title: Char 2C

text: General Philippe Pétain, the new High Commander of the French Army, asked Estienne to use his position to end the project. Estienne told Pétain that this was ill-advised while the public was questioning why these heavy tanks had not been produced. Besides, the allies (specifically the British and the US) would only consent to give France 700 of the new Mark VIII "Liberty" design if France had made at least a token effort to produce its own heavy tanks. Thus the French authorities had to delay the project while outwardly endorsing it. Estienne had already set this course by choosing the heaviest version, the "C", for production, requiring a completely new prototype, causing a considerable delay. Then Pétain demanded unreasonably high production numbers, thus delaying planning and initiating a political row.


title: Char 2C

text: Pétain asked for 300 heavy tanks to be ready by March 1919, causing a quarrel to erupt between Clemenceau, who was both Prime-Minister and Minister of War, and Loucheur, the Minister of Armament, who felt it was impossible to provide the labour and steel required. Meanwhile, Estienne and Pétain complicated the issue with further demands. Pétain asked for special pontoons, and Estienne demanded battering rams and electronic mine detectors to be fixed. When the war ended, not a single tank had been built.


title: Char 2C

text: At first, the production order for the Char 2C was cancelled. Despite the end of hostilities, however, strong political pressure to adopt new heavy tank projects remained, as there was now a considerable surplus capacity in the heavy industry. To stop this, the "Direction de l’Artillerie d’Assaut" on instigation of Estienne decided in April 1919 to procure ten Char 2Cs after all, and use this as an argument to reject any other projects. This was not completely successful; as late as 1920 it was proposed to the "Section Technique des Appareils de Combat" to build a 600-tonne tank with 250 mm armour. At FCM Jammy and Savatier finished the Char 2C prototype, the other nine tanks being built almost simultaneously; all ten were delivered in 1921 and modified by the factory until 1923. They would be the last French tanks to be produced for the home market till the Char D1 pre-series of 1931.


title: Char 2C

text: The Char 2C was the only super-heavy tank ever to attain operational status – a super-heavy tank is not simply a tank that is very heavy but one that has been deliberately made much heavier than regular tanks of its period. The next operational tank to approach its weight would be the German Tiger II heavy tank of World War II.


title: Char 2C

text: The Char 2C had a loaded weight of 69 tonnes, partly because of its armour, which was among the thickest of World War I-era tanks, but mostly because of its huge size. It is still easily the largest tank ever taken into production. With the tail fitted, the hull was over long. Without tail, the hull length was 10.372 metres, the width 2.95 metres, the height 3.8 metres. Adding the cupola, normally detached for transport, brought height to . The armour thickness was 30 mm at the front, 22 mm at the sides, 13 mm at the top and 10 mm at the bottom. In 1930 and 1931, the vehicles were rebuilt with a frontal armour of .


title: Char 2C

text: Within its ample frame there was room for two fighting compartments. The forward compartment was crowned by a three-man turret – the first such in history – mounting a shortened 75 mm field gun of the "Canon de 75 modèle 1897" type, with 124 rounds and a muzzle velocity of , and the second, at the rear of the tank, was topped by a machine-gun turret armed with a Hotchkiss 8 mm. The front turret, made of 35 mm plates, was placed so high that its crew had to climb into it by means of a ladder, sitting on seats suspended from the turret roof and operating on an elevated level compared to the hull machine gunners below. The rear turret was made of 22 mm thick plates. Both turrets had stroboscopic cupolas. The three independent 8 mm machine gun positions, one at each side and one to the right of the driver at the front, all in ballmounts, gave protection against infantry assault. The machineguns had an ammunition load of 9,504 rounds.


title: Char 2C

text: The fighting compartments were connected by the engine room. In the design four engines had been planned but this was reduced to two, each track being powered by its own engine via an electrical transmission. The first engines were of the Chenu type, of each. In 1923, these were replaced by captured German 6-cylinder Mercedes engines allowing for a top speed of . These original engines wore out quickly and were eventually in turn replaced by two Maybach engines, 16,950 cc, which rendered a maximum speed of . Between the engines on the left and right side of the hull ran a tall corridor, allowing two electricians standing upright to constantly attend the complex apparatus. Seven fuel tanks, four to the left and three to the right, containing 1,260 litres, gave it a range of 150 kilometres. The suspension contained thirty-nine interleaving road wheels on each side, making for a total of ninety wheels on the tank. Designed to negotiate the challenging terrain of trench warfare, the type had in principle excellent mobility. The Char 2C could cross a trench 425 centimetres wide, enough to pass the typical canal sluices in northern France. A vertical obstacle could be climbed of 170 centimetres and a slope of 70%. The wading capacity was 140 centimetres. Ground clearance was sixty centimetres. The axle track, measured between the inner track sides, was 225 centimetres.


title: Char 2C

text: To man the tank required a crew of twelve: driver, commander, gunner, loader, four machine gunners, mechanic, electrician, assistant-electrician/mechanic and a radio operator. Some sources report thirteen, probably due to pictures of the crews that included the company commander. The assistant-mechanic was seated to the front right of the rear fighting compartment, on top of an escape hatch, and the radio operator was seated at the front left.


title: Char 2C

text: The ten tanks were part of several consecutive units, their organic strength at one time reduced to three. Their military value slowly decreased as more advanced tanks were developed throughout the 1920s and 1930s. By the end of the 1930s they were largely obsolete, because their slow speed and high-profile made them vulnerable to advances in anti-tank guns.


title: Char 2C

text: Nevertheless, during the French mobilisation of 1939, all ten were activated and put into their own unit, the 51st "Bataillon de Chars de Combat". For propaganda, each tank had been named after one of the ancient regions of France, numbers 90-99 being named "Poitou; Provence; Picardie; Alsace; Bretagne; Touraine; Anjou; Normandie; Berry; Champagne" respectively. In 1939, the "Normandie" was renamed "Lorraine". As their main value was in propaganda, the giants were kept carefully out of harm's way and did not participate in the September 1939 attack on the Siegfried Line. They were used instead for numerous morale-boosting movies, in which they were often shown climbing and crushing old French forts. To the public, they obtained the reputation of invincible super tanks, the imagined dimensions of which far surpassed the actual particulars.


title: Char 2C

text: French command was aware that this reputation was undeserved. When the German "Panzerdivisionen", in the execution of Operation "Fall Rot", breached the French lines after 10 June 1940, the decision was made to prevent the capture of the famous equipment. On 12 June 1940 the order was given to send the tanks south by rail transport. The broken down tanks N° 92 and 95 were destroyed, at Mairy-Mainville and Piennes respectively. The six remaining tanks hastily embarked on two trains at the station of Landres on 13 June. During the night they hid, still loaded, in the forest of Badonviller. As no orders had been received regarding their destination, they remained at this spot during the 14th, being bombed in the early afternoon but without incurring any damage. In the late afternoon, an order arrived to send the tanks to Neufchâteau which was reached in the early morning of 15 June. There it was decided to travel to Dijon. However, fifteen kilometres south of Neufchâteau near the Meuse-sur-Meuse station, in a curve of the railway, the track was blocked by a blazing fuel train, while other trains jammed the exit to the rear. Due to the curve, it was impossible to unload the tanks. To prevent a capture of the matériel by the enemy, it was ordered to destroy the vehicles. Charges were placed and the fuel pipes cut. The gasoline was lit and the tanks exploded around 19:00. The crews escaped to the south. The wrecks were subsequently discovered by the "8. Panzerdivision". Later Joseph Goebbels and Hermann Goering claimed that the tanks had been destroyed by German dive bombers. This German propaganda myth was accepted as an authentic event by contemporary writers and later repeated in many postwar sources. One tank, the "Champagne", was nevertheless captured more or less intact and brought to Berlin to be exhibited as a war trophy until disappearing in 1948. After the war, rumours circulated that this vehicle had been transported to the Soviet Union.


title: Char 2C

text: After a decision taken in December 1922, from 1923 until 1926 the later "Champagne" was modified at La Seyne into the Char 2C bis, an experimental type with a 155 mm howitzer in a rounded cast steel turret. The howitzer had a muzzle velocity of 200 m/s. New engines of the Soutter-Harlé type were fitted and the three independent machine gun positions deleted. In this configuration the tank weighed perhaps 74 tons. The change was only temporary though, as the vehicle was brought back into its previous condition after 1934; the new turret was used in the Tunisian Mareth Line.


title: Char 2C

text: Between 15 November and 15 December 1939 the "Lorraine", as the company command tank, was experimentally up-armoured at the "Société des Aciéries d'Homecourt" to make it immune to standard German antitank guns. The front armour was enhanced to 90 mm, the side to 65 mm. In this configuration, weighing about 75 tons, the "Lorraine" had at that time the thickest armour of any operational tank, and is probably still the heaviest operational tank ever.


title: Char 2C

text: In 1940, twelve FCM F1 tanks were ordered, another very large twin-turret tank. France was defeated before they entered service.


title: ReCAPTCHA

text: reCAPTCHA is a CAPTCHA system that enables web hosts to distinguish between human and automated access to websites. The original version asked users to decipher hard to read text or match images. Version 2 also asked users to decipher text or match images if the analysis of cookies and canvas rendering suggested the page was being downloaded automatically. Since version 3, reCAPTCHA will never interrupt users and is intended to run automatically when users load pages or click buttons. reCAPTCHA is owned by Google.


title: ReCAPTCHA

text: The original iteration of the service was a mass collaboration platform designed for the digitization of books, particularly those that were too illegible to be scanned by computers. The verification prompts utilized pairs of words from scanned pages, with one known word used as a control for verification, and the second used to crowdsource the reading of an uncertain word. reCAPTCHA was originally developed by Luis von Ahn, David Abraham, Manuel Blum, Michael Crawford, Ben Maurer, Colin McMillen, and Edison Tan at Carnegie Mellon University's main Pittsburgh campus. It was acquired by Google in September 2009. The system helped to digitize the archives of "The New York Times", and was subsequently used by Google Books for similar purposes.


title: ReCAPTCHA

text: The system was reported as displaying over 100 million CAPTCHAs every day, on sites such as Facebook, TicketMaster, Twitter, 4chan, CNN.com, StumbleUpon, Craigslist (since June 2008), and the U.S. National Telecommunications and Information Administration's digital TV converter box coupon program website (as part of the US DTV transition).


title: ReCAPTCHA

text: In 2014, Google pivoted the service away from its original concept, with a focus on reducing the amount of user interaction needed to verify a user, and only presenting human recognition challenges (such as identifying images in a set that satisfy a specific prompt) if behavioral analysis suspects that the user may be a bot.


title: ReCAPTCHA

text: Distributed Proofreaders was the first project to volunteer its time to decipher scanned text that could not be read by optical character recognition (OCR) programs. It works with Project Gutenberg to digitize public domain material and uses methods quite different from reCAPTCHA.


title: ReCAPTCHA

text: The reCAPTCHA program originated with Guatemalan computer scientist Luis von Ahn, and was aided by a MacArthur Fellowship. An early CAPTCHA developer, he realized "he had unwittingly created a system that was frittering away, in ten-second increments, millions of hours of a most precious resource: human brain cycles".


title: ReCAPTCHA

text: Scanned text is subjected to analysis by two different OCRs. Any word that is deciphered differently by the two OCR programs or that is not in an English dictionary is marked as "suspicious" and converted into a CAPTCHA. The suspicious word is displayed, out of context, sometimes along with a control word already known. If the human types the control word correctly, then the response to the questionable word is accepted as probably valid. If enough users were to correctly type the control word, but incorrectly type the second word which OCR had failed to recognize, then the digital version of documents could end up containing the incorrect word. The identification performed by each OCR program is given a value of 0.5 points, and each interpretation by a human is given a full point. Once a given identification hits 2.5 points, the word is considered valid. Those words that are consistently given a single identity by human judges are later recycled as control words. If the first three guesses match each other but do not match either of the OCRs, they are considered a correct answer, and the word becomes a control word. When six users reject a word before any correct spelling is chosen, the word is discarded as unreadable.


title: ReCAPTCHA

text: The original reCAPTCHA method was designed to show the questionable words separately, as out-of-context correction, rather than in use, such as within a phrase of five words from the original document. Also, the control word might mislead context for the second word, such as a request of "/metal/ /fife/" being entered as "metal file" due to the logical connection of filing with a metal tool being considered more common than the musical instrument "fife".


title: ReCAPTCHA

text: In 2012, reCAPTCHA began using photographs taken from Google Street View project, in addition to scanned words. It will ask the user to identify images of crosswalks, street lights, and other objects. Some online have speculated if the data was being used by Google's self-driving company, Waymo. However, this was confirmed to not be the case.


title: ReCAPTCHA

text: Google charges for the use of reCAPTCHA all websites that make over a million reCAPTCHA queries a month.


title: ReCAPTCHA

text: In 2013, reCAPTCHA began implementing behavioral analysis of the browser's interactions to predict whether the user was a human or a bot. The following year, Google began to deploy a new reCAPTCHA API, featuring the "no CAPTCHA reCAPTCHA" — where users deemed to be of low risk only need to click a single checkbox to verify their identity. A CAPTCHA may still be presented if the system is uncertain of the user's risk; Google also introduced a new type of CAPTCHA challenge designed to be more accessible to mobile users, where the user must select images matching a specific prompt from a grid.


title: ReCAPTCHA

text: In 2017, Google introduced a new "invisible" reCAPTCHA, where verification occurs in the background, and no challenges are displayed at all if the user is deemed to be of low risk. According to former Google "click fraud czar" Shuman Ghosemajumder, this capability "creates a new sort of challenge that very advanced bots can still get around, but introduces a lot less friction to the legitimate human."


title: ReCAPTCHA

text: The reCAPTCHA tests are displayed from the central site of the reCAPTCHA project, which supplies the words to be deciphered. This is done through a JavaScript API with the server making a callback to reCAPTCHA after the request has been submitted. The reCAPTCHA project provides libraries for various programming languages and applications to make this process easier. reCAPTCHA is a free-of-charge service provided to websites for assistance with the decipherment, but the reCAPTCHA software is not open-source.


title: ReCAPTCHA

text: Also, reCAPTCHA offers plugins for several web-application platforms including ASP.NET, Ruby, and PHP, to ease the implementation of the service.


title: ReCAPTCHA

text: The main purpose of a CAPTCHA system is to block spambots while allowing human users. On December 14, 2009, Jonathan Wilkins released a paper describing weaknesses in reCAPTCHA that allowed bots to achieve a solve rate of 18%.


title: ReCAPTCHA

text: On August 1, 2010, Chad Houck gave a presentation to the DEF CON 18 Hacking Conference detailing a method to reverse the distortion added to images which allowed a computer program to determine a valid response 10% of the time. The reCAPTCHA system was modified on July 21, 2010, before Houck was to speak on his method. Houck modified his method to what he described as an "easier" CAPTCHA to determine a valid response 31.8% of the time. Houck also mentioned security defenses in the system, including a high-security lockout if an invalid response is given 32 times in a row.


title: ReCAPTCHA

text: On May 26, 2012, Adam, C-P and Jeffball of DC949 gave a presentation at the LayerOne hacker conference detailing how they were able to achieve an automated solution with an accuracy rate of 99.1%. Their tactic was to use techniques from machine learning, a subfield of artificial intelligence, to analyse the audio version of reCAPTCHA which is available for the visually impaired. Google released a new version of reCAPTCHA just hours before their talk, making major changes to both the audio and visual versions of their service. In this release, the audio version was increased in length from 8 seconds to 30 seconds, and is much more difficult to understand, both for humans as well as bots. In response to this update and the following one, the members of DC949 released two more versions of Stiltwalker which beat reCAPTCHA with an accuracy of 60.95% and 59.4% respectively. After each successive break, Google updated reCAPTCHA within a few days. According to DC949, they often reverted to features that had been previously hacked.


title: ReCAPTCHA

text: On June 27, 2012, Claudia Cruz, Fernando Uceda, and Leobardo Reyes published a paper showing a system running on reCAPTCHA images with an accuracy of 82%. The authors have not said if their system can solve recent reCAPTCHA images, although they claim their work to be intelligent OCR and robust to some, if not all changes in the image database.


title: ReCAPTCHA

text: In an August 2012 presentation given at BsidesLV 2012, DC949 called the latest version "unfathomably impossible for humans" – they were not able to solve them manually either. The web accessibility organization WebAIM reported in May 2012, "Over 90% of respondents [screen reader users] find CAPTCHA to be very or somewhat difficult."


title: ReCAPTCHA

text: The original iteration of reCAPTCHA was criticized as being a source of unpaid work to assist in transcribing efforts.


title: ReCAPTCHA

text: The current iteration of the system has been criticized for its reliance on tracking cookies and promotion of vendor lock-in with Google services; administrators are encouraged to include reCAPTCHA tracking code in all pages of their website to analyze the behavior and "risk" of users, which determines the level of friction presented when a reCAPTCHA prompt is used. Google stated in its privacy policy that user data collected in this manner is not used for personalized advertising. It was also discovered that the system favors those who have an active Google account login, and displays a higher risk towards those using anonymizing proxies and VPN services.


title: ReCAPTCHA

text: Concerns were raised regarding privacy when Google announced reCAPTCHA v3.0, as it allows Google to track users on non-Google websites.


title: ReCAPTCHA

text: In April 2020, Cloudflare switched from reCAPTCHA to hCaptcha, citing privacy concerns over Google's potential use of the data they recollect through reCAPTCHA for targeted advertising and to cut down on operating costs since a considerable portion of Cloudflare's customers are free, non-paying customers. In response, Google told PC Magazine that the data from reCAPTCHA is never used for personalized advertising purposes.


title: ReCAPTCHA

text: Google's help center states that reCAPTCHA is not supported for the deafblind community, effectively locking such users out of all pages that use the service. However, reCAPTCHA does currently have the longest list of accessibility considerations of any CAPTCHA service.


title: ReCAPTCHA

text: In one of the variants of CAPTCHA challenges, images are not incrementally highlighted, but fade out when clicked, and replaced with a new image fading in, resembling whack-a-mole.


title: ReCAPTCHA

text: reCAPTCHA had also created project Mailhide, which protects email addresses on web pages from being harvested by spammers. By default, the email address was converted into a format that did not allow a crawler to see the full email address; for example, "mailme@example.com" would have been converted to "mai...@example.com". The visitor would then click on the "..." and solve the CAPTCHA in order to obtain the full email address. One could also edit the pop-up code so that none of the address was visible. Mailhide was discontinued in 2018 because it relied on reCAPTCHA v1.


title: Geosynchronous orbit

text: A geosynchronous orbit (sometimes abbreviated GSO) is an Earth-centered orbit with an orbital period that matches Earth's rotation on its axis, 23 hours, 56 minutes, and 4 seconds (one sidereal day). The synchronization of rotation and orbital period means that, for an observer on Earth's surface, an object in geosynchronous orbit returns to exactly the same position in the sky after a period of one sidereal day. Over the course of a day, the object's position in the sky may remain still or trace out a path, typically in a figure-8 form, whose precise characteristics depend on the orbit's inclination and eccentricity. A circular geosynchronous orbit has a constant altitude of .


title: Geosynchronous orbit

text: A special case of geosynchronous orbit is the geostationary orbit, which is a circular geosynchronous orbit in Earth's equatorial plane with both inclination and eccentricity equal to 0. A satellite in a geostationary orbit remains in the same position in the sky to observers on the surface.


title: Geosynchronous orbit

text: Communications satellites are often given geostationary or close to geostationary orbits so that the satellite antennas that communicate with them do not have to move, but can be pointed permanently at the fixed location in the sky where the satellite appears.


title: Geosynchronous orbit

text: In 1929, Herman Potočnik described both geosynchronous orbits in general and the special case of the geostationary Earth orbit in particular as useful orbits for space stations. The first appearance of a geosynchronous orbit in popular literature was in October 1942, in the first Venus Equilateral story by George O. Smith, but Smith did not go into details. British science fiction author Arthur C. Clarke popularised and expanded the concept in a 1945 paper entitled "Extra-Terrestrial Relays – Can Rocket Stations Give Worldwide Radio Coverage?", published in "Wireless World" magazine. Clarke acknowledged the connection in his introduction to "The Complete Venus Equilateral". The orbit, which Clarke first described as useful for broadcast and relay communications satellites, is sometimes called the Clarke Orbit. Similarly, the collection of artificial satellites in this orbit is known as the Clarke Belt.


title: Geosynchronous orbit

text: In technical terminology, the geosynchronous orbits are often referred to as geostationary if they are roughly over the equator, but the terms are used somewhat interchangeably. Specifically, geosynchronous Earth orbit (GEO) may be a synonym for "geosynchronous equatorial orbit", or "geostationary Earth orbit".


title: Geosynchronous orbit

text: The first geosynchronous satellite was designed by Harold Rosen while he was working at Hughes Aircraft in 1959. Inspired by Sputnik 1, he wanted to use a geostationary (geosynchronous equatorial) satellite to globalise communications. Telecommunications between the US and Europe was then possible between just 136 people at a time, and reliant on high frequency radios and an undersea cable.


title: Geosynchronous orbit

text: Conventional wisdom at the time was that it would require too much rocket power to place a satellite in a geosynchronous orbit and it would not survive long enough to justify the expense, so early efforts were put towards constellations of satellites in low or medium Earth orbit. The first of these were the passive Echo balloon satellites in 1960, followed by Telstar 1 in 1962. Although these projects had difficulties with signal strength and tracking that could be solved through geosynchronous satellites, the concept was seen as impractical, so Hughes often withheld funds and support.


title: Geosynchronous orbit

text: By 1961, Rosen and his team had produced a cylindrical prototype with a diameter of , height of , weighing ; it was light, and small, enough to be placed into orbit by then-available rocketry, was spin stabilised and used dipole antennas producing a pancake-shaped waveform. In August 1961, they were contracted to begin building the working satellite. They lost Syncom 1 to electronics failure, but Syncom 2 was successfully placed into a geosynchronous orbit in 1963. Although its inclined orbit still required moving antennas, it was able to relay TV transmissions, and allowed for US President John F. Kennedy to phone Nigerian prime minister Abubakar Tafawa Balewa from a ship on August 23, 1963.


title: Geosynchronous orbit

text: Today there are hundreds of geosynchronous satellites providing remote sensing, navigation and communications.


title: Geosynchronous orbit

text: Although most populated land locations on the planet now have terrestrial communications facilities (microwave, fiber-optic), which often have latency and bandwidth advantages, and telephone access covering 96% of the population and internet access 90% as of 2018, some rural and remote areas in developed countries are still reliant on satellite communications.


title: Geosynchronous orbit

text: A geostationary equatorial orbit (GEO) is a circular geosynchronous orbit in the plane of the Earth's equator with a radius of approximately (measured from the center of the Earth). A satellite in such an orbit is at an altitude of approximately above mean sea level. It maintains the same position relative to the Earth's surface. If one could see a satellite in geostationary orbit, it would appear to hover at the same point in the sky, i.e., not exhibit diurnal motion, while the Sun, Moon, and stars would traverse the skies behind it. Such orbits are useful for telecommunications satellites.


title: Geosynchronous orbit

text: A perfectly stable geostationary orbit is an ideal that can only be approximated. In practice the satellite drifts out of this orbit because of perturbations such as the solar wind, radiation pressure, variations in the Earth's gravitational field, and the gravitational effect of the Moon and Sun, and thrusters are used to maintain the orbit in a process known as station-keeping.


title: Geosynchronous orbit

text: Eventually, without the use of thrusters, the orbit will become inclined, oscillating between 0° and 15° every 55 years. At the end of the satellite's lifetime, when fuel approaches depletion, satellite operators may decide to omit these expensive manoeuvres to correct inclination and only control eccentricity. This prolongs the life-time of the satellite as it consumes less fuel over time, but the satellite can then only be used by ground antennas capable of following the N-S movement.


title: Geosynchronous orbit

text: Geostationary satellites will also tend to drift around one of two stable longitudes of 75° and 255° without station keeping.


title: Geosynchronous orbit

text: Many objects in geosynchronous orbits have eccentric and/or inclined orbits. Eccentricity makes the orbit elliptical and appear to oscillate E-W in the sky from the viewpoint of a ground station, while inclination tilts the orbit compared to the equator and makes it appear to oscillate N-S from a groundstation. These effects combine to form an analemma (figure-8).


title: Geosynchronous orbit

text: The Tundra orbit is an eccentric geosynchronous orbit, which allows the satellite to spend most of its time dwelling over one high latitude location. It sits at an inclination of 63.4°, which is a frozen orbit, which reduces the need for stationkeeping. At least two satellites are needed to provide continuous coverage over an area. It was used by the Sirius XM Satellite Radio to improve signal strength in the northern US and Canada.


title: Geosynchronous orbit

text: The Quasi-Zenith Satellite System (QZSS) is a four-satellite system that operates in a geosynchronous orbit at an inclination of 42° and a 0.075 eccentricity. Each satellite dwells over Japan, allowing signals to reach receivers in urban canyons then passes quickly over Australia.


title: Geosynchronous orbit

text: Geosynchronous satellites are launched to the east into a prograde orbit that matches the rotation rate of the equator. The smallest inclination that a satellite can be launched into is that of the launch site's latitude, so launching the satellite from close to the equator limits the amount of inclination change needed later. Additionally, launching from close to the equator allows the speed of the Earth's rotation to give the satellite a boost. A launch site should have water or deserts to the east, so any failed rockets do not fall on a populated area.


title: Geosynchronous orbit

text: Most launch vehicles place geosynchronous satellites directly into a geosynchronous transfer orbit (GTO), an elliptical orbit with an apogee at GSO height and a low perigee. On-board satellite propulsion is then used to raise the perigee, circularise and reach GSO.


title: Geosynchronous orbit

text: Once in a viable geostationary orbit, spacecraft can change their longitudinal position by adjusting their semi-major axis such that the new period is shorter or longer than a sidereal day, in order to effect an apparent "drift" Eastward or Westward, respectively. Once at the desired longitude, the spacecraft's period is restored to geosynchronous.


title: Geosynchronous orbit

text: A statite is a hypothetical satellite that uses radiation pressure from the sun against a solar sail to modify its orbit.


title: Geosynchronous orbit

text: It would hold its location over the dark side of the Earth at a latitude of approximately 30 degrees. It would return to the same spot in the sky every 24 hours from an Earth-based viewer's perspective, so be functionally similar to a geosynchronous orbit.


title: Geosynchronous orbit

text: A further form of geosynchronous orbit is the theoretical space elevator. When one end is attached to the ground, for altitudes below the geostationary belt the elevator maintains a shorter orbital period than by gravity alone.


title: Geosynchronous orbit

text: Geosynchronous satellites require some station keeping to keep their position, and once they run out of thruster fuel and are no longer useful they are moved into a higher graveyard orbit. It is not feasible to deorbit geosynchronous satellites as it would take far more fuel than slightly elevating the orbit, and atmospheric drag is negligible, giving GSOs lifetimes of thousands of years.


title: Geosynchronous orbit

text: The retirement process is becoming increasingly regulated and satellites must have a 90% chance of moving over 200 km above the geostationary belt at end of life.


title: Geosynchronous orbit

text: Space debris in geosynchronous orbits typically has a lower collision speed than at LEO since most GSO satellites orbit in the same plane, altitude and speed; however, the presence of satellites in eccentric orbits allows for collisions at up to 4 km/s. Although a collision is comparatively unlikely, GSO satellites have a limited ability to avoid any debris.


title: Geosynchronous orbit

text: Debris less than 10 cm in diameter cannot be seen from the Earth, making it difficult to assess their prevalence.


title: Geosynchronous orbit

text: Despite efforts to reduce risk, spacecraft collisions have occurred. The European Space Agency telecom satellite Olympus-1 was struck by a meteoroid on August 11, 1993 and eventually moved to a graveyard orbit, and in 2006 the Russian Express-AM11 communications satellite was struck by an unknown object and rendered inoperable, although its engineers had enough contact time with the satellite to send it into a graveyard orbit. In 2017 both AMC-9 and Telkom-1 broke apart from an unknown cause.


title: Geosynchronous orbit

text: All geosynchronous orbits have an orbital period equal to exactly one sidereal day. This means that the satellite will return to the same point above the Earth's surface every (sidereal) day, regardless of other orbital properties. This orbital period, T, is directly related to the semi-major axis of the orbit through the formula:


title: Geosynchronous orbit

text: Satellites commonly have an inclination of zero, ensuring that the orbit remains over the equator at all times, making it stationary with respect to latitude from the point of view of a ground observer (and in the ECEF reference frame).


title: Geosynchronous orbit

text: Another popular inclinations is 63.4° for a Tundra orbit, which ensures that the orbit's argument of perigee doesn't change over time.


title: Geosynchronous orbit

text: In the special case of a geostationary orbit, the ground track of a satellite is a single point on the equator. In the general case of a geosynchronous orbit with a non-zero inclination or eccentricity, the ground track is a more or less distorted figure-eight, returning to the same places once per sidereal day.


title: Convergence of random variables

text: In probability theory, there exist several different notions of convergence of random variables. The convergence of sequences of random variables to some limit random variable is an important concept in probability theory, and its applications to statistics and stochastic processes. The same concepts are known in more general mathematics as stochastic convergence and they formalize the idea that a sequence of essentially random or unpredictable events can sometimes be expected to settle down into a behavior that is essentially unchanging when items far enough into the sequence are studied. The different possible notions of convergence relate to how such a behavior can be characterized: two readily understood behaviors are that the sequence eventually takes a constant value, and that values in the sequence continue to change but can be described by an unchanging probability distribution.


title: Convergence of random variables

text: "Stochastic convergence" formalizes the idea that a sequence of essentially random or unpredictable events can sometimes be expected to settle into a pattern. The pattern may for instance be


title: Convergence of random variables

text: These other types of patterns that may arise are reflected in the different types of stochastic convergence that have been studied.


title: Convergence of random variables

text: While the above discussion has related to the convergence of a single series to a limiting value, the notion of the convergence of two series towards each other is also important, but this is easily handled by studying the sequence defined as either the difference or the ratio of the two series.


title: Convergence of random variables

text: For example, if the average of "n" independent random variables "Y", "i" = 1, ..., "n", all having the same finite mean and variance, is given by


title: Convergence of random variables

text: then as "n" tends to infinity, converges "in probability" (see below) to the common mean, μ, of the random variables "Y". This result is known as the weak law of large numbers. Other forms of convergence are important in other useful theorems, including the central limit theorem.


title: Convergence of random variables

text: Throughout the following, we assume that ("X") is a sequence of random variables, and "X" is a random variable, and all of them are defined on the same probability space formula_2.


title: Convergence of random variables

text: With this mode of convergence, we increasingly expect to see the next outcome in a sequence of random experiments becoming better and better modeled by a given probability distribution.


title: Convergence of random variables

text: Convergence in distribution is the weakest form of convergence typically discussed, since it is implied by all other types of convergence mentioned in this article. However, convergence in distribution is very frequently used in practice; most often it arises from application of the central limit theorem.


title: Convergence of random variables

text: A sequence formula_4 of real-valued random variables, with cumulative distribution functions formula_5, is said to converge in distribution, or converge weakly, or converge in law to a random variable with cumulative distribution function if


title: Convergence of random variables

text: The requirement that only the continuity points of should be considered is essential. For example, if are distributed uniformly on intervals , then this sequence converges in distribution to the degenerate random variable . Indeed, for all "n" when , and for all when . However, for this limiting random variable , even though for all . Thus the convergence of cdfs fails at the point where is discontinuous.


title: Convergence of random variables

text: where formula_8 is the law (probability distribution) of . For example, if is standard normal we can write formula_9.


title: Convergence of random variables

text: For random vectors the convergence in distribution is defined similarly. We say that this sequence converges in distribution to a random -vector if


title: Convergence of random variables

text: The definition of convergence in distribution may be extended from random vectors to more general random elements in arbitrary metric spaces, and even to the “random variables” which are not measurable — a situation which occurs for example in the study of empirical processes. This is the “weak convergence of laws without laws being defined” — except asymptotically.


title: Convergence of random variables

text: In this case the term weak convergence is preferable (see weak convergence of measures), and we say that a sequence of random elements converges weakly to (denoted as ) if


title: Convergence of random variables

text: for all continuous bounded functions . Here E* denotes the "outer expectation", that is the expectation of a “smallest measurable function that dominates ”.


title: Convergence of random variables

text: The basic idea behind this type of convergence is that the probability of an “unusual” outcome becomes smaller and smaller as the sequence progresses.


title: Convergence of random variables

text: The concept of convergence in probability is used very often in statistics. For example, an estimator is called consistent if it converges in probability to the quantity being estimated. Convergence in probability is also the type of convergence established by the weak law of large numbers.


title: Convergence of random variables

text: A sequence {"X"} of random variables converges in probability towards the random variable "X" if for all "ε" > 0


title: Convergence of random variables

text: More explicitly, let "P"("ε") be the probability that "X" is outside the ball of radius "ε" centered at "X". Then is said to converge in probability to "X" if for any and any "δ" > 0 there exists a number "N" (which may depend on "ε" and "δ") such that for all "n" ≥ "N", "P"("ε") < "δ" (the definition of limit).


title: Convergence of random variables

text: Notice that for the condition to be satisfied, it is not possible that for each "n" the random variables "X" and "X" are independent (and thus convergence in probability is a condition on the joint cdf's, as opposed to convergence in distribution, which is a condition on the individual cdf's), unless "X" is deterministic like for the weak law of large numbers. At the same time, the case of a deterministic "X" cannot, whenever the deterministic value is a discontinuity point (not isolated), be handled by convergence in distribution, where discontinuity points have to be explicitly excluded.


title: Convergence of random variables

text: Convergence in probability is denoted by adding the letter "p" over an arrow indicating convergence, or using the "plim" probability limit operator:


title: Convergence of random variables

text: For random elements {"X"} on a separable metric space , convergence in probability is defined similarly by


title: Convergence of random variables

text: This is the type of stochastic convergence that is most similar to pointwise convergence known from elementary real analysis.


title: Convergence of random variables

text: To say that the sequence converges almost surely or almost everywhere or with probability 1 or strongly towards "X" means that


title: Convergence of random variables

text: This means that the values of approach the value of "X", in the sense (see almost surely) that events for which does not converge to "X" have probability 0. Using the probability space formula_39 and the concept of the random variable as a function from Ω to R, this is equivalent to the statement


title: Convergence of random variables

text: Almost sure convergence is often denoted by adding the letters "a.s." over an arrow indicating convergence:


title: Convergence of random variables

text: For generic random elements {"X"} on a metric space formula_42, convergence almost surely is defined similarly:


title: Convergence of random variables

text: To say that the sequence of random variables ("X") defined over the same probability space (i.e., a random process) converges surely or everywhere or pointwise towards "X" means


title: Convergence of random variables

text: where Ω is the sample space of the underlying probability space over which the random variables are defined.


title: Convergence of random variables

text: This is the notion of pointwise convergence of a sequence of functions extended to a sequence of random variables. (Note that random variables themselves are functions).


title: Convergence of random variables

text: Sure convergence of a random variable implies all the other kinds of convergence stated above, but there is no payoff in probability theory by using sure convergence compared to using almost sure convergence. The difference between the two only exists on sets with probability zero. This is why the concept of sure convergence of random variables is very rarely used.


title: Convergence of random variables

text: Given a real number , we say that the sequence converges in the "r"-th mean (or in the "L"-norm) towards the random variable "X", if the -th absolute moments E(|"X"|) and E(|"X"|) of and "X" exist, and


title: Convergence of random variables

text: where the operator E denotes the expected value. Convergence in -th mean tells us that the expectation of the -th power of the difference between formula_47 and formula_27 converges to zero.


title: Convergence of random variables

text: This type of convergence is often denoted by adding the letter "L" over an arrow indicating convergence:


title: Convergence of random variables

text: Convergence in the "r"-th mean, for "r" ≥ 1, implies convergence in probability (by Markov's inequality). Furthermore, if "r" > "s" ≥ 1, convergence in "r"-th mean implies convergence in "s"-th mean. Hence, convergence in mean square implies convergence in mean.


title: Convergence of random variables

text: The chain of implications between the various notions of convergence are noted in their respective sections. They are, using the arrow notation:


title: Convergence of random variables

text: These properties, together with a number of other special cases, are summarized in the following list:


title: Peter Boghossian

text: Peter Gregory Boghossian (; born July 25, 1966) is an American philosopher and pedagogist. Born in Boston, he was a non-tenure track assistant professor of philosophy at Portland State University for ten years, and his areas of academic focus include atheism, critical thinking, pedagogy, scientific skepticism, and the Socratic method. He is the author of "A Manual for Creating Atheists" and (with James Lindsay) "How to Have Impossible Conversations: A Very Practical Guide".


title: Peter Boghossian

text: Boghossian was involved in the grievance studies affair (also called "Sokal Squared" in media coverage) with collaborators James A. Lindsay and Helen Pluckrose, in predominantly low impact academic journals, which put forth intentionally preposterous ideas in peer review publications related to gender studies and other fields. After an investigation, Portland State University restricted Boghossian's future work on the basis of research misconduct, including failure to adhere to institutional review board (IRB) processes. In September 2021, Boghossian resigned his position from Portland State University, citing harassment and a lack of intellectual freedom.


title: Peter Boghossian

text: Boghossian coined the term for a set of conversational techniques he described, which are designed to enable examination of strongly held beliefs, especially of the religious kind, in a non-confrontational manner.


title: Peter Boghossian

text: Boghossian's primary interests are critical thinking, philosophy of education, and moral reasoning. His thesis looked at the use of the Socratic method with prison inmates for critical thinking and moral reasoning with the intention of decreasing ongoing criminal behavior. The research was funded by the State of Oregon. Boghossian was Chairman of the Prison Advisory Committee for the Columbia River Correctional Institution. He is a fellow at the Center for Prison Reform. He was employed as an assistant professor at Portland State University, quitting in protest due to what he viewed as a culture of illiberalism.


title: Peter Boghossian

text: Boghossian is the author of two books, "A Manual for Creating Atheists" (2013), a book with a foreword by Michael Shermer, and "How to Have Impossible Conversations: A Very Practical Guide" (2019). He also contributed a foreword to Stefan Molyneux's book "Against the Gods". He is a longtime collaborator with Molyneux.


title: Peter Boghossian

text: In 2017, Boghossian was featured in "Reasons To Believe", a documentary focusing on psychology and the science of belief.


title: Peter Boghossian

text: He has been a speaker for the Center for Inquiry, the Richard Dawkins Foundation for Reason and Science, and the Secular Student Alliance.


title: Peter Boghossian

text: In September 2021, Boghossian resigned his position from Portland State University. In his resignation letter, he called the university a "Social Justice factory" and said that he faced harassment and retaliation for speaking out. The letter also accuses the university of creating a culture where students are "afraid to speak openly and honestly," of training students to "mimic the moral certainty of ideologues," and of "[driving] intolerance of divergent beliefs and opinions".


title: Peter Boghossian

text: On February 17, 2022, he gave a conference on "wokism" at the Mathias Corvinus Collegium (MCC) in Budapest, Hungary.


title: Peter Boghossian

text: Boghossian has called all faith-based beliefs "delusions". He has been described by "The Daily Beast" as aligned with the New Atheist movement. He advocates using the Socratic method to dissuade religious believers, though he recommends focusing on criticism of faith as a way of knowing (he calls it an "unreliable epistemology"), rather than the outward trappings of religious communities.


title: Peter Boghossian

text: In a 2015 interview with Dave Rubin, Boghossian described himself as a classical liberal who has never voted for a Republican candidate, but is "not a fan" of the Democrats. He stated that any of the Republican candidates for the 2016 presidential election "would be an unmitigated disaster". He donated to and endorsed Andrew Yang for the 2020 United States presidential election.


title: Peter Boghossian

text: According to Boghossian, "the regressive left have taken over academia". He has often stated that cultural relativism and egalitarianism are contradictory values.


title: Peter Boghossian

text: In the grievance studies affair, also referred to as the "Sokal Squared" scandal, Boghossian, James A. Lindsay and Helen Pluckrose submitted a series of hoax academic papers for peer-review to journals in academic fields which they termed "grievance studies"—race, gender, feminist and sexuality studies which they believed were characterized by low scientific standards. Several of the papers, offering preposterous, jargon-laded theories, were accepted.


title: Peter Boghossian

text: In 2017, Boghossian and Lindsay published a hoax paper titled "The Conceptual Penis as a Social Construct". The paper, which the authors said was intentionally absurd and written in a way that imitated the style of "poststructuralist discursive gender theory", argued that the penis should be seen "not as an anatomical organ but as a social construct isomorphic to performative toxic masculinity". Boghossian and Lindsay initially submitted the paper to "Norma", where it was rejected. They later submitted the paper to "Cogent Social Sciences", an open access journal which has been criticized as a pay-to-publish operation. The authors later revealed the hoax in "Skeptic" magazine. Boghossian and Lindsay stated that they intended to demonstrate that "gender studies is crippled academically by an overriding almost-religious belief that maleness is the root of all evil", and also to highlight problems with the review processes of open-access journals.


title: Peter Boghossian

text: A number of critics questioned whether Boghossian and Lindsay's paper demonstrated a problem in the field of gender studies. Alan Sokal, a mathematics professor who was responsible for a similar hoax in 1996, noted that "Cogent Social Sciences" was a low-tiered open access journal that did not specialize in gender studies, and said that it seemed unlikely the paper would have been accepted at a mainstream gender studies journal. While the journal did conduct a postmortem, Boghossian and Lindsay concluded the "impact [of the hoax] was very limited, and much criticism of it was legitimate".


title: Peter Boghossian

text: A 2021 study assessing the grievance studies affair concluded, (1) journals with higher impact factors were more likely to reject papers submitted as part of the project; (2) the chances were better, if the manuscript was allegedly based on empirical data; (3) peer reviews can be an important asset in the process of revising a manuscript; and (4) when the project authors, with academic education from neighboring disciplines, closely followed the reviewers’ advice, they were able to learn relatively quickly what is needed for writing an acceptable article. The boundary between a seriously written paper and a “hoax” gradually became blurred. Finally (5), the way the project ended showed that in the long run, the scientific community will uncover fraudulent practices."


title: Peter Boghossian

text: Beginning in August 2017, Boghossian, Lindsay, and Pluckrose began a much larger attempt in which they wrote 20 hoax papers, submitting them to peer-reviewed journals under a variety of pseudonyms as well as the name of Richard Baldwin, a professor emeritus at Florida's Gulf Coast State College and friend of Boghossian. The project was halted early after one of the papers in the feminist geography journal "Gender, Place & Culture" was criticized on social media, and then its authenticity questioned on Campus Reform.


title: Peter Boghossian

text: After this, the trio revealed the full extent of their work in a YouTube video created and released by documentary filmmaker Mike Nayna, alongside an investigation by "The Wall Street Journal". By the time of the revelation seven of their twenty papers had been accepted, seven were still under review, and six had been rejected. One paper, which was accepted by feminist social work journal "Affilia", transposed up-to-date jargon into passages lifted from Adolf Hitler's "Mein Kampf".


title: Peter Boghossian

text: Tom Whipple of "The Times" wrote that academic reviewers had praised the studies prior to the revelation of the hoax as "a rich and exciting contribution to the study of ... the intersection between masculinity and anality", "excellent and very timely", and "important dialogue for social workers and feminist scholars".


title: Peter Boghossian

text: The project drew both praise and criticism, with author Yascha Mounk dubbing it 'Sokal squared' in reference to the Sokal Affair hoax perpetrated by Alan Sokal and saying "The result is hilarious and delightful. It also showcases a serious problem with big parts of academia." Harvard psychologist Steven Pinker said the project posed the question "is there any idea so outlandish that it won't be published in a Critical/PoMo/Identity/'Theory' journal?" Daniel Engber of online magazine Slate criticised the project, saying "one could have run this sting on almost any empirical discipline and returned the same result". In an open letter, eleven of Boghossian's colleagues at Portland State University wrote that the hoaxes "violat[ed] acceptable norms of research," and were "fraudulent, time-wasting, anti-intellectual activities". Joel P. Christensen and Matthew A. Sears said it was "the academic equivalent of the fraudulent hit pieces on Planned Parenthood" produced in 2015. Carl Bergstrom claimed "the hoaxers appear woefully naïve about how the [peer review] system actually works".


title: Peter Boghossian

text: In 2018, Boghossian's employer, Portland State University, initiated a research misconduct inquiry relating to the grievance studies affair. According to the "Chronicle of Higher Education", the university's institutional review board (IRB) concluded that Boghossian violated the ethical guidelines by conducting research on human subjects without approval. The University also said it is "considering a further charge that he had falsified data".


title: Peter Boghossian

text: After news of the research conduct investigation broke, a number of prominent academics wrote letters defending Boghossian, including evolutionary biologist Richard Dawkins, Harvard psychologist Steven Pinker, mathematician and physicist Alan Sokal, philosopher Daniel Dennett, social psychologist Jonathan Haidt, and psychologist Jordan Peterson. Pinker wrote that Portland State University's investigation struck him and his colleagues "as an attempt to weaponize an important [principle] of academic ethics in order to punish a scholar for expressing an unpopular opinion". Dawkins suggested that the investigation could be politically motivated: "If the members of your committee of inquiry object to the very idea of satire as a form of creative expression, they should come out honestly and say so. But to pretend that this is a matter of publishing false data is so obviously ridiculous that one cannot help suspecting an ulterior motive." Peterson said that those pursuing allegations against Boghossian, and not Boghossian himself, were guilty of academic misconduct.


title: Peter Boghossian

text: On the other hand, IRB experts interviewed by Jesse Singal for "New York" magazine agreed that Boghossian should have sought IRB approval for the study.


title: Peter Boghossian

text: In December 2018, Portland State University ruled that Boghossian had "violated ethical guidelines on human-subjects research". Consequently, he was banned from doing research until he had "completed training and could demonstrate that he understood how to protect the rights of human subjects".


title: Peter Boghossian

text: Street epistemology (often abbreviated to SE) is a term coined by Boghossian in his book "A Manual for Creating Atheists". This is a set of non-confrontational conversational techniques for discussing a strongly-held belief, designed to promote thoughtful reflection and open-mindedness in a participant regarding the belief. Boghossian outlined the method and its application in helping religious believers to reflect on the reliability of faith as an epistemology. However, it has also been found effective in many other contexts, and Boghossian later co-authored with James Lindsay "How to Have Impossible Conversations", which describes the application of street epistemology to an examination of a wider range of beliefs including nonreligious ones.


title: Peter Boghossian

text: One popularizer of street epistemology is Anthony Magnabosco, who has uploaded many examples of SE conversations he has had to his YouTube channel. He has created many other resources surrounding the topic, and engages with a community of street epistemologists looking to become proficient in the method and apply it in their lives. Magnabosco is the founder of Street Epistemology International, a non-profit organization "whose mission is to encourage and normalize critical thinking and skepticism while providing people around the world with the resources needed to develop and promote street epistemology". Resources are available for the community of SE practitioners, which include a guide on how to perform interviews using the style.


title: Shawn Nelson (criminal)

text: Shawn Timothy Nelson (August 21, 1959 – May 17, 1995) was an American veteran who stole an M60A3 tank from a California Army National Guard armory in San Diego and went on a rampage on May 17, 1995. He destroyed numerous cars, fire hydrants and an RV before being shot and killed by San Diego police officer Rick Piner.


title: Shawn Nelson (criminal)

text: Shawn Nelson was born in Birdseye, Utah, on August 21, 1959, the second of three sons. He grew up in the Clairemont neighborhood of San Diego, California, and graduated from Madison High School prior to his enlistment in the United States Army, where he served for two years until his honorable discharge in 1980. After his discharge, he returned to San Diego and worked as a plumber.


title: Shawn Nelson (criminal)

text: Nelson's mother died in 1988 and his father died in 1992. In between, his wife of six years filed for divorce in 1990. That same year, he was hospitalized at Sharp Memorial Hospital for neck and back injuries sustained in a motorcycle accident. Nelson later sued the hospital for $1.6 million, citing negligence, assault, battery and false imprisonment. A superior court judge dismissed the case and the hospital counter-sued for $6,640 in medical fees and legal expenses. Nelson claimed he was forced to be treated without his consent.


title: Shawn Nelson (criminal)

text: Nelson's brother, Scott, said that he became addicted to methamphetamine in the few years prior to the tank incident. His neighbors complained to authorities of him yelling at his roommate at night. Nelson then began to exhibit unusual behavior. On one occasion, he dug a hole deep in his backyard in an attempt to mine for gold. One of his friends, Carson Honings, referred to the mine shaft as Nelson's "new hobby". In April, he filed two damage claims against the cityfor police negligence and false arrest totaling $2 million.


title: Shawn Nelson (criminal)

text: Nelson's neck and back problems, combined with the theft of plumbing equipment from his truck in June 1994, effectively halted his business. With no income, his utilities were cut off and his house went into foreclosure. In April 1995, Nelson's live-in girlfriend moved out of their shared home.


title: Shawn Nelson (criminal)

text: According to San Diego police, in the week before his tank rampage, Nelson told a friend that he was thinking of committing suicide. The following weekend, he told a friend that "Oklahoma was good stuff", in apparent reference to the Oklahoma City bombing which happened about a month before. Whether Nelson condoned the attack or simply meant that he enjoyed the drama was not clear. Police did not believe Nelson had any connection with the bombing or with a terrorist group.


title: Shawn Nelson (criminal)

text: Around 6:30 p.m. on Wednesday, May 17, 1995, Nelson drove his Chevrolet van to the California Army National Guard Armory on Mesa College Drive in the Kearny Mesa neighborhood of San Diego. Employees at the armory were working late and the gate to the vehicle yard, which was completely deserted, was left open.


title: Shawn Nelson (criminal)

text: The tanks at the armory started with a push button and did not require an ignition key. The first two tanks Nelson broke into would not start. As he lowered himself into the third tank, a 57-ton M60A3 Patton, he was finally noticed by a guardsman, who approached the tank. Nelson started the vehicle and with little chance of stopping him, the guardsman rushed to a phone to call police. Since ammunition was kept in another building, none of the vehicle's weapons could be loaded or used by Nelson.


title: Shawn Nelson (criminal)

text: Nelson led police on a 23-minute, televised chase through the streets of Clairemont. The various agencies involved in the chase included the San Diego police, the San Diego County Sheriff's Department, and the California Highway Patrol. The tank had a top speed of , making the chase slow compared to police chases involving automobiles.


title: Shawn Nelson (criminal)

text: The 57-ton tank easily plowed through road signs, traffic lights, utility poles and fire hydrants, crushing about 40 parked vehicles, including an RV. The damage to utility poles knocked out power to around 5,100 San Diego Gas & Electric customers in the Linda Vista neighborhood.


title: Shawn Nelson (criminal)

text: From the armory, Nelson traveled along neighborhood streets, eventually turning north on Convoy Street, west onto Balboa Avenue (then signed as State Route 274) and entered Interstate 805 heading south. While on I-805, he attempted to knock down a pedestrian bridge by running into the columns, possibly with the intent of blockading pursuing police cars but failed after a few hits and decided to continue down the freeway. Nelson then drove the tank onto the State Route 163 freeway heading southbound, resulting in the freeway being closed and thousands of motorists being stuck.


title: Shawn Nelson (criminal)

text: At least one news article speculated that he may have been headed to Sharp Memorial Hospital, which he had unsuccessfully sued in 1990 and partially blamed for his mother's death. After Nelson attempted to cross into the northbound lanes of State Route 163, the tank became caught on the concrete median barrier and lost one track.


title: Shawn Nelson (criminal)

text: After the tank was immobilized, four policemen climbed onto it. San Diego Police officer Paul Paxton, a gunnery sergeant at the time with the Marine Corps Reserve, opened a hatch using bolt cutters. They ordered Nelson to surrender but he said nothing and began rocking the tank back and forth in an attempt to free it from the median. Paxton's partner, Officer Richard Piner, leaned in and shot Nelson. The bullet entered through Nelson's neck.


title: Shawn Nelson (criminal)

text: Nelson later died at Sharp Memorial Hospital. Despite widespread property destruction, he was the only fatality reported during the rampage. The state of California paid $149,201 () to cover property damage along Nelson's route.


title: Shawn Nelson (criminal)

text: Police Captain Tom Hall justified the lethal force used against Nelson because if he had managed to free the tank, he "could have taken out no less than 35 vehicles that were passing at that moment". Police decided that if non-lethal action such as tear gas were used, this might have stopped Nelson but not the tank and officers would not be able to enter the tank if it were still mobile with tear gas present. According to live news coverage at the time, officials were seriously considering asking for help from the Marine Corps at Camp Pendleton in the form of a Bell AH-1 Cobra attack helicopter, since the police force lacked the ability to disable a tank. Shawn’s brother, Scott, stated that police were justified in the shooting.


title: Shawn Nelson (criminal)

text: Officials at the armory where Nelson stole the tank were criticized for what appeared to be a huge lapse in security, especially after the attack in Oklahoma City the previous month. In addition to the open, unguarded gate to the vehicle lot, the fence surrounding the lot had damaged barbed wire in some places. Residents near the armory said that even if the gate had been locked, Nelson could have simply climbed the fence in sections where the barbed wire was damaged.


title: Shawn Nelson (criminal)

text: Armory officials said that the vehicles were kept far away from fences to make them difficult to reach, that only someone with the proper knowledge could operate and start a tank, and that there was no way to foresee such an event taking place. After Nelson's theft of the tank, security was improved at the Kearny Mesa armory.


title: Appalachian State University

text: Appalachian State University (; Appalachian, App State, App, or ASU) is a public university in Boone, North Carolina. It was founded as a teachers college in 1899 by brothers B. B. and D. D. Dougherty and the latter's wife, Lillie Shull Dougherty. The university expanded to include other programs in 1967 and joined the University of North Carolina System in 1971.


title: Appalachian State University

text: The university enrolls more than 20,600 students. It offers more than 150 bachelor's degrees and 70 graduate degree programs, including two doctoral programs. The university has 8 colleges: the College of Arts and Sciences, the Walker College of Business, the Reich College of Education, the College of Fine and Applied Arts, the Beaver College of Health Sciences, the Honors College, the Hayes School of Music, and University College.


title: Appalachian State University

text: The Athletic Teams compete in the Sun Belt Conference, except for a few sports which compete in the Southern Conference, such as wrestling. The teams are known as the Mountaineers.


title: Appalachian State University

text: Appalachian State University began in 1899 when a group of residents in Watauga County, under the leadership of Blanford B. Dougherty and his brother Dauphin D. Dougherty, began a movement to educate teachers in northwestern North Carolina. Land was donated by Daniel B. Dougherty, father of the leaders in the enterprise, and by J. F. Hardin. On this site a wood-frame building, costing $1,000, was erected by contributions from citizens of the town and county. In the fall of 1899, the Dougherty brothers, acting as co-principals, began the school, which was then called Watauga Academy. The first year saw 53 students enrolled in three grades. D. D. Dougherty's wife, Lillie Shull Dougherty, taught classes and contributed to administrative decisions.


title: Appalachian State University

text: In 1903, after interest in the school had spread to adjoining counties, D. D. Doughterty was convinced the state would fund institutions established to train teachers. He traveled to the state capital, Raleigh, after drafting a bill. W. C. Newland of Caldwell County introduced the bill in the North Carolina Legislature to make this a state school, with an appropriation for maintenance and for building. Captain E. F. Lovill of Watauga County, R. B. White of Franklin County, Clyde Hoey of Cleveland County and E. J. Justice of McDowell County spoke in favor of the measure. On March 9, 1903, the bill became law, and the Appalachian Training School for Teachers was established. The school opened on October 5, 1903, with $2,000 from the state and 325 students.


title: Appalachian State University

text: For 22 years, there was a period of steady growth, academic development, and valuable service to the state. In 1925, the legislature changed the name to the Appalachian State Normal School and appropriated additional funding for maintenance and permanent improvement. Four years later, in 1929, the school became a four-year degree granting institution and was renamed Appalachian State Teachers College. Over 1,300 students were enrolled in degree programs offered for primary grades education, physical education, math, English, science, and history.


title: Appalachian State University

text: Appalachian attained national standards by becoming accredited by the American Association for Teacher Education in 1939, and the Southern Association of Colleges and Schools in 1942. In 1948 a Graduate School was formed. Dr. Dougherty retired in 1955, after 56 years of serving the school. J. D. Rankin became interim president until Dr. William H. Plemmons was installed. Plemmons lead from 1955 to 1969, and his administration oversaw the addition of new buildings as the campus expanded and enrollment grew to nearly 5,000 students.


title: Appalachian State University

text: Appalachian was transformed from a single-purpose teachers' college into a multipurpose regional university and Appalachian State Teacher's College became Appalachian State University in 1967. Growth continued in the 1970s to around 9,500 students and 550 faculty. Afterward, four degree granting undergraduate colleges were created: Arts and Sciences, Business, Fine and Applied Arts, and Education. Dr. Herbert Wey succeeded Plemmons as president in 1969 and was named chancellor in 1971. In 1972, Appalachian State became part of the University of North Carolina system.


title: Appalachian State University

text: Located in the Blue Ridge Mountains of northwestern North Carolina, Appalachian State University has one of the highest elevations of any university in the United States east of the Mississippi River, at . The university's main campus is in downtown Boone, a town of 19,092 compared to an ASU enrollment of 19,108 students. The campus encompasses , including a main campus of with 20 residence halls, 3 main dining facilities, 30 academic buildings, and 11 recreation/athletic facilities.


title: Appalachian State University

text: The center of campus is nicknamed Sanford Mall, an open grassy quad between the student union, dining halls, and library. Sanford Hall, located on the mall's edge, is named for Terry Sanford, a former governor of the state. Rivers Street, a thoroughfare for town and university traffic, essentially divides the campus into east and west sections with tunnels and a pedestrian bridge connecting the two halves. The eastern half includes Sanford Mall, Plemmons Student Union, Roess Dining Hall (formerly known as Central Dining Hall), and Belk Library, along with two communities of residence halls. The west side has Trivette Dining Hall, the Student Recreation Center (or SRC), the Quinn Recreation Center, Kidd Brewer Stadium, and Stadium Heights and Yosef Hollow, the two remaining residence hall communities. At the north end, Bodenheimer Drive crosses over Rivers Street and leads to Appalachian Heights (an apartment-style residence hall), Mountaineer Hall, the Chancellor's House, the Living Learning Center, and Jim and Bettie Smith Stadium. The George M. Holmes Convocation Center at the south end of Rivers Street is the gateway and entrance to campus.


title: Appalachian State University

text: The Turchin Center for the Visual Arts on the edge of main campus is the university's visual art center. The Turchin Center is the largest visual arts center in northwestern North Carolina, eastern Tennessee, and southwestern Virginia. It displays rotating exhibits indoors and outdoors, some exhibits being culturally specific to the Appalachians, and offers community outreach programs through art courses. The center was opened by Appalachian State in 2003. The newly renovated Schaefer Center for the Performing Arts, a 1,635 seat performance venue, hosts artists from around the world.


title: Appalachian State University

text: The Appalachian State University Nature Preserve consists of 67 acres of protected woodlands located by the heart of campus. The land was dedicated as a State Natural Area in 1999 through the North Carolina Nature Preserves Act, and serves as an outdoor classroom for students and faculty. The primary purposes of the preserve are to enable conservation, education and recreation for students, staff, and faculty.


title: Appalachian State University

text: The University of North Carolina's Board of Governors plans and develops the coordinated system of higher education within the state. They set university policy but delegate Appalachian State's daily operations to a chancellor. The chancellor likewise delegates some duties to the provost, several vice-chancellors, and other administrative offices. These administrative offices are advised by several university committees on the needs of campus constituents, as represented by a Faculty Senate, Staff Senate, Graduate Student Association Senate, and the Student Government Association.


title: Appalachian State University

text: In 2005, the Carol Grotnes Belk Library & Information Commons opened in a new five-story building. Belk Library holds over 1.871 million bound books and periodicals, 1.5 million microforms, 24,000 sound recordings, and 14,000 videos. The Library holds varying collections, including the W.L Eury Appalachian Collection for regional studies and the Stock Car Racing Collection. With the opening of the new library building in 2005, Bill and Maureen Rhinehart of Long Island, New York, donated a large collection of rare books in English history, spanning from the 16th to the 19th centuries. The university created a special collections room for this valuable donation which includes some 900 volumes comprising nearly 450 titles. The entire collection was published in two volumes of an annotated bibliography, comprised by retired English professor Dr. M. John Higby. Both volumes comprise almost 240 pages and are excellent in both scholarship and thoroughness. It was the last major endeavor of his career in education. The library is also home to an impressive stock car racing collection including a donation from the family of Richard "The King" Petty. Besides serving university patrons, the library also serves the local community with circulation available to registered patrons.


title: Appalachian State University

text: Appalachian State offers 176 undergraduate and 42 graduate majors. The average GPA for incoming freshmen in 2017 was 4.20. Courses at Appalachian are organized into seven colleges and one graduate school:


title: Appalachian State University

text: Watauga Residential College (formerly Watauga Global Community) is a residential college founded in 1972. Watauga College was founded to be an "interdisciplinary, experimental, residential, coed alternative for social science and humanities general education requirements." Watauga Residential College was developed as "response to rising criticism of American education during the sixties and to the artificial fragmentation of knowledge in the academy; it was seen as a return to the world, where problems and themes do not recognize disciplinary boundaries and education is reconnected with individual learners."


title: Appalachian State University

text: Although it has changed names over the years, Watauga College in 1972, Watauga Global Community in 2008, and Watauga Residential College in 2014, its mission has remained relatively the same. "Watauga Residential College pursues its mission through a sequenced, interdisciplinary, experiential curriculum that requires students to integrate class content, community-based research, and multicultural immersion. This innovative curriculum, in conjunction with the academic and residential community, creates an atmosphere for the emergence of dynamic learning experiences through unique interactions among students and faculty." A key focus of Watauga is on the residential community so for the first year students are required to live in the living learning center.


title: Appalachian State University

text: Watauga College was first based in Watauga Hall, then for decades was based in East Hall, a large U-shaped dormitory on the east end of Campus. The dorm was known campus-wide as having the largest rooms of any dorm on the Appalachian campus, yet it was one of the oldest dorms on campus. Upon the completion of the Living Learning Center in 2003, Watauga College relocated and East Hall will either be renovated or destroyed because of the high cost of renovating such an old building.


title: Appalachian State University

text: Appalachian State University offers off-campus courses through three off-campus centers and online. These centers are:


title: Appalachian State University

text: Off-campus programs offer students the ability to maintain family and careers while working toward a degree. Full-time undergraduate programs are available in Elementary Education, Advertising, Criminal Justice, Management, Social Work and Psychology. Appalachian provides a variety of off-campus, part-time undergraduate and graduate programs.


title: Appalachian State University

text: The history department of ASU publishes "History Matters: An Undergraduate Journal of Historical Research" (), an undergraduate research journal. It was established in 2003 by Eric Burnnette, an ASU undergraduate student of history. The journal accepts submissions from all undergraduates nationwide and internationally, with special attention to papers that utilize primary sources. The editorial board consists of undergraduate and faculty advisors at ASU.


title: Appalachian State University

text: Members of the ASU Department of Physics and Astronomy serve as editors for the journal "The Physics Teacher."


title: Appalachian State University

text: Students at ASU enjoy a variety of outdoor activities. The mountains offer snowboarding, skiing, tubing, rock climbing, hiking, rafting, camping, and fishing on and around the Blue Ridge Parkway. ASU also has over 400 clubs and organizations run by the McCaskey Center for Student Involvement and Leadership, such as Greek organizations, academic and diversity clubs, and sports clubs. Before the start of every semester, the university hosts a 'Club Expo' featuring all the clubs and organizations on campus. This event is for students to find an organization or club that suits them and to become involved. The university also has volunteer centers including the Multicultural Center, the LGBT Center, and the Women's Center (which is the only completely volunteer-run Women's Center in the state of North Carolina). All three centers are under the supervision of the Multicultural Student Development Office. On November 11, 2016, ASU opened a fourth center in their student union; the Student Veterans Resource Center. The campus also sports 3 indoor fitness facilities as well as an athletics field and an outdoor recreation center.


title: Appalachian State University

text: The Appalachian Popular Programming Society (A.P.P.S.) is a university funded organization that exists to plan and provide diverse educational, enriching, and entertaining events for the community and student body of Appalachian State. Through its seven programming councils, A.P.P.S. members select, plan, promote, and present a diverse variety of popular entertainment programs and films which enhance the social and cultural life for Appalachian students. A.P.P.S. was founded in 1985 to help with the student nightlife and to support retention. APPS plays a vital role in fostering and developing an inclusive Appalachian State University community. The seven councils of A.P.P.S. include Heritage, Club Shows, Main Stage, Representation and Intentional Student Engagement (RISE), Films, Special Events, and Spirit & Traditions. Students can enjoy concerts and other miscellaneous events at Legends, an entertainment facility located on campus. ASU also offers an in-house movie theater within Plemmons Student Union, Greenbriar Theater, where students can go to watch movies.


title: Appalachian State University

text: Appalachian's sports teams are nicknamed the Mountaineers. The Mountaineers compete in NCAA Division I and are members of the Sun Belt Conference. Appalachian fields varsity teams in 17 sports, 7 for men and 10 for women. The Mountaineer football team started competing in the NCAA Football Bowl Subdivision (FBS) in the 2014–2015 academic year.


title: Appalachian State University

text: Kidd Brewer Stadium is the 30,000-seat home of Appalachian football. Nicknamed "The Rock", the stadium is located at an elevation of . In 2017, App State added a new video board, sound system and LED ribbon displays. Kidd Brewer Stadium also offers additional stadium seating with 18 luxury suites, 600 club seats, and the Chancellor's Box areas that offer a great view of the field and campus.


title: Appalachian State University

text: The George M. Holmes Convocation Center is the home court for Appalachian's basketball teams. The arena, with seating for 8,325, is also the home for volleyball and indoor track and field. In 2017, a new Daktronics video board was installed. The board is made up of nine displays totaling a square footage of 1,200.


title: Appalachian State University

text: University Recreation (UREC) also offers 20 club sports that compete with other regional institutions on a non-varsity level: lacrosse (men's and women's), rugby (men's and women's), soccer (men's and women's), ultimate frisbee (men's and women's), volleyball (men's and women's), climbing, cycling, equestrian, fencing, ice hockey, skiing, racquetball, snowboarding, swimming, and triathlon.


title: Appalachian State University

text: The university's cycling team has had success at the regional and national level; they compete within the Atlantic Collegiate Cycling Conference. The team competes in every discipline of bicycle racing that is acknowledged by National Collegiate Cycling Association within USA Cycling. This includes road bicycle racing, Mountain bike racing and Cyclocross. The team won the Division 2, as established by USA Cycling, collegiate team mountain bike national championships in 2008. They won the Division 2 collegiate team cyclocross national championships in 2008 and 2009. The team is now recognized as a Division 1 team.


title: Appalachian State University

text: On February 19, 2011, the Appalachian State Mountaineer women's basketball team won the 2011 Southern Conference regular-season title. The last time they had won the title was 1996. This is a first for Head Coach Darcie Vincent. On May 18, 2012, the Appalachian State baseball team beat Western Carolina University, becoming Southern Conference baseball champions for the first time since 1985.


title: Appalachian State University

text: Appalachian won three consecutive Division I FCS (I-AA) national championships in 2005, 2006, and 2007, over the University of Northern Iowa, the University of Massachusetts, and the University of Delaware, respectively. The Mountaineers are the first FCS football team to win three straight national championships since the playoffs began in 1978. They are also the first Division I program to win three consecutive national championships since Army accomplished the feat in 1944, 1945, and 1946.


title: Appalachian State University

text: In a milestone for ASU athletics, on September 1, 2007, the Appalachian State football team played their season opener at the fifth-ranked University of Michigan in front of the largest crowd to ever witness an ASU football game. Appalachian State beat Michigan in the game that would become known as the "Alltime Upset" by Sports Illustrated with a final score of 34–32 and became the first Division I FCS (I-AA) football team to defeat a Division I FBS (I-A) team ranked in the AP poll.


title: Appalachian State University

text: Appalachian State moved to the FBS subdivision in 2014, finishing its first season with a winning record but ineligible for a bowl bid per NCAA rules. Each season from 2015 to 2019, App State won both its conference championship and final bowl game. In 2020, although the Mountaineers did not win the Sun Belt Conference, they did win their sixth consecutive bowl game, defeating North Texas 56–28 in the inaugural Myrtle Beach Bowl.


title: Appalachian State University

text: The Hayes School of Music provides support for the Mountaineers at all home football games with the Marching Mountaineers, and at all home basketball games with the Appalachian Pep Band. The Marching Mountaineers travel to a select few away games each football season. The director of the athletic bands is Dr. Jason P. Gardner. In addition to supporting the athletic department, the Marching Mountaineers have assisted the Rho Tau chapter of Phi Mu Alpha Sinfonia in hosting the Appalachian Marching Band Festival annually. The festival has been on hiatus since 2019 due to stadium construction and the COVID-19 pandemic.


title: Appalachian State University

text: In 2004, a committee for the Appalachian Family Caravan tour created a promotional video titled "Hot Hot Hot", shown throughout the area by Chancellor Kenneth E. Peacock. The video became an inadvertent internet phenomenon and was featured on VH1's "Web Junk 20" program in early 2006. The video was never intended to promote Appalachian State to anyone but the Family Caravan, much less as a recruiting tool for prospective students. The video is no longer used by the university, due to student and alumni protests.


title: Appalachian State University

text: In 2002, MTV's program "Road Rules" visited ASU to produce an episode called "Campus Crawl", aired on-campus during an annual, winter student swimming event called the "Polar Plunge". The show's participants also crossed a high-wire strung between Coltrane and Gardner Halls.


title: Appalachian State University

text: On March 16, 2012, Appalachian State placed a tenured sociology professor on administrative leave for a variety of charges, which included showing an anti-pornography documentary, "The Price of Pleasure". This move gained national attention from the academic community.


title: Rossy de Palma

text: Rosa Elena García Echave (born 16 September 1964), known professionally as Rossy de Palma, is a Spanish actress and model. She is well known for her roles in films by Pedro Almodóvar such as "Law of Desire", "Women on the Verge of a Nervous Breakdown", "Kika", "The Flower of My Secret", "Julieta", and "Parallel Mothers".


title: Rossy de Palma

text: Born in Palma de Mallorca, and her father was a mason from Asturias. In the 1980s, during the Movida cultural movement she moved to Madrid.


title: Rossy de Palma

text: In 1984 she founded the pop music group for which she was a singer and a dancer. In 1986 she met Pedro Almodóvar in a café in Madrid. He was impressed by her performance during one of the group's concerts. He proposed a role in his next film, "Law of Desire". Rossy lent some of her personal dresses to Carmen Maura, who was playing the main female character of the film, Tina Quintero.


title: Rossy de Palma

text: Her first major role was in 1988 in Almodóvar's "Women on the Verge of a Nervous Breakdown," and she would go on to be one of Almodóvar's recurring cast. She became a model for designers Jean-Paul Gaultier, Thierry Mugler, and Sybilla. She then appeared in Robert Altman's 1994 satirical fashion film "Prêt-à-Porter" and in the music video of George Michael's "Too Funky" song.


title: Rossy de Palma

text: She has two children and currently lives in Paris, where she acts and models. As of 2010, she is a theater actress, charity spokeswoman for the Ghanaian charity OrphanAid Africa, and the face of luxury ad campaigns. In 2007, she released a perfume line under her name with Etat libre d'Orange. In 2009, she posed nude in an information campaign on breast cancer for the magazine "Marie Claire". She was selected to be on the jury for the main competition section of the 2015 Cannes Film Festival.


title: Rossy de Palma

text: She is an ambassador for the charity OAfrica, which advocates for a family for every child in Ghana, West Africa, and the closure of illegal orphanages.


title: Rossy de Palma

text: In 2018, she collaborated with singer Rosalía for her second studio album "El mal querer" writing the song "Preso" with her and Ferrán Echegaray. Her vocals were also used in the song.


title: Rossy de Palma

text: In 2011, she was one of the contestants during the first season of "Danse avec les stars". With her partner Christophe Licata, she finished in the 7th position (second-to-last).


title: Electron mobility

text: In solid-state physics, the electron mobility characterises how quickly an electron can move through a metal or semiconductor when pulled by an electric field. There is an analogous quantity for holes, called hole mobility. The term carrier mobility refers in general to both electron and hole mobility.


title: Electron mobility

text: Electron and hole mobility are special cases of electrical mobility of charged particles in a fluid under an applied electric field.


title: Electron mobility

text: When an electric field "E" is applied across a piece of material, the electrons respond by moving with an average velocity called the drift velocity, formula_1. Then the electron mobility "μ" is defined as


title: Electron mobility

text: Electron mobility is almost always specified in units of cm/(V⋅s). This is different from the SI unit of mobility, m/(V⋅s). They are related by 1 m/(V⋅s) = 10 cm/(V⋅s).


title: Electron mobility

text: Conductivity is proportional to the product of mobility and carrier concentration. For example, the same conductivity could come from a small number of electrons with high mobility for each, or a large number of electrons with a small mobility for each. For semiconductors, the behavior of transistors and other devices can be very different depending on whether there are many electrons with low mobility or few electrons with high mobility. Therefore mobility is a very important parameter for semiconductor materials. Almost always, higher mobility leads to better device performance, with other things equal.


title: Electron mobility

text: Semiconductor mobility depends on the impurity concentrations (including donor and acceptor concentrations), defect concentration, temperature, and electron and hole concentrations. It also depends on the electric field, particularly at high fields when velocity saturation occurs. It can be determined by the Hall effect, or inferred from transistor behavior.


title: Electron mobility

text: Without any applied electric field, in a solid, electrons and holes move around randomly. Therefore, on average there will be no overall motion of charge carriers in any particular direction over time.


title: Electron mobility

text: However, when an electric field is applied, each electron or hole is accelerated by the electric field. If the electron were in a vacuum, it would be accelerated to ever-increasing velocity (called ballistic transport). However, in a solid, the electron repeatedly scatters off crystal defects, phonons, impurities, etc., so that it loses some energy and changes direction. The final result is that the electron moves with a finite average velocity, called the drift velocity. This net electron motion is usually much slower than the normally occurring random motion.


title: Electron mobility

text: The two charge carriers, electrons and holes, will typically have different drift velocities for the same electric field.


title: Electron mobility

text: Quasi-ballistic transport is possible in solids if the electrons are accelerated across a very small distance (as small as the mean free path), or for a very short time (as short as the mean free time). In these cases, drift velocity and mobility are not meaningful.


title: Electron mobility

text: Usually, the electron drift velocity in a material is directly proportional to the electric field, which means that the electron mobility is a constant (independent of the electric field). When this is not true (for example, in very large electric fields), mobility depends on the electric field.


title: Electron mobility

text: The SI unit of velocity is m/s, and the SI unit of electric field is V/m. Therefore the SI unit of mobility is (m/s)/(V/m) = m/(V⋅s). However, mobility is much more commonly expressed in cm/(V⋅s) = 10 m/(V⋅s).


title: Electron mobility

text: Mobility is usually a strong function of material impurities and temperature, and is determined empirically. Mobility values are typically presented in table or chart form. Mobility is also different for electrons and holes in a given material.


title: Electron mobility

text: Since we only care about how the drift velocity changes with the electric field, we lump the loose terms together to get


title: Electron mobility

text: Note that both electron mobility and hole mobility are positive. A minus sign is added for electron drift velocity to account for the minus charge.


title: Electron mobility

text: The drift current density resulting from an electric field can be calculated from the drift velocity. Consider a sample with cross-sectional area A, length l and an electron concentration of n. The current carried by each electron must be formula_14, so that the total current density due to electrons is given by:


title: Electron mobility

text: A similar set of equations applies to the holes, (noting that the charge on a hole is positive). Therefore the current density due to holes is given by


title: Electron mobility

text: In a region where n and p vary with distance, a diffusion current is superimposed on that due to conductivity. This diffusion current is governed by Fick's Law:


title: Electron mobility

text: Typical electron mobility at room temperature (300 K) in metals like gold, copper and silver is 30–50 cm/ (V⋅s). Carrier mobility in semiconductors is doping dependent. In silicon (Si) the electron mobility is of the order of 1,000, in germanium around 4,000, and in gallium arsenide up to 10,000 cm/ (V⋅s). Hole mobilities are generally lower and range from around 100 cm/ (V⋅s) in gallium arsenide, to 450 in silicon, and 2,000 in germanium.


title: Electron mobility

text: Very high mobility has been found in several ultrapure low-dimensional systems, such as two-dimensional electron gases (2DEG) (35,000,000 cm/(V⋅s) at low temperature), carbon nanotubes (100,000 cm/(V⋅s) at room temperature) and freestanding graphene (200,000 cm/ V⋅s at low temperature).


title: Electron mobility

text: Organic semiconductors (polymer, oligomer) developed thus far have carrier mobilities below 50 cm/(V⋅s), and typically below 1, with well performing materials measured below 10.


title: Electron mobility

text: At low fields, the drift velocity "v" is proportional to the electric field "E", so mobility "μ" is constant. This value of "μ" is called the "low-field mobility".


title: Electron mobility

text: As the electric field is increased, however, the carrier velocity increases sublinearly and asymptotically towards a maximum possible value, called the "saturation velocity" "v". For example, the value of "v" is on the order of 1×10 cm/s for both electrons and holes in Si. It is on the order of 6×10 cm/s for Ge. This velocity is a characteristic of the material and a strong function of doping or impurity levels and temperature. It is one of the key material and semiconductor device properties that determine a device such as a transistor's ultimate limit of speed of response and frequency.


title: Electron mobility

text: This velocity saturation phenomenon results from a process called "optical phonon scattering". At high fields, carriers are accelerated enough to gain sufficient kinetic energy between collisions to emit an optical phonon, and they do so very quickly, before being accelerated once again. The velocity that the electron reaches before emitting a phonon is:


title: Electron mobility

text: where "ω" is the optical-phonon angular frequency and m* the carrier effective mass in the direction of the electric field. The value of "E" is 0.063 eV for Si and 0.034 eV for GaAs and Ge. The saturation velocity is only one-half of "v", because the electron starts at zero velocity and accelerates up to "v" in each cycle. (This is a somewhat oversimplified description.)


title: Electron mobility

text: Velocity saturation is not the only possible high-field behavior. Another is the Gunn effect, where a sufficiently high electric field can cause intervalley electron transfer, which reduces drift velocity. This is unusual; increasing the electric field almost always "increases" the drift velocity, or else leaves it unchanged. The result is negative differential resistance.


title: Electron mobility

text: In the regime of velocity saturation (or other high-field effects), mobility is a strong function of electric field. This means that mobility is a somewhat less useful concept, compared to simply discussing drift velocity directly.