title: Isaac II Angelos

text: Isaac II Angelos strengthened his position as emperor with dynastic marriages in 1185 and 1186. His niece Eudokia Angelina was married to Stefan, son of Stefan Nemanja of Serbia. Isaac's sister Theodora was married to the Italian marquis Conrad of Montferrat. In January 1186, Isaac himself married Margaret of Hungary (renamed Maria), daughter of King Béla III. Hungary was one of the Empire's largest and most powerful neighbours, and Margaret also had the benefit of high aristocratic descent, being related to the royal families of Kyiv, the Holy Roman Empire, Italy, Provence, and earlier Byzantine dynasties.


title: Isaac II Angelos

text: Isaac inaugurated his reign with a decisive victory over the Norman King of Sicily, William II, at the Battle of Demetritzes on 7 November 1185. William had invaded the Balkans with 80,000 men and 200 ships towards the end of Andronikos I's reign. Elsewhere Isaac's policy was less successful. In late 1185, he sent a fleet of 80 galleys to liberate his brother Alexius III from Acre, but the fleet was destroyed by the Normans of Sicily. He then sent a fleet of 70 ships, but it failed to recover Cyprus from the rebellious noble Isaac Komnenos, thanks to Norman interference. This fleet was misinterpreted by many in the Holy Land as naval support for the Muslim offensive in accordance with Isaac's alliance with Saladin. However the theory of a supposed alliance between Isaac and Saladin against the Third Crusade has been debunked by the historian Jonathan Harris.


title: Isaac II Angelos

text: Isaac's administration was dominated by two figures: his maternal uncle Theodore Kastamonites, who became virtually a co-emperor and handled all civil government until his death in 1193; and his replacement, Constantine Mesopotamites, who acquired even more influence over the emperor.


title: Isaac II Angelos

text: The oppressiveness of his taxes, increased to pay his armies and finance his marriage, resulted in a Vlach-Bulgarian uprising late in 1185. The rebellion led to the establishment of the Vlach-Bulgarian Empire under the Asen dynasty. In 1187 Alexios Branas, the victor over the Normans, was sent against the Bulgarians but turned his arms against his master and attempted to seize Constantinople, only to be defeated and slain by Isaac's brother-in-law Conrad of Montferrat. Also in 1187 an agreement was made with Venice, in which the Venetian Republic would provide between 40 and 100 galleys at six months' notice in exchange for favorable trading concessions. Because each Venetian galley was manned by 140 oarsmen, there were about 18,000 Venetians still in the Empire even after Manuel I's arrests.


title: Isaac II Angelos

text: The Emperor's attention was next demanded in the east, where several claimants to the throne successively rose and fell. In 1189 the Holy Roman Emperor Frederick I Barbarossa sought and obtained permission to lead his troops on the Third Crusade through the Byzantine Empire. But Isaac was suspicious that Barbarossa wished to conquer Byzantium: the reasons for this suspicious attitude were the diplomatic contact of Frederick with the Bulgarians and the Serbians, foes of the Byzantine Empire during this period, also Barbarossa's previous feud with Manuel. The rumors of 1160s about a German invasion in the Byzantine Empire were still remembered in the Byzantine court during Isaac’s reign. In retaliation Barbarossa's army occupied the city of Philippopolis and defeated a Byzantine army of 3,000 men that attempted to recapture the city. The Byzantine troops managed to constantly and successfully harass the Crusaders but a group of Armenians revealed to the Germans the strategic plan of the Byzantines. The Crusaders, who outnumbered the Byzantines, caught them unprepared and defeated them. Thus compelled by force of arms, Isaac II was forced to fulfill his engagements in 1190, when he released imprisoned German emissaries who were held in Constantinople, and exchanged hostages with Barbarossa, as a guarantee that the crusaders would not sack local settlements until they departed the Byzantine territory. In March 1190, Barbarossa left Adrianople to Gallipoli at the Dardanelles to embark to Asia Minor.


title: Isaac II Angelos

text: The next five years were disturbed by continued warfare with Bulgaria, against which Isaac led several expeditions in person. In spite of their promising start these ventures had little effect, and on one occasion in 1190 Isaac barely escaped with his life. The Byzantines suffered yet another major defeat in the Battle of Arcadiopolis in 1194. Isaac organized yet another offensive against Bulgaria in 1195 in cooperation with the Kingdom of Hungary, but Alexios Angelos, the Emperor's older brother, taking advantage of Isaac's absence from camp on a hunting expedition, proclaimed himself emperor and was readily recognised by the soldiers as Emperor Alexios III on 8 (or 9) April. Alexios then canceled the expedition and ordered Isaac to be blinded and imprisoned in Constantinople.


title: Isaac II Angelos

text: After eight years of captivity, Isaac II was raised from the dungeon to the throne once more after the arrival of the Fourth Crusade and the flight of Alexios III from the capital. Both his mind and body had been enfeebled by confinement, and his son Alexios IV Angelos was associated on the throne as the effective monarch.


title: Isaac II Angelos

text: Heavily beholden to the crusaders, Alexios IV was unable to meet his obligations and his vacillation caused him to lose the support of both his crusader allies and his subjects. At the end of January 1204 the influential court official Alexios Doukas "Mourtzouphlos" took advantage of riots in the capital to imprison Alexios IV and seize the throne as Alexios V. At this point Isaac II died, allegedly of shock, while Alexios IV was strangled.


title: Isaac II Angelos

text: Several pretenders rose up and attempted to wrest the throne from Isaac during his reign. These included:


title: Isaac II Angelos

text: Isaac has the reputation as one of the most unsuccessful rulers to occupy the Byzantine throne. Surrounded by a crowd of slaves, mistresses, and flatterers, he permitted his empire to be administered by unworthy favourites, while he squandered the money wrung from his provinces on costly buildings and expensive gifts to the churches of his metropolis. In 1185, the Empire lost Lefkada, Kefallonia, and Zakynthos to the Normans. In the same year the Vlach – Bulgarian Empire was restored after the rebellion of the brothers Asen and Peter, thus losing Moesia and parts of Thrace and Macedonia. After that Cilicia was retaken by the Armenians, and Cyprus wrested from the empire by the Franks.


title: Isaac II Angelos

text: Isaac II's first wife's name, Herina (i.e., Irene), is found on the necrology of Speyer Cathedral, where their daughter Irene is interred. The first wife of Isaac II is usually considered to be a Byzantine noblewoman of unknown name. In an Italian edition of the chronicle of Nicetas Choniates "Greatness and catastrophe of Byzantium" can be found an interesting note to the XIV Book. The names of Isaac II's first wife and eldest daughter, unknown from Byzantine sources, are found in an obituary in the Cathedral of Speyer, the pantheon of German kings. Here, the wife of Philip of Swabia is said to be the daughter of Isaac and Irene (there is reference to the following article: R. Hiestand, Die erste Ehe Isaaks II. Angelos und seine Kinder, in Jahrbuch der Osterreichischen Byzantinisk, XLVII 1997 pp. 199–208). This Irene could be identified with the daughter of George Paleologus Ducas Comnenus and wife Aspae, Bagratiid Princess of Ossetia; the son of this one, Andronicus Paleologus Comnenoducas is known as gambrox (gamma alpha mu beta rho o x) of Isaac II. Isaac's wife was possibly daughter of Andronikos I Komnenos, Byzantine Emperor (died 1185). A potential foreign origin is also given to her due to having the same name as her daughter, contrary to long-standing Greek custom. Their third child was born in 1182 or 1183 and she was dead or divorced by 1185, when Isaac remarried. Their children were:


title: Isaac II Angelos

text: By his second wife, Margaret of Hungary (who took the baptismal name "Maria"), Isaac II had two sons:


title: Gambit (unproduced film)

text: Gambit is an unproduced American superhero film based on the Marvel Comics character of the same name. It was intended to be an installment of the "X-Men" film series. Before its cancellation, the film had been written by Josh Zetumer based on a story by the character's creator Chris Claremont. Channing Tatum was set to star in the title role.


title: Gambit (unproduced film)

text: Tatum was looked at for early attempts to include Gambit in the "X-Men" films but was not available for that character's film introduction in "" (2009). Taylor Kitsch portrayed the character instead, but was not well received. Producer Lauren Shuler Donner expressed interest in a Gambit film starring Tatum in early 2014, and the actor officially signed on that May. The film had been in development hell since then, with Rupert Wyatt, Doug Liman, and Gore Verbinski attached as director to the film at different times over the years, with Tatum and his producing partner Reid Carolin also lobbying to direct, and the film's release date also pushed back numerous times. "Gambit" was scheduled for release on March 13, 2020, but development of the film was placed on hold due to the acquisition of 21st Century Fox by Disney. After taking over the film, Disney officially cancelled it in May 2019.


title: Gambit (unproduced film)

text: For the 2003 film "X2", director Bryan Singer asked stunt double James Bamford to film a short cameo as the character Gambit. The scene was ultimately cut from the film, and Bamford believed that a better known actor would be cast in the role for any future appearance. Singer wanted the character to have a large part in the sequel, "" (2006), with Keanu Reeves in the role, but ultimately did not return to direct that film. A new writing team of Simon Kinberg and Zak Penn were set to write the sequel's screenplay by 20th Century Fox after Singer's departure, and though the pair wanted to include the character, they felt there was only room for a cameo appearance given the number of new characters more relevant to the film's storylines. They decided to save Gambit for a larger role in a future film. Before that decision was made, Josh Holloway had been looked at for the part but was unavailable due to the filming schedule of his series "Lost". Channing Tatum was then chosen for the role, but the character was written out of the script before he was officially cast.


title: Gambit (unproduced film)

text: By October 2007, Gambit was believed to be appearing in the spin-off film "", set for release in 2009. Tatum was unable to re-commit to the part at that time because of scheduling conflicts with "" (2009), and Taylor Kitsch was ultimately cast in the role. Kitsch signed a three-picture deal. Fox executive Jeff Katz was confident that the character would be well received, saying, "there is a level of strategy in how we grow these things, and what characters can transition between multiple films", indicating that the character could move on to his own standalone film as was the plan with Ryan Reynolds' Deadpool. However, "Wolverine" was not well received by critics, and Kitsch's performance did not make him the breakout hit that Fox executives had expected. In September 2013, Tatum expressed interest in taking over the role from Kitsch, saying, "Gambit's my favorite. I’m from New Orleans, around that area. My dad's from New Orleans, and I like to do a Cajun accent. I could do it for real. No knock on Taylor Kitsch, though, ’cause I actually like his Gambit, but I’ve always lived around Cajun people ... Gambit was always like the woman-loving, cigarette-smoking, drinking [guy]. He was the punk rock of all the superheroes."


title: Gambit (unproduced film)

text: "X-Men" franchise producer Lauren Shuler Donner revealed in January 2014 that she had begun planning a Gambit film with Tatum. She said it "doesn't have to be a great big movie. It's a thief in New Orleans, it's a whole different story. [Tatum]'s on board, and I have to get the studio on board." That May, Tatum officially signed on to star in a Gambit film that was intended to begin a new standalone franchise; he would introduce his version of the character in "" (2016). By October, the producers were discussing the film's story and looking for a writer, with Josh Zetumer hired in the role at the end of the month, working off a story treatment by Gambit's comic creator Chris Claremont. Alongside Donner and Kinberg, Tatum was set to produce the film with Reid Carolin of their company Free Association. In January 2015, Fox gave the film an October 7, 2016 release date. Over several months, Tatum approached Bennett Miller, Darren Aronofsky, Gareth Evans, and J.C. Chandor to direct the film, but they all turned him down. In May, Zetumer completed his first draft of the script, which Tatum described as a "killer" origin story that changed "some of the tropes of these movies".


title: Gambit (unproduced film)

text: In June 2015, Rupert Wyatt signed on to direct the film, with Tatum saying, "We finally found someone that I really do believe wants to make "Gambit"". Tatum added that the film was "a really unique opportunity" among superhero films, and was no longer set to appear in "Apocalypse". He had begun learning to throw cards and sleight-of-hand tricks for the part from magician David Kwong, a friend of Carolin's from College. Filming was set to begin in New Orleans in late October or early November of that year. By the end of July, the film was believed to focus on "mobsters and thieves [rather than] 'end-of-the-world' stakes", but Fox also wanted to "load up on spectacle and make this character as popular as possible" with a large $154 million budget to be mostly spent in Louisiana. Several actresses were being tested for the female lead, including Léa Seydoux.


title: Gambit (unproduced film)

text: Tatum was renegotiating his contract with Fox at the end of July 2015, and was believed to be close to dropping out of the project due to Fox's intention to have Tatum become one of the "anchor characters" of the franchise following the impending retirement of Hugh Jackman as the series' former lead character Wolverine. This would be a major commitment for Tatum to make. Backend compensation was also an issue. Within days, the issues had been resolved and Tatum was once again set to star and produce; it was said that his "participation hardly was in any real danger" due to the commitments Tatum had already made to the project. Rebecca Ferguson and Abbey Lee were also testing for the "hotly contested" female lead of Belladonna Boudreaux, but Ferguson soon chose a role in "The Girl on the Train" (2016) instead. Seydoux was cast in the role by the end of August.


title: Gambit (unproduced film)

text: In September, Wyatt left the film after changes to its schedule caused a clash with another project he was committed to. Wyatt was also believed to have become "skittish" about directing the film due to wanting to rewrite the script and "conceive the world that he is filming", leading to differences in opinion on the script with Fox, Tatum, and Kinberg. Wyatt later stated in March 2019, that he left the film because the studio "slashed [the budget] quite considerably" following the financial failure of "Fantastic Four" (2015), but was not willing to let the script be re-written to match the new budget before the beginning of production which then was around 10 weeks away.


title: Gambit (unproduced film)

text: Fox began "furiously" meeting with potential replacements for Wyatt in hopes of keeping the film's release date, including directors Doug Liman, Joe Cornish, Shane Black, and F. Gary Gray. Liman was in final talks to take on the film in November 2015. He had already begun working on the screenplay with Tatum, Carolin, Zetumer, and Kinberg. The latter noted that the "X-Men" franchise was beginning to branch out into different tones with the irreverent, R-rated "Deadpool" (2016), and that ""Gambit" will have its own different flavor and tone to it, will be more like a heist movie and a sexy thriller in a way." In January, filming was set for March 2016.


title: Gambit (unproduced film)

text: Fox officially removed "Gambit" from its October release date in February 2016. Liman soon chose to direct the film "The Wall" (2017) while waiting for a new draft of the "Gambit" script, intending to then begin production on "Gambit" at the end of 2016. Tatum and Carolin were looking for a new writer to undertake the rewrite and pursue a different creative direction for the film, while Liman was expected to discard Wyatt's casting of Seydoux and begin casting from scratch himself. Kinberg explained in May that the group had collectively been unhappy with the film's script, but were now "very close" to completing it. He added that "the most important thing is getting the tone and the voice right ... [we are] hoping that "Gambit" is like what "Deadpool" was—the start of a new franchise within the "X-Men" universe—we want to make sure we get it right."


title: Gambit (unproduced film)

text: In July, Kinberg praised the script for "Gambit" and said that they were now aiming to begin filming at the beginning of 2017. However, Liman left the project the next month in a "mutual split" with Fox, choosing to instead direct the DC Comics-based film "Dark Universe". Liman later explained that he is "all about the script, and I just wasn't feeling it. I've gotta connect to the script."


title: Gambit (unproduced film)

text: In November 2016, "Gambit" was expected to begin development again with a new director after Tatum completed work on the film "Logan Lucky" (2017). The next January, Donner confirmed that Tatum was still attached to the project, and a month later Kinberg described the film as being in "active development". He stated his hope for the project to be ready by the end of 2017, for filming to then begin at the start of 2018. He noted that there were already three "X-Men" franchise films set for release in 2018 at that point, so "Gambit" "can wait for a moment." Kinberg compared Tatum's commitment to the role of Gambit to the determination shown by Reynolds and Jackman to get their most recent "X-Men" films ("Deadpool" and "Logan" (2017), respectively) made "right", and reiterated Fox's intention to build a new "Gambit" film franchise.


title: Gambit (unproduced film)

text: At the end of May 2017, "X-Men" producer Hutch Parker was unable to provide an update on the film, but said "there's still a desire and a passionate interest to see ["Gambit"] made." Tatum reiterated that he was still actively working on the film in July, and discussed the long development period for the film and the many delays to the production, saying, I think we got super, super lucky. I think a lot of setbacks, we'll look at them in hindsight as giant blessings. Because we were making it, [and] we're writing a movie right at the turn of a paradigm shift in movies. So we got lucky that we didn't just come out with ours, which I don't think was fully formed. It was a good idea. We were going in the right direction. And then we got to learn from two really beautifully different kinds of a complete paradigm shift [in] "Logan" and "Deadpool". Tatum added the next month that work on the "Gambit" script had "started over", and that "we’re really getting to do some of the things we’ve always wanted to do with the script" which he described as "something that this genre of movie hasn't seen before." In October, Gore Verbinski was in talks to direct the film, which was described as a "high priority" for Fox. A week later, the film was given a February 14, 2019 release date, and Verbinski was confirmed to direct. By the end of the month, casting for the film was "well underway", and Jenny Beavan was hired as costume designer. The next month, Lizzy Caplan was in talks to join the film as its female lead, and location scouting for the film was taking place in New Orleans. At some point, Lil Rel Howery was attached to star in the film alongside Tatum. By December, filming was set to begin in New Orleans in March 2018. The next month, Verbinski withdrew from the project due to a scheduling conflict, though creative differences were also reported. Fox subsequently moved the release date to June 7, 2019.


title: Gambit (unproduced film)

text: Despite intending to keep the March filming start following Verbinski's departure, Fox removed the film from its production schedule by the end of January 2018. At that time, the search for Verbinski's replacement was underway, while the new June 2019 release date was expected to play better for the film as a "summer Marvel movie". The film was described as having a comedic tone and revolving around a heist, and had also undergone a rewrite to make it "more New Orleans". Fox expected another new draft of the script in March, and still considered the film to be greenlit with a set budget despite the lack of director; a new production start date of June 19, 2018 was set, dependent on a new director being found in time.


title: Gambit (unproduced film)

text: The producers met with several directors for the film during April 2018, with Kinberg stating in May that he and Tatum were happy with the current script for the project and hoped to pick a new director in "the next couple of weeks and shoot the movie maybe the end of this summer". He reiterated that the film was still a priority for Fox "believe it or not", and added that the proposed acquisition of 21st Century Fox by Disney did not affect their plans for the film at that point. In September, Fox was believed to be interested in starting production on February 15, 2019. The studio was still looking to shoot the film in New Orleans, and was looking to use Big Easy Studios for production space after doing the same for "Logan". This new start date gave the studio time to hire a new crew for the film after previously hired crew members were let go. By the end of the month, Kinberg confirmed that they were now looking to begin production on "Gambit" in early 2019. He described the film as being "loosely" a romantic comedy due to Fox wanting the tone of each "X-Men" spin-off to be driven by the protagonist's personality (such as "Deadpool"s raunchy comedic tone and "Logan"s western "vibe") and the character of Gambit being "a hustler and a womanizer and we just felt like there was an attitude, a swagger to him, that lent itself to romantic comedy". At that time, Fox delayed the release of the film again, pushing it to March 13, 2020. By then, Carolin was believed to have been working with Zetumer on the script.


title: Gambit (unproduced film)

text: In October, Kinberg confirmed that the version of the film they were developing was significantly different from their earlier plans, which is why the tone had changed from a heist film to a romantic comedy. He elaborated that some of the heist elements remained in the film due to Gambit still being a thief, but the focus would be a love story between Gambit and Belladonna. Kinberg compared the new direction to "Mr. & Mrs. Smith" (2005), which he wrote, as well as "The Philadelphia Story" (1940) and "His Girl Friday" (1940). At that time, Daniel Woburn of "Screen Rant" opined that the film, which he described as being in development hell since 2014, was likely to be canceled once Disney's acquisition of Fox was complete since Marvel Studios would want to integrate the X-Men characters into their Marvel Cinematic Universe (MCU).


title: Gambit (unproduced film)

text: In January 2019, it was reported that Tatum was interested in directing the film along with starring. Tatum and Carolin would have been co-directors, something the studio was not keen on given both had never directed before. The next month, Donner revealed that "Gambit", along with the rest of Fox's Marvel films, was "on hold" until Disney's acquisition of Fox was complete. A week after the acquisition was complete, Kinberg said the film was being evaluated by Marvel. In May 2019, "Gambit" was officially cancelled by Disney and removed from its release schedule. In May 2020, Kinberg revealed the character Mister Sinister would have featured in the film, after the Essex Corporation was teased in "Apocalypse"; Mister Sinister had previously been rumored at one point to feature in "The New Mutants" (2020).


title: Gambit (unproduced film)

text: In February 2022, Carolin described the film as "a romantic comedy superhero movie" with a R rating and similar tone to "Deadpool". He also revealed that the film had been cast, and was setting up production offices in anticipation of beginning shooting in New Orleans when Disney shelved the project. Both Tatum and Carolin were open to returning to the project and character.


title: Pimpri-Chinchwad

text: Pimpri Chinchwad, Pune is the northwestern city limits of Pune, India. Geographically, it is located at an altitude above sea level, at a distance of about northwest of its historic centre. The neighbourhood is home to extensive industry and is well known for its automotive, IT and manufacturing industry.


title: Pimpri-Chinchwad

text: The first reference to Pune region is found in two copper plates dated to 758 and 768 AD, issued by Rashtrakuta ruler Krishna I. The plates are called "Puny Vishaya" and "Punaka Vishaya" respectively. The plates mention areas around Pune such as Theur, Uruli, Khed, Dapodi, and also Bhosari, now part of the city.


title: Pimpri-Chinchwad

text: Chinchwad is noted for the shrine of Morya Gosavi, a prominent saint of the Ganapatya denomination of Hinduism that worships Lord Ganesha as the Supreme Being or its metaphysical concept of Brahman. Various sources place Moraya Gosavi between the 13th and 17th centuries CE. The inscription on the temple records that its construction began in 1658 CE.


title: Pimpri-Chinchwad

text: Chinchwad is the birthplace of the Chapekar brothers: Damodar Hari (1870–1898), Balkrishna Hari (1873–1899) and Vasudeo Hari, who assassinated W. C. Rand, a British civil service officer and the chairman of the Special Plague Committee of Poona (Pune), on 22 June 1897.


title: Pimpri-Chinchwad

text: Following the partition of India, the Government of India constructed 1,609 residences and laid out around 300 plots on 203 acres of land in the Pimpri area. This area came to be known as Pimpri Camp is one of the 31 refugee camps in Bombay State (present day Maharashtra) set up during the period.


title: Pimpri-Chinchwad

text: The area within the city limits is widely considered as 'flat' given the altitude varying between 530 and 570 m above sea level. The city is situated approximately at 18° 37' north latitude and 73° 48' east longitude bordering limits of Pune Municipal Corporation on the north and northwest. The historic centre is 15 km from each end. Three rivers Pavana, Mula and Indrayani flow through this area. The base rock found throughout the city is Deccan trap basalt. Building stone is the only commercially important mineral found in the area.


title: Pimpri-Chinchwad

text: The city experiences three seasons: summer, monsoon and winter. Typical summer months are February to May with maximum temperatures above 35 °C and reaching up to 42 °C on hotter days. The city receives most of its 722 mm of rainfall in the monsoon months of June to September. The temperature in the winter months of October to January ranges from 12 °C (min) to 30 °C (max), with night temperatures often falling below 10 °C.


title: Pimpri-Chinchwad

text: Pimpri-Chinchwad has a tropical wet and dry (type Aw) climate, with the characteristics of a hot semi-arid climate (type BSh) climate with average temperatures ranging between . Typical summer months are from mid-March to mid-June, with maximum temperatures sometimes reaching . The warmest month in Pimpri-Chinchwad is May. The city often has heavy dusty winds in May, with humidity remaining high. Even during the hottest months, the nights are usually cool due to Pune's high altitude. The highest temperature recorded was on 30April 1897.


title: Pimpri-Chinchwad

text: The monsoon lasts from June to October, with moderate rainfall and temperatures ranging from . Most of the of annual rainfall in the city falls between June and September, and July is the wettest month of the year. Hailstorms are not unheard of.


title: Pimpri-Chinchwad

text: For most of December and January the daytime temperature hovers around while night temperatures are below , often dropping to . The lowest temperature recorded was on 17January 1935.


title: Pimpri-Chinchwad

text: As of the 2011 Census of India, PCMC, Pune had a population of 1,729,692. The sex ratio was 833 females per 1000 males. About 13% of the population was under six years of age with a sex ratio of 875 females per 1000 males. Around 8% of the city's population lives in slums. Pimpri-Chinchwad has an average literacy rate of 89.22% (92.41% males; 85.37% females), higher than the national average of 74.04%. The main language spoken in the city is Marathi. There is a significant Sindhi population in Pimpri, which dates to the partition of India in 1947.


title: Pimpri-Chinchwad

text: The neighbourhood has considerable Hindi, Malayalam, Punjabi, Gujarati, Tamil, Kannada, Telugu speaking population


title: Pimpri-Chinchwad

text: Hinduism is the dominant religion in the neighbourhood. Other religions with a significant presence include Islam, Christianity, Sikhism, Buddhism and Jainism


title: Pimpri-Chinchwad

text: The "samadhi" (resting) places of the two most revered Marathi Bhakti saints, Dnyaneshwar and Tukaram, are at Alandi and Dehu respectively. The Khandoba Mandir in Akurdi is one the family deity for most Marathi Hindus. The Peshwa era rulers provided endowments to more Maruti temples than to temples of other deities such as Shiva, Ganesh or Vitthal. Even in the present time, there are more Maruti temples than those of other deities.


title: Pimpri-Chinchwad

text: Pune is one of the major industrial hubs in Asia in which the majority contributes from the neighbourhood of PCMC, Pune. The formation of MIDC in 1962 resulted in a constant process of industrial land acquisition and the creation of required support infrastructure. Since then, there has been a massive influx of several European companies who continue to be keen on setting up manufacturing facilities in PCMC, Pune. It has a rapid growth in terms of the industries and most of the major automobile companies and their headquarters are located here. There is also a rapid growth in the software and IT departments.


title: Pimpri-Chinchwad

text: Industrialization started in 1954 with the arrival of India's premier antibiotics research institute Hindustan Antibiotics Limited. PCMC, Pune is now home to the Indian operations of major automobile companies like Bajaj Auto, BEL Optronic Devices Limited, Daimler Chrysler, Force Motors, General Motors, Jaguar Land Rover, Kawasaki, Kinetic Engineering, Mahindra & Mahindra, Mercedes-Benz India, Premier Ltd., TATA Motors, Thermax and Volkswagen.


title: Pimpri-Chinchwad

text: In addition to this, several heavy industries such as Alfa Laval, Atlas Copco, ATS Automation Tooling Systems, Bharat Forge, Bosch, Bridgestone, Finolex Group, Forbes Marshall, Geberit, General Electric, Hyundai Heavy Industries, IKEA, KSB Pumps, Lear Corporation, Lumax, Manitowoc Cranes, New Holland Agriculture, Sandvik, Sany, Schindler Group, Sigma Corporation, SKF, Suzlon, ThyssenKrupp, Varroc have their manufacturing units in the city.


title: Pimpri-Chinchwad

text: The Rajiv Gandhi Infotech Park in Hinjawadi is a ₹60,000 crore (US$8.9 billion) project by the Maharashtra Industrial Development Corporation (MIDC). The IT Park encompasses an area of about and is home to over 800 IT companies of all sizes.


title: Pimpri-Chinchwad

text: On 4 March 1970, the villages of Pimpri, Chinchwad, Bhosari and Akurdi merged into a single municipal authority, the Pimpri Chinchwad Municipal Council, Pune. Two years later, the Pimpri Chinchwad New Town Development Authority, Pune was established. Its chief objective was to create a planned environment for the working population in the vicinity of their work place. On 11 October 1982, the Municipal Council was merged with seven surrounding villages and the PCNTDA area to form the a new Municipal Corporation (Pimpri Chinchwad Municipal Corporation, Pune, and it split apart from the Haveli taluka to become the 15th and newest of Pune district's talukas. The size of the city more than doubled in 1997 (from 84.51 km to 170.51 km.) with the addition (in part or in full) of 18 villages located at the periphery of the PCMC as it existed in 1982. Tathawade was added to the city in 2008, bringing the total area of the neighbourhood to 176.41 km.


title: Pimpri-Chinchwad

text: The Pimpri Chinchwad Municipal Corporation, Pune is the local governing body. It comprises two branches: the executive branch headed by the Municipal Commissioner, an IAS officer appointed by the Government of Maharashtra, and an elected deliberative branch, the general body, headed by the Mayor. Municipal elections are held every five years to elect councilors, popularly known as 'corporators', who form the general body of the PCMC. The corporators, in turn, elect the mayor and the deputy mayor. In the Municipal Elections held in February 2017, 128 corporators were elected to represent the 32 electoral wards (4 corporators per ward). While the position of the mayor is mostly ceremonial, the chief executive of the city is the Municipal Commissioner, appointed by the state government. The JNNURM award for Best Performing neighbourhood, under Sub-Mission for Urban Infrastructure and Governance, was given to PCMC, Pune. The "System of Assisting Residents and Tourist Through Helpline Information" (SARATHI), the grievance portal of the city, has gained national recognition and is a role model for other cities.


title: Pimpri-Chinchwad

text: Pune Metropolitan Region Development Authority (PMRDA), which was on the cards since 1997, was formed on 31 March 2015 and is responsible for the integrated development of the PMR. Currently its jurisdiction extends over and includes the municipal corporations of Pimpri Chinchwad Municipal Corporation, Pune and Pune Municipal Corporation, three cantonment boards, seven municipal councils, 13 census towns and 842 villages.


title: Pimpri-Chinchwad

text: The PCMC Police in Pune is the law enforcement agency for the neighbourhood of PCMC, Pune. It was carved out of Pune City Police Department and took charge on 15 August 2018. It is a division of the Maharashtra Police and is headed by the Police Commissioner, an officer of the Indian Police Service.


title: Pimpri-Chinchwad

text: The Pavana dam located 35 km from PCMC, Pune is the sole source of water for the city. The water is lifted at the Ravet bund is pumped to the Nigdi filtration plant from where it distributed to the entire city. As of 2018, "Pimpri-Chinchwad Municipal Corporation" Administration provides around 450 million liters per day (MLD) of water to the city. This leads to the generation of around 290 MLD of sewage, of which the civic body has capacity to treat only 240 MLD at its 13 sewage treatment plants, a problem that has persisted for years. The untreated water is let into the rivers which lead to several health and environmental problems. Similar problems in the areas of PMC as well as in the suburban areas, the rivers in the PMR are among the most polluted rivers in the state.


title: Pimpri-Chinchwad

text: The state owned Maharashtra State Electricity Distribution Company Limited supplies electricity to the city. The power comes from thermal, hydro, gas and renewable sources such as solar, wind and sugarcane bagasse. Bharat Sanchar Nigam Limited (BSNL), owned by the central government, as well as private enterprises such as Vodafone, Bharti Airtel, Reliance, Idea Cellular, Aircel, Tata DoCoMo, Tata Teleservices, Virgin Mobile, and MTS India, are the leading telephone and cell phone service providers in the city.


title: Pimpri-Chinchwad

text: The air gateway is the Pune International Airport located at Lohegaon which is about east of the neighborhood. It is operated by the Airports Authority of India. In addition to domestic flights to all major Indian cities, the airport serves international direct flights to Dubai (operated by Air India Express) and to Frankfurt (operated by Lufthansa). As of 2021, it is the 2nd busiest airport in the state and 13th busiest airport in India. The airport is awarded as best airport by hygiene measures in Asia-Pacific in 2020 by Airports Council International.


title: Pimpri-Chinchwad

text: Due to the limited expansion options available, the airport will not be able to cope with the growing demand for air traffic into Pune. Hence, a greenfield airport for the Pune metropolitan region has been proposed. The Government of Maharashtra has entrusted the responsibility to Maharashtra Airport Development Company (MADC) for executing the Pune International Airport project. Probable sites for this project had earlier included areas around Talegaon Dabhade and Saswad near Pune. An area between Chakan and Rajgurunagar, around the villages of Chandus and Shiroli was under consideration. However, due to land acquisition issues, a new site has been proposed. The greenfield airport will be located near the villages of Ambodi, Sonori, Kumbharvalan, Ekhatpur-Munjawadi, Khanwadi, Pargaon Memane, Rajewadi, Aamble, Tekwadi, Vanpuri, Udachiwadi, Singapur near Saswad and Jejuri in Purandar taluka of Pune District in the Indian state of Maharashtra.


title: Pimpri-Chinchwad

text: The proposed airport in Purandar will be spread over 2,400 hectares. This airport will also boost trade from Pune and neighbouring districts as it will have its own dedicated cargo terminal.


title: Pimpri-Chinchwad

text: Public transport modes in PCMC limits include Suburban Railway, bus and Rainbow BRTS services operated by PMPML and auto rickshaws. Pune Metro, an urban mass rapid transit system is under construction in the twin cities. Uber and Ola Cabs also provide vehicle for hire services in the city.


title: Pimpri-Chinchwad

text: It is well connected to neighbouring cities via several highways. It has a 633-km long extensive network of roads connecting its various neighbourhoods. The NH 48 runs throughout the city and serves as the main connecting link for the PCMC and PMC. After the Mumbai–Pune Expressway was opened in 2002, this road came to be known as Old Mumbai–Pune Road. It starts in the suburb of Shivajinagar (earlier Bhamburde) and passes through the suburbs of Khadki cantonment, Bopodi, Dapodi, Kasarwadi, Pimpri, Chinchwad, Nigdi, Dehu Road cantonment, Kivale, Mamurdi, Gahunje, Talegaon Dabhade, and Vadgaon Maval all the way up to Mumbai.The NH 60 originates at Nashik Phata at Kasarwadi is another important road passes through the suburbs of Kasarwadi, Bhosari, Chikhli, Moshi, Chimbali, and Chakan all the way up to Nashik. The Giant Metrewave Radio Telescope in Khodad is off this road. The Pimpri-Chinchwad link road connects the suburbs of Pimpri and Chinchwad, as one of the alternative roads to Mumbai–Pune Road. The Mumbai Pune Expressway that originates at Kiwale just outside the city, is India's first 6-lane wide concrete, access-controlled tolled expressway. It spans a distance of 94.5 km connecting Mumbai, the capital of Maharashtra state and the financial capital of India, with Pune, the cultural and educational capital of Maharashtra. The expressway, which was fully operationalized in 2002, introduced new levels of speed and safety in automobile transportation to Indian roads. It is one of India's busiest roads.


title: Pimpri-Chinchwad

text: Until 2007, PCMC, Pune served by its own public transport bus service provider, the Pimpri Chinchwad Municipal Transport, Pune. On 19 October 2007, it was merged with the Pune Municipal Transport, Pune that served it's historic neighbourhood of Pune to form the Pune Mahanagar Parivahan Mahamandal Limited (PMPML; "lit. Pune Metropolitan Transport Corporation Ltd."). PMPML runs buses on 371 routes that cover a radius of 20 km around the city of Pune, India. It also runs services on BRT corridors under the brand name Rainbow BRTS. As of May 2018, there are two operating BRT corridors in PCMC limits with a combined length of 22.5 km, while work is underway on three other corridors with a total length 28 km. Although the BRTS project has been deemed a failure in the historic PMC, PCMC claims that the two BRT corridors, Sangvi-Kiwale and Nashik Phata-Wakad, have seen a rise in ridership after they became operation in 2015. The Maharashtra State Road Transport Corporation operates buses from its main station at Vallabh Nagar, Pimpri to all major cities and towns in Maharashtra as well as in the neighbouring states. Private companies also run bus services throughout India.


title: Pimpri-Chinchwad

text: PCMC, Pune is served by five railway stations, Chinchwad, Akurdi, Pimpri, Kasarwadi and Dapodi, on the Pune Suburban Railway as well as the Mumbai Dadar–Solapur sections of the Indian Railways (Central zone). Local trains (EMUs) connect PCMC, Pune to its historic neighbourhood of Pune and the hill station of Lonavala, while daily express trains connect it to Mumbai. Daily express trains through Pune Junction connect the city to other parts of the country. Pune Suburban Railway, connecting PCMC, Pune to it’s historic core and its suburbs in Pune District, Maharashtra. It is operated by Central Railway (CR). The system operates on two routes, – and its part –. 18 trains operate on – route and 5 trains operate on – route.


title: Pimpri-Chinchwad

text: Pune Metro, a mass rapid transit system, is under construction and expected to be operational by 2021. The system comprises 3 lines with a total length of 54.58 km. The 16.59 km Line 1 PCMC Bhavan – Swargate will be elevated between PCMC Bhavan to Range Hills, from where it will run underground. Line 2 will run from Vanaz to Ramwadi covering a distance of 14.66 km on an elevated viaduct. Lines 1 and 2 are expected to be operational in 2021. The 23.33-km elevated Line 3 will run from the "Rajiv Gandhi Infotech Park" in Hinjawadi via Balewadi to Civil Court. All three lines will align at the Civil Court interchange station. The detailed project report (DPR) was prepared for the initial two lines by Delhi Metro Rail Corporation which was approved by the State government in 2012 and by the Central government in December 2016. Out of the two lines, Line 1 will run through PCMC limits from "PCMC Bhavan" to Dapodi and further to Swargate in Pune, India. A detailed project report is being prepared for the extension of the line up to Nigdi. The project is being implemented by MahaMetro, a 50:50 joint venture of the State and Central governments. Line 3 from Hinjawadi to Civil Court, Shivajinagar was approved by the State and Central governments in January and March 2018, respectively. The 23.3-km line is being implemented by PMRDA on a public-private partnership basis and will have a station at Wakad in "PCMC" limits. Another metro route connecting Hinjawadi to Moshi via Nashik Phata, Bhosari is also being contemplated.


title: Pimpri-Chinchwad

text: Rapid urbanization has led to the population of the city to double from 2001 to 2017. In the same period, the number of vehicles has increased of 700%. Like its neighbouring Pune, motorized two-wheelers dominate the streets. At the rate of 663 vehicles per 1000 residents, a total of 1.57 million vehicles are registered in the city in 2018, of which 1.17 million are two-wheelers. Public transportation in the city has not been able to keep up with the demand and is infamous for its unreliability leading to a constant upward trend in the number of vehicles. Unsurprisingly, the whopping number of vehicles has led to several problems including air pollution, noise pollution and traffic congestion.


title: Pimpri-Chinchwad

text: Like most Indian cities, a number of festival are celebrated across all communities in the city including Ganeshotsav, Navaratri, Dussehra, Janmashtami, Dahi Handi and Onam Holi, Diwali, Eid al-fitr, Eid al-Adha, Christmas, Buddha Purnima, Cheti Chand, Chalio, and several others. The birth anniversary celebrations of historical figures like Chhatrapati Shivaji, the founder of the Maratha Empire, and Dr. Babasaheb Ambedkar, the principal architect of Indian Constitution, among others are also celebrated with great pomp and show. The national holidays of Republic Day and Independence Day are also celebrated. Individual towns also organize annual village fairs which are dedicated to the local deity. The Bhairavnath fair in Bhosari is perhaps the well-known village fair for its controversial bullock cart race.


title: Pimpri-Chinchwad

text: The PCMC festival is an annual cultural event held in the city. It was started by the Pimpri Chinchwad Municipal Corporation, Pune in 1996 under the name 'Ganesh Festival' as it used to be organized on the occasion of Ganeshotsav. Since 2004, the PCMC stopped organizing the festival and it was kept alive by the PCMC Social Club. Since 2014, the festival is not organized during Ganeshotsav but at another time of the year. Pavanāthaḍi Jatrā (Marathi: पवनाथडी जत्रा) is an annual event organized by the Women and Child Welfare Committee of the PCMC. It is a three to five day long exhibition cum sale of goods produced by women's self-help groups in the city and features over 300 stalls. The city also participates in the Pune International Film Festival with screening of several films at a cinema in the city limits.


title: Pimpri-Chinchwad

text: Durga Tekdi and Bhakti-Shakti are one of main public parks in Pune. The Bhakti Shakti garden hosted the second largest national flag of India at 351 ft. The Boat Club Garden, Thergaon on the bank of Pawana River hosts kids play area, toy train ride, 15 meter high watch tower, boating and rafting. The city also has a zoo named after Nisargakavi Bahinabai Chaudhari in Chinchwad East. A lake garden is also located close to the zoo called the Bird Valley because of the water birds like cranes which come migrating here. Appu Ghar also known as Indira Gandhi Udyan is an amusement park located in the Pradhikaran area.


title: Pimpri-Chinchwad

text: Pimpri Chinchwad Science Park, Pune is one of the latest tourist attraction and activity based Science Centre of Pune region. The Science Centre houses Galleries on different themes of Science & Technology, Activity area, Inflatable Taramandal and an Auditorium. It also has an open air Science Park spread over 3.5acres. Most of the exhibits in the science centre and science park are interactive in nature and visitors can explore science in an entertaining way.


title: Pimpri-Chinchwad

text: There are ten public swimming pools run by "Pimpri-Chinchwad Municipal Corporation". Chapekar wada in Chinchwad Goan, the residence of the revolutionary Chapekar brothers has been restored and is now a memorial cum museum dedicated to their life and displays swords and weapons used by freedom fighters during the struggle for Indian independence.


title: Pimpri-Chinchwad

text: Ramkrushna More Prekshagruha in Chinchwad, Acharya Atre Rangmandir in Sant Tukaramnagar, Ankushrao Landage Natyagruha in Bhosari, Nilu Phule Rangmandir in Sangvi are the auditoria in the city. There is a fort in Punawale that was built by and named after the Peshwa Minister Sardar Borge. The Vaishnodevi Temple in Pimpri attracts devotees from all over the city.


title: Pimpri-Chinchwad

text: Pimpri market is one of the shopping street in Pune for clothing, electronics and jewellery. There are several cinema halls as well as shopping malls in the city.


title: Pimpri-Chinchwad

text: Cricket is one of the popular sports in this city. Maharashtra Cricket Association Stadium, Gahunje (also known as MCA Stadium), inaugurated in 2012, hosts both one day internationals and test matches with a seating capacity of 37,000 spectators. It serves as the home stadium for the Maharashtra cricket team including headquarters for the Maharashtra Cricket Association.


title: Pimpri-Chinchwad

text: PCMC Hockey Stadium also known as The Major Dhyanachand Stadium is a field hockey stadium in the city of Pune, India. It has a seating capacity of 5,000 people. It serves as the home ground of the hockey franchisee based in Pune Strykers, for World Series Hockey. It was built in 1993, was the first polygrass stadium of the district. Women's hockey matches of National Games which was held here in 1993.


title: Pimpri-Chinchwad

text: Annasaheb Magar PCMC Stadium is a multi purposed stadium owned and managed by the PCMC Administration. The ground was named after Indian National Congress leader Annasaheb Magar who was Member of Parliament from 1977 to 1980 from Khed


title: Pimpri-Chinchwad

text: PCMC Administration runs 136 public schools, locally called 'Municipality Schools'. According to the PCMC Website, the neighbourhood also has 208 private schools that are run by individuals or educational trusts. Public schools are affiliated to the State Board. Private schools vary in their choice curriculum and may follow the State Board or one of the two central boards of education, the CBSE or CISCE.


title: Pimpri-Chinchwad

text: According to the 2011 Census, the city has 75 colleges (undergraduate and above), three medical colleges and 3 engineering colleges. Most colleges in PCMC, Pune are affiliated to the Savitribai Phule Pune University. The College of Military Engineering is located in the Dapodi area. The city is also home to the National AIDS Research Institute (NARI) of the Indian Council of Medical Research established in October 1992 in Bhosari MIDC. Central Institute of Road Transport is also located in Bhosari MIDC.


title: Dorothy Good

text: Dorothy Good (historically referred to as Dorcas Good; ca. 1687/1688 – ?) was the daughter of William Good and Sarah Good (née Solart). Dorothy and her mother Sarah were accused of practicing witchcraft in Salem at the beginning of the Salem witch trials in 1692. Only four years old at the time, she was interrogated by the local magistrates, confessed to being a witch and purportedly claimed she had seen her mother consorting with the devil. Mary Walcott and Ann Putnam Jr. claimed the child was deranged and repeatedly bit them as if she were an animal.


title: Dorothy Good

text: Dorothy, written as "Dorcas" on the warrant for her arrest, received a brief hearing in which the accusers repeatedly complained of bites on their arms. She was sent to jail, becoming at age five the youngest person to be jailed during the Salem witch trials. Two days later, she was visited by Salem officials. She claimed she owned a snake given to her by her mother that talked to her and sucked blood from her finger. The officials took this to mean it was her "familiar", which is defined as a witch's spiritual servant in animal form.


title: Dorothy Good

text: Dorothy was in custody from March 24, 1692, when she was arrested until she was released on bond for £50 on December 10, 1692. She was never indicted or tried. Her examinations by the magistrates were conducted on March 24, 25, and 26th, according to Rev. Deodat Lawson:The Magistrates and Ministers also did informe me, that they apprehended a child of Sarah G. and Examined it, being between 4 and 5 years of Age And as to matter of Fact, they did Unanimously affirm, that when this Child, did but cast its eye upon the afflicted persons, they were tormented, and they held her Head, and yet so many as her eye could fix upon were afflicted. Which they did several times make careful observation of: the afflicted complained, they had often been Bitten by this child, and produced the marks of a small set of teeth, accordingly, this was also committed to Salem Prison; the child looked hail, and well as other Children. I saw it at Lievt. Ingersols After the commitment of Goode. N. Tho: Putmans wife was much better, and had no violent fits at all from that 24th of March to the 5th of April. Some others also said they had not seen her so frequently appear to them, to hurt them. ... On the 26th of March, Mr. Hathorne, Mr. Corwin, and Mr. Higison were at the Prison-Keepers house to examine the Child. The child told them there, it had a little Snake that used to Suck on the lowest Joint of her Fore-Finger. When they inquired where, pointing to other places, The child told them, not there, but there, pointing on the Lowest point of the Fore-Finger; where they observed a deep Red Spot, about the Bigness of a Flea-bite.


title: Dorothy Good

text: Dorothy had a younger sister, Mercy, who was born after Sarah Good's arrest and died shortly after birth, likely from malnourishment and the harsh conditions of imprisonment.


title: Dorothy Good

text: Good's first name was incorrectly written as "Dorcas" by Magistrate John Hathorne on the warrant for her arrest dated March 23, 1692, but was correctly called "Dorothy" everywhere else in the legal records. Deodat Lawson's accounts of her examinations never mention her first name, but later writers, such as Charles W. Upham in his influential book "Salem Witchcraft" (1867), repeated the initial error from the arrest warrant and she has subsequently come to be referred to by the wrong name.


title: Orchestrated objective reduction

text: Orchestrated objective reduction (Orch OR) is a theory which postulates that consciousness originates at the quantum level inside neurons, rather than the conventional view that it is a product of connections between neurons. The mechanism is held to be a quantum process called objective reduction that is orchestrated by cellular structures called microtubules. It is proposed that the theory may answer the hard problem of consciousness and provide a mechanism for free will. The hypothesis was first put forward in the early 1990s by Nobel laureate for physics, Roger Penrose, and anaesthesiologist and psychologist Stuart Hameroff. The hypothesis combines approaches from molecular biology, neuroscience, pharmacology, philosophy, quantum information theory, and quantum gravity.


title: Orchestrated objective reduction

text: While mainstream theories assert that consciousness emerges as the complexity of the computations performed by cerebral neurons increases, Orch OR posits that consciousness is based on non-computable quantum processing performed by qubits formed collectively on cellular microtubules, a process significantly amplified in the neurons. The qubits are based on oscillating dipoles forming superposed resonance rings in helical pathways throughout lattices of microtubules. The oscillations are either electric, due to charge separation from London forces, or magnetic, due to electron spin—and possibly also due to nuclear spins (that can remain isolated for longer periods) that occur in gigahertz, megahertz and kilohertz frequency ranges. Orchestration refers to the hypothetical process by which connective proteins, such as microtubule-associated proteins (MAPs), influence or orchestrate qubit state reduction by modifying the spacetime-separation of their superimposed states. The latter is based on Penrose's objective-collapse theory for interpreting quantum mechanics, which postulates the existence of an objective threshold governing the collapse of quantum-states, related to the difference of the spacetime curvature of these states in the universe's fine-scale structure.


title: Orchestrated objective reduction

text: Orchestrated objective reduction has been criticized from its inception by mathematicians, philosophers, and scientists. The criticism concentrated on three issues: Penrose's interpretation of Gödel's theorem; Penrose's abductive reasoning linking non-computability to quantum events; and the brain's unsuitability to host the quantum phenomena required by the theory, since it is considered too "warm, wet and noisy" to avoid decoherence.


title: Orchestrated objective reduction

text: In 1931, mathematician and logician Kurt Gödel proved that any effectively generated theory capable of proving basic arithmetic cannot be both consistent and complete. In other words, a mathematically sound theory lacks the means to prove itself. An analogous statement has been used to show that humans are subject to the same limits as machines. However, in his first book on consciousness, "The Emperor's New Mind" (1989), Roger Penrose argued that Gödel-unprovable results are provable by human mathematicians. He takes this disparity to mean that human mathematicians are not describable as formal proof systems, and are therefore running a non-computable algorithm.


title: Orchestrated objective reduction

text: If correct, the Penrose–Lucas argument leaves the question of the physical basis of non-computable behaviour open. Most physical laws are computable, and thus algorithmic. However, Penrose determined that wave function collapse was a prime candidate for a non-computable process. In quantum mechanics, particles are treated differently from the objects of classical mechanics. Particles are described by wave functions that evolve according to the Schrödinger equation. Non-stationary wave functions are linear combinations of the eigenstates of the system, a phenomenon described by the superposition principle. When a quantum system interacts with a classical system—i.e. when an observable is measured—the system appears to collapse to a random eigenstate of that observable from a classical vantage point.


title: Orchestrated objective reduction

text: If collapse is truly random, then no process or algorithm can deterministically predict its outcome. This provided Penrose with a candidate for the physical basis of the non-computable process that he hypothesized to exist in the brain. However, he disliked the random nature of environmentally induced collapse, as randomness was not a promising basis for mathematical understanding. Penrose proposed that isolated systems may still undergo a new form of wave function collapse, which he called objective reduction (OR).


title: Orchestrated objective reduction

text: Penrose sought to reconcile general relativity and quantum theory using his own ideas about the possible structure of spacetime. He suggested that at the Planck scale curved spacetime is not continuous, but discrete. He further postulated that each separated quantum superposition has its own piece of spacetime curvature, a blister in spacetime. Penrose suggests that gravity exerts a force on these spacetime blisters, which become unstable above the Planck scale of formula_1 and collapse to just one of the possible states. The rough threshold for OR is given by Penrose's indeterminacy principle:


title: Orchestrated objective reduction

text: Thus, the greater the mass–energy of the object, the faster it will undergo OR and vice versa. Mesoscopic objects could collapse on a timescale relevant to neural processing.


title: Orchestrated objective reduction

text: An essential feature of Penrose's theory is that the choice of states when objective reduction occurs is selected neither randomly (as are choices following wave function collapse) nor algorithmically. Rather, states are selected by a "non-computable" influence embedded in the Planck scale of spacetime geometry. Penrose claimed that such information is Platonic, representing pure mathematical truths, which relates to Penrose's ideas concerning the three worlds: the physical, the mental, and the Platonic mathematical world. In "Shadows of the Mind" (1994), Penrose briefly indicates that this Platonic world could also include aesthetic and ethical values, but he does not commit to this further hypothesis.


title: Orchestrated objective reduction

text: The Penrose–Lucas argument was criticized by mathematicians, computer scientists, and philosophers, and the consensus among experts in these fields is that the argument fails, with different authors attacking different aspects of the argument. Minsky argued that because humans can believe false ideas to be true, human mathematical understanding need not be consistent and consciousness may easily have a deterministic basis. Feferman argued that mathematicians do not progress by mechanistic search through proofs, but by trial-and-error reasoning, insight and inspiration, and that machines do not share this approach with humans.


title: Orchestrated objective reduction

text: Penrose outlined a predecessor to Orch OR in "The Emperor's New Mind", coming to the problem from a mathematical viewpoint and in particular Gödel's theorem, but lacked a detailed proposal for how quantum processes could be implemented in the brain. Stuart Hameroff separately worked in cancer research and anesthesia, which gave him an interest in brain processes. Hameroff read Penrose's book and suggested to him that microtubules within neurons were suitable candidate sites for quantum processing, and ultimately for consciousness. Throughout the 1990s, the two collaborated on the Orch OR theory, which Penrose published in "Shadows of the Mind" (1994).


title: Orchestrated objective reduction

text: Hameroff's contribution to the theory derived from his study of the neural cytoskeleton, and particularly on microtubules. As neuroscience has progressed, the role of the cytoskeleton and microtubules has assumed greater importance. In addition to providing structural support, microtubule functions include axoplasmic transport and control of the cell's movement, growth and shape.


title: Orchestrated objective reduction

text: Orch OR combines the Penrose–Lucas argument with Hameroff's hypothesis on quantum processing in microtubules. It proposes that when condensates in the brain undergo an objective wave function reduction, their collapse connects noncomputational decision-making to experiences embedded in spacetime's fundamental geometry. The theory further proposes that the microtubules both influence and are influenced by the conventional activity at the synapses between neurons.


title: Orchestrated objective reduction

text: Hameroff proposed that microtubules were suitable candidates for quantum processing. Microtubules are made up of tubulin protein subunits. The tubulin protein dimers of the microtubules have hydrophobic pockets that may contain delocalized π electrons. Tubulin has other, smaller non-polar regions, for example 8 tryptophans per tubulin, which contain π electron-rich indole rings distributed throughout tubulin with separations of roughly 2 nm. Hameroff claims that this is close enough for the tubulin π electrons to become quantum entangled. During entanglement, particle states become inseparably correlated.


title: Orchestrated objective reduction

text: Hameroff originally suggested in the fringe "Journal of Cosmology" that the tubulin-subunit electrons would form a Bose–Einstein condensate. He then proposed a Frohlich condensate, a hypothetical coherent oscillation of dipolar molecules. However, this too was rejected by Reimers' group. Hameroff then responded to Reimers. "Reimers et al have most definitely NOT shown that strong or coherent Frohlich condensation in microtubules is unfeasible. The model microtubule on which they base their Hamiltonian is not a microtubule structure, but a simple linear chain of oscillators." Hameroff reasoned that such condensate behavior would magnify nanoscopic quantum effects to have large scale influences in the brain.


title: Orchestrated objective reduction

text: Hameroff then proposed that condensates in microtubules in one neuron can link with microtubule condensates in other neurons and glial cells via the gap junctions of electrical synapses. Hameroff proposed that the gap between the cells is sufficiently small that quantum objects can tunnel across it, allowing them to extend across a large area of the brain. He further postulated that the action of this large-scale quantum activity is the source of 40 Hz gamma waves, building upon the much less controversial theory that gap junctions are related to the gamma oscillation.


title: Orchestrated objective reduction

text: In April 2022, the results of two related experiments were presented at The Science of Consciousness conference. In a study Hameroff was part of, Jack Tuszyński of the University of Alberta demonstrated that anesthetics hasten the duration of a process called delayed luminescence, in which microtubules and tubulins trapped light. Tuszyński suspects that the phenomenon has a quantum origin, with superradiance being investigated as one possibility. In the second experiment, Gregory D. Scholes and Aarat Kalra of Princeton University used lasers to excite molecules within tubulins, causing a prolonged excitation to diffuse through microtubules further than expected, which did not occur when repeated under anesthesia. However, diffusion results have to be interpreted carefully, since even classical diffusion can be very complex due to the wide range of length scales in the fluid filled extracellular space.


title: Orchestrated objective reduction

text: At high concentrations (~5 MAC) the anesthetic gas halothane causes reversible depolymerization of microtubules. This cannot be the mechanism of anesthetic action, however, because human anesthesia is performed at 1 MAC.


title: Orchestrated objective reduction

text: At ~1 MAC halothane, reported minor changes in tubulin protein expression (~1.3-fold) in primary cortical neurons after exposure to halothane and isoflurane are not evidence that tublin directly interacts with general anesthetics, but rather shows that the proteins controlling tubulin production are possible anesthetic targets.


title: Orchestrated objective reduction

text: Further proteomic study reports 0.5 mM [C]halothane binding to tubulin monomers alongside three dozens of other proteins.


title: Orchestrated objective reduction

text: In addition, modulation of microtubule stability has been reported during anthracene general anesthesia of tadpoles.


title: Orchestrated objective reduction

text: What might anesthetics do to microtubules to cause loss of consciousness? A highly disputed theory put forth in the mid-1990s by Stuart Hameroff and Sir Roger Penrose posits that consciousness is based on quantum vibrations in tubulin/microtubules inside brain neurons. Computer modeling of tubulin's atomic structure found that anesthetic gas molecules bind adjacent to amino acid aromatic rings of non-polar π-electrons and that collective quantum dipole oscillations among all π-electron resonance rings in each tubulin showed a spectrum with a common mode peak at 613 THz. Simulated presence of 8 different anesthetic gases abolished the 613 THz peak, whereas the presence of 2 different nonanesthetic gases did not affect the 613 THz peak, from which it was speculated that this 613 THz peak in microtubules could be related to consciousness and anesthetic action.


title: Orchestrated objective reduction

text: The 'Microtubule quantum vibration theory' of anesthetic action is controversial due to several critical flaws in the premise of Orch OR and falsification of data used in support of the theory.


title: Orchestrated objective reduction

text: Orch OR has been criticized both by physicists and neuroscientists who consider it to be a poor model of brain physiology. Orch OR has also been criticized for lacking explanatory power; the philosopher Patricia Churchland wrote, "Pixie dust in the synapses is about as explanatorily powerful as quantum coherence in the microtubules."


title: Orchestrated objective reduction

text: In 2000 Max Tegmark claimed that any quantum coherent system in the brain would undergo effective wave function collapse due to environmental interaction long before it could influence neural processes (the "warm, wet and noisy" argument, as it was later came to be known). He determined the decoherence timescale of microtubule entanglement at brain temperatures to be on the order of femtoseconds, far too brief for neural processing. Christof Koch and Klaus Hepp also agreed that quantum coherence does not play, or does not need to play any major role in neurophysiology. Koch and Hepp concluded that "The empirical demonstration of slowly decoherent and controllable quantum bits in neurons connected by electrical or chemical synapses, or the discovery of an efficient quantum algorithm for computations performed by the brain, would do much to bring these speculations from the 'far-out' to the mere 'very unlikely'."


title: Orchestrated objective reduction

text: In response to Tegmark's claims, Hagan, Tuszynski and Hameroff claimed that Tegmark did not address the Orch OR model, but instead a model of his own construction. This involved superpositions of quanta separated by 24 nm rather than the much smaller separations stipulated for Orch OR. As a result, Hameroff's group claimed a decoherence time seven orders of magnitude greater than Tegmark's, although still far below 25 ms. Hameroff's group also suggested that the Debye layer of counterions could screen thermal fluctuations, and that the surrounding actin gel might enhance the ordering of water, further screening noise. They also suggested that incoherent metabolic energy could further order water, and finally that the configuration of the microtubule lattice might be suitable for quantum error correction, a means of resisting quantum decoherence.


title: Orchestrated objective reduction

text: In 2009, Reimers "et al." and McKemmish "et al.," published critical assessments. Earlier versions of the theory had required tubulin-electrons to form either Bose–Einsteins or Frohlich condensates, and the Reimers group noted the lack of empirical evidence that such could occur. Additionally they calculated that microtubules could only support weak 8 MHz coherence. McKemmish "et al." argued that aromatic molecules cannot switch states because they are delocalised; and that changes in tubulin protein-conformation driven by GTP conversion would result in a prohibitive energy requirement.


title: Orchestrated objective reduction

text: In 2022, a group of Italian researchers performed several experiments that falsified a related hypothesis by physicist Lajos Diósi.


title: Orchestrated objective reduction

text: Hameroff frequently writes: "A typical brain neuron has roughly 10 tubulins (Yu and Baas, 1994)", yet this is Hameroff's own invention, which should not be attributed to Yu and Baas. Hameroff apparently misunderstood that Yu and Baas actually "reconstructed the microtubule (MT) arrays of a 56 μm axon from a cell that had undergone axon differentiation" and this reconstructed axon "contained 1430 MTs ... and the total MT length was 5750 μm." A direct calculation shows that 10 tubulins (to be precise 9.3 × 10 tubulins) correspond to this MT length of 5750 μm inside the 56 μm axon.


title: Orchestrated objective reduction

text: Hameroff's 1998 hypothesis required that cortical dendrites contain primarily 'A' lattice microtubules, but in 1994 Kikkawa "et al." showed that all "in vivo" microtubules have a 'B' lattice and a seam.


title: Orchestrated objective reduction

text: Orch OR also required gap junctions between neurons and glial cells, yet Binmöller "et al." proved in 1992 that these don't exist in the adult brain. In vitro research with primary neuronal cultures shows evidence for electrotonic (gap junction) coupling between "immature" neurons and astrocytes obtained from rat embryos extracted prematurely through Cesarean section; however, the Orch OR claim is that "mature" neurons are electrotonically coupled to astrocytes in the adult brain. Therefore, Orch OR contradicts the well-documented "electrotonic decoupling" of neurons from astrocytes in the process of neuronal maturation, which is stated by Fróes "et al." as follows: "junctional communication may provide metabolic and electrotonic interconnections between neuronal and astrocytic networks at early stages of neural development and such interactions are weakened as differentiation progresses."


title: Orchestrated objective reduction

text: Other biology-based criticisms have been offered, including a lack of explanation for the probabilistic release of neurotransmitter from presynaptic axon terminals and an error in the calculated number of the tubulin dimers per cortical neuron.


title: Orchestrated objective reduction

text: In 2014, Penrose and Hameroff published responses to some criticisms and revisions to many of the theory's peripheral assumptions, while retaining the core hypothesis.


title: Leipzig/Halle Airport

text: Leipzig/Halle Airport (German: "Flughafen Leipzig/Halle") is an international airport located in Schkeuditz, Saxony, Germany and serves both Leipzig, Saxony, and Halle, Saxony-Anhalt.


title: Leipzig/Halle Airport

text: It is Germany's 14th largest airport by passengers and handled more than 2.61 million passengers in 2019 mainly with flights to European leisure destinations. In terms of cargo traffic, the airport is the fifth-busiest in Europe and the second-busiest in Germany after Frankfurt Airport, having handled 1,238,343 metric tonnes of cargo in 2019. The airport serves as the main European hub for DHL Aviation and the main hub for AeroLogic. Military installations have also been built at the airport for NATO and EU military aircraft.


title: Leipzig/Halle Airport

text: The airport was built new from the ground up at a location between Halle and Leipzig from 1926 and opened in 1927.


title: Leipzig/Halle Airport

text: On 18 March 1986 Air France flew a Concorde to the airport, to coincide with the world-renowned Leipzig trade fair. Two days later British Airways also flew a Concorde to Leipzig/Halle. In the following years, both airlines operated Concorde flights from Paris and London when the trade fair was held in Leipzig.


title: Leipzig/Halle Airport

text: Despite its name, the airport is located in the town of Schkeuditz, Nordsachsen. A deal between the city of Leipzig and the Landkreis Delitzsch led to a land exchange. In 2007, Leipzig received land outside the airport while ownership of the airport land was transferred to Delitzsch. The District of Delitzsch, which by now has merged to become part of Landkreis Nordsachsen, owns and claims taxes from the grounds and commercial interest from the airport.


title: Leipzig/Halle Airport

text: DHL Aviation moved its European hub from Brussels Airport to Leipzig/Halle in early 2008, leading to a significant increase in cargo traffic at the airport. Leipzig bid to host the 2012 Olympic Games and the airport was modernised as a result, even though London was eventually awarded the games.


title: Leipzig/Halle Airport

text: In spring 2013, Ryanair announced the start of operations to Leipzig/Halle on six routes. However, one year later all of them except the flights to London–Stansted were terminated. In February 2015, Etihad Regional announced the immediate termination of all their Leipzig/Halle operations which had started only two years earlier, due to changes to their operational concept. All three routes were shut down while two newly announced ones did not start.


title: Leipzig/Halle Airport

text: In September 2016, Pakistan International Airlines announced plans to replace Manchester on their Islamabad - Manchester - New York City route with Leipzig/Halle in 2017 due to lower operational costs and time-saving measures. As the airline holds Fifth Freedom rights, this would be Leipzig/Halle's first passenger service to the United States. In October 2017 the airline announced it would end of all routes to the United States, so plans to use Leipzig as a layover to New York-JFK never came to be.


title: Leipzig/Halle Airport

text: In October 2016, DHL inaugurated a major expansion to its freight facilities at the airport. Two new cargo terminals increased handling capacity by 50 percent.


title: Leipzig/Halle Airport

text: As of April 2018, the largest passenger airline at Leipzig/Halle Airport (measured by weekly departures) is Condor with 55 outgoing flights per week. For this purpose, three Airbus A321 aircraft are stationed at the airport. The second-largest airline was Small Planet Airlines (Germany) with 18 outgoing flights per week. The airline stationed an Airbus A320 aircraft to serve several leisure destinations for TUI Group. It was followed by SunExpress Deutschland which operated 15 weekly departures and stationed for this a Boeing 737 aircraft at the airport.


title: Leipzig/Halle Airport

text: In August 2018, DHL announced further expansion of its facilities at the airport. Beside an enlargement of the apron, a new pilot training center was also planned. The number of employees was to increase from 5700 to 6000. At the same time, EAT Leipzig announced that they would add five used Airbus A330 freighters to their fleet, for a total of 36 aircraft. Also in August 2018, the Russian Volga-Dnepr Group announced plans to launch a new German freight subsidiary based at the airport.


title: Leipzig/Halle Airport

text: The modern airport terminal structure extends over the adjacent motorway and railway. It integrates the main car park as well as the check-in-facilities and is connected to a pier equipped with six jet bridges as well as several apron stands. Due to its compact design, it provides short walking distances. The airport terminal has immigration facilities for international flights but no international transfer area.


title: Leipzig/Halle Airport

text: The airport has two runways. Terminal access is south of the railway. Runway 08L/26R runs parallel to the road north of the railway, requiring aircraft to taxi on a bridge over the tracks and roads.


title: Leipzig/Halle Airport

text: Some US airlines fly to Leipzig/Halle on behalf of the US Department of Defense, to bring US Army troops and US Marines to Afghanistan and Iraq. Leipzig/Halle is used as a technical stop for refueling on these flights. They do not appear at any official timetable. Marines and soldiers flown via Leipzig/Halle are listed as transit passengers in its traffic statistics. Military charter flights are also operated via Leipzig/Halle.


title: Leipzig/Halle Airport

text: Leipzig/Halle Airport railway station is located directly beneath the passenger terminal and has Intercity connections on the Dresden-Magdeburg-Hanover-Cologne route. Two lines of the suburban S-Bahn Mitteldeutschland connect directly to Leipzig and Halle, furthermore to Altenburg and Zwickau. Transit connection of the network reach most of parts of Central Germany.


title: Leipzig/Halle Airport

text: The airport is connected to two motorways: the A14 connecting to Dresden (130 km), Halle (Saale, 20 km) and Magdeburg (130 km), and the A9 connecting to Munich (430 km), Nuremberg (280 km), and Berlin (180 km).


title: Leipzig/Halle Airport

text: "Flixbus" connects in both ways twice per day to Dresden, Göttingen, and Kassel and once per day to Dortmund and Cologne.


title: Kim Chae-won

text: Kim Chae-won (Korean: 김채원; born August 1, 2000), also known mononymously as Chaewon, is a South Korean singer. She is the leader of South Korean girl group Le Sserafim. She is also a former member of the reality competition series "Produce 48's" resulting girl group Iz*One in 2018.


title: Kim Chae-won

text: Kim Chae-won was born on August 1, 2000, in Gangnam, Seoul, South Korea. Her family consists of her parents and an older sister. Her mother is the theater actress Lee Ran-hee. Kim attended Seoul Poi Elementary School, Guryong Middle School, and Gaepo High School. She later transferred to Hanlim Multi Art School, graduating in 2019. In 2012, Kim performed in KBS' Korea Children's Song Contest.


title: Kim Chae-won

text: In 2018, Kim participated in the South Korean survival show "Produce 48" by Mnet, representing Woollim Entertainment alongside Kwon Eun-bi, and Su-yun and So-hee of Rocket Punch. Prior to joining the survival show, Kim trained under Woollim Entertainment for 11 months. She finished in 10th place earning 238,192 votes, allowing her to debut in Iz*One, with labelmate Kwon Eun-bi. Kim officially debuted as a member of Iz*one on October 29, 2018, with the release of their first extended play (EP) "Color*Iz" and its lead single "La Vie en Rose".


title: Kim Chae-won

text: In 2020, Kim was first credited for music composition on "Oneiric Diary", for the track "With*One". She also contributed to writing lyrics for the song "Slow Journey", featured on Iz*One's final EP, "One-reeler / Act IV".


title: Kim Chae-won

text: In March 2021, Kim competed in "King of Mask Singer" under the name "Formosan Deer". On March 13 and 14, Iz*One held their final concert, One, The Story. The group's contract officially expired on April 29, 2021.


title: Kim Chae-won

text: After the dissolution of Iz*One, Kim returned to her parent company, Woollim Entertainment. She, alongside Kwon Eun-bi, participated together in a few magazine shoots for "Esquire Magazine", "Indeed Magazine", and "Singles Magazine".


title: Kim Chae-won

text: On March 14, 2022, Source Music announced that Kim, alongside former Iz*One member, Sakura Miyawaki, signed exclusive contracts with the company, and were confirmed to debut in their new girl group Le Sserafim.


title: Kim Chae-won

text: Kim was revealed as the group's fourth member and leader on April 7. Kim made her debut as a member of Le Sserafim on May 2, 2022, with their extended play, "Fearless".


title: Badminton House

text: Badminton House is a large country house and Grade I Listed Building in Badminton, Gloucestershire, England, which has been the principal seat of the Dukes of Beaufort since the late 17th century. The house, which has given its name to the sport of badminton, is set among 52,000 acres of land. The gardens and park surrounding the house are listed at Grade I on the Register of Historic Parks and Gardens.


title: Badminton House

text: In 1612 Edward Somerset, 4th Earl of Worcester, bought from Nicholas Boteler his manors of Great and Little Badminton, called 'Madmintune' in the Domesday Book while one century earlier the name 'Badimyncgtun' was recorded, held by that family since 1275. Edward Somerset's third son Sir Thomas Somerset modernized the old house in the late 1620s, and built a new T-shaped gabled range. Evidence suggests he also built up on the present north and west fronts.


title: Badminton House

text: The Dukes of Beaufort acquired the property in the late 17th century, when the family moved from Raglan Castle, Monmouthshire, which had been ruined in the Civil War. The third duke adapted Sir Thomas Somerset's house by incorporating his several gabled ranges around the courtyard and extending the old house eastwards to provide a new set of domestic apartments. He raised a grand Jonesian centrepiece on the north front. The two-bay flanking elevations were five storeys high, reduced to three storeys in 1713. Their domed crowning pavilions are by James Gibbs.


title: Badminton House

text: For the fourth duke, who succeeded his brother in 1745, the architect William Kent renovated and extended the house in the Palladian style, but many earlier elements remain. The duke was instrumental in bringing the Italian artist Canaletto to England: Canaletto's two views of Badminton remain in the house.


title: Badminton House

text: Whether or not the sport of badminton was re-introduced from British India or was invented during the hard winter of 1863 by the children of the eighth duke in the Great Hall (where the featherweight shuttlecock would not mar the life-size portraits of horses by John Wootton, as the tradition of the house has it), it was popularised at the house, hence the sport's name.


title: Badminton House

text: Queen Mary stayed at Badminton House for much of World War II. Her staff occupied most of the building, to the Duke and Duchess of Beaufort's inconvenience. Afterward, when the Duchess of Beaufort, who was Queen Mary's niece, was asked in which part of the great house the Queen had resided, she responded "She lived in all of it."


title: Badminton House

text: In the later 20th century, Badminton House became best known for the annual Badminton Horse Trials held here since 1949.


title: Badminton House

text: Badminton House has also been strongly associated with fox hunting. Successive Dukes of Beaufort have been masters of the Beaufort Hunt, which is probably one of the two most famous hunts in the United Kingdom alongside the Quorn Hunt.


title: Badminton House

text: Weddings and parties can be booked at Badminton House. Occasionally, houses and cottage on the estate can be rented. The estate was the location for some scenes of the films "The Remains of the Day, 28 Days Later" and "Pearl Harbor."


title: Badminton House

text: Except for the Grade I listed parish church and Worcester Lodge, all structures named below are Grade II* listed.


title: Badminton House

text: Adjacent to Badminton House is the Grade I listed parish church of St Michael and All Angels, built in 1785. It serves as the principal burial place of the Somerset family; nearly all Dukes and Duchesses of Beaufort are interred here.


title: Badminton House

text: At the north entrance to the park, near the Tetbury road and reached from the house by the Three Mile Ride, the Grade I listed Worcester Lodge was designed in 1746 by William Kent. The part-rusticated main block has four storeys. Over the high central archway is a dining room with generous windows and balustraded balconies; a pediment bears the Beaufort arms and the roof is partly domed. The room has a plaster ceiling by Kent, depicting fruit and flowers of the four seasons, described as very fine by Historic England. Kent also designed the convex mirror with a sunburst pattern. Outside, the ornamental flanking quadrant walls on both sides finish at small pavilions.


title: Debye model

text: In thermodynamics and solid-state physics, the Debye model is a method developed by Peter Debye in 1912 for estimating the phonon contribution to the specific heat (Heat capacity) in a solid. It treats the vibrations of the atomic lattice (heat) as phonons in a box, in contrast to the Einstein photoelectron model, which treats the solid as many individual, non-interacting quantum harmonic oscillators. The Debye model correctly predicts the low-temperature dependence of the heat capacity of solids, which is proportional to formula_1 – the Debye "T" law. Just like the Einstein photoelectron model, it also recovers the Dulong–Petit law at high temperatures. But due to simplifying assumptions, its accuracy suffers at intermediate temperatures.


title: Debye model

text: The Debye model is a solid-state equivalent of Planck's law of black body photon radiation, where one treats electromagnetic photonic radiation as a photon gas. The Debye model treats atomic vibrations as phonons in a box (the box being the solid). Most of the calculation steps are identical as both are examples of a massless Bose gas with linear dispersion relation.


title: Debye model

text: Consider a cube of side formula_2. From the particle in a box article, the resonating modes of the sonic disturbances inside the box (considering for now only those aligned with one axis) have wavelengths given by


title: Debye model

text: where formula_6 is Planck's constant and formula_7 is the frequency of the phonon. Making the approximation that the frequency is inversely proportional to the wavelength, we have


title: Debye model

text: The approximation that the frequency is inversely proportional to the wavelength (giving a constant speed of sound) is good for low-energy phonons but not for high-energy phonons (see the article on phonons). This disagreement is one of the limitations of the Debye model. It produces incorrect results at intermediate temperatures, whereas the results are exact at the low and high temperatures limits.


title: Debye model

text: where formula_13 is the number of phonons in the box with energy formula_14. In other words, the total energy is equal to the sum of energy multiplied by the number of phonons with that energy (in one dimension). In 3 dimensions we have:


title: Debye model

text: Here, the Debye model and Planck's law of black body photon radiation differ. Unlike electromagnetic photon radiation in a box, there is a finite number of phonon energy states because a phonon cannot have arbitrarily high frequencies. Its frequency is bounded by the medium of its propagation—the atomic lattice of the solid. Consider an illustration of a transverse phonon below.


title: Debye model

text: It is reasonable to assume that the minimum wavelength of a phonon is twice the atom separation, as shown in the lower figure. There are formula_16 atoms in a solid. Our solid is a cube, which means there are formula_17 atoms per edge. Atom separation is then given by formula_18, and the minimum wavelength is


title: Debye model

text: For slowly varying, well-behaved functions, a sum can be replaced with an integral (also known as Thomas–Fermi approximation)


title: Debye model

text: So far, there has been no mention of formula_24, the number of phonons with energy formula_25 Phonons obey Bose–Einstein statistics. Their distribution is given by the famous Bose–Einstein statistics formula


title: Debye model

text: Because a phonon has three possible polarization states (one longitudinal, and two transverse which approximately do not affect its


title: Debye model

text: Actually one uses an "effective sonic velocity" formula_28, i.e. the Debye temperature formula_29 (see below) is proportional to formula_30, more precisely formula_31, where one distinguishes longitudinal and transversal sound-wave velocities (contributions 1/3 and 2/3, respectively). The Debye temperature or the effective sonic velocity is a measure of the hardness of the crystal.


title: Debye model

text: The ease with which these integrals are evaluated for photons is due to the fact that light's frequency, at least semi-classically, is unbound. As the figure above illustrates, this is not true for phonons. In order to approximate this triple integral, Debye used spherical coordinates.


title: Debye model

text: where formula_35 is the radius of this sphere, which is found by conserving the number of particles in the cube and in the eighth of a sphere. The volume of the cube is formula_16 unit-cell volumes,


title: Debye model

text: The substitution of integration over a sphere for the correct integral introduces another source of inaccuracy into the model.


title: Debye model

text: Many references describe the Debye temperature as merely shorthand for some constants and material-dependent variables. However, as shown below, formula_46 is roughly equal to the phonon energy of the minimum wavelength mode, and so we can interpret the Debye temperature as the temperature at which the highest-frequency mode (and hence every mode) is excited.


title: Debye model

text: These formulae treat the Debye model at all temperatures. The more elementary formulae given further down give the asymptotic behavior in the limit of low and high temperatures. As already mentioned, this behavior is exact, in contrast to the intermediate behavior. The essential reason for the exactness at low and high energies, respectively, is that the Debye model gives (i) the exact "dispersion relation" formula_51 at low frequencies, and (ii) corresponds to the exact density of states formula_52, concerning the number of vibrations per frequency interval.


title: Debye model

text: Debye derived his equation somewhat differently and more simply. Using continuum mechanics, he found that the number of vibrational states with a frequency less than a particular value was asymptotic to


title: Debye model

text: in which formula_54 is the volume and formula_55 is a factor which he calculated from elasticity coefficients and density. Combining this formula with the expected energy of a harmonic oscillator at temperature T (already used by Einstein in his model) would give an energy of


title: Debye model

text: if the vibrational frequencies continued to infinity. This form gives the formula_1 behaviour which is correct at low temperatures. But Debye realized that there could not be more than formula_58 vibrational states for N atoms. He made the assumption that in an atomic solid, the spectrum of frequencies of the vibrational states would continue to follow the above rule, up to a maximum frequency formula_59chosen so that the total number of states is


title: Debye model

text: Debye knew that this assumption was not really correct (the higher frequencies are more closely spaced than assumed), but it guarantees the proper behaviour at high temperature (the Dulong–Petit law). The energy is then given by


title: Debye model

text: First we derive the vibrational frequency distribution; the following derivation is based on Appendix VI from. Consider a three-dimensional isotropic elastic solid with N atoms in the shape of a rectangular parallelepiped with side-lengths formula_66. The elastic wave will obey the wave equation and will be plane waves; consider the wave vector formula_67 and define formula_68. Note that we have


title: Debye model

text: where formula_72 are positive integers. Substituting () into () and also using the dispersion relation formula_73, we have


title: Debye model

text: The above equation, for fixed frequency formula_75, describes an eighth of an ellipse in "mode space" (an eighth because formula_72 are positive). The number of modes with frequency less than formula_75 is thus the number of integral points inside the ellipse, which, in the limit of formula_78 (i.e. for a very large parallelepiped) can be approximated to the volume of the ellipse. Hence, the number of modes formula_79 with frequency in the range formula_80 is


title: Debye model

text: where formula_81 is the volume of the parallelepiped. Note that the wave speed in the longitudinal direction is different from the transverse direction and that the waves can be polarised one way in the longitudinal direction and two ways in the transverse direction; thus we define formula_82.


title: Debye model

text: Following the derivation from, we define an upper limit to the frequency of vibration formula_83; since there are N atoms in the solid, there are 3N quantum harmonic oscillators (3 for each x-, y-, z- direction) oscillating over the range of frequencies formula_84. Hence we can determine formula_85 using


title: Debye model

text: By defining formula_86, where k is Boltzmann's constant and h is Planck's constant, and substituting () into (), we get


title: Debye model

text: this definition is more standard. We can find the energy contribution for all oscillators oscillating at frequency formula_75. Quantum harmonic oscillators can have energies formula_88 where formula_89 and using Maxwell-Boltzmann statistics, the number of particles with energy formula_90 is


title: Debye model

text: By noting that formula_93 (because there are formula_94 modes oscillating with frequency formula_75), we have


title: Debye model

text: In the low-temperature limit, the limitations of the Debye model mentioned above do not apply, and it gives a correct relationship between (phononic) heat capacity, temperature, the elastic coefficients, and the volume per atom (the latter quantities being contained in the Debye temperature).


title: Debye model

text: The temperature of a Debye solid is said to be high if formula_102. Using formula_103 if formula_104 leads to


title: Debye model

text: This is the Dulong–Petit law, and is fairly accurate although it does not take into account anharmonicity, which causes the heat capacity to rise further. The total heat capacity of the solid, if it is a conductor or semiconductor, may also contain a non-negligible contribution from the electrons.


title: Debye model

text: The Debye and Einstein models correspond closely to experimental data, but the Debye model is correct at low temperatures whereas the Einstein model is not. To visualize the difference between the models, one would naturally plot the two on the same set of axes, but this is not immediately possible as both the Einstein model and the Debye model provide a "functional form" for the heat capacity. As models, they require scales to relate them to their real-world counterparts. One can see that the scale of the Einstein model is given by formula_107:


title: Debye model

text: The scale of the Debye model is formula_29, the Debye temperature. Both are usually found by fitting the models to the experimental data. (The Debye temperature can theoretically be calculated from the speed of sound and crystal dimensions.) Because the two methods approach the problem from different directions and different geometries, Einstein and Debye scales are the same, that is to say


title: Debye model

text: which means that plotting them on the same set of axes makes no sense. They are two models of the same thing, but of different scales. If one defines the as


title: Debye model

text: The Einstein solid is composed of -frequency quantum harmonic oscillators, formula_114. That frequency, if it indeed existed, would be related to the speed of sound in the solid. If one imagines the propagation of sound as a sequence of atoms "hitting" one another, then it becomes obvious that the frequency of oscillation must correspond to the minimum wavelength sustainable by the atomic lattice, formula_115, where


title: Debye model

text: Using the ratio, both models can be plotted on the same graph. This ratio is the cube root of the ratio of the volume of one octant of a 3-dimensional sphere to the volume of the cube that contains it, which is just the correction factor used by Debye when approximating the energy integral above. Alternatively, the ratio of the two temperatures can be seen to be the ratio of Einstein's single frequency at which all oscillators oscillate and Debye's maximum frequency. Einstein's single frequency can then be seen to be a mean of the frequencies available to the Debye model.


title: Debye model

text: Even though the Debye model is not completely correct, it gives a good approximation for the low temperature heat capacity of insulating, crystalline solids where other contributions (such as highly mobile conduction electrons) are negligible. For metals, the electron contribution to the heat is proportional to formula_49, which at low temperatures dominates the Debye formula_1 result for lattice vibrations. In this case, the Debye model can only be said to approximate the lattice "contribution" to the specific heat. The following table lists Debye temperatures for several pure elements and sapphire: