Dirichlet and Neumann boundary data, while is the initial condition. The first equation is the momentum balance equation, while the second represents the mass conservation, namely the continuity equation.


title: Navier–Stokes equations

text: and exploiting mass conservation, the divergence of the total stress tensor in the momentum equation can also be expressed as:


title: Navier–Stokes equations

text: In order to find the weak form of the Navier–Stokes equations, firstly, consider the momentum equation


title: Navier–Stokes equations

text: multiply it for a test function , defined in a suitable space , and integrate both members with respect to the domain :


title: Navier–Stokes equations

text: In the same fashion, the continuity equation is multiplied for a test function belonging to a space and integrated in the domain :


title: Navier–Stokes equations

text: Considering that the test function vanishes on the Dirichlet boundary and considering the Neumann condition, the integral on the boundary can be rearranged as:


title: Navier–Stokes equations

text: With partitioning of the problem domain and defining basis functions on the partitioned domain, the discrete form of the governing equation is


title: Navier–Stokes equations

text: It is desirable to choose basis functions that reflect the essential feature of incompressible flow – the elements must be divergence-free. While the velocity is the variable of interest, the existence of the stream function or vector potential is necessary by the Helmholtz theorem. Further, to determine fluid flow in the absence of a pressure gradient, one can specify the difference of stream function values across a 2D channel, or the line integral of the tangential component of the vector potential around the channel in 3D, the flow being given by Stokes' theorem. Discussion will be restricted to 2D in the following.


title: Navier–Stokes equations

text: We further restrict discussion to continuous Hermite finite elements which have at least first-derivative degrees-of-freedom. With this, one can draw a large number of candidate triangular and rectangular elements from the plate-bending literature. These elements have derivatives as components of the gradient. In 2D, the gradient and curl of a scalar are clearly orthogonal, given by the expressions,


title: Navier–Stokes equations

text: Adopting continuous plate-bending elements, interchanging the derivative degrees-of-freedom and changing the sign of the appropriate one gives many families of stream function elements.


title: Navier–Stokes equations

text: Taking the curl of the scalar stream function elements gives divergence-free velocity elements. The requirement that the stream function elements be continuous assures that the normal component of the velocity is continuous across element interfaces, all that is necessary for vanishing divergence on these interfaces.


title: Navier–Stokes equations

text: Boundary conditions are simple to apply. The stream function is constant on no-flow surfaces, with no-slip velocity conditions on surfaces.