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A study published in 2012 examined the phylogenetic relationships between the Eurasian and North African species in the Bufo bufo group and indicated a long evolutionary history for the group. Nine to thirteen million years ago, Bufo eichwaldi, a recently described species from south Azerbaijan and Iran, split from the main lineage. Further divisions occurred with Bufo spinosus splitting off about five million years ago when the Pyrenees were being uplifted, an event which isolated the populations in the Iberian Peninsula from those in the rest of Europe. The remaining European lineage split into Bufo bufo and Bufo verrucosissimus less than three million years ago during the Pleistocene. Very occasionally the common toad hybridizes with the natterjack toad (Bufo calamita) or the European green toad (Bufo viridis).
Description
The common toad can reach about in length. Females are normally stouter than males and southern specimens tend to be larger than northern ones. The head is broad with a wide mouth below the terminal snout which has two small nostrils. There are no teeth. The bulbous, protruding eyes have yellow or copper coloured irises and horizontal slit-shaped pupils. Just behind the eyes are two bulging regions, the paratoid glands, which are positioned obliquely. They contain a noxious substance, bufotoxin, which is used to deter potential predators. The head joins the body without a noticeable neck and there is no external vocal sac. The body is broad and squat and positioned close to the ground. The fore limbs are short with the toes of the fore feet turning inwards. At breeding time, the male develops nuptial pads on the first three fingers. He uses these to grasp the female when mating. The hind legs are short relative to other frogs' legs and the hind feet have long, unwebbed toes. There is no tail. The skin is dry and covered with small wart-like lumps. The colour is a fairly uniform shade of brown, olive-brown or greyish-brown, sometimes partly blotched or banded with a darker shade. The common toad tends to be sexually dimorphic with the females being browner and the males greyer. The underside is a dirty white speckled with grey and black patches. | Common toad | Wikipedia | 462 | 969943 | https://en.wikipedia.org/wiki/Common%20toad | Biology and health sciences | Frogs and toads | Animals |
Other species with which the common toad could be confused include the natterjack toad (Bufo calamita) and the European green toad (Bufo viridis). The former is usually smaller and has a yellow band running down its back while the latter has a distinctive mottled pattern. The paratoid glands of both are parallel rather than slanting as in the common toad. The common frog (Rana temporaria) is also similar in appearance but it has a less rounded snout, damp smooth skin, and usually moves by leaping.
Common toads can live for many years and have survived for fifty years in captivity. In the wild, common toads are thought to live for about ten to twelve years. Their age can be determined by counting the number of annual growth rings in the bones of their phalanges.
Distribution and habitat
After the common frog (Rana temporaria), the edible frog (Pelophylax esculentus) and the smooth newt (Lissotriton vulgaris), the common toad is the fourth most common amphibian in Europe. It is found throughout the continent with the exception of Iceland, the cold northern parts of Scandinavia, Ireland and a number of Mediterranean islands. These include Malta, Crete, Corsica, Sardinia and the Balearic Islands. Its easterly range extends to Irkutsk in Siberia and its southerly range includes parts of northwestern Africa in the northern mountain ranges of Morocco, Algeria and Tunisia. A closely related variant lives in eastern Asia including Japan. The common toad is found at altitudes of up to in the southern part of its range. It is largely found in forested areas with coniferous, deciduous and mixed woodland, especially in wet locations. It also inhabits open countryside, fields, copses, parks and gardens, and often occurs in dry areas well away from standing water.
Behaviour and lifecycle | Common toad | Wikipedia | 383 | 969943 | https://en.wikipedia.org/wiki/Common%20toad | Biology and health sciences | Frogs and toads | Animals |
The common toad usually moves by walking rather slowly or in short shuffling jumps involving all four legs. It spends the day concealed in a lair that it has hollowed out under foliage or beneath a root or a stone where its colouring makes it inconspicuous. It emerges at dusk and may travel some distance in the dark while hunting. It is most active in wet weather. By morning it has returned to its base and may occupy the same place for several months. It is voracious and eats woodlice, slugs, beetles, caterpillars, flies, ants, spiders, earthworms and even small mice. Small, fast moving prey may be caught by a flick of the tongue while larger items are grabbed with the jaws. Having no teeth, it swallows food whole in a series of gulps. It does not recognise its prey as such but will try to consume any small, dark coloured, moving object it encounters at night. A research study showed that it would snap at a moving piece of black paper as if it were prey but would disregard a larger moving piece. Toads seem to use visual cues for feeding and can see their prey at low light intensities where humans are unable to discern anything. Periodically, the common toad sheds its skin. This comes away in tattered pieces and is then consumed.
In 2007, researchers using a remotely operated underwater vehicle to survey Loch Ness, Scotland, observed a common toad moving along the bottom of the lake at a depth of . They were surprised to find that an air-breathing animal could survive in such a location.
The annual life cycle of the common toad is divided into three periods: the winter sleep, the time of mating and feeding period. | Common toad | Wikipedia | 347 | 969943 | https://en.wikipedia.org/wiki/Common%20toad | Biology and health sciences | Frogs and toads | Animals |
Predators and parasites
When attacked, the common toad adopts a characteristic stance, inflating its body and standing with its hindquarters raised and its head lowered. Its chief means of defence lies in the foul tasting secretion that is produced by its paratoid glands and other glands on its skin. This contains a toxin called bufagin and is enough to deter many predators although grass snakes seem to be unaffected by it. Other predators of adult toads include hedgehogs, rats, mink, and even domestic cats. Birds that feed on toads include herons, crows and birds of prey. Crows have been observed to puncture the skin with their beak and then peck out the toad's liver, thus avoiding the toxin. The tadpoles also exude noxious substances which deter fish from eating them but not the great crested newt. Aquatic invertebrates that feed on toad tadpoles include dragonfly larvae, diving beetles and water boatmen. These usually avoid the noxious secretion by puncturing the tadpole's skin and sucking out its juices.
A parasitic fly, Lucilia bufonivora, attacks adult common toads. It lays its eggs on the toad's skin and when these hatch, the larvae crawl into the toad's nostrils and eat its flesh internally with lethal consequences. The European fingernail clam (Sphaerium corneum) is unusual in that it can climb up water plants and move around on its muscular foot. It sometimes clings to the toe of a common toad and this is believed to be one of the means by which it disperses to new locations.
Reproduction
The common toad emerges from hibernation in spring and there is a mass migration towards the breeding sites. The toads converge on certain ponds that they favour while avoiding other stretches of water that seem eminently suitable. Adults use the same location year after year and over 80% of males marked as juveniles have been found to return to the pond at which they were spawned. They find their way to these by using a suite of orientation cues, including olfactory and magnetic cues, but also visual cues help guide their journeys. Toads experimentally moved elsewhere and fitted with tracking devices have been found to be able to locate their chosen breeding pond when the displacement exceeded three kilometres (two miles). | Common toad | Wikipedia | 470 | 969943 | https://en.wikipedia.org/wiki/Common%20toad | Biology and health sciences | Frogs and toads | Animals |
The males arrive first and remain in the location for several weeks while the females only stay long enough to mate and spawn. Rather than fighting for the right to mate with a female, male toads may settle disputes by means of the pitch of their voice. Croaking provides a reliable sign of body size and hence of prowess. Nevertheless, fights occur in some instances. In a study at one pond where males outnumbered females by four or five to one, it was found that 38% of the males won the right to mate by defeating rivals in combat or by displacing other males already mounted on females. Male toads generally outnumber female toads at breeding ponds. A Swedish study found that female mortality was higher than that of males and that 41% of females did not come to the breeding pond in the spring and missed a year before reproducing again.
The males mount the females' backs, grasping them with their fore limbs under the armpits in a grip that is known as amplexus. The males are enthusiastic, will try to grasp fish or inanimate objects and often mount the backs of other males. Sometimes several toads form a heap, each male trying to grasp the female at the base. It is a stressful period and mortality is high among breeding toads. A successful male stays in amplexus for several days and, as the female lays a long, double string of small black eggs, he fertilises them with his sperm. As the pair wander piggyback around the shallow edges of the pond, the gelatinous egg strings, which may contain 1,500 to 6,000 eggs and be in length, get tangled in plant stalks. | Common toad | Wikipedia | 346 | 969943 | https://en.wikipedia.org/wiki/Common%20toad | Biology and health sciences | Frogs and toads | Animals |
The strings of eggs absorb water and swell in size, and small tadpoles hatch out after 10 days. At first they cling to the remains of the strings and feed on the jelly. They later attach themselves to the underside of the leaves of water weed before becoming free swimming. The tadpoles at first look similar to those of the common frog (Rana temporaria) but they are a darker colour, being blackish above and dark grey below. They can be distinguished from the tadpoles of other species by the fact that the mouth is the same width as the space between the eyes, and this is twice as large as the distance between the nostrils. Over the course of a few weeks their legs develop and their tail gradually gets reabsorbed. By twelve weeks of age they are miniature toads measuring about long and ready to leave the pond.
Development and growth
The common toad reaches maturity at three to seven years old but there is great variability between populations. Juveniles are often parasitised by the lung nematode Rhabdias bufonis. This slows growth rates and reduces stamina and fitness. Larger juveniles at metamorphosis always outgrow smaller ones that have been reared in more crowded ponds. Even when they have heavy worm burdens, large juveniles grow faster than smaller individuals with light worm burdens. After several months of heavy worm infection, some juveniles in a study were only half as heavy as control juveniles. Their parasite-induced anorexia caused a decrease in food intake and some died. Another study investigated whether the use of nitrogenous fertilisers affects the development of common toad tadpoles. The toadlets were kept in dilute solutions of ammonium nitrate of various strengths. It was found that at certain concentrations, which were well above any normally found in the field, growth was increased and metamorphosis accelerated, but at others, there was no significant difference between the experimental tadpoles and controls. Nevertheless, certain unusual swimming patterns and a few deformities were found among the experimental animals. | Common toad | Wikipedia | 418 | 969943 | https://en.wikipedia.org/wiki/Common%20toad | Biology and health sciences | Frogs and toads | Animals |
A comparison was made between the growth rate of newly metamorphosed juveniles from different altitudes and latitudes, the specimens studied being from Norway, Germany, Switzerland, the Netherlands and France. At first the growth rates for males and females was identical. By the time they became mature their growth rate had slowed down to about 21% of the initial rate and they had reached 95% of their expected adult size. Some females that were on a biennial breeding cycle carried on growing rapidly for a longer time. Adjusting for differences in temperature and the length of the growing season, the toads grew and matured at much the same rate from the four colder localities. These juveniles reached maturity after 1.09 years for males and 1.55 years for females. However, the young toads from lowland France grew faster and longer to a much greater size taking an average 1.77 years for males and 2.49 years for females before reaching maturity.
Winter sleep
Common toads winter in various holes in the ground, sometimes in basements, often in droves with other amphibians. Rarely they spend the winter in flowing waters with the common frogs and green frogs.
Sperm senescence
The post-meiotic intra-testicular sperm of B. bufo undergoes senescence over time as measured by sperm motility. This type of sperm senescence does not occur at a genetically fixed rate, but rather is influenced by environmental conditions that include availability of mating partners and temperature.
Conservation
The IUCN Red List of Threatened Species considers the common toad as being of "least concern". This is because it has a wide distribution and is, over most of its range, a common species. It is not particularly threatened by habitat loss because it is adaptable and is found in deciduous and coniferous forests, scrubland, meadows, parks and gardens. It prefers damp areas with dense foliage. The major threats it faces include loss of habitat locally, the drainage of wetlands where it breeds, agricultural activities, pollution, and mortality on roads. Chytridiomycosis, an infectious disease of amphibians, has been reported in common toads in Spain and the United Kingdom and may affect some populations. | Common toad | Wikipedia | 439 | 969943 | https://en.wikipedia.org/wiki/Common%20toad | Biology and health sciences | Frogs and toads | Animals |
There are parts of its range where the common toad seems to be in decline. In Spain, increased aridity and habitat loss have led to a diminution in numbers and it is regarded as "near threatened". A population in the Sierra de Gredos mountain range is facing predation by otters and increased competition from the frog Pelophylax perezi. Both otter and frog seem to be extending their ranges to higher altitudes. The common toad cannot be legally sold or traded in the United Kingdom but there is a slow decline in toad numbers and it has therefore been declared a Biodiversity Action Plan priority species. In Russia, it is considered to be a "Rare Species" in the Bashkortostan Republic, the Tatarstan Republic, the Yamalo-Nenets Autonomous Okrug, and the Irkutsk Oblast, but during the 1990s, it became more abundant in Moscow Oblast.
It has been found that urban populations of common toad occupying small areas and isolated by development show a lower level of genetic diversity and reduced fitness as compared to nearby rural populations. The researchers demonstrated this by genetic analysis and by noting the greater number of physical abnormalities among urban as against rural tadpoles when raised in a controlled environment. It was considered that long term depletion in numbers and habitat fragmentation can reduce population persistence in such urban environments.
Roadkill
Many toads are killed by traffic while migrating to their breeding grounds. In Europe they have the highest rate of mortality from roadkill among amphibians. Many of the deaths take place on stretches of road where streams flow underneath showing that migration routes often follow water courses. In some places in Germany, Belgium, the Netherlands, Great Britain, Northern Italy and Poland, special tunnels have been constructed so that toads can cross under roads in safety. In other places, local wildlife groups run "toad patrols", carrying the amphibians across roads at busy crossing points in buckets. The toads start moving at dusk and for them to travel far, the temperature needs to remain above . On a warm wet night they may continue moving all night but if it cools down, they may stop earlier. An estimate was made of the significance of roadkill in toad populations in the Netherlands. The number of females killed in the spring migration on a quiet country road (ten vehicles per hour) was compared with the number of strings of eggs laid in nearby fens. A 30% mortality rate was found, with the rate for deaths among males likely to be of a similar order. | Common toad | Wikipedia | 508 | 969943 | https://en.wikipedia.org/wiki/Common%20toad | Biology and health sciences | Frogs and toads | Animals |
Bufotoxin
The main substance found in the parotoid gland and skin of the common toad is called bufotoxin. It was first isolated by Heinrich Wieland and his colleagues in 1922, and they succeeded in identifying its structure about 20 years later. Meanwhile, other researchers succeeded in isolating the same compound (and its parent steroid, bufotalin) from the Japanese toad, Bufo japonicus.
By 1986, researchers at Arizona State University had succeeded in synthesizing the toad toxin constituents bufotalin, bufalitoxin and bufotoxin. The chemical formula of bufotoxin is C40H60N4O10. Its physical effects resemble those of digoxin, which, in small doses, increases the strength with which the heart muscle contracts; synthesized from foxglove plants (Digitalis purpurea), digoxin is used in the treatment of congestive heart failure. The skin of the South American cane toad contains enough similar toxin to cause serious symptoms (or even death) in animals, including humans. Clinical effects include severe irritation and pain to eyes, mouth, nose and throat, cardiovascular and respiratory symptoms, paralysis and seizures, increased salivation, vomiting, hyperkalemia, cyanosis and hallucinations. There is no known anti-venom. Treatment consists of supporting respiratory and cardiovascular functions, prevention of absorption and electrocardiography to monitor the condition. Atropine, phenytoin, cholestyramine and lidocaine may prove useful in its management.
Cultural significance | Common toad | Wikipedia | 321 | 969943 | https://en.wikipedia.org/wiki/Common%20toad | Biology and health sciences | Frogs and toads | Animals |
The toad has long been considered to be an animal of ill omen or a connection to a spirit world. This may have its origins in the fact that it is at home both on land and in the water. It may cause repugnance because of its drab, wart-like skin, its slow movements and the way it emerges from some dark hole. In Europe in the Middle Ages, the toad was associated with the Devil, for whom a coat-of-arms was invented emblazoned with three toads. It was known that the toad could poison people and, as the witch's familiar, it was thought to possess magical powers. Even ordinary people made use of dried toads, their bile, faeces and blood. In some areas, the finding of a toad in a house was considered evidence that a witch was present. In the Basque Country, the familiars were believed to be toads wearing elegant robes. These were herded by children who were being trained as witches. Between 1610 and 1612, the Spanish inquisitor Alonso de Salazar Frías investigated witchcraft in the region and searched the houses of suspected witches for dressed toads. He found none. These witches were reputed to use undomesticated toads as ingredients in their liniments and brews.
An English folk tale tells how an old woman, a supposed witch, cursed her landlord and all his possessions when he demanded the unpaid rent for her cottage. Soon afterwards, a large toad fell on his wife and caused her to collapse. The toad was thrown into the fire but escaped with severe burns. Meanwhile, the old witch's cottage had caught fire and she was badly burnt. By next day, both toad and witch had died, and it was found that the woman's burns exactly mirrored those of the toad.
The saliva of the toad was considered poisonous and was known as "sweltered venom" and it was believed that it could spit or vomit poisonous fire. Toads were associated with devils and demons and in Paradise Lost, John Milton depicted Satan as a toad when he poured poison into Eve's ear. The First Witch in Shakespeare's Macbeth gave instructions on using a toad in the concoction of spells:
It was also believed that there was a jewel inside a toad's head, a "toadstone", that when worn as a necklace or ring would warn the wearer of attempts to poison them. Shakespeare mentioned this in As You Like It: | Common toad | Wikipedia | 502 | 969943 | https://en.wikipedia.org/wiki/Common%20toad | Biology and health sciences | Frogs and toads | Animals |
Mr. Toad is one of the main characters in the children's novel The Wind in the Willows, by Kenneth Grahame. This has been dramatized by several authors including A. A. Milne who called his play Toad of Toad Hall. Mr. Toad is a conceited, anthropomorphic toad and in the book he composes a ditty in his own praise which starts like this:
George Orwell in his essay Some Thoughts on the Common Toad described the emergence of the common toad from hibernation as one of the most moving signs of spring. | Common toad | Wikipedia | 116 | 969943 | https://en.wikipedia.org/wiki/Common%20toad | Biology and health sciences | Frogs and toads | Animals |
The Centaurus A/M83 Group is a complex group of galaxies in the constellations Hydra, Centaurus, and Virgo. The group may be roughly divided into two subgroups. The Cen A Subgroup, at a distance of 11.9 Mly (3.66 Mpc), is centered on Centaurus A, a nearby radio galaxy. The M83 Subgroup, at a distance of 14.9 Mly (4.56 Mpc), is centered on the Messier 83 (M83), a face-on spiral galaxy.
This group is sometimes identified as one group and sometimes identified as two groups. Hence, some references will refer to two objects named the Centaurus A Group and the M83 Group. However, the galaxies around Centaurus A and the galaxies around M83 are physically close to each other, and both subgroups appear not to be moving relative to each other.
The Centaurus A/M83 Group is part of the Virgo Supercluster, the local supercluster of which the Local Group is an outlying member.
Members
Member identification
The brightest group members were frequently identified in early galaxy group identification surveys. However, many of the dwarf galaxies in the group were only identified in more intensive studies. One of the first of these identified 145 faint objects on
optical images from the UK Schmidt Telescope and followed these up in hydrogen line emission with the Parkes Radio Telescope and in the hydrogen-alpha spectral line with the Siding Spring 2.3 m Telescope. This
identified 20 dwarf galaxies as members of the group. The HIPASS survey, which was a blind radio survey for hydrogen spectral line emission, found five uncatalogued galaxies in the group and also identified five previously-catalogued galaxies as members. An additional dwarf galaxy was identified as a group member in the HIDEEP survey, which was a more intensive radio survey for hydrogen emission within a smaller region of the sky. Several optical surveys later identified 20 more candidate objects to the group.
In 2007, the Cen A group membership of NGC 5011C was established.
While this galaxy is a well-known stellar system
listed with a NGC number, its true identity remained hidden because of coordinate confusion and wrong redshifts in the literature. From 2015 to 2017 a full optical survey was conducted using the Dark Energy Camera, covering 550 square degrees in the sky and doubling the number of known dwarf galaxies in this group. Another deep but spatially limited survey around Centaurus A revealed numerous new dwarfs. | Centaurus A/M83 Group | Wikipedia | 512 | 970554 | https://en.wikipedia.org/wiki/Centaurus%20A/M83%20Group | Physical sciences | Notable galaxy clusters | Astronomy |
The dwarf spheroidal galaxies of the Centaurus A group have been studied and have been found to have old, metal-poor stellar populations similar to those in the Local Group, and follow a similar metallicity–luminosity relation. One dwarf galaxy, KK98 203 (LEDA 166167), has an extended ring of Hα emission.
Member list
The table below lists galaxies that have been identified as associated with the Centaurus A/M83 Group by I. D. Karachentsev and collaborators. Note that Karachentsev divides this group into two subgroups centered on Centaurus A and Messier 83.
Additionally, ESO 219-010, PGC 39032, and PGC 51659 are listed as possibly being members of the Centaurus A Subgroup, and ESO 381-018, NGC 5408, and PGC 43048 are listed as possibly being members of the M83 Subgroup. Although HIPASS J1337-39 is only listed as a possible member of the M83 Subgroup in the later list published by Karachentsev, later analyses indicate that this galaxy is within the subgroup.
Saviane and Jerjen found that NGC 5011C has an optical redshift of 647 km/s and thus is a member of the Cen A group
rather than of the distant Centaurus galaxy cluster as believed since 1983. | Centaurus A/M83 Group | Wikipedia | 290 | 970554 | https://en.wikipedia.org/wiki/Centaurus%20A/M83%20Group | Physical sciences | Notable galaxy clusters | Astronomy |
LinkedIn () is a business and employment-focused social media platform that works through websites and mobile apps. It was launched on May 5, 2003 by Reid Hoffman and Eric Ly. Since December 2016, LinkedIn has been a wholly owned subsidiary of Microsoft. The platform is primarily used for professional networking and career development, and allows jobseekers to post their CVs and employers to post jobs. From 2015, most of the company's revenue came from selling access to information about its members to recruiters and sales professionals and has also introduced their own ad portal named LinkedIn Ads to let companies advertise in their platform. LinkedIn has more than 1 billion registered members from over 200 countries and territories.
LinkedIn allows members (both employees and employers) to create profiles and connect with each other in an online social network which may represent real-world professional relationships. Members can invite anyone (whether an existing member or not) to become a connection. LinkedIn can also be used to organize offline events, join groups, write articles, publish job postings, post photos and videos, and more.
Company overview
Founded in Mountain View, California, LinkedIn is currently headquartered in Mountain View, with 36 global offices as of February 11, 2024. In February 2024, the company had around 18,500 employees.
LinkedIn's current CEO is Ryan Roslansky. Jeff Weiner, previously CEO of LinkedIn, is now serving as the Executive Chairman. Reid Hoffman, founder of LinkedIn, is chairman of the board. It was funded by Sequoia Capital, Greylock, Bain Capital Ventures, Bessemer Venture Partners and the European Founders Fund. LinkedIn reached profitability in March 2006. Since January 2011, the company had received a total of $103 million (about $ in ) of investment. LinkedIn filed for an initial public offering in January 2011 and traded its first shares in May, under the NYSE symbol "LNKD".
History
Founding from 2002 to 2011 | LinkedIn | Wikipedia | 407 | 970755 | https://en.wikipedia.org/wiki/LinkedIn | Technology | Social network and blogging | null |
The company was founded in December 2002 by Reid Hoffman and the founding team members from PayPal and Socialnet.com (Allen Blue, Eric Ly, Jean-Luc Vaillant, Lee Hower, Konstantin Guericke, Stephen Beitzel, David Eves, Ian McNish, Yan Pujante, Chris Saccheri). In late 2003, Sequoia Capital led the Series A investment in the company. In August 2004, LinkedIn reached 1 million users. In March 2006, LinkedIn achieved its first month of profitability. In April 2007, LinkedIn reached 10 million users. In February 2008, LinkedIn launched a mobile version of the site.
In June 2008, Sequoia Capital, Greylock Partners, and other venture capital firms purchased a 5% stake in the company for $53 million, giving the company a post-money valuation of approximately $1 billion. In November 2009, LinkedIn opened its office in Mumbai and soon thereafter in Sydney, as it started its Asia-Pacific team expansion. In 2010, LinkedIn opened an International Headquarters in Dublin, Ireland, received a $20 million investment from Tiger Global Management LLC at a valuation of approximately $2 billion, announced its first acquisition, Mspoke, and improved its 1% premium subscription ratio. In October of that year, Silicon Valley Insider ranked the company No. 10 on its Top 100 List of most valuable startups. By December, the company was valued at $1.575 billion in private markets. LinkedIn started its India operations in 2009 and a major part of the first year was dedicated to understanding professionals in India and educating members to leverage LinkedIn for career development.
2011 to present | LinkedIn | Wikipedia | 342 | 970755 | https://en.wikipedia.org/wiki/LinkedIn | Technology | Social network and blogging | null |
LinkedIn filed for an initial public offering in January 2011. The company traded its first shares on May 19, 2011, under the NYSE symbol "LNKD", at $45 (~$ in ) per share. Shares of LinkedIn rose as much as 171% on their first day of trade on the New York Stock Exchange and closed at $94.25, more than 109% above IPO price. Shortly after the IPO, the site's underlying infrastructure was revised to allow accelerated revision-release cycles. In 2011, LinkedIn earned $154.6 million in advertising revenue alone, surpassing Twitter, which earned $139.5 million. LinkedIn's fourth-quarter 2011, earnings soared because of the company's increase in success in the social media world. By this point, LinkedIn had about 2,100 full-time employees compared to the 500 that it had in 2010.
In April 2014, LinkedIn announced that it had leased 222 Second Street, a 26-story building under construction in San Francisco's SoMa district, to accommodate up to 2,500 of its employees, with the lease covering 10 years. The goal was to join all San Francisco-based staff (1,250 as of January 2016) in one building, bringing sales and marketing employees together with the research and development team. In March 2016 they started to move in. In February 2016 following an earnings report, LinkedIn's shares dropped 43.6% within a single day, down to $108.38 per share. LinkedIn lost $10 billion of its market capitalization that day.
In 2016, access to LinkedIn was blocked by Russian authorities for non-compliance with the 2015 national legislation that requires social media networks to store citizens' personal data on servers located in Russia.
In June 2016, Microsoft announced that it would acquire LinkedIn for $196 a share, a total value of $26.2 billion. It was the largest acquisition made by Microsoft, until the acquisition of Activision Blizzard in 2022. The acquisition would be an all-cash, debt-financed transaction. Microsoft would allow LinkedIn to "retain its distinct brand, culture and independence", with Weiner to remain as CEO, who would then report to Microsoft CEO Satya Nadella. Analysts believed Microsoft saw the opportunity to integrate LinkedIn with its Office product suite to help better integrate the professional network system with its products. The deal was completed on December 8, 2016. | LinkedIn | Wikipedia | 500 | 970755 | https://en.wikipedia.org/wiki/LinkedIn | Technology | Social network and blogging | null |
In late 2016, LinkedIn announced a planned increase of 200 new positions in its Dublin office, which would bring the total employee count to 1,200. Since 2017 94% of B2B marketers use LinkedIn to distribute content.
Soon after LinkedIn's acquisition by Microsoft, LinkedIn's new desktop version was introduced. The new version was meant to make the user experience similar across mobile and desktop. Some changes were made according to the feedback received from the previously launched mobile app. Features that were not heavily used were removed. For example, the contact tagging and filtering features are not supported anymore.
Following the launch of the new user interface (UI), some users complained about the missing features which were there in the older version, slowness, and bugs in it. The issues were faced by free and premium users and with both the desktop and mobile versions of the site.
In 2019, LinkedIn launched globally the feature Open for Business that enables freelancers to be discovered on the platform. LinkedIn Events was launched in the same year.
In June 2020, Jeff Weiner stepped down as CEO and become executive chairman after 11 years in the role. Ryan Roslansky stepped up as CEO from his previous position as the senior vice president of product. In late July 2020, LinkedIn announced it laid off 960 employees, about 6 percent of the total workforce, from the talent acquisition and global sales teams. In an email to all employees, CEO Ryan Roslansky said the cuts were due to effects of the global COVID-19 pandemic.
In April 2021, CyberNews claimed that 500 million LinkedIn's accounts have leaked online. However, LinkedIn stated that "We have investigated an alleged set of LinkedIn data that has been posted for sale and have determined that it is actually an aggregation of data from a number of websites and companies".
In June 2021, PrivacySharks claimed that more than 700 million LinkedIn records were on sale on a hacker forum. LinkedIn later stated that this is not a breach, but scraped data which is also a violation of their Terms of Service.
Microsoft ended LinkedIn operations in China in October 2021.
In 2022, LinkedIn earned $13.8 billion in revenue, compared to $10.3 billion in 2021. | LinkedIn | Wikipedia | 466 | 970755 | https://en.wikipedia.org/wiki/LinkedIn | Technology | Social network and blogging | null |
In May 2023, LinkedIn cut 716 positions from its 20,000 workforce. The move, according to a letter from the company's CEO Ryan Roslansky, was made to streamline the business's operations. Roslansky further stated that this decision would result in the creation of 250 job opportunities. Additionally, LinkedIn also announced the discontinuance of its China local job apps.
In June 2024, Axios reported LinkedIn was testing a new AI assistant for its paid Premium users.
In September 2024, LinkedIn suspended its use of UK user data for AI model training after concerns were raised by the Information Commissioner's Office (ICO). The platform had quietly opted in users globally for data use in AI training. However, following ICO feedback, LinkedIn paused this practice for UK users. A company spokesperson stated that LinkedIn has always allowed users to control how their data is used and has now provided UK users with an opt-out option.
In November 2024, Linkedin challenged Australian legislation which sought to ban under-16's from social media platforms on the grounds that it does 'not have content interesting and appealing to minors.'
Acquisitions
In July 2012, LinkedIn acquired 15 key Digg patents for $4 million including a "click a button to vote up a story" patent.
Perkins lawsuit
In 2013, a class action lawsuit entitled Perkins vs. LinkedIn Corp was filed against the company, accusing it of automatically sending invitations to contacts in a member's email address book without permission. The court agreed with LinkedIn that permission had in fact been given for invitations to be sent, but not for the two further reminder emails. LinkedIn settled the lawsuit in 2015 for $13 million (~$ in ). Many members should have received a notice in their email with the subject line "Legal Notice of Settlement of Class Action". The Case No. is 13-CV-04303-LHK.
hiQ Labs v. LinkedIn | LinkedIn | Wikipedia | 408 | 970755 | https://en.wikipedia.org/wiki/LinkedIn | Technology | Social network and blogging | null |
In May 2017, LinkedIn sent a Cease-And-Desist letter to hiQ Labs, a Silicon Valley startup that collects data from public profiles and provides analysis of this data to its customers. The letter demanded that hiQ immediately cease "scraping" data from LinkedIn's servers, claiming violations of the CFAA (Computer Fraud and Abuse Act) and the DMCA (Digital Millennium Copyright Act). In response hiQ sued LinkedIn in the Northern District of California in San Francisco, asking the court to prohibit LinkedIn from blocking its access to public profiles while the court considered the merits of its request. The court served a preliminary injunction against LinkedIn, which was then forced to allow hiQ to continue to collect public data. LinkedIn appealed this ruling; in September 2019, the appeals court rejected LinkedIn's arguments and the preliminary injunction was upheld. The dispute is ongoing.
Membership
In 2015, LinkedIn had more than 400 million members in over 200 countries and territories, which was significantly more than competitor Viadeo (50 million as of 2013.) In 2011, its membership grew by approximately two new members every second. In 2020, LinkedIn's membership grew to over 690 million LinkedIn members. As of September 2021, LinkedIn had 774+ million registered members from over 200 countries and territories. In November 2023, LinkedIn reached a member count of one billion.
Platform and features
User profile network
Basic functionality
The basic functionality of LinkedIn allows users to create profiles, which for employees typically consist of a curriculum vitae describing their work experience, education and training, skills, and a personal photo. Employers can list jobs and search for potential candidates. Users can find jobs, people and business opportunities recommended by someone in one's contact network. Users can save jobs that they would like to apply for. Users also have the ability to follow different companies.
The site also enables members to make "connections" to each other in an online social network which may represent real-world professional relationships. Members can invite anyone to become a connection. Users can obtain introductions to the connections of connections (termed second-degree connections) and connections of second-degree connections (termed third-degree connections). | LinkedIn | Wikipedia | 448 | 970755 | https://en.wikipedia.org/wiki/LinkedIn | Technology | Social network and blogging | null |
A member's list of connections can be used in a number of ways. For example, users can search for second-degree connections who work at a company they are interested in, and then ask a specific first-degree connection in common for an introduction. The "gated-access approach" (where contact with any professional requires either an existing relationship, or the intervention of a contact of theirs) is intended to build trust among the service's users. LinkedIn participated in the EU's International Safe Harbor Privacy Principles.
Users can interact with each other in a variety of ways:
Connections can interact by choosing to "like" posts and "congratulate" others on updates such as birthdays, anniversaries and new positions, as well as by direct messaging.
Users can share video with text and filters with the introduction of LinkedIn Video.
Users can write posts and articles within the LinkedIn platform to share with their network.
Since September 2012, LinkedIn has enabled users to "endorse" each other's skills. However, there is no way of flagging anything other than positive content. LinkedIn solicits endorsements using algorithms that generate skills members might have. Members cannot opt out of such solicitations, with the result that it sometimes appears that a member is soliciting an endorsement for a non-existent skill.
Applications
LinkedIn 'applications' often refer to external third-party applications that interact with LinkedIn's developer API. However, in some cases, it could refer to sanctioned applications featured on a user's profile page.
External, third party applications
In February 2015, LinkedIn released an updated terms of use for their developer API. The developer API allows both companies and individuals the ability to interact with LinkedIn's data through creation of managed third-party applications. Applications must go through a review process and request permission from the user before accessing a user's data.
Normal use of the API is outlined in LinkedIn's developer documents, including:
Sign into external services using LinkedIn
Add items or attributes to a user profile
Share items or articles to user's timeline | LinkedIn | Wikipedia | 434 | 970755 | https://en.wikipedia.org/wiki/LinkedIn | Technology | Social network and blogging | null |
Embedded in profile
In October 2008, LinkedIn enabled an "applications platform" which allows external online services to be embedded within a member's profile page. Among the initial applications were an Amazon Reading List that allows LinkedIn members to display books they are reading, a connection to Tripit, and a Six Apart, WordPress and TypePad application that allows members to display their latest blog postings within their LinkedIn profile. In November 2010, LinkedIn allowed businesses to list products and services on company profile pages; it also permitted LinkedIn members to "recommend" products and services and write reviews. Shortly after, some of the external services were no longer supported, including Amazon's Reading List.
Mobile
A mobile version of the site was launched in February 2008 and made available in six languages: Chinese, English, French, German, Japanese and Spanish. In January 2011, LinkedIn acquired CardMunch, a mobile app maker that scans business cards and converts into contacts. In June 2013, CardMunch was noted as an available LinkedIn app. In October 2013, LinkedIn announced a service for iPhone users called "Intro", which inserts a thumbnail of a person's LinkedIn profile in correspondence with that person when reading mail messages in the native iOS Mail program. This is accomplished by re-routing all emails from and to the iPhone through LinkedIn servers, which security firm Bishop Fox asserts has serious privacy implications, violates many organizations' security policies, and resembles a man-in-the-middle attack. | LinkedIn | Wikipedia | 308 | 970755 | https://en.wikipedia.org/wiki/LinkedIn | Technology | Social network and blogging | null |
Groups
LinkedIn also supports daily the formation of interest groups. In 2012, there were 1,248,019 such groups whose membership varies from 1 to 744,662. Groups support a limited form of discussion area, moderated by the group owners and managers. Groups may be private, accessible to members only or may be open to Internet users in general to read, though they must join in order to post messages. Since groups offer the functionality to reach a wide audience without so easily falling foul of anti-spam solutions, there is a constant stream of spam postings, and there now exists a range of firms who offer a spamming service for this very purpose. LinkedIn has devised a few mechanisms to reduce the volume of spam, but recently decided to remove the ability of group owners to inspect the email address of new members in order to determine if they were spammers. Groups also keep their members informed through emails with updates to the group, including most talked about discussions within your professional circles.
In December 2011, LinkedIn announced that they are rolling out polls to groups. In November 2013, LinkedIn announced the addition of Showcase Pages to the platform. In 2014, LinkedIn announced they were going to be removing Product and Services Pages paving the way for a greater focus on Showcase Pages.
Knowledge graph
LinkedIn maintains an internal knowledge graph of entities (people, organizations, groups) that helps it connect everyone working in a field or at an organization or network. This can be used to query the neighborhood around each entity to find updates that might be related to it.
This also lets them train machine learning models that can infer new properties about an entity or further information that may apply to it for both summary views and analytics.
Discontinued features
In January 2013, LinkedIn dropped support for LinkedIn Answers and cited a new 'focus on development of new and more engaging ways to share and discuss professional topics across LinkedIn' as the reason for the retirement of the feature. The feature had been launched in 2007 and allowed users to post questions to their network and allowed users to rank answers.
In 2014, LinkedIn retired InMaps, a feature which allowed you to visualize your professional network. The feature had been in use since January 2011.
According to the company's website, LinkedIn Referrals will no longer be available after May 2018.
In September 2021, LinkedIn discontinued LinkedIn stories, a feature that was rolled out worldwide in October 2020.
Usage
Personal branding | LinkedIn | Wikipedia | 502 | 970755 | https://en.wikipedia.org/wiki/LinkedIn | Technology | Social network and blogging | null |
LinkedIn is particularly well-suited for personal branding, which, according to Sandra Long, entails "actively managing one's image and unique value" to position oneself for career opportunities. LinkedIn has evolved from being a mere platform for job searchers into a social network which allows users a chance to create a personal brand. Career coach Pamela Green describes a personal brand as the "emotional experience you want people to have as a result of interacting with you," and a LinkedIn profile is an aspect of that. A contrasting report suggests that a personal brand is "a public-facing persona, exhibited on LinkedIn, Twitter and other networks, that showcases expertise and fosters new connections."
LinkedIn allows professionals to build exposure for their brand within the site itself and on the World Wide Web as a whole. With a tool that LinkedIn dubs a Profile Strength Meter, the site encourages users to offer enough information in their profile to optimize visibility by search engines. It can strengthen a user's LinkedIn presence if they belong to professional groups on the site. The site enables users to add a video to their profiles. Some users hire a professional photographer for their profile photo. Video presentations can be added to one's profile. LinkedIn's capabilities have been expanding so rapidly that a cottage industry of outside consultants has grown up to help users navigate the system. A particular emphasis is helping users with their LinkedIn profiles.
In October 2012, LinkedIn launched the LinkedIn Influencers program, which features global thought leaders who share their professional insights with LinkedIn's members. As of May 2016, there are 750+ Influencers. The program is invite-only and features leaders from a range of industries, including Richard Branson, Narendra Modi, Arianna Huffington, Greg McKeown, Rahm Emanuel, Jamie Dimon, Martha Stewart, Deepak Chopra, Jack Welch, and Bill Gates.
Job seeking
Job seekers and employers widely use LinkedIn. According to Jack Meyer, the site has become the "premier digital platform" for professionals to network online. In Australia, which has approximately twelve million working professionals, ten million of them are on LinkedIn, according to Anastasia Santoreneos, suggesting that the probability was high that one's "future employer is probably on the site." According to one estimate based on worldwide figures, 122 million users got job interviews via LinkedIn and 35 million were hired by a LinkedIn online connection. | LinkedIn | Wikipedia | 500 | 970755 | https://en.wikipedia.org/wiki/LinkedIn | Technology | Social network and blogging | null |
LinkedIn also allows users to research companies, non-profit organizations, and governments they may be interested in working for. Typing the name of a company or organization in the search box causes pop-up data about the company or organization to appear. Such data may include the ratio of female to male employees, the percentage of the most common titles/positions held within the company, the location of the company's headquarters and offices, and a list of present and former employees. In July 2011, LinkedIn launched a new feature allowing companies to include an "Apply with LinkedIn" button on job listing pages. The new plugin allowed potential employees to apply for positions using their LinkedIn profiles as resumes.
LinkedIn can help small businesses connect with customers. In the site's parlance, two users have a "first-degree connection" when one accepts an invitation from another. People connected to each of them are "second-degree connections" and persons connected to the second-degree connections are "third-degree connections." This forms a user's internal LinkedIn network, making the user's profile more likely to appear in searches.
LinkedIn's Profinder is a marketplace where freelancers can (for a monthly subscription fee) bid for project proposals submitted by individuals and small businesses. In 2017, it had around 60,000 freelancers in more than 140 service areas, such as headshot photography, bookkeeping or tax filing.
The premise for connecting with someone has shifted significantly in recent years. Before the 2017 new interface was launched, LinkedIn encouraged connections between people who'd already worked, studied, done business, or the like. Since 2017, that step has been removed from the connection request process - and users are allowed to connect with up to 30,000 people. This change means LinkedIn is a more proactive networking site for job applicants trying to secure a career move or for salespeople wanting to generate new client leads. | LinkedIn | Wikipedia | 397 | 970755 | https://en.wikipedia.org/wiki/LinkedIn | Technology | Social network and blogging | null |
Top Companies
LinkedIn Top Companies is a series of lists published by LinkedIn, identifying companies in the United States, Australia, Brazil, Canada, China, France, Germany, India, Japan, Mexico, South Korea, Spain, and the United Kingdom that are attracting the most intense interest from job candidates. The 2019 lists identified Google's parent company, Alphabet, as the most sought-after U.S. company, with Facebook ranked second and Amazon ranked third. The lists are based on more than one billion actions by LinkedIn members worldwide. The Top Companies lists were started in 2016 and are published annually. The 2021 top list identified Amazon as the top company, with Alphabet ranked second and JPMorgan & Chase Co. ranked third.
Top Voices and other rankings
Since 2015, LinkedIn has published annual rankings of Top Voices on the platform, recognizing "members that generated the most engagement and interaction with their posts." The 2020 lists included 14 industry categories, ranging from data science to sports, as well as 14 country lists, extending from Australia to Italy.
LinkedIn also publishes data-driven annual rankings of the Top Startups in more than a dozen countries, based on "employment growth, job interest from potential candidates, engagement, and attraction of top talent."
Advertising and for-pay research
In 2008, LinkedIn launched LinkedIn DirectAds as a form of sponsored advertising. In October 2008, LinkedIn revealed plans to open its social network of 30 million professionals globally as a potential sample for business-to-business research. It is testing a potential social network revenue model – research that, to some, appears more promising than advertising. On July 23, 2013, LinkedIn announced its Sponsored Updates ad service. Individuals and companies can now pay a fee to have LinkedIn sponsor their content and spread it to their user base. This is a common way for social media sites such as LinkedIn to generate revenue.
LinkedIn launched its carousel ads feature in 2018, making it the newest addition to the platform's advertising options. With carousel ads, businesses can showcase their products or services through a series of swipeable cards, each with its unique image, headline, and description. They can be used for various marketing objectives, such as promoting a new product launch, driving website traffic, generating leads, or building brand awareness.
Business Manager
LinkedIn today announced the creation of Business Manager. The new Business Manager is a centralized platform designed to make it easier for large companies and agencies to manage people, ad accounts, and business pages. | LinkedIn | Wikipedia | 509 | 970755 | https://en.wikipedia.org/wiki/LinkedIn | Technology | Social network and blogging | null |
Publishing platform
In 2015, LinkedIn added an analytics tool to its publishing platform. The tool allows authors to better track the traffic that their posts receive. In relation to this functionality, LinkedIn has gained more users over the years in the interest of clearly monitoring users' posts through post-performance analytics
Future plans
Economic graph
Inspired by Facebook's "social graph", LinkedIn CEO Jeff Weiner set a goal in 2012 to create an "economic graph" within a decade. The goal was to create a comprehensive digital map of the world economy and the connections within it. The economic graph was to be built on the company's current platform with data nodes including companies, jobs, skills, volunteer opportunities, educational institutions, and content. They have been hoping to include all the job listings in the world, all the skills required to get those jobs, all the professionals who could fill them, and all the companies (nonprofit and for-profit) at which they work. The ultimate goal is to make the world economy and job market more efficient through increased transparency. In June 2014, the company announced its "Galene" search architecture to give users access to the economic graph's data with more thorough filtering of data, via user searches like "Engineers with Hadoop experience in Brazil."
LinkedIn has published blog posts using economic graph data to research several topics on the job market, including popular destination cities of recent college graduates, areas with high concentrations of technology skills, and common career transitions. LinkedIn provided the City of New York with data from economic graph showing "in-demand" tech skills for the city's "Tech Talent Pipeline" project.
Role in networking
LinkedIn has been described by online trade publication TechRepublic as having "become the de facto tool for professional networking". LinkedIn has also been praised for its usefulness in fostering business relationships. "LinkedIn is, far and away, the most advantageous social networking tool available to job seekers and business professionals today," according to Forbes. LinkedIn has inspired the creation of specialised professional networking opportunities, such as co-founder Eddie Lou's Chicago startup, Shiftgig (released in 2012 as a platform for hourly workers).
Criticism and controversies
Controversial design choices | LinkedIn | Wikipedia | 453 | 970755 | https://en.wikipedia.org/wiki/LinkedIn | Technology | Social network and blogging | null |
Endorsement feature
The feature that allows LinkedIn members to "endorse" each other's skills and experience has been criticized as meaningless, since the endorsements are not necessarily accurate or given by people who have familiarity with the member's skills. In October 2016, LinkedIn acknowledged that it "really does matter who endorsed you" and began highlighting endorsements from "coworkers and other mutual connections" to address the criticism.
Use of e-mail accounts of members for spam sending
LinkedIn sends "invite emails" to Outlook contacts from its members' email accounts, without obtaining their consent. The "invitations" give the impression that the e-mail holder themself has sent the invitation. If there is no response, the answer will be repeated several times ("You have not yet answered XY's invitation.") LinkedIn was sued in the United States on charges of hijacking e-mail accounts and spamming. The company argued with the right to freedom of expression. In addition, the users concerned would be supported in building a network.
The sign-up process includes users entering their email password (there is an opt-out feature). LinkedIn will then offer to send out contact invitations to all members in that address book or that the user has had email conversations with. When the member's email address book is opened, it is opened with all email addresses selected, and the member is advised invitations will be sent to "selected" email addresses, or to all. LinkedIn was sued for sending out another two follow-up invitations to each contact from members to link to friends who had ignored the initial, authorized invitation.
In November 2014, LinkedIn lost a motion to dismiss the lawsuit, in a ruling that the invitations were advertisements not broadly protected by free speech rights that would otherwise permit use of people's names and images without authorization. The lawsuit was eventually settled in 2015 in favor of LinkedIn members.
Moving emails to LinkedIn servers
At the end of 2013 it was announced that the LinkedIn app intercepted users' emails and quietly moved them to LinkedIn servers for full access. LinkedIn used man-in-the-middle attacks.
Security incidents
2012 hack | LinkedIn | Wikipedia | 445 | 970755 | https://en.wikipedia.org/wiki/LinkedIn | Technology | Social network and blogging | null |
In June 2012, cryptographic hashes of approximately 6.4 million LinkedIn user passwords were stolen by Yevgeniy Nikulin and other hackers who then published the stolen hashes online. This action is known as the 2012 LinkedIn hack. In response to the incident, LinkedIn asked its users to change their passwords. Security experts criticized LinkedIn for not salting their password file and for using a single iteration of SHA-1. On May 31, 2013, LinkedIn added two-factor authentication, an important security enhancement for preventing hackers from gaining access to accounts. In May 2016, 117 million LinkedIn usernames and passwords were offered for sale online for the equivalent of $2,200 (~$ in ). These account details are believed to be sourced from the original 2012 LinkedIn hack, in which the number of user IDs stolen had been underestimated. To handle the large volume of emails sent to its users every day with notifications for messages, profile views, important happenings in their network, and other things, LinkedIn uses the Momentum email platform from Message Systems.
2021 breaches
A breach disclosed in April 2021 affected 500 million users. A breach disclosed in June 2021 was thought to have affected 92% of users, exposing contact information, employment information. LinkedIn asserted that the data was aggregated via web scraping from LinkedIn as well as several other sites, and noted that "only information that people listed publicly in their profiles" was included.
Malicious behavior on LinkedIn
Phishing
In what is known as Operation Socialist, documents released by Edward Snowden in the 2013 global surveillance disclosures revealed that British Government Communications Headquarters (GCHQ) (an intelligence and security organisation) infiltrated the Belgian telecommunications network Belgacom by luring employees to a false LinkedIn page.
In 2014, Dell SecureWorks Counter Threat Unit (CTU) discovered that Threat Group-2889, an Iran-based group, created 25 fake LinkedIn accounts. The accounts were either fully developed personas or supporting personas. They use spearphishing and malicious websites against their victims.
According to reporting by Le Figaro, France's General Directorate for Internal Security and Directorate-General for External Security believe that Chinese spies have used LinkedIn to target thousands of business and government officials as potential sources of information. | LinkedIn | Wikipedia | 474 | 970755 | https://en.wikipedia.org/wiki/LinkedIn | Technology | Social network and blogging | null |
In 2017, Germany's Federal Office for the Protection of the Constitution (BfV) published information alleging that Chinese intelligence services had created fake social media profiles on sites such as LinkedIn, using them to gather information on German politicians and government officials.
In 2022, the company ranked first in a list of brands most likely to be imitated in phishing attempts.
In August 2023, several Linkedin users were targeted by hackers in hijacking and phishing bid. Users were locked out of their accounts and threatened with permanent account deletion if they did not pay a ransom.
False and misleading information
LinkedIn has come under scrutiny for its handling of misinformation and disinformation. The platform has struggled to deal with fake profiles and falsehoods about COVID-19 and the 2020 US presidential election.
Policies
Privacy policy
The German Stiftung Warentest has criticized that the balance of rights between users and LinkedIn is disproportionate, restricting users' rights excessively while granting the company far-reaching rights. It has also been claimed that LinkedIn does not respond to consumer protection center requests.
Research on labor market effects
In 2010, Social Science Computer Review published research by economists Ralf Caers and Vanessa Castelyns who sent an online questionnaire to 398 and 353 LinkedIn and Facebook users respectively in Belgium and found that both sites had become tools for recruiting job applicants for professional occupations as well as additional information about applicants, and that it was being used by recruiters to decide which applicants would receive interviews. In May 2017, Research Policy published an analysis of PhD holders use of LinkedIn and found that PhD holders who move into industry were more likely to have LinkedIn accounts and to have larger networks of LinkedIn connections, were more likely to use LinkedIn if they had co-authors abroad, and to have wider networks if they moved abroad after obtaining their PhD. | LinkedIn | Wikipedia | 389 | 970755 | https://en.wikipedia.org/wiki/LinkedIn | Technology | Social network and blogging | null |
Also in 2017, sociologist Ofer Sharone conducted interviews with unemployed workers to research the effects of LinkedIn and Facebook as labor market intermediaries and found that social networking services (SNS) have had a filtration effect that has little to do with evaluations of merit, and that the SNS filtration effect has exerted new pressures on workers to manage their careers to conform to the logic of the SNS filtration effect. In October 2018, Foster School of Business professors Melissa Rhee, Elina Hwang, and Yong Tan performed an empirical analysis of whether the common professional networking tactic by job seekers of creating LinkedIn connections with professionals who work at a target company or in a target field is actually instrumental in obtaining referrals and found instead that job seekers were less likely to be referred by employees who were employed by the target company or in the target field due to job similarity and self-protection from competition. Rhee, Hwang, and Tan further found that referring employees in higher hierarchical positions than the job candidates were more likely to provide referrals and that gender homophily did not reduce the competition self-protection effect.
In July 2019, sociologists Steve McDonald, Amanda K. Damarin, Jenelle Lawhorne, and Annika Wilcox performed qualitative interviews with 61 human resources recruiters in two metropolitan areas in the Southern United States and found that recruiters filling low- and general-skilled positions typically posted advertisements on online job boards while recruiters filling high-skilled or supervisor positions targeted passive candidates on LinkedIn (i.e. employed workers not actively seeking work but possibly willing to change positions), and concluded that this is resulting in a bifurcated winner-takes-all job market with recruiters focusing their efforts on poaching already employed high-skilled workers while active job seekers are relegated to hyper-competitive online job boards. In December 2001, the ACM SIGGROUP Bulletin published a study on the use of mobile phones by blue-collar workers that noted that research about tools for blue-collar workers to find work in the digital age was strangely absent and expressed concern that the absence of such research could lead to technology design choices that would concentrate greater power in the hands of managers rather than workers. | LinkedIn | Wikipedia | 458 | 970755 | https://en.wikipedia.org/wiki/LinkedIn | Technology | Social network and blogging | null |
In a September 2019 working paper, economists Laurel Wheeler, Robert Garlick, and RTI International scholars Eric Johnson, Patrick Shaw, and Marissa Gargano ran a randomized evaluation of training job seekers in South Africa to use LinkedIn as part of job readiness programs. The evaluation found that the training increased the job seekers employment by approximately 10 percent by reducing information frictions between job seekers and prospective employers, that the training had this effect for approximately 12 months, and that while the training may also have facilitated referrals, it did not reduce job search costs and the jobs for the treatment and control groups in the evaluation had equal probabilities of retention, promotion, and obtaining a permanent contract. In 2020, Applied Economics published research by economists Steffen Brenner, Sezen Aksin Sivrikaya, and Joachim Schwalbach using LinkedIn demonstrating that high status individuals self-select into professional networking services rather than workers unsatisfied with their career status adversely selecting into the services to receive networking benefits.
International restrictions
In February 2011, it was reported that LinkedIn was being blocked in China after calls for a "Jasmine Revolution". It was speculated to have been blocked because it is an easy way for dissidents to access Twitter, which had been blocked previously. After a day of being blocked, LinkedIn access was restored in China.
In February 2014, LinkedIn launched its Simplified Chinese language version named "" (), officially extending their service in China. LinkedIn CEO Jeff Weiner acknowledged in a blog post that they would have to censor some of the content that users post on its website in order to comply with Chinese rules, but he also said the benefits of providing its online service to people in China outweighed those concerns. Since Autumn 2017 job postings from western countries for China aren't possible anymore.
In 2016, a Moscow court ruled that LinkedIn must be blocked in Russia for violating a data retention law which requires the user data of Russian citizens to be stored on servers within the country. The relevant law had been in force there since 2014. This ban was upheld on November 10, 2016, and all Russian ISPs began blocking LinkedIn thereafter. LinkedIn's mobile app was also banned from Google Play Store and iOS App Store in Russia in January 2017. In July 2021 it was also blocked in Kazakhstan. | LinkedIn | Wikipedia | 477 | 970755 | https://en.wikipedia.org/wiki/LinkedIn | Technology | Social network and blogging | null |
In October 2021, after reports of several academicians and reporters who received notifications regarding their profiles will be blocked in China, Microsoft confirmed that LinkedIn will be shutting down in China and replaced with InJobs, a China exclusive app, citing difficulties in operating environments and increasing compliance requirements. In May 2023, LinkedIn announced that it would be phasing out the app by 9 August 2023.
Account banning
Without giving its users any prior notice, Linkedin has been removing accounts that do not follow its criteria since 2022.
Open-source contributions
Since 2010, LinkedIn has contributed several internal technologies, tools, and software products to the open source domain. Notable among these projects is Apache Kafka, which was built and open sourced at LinkedIn in 2011.
Research using data from the platform
Massive amounts of data from LinkedIn allow scientists and machine learning researchers to extract insights and build product features. For example, this data can help to shape patterns of deception in resumes. Findings suggested that people commonly lie about their hobbies rather than their work experience on online resumes. | LinkedIn | Wikipedia | 219 | 970755 | https://en.wikipedia.org/wiki/LinkedIn | Technology | Social network and blogging | null |
In astronomy, a trojan is a small celestial body (mostly asteroids) that shares the orbit of a larger body, remaining in a stable orbit approximately 60° ahead of or behind the main body near one of its Lagrangian points and . Trojans can share the orbits of planets or of large moons.
Trojans are one type of co-orbital object. In this arrangement, a star and a planet orbit about their common barycenter, which is close to the center of the star because it is usually much more massive than the orbiting planet. In turn, a much smaller mass than both the star and the planet, located at one of the Lagrangian points of the star–planet system, is subject to a combined gravitational force that acts through this barycenter. Hence the smallest object orbits around the barycenter with the same orbital period as the planet, and the arrangement can remain stable over time.
In the Solar System, most known trojans share the orbit of Jupiter. They are divided into the Greek camp at (ahead of Jupiter) and the Trojan camp at (trailing Jupiter). More than a million Jupiter trojans larger than one kilometer are thought to exist, of which more than 7,000 are currently catalogued. In other planetary orbits only nine Mars trojans, 31 Neptune trojans, two Uranus trojans, and two Earth trojans, have been found to date. A temporary Venus trojan is also known. Numerical orbital dynamics stability simulations indicate that Saturn probably does not have any primordial trojans.
The same arrangement can appear when the primary object is a planet and the secondary is one of its moons, whereby much smaller trojan moons can share its orbit. All known trojan moons are part of the Saturn system. Telesto and Calypso are trojans of Tethys, and Helene and Polydeuces of Dione.
Trojan minor planets
In 1772, the Italian–French mathematician and astronomer Joseph-Louis Lagrange obtained two constant-pattern solutions (collinear and equilateral) of the general three-body problem. In the restricted three-body problem, with one mass negligible (which Lagrange did not consider), the five possible positions of that mass are now termed Lagrange points. | Trojan (celestial body) | Wikipedia | 464 | 7108409 | https://en.wikipedia.org/wiki/Trojan%20%28celestial%20body%29 | Physical sciences | Planetary science | Astronomy |
The term "trojan" originally referred to the "trojan asteroids" (Jovian trojans) that orbit close to the Lagrangian points of Jupiter. These have long been named for figures from the Trojan War of Greek mythology. By convention, the asteroids orbiting near the point of Jupiter are named for the characters from the Greek side of the war, whereas those orbiting near the of Jupiter are from the Trojan side. There are two exceptions, named before the convention was adopted: 624 Hektor in the L4 group, and 617 Patroclus in the L5 group.
Astronomers estimate that the Jovian trojans are about as numerous as the asteroids of the asteroid belt.
Later on, objects were found orbiting near the Lagrangian points of Neptune, Mars, Earth, Uranus, and Venus. Minor planets at the Lagrangian points of planets other than Jupiter may be called Lagrangian minor planets.
Four Martian trojans are known: 5261 Eureka, , , and – the only Trojan body in the leading "cloud" at , There seem to be, also, , , and , but these have not yet been accepted by the Minor Planet Center.
There are 28 known Neptunian trojans, but the large Neptunian trojans are expected to outnumber the large Jovian trojans by an order of magnitude.
was confirmed to be the first known Earth trojan in 2011. It is located in the Lagrangian point, which lies ahead of the Earth. was found to be another Earth trojan in 2021. It is also at L4.
was identified as the first Uranus trojan in 2013. It is located at the Lagrangian point. A second one, , was announced in 2017.
is a temporary Venusian trojan, the first one to be identified.
The large asteroids Ceres and Vesta have temporary trojans.
Saturn has 1 known trojan in the L4 Lagrangian Point, 2019 UO14.
Trojans by planet
Stability
Whether or not a system of star, planet, and trojan is stable depends on how large the perturbations are to which it is subject. If, for example, the planet is the mass of Earth, and there is also a Jupiter-mass object orbiting that star, the trojan's orbit would be much less stable than if the second planet had the mass of Pluto. | Trojan (celestial body) | Wikipedia | 489 | 7108409 | https://en.wikipedia.org/wiki/Trojan%20%28celestial%20body%29 | Physical sciences | Planetary science | Astronomy |
As a rule of thumb, the system is likely to be long-lived if m1 > 100m2 > 10,000m3 (in which m1, m2, and m3 are the masses of the star, planet, and trojan).
More formally, in a three-body system with circular orbits, the stability condition is 27(m1m2 + m2m3 + m3m1) < (m1 + m2 + m3)2. So the trojan being a mote of dust, m3→0, imposes a lower bound on of ≈ 24.9599. And if the star were hyper-massive, m1→+∞, then under Newtonian gravity, the system is stable whatever the planet and trojan masses. And if = , then both must exceed 13+√168 ≈ 25.9615. However, this all assumes a three-body system; once other bodies are introduced, even if distant and small, stability of the system requires even larger ratios. | Trojan (celestial body) | Wikipedia | 200 | 7108409 | https://en.wikipedia.org/wiki/Trojan%20%28celestial%20body%29 | Physical sciences | Planetary science | Astronomy |
The ringtail (Bassariscus astutus) is a mammal of the raccoon family native to arid regions of North America. It is widely distributed and well-adapted to its distributed areas. It has been legally trapped for its fur. Globally, it is listed as Least Concern on the IUCN Red List but is a Conservation Strategy Species in Oregon and Fully Protected in California The species is known by a variety of names, such as ring-tailed cat, miner's cat, civet cat, and cacomistle (or cacomixtle), though the last of these can refer to B. sumichrasti.
The ringtail is the state mammal of Arizona.
Description
The ringtail is black to dark brown in color with pale underparts. The animal has a pointed muzzle with long whiskers, similar to that of a fox (its Latin name means 'clever little fox') and its body resembles that of a cat. The ringtail's face resembles a mask as dark brown and black hair surround its eyes.
These animals are characterized by a long black and white "ringed" tail with 14–16 stripes, which is about the same length as its body.
Ringtails are primarily nocturnal, with large eyes and upright ears that make it easier for them to navigate and forage in the dark. An adept climber, it uses its long tail for balance. The rings on its tail can also act as a distraction for predators. The white rings act as a target, so when the tail rather than the body is caught, the ringtail has a greater chance of escaping.
The claws are short, straight, and semi-retractable, well-suited for climbing.
Smaller than a house cat, it is one of the smallest extant procyonids (only the smallest in the olingo species group average smaller). Its body alone measures and its tail averages from its base. It typically weighs around .
Its dental formula is = 40.
The ankle joint is flexible and is able to rotate over 180 degrees, making the animal an agile climber. The long tail provides balance for negotiating narrow ledges and limbs, even allowing individuals to reverse directions by performing a cartwheel. Ringtails also can ascend narrow passages by stemming (pressing all feet on one wall and their back against the other or pressing both right feet on one wall and both left feet on the other), and wider cracks or openings by ricocheting between the walls. | Ringtail | Wikipedia | 502 | 154237 | https://en.wikipedia.org/wiki/Ringtail | Biology and health sciences | Procyonidae | Animals |
As adults, these mammals lead solitary lives, generally coming together only to mate. A typical call is a very loud, plaintive bark. They produce a variety of sounds, including clicks and chatters reminiscent of raccoons.
Ringtails have been reported to exhibit fecal marking behavior as a form of intraspecific communication to define territory boundaries or attract potential mates. It has been suggested that ringtails use feces as a way to mark territory. In 2003, a study in Mexico City found that ringtails tended to defecate in similar areas in a seemingly nonrandom pattern, mimicking that of other carnivores that utilized excretions to mark territories.
Ringtails prefer a solitary existence but may share a den or be found mutually grooming one another. They exhibit limited interaction except during the breeding season, which occurs in the early spring. Ringtails can survive for long periods on water derived from food alone, and have urine which is more concentrated than any other mammal studied, an adaptation that allows for maximum water retention.
Reproduction
Ringtails mate in the spring. The gestation period is 45–50 days, during which the male will procure food for the female. There will be 2–4 kits in a litter. The cubs open their eyes after one month, and will hunt for themselves after four months. They reach sexual maturity at 10 months. The ringtail's lifespan in the wild is about seven years.
Range and habitat
The ringtail is commonly found in rocky desert habitats, where it nests in the hollows of trees or abandoned wooden structures. It has been found throughout the Great Basin Desert, which stretches over several states (Nevada, Utah, California, Idaho, and Oregon) as well as the Sonoran Desert in Arizona, and the Chihuahuan Desert in New Mexico, Texas, and northern Mexico. The ringtail also prefers rocky habitats associated with water, such as the riparian canyons, caves, or mine shafts.
In areas with a bountiful source of water, as many as 50 ringtails/sq. mile (20/km2) have been found. Ranging from , the territories of male ringtails occasionally intersect with several females. | Ringtail | Wikipedia | 443 | 154237 | https://en.wikipedia.org/wiki/Ringtail | Biology and health sciences | Procyonidae | Animals |
The ringtail is found in the Southwestern United States in southern Oregon, California, eastern Kansas, Oklahoma, Arizona, New Mexico, Colorado, southern Nevada, Utah, Louisiana and Texas. In Mexico it ranges from the northern desert state of Baja California to Oaxaca. Its distribution overlaps that of B. sumichrasti in the Mexican states of Guerrero, Oaxaca, and Veracruz.
Fossils assigned to B. astutus dating back to the early Pliocene epoch have been found as far north as Washington.
Diet
Small vertebrates such as passerine birds, rats, mice, squirrels, rabbits, snakes, lizards, frogs, and toads are the most important foods during winters. However, the ringtail is omnivorous, as are all procyonids. Berries and insects are important in the diet year-round, and become the primary part of the diet in spring and summer, along with other fruit.
As an omnivore the ringtail enjoys a variety of foods in its diet, the majority of which is made up of animal matter. Insects and small mammals such as rabbits, mice, rats and ground squirrels are some examples of the ringtail's carnivorous tendencies. Occasionally the ringtail will also eat fish, lizards, birds, snakes and carrion. The ringtail also enjoys juniper, hack and black berries, persimmon, prickly pear, and fruit in general. They have even been observed partaking from birdseed feeders, hummingbird feeders, sweet nectar or sweetened water.
The results of a study of scat from ringtails on Isla San José, Baja California Sur, showed that the ringtail tended to prey on whatever was most abundant during each respective season. During the spring the ringtail's diet consisted largely of insects, showing up in about 50% of the analyzed feces. Small rodents, snakes, and some lizards were also present. Plant matter was presented in large amounts, around 59% of the collected feces contained some type of plant, with fruits of Phaulothamnus, Lycium, and Solanum most common. The large amount of ironwood seeds and leaves demonstrated that these fleshy fruits were an obvious favorite of the ringtail. | Ringtail | Wikipedia | 451 | 154237 | https://en.wikipedia.org/wiki/Ringtail | Biology and health sciences | Procyonidae | Animals |
Ecology
Foxes, coyotes, raccoons, bobcats, hawks, and owls opportunistically prey upon ringtails of all ages, though predominantly on younger, more vulnerable specimens. Also occasional prey to coatis, lynxes, and mountain lions, the ringtail is rather adept at avoiding predators. The ringtail's success in deterring potential predators is largely attributed to its ability to excrete musk when startled or threatened. The main predators of the ringtail are the great horned owl and the red-tailed hawk.
Ringtails have occasionally been hunted for their pelts, but the fur is not especially valuable. Fur trapping has slowed down considerably, but current population sizes and growth rates remain unclear.
Tameability
Ringtail are said to be easily tamed / habituated to humans, and can make an affectionate pet and effective mouser. Miners and settlers once kept pet ringtails to keep their cabins free of vermin; hence, the common name of "miner's cat". | Ringtail | Wikipedia | 204 | 154237 | https://en.wikipedia.org/wiki/Ringtail | Biology and health sciences | Procyonidae | Animals |
Procyonidae ( ) is a New World family of the order Carnivora. It includes the raccoons, ringtails, cacomistles, coatis, kinkajous, olingos, and olinguitos. Procyonids inhabit a wide range of environments and are generally omnivorous.
Characteristics
Procyonids are relatively small animals, with generally slender bodies and long tails, though the common raccoon tends to be bulky.
Because of their general build, the Procyonidae are often popularly viewed as smaller cousins of the bear family. This is apparent in their German name, Kleinbären (small bears), including the names of the species: a raccoon is called a Waschbär (washing bear, as it "washes" its food before eating), a coati is a Nasenbär (nose-bear), while a kinkajou is a Honigbär (honey-bear). Dutch follows suit, calling the animals wasbeer, neusbeer and rolstaartbeer (curl-tail bear) respectively. However, it is now believed that procyonids are more closely related to mustelids than to bears. Procyonids share common morphological characteristics including a shortened rostrum, absent alisphenoid canals, and a relatively flat mandibular fossa. Kinkajous have unique morphological characteristics consistent with their arboreally adapted locomotion, including a prehensile tail and unique femoral structure.
Due to their omnivorous diet, procyonids have lost some of the adaptations for flesh-eating found in their carnivorous relatives. While they do have carnassial teeth, these are poorly developed in most species, especially the raccoons. Apart from the kinkajou, procyonids have the dental formula: for a total of 40 teeth. The kinkajou has one fewer premolar in each row: for a total of 36 teeth.
Most members of Procyonidae are solitary; however, some species form groups. Coati females will form bands of 4 to 24 individuals that forage together, while kinkajous have been found to form social groups of two males and one female. Certain procyonids give birth to one offspring like ringtails, olingos, and kinkajous while raccoons and coatis give birth to litters that range in size from 2 to 6 offspring.
Evolution | Procyonidae | Wikipedia | 508 | 154406 | https://en.wikipedia.org/wiki/Procyonidae | Biology and health sciences | Carnivora | null |
Procyonid fossils once believed to belong to the genus Bassariscus, which includes the modern ringtail and cacomistle, have been identified from the Miocene epoch, around 20 million years (Ma) ago. It has been suggested that early procyonids were an offshoot of the canids that adapted to a more omnivorous diet. The recent evolution of procyonids has been centered on Central America (where their diversity is greatest); they entered the formerly isolated South America as part of the Great American Interchange, beginning about 7.3 Ma ago in the late Miocene, with the appearance of Cyonasua. Some fossil procyonids such as Stromeriella were also present in the Old World, before going extinct in the Pliocene.
Genetic studies have shown that kinkajous are a sister group to all other extant procyonids; they split off about 22.6 Ma ago. The clades leading to coatis and olingos on one branch, and to ringtails and raccoons on the other, separated about 17.7 Ma ago. The divergence between olingos and coatis is estimated to have occurred about 10.2 Ma ago, at about the same time that ringtails and raccoons parted ways. The separation between coatis and mountain coatis is estimated to have occurred 7.7 Ma ago.
Classification
There has been considerable historical uncertainty over the correct classification of several members. The red panda was previously classified in this family, but it is now classified in its own family, the Ailuridae, based on molecular biology studies. The status of the various olingos was disputed: some regarded them all as subspecies of Bassaricyon gabbii before DNA sequence data demonstrated otherwise.
The traditional classification scheme shown below on the left predates the recent revolution in our understanding of procyonid phylogeny based on genetic sequence analysis. This outdated classification groups kinkajous and olingos together on the basis of similarities in morphology that are now known to be an example of parallel evolution; similarly, coatis are shown as being most closely related to raccoons, when in fact they are closest to olingos. Below right is a cladogram showing the results of molecular studies . Genus Nasuella was not included in these studies, but in a separate study was found to nest within Nasua. | Procyonidae | Wikipedia | 490 | 154406 | https://en.wikipedia.org/wiki/Procyonidae | Biology and health sciences | Carnivora | null |
FAMILY PROCYONIDAE
Subfamily Procyoninae (nine species in four genera)
Tribe Procyonini
Subtribe Procyonina
Raccoons, Procyon
Crab-eating raccoon, Procyon cancrivorus
Cozumel raccoon, Procyon pygmaeus
Common raccoon, Procyon lotor
Subtribe Nasuina
Nasua
South American coati or ring-tailed coati, Nasua nasua
White-nosed coati, Nasua narica
Nasuella
Western mountain coati, Nasuella olivacea
Eastern mountain coati, Nasuella meridensis
Tribe Bassariscini
Bassariscus
Ringtail, Bassariscus astutus
Cacomistle, Bassariscus sumichrasti
Subfamily Potosinae (five species in two genera)
Potos
Kinkajou, Potos flavus
Bassaricyon
Northern olingo or Gabbi's olingo, Bassaricyon gabbii
Eastern lowland olingo, Bassaricyon alleni
Western lowland olingo, Bassaricyon medius
Olinguito, Bassaricyon neblina
Phylogeny
Several recent molecular studies have resolved the phylogenetic relationships between the procyonids, as illustrated in the cladogram below. | Procyonidae | Wikipedia | 272 | 154406 | https://en.wikipedia.org/wiki/Procyonidae | Biology and health sciences | Carnivora | null |
Extinct taxa
Below is a list of extinct taxa (many of which are fossil genera and species) compiled in alphabetical order under their respective subfamilies.
Procyonidae J.E. Gray, 1825
†Broilianinae Dehm, 1950
†Broiliana Dehm, 1950
†B. dehmi Beaumont & Mein, 1973
†B. nobilis Dehm, 1950
†Stromeriella Dehm, 1950
†S. depressa Morlo, 1996
†S. franconica Dehm, 1950
Potosinae Trouessart, 1904
†Parapotos J.A. Baskin, 2003
†P. tedfordi J.A. Baskin, 2003
Procyoninae J.E. Gray, 1825
†Arctonasua J.A. Baskin, 1982
†A. eurybates J.A. Baskin, 1982
†A. fricki J.A. Baskin, 1982
†A. floridana J.A. Baskin, 1982
†A. gracilis J.A. Baskin, 1982
†A. minima J.A. Baskin, 1982
†Bassaricyonoides J.A. Baskin & Morea, 2003
†B. stewartae J.A. Baskin & Morea, 2003
†B. phyllismillerae J.A. Baskin & Morea, 2003
Bassariscus Coues, 1887
†B. antiquus Matthew & Cook, 1909
†B. casei Hibbard, 1952
†B. minimus J.A. Baskin, 2004
†B. ogallalae Hibbard, 1933
†B. parvus Hall, 1927
†Chapalmalania Ameghino, 1908
†C. altaefrontis Kraglievich & Olazábal, 1959
†C. ortognatha Ameghino, 1908
†Cyonasua Ameghino, 1885 [=Amphinasua Moreno & Mercerat, 1891; Brachynasua Ameghino & Kraglievich 1925; Pachynasua Ameghino, 1904]
†C. argentina Ameghino 1885
†C. argentinus (Burmeister, 1891)
†C. brevirostris (Moreno & Mercerat, 1891) [=Amphinasua brevirostris Moreno & Mercerat, 1891] | Procyonidae | Wikipedia | 495 | 154406 | https://en.wikipedia.org/wiki/Procyonidae | Biology and health sciences | Carnivora | null |
†C. clausa (Ameghino, 1904) [=Pachynasua clausa Ameghino, 1904]
†C. groeberi Kraglievich & Reig, 1954 [=Amphinasua groeberi Cabrera, 1936]
†C. longirostris (Rovereto, 1914)
†C. lutaria (Cabrera, 1936) [=Amphinasua lutaria Cabrera, 1936]
†C. meranii (Ameghino & Kraglievich 1925) [=Brachynasua meranii Ameghino & Kraglievich 1925]
†C. pascuali Linares, 1981 [=Amphinasua pascuali Linares, 1981]
†C. robusta (Rovereto, 1914)
†Edaphocyon Wilson, 1960
†E. lautus J.A. Baskin, 1982
†E. palmeri J.A. Baskin & Morea, 2003
†E. pointblankensis Wilson, 1960
Nasua Storr, 1780
†N. pronarica Dalquest, 1978
†N. mastodonta Emmert & Short, 2018
†N. nicaeensis Holl, 1829
†Parahyaenodon Ameghino, 1904
†P. argentinus Ameghino, 1904
†Paranasua J.A. Baskin, 1982
†P. biradica J.A. Baskin, 1982
†Probassariscus Merriam, 1911
†P. matthewi Merriam, 1911
Procyon Storr, 1780
†P. gipsoni Emmert & Short, 2018
†P. megalokolos Emmert & Short, 2018
†P. rexroadensis Hibbard, 1941
†Protoprocyon Linares, 1981 [=Lichnocyon J.A. Baskin, 1982]
†P. savagei Linares, 1981 [=Lichnocyon savagei J.A. Baskin, 1982]
†Tetraprothomo Ameghino, 1908
†T. argentinus Ameghino, 1908 | Procyonidae | Wikipedia | 448 | 154406 | https://en.wikipedia.org/wiki/Procyonidae | Biology and health sciences | Carnivora | null |
A fathom is a unit of length in the imperial and the U.S. customary systems equal to , used especially for measuring the depth of water. The fathom is neither an international standard (SI) unit, nor an internationally accepted non-SI unit. Historically it was the maritime measure of depth in the English-speaking world but, apart from within the US, charts now use metres.
There are two yards (6 feet) in an imperial fathom. Originally the span of a man's outstretched arms, the size of a fathom has varied slightly depending on whether it was defined as a thousandth of an (Admiralty) nautical mile or as a multiple of the imperial yard. Formerly, the term was used for any of several units of length varying around .
Etymology
The term (pronounced ) derives (via Middle English fathme) from the Old English fæðm, which is cognate with the Danish word favn (via the Vikings) and means "embracing arms" or "pair of outstretched arms". It is maybe also cognate with the Old High German word "fadum", which has the same meaning and also means "yarn (originally stretching between the outstretched fingertips)".
Forms
Ancient fathoms
The Ancient Greek measure known as the orguia (, orgyiá, ."outstretched") is usually translated as "fathom". By the Byzantine period, this unit came in two forms: a "simple orguia" (, haplē orguiá) roughly equivalent to the old Greek fathom (6 Byzantine feet, m) and an "imperial" (, basilikē) or "geometric orguia" (, geōmetrikē orguiá) that was one-eighth longer (6 feet and a span, m).
International fathom
One international fathom is equal to:
1.8288 metres exactly (Official international definition of the fathom)
British fathom
The British Admiralty defined a fathom to be a thousandth of an imperial nautical mile (which was 6080 ft) or . In practice the "warship fathom" of exactly was used in Britain and the United States. No conflict between the definitions existed in practice, since depths on imperial nautical charts were indicated in feet if less than and in fathoms for depths greater than that. Until the 19th century in England, the length of the fathom was more variable: from feet on merchant vessels to either on fishing vessels (from ). | Fathom | Wikipedia | 508 | 154456 | https://en.wikipedia.org/wiki/Fathom | Physical sciences | English | Basics and measurement |
Other definitions
Other definitions of fathom include:
1.828804 m (Obsolete measurement of the fathom based on the US survey foot, only for use of historical and legacy applications)
2 yards exactly
18 hands
One metre is about 0.5468 fathoms
In the international yard and pound agreement of 1959 the United States, Australia, Canada, New Zealand, South Africa, and the United Kingdom defined the length of the international yard to be exactly 0.9144 metre. In 1959 United States kept the US survey foot as definition for the fathom.
In October 2019, the U.S. National Geodetic Survey and the National Institute of Standards and Technology announced their joint intent to retire the U.S. survey foot, with effect from the end of 2022. The fathom in U.S. Customary units is thereafter defined based on the International 1959 foot, giving the length of the fathom as exactly 1.8288 metres in the United States as well.
Derived units
At one time, a quarter meant one-quarter of a fathom.
A cable length, based on the length of a ship's cable, has been variously reckoned as equal to 100 or 120 fathoms.
Use of the fathom
Water depth
Most modern nautical charts indicate depth in metres. However, the U.S. Hydrographic Office uses feet and fathoms. A nautical chart will always explicitly indicate the units of depth used.
To measure the depth of shallow waters, boatmen used a sounding line containing fathom points, some marked and others in between, called deeps, unmarked but estimated by the user. Water near the coast and not too deep to be fathomed by a hand sounding line was referred to as in soundings or on soundings. The area offshore beyond the 100 fathom line, too deep to be fathomed by a hand sounding line, was referred to as out of soundings or off soundings. A deep-sea lead, the heaviest of sounding leads, was used in water exceeding 100 fathoms in depth.
This technique has been superseded by sonic depth finders for measuring mechanically the depth of water beneath a ship, one version of which is the Fathometer (trademark). The record made by such a device is a fathogram. A fathom line or fathom curve, a usually sinuous line on a nautical chart, joins all points having the same depth of water, thereby indicating the contour of the ocean floor. | Fathom | Wikipedia | 508 | 154456 | https://en.wikipedia.org/wiki/Fathom | Physical sciences | English | Basics and measurement |
Some extensive flat areas of the sea bottom with constant depth are known by their fathom number, like the Broad Fourteens or the Long Forties, both in the North Sea.
Line length
The components of a commercial fisherman's setline were measured in fathoms. The rope called a groundline, used to form the main line of a setline, was usually provided in bundles of 300 fathoms. A single skein of this rope was referred to as a line. Especially in Pacific coast fisheries the setline was composed of units called skates, each consisting of several hundred fathoms of groundline, with gangions and hooks attached. A tuck seine or tuck net about long, and very deep in the middle, was used to take fish from a larger seine.
A line attached to a whaling harpoon was about . A forerunner — a piece of cloth tied on a ship's log line some fathoms from the outboard end — marked the limit of drift line. A kite was a drag, towed under water at any depth up to about , which upon striking bottom, was upset and rose to the surface.
A shot, one of the forged lengths of chain joined by shackles to form an anchor cable, was usually .
A shackle, a length of cable or chain equal to . In 1949, the British navy redefined the shackle to be .
The Finnish fathom (syli) is occasionally used: nautical mile or cable length.
Burial
A burial at sea (where the body is weighted to force it to the bottom) requires a minimum of six fathoms of water. This is the origin of the phrase "to deep six" as meaning to discard, or dispose of.
The phrase is echoed in Shakespeare's The Tempest, where Ariel tells Ferdinand, "Full fathom five thy father lies". | Fathom | Wikipedia | 376 | 154456 | https://en.wikipedia.org/wiki/Fathom | Physical sciences | English | Basics and measurement |
On land
Until early in the 20th century, it was the unit used to measure the depth of mines (mineral extraction) in the United Kingdom. Miners also use it as a unit of area equal to 6 feet square (3.34 m2) in the plane of a vein. In Britain, it can mean the quantity of wood in a pile of any length measuring square in cross section. In Central Europe, the klafter was the corresponding unit of comparable length, as was the toise in France. In Hungary the square fathom ("négyszögöl") is still in use as an unofficial measure of land area, primarily for small lots suitable for construction. | Fathom | Wikipedia | 138 | 154456 | https://en.wikipedia.org/wiki/Fathom | Physical sciences | English | Basics and measurement |
The Fermi level of a solid-state body is the thermodynamic work required to add one electron to the body. It is a thermodynamic quantity usually denoted by μ or EF
for brevity. The Fermi level does not include the work required to remove the electron from wherever it came from.
A precise understanding of the Fermi level—how it relates to electronic band structure in determining electronic properties; how it relates to the voltage and flow of charge in an electronic circuit—is essential to an understanding of solid-state physics.
In band structure theory, used in solid state physics to analyze the energy levels in a solid, the Fermi level can be considered to be a hypothetical energy level of an electron, such that at thermodynamic equilibrium this energy level would have a 50% probability of being occupied at any given time.
The position of the Fermi level in relation to the band energy levels is a crucial factor in determining electrical properties.
The Fermi level does not necessarily correspond to an actual energy level (in an insulator the Fermi level lies in the band gap), nor does it require the existence of a band structure.
Nonetheless, the Fermi level is a precisely defined thermodynamic quantity, and differences in Fermi level can be measured simply with a voltmeter.
Voltage measurement
Sometimes it is said that electric currents are driven by differences in electrostatic potential (Galvani potential), but this is not exactly true.
As a counterexample, multi-material devices such as p–n junctions contain internal electrostatic potential differences at equilibrium, yet without any accompanying net current; if a voltmeter is attached to the junction, one simply measures zero volts.
Clearly, the electrostatic potential is not the only factor influencing the flow of charge in a material—Pauli repulsion, carrier concentration gradients, electromagnetic induction, and thermal effects also play an important role.
In fact, the quantity called voltage as measured in an electronic circuit has a simple relationship to the chemical potential for electrons (Fermi level).
When the leads of a voltmeter are attached to two points in a circuit, the displayed voltage is a measure of the total work transferred when a unit charge is allowed to move from one point to the other.
If a simple wire is connected between two points of differing voltage (forming a short circuit), current will flow from positive to negative voltage, converting the available work into heat. | Fermi level | Wikipedia | 503 | 154473 | https://en.wikipedia.org/wiki/Fermi%20level | Physical sciences | Basics_2 | Physics |
The Fermi level of a body expresses the work required to add an electron to it, or equally the work obtained by removing an electron.
Therefore, VA − VB, the observed difference in voltage between two points, A and B, in an electronic circuit is exactly related to the corresponding chemical potential difference, μA − μB, in Fermi level by the formula
where −e is the electron charge.
From the above discussion it can be seen that electrons will move from a body of high μ (low voltage) to low μ (high voltage) if a simple path is provided.
This flow of electrons will cause the lower μ to increase (due to charging or other repulsion effects) and likewise cause the higher μ to decrease.
Eventually, μ will settle down to the same value in both bodies.
This leads to an important fact regarding the equilibrium (off) state of an electronic circuit:
This also means that the voltage (measured with a voltmeter) between any two points will be zero, at equilibrium.
Note that thermodynamic equilibrium here requires that the circuit be internally connected and not contain any batteries or other power sources, nor any variations in temperature.
Band structure of solids
In the band theory of solids, electrons occupy a series of bands composed of single-particle energy eigenstates each labelled by ϵ. Although this single particle picture is an approximation, it greatly simplifies the understanding of electronic behaviour and it generally provides correct results when applied correctly.
The Fermi–Dirac distribution, , gives the probability that (at thermodynamic equilibrium) a state having energy ϵ is occupied by an electron:
Here, T is the absolute temperature and kB is the Boltzmann constant. If there is a state at the Fermi level (ϵ = μ), then this state will have a 50% chance of being occupied. The distribution is plotted in the left figure. The closer f is to 1, the higher chance this state is occupied. The closer f is to 0, the higher chance this state is empty. | Fermi level | Wikipedia | 416 | 154473 | https://en.wikipedia.org/wiki/Fermi%20level | Physical sciences | Basics_2 | Physics |
The location of μ within a material's band structure is important in determining the electrical behaviour of the material.
In an insulator, μ lies within a large band gap, far away from any states that are able to carry current.
In a metal, semimetal or degenerate semiconductor, μ lies within a delocalized band. A large number of states nearby μ are thermally active and readily carry current.
In an intrinsic or lightly doped semiconductor, μ is close enough to a band edge that there are a dilute number of thermally excited carriers residing near that band edge.
In semiconductors and semimetals the position of μ relative to the band structure can usually be controlled to a significant degree by doping or gating. These controls do not change μ which is fixed by the electrodes, but rather they cause the entire band structure to shift up and down (sometimes also changing the band structure's shape). For further information about the Fermi levels of semiconductors, see (for example) Sze.
Local conduction band referencing, internal chemical potential and the parameter ζ
If the symbol ℰ is used to denote an electron energy level measured relative to the energy of the edge of its enclosing band, ϵC, then in general we have We can define a parameter ζ that references the Fermi level with respect to the band edge:It follows that the Fermi–Dirac distribution function can be written asThe band theory of metals was initially developed by Sommerfeld, from 1927 onwards, who paid great attention to the underlying thermodynamics and statistical mechanics. Confusingly, in some contexts the band-referenced quantity ζ may be called the Fermi level, chemical potential, or electrochemical potential, leading to ambiguity with the globally-referenced Fermi level.
In this article, the terms conduction-band referenced Fermi level or internal chemical potential are used to refer to ζ.
ζ is directly related to the number of active charge carriers as well as their typical kinetic energy, and hence it is directly involved in determining the local properties of the material (such as electrical conductivity).
For this reason it is common to focus on the value of ζ when concentrating on the properties of electrons in a single, homogeneous conductive material.
By analogy to the energy states of a free electron, the ℰ of a state is the kinetic energy of that state and ϵC is its potential energy. With this in mind, the parameter, ζ, could also be labelled the Fermi kinetic energy. | Fermi level | Wikipedia | 508 | 154473 | https://en.wikipedia.org/wiki/Fermi%20level | Physical sciences | Basics_2 | Physics |
Unlike μ, the parameter, ζ, is not a constant at equilibrium, but rather varies from location to location in a material due to variations in ϵC, which is determined by factors such as material quality and impurities/dopants.
Near the surface of a semiconductor or semimetal, ζ can be strongly controlled by externally applied electric fields, as is done in a field effect transistor. In a multi-band material, ζ may even take on multiple values in a single location.
For example, in a piece of aluminum there are two conduction bands crossing the Fermi level (even more bands in other materials); each band has a different edge energy, ϵC, and a different ζ.
The value of ζ at zero temperature is widely known as the Fermi energy, sometimes written ζ0. Confusingly (again), the name Fermi energy sometimes is used to refer to ζ at non-zero temperature.
Temperature out of equilibrium
The Fermi level, μ, and temperature, T, are well defined constants for a solid-state device in thermodynamic equilibrium situation, such as when it is sitting on the shelf doing nothing. When the device is brought out of equilibrium and put into use, then strictly speaking the Fermi level and temperature are no longer well defined. Fortunately, it is often possible to define a quasi-Fermi level and quasi-temperature for a given location, that accurately describe the occupation of states in terms of a thermal distribution. The device is said to be in quasi-equilibrium when and where such a description is possible. | Fermi level | Wikipedia | 319 | 154473 | https://en.wikipedia.org/wiki/Fermi%20level | Physical sciences | Basics_2 | Physics |
The quasi-equilibrium approach allows one to build a simple picture of some non-equilibrium effects as the electrical conductivity of a piece of metal (as resulting from a gradient of μ) or its thermal conductivity (as resulting from a gradient in T). The quasi-μ and quasi-T can vary (or not exist at all) in any non-equilibrium situation, such as:
If the system contains a chemical imbalance (as in a battery).
If the system is exposed to changing electromagnetic fields (as in capacitors, inductors, and transformers).
Under illumination from a light-source with a different temperature, such as the sun (as in solar cells),
When the temperature is not constant within the device (as in thermocouples),
When the device has been altered, but has not had enough time to re-equilibrate (as in piezoelectric or pyroelectric substances).
In some situations, such as immediately after a material experiences a high-energy laser pulse, the electron distribution cannot be described by any thermal distribution.
One cannot define the quasi-Fermi level or quasi-temperature in this case; the electrons are simply said to be non-thermalized. In less dramatic situations, such as in a solar cell under constant illumination, a quasi-equilibrium description may be possible but requiring the assignment of distinct values of μ and T to different bands (conduction band vs. valence band). Even then, the values of μ and T may jump discontinuously across a material interface (e.g., p–n junction) when a current is being driven, and be ill-defined at the interface itself.
Technicalities
Nomenclature | Fermi level | Wikipedia | 352 | 154473 | https://en.wikipedia.org/wiki/Fermi%20level | Physical sciences | Basics_2 | Physics |
The term Fermi level is mainly used in discussing the solid state physics of electrons in semiconductors, and a precise usage of this term is necessary to describe band diagrams in devices comprising different materials with different levels of doping.
In these contexts, however, one may also see Fermi level used imprecisely to refer to the band-referenced Fermi level, μ − ϵC, called ζ above.
It is common to see scientists and engineers refer to "controlling", "pinning", or "tuning" the Fermi level inside a conductor, when they are in fact describing changes in ϵC due to doping or the field effect.
In fact, thermodynamic equilibrium guarantees that the Fermi level in a conductor is always fixed to be exactly equal to the Fermi level of the electrodes; only the band structure (not the Fermi level) can be changed by doping or the field effect (see also band diagram).
A similar ambiguity exists between the terms, chemical potential and electrochemical potential.
It is also important to note that Fermi level is not necessarily the same thing as Fermi energy.
In the wider context of quantum mechanics, the term Fermi energy usually refers to the maximum kinetic energy of a fermion in an idealized non-interacting, disorder free, zero temperature Fermi gas.
This concept is very theoretical (there is no such thing as a non-interacting Fermi gas, and zero temperature is impossible to achieve). However, it finds some use in approximately describing white dwarfs, neutron stars, atomic nuclei, and electrons in a metal.
On the other hand, in the fields of semiconductor physics and engineering, Fermi energy often is used to refer to the Fermi level described in this article.
Fermi level referencing and the location of zero Fermi level
Much like the choice of origin in a coordinate system, the zero point of energy can be defined arbitrarily. Observable phenomena only depend on energy differences.
When comparing distinct bodies, however, it is important that they all be consistent in their choice of the location of zero energy, or else nonsensical results will be obtained.
It can therefore be helpful to explicitly name a common point to ensure that different components are in agreement.
On the other hand, if a reference point is inherently ambiguous (such as "the vacuum", see below) it will instead cause more problems. | Fermi level | Wikipedia | 485 | 154473 | https://en.wikipedia.org/wiki/Fermi%20level | Physical sciences | Basics_2 | Physics |
A practical and well-justified choice of common point is a bulky, physical conductor, such as the electrical ground or earth.
Such a conductor can be considered to be in a good thermodynamic equilibrium and so its μ is well defined.
It provides a reservoir of charge, so that large numbers of electrons may be added or removed without incurring charging effects.
It also has the advantage of being accessible, so that the Fermi level of any other object can be measured simply with a voltmeter.
Why it is not advisable to use "the energy in vacuum" as a reference zero
In principle, one might consider using the state of a stationary electron in the vacuum as a reference point for energies.
This approach is not advisable unless one is careful to define exactly where the vacuum is. The problem is that not all points in the vacuum are equivalent.
At thermodynamic equilibrium, it is typical for electrical potential differences of order 1 V to exist in the vacuum (Volta potentials).
The source of this vacuum potential variation is the variation in work function between the different conducting materials exposed to vacuum.
Just outside a conductor, the electrostatic potential depends sensitively on the material, as well as which surface is selected (its crystal orientation, contamination, and other details).
The parameter that gives the best approximation to universality is the Earth-referenced Fermi level suggested above. This also has the advantage that it can be measured with a voltmeter.
Discrete charging effects in small systems
In cases where the "charging effects" due to a single electron are non-negligible, the above definitions should be clarified. For example, consider a capacitor made of two identical parallel-plates. If the capacitor is uncharged, the Fermi level is the same on both sides, so one might think that it should take no energy to move an electron from one plate to the other. But when the electron has been moved, the capacitor has become (slightly) charged, so this does take a slight amount of energy. In a normal capacitor, this is negligible, but in a nano-scale capacitor it can be more important.
In this case one must be precise about the thermodynamic definition of the chemical potential as well as the state of the device: is it electrically isolated, or is it connected to an electrode? | Fermi level | Wikipedia | 490 | 154473 | https://en.wikipedia.org/wiki/Fermi%20level | Physical sciences | Basics_2 | Physics |
When the body is able to exchange electrons and energy with an electrode (reservoir), it is described by the grand canonical ensemble. The value of chemical potential can be said to be fixed by the electrode, and the number of electrons on the body may fluctuate. In this case, the chemical potential of a body is the infinitesimal amount of work needed to increase the average number of electrons by an infinitesimal amount (even though the number of electrons at any time is an integer, the average number varies continuously.): where is the free energy function of the grand canonical ensemble.
If the number of electrons in the body is fixed (but the body is still thermally connected to a heat bath), then it is in the canonical ensemble. We can define a "chemical potential" in this case literally as the work required to add one electron to a body that already has exactly electrons, where is the free energy function of the canonical ensemble, alternatively,
These chemical potentials are not equivalent, , except in the thermodynamic limit. The distinction is important in small systems such as those showing Coulomb blockade.
The parameter, , (i.e., in the case where the number of electrons is allowed to fluctuate) remains exactly related to the voltmeter voltage, even in small systems.
To be precise, then, the Fermi level is defined not by a deterministic charging event by one electron charge, but rather a statistical charging event by an infinitesimal fraction of an electron. | Fermi level | Wikipedia | 311 | 154473 | https://en.wikipedia.org/wiki/Fermi%20level | Physical sciences | Basics_2 | Physics |
Type 2 diabetes (T2D), formerly known as adult-onset diabetes, is a form of diabetes mellitus that is characterized by high blood sugar, insulin resistance, and relative lack of insulin. Common symptoms include increased thirst, frequent urination, fatigue and unexplained weight loss. Other symptoms include increased hunger, having a sensation of pins and needles, and sores (wounds) that heal slowly. Symptoms often develop slowly. Long-term complications from high blood sugar include heart disease, stroke, diabetic retinopathy, which can result in blindness, kidney failure, and poor blood flow in the lower-limbs, which may lead to amputations. The sudden onset of hyperosmolar hyperglycemic state may occur; however, ketoacidosis is uncommon.
Type 2 diabetes primarily occurs as a result of obesity and lack of exercise. Some people are genetically more at risk than others.
Type 2 diabetes makes up about 90% of cases of diabetes, with the other 10% due primarily to type 1 diabetes and gestational diabetes. In type 1 diabetes, there is a lower total level of insulin to control blood glucose, due to an autoimmune-induced loss of insulin-producing beta cells in the pancreas. Diagnosis of diabetes is by blood tests such as fasting plasma glucose, oral glucose tolerance test, or glycated hemoglobin (A1c).
Type 2 diabetes is largely preventable by staying at a normal weight, exercising regularly, and eating a healthy diet (high in fruits and vegetables and low in sugar and saturated fat).
Treatment involves exercise and dietary changes. If blood sugar levels are not adequately lowered, the medication metformin is typically recommended. Many people may eventually also require insulin injections. In those on insulin, routinely checking blood sugar levels (such as through a continuous glucose monitor) is advised; however, this may not be needed in those who are not on insulin therapy. Bariatric surgery often improves diabetes in those who are obese. | Type 2 diabetes | Wikipedia | 416 | 154502 | https://en.wikipedia.org/wiki/Type%202%20diabetes | Biology and health sciences | Specific diseases | Health |
Rates of type 2 diabetes have increased markedly since 1960 in parallel with obesity. As of 2015, there were approximately 392 million people diagnosed with the disease compared to around 30 million in 1985. Typically, it begins in middle or older age, although rates of type 2 diabetes are increasing in young people. Type 2 diabetes is associated with a ten-year-shorter life expectancy. Diabetes was one of the first diseases ever described, dating back to an Egyptian manuscript from BCE. Type 1 and type 2 diabetes were identified as separate conditions in 400–500 CE with type 1 associated with youth and type 2 with being overweight. The importance of insulin in the disease was determined in the 1920s.
Signs and symptoms
The classic symptoms of diabetes are frequent urination (polyuria), increased thirst (polydipsia), increased hunger (polyphagia), and weight loss. Other symptoms that are commonly present at diagnosis include a history of blurred vision, itchiness, peripheral neuropathy, recurrent vaginal infections, and fatigue. Other symptoms may include loss of taste. Many people, however, have no symptoms during the first few years and are diagnosed on routine testing. A small number of people with type 2 diabetes can develop a hyperosmolar hyperglycemic state (a condition of very high blood sugar associated with a decreased level of consciousness and low blood pressure).
Complications
Type 2 diabetes is typically a chronic disease associated with a ten-year-shorter life expectancy. This is partly due to a number of complications with which it is associated, including: two to four times the risk of cardiovascular disease, including ischemic heart disease and stroke; a 20-fold increase in lower limb amputations, and increased rates of hospitalizations. In the developed world, and increasingly elsewhere, type 2 diabetes is the largest cause of nontraumatic blindness and kidney failure. It has also been associated with an increased risk of cognitive dysfunction and dementia through disease processes such as Alzheimer's disease and vascular dementia. Other complications include hyperpigmentation of skin (acanthosis nigricans), sexual dysfunction, diabetic ketoacidosis, and frequent infections. There is also an association between type 2 diabetes and mild hearing loss. | Type 2 diabetes | Wikipedia | 456 | 154502 | https://en.wikipedia.org/wiki/Type%202%20diabetes | Biology and health sciences | Specific diseases | Health |
Causes
The development of type 2 diabetes is caused by a combination of lifestyle and genetic factors. While some of these factors are under personal control, such as diet and obesity, other factors are not, such as increasing age, female sex, and genetics. Generous consumption of alcohol is also a risk factor. Obesity is more common in women than men in many parts of Africa. The nutritional status of a mother during fetal development may also play a role.
Lifestyle
Lifestyle factors are important to the development of type 2 diabetes, including obesity and being overweight (defined by a body mass index of greater than 25), lack of physical activity, poor diet, psychological stress, and urbanization. Excess body fat is associated with 30% of cases in those of Chinese and Japanese descent, 60–80% of cases in those of European and African descent, and 100% of cases in Pima Indians and Pacific Islanders. Among those who are not obese, a high waist–hip ratio is often present. Smoking appears to increase the risk of type 2 diabetes. Lack of sleep has also been linked to type 2 diabetes. Laboratory studies have linked short-term sleep deprivations to changes in glucose metabolism, nervous system activity, or hormonal factors that may lead to diabetes.
Dietary factors also influence the risk of developing type 2 diabetes. Consumption of sugar-sweetened drinks in excess is associated with an increased risk. The type of fats in the diet are important, with saturated fat and trans fatty acids increasing the risk, and polyunsaturated and monounsaturated fat decreasing the risk. Eating a lot of white rice appears to play a role in increasing risk. A lack of exercise is believed to cause 7% of cases. Sedentary lifestyle is another risk factor. Persistent organic pollutants may also play a role.
Genetics | Type 2 diabetes | Wikipedia | 369 | 154502 | https://en.wikipedia.org/wiki/Type%202%20diabetes | Biology and health sciences | Specific diseases | Health |
Most cases of diabetes involve many genes, with each being a small contributor to an increased probability of becoming a type 2 diabetic. The proportion of diabetes that is inherited is estimated at 72%. More than 36 genes and 80 single nucleotide polymorphisms (SNPs) had been found that contribute to the risk of type 2 diabetes. All of these genes together still only account for 10% of the total heritable component of the disease. The TCF7L2 allele, for example, increases the risk of developing diabetes by 1.5 times and is the greatest risk of the common genetic variants. Most of the genes linked to diabetes are involved in pancreatic beta cell functions.
There are a number of rare cases of diabetes that arise due to an abnormality in a single gene (known as monogenic forms of diabetes or "other specific types of diabetes"). These include maturity onset diabetes of the young (MODY), Donohue syndrome, and Rabson–Mendenhall syndrome, among others. Maturity onset diabetes of the young constitute 1–5% of all cases of diabetes in young people.
Epigenetic regulation may have a role in type 2 diabetes.
Medical conditions
There are a number of medications and other health problems that can predispose to diabetes. Some of the medications include: glucocorticoids, thiazides, beta blockers, atypical antipsychotics, and statins. Those who have previously had gestational diabetes are at a higher risk of developing type 2 diabetes. Other health problems that are associated include: acromegaly, Cushing's syndrome, hyperthyroidism, pheochromocytoma, and certain cancers such as glucagonomas. Individuals with cancer may be at a higher risk of mortality if they also have diabetes. Testosterone deficiency is also associated with type 2 diabetes. Eating disorders may also interact with type 2 diabetes, with bulimia nervosa increasing the risk and anorexia nervosa decreasing it.
Pathophysiology | Type 2 diabetes | Wikipedia | 427 | 154502 | https://en.wikipedia.org/wiki/Type%202%20diabetes | Biology and health sciences | Specific diseases | Health |
Type 2 diabetes is due to insufficient insulin production from beta cells in the setting of insulin resistance. Insulin resistance, which is the inability of cells to respond adequately to normal levels of insulin, occurs primarily within the muscles, liver, and fat tissue. In the liver, insulin normally suppresses glucose release. However, in the setting of insulin resistance, the liver inappropriately releases glucose into the blood. The proportion of insulin resistance versus beta cell dysfunction differs among individuals, with some having primarily insulin resistance and only a minor defect in insulin secretion and others with slight insulin resistance and primarily a lack of insulin secretion.
Other potentially important mechanisms associated with type 2 diabetes and insulin resistance include: increased breakdown of lipids within fat cells, resistance to and lack of incretin, high glucagon levels in the blood, increased retention of salt and water by the kidneys, and inappropriate regulation of metabolism by the central nervous system. However, not all people with insulin resistance develop diabetes since an impairment of insulin secretion by pancreatic beta cells is also required.
In the early stages of insulin resistance, the mass of beta cells expands, increasing the output of insulin to compensate for the insulin insensitivity, so that the disposition index remains constant. But when type 2 diabetes has become manifest, the person will have lost about half of their beta cells.
The causes of the aging-related insulin resistance seen in obesity and in type 2 diabetes are uncertain. Effects of intracellular lipid metabolism and ATP production in liver and muscle cells may contribute to insulin resistance.
Diagnosis | Type 2 diabetes | Wikipedia | 314 | 154502 | https://en.wikipedia.org/wiki/Type%202%20diabetes | Biology and health sciences | Specific diseases | Health |
The World Health Organization definition of diabetes (both type 1 and type 2) is for a single raised glucose reading with symptoms, otherwise raised values on two occasions, of either:
fasting plasma glucose ≥ 7.0 mmol/L (126 mg/dL)
or
glucose tolerance test with two hours after the oral dose a plasma glucose ≥ 11.1 mmol/L (200 mg/dL)
A random blood sugar of greater than 11.1 mmol/L (200 mg/dL) in association with typical symptoms or a glycated hemoglobin (HbA1c) of ≥ 48 mmol/mol (≥ 6.5 DCCT %) is another method of diagnosing diabetes. In 2009, an International Expert Committee that included representatives of the American Diabetes Association (ADA), the International Diabetes Federation (IDF), and the European Association for the Study of Diabetes (EASD) recommended that a HbA1c threshold of ≥ 48 mmol/mol (≥ 6.5 DCCT %) should be used to diagnose diabetes. This recommendation was adopted by the American Diabetes Association in 2010. Positive tests should be repeated unless the person presents with typical symptoms and blood sugar >11.1 mmol/L (>200 mg/dL).
Threshold for diagnosis of diabetes is based on the relationship between results of glucose tolerance tests, fasting glucose or HbA1c and complications such as retinal problems. A fasting or random blood sugar is preferred over the glucose tolerance test, as they are more convenient for people. HbA1c has the advantages that fasting is not required and results are more stable but has the disadvantage that the test is more costly than measurement of blood glucose. It is estimated that 20% of people with diabetes in the United States do not realize that they have the disease.
Type 2 diabetes is characterized by high blood glucose in the context of insulin resistance and relative insulin deficiency. This is in contrast to type 1 diabetes in which there is an absolute insulin deficiency due to destruction of islet cells in the pancreas and gestational diabetes that is a new onset of high blood sugars associated with pregnancy. Type 1 and type 2 diabetes can typically be distinguished based on the presenting circumstances. If the diagnosis is in doubt antibody testing may be useful to confirm type 1 diabetes and C-peptide levels may be useful to confirm type 2 diabetes, with C-peptide levels normal or high in type 2 diabetes, but low in type 1 diabetes. | Type 2 diabetes | Wikipedia | 511 | 154502 | https://en.wikipedia.org/wiki/Type%202%20diabetes | Biology and health sciences | Specific diseases | Health |
Screening
Universal screening for diabetes in people without risk factors or symptoms is not recommended.
The United States Preventive Services Task Force (USPSTF) recommended in 2021 screening for type 2 diabetes in adults aged 35 to 70 years old who are overweight (i.e. BMI over 25) or have obesity. For people of Asian descent, screening is recommended if they have a BMI over 23. Screening at an earlier age may be considered in people with a family history of diabetes; some ethnic groups, including Hispanics, African Americans, and Native Americans; a history of gestational diabetes; polycystic ovary syndrome. Screening can be repeated every 3 years.
The American Diabetes Association (ADA) recommended in 2024 screening in all adults from the age of 35 years. ADA also recommends screening in adults of all ages with a BMI over 25 (or over 23 in Asian Americans) with another risk factor: first-degree relative with diabetes, ethnicity at high risk for diabetes, blood pressure ≥130/80 mmHg or on therapy for hypertension, history of cardiovascular disease, physical inactivity, polycystic ovary syndrome or severe obesity. ADA recommends repeat screening every 3 years at minimum. ADA recommends yearly tests in people with prediabetes. People with previous gestational diabetes or pancreatitis are also recommended screening.
There is no evidence that screening changes the risk of death and any benefit of screening on adverse effects, incidence of type 2 diabetes, HbA1c or socioeconomic effects are not clear.
In the UK, NICE guidelines suggest taking action to prevent diabetes for people with a body mass index (BMI) of 30 or more. For people of Black African, African-Caribbean, South Asian and Chinese descent the recommendation to start prevention starts at the BMI of 27,5. A study based on a large sample of people in England suggest even lower BMIs for certain ethnic groups for the start of prevention, for example 24 in South Asian and 21 in Bangladeshi populations.
Prevention | Type 2 diabetes | Wikipedia | 410 | 154502 | https://en.wikipedia.org/wiki/Type%202%20diabetes | Biology and health sciences | Specific diseases | Health |
Onset of type 2 diabetes can be delayed or prevented through proper nutrition and regular exercise. Intensive lifestyle measures may reduce the risk by over half. The benefit of exercise occurs regardless of the person's initial weight or subsequent weight loss. High levels of physical activity reduce the risk of diabetes by about 28%. Evidence for the benefit of dietary changes alone, however, is limited, with some evidence for a diet high in green leafy vegetables and some for limiting the intake of sugary drinks. There is an association between higher intake of sugar-sweetened fruit juice and diabetes, but no evidence of an association with 100% fruit juice. A 2019 review found evidence of benefit from dietary fiber.
A 2017 review found that, long term, lifestyle changes decreased the risk by 28%, while medication does not reduce risk after withdrawal. While low vitamin D levels are associated with an increased risk of diabetes, correcting the levels by supplementing vitamin D3 does not improve that risk.
In those with prediabetes, diet in combination with physical activity delays or reduces the risk of type 2 diabetes, according to a 2017 Cochrane review. In those with prediabetes, metformin may delay or reduce the risk of developing type 2 diabetes compared to diet and exercise or a placebo intervention, but not compared to intensive diet and exercise, and there was not enough data on outcomes such as mortality and diabetic complications and health-related quality of life, according to a 2019 Cochrane review. In those with prediabetes, alpha-glucosidase inhibitors such as acarbose may delay or reduce the risk of type 2 diabetes when compared to placebo, however there was no conclusive evidence that acarbose improved cardiovascular mortality or cardiovascular events, according to a 2018 Cochrane review. In those with prediabetes, pioglitazone may delay or reduce the risk of developing type 2 diabetes compared to placebo or no intervention, but no difference was seen compared to metformin, and data were missing on mortality and complications and quality of life, according to a 2020 Cochrane review. In those with prediabetes, there was insufficient data to draw any conclusions on whether SGLT2 inhibitors may delay or reduce the risk of developing type 2 diabetes, according to a 2016 Cochrane review.
Management | Type 2 diabetes | Wikipedia | 467 | 154502 | https://en.wikipedia.org/wiki/Type%202%20diabetes | Biology and health sciences | Specific diseases | Health |
Management of type 2 diabetes focuses on lifestyle interventions, lowering other cardiovascular risk factors, and maintaining blood glucose levels in the normal range. Self-monitoring of blood glucose for people with newly diagnosed type 2 diabetes may be used in combination with education, although the benefit of self-monitoring in those not using multi-dose insulin is questionable. In those who do not want to measure blood levels, measuring urine levels may be done. Managing other cardiovascular risk factors, such as hypertension, high cholesterol, and microalbuminuria, improves a person's life expectancy. Decreasing the systolic blood pressure to less than 140 mmHg is associated with a lower risk of death and better outcomes. Intensive blood pressure management (less than 130/80 mmHg) as opposed to standard blood pressure management (less than 140–160 mmHg systolic to 85–100 mmHg diastolic) results in a slight decrease in stroke risk but no effect on overall risk of death.
Intensive blood sugar lowering (HbA1c < 6%) as opposed to standard blood sugar lowering (HbA1c of 7–7.9%) does not appear to change mortality. The goal of treatment is typically an HbA1c of 7 to 8% or a fasting glucose of less than 7.2 mmol/L (130 mg/dL); however these goals may be changed after professional clinical consultation, taking into account particular risks of hypoglycemia and life expectancy. Hypoglycemia is associated with adverse outcomes in older people with type 2 diabetes. Despite guidelines recommending that intensive blood sugar control be based on balancing immediate harms with long-term benefits, many people – for example people with a life expectancy of less than nine years who will not benefit, are over-treated.
It is recommended that all people with type 2 diabetes get regular eye examinations. There is moderate evidence suggesting that treating gum disease by scaling and root planing results in an improvement in blood sugar levels for people with diabetes.
Lifestyle
Exercise
A proper diet and regular exercise are foundations of diabetic care, with one review indicating that a greater amount of exercise improved outcomes. Regular exercise may improve blood sugar control, decrease body fat content, and decrease blood lipid levels.
Diet | Type 2 diabetes | Wikipedia | 465 | 154502 | https://en.wikipedia.org/wiki/Type%202%20diabetes | Biology and health sciences | Specific diseases | Health |
Calorie restriction to promote weight loss is generally recommended. Around 80 percent of obese people with type 2 diabetes achieve complete remission with no need for medication if they sustain a weight loss of at least , but most patients are not able to achieve or sustain significant weight loss. Even modest weight loss can produce significant improvements in glycemic control and reduce the need for medication.
Several diets may be effective such as the DASH diet, Mediterranean diet, low-fat diet, or monitored carbohydrate diets such as a low carbohydrate diet. Other recommendations include emphasizing intake of fruits, vegetables, reduced saturated fat and low-fat dairy products, and with a macronutrient intake tailored to the individual, to distribute calories and carbohydrates throughout the day. A 2021 review showed that consumption of tree nuts (walnuts, almonds, and hazelnuts) reduced fasting blood glucose in diabetic people. , there is insufficient data to recommend nonnutritive sweeteners, which may help reduce caloric intake. An elevated intake of microbiota-accessible carbohydrates can help reducing the effects of T2D. Viscous fiber supplements may be useful in those with diabetes.
Culturally appropriate education may help people with type 2 diabetes control their blood sugar levels for up to 24 months. There is not enough evidence to determine if lifestyle interventions affect mortality in those who already have type 2 diabetes.
Stress management
Although psychological stress is recognized as a risk factor for type 2 diabetes, the effect of stress management interventions on disease progression are not established. A Cochrane review is under way to assess the effects of mindfulness‐based interventions for adults with type 2 diabetes.
Medications
Blood sugar control
There are several classes of diabetes medications available. Metformin is generally recommended as a first line treatment as there is some evidence that it decreases mortality; however, this conclusion is questioned. Metformin should not be used in those with severe kidney or liver problems. The American Diabetes Association and European Association for the Study of Diabetes recommend using a GLP-1 receptor agonist or SGLT2 inhibitor as the first-line treatment in patients who have or are at high risk for atherosclerotic cardiovascular disease, heart failure, or chronic kidney disease. The higher cost of these drugs compared to metformin has limited their use. | Type 2 diabetes | Wikipedia | 482 | 154502 | https://en.wikipedia.org/wiki/Type%202%20diabetes | Biology and health sciences | Specific diseases | Health |
Other classes of medications include: sulfonylureas, thiazolidinediones, dipeptidyl peptidase-4 inhibitors, SGLT2 inhibitors, and GLP-1 receptor agonists. A 2018 review found that SGLT2 inhibitors and GLP-1 agonists, but not DPP-4 inhibitors, were associated with lower mortality than placebo or no treatment. Rosiglitazone, a thiazolidinedione, has not been found to improve long-term outcomes even though it improves blood sugar levels. Additionally it is associated with increased rates of heart disease and death.
Injections of insulin may either be added to oral medication or used alone. Most people do not initially need insulin. When it is used, a long-acting formulation is typically added at night, with oral medications being continued. Doses are then increased to effect (blood sugar levels being well controlled). When nightly insulin is insufficient, twice daily insulin may achieve better control. The long acting insulins glargine and detemir are equally safe and effective, and do not appear much better than NPH insulin, but as they are significantly more expensive, they are not cost effective as of 2010. In those who are pregnant, insulin is generally the treatment of choice.
Blood pressure lowering
Many international guidelines recommend blood pressure treatment targets that are lower than 140/90 mmHg for people with diabetes. However, there is only limited evidence regarding what the lower targets should be. A 2016 systematic review found potential harm to treating to targets lower than 140 mmHg, and a subsequent review in 2019 found no evidence of additional benefit from blood pressure lowering to between 130 and 140 mmHg, although there was an increased risk of adverse events.
In people with diabetes and hypertension and either albuminuria or chronic kidney disease, an inhibitor of the renin-angiotensin system (such as an ACE inhibitor or angiotensin receptor blocker) to reduce the risks of progression of kidney disease and present cardiovascular events. There is some evidence that angiotensin converting enzyme inhibitors (ACEIs) are superior to other inhibitors of the renin-angiotensin system such as angiotensin receptor blockers (ARBs), or aliskiren in preventing cardiovascular disease. Although a 2016 review found similar effects of ACEIs and ARBs on major cardiovascular and renal outcomes. There is no evidence that combining ACEIs and ARBs provides additional benefits. | Type 2 diabetes | Wikipedia | 505 | 154502 | https://en.wikipedia.org/wiki/Type%202%20diabetes | Biology and health sciences | Specific diseases | Health |
Other
The use of statins in diabetes to prevent cardiovascular disease should be considered after evaluating the person's total risk for cardiovascular disease.
The use of aspirin (acetylsalicylic acid) to prevent cardiovascular disease in diabetes is controversial. Aspirin is recommended in people with previous cardiovascular disease, however routine use of aspirin has not been found to improve outcomes in uncomplicated diabetes. Aspirin as primary prevention may have greater risk than benefit, but could be considered in people aged 50 to 70 with another significant cardiovascular risk factor and low risk of bleeding after information about possible risks and benefits as part of shared-decision making.
Vitamin D supplementation to people with type 2 diabetes may improve markers of insulin resistance and HbA1c.
Sharing their electronic health records with people who have type 2 diabetes helps them to reduce their blood sugar levels. It is a way of helping people understand their own health condition and involving them actively in its management.
Surgery
Weight loss surgery in those who are obese is an effective measure to treat diabetes. Many are able to maintain normal blood sugar levels with little or no medication following surgery and long-term mortality is decreased. There however is some short-term mortality risk of less than 1% from the surgery. The body mass index cutoffs for when surgery is appropriate are not yet clear. It is recommended that this option be considered in those who are unable to get both their weight and blood sugar under control.
Epidemiology
The International Diabetes Federation estimates nearly 537 million people lived with diabetes worldwide in 2021, 90–95% of whom have type 2 diabetes. Diabetes is common both in the developed and the developing world.
Some ethnic groups such as South Asians, Pacific Islanders, Latinos, and Native Americans are at particularly high risk of developing type 2 diabetes. Type 2 diabetes in normal weight individuals represents 60 to 80 percent of all cases in some Asian countries. The mechanism causing diabetes in non-obese individuals is poorly understood. | Type 2 diabetes | Wikipedia | 403 | 154502 | https://en.wikipedia.org/wiki/Type%202%20diabetes | Biology and health sciences | Specific diseases | Health |
Rates of diabetes in 1985 were estimated at 30 million, increasing to 135 million in 1995 and 217 million in 2005. This increase is believed to be primarily due to the global population aging, a decrease in exercise, and increasing rates of obesity. Traditionally considered a disease of adults, type 2 diabetes is increasingly diagnosed in children in parallel with rising obesity rates. The five countries with the greatest number of people with diabetes as of 2000 are India having 31.7 million, China 20.8 million, the United States 17.7 million, Indonesia 8.4 million, and Japan 6.8 million. It is recognized as a global epidemic by the World Health Organization.
History
Diabetes is one of the first diseases described with an Egyptian manuscript from BCE mentioning "too great emptying of the urine." The first described cases are believed to be of type 1 diabetes. Indian physicians around the same time identified the disease and classified it as madhumeha or honey urine noting that the urine would attract ants. The term "diabetes" or "to pass through" was first used in 230 BCE by the Greek Apollonius Memphites. The disease was rare during the time of the Roman empire with Galen commenting that he had only seen two cases during his career.
Type 1 and type 2 diabetes were identified as separate conditions for the first time by the Indian physicians Sushruta and Charaka in 400–500 CE with type 1 associated with youth and type 2 with being overweight. Effective treatment was not developed until the early part of the 20th century when the Canadians Frederick Banting and Charles Best discovered insulin in 1921 and 1922. This was followed by the development of the longer acting NPH insulin in the 1940s.
In 1916, Elliot Joslin proposed that in people with diabetes, periods of fasting are helpful. Subsequent research has supported this, and weight loss is a first line treatment in type 2 diabetes.
Research
In 2020, Diabetes Severity Score (DISSCO) was developed which is a tool that might better than HbA1c identify if a person's condition is declining. It uses a computer algorithm to analyse data from anonymised electronic patient records and produces a score based on 34 indicators.
Stem cells
In April 2024 scientists reported the first case of reversion of type 2 diabetes by use of stem cells in a 59-year-old man treated in 2021 who has since remain insulin-free. Replication in more patients and evidence over longer periods would be needed before considering this treatment as a possible cure. | Type 2 diabetes | Wikipedia | 507 | 154502 | https://en.wikipedia.org/wiki/Type%202%20diabetes | Biology and health sciences | Specific diseases | Health |
A digital signal processor (DSP) is a specialized microprocessor chip, with its architecture optimized for the operational needs of digital signal processing. DSPs are fabricated on metal–oxide–semiconductor (MOS) integrated circuit chips. They are widely used in audio signal processing, telecommunications, digital image processing, radar, sonar and speech recognition systems, and in common consumer electronic devices such as mobile phones, disk drives and high-definition television (HDTV) products.
The goal of a DSP is usually to measure, filter or compress continuous real-world analog signals. Most general-purpose microprocessors can also execute digital signal processing algorithms successfully, but may not be able to keep up with such processing continuously in real-time. Also, dedicated DSPs usually have better power efficiency, thus they are more suitable in portable devices such as mobile phones because of power consumption constraints. DSPs often use special memory architectures that are able to fetch multiple data or instructions at the same time.
Overview
Digital signal processing (DSP) algorithms typically require a large number of mathematical operations to be performed quickly and repeatedly on a series of data samples. Signals (perhaps from audio or video sensors) are constantly converted from analog to digital, manipulated digitally, and then converted back to analog form. Many DSP applications have constraints on latency; that is, for the system to work, the DSP operation must be completed within some fixed time, and deferred (or batch) processing is not viable.
Most general-purpose microprocessors and operating systems can execute DSP algorithms successfully, but are not suitable for use in portable devices such as mobile phones and PDAs because of power efficiency constraints. A specialized DSP, however, will tend to provide a lower-cost solution, with better performance, lower latency, and no requirements for specialised cooling or large batteries.
Such performance improvements have led to the introduction of digital signal processing in commercial communications satellites where hundreds or even thousands of analog filters, switches, frequency converters and so on are required to receive and process the uplinked signals and ready them for downlinking, and can be replaced with specialised DSPs with significant benefits to the satellites' weight, power consumption, complexity/cost of construction, reliability and flexibility of operation. For example, the SES-12 and SES-14 satellites from operator SES launched in 2018, were both built by Airbus Defence and Space with 25% of capacity using DSP. | Digital signal processor | Wikipedia | 506 | 154505 | https://en.wikipedia.org/wiki/Digital%20signal%20processor | Technology | Computer hardware | null |
The architecture of a DSP is optimized specifically for digital signal processing. Most also support some of the features of an applications processor or microcontroller, since signal processing is rarely the only task of a system. Some useful features for optimizing DSP algorithms are outlined below.
Architecture
Software architecture
By the standards of general-purpose processors, DSP instruction sets are often highly irregular; while traditional instruction sets are made up of more general instructions that allow them to perform a wider variety of operations, instruction sets optimized for digital signal processing contain instructions for common mathematical operations that occur frequently in DSP calculations. Both traditional and DSP-optimized instruction sets are able to compute any arbitrary operation but an operation that might require multiple ARM or x86 instructions to compute might require only one instruction in a DSP optimized instruction set.
One implication for software architecture is that hand-optimized assembly-code routines (assembly programs) are commonly packaged into libraries for re-use, instead of relying on advanced compiler technologies to handle essential algorithms. Even with modern compiler optimizations hand-optimized assembly code is more efficient and many common algorithms involved in DSP calculations are hand-written in order to take full advantage of the architectural optimizations.
Instruction sets
multiply–accumulates (MACs, including fused multiply–add, FMA) operations
used extensively in all kinds of matrix operations
convolution for filtering
dot product
polynomial evaluation
Fundamental DSP algorithms depend heavily on multiply–accumulate performance
FIR filters
Fast Fourier transform (FFT)
related instructions:
SIMD
VLIW
Specialized instructions for modulo addressing in ring buffers and bit-reversed addressing mode for FFT cross-referencing
DSPs sometimes use time-stationary encoding to simplify hardware and increase coding efficiency.
Multiple arithmetic units may require memory architectures to support several accesses per instruction cycle – typically supporting reading 2 data values from 2 separate data buses and the next instruction (from the instruction cache, or a 3rd program memory) simultaneously.
Special loop controls, such as architectural support for executing a few instruction words in a very tight loop without overhead for instruction fetches or exit testing—such as zero-overhead looping and hardware loop buffers. | Digital signal processor | Wikipedia | 451 | 154505 | https://en.wikipedia.org/wiki/Digital%20signal%20processor | Technology | Computer hardware | null |
Data instructions
Saturation arithmetic, in which operations that produce overflows will accumulate at the maximum (or minimum) values that the register can hold rather than wrapping around (maximum+1 doesn't overflow to minimum as in many general-purpose CPUs, instead it stays at maximum). Sometimes various sticky bits operation modes are available.
Fixed-point arithmetic is often used to speed up arithmetic processing.
Single-cycle operations to increase the benefits of pipelining.
Program flow
Floating-point unit integrated directly into the datapath
Pipelined architecture
Highly parallel multiplier–accumulators (MAC units)
Hardware-controlled looping, to reduce or eliminate the overhead required for looping operations
Hardware architecture
Memory architecture
DSPs are usually optimized for streaming data and use special memory architectures that are able to fetch multiple data or instructions at the same time, such as the Harvard architecture or Modified von Neumann architecture, which use separate program and data memories (sometimes even concurrent access on multiple data buses).
DSPs can sometimes rely on supporting code to know about cache hierarchies and the associated delays. This is a tradeoff that allows for better performance. In addition, extensive use of DMA is employed.
Addressing and virtual memory
DSPs frequently use multi-tasking operating systems, but have no support for virtual memory or memory protection. Operating systems that use virtual memory require more time for context switching among processes, which increases latency.
Hardware modulo addressing
Allows circular buffers to be implemented without having to test for wrapping
Bit-reversed addressing, a special addressing mode
useful for calculating FFTs
Exclusion of a memory management unit
Address generation unit
History
Development
In 1976, Richard Wiggins proposed the Speak & Spell concept to Paul Breedlove, Larry Brantingham, and Gene Frantz at Texas Instruments' Dallas research facility. Two years later in 1978, they produced the first Speak & Spell, with the technological centerpiece being the TMS5100, the industry's first digital signal processor. It also set other milestones, being the first chip to use linear predictive coding to perform speech synthesis. The chip was made possible with a 7 μm PMOS fabrication process. | Digital signal processor | Wikipedia | 440 | 154505 | https://en.wikipedia.org/wiki/Digital%20signal%20processor | Technology | Computer hardware | null |
In 1978, American Microsystems (AMI) released the S2811. The AMI S2811 "signal processing peripheral", like many later DSPs, has a hardware multiplier that enables it to do multiply–accumulate operation in a single instruction. The S2281 was the first integrated circuit chip specifically designed as a DSP, and fabricated using vertical metal oxide semiconductor (VMOS, V-groove MOS), a technology that had previously not been mass-produced. It was designed as a microprocessor peripheral, for the Motorola 6800, and it had to be initialized by the host. The S2811 was not successful in the market.
In 1979, Intel released the 2920 as an "analog signal processor". It had an on-chip ADC/DAC with an internal signal processor, but it didn't have a hardware multiplier and was not successful in the market.
In 1980, the first stand-alone, complete DSPs – Nippon Electric Corporation's NEC μPD7720 based on the modified Harvard architecture and AT&T's DSP1 – were presented at the International Solid-State Circuits Conference '80. Both processors were inspired by the research in public switched telephone network (PSTN) telecommunications. The μPD7720, introduced for voiceband applications, was one of the most commercially successful early DSPs.
The Altamira DX-1 was another early DSP, utilizing quad integer pipelines with delayed branches and branch prediction.
Another DSP produced by Texas Instruments (TI), the TMS32010 presented in 1983, proved to be an even bigger success. It was based on the Harvard architecture, and so had separate instruction and data memory. It already had a special instruction set, with instructions like load-and-accumulate or multiply-and-accumulate. It could work on 16-bit numbers and needed 390 ns for a multiply–add operation. TI is now the market leader in general-purpose DSPs.
About five years later, the second generation of DSPs began to spread. They had 3 memories for storing two operands simultaneously and included hardware to accelerate tight loops; they also had an addressing unit capable of loop-addressing. Some of them operated on 24-bit variables and a typical model only required about 21 ns for a MAC. Members of this generation were for example the AT&T DSP16A or the Motorola 56000. | Digital signal processor | Wikipedia | 504 | 154505 | https://en.wikipedia.org/wiki/Digital%20signal%20processor | Technology | Computer hardware | null |
The main improvement in the third generation was the appearance of application-specific units and instructions in the data path, or sometimes as coprocessors. These units allowed direct hardware acceleration of very specific but complex mathematical problems, like the Fourier-transform or matrix operations. Some chips, like the Motorola MC68356, even included more than one processor core to work in parallel. Other DSPs from 1995 are the TI TMS320C541 or the TMS 320C80.
The fourth generation is best characterized by the changes in the instruction set and the instruction encoding/decoding. SIMD extensions were added, and VLIW and the superscalar architecture appeared. As always, the clock-speeds have increased; a 3 ns MAC now became possible.
Modern DSPs
Modern signal processors yield greater performance; this is due in part to both technological and architectural advancements like lower design rules, fast-access two-level cache, (E)DMA circuitry, and a wider bus system. Not all DSPs provide the same speed and many kinds of signal processors exist, each one of them being better suited for a specific task, ranging in price from about US$1.50 to US$300.
Texas Instruments produces the C6000 series DSPs, which have clock speeds of 1.2 GHz and implement separate instruction and data caches. They also have an 8 MiB 2nd level cache and 64 EDMA channels. The top models are capable of as many as 8000 MIPS (millions of instructions per second), use VLIW (very long instruction word), perform eight operations per clock-cycle and are compatible with a broad range of external peripherals and various buses (PCI/serial/etc). TMS320C6474 chips each have three such DSPs, and the newest generation C6000 chips support floating point as well as fixed point processing.
Freescale produces a multi-core DSP family, the MSC81xx. The MSC81xx is based on StarCore Architecture processors and the latest MSC8144 DSP combines four programmable SC3400 StarCore DSP cores. Each SC3400 StarCore DSP core has a clock speed of 1 GHz. | Digital signal processor | Wikipedia | 460 | 154505 | https://en.wikipedia.org/wiki/Digital%20signal%20processor | Technology | Computer hardware | null |
XMOS produces a multi-core multi-threaded line of processor well suited to DSP operations, They come in various speeds ranging from 400 to 1600 MIPS. The processors have a multi-threaded architecture that allows up to 8 real-time threads per core, meaning that a 4 core device would support up to 32 real time threads. Threads communicate between each other with buffered channels that are capable of up to 80 Mbit/s. The devices are easily programmable in C and aim at bridging the gap between conventional micro-controllers and FPGAs
CEVA, Inc. produces and licenses three distinct families of DSPs. Perhaps the best known and most widely deployed is the CEVA-TeakLite DSP family, a classic memory-based architecture, with 16-bit or 32-bit word-widths and single or dual MACs. The CEVA-X DSP family offers a combination of VLIW and SIMD architectures, with different members of the family offering dual or quad 16-bit MACs. The CEVA-XC DSP family targets Software-defined Radio (SDR) modem designs and leverages a unique combination of VLIW and Vector architectures with 32 16-bit MACs.
Analog Devices produce the SHARC-based DSP and range in performance from 66 MHz/198 MFLOPS (million floating-point operations per second) to 400 MHz/2400 MFLOPS. Some models support multiple multipliers and ALUs, SIMD instructions and audio processing-specific components and peripherals. The Blackfin family of embedded digital signal processors combine the features of a DSP with those of a general use processor. As a result, these processors can run simple operating systems like μCLinux, velocity and Nucleus RTOS while operating on real-time data. The SHARC-based ADSP-210xx provides both delayed branches and non-delayed branches.
NXP Semiconductors produce DSPs based on TriMedia VLIW technology, optimized for audio and video processing. In some products the DSP core is hidden as a fixed-function block into a SoC, but NXP also provides a range of flexible single core media processors. The TriMedia media processors support both fixed-point arithmetic as well as floating-point arithmetic, and have specific instructions to deal with complex filters and entropy coding. | Digital signal processor | Wikipedia | 488 | 154505 | https://en.wikipedia.org/wiki/Digital%20signal%20processor | Technology | Computer hardware | null |
CSR produces the Quatro family of SoCs that contain one or more custom Imaging DSPs optimized for processing document image data for scanner and copier applications.
Microchip Technology produces the PIC24 based dsPIC line of DSPs. Introduced in 2004, the dsPIC is designed for applications needing a true DSP as well as a true microcontroller, such as motor control and in power supplies. The dsPIC runs at up to 40MIPS, and has support for 16 bit fixed point MAC, bit reverse and modulo addressing, as well as DMA.
Most DSPs use fixed-point arithmetic, because in real world signal processing the additional range provided by floating point is not needed, and there is a large speed benefit and cost benefit due to reduced hardware complexity. Floating point DSPs may be invaluable in applications where a wide dynamic range is required. Product developers might also use floating point DSPs to reduce the cost and complexity of software development in exchange for more expensive hardware, since it is generally easier to implement algorithms in floating point.
Generally, DSPs are dedicated integrated circuits; however DSP functionality can also be produced by using field-programmable gate array chips (FPGAs).
Embedded general-purpose RISC processors are becoming increasingly DSP like in functionality. For example, the OMAP3 processors include an ARM Cortex-A8 and C6000 DSP.
In Communications a new breed of DSPs offering the fusion of both DSP functions and H/W acceleration function is making its way into the mainstream. Such Modem processors include ASOCS ModemX and CEVA's XC4000.
In May 2018, Huarui-2 designed by Nanjing Research Institute of Electronics Technology of China Electronics Technology Group passed acceptance. With a processing speed of 0.4 TFLOPS, the chip can achieve better performance than current mainstream DSP chips. The design team has begun to create Huarui-3, which has a processing speed in TFLOPS level and a support for artificial intelligence. | Digital signal processor | Wikipedia | 419 | 154505 | https://en.wikipedia.org/wiki/Digital%20signal%20processor | Technology | Computer hardware | null |
Hilbert's problems are 23 problems in mathematics published by German mathematician David Hilbert in 1900. They were all unsolved at the time, and several proved to be very influential for 20th-century mathematics. Hilbert presented ten of the problems (1, 2, 6, 7, 8, 13, 16, 19, 21, and 22) at the Paris conference of the International Congress of Mathematicians, speaking on August 8 at the Sorbonne. The complete list of 23 problems was published later, in English translation in 1902 by Mary Frances Winston Newson in the Bulletin of the American Mathematical Society. Earlier publications (in the original German) appeared in Archiv der Mathematik und Physik.
List of Hilbert's Problems
The following are the headers for Hilbert's 23 problems as they appeared in the 1902 translation in the Bulletin of the American Mathematical Society. | Hilbert's problems | Wikipedia | 174 | 154584 | https://en.wikipedia.org/wiki/Hilbert%27s%20problems | Mathematics | Basics | null |
1. Cantor's problem of the cardinal number of the continuum.
2. The compatibility of the arithmetical axioms.
3. The equality of the volumes of two tetrahedra of equal bases and equal altitudes.
4. Problem of the straight line as the shortest distance between two points.
5. Lie's concept of a continuous group of transformations without the assumption of the differentiability of the functions defining the group.
6. Mathematical treatment of the axioms of physics.
7. Irrationality and transcendence of certain numbers.
8. Problems of prime numbers (The "Riemann Hypothesis").
9. Proof of the most general law of reciprocity in any number field.
10. Determination of the solvability of a Diophantine equation.
11. Quadratic forms with any algebraic numerical coefficients
12. Extensions of Kronecker's theorem on Abelian fields to any algebraic realm of rationality
13. Impossibility of the solution of the general equation of 7th degree by means of functions of only two arguments.
14. Proof of the finiteness of certain complete systems of functions.
15. Rigorous foundation of Schubert's enumerative calculus.
16. Problem of the topology of algebraic curves and surfaces.
17. Expression of definite forms by squares.
18. Building up of space from congruent polyhedra.
19. Are the solutions of regular problems in the calculus of variations always necessarily analytic?
20. The general problem of boundary values (Boundary value problems in PD)
21. Proof of the existence of linear differential equations having a prescribed monodromy group.
22. Uniformization of analytic relations by means of automorphic functions.
23. Further development of the methods of the calculus of variations. | Hilbert's problems | Wikipedia | 352 | 154584 | https://en.wikipedia.org/wiki/Hilbert%27s%20problems | Mathematics | Basics | null |
Nature and influence of the problems
Hilbert's problems ranged greatly in topic and precision. Some of them, like the 3rd problem, which was the first to be solved, or the 8th problem (the Riemann hypothesis), which still remains unresolved, were presented precisely enough to enable a clear affirmative or negative answer. For other problems, such as the 5th, experts have traditionally agreed on a single interpretation, and a solution to the accepted interpretation has been given, but closely related unsolved problems exist. Some of Hilbert's statements were not precise enough to specify a particular problem, but were suggestive enough that certain problems of contemporary nature seem to apply; for example, most modern number theorists would probably see the 9th problem as referring to the conjectural Langlands correspondence on representations of the absolute Galois group of a number field. Still other problems, such as the 11th and the 16th, concern what are now flourishing mathematical subdisciplines, like the theories of quadratic forms and real algebraic curves.
There are two problems that are not only unresolved but may in fact be unresolvable by modern standards. The 6th problem concerns the axiomatization of physics, a goal that 20th-century developments seem to render both more remote and less important than in Hilbert's time. Also, the 4th problem concerns the foundations of geometry, in a manner that is now generally judged to be too vague to enable a definitive answer.
The 23rd problem was purposefully set as a general indication by Hilbert to highlight the calculus of variations as an underappreciated and understudied field. In the lecture introducing these problems, Hilbert made the following introductory remark to the 23rd problem:
The other 21 problems have all received significant attention, and late into the 20th century work on these problems was still considered to be of the greatest importance. Paul Cohen received the Fields Medal in 1966 for his work on the first problem, and the negative solution of the tenth problem in 1970 by Yuri Matiyasevich (completing work by Julia Robinson, Hilary Putnam, and Martin Davis) generated similar acclaim. Aspects of these problems are still of great interest today. | Hilbert's problems | Wikipedia | 436 | 154584 | https://en.wikipedia.org/wiki/Hilbert%27s%20problems | Mathematics | Basics | null |
Knowability
Following Gottlob Frege and Bertrand Russell, Hilbert sought to define mathematics logically using the method of formal systems, i.e., finitistic proofs from an agreed-upon set of axioms. One of the main goals of Hilbert's program was a finitistic proof of the consistency of the axioms of arithmetic: that is his second problem.
However, Gödel's second incompleteness theorem gives a precise sense in which such a finitistic proof of the consistency of arithmetic is provably impossible. Hilbert lived for 12 years after Kurt Gödel published his theorem, but does not seem to have written any formal response to Gödel's work.
Hilbert's tenth problem does not ask whether there exists an algorithm for deciding the solvability of Diophantine equations, but rather asks for the construction of such an algorithm: "to devise a process according to which it can be determined in a finite number of operations whether the equation is solvable in rational integers". That this problem was solved by showing that there cannot be any such algorithm contradicted Hilbert's philosophy of mathematics.
In discussing his opinion that every mathematical problem should have a solution, Hilbert allows for the possibility that the solution could be a proof that the original problem is impossible. He stated that the point is to know one way or the other what the solution is, and he believed that we always can know this, that in mathematics there is not any "ignorabimus" (statement whose truth can never be known). It seems unclear whether he would have regarded the solution of the tenth problem as an instance of ignorabimus.
On the other hand, the status of the first and second problems is even more complicated: there is no clear mathematical consensus as to whether the results of Gödel (in the case of the second problem), or Gödel and Cohen (in the case of the first problem) give definitive negative solutions or not, since these solutions apply to a certain formalization of the problems, which is not necessarily the only possible one.
The 24th problem
Hilbert originally included 24 problems on his list, but decided against including one of them in the published list. The "24th problem" (in proof theory, on a criterion for simplicity and general methods) was rediscovered in Hilbert's original manuscript notes by German historian Rüdiger Thiele in 2000. | Hilbert's problems | Wikipedia | 487 | 154584 | https://en.wikipedia.org/wiki/Hilbert%27s%20problems | Mathematics | Basics | null |
Follow-ups
Since 1900, mathematicians and mathematical organizations have announced problem lists but, with few exceptions, these have not had nearly as much influence nor generated as much work as Hilbert's problems.
One exception consists of three conjectures made by André Weil in the late 1940s (the Weil conjectures). In the fields of algebraic geometry, number theory and the links between the two, the Weil conjectures were very important. The first of these was proved by Bernard Dwork; a completely different proof of the first two, via ℓ-adic cohomology, was given by Alexander Grothendieck. The last and deepest of the Weil conjectures (an analogue of the Riemann hypothesis) was proved by Pierre Deligne. Both Grothendieck and Deligne were awarded the Fields medal. However, the Weil conjectures were, in their scope, more like a single Hilbert problem, and Weil never intended them as a programme for all mathematics. This is somewhat ironic, since arguably Weil was the mathematician of the 1940s and 1950s who best played the Hilbert role, being conversant with nearly all areas of (theoretical) mathematics and having figured importantly in the development of many of them.
Paul Erdős posed hundreds, if not thousands, of mathematical problems, many of them profound. Erdős often offered monetary rewards; the size of the reward depended on the perceived difficulty of the problem.
The end of the millennium, which was also the centennial of Hilbert's announcement of his problems, provided a natural occasion to propose "a new set of Hilbert problems". Several mathematicians accepted the challenge, notably Fields Medalist Steve Smale, who responded to a request by Vladimir Arnold to propose a list of 18 problems (Smale's problems).
At least in the mainstream media, the de facto 21st century analogue of Hilbert's problems is the list of seven Millennium Prize Problems chosen during 2000 by the Clay Mathematics Institute. Unlike the Hilbert problems, where the primary award was the admiration of Hilbert in particular and mathematicians in general, each prize problem includes a million-dollar bounty. As with the Hilbert problems, one of the prize problems (the Poincaré conjecture) was solved relatively soon after the problems were announced. | Hilbert's problems | Wikipedia | 457 | 154584 | https://en.wikipedia.org/wiki/Hilbert%27s%20problems | Mathematics | Basics | null |
The Riemann hypothesis is noteworthy for its appearance on the list of Hilbert problems, Smale's list, the list of Millennium Prize Problems, and even the Weil conjectures, in its geometric guise. Although it has been attacked by major mathematicians of our day, many experts believe that it will still be part of unsolved problems lists for many centuries. Hilbert himself declared: "If I were to awaken after having slept for a thousand years, my first question would be: Has the Riemann hypothesis been proved?"
In 2008, DARPA announced its own list of 23 problems that it hoped could lead to major mathematical breakthroughs, "thereby strengthening the scientific and technological capabilities of the DoD". The DARPA list also includes a few problems from Hilbert's list, e.g. the Riemann hypothesis.
Summary
Of the cleanly formulated Hilbert problems, numbers 3, 7, 10, 14, 17, 18, 19, and 20 have resolutions that are accepted by consensus of the mathematical community. Problems 1, 2, 5, 6, 9, 11, 12, 15, 21, and 22 have solutions that have partial acceptance, but there exists some controversy as to whether they resolve the problems.
That leaves 8 (the Riemann hypothesis), 13 and 16 unresolved, and 4 and 23 as too vague to ever be described as solved. The withdrawn 24 would also be in this class.
Table of problems
Hilbert's 23 problems are (for details on the solutions and references, see the articles that are linked to in the first column): | Hilbert's problems | Wikipedia | 318 | 154584 | https://en.wikipedia.org/wiki/Hilbert%27s%20problems | Mathematics | Basics | null |
In mathematics, a negative number is the opposite of a positive real number. Equivalently, a negative number is a real number that is less than zero. Negative numbers are often used to represent the magnitude of a loss or deficiency. A debt that is owed may be thought of as a negative asset. If a quantity, such as the charge on an electron, may have either of two opposite senses, then one may choose to distinguish between those senses—perhaps arbitrarily—as positive and negative. Negative numbers are used to describe values on a scale that goes below zero, such as the Celsius and Fahrenheit scales for temperature. The laws of arithmetic for negative numbers ensure that the common-sense idea of an opposite is reflected in arithmetic. For example, −(−3) = 3 because the opposite of an opposite is the original value.
Negative numbers are usually written with a minus sign in front. For example, −3 represents a negative quantity with a magnitude of three, and is pronounced "minus three" or "negative three". Conversely, a number that is greater than zero is called positive; zero is usually (but not always) thought of as neither positive nor negative. The positivity of a number may be emphasized by placing a plus sign before it, e.g. +3. In general, the negativity or positivity of a number is referred to as its sign.
Every real number other than zero is either positive or negative. The non-negative whole numbers are referred to as natural numbers (i.e., 0, 1, 2, 3...), while the positive and negative whole numbers (together with zero) are referred to as integers. (Some definitions of the natural numbers exclude zero.)
In bookkeeping, amounts owed are often represented by red numbers, or a number in parentheses, as an alternative notation to represent negative numbers. | Negative number | Wikipedia | 388 | 154616 | https://en.wikipedia.org/wiki/Negative%20number | Mathematics | Basics | null |
Negative numbers were used in the Nine Chapters on the Mathematical Art, which in its present form dates from the period of the Chinese Han dynasty (202 BC – AD 220), but may well contain much older material. Liu Hui (c. 3rd century) established rules for adding and subtracting negative numbers. By the 7th century, Indian mathematicians such as Brahmagupta were describing the use of negative numbers. Islamic mathematicians further developed the rules of subtracting and multiplying negative numbers and solved problems with negative coefficients. Prior to the concept of negative numbers, mathematicians such as Diophantus considered negative solutions to problems "false" and equations requiring negative solutions were described as absurd. Western mathematicians like Leibniz held that negative numbers were invalid, but still used them in calculations.
Introduction
The number line
The relationship between negative numbers, positive numbers, and zero is often expressed in the form of a number line:
Numbers appearing farther to the right on this line are greater, while numbers appearing farther to the left are lesser. Thus zero appears in the middle, with the positive numbers to the right and the negative numbers to the left.
Note that a negative number with greater magnitude is considered less. For example, even though (positive) is greater than (positive) , written
negative is considered to be less than negative :
Signed numbers
In the context of negative numbers, a number that is greater than zero is referred to as positive. Thus every real number other than zero is either positive or negative, while zero itself is not considered to have a sign. Positive numbers are sometimes written with a plus sign in front, e.g. denotes a positive three.
Because zero is neither positive nor negative, the term nonnegative is sometimes used to refer to a number that is either positive or zero, while nonpositive is used to refer to a number that is either negative or zero. Zero is a neutral number.
As the result of subtraction
Negative numbers can be thought of as resulting from the subtraction of a larger number from a smaller. For example, negative three is the result of subtracting three from zero:
In general, the subtraction of a larger number from a smaller yields a negative result, with the magnitude of the result being the difference between the two numbers. For example,
since .
Everyday uses of negative numbers
Sport | Negative number | Wikipedia | 474 | 154616 | https://en.wikipedia.org/wiki/Negative%20number | Mathematics | Basics | null |
Goal difference in association football and hockey; points difference in rugby football; net run rate in cricket; golf scores relative to par.
Plus-minus differential in ice hockey: the difference in total goals scored for the team (+) and against the team (−) when a particular player is on the ice is the player's +/− rating. Players can have a negative (+/−) rating.
Run differential in baseball: the run differential is negative if the team allows more runs than they scored.
Clubs may be deducted points for breaches of the laws, and thus have a negative points total until they have earned at least that many points that season.
Lap (or sector) times in Formula 1 may be given as the difference compared to a previous lap (or sector) (such as the previous record, or the lap just completed by a driver in front), and will be positive if slower and negative if faster.
In some athletics events, such as sprint races, the hurdles, the triple jump and the long jump, the wind assistance is measured and recorded, and is positive for a tailwind and negative for a headwind.
Science
Temperatures which are colder than 0 °C or 0 °F.
Latitudes south of the equator and longitudes west of the prime meridian.
Topographical features of the earth's surface are given a height above sea level, which can be negative (e.g. the surface elevation of the Dead Sea or Death Valley, or the elevation of the Thames Tideway Tunnel).
Electrical circuits. When a battery is connected in reverse polarity, the voltage applied is said to be the opposite of its rated voltage. For example, a 6-volt battery connected in reverse applies a voltage of −6 volts.
Ions have a positive or negative electrical charge.
Impedance of an AM broadcast tower used in multi-tower directional antenna arrays, which can be positive or negative. | Negative number | Wikipedia | 387 | 154616 | https://en.wikipedia.org/wiki/Negative%20number | Mathematics | Basics | null |
Finance
Financial statements can include negative balances, indicated either by a minus sign or by enclosing the balance in parentheses. Examples include bank account overdrafts and business losses (negative earnings).
The annual percentage growth in a country's GDP might be negative, which is one indicator of being in a recession.
Occasionally, a rate of inflation may be negative (deflation), indicating a fall in average prices.
The daily change in a share price or stock market index, such as the FTSE 100 or the Dow Jones.
A negative number in financing is synonymous with "debt" and "deficit" which are also known as "being in the red".
Interest rates can be negative, when the lender is charged to deposit their money.
Other
The numbering of stories in a building below the ground floor.
When playing an audio file on a portable media player, such as an iPod, the screen display may show the time remaining as a negative number, which increases up to zero time remaining at the same rate as the time already played increases from zero.
Television game shows:
Participants on QI often finish with a negative points score.
Teams on University Challenge have a negative score if their first answers are incorrect and interrupt the question.
Jeopardy! has a negative money score – contestants play for an amount of money and any incorrect answer that costs them more than what they have now can result in a negative score.
In The Price Is Rights pricing game Buy or Sell, if an amount of money is lost that is more than the amount currently in the bank, it incurs a negative score.
The change in support for a political party between elections, known as swing.
A politician's approval rating.
In video games, a negative number indicates loss of life, damage, a score penalty, or consumption of a resource, depending on the genre of the simulation.
Employees with flexible working hours may have a negative balance on their timesheet if they have worked fewer total hours than contracted to that point. Employees may be able to take more than their annual holiday allowance in a year, and carry forward a negative balance to the next year.
Transposing notes on an electronic keyboard are shown on the display with positive numbers for increases and negative numbers for decreases, e.g. "−1" for one semitone down. | Negative number | Wikipedia | 467 | 154616 | https://en.wikipedia.org/wiki/Negative%20number | Mathematics | Basics | null |
Arithmetic involving negative numbers
The minus sign "−" signifies the operator for both the binary (two-operand) operation of subtraction (as in ) and the unary (one-operand) operation of negation (as in , or twice in ). A special case of unary negation occurs when it operates on a positive number, in which case the result is a negative number (as in ).
The ambiguity of the "−" symbol does not generally lead to ambiguity in arithmetical expressions, because the order of operations makes only one interpretation or the other possible for each "−". However, it can lead to confusion and be difficult for a person to understand an expression when operator symbols appear adjacent to one another. A solution can be to parenthesize the unary "−" along with its operand.
For example, the expression may be clearer if written (even though they mean exactly the same thing formally). The subtraction expression is a different expression that doesn't represent the same operations, but it evaluates to the same result.
Sometimes in elementary schools a number may be prefixed by a superscript minus sign or plus sign to explicitly distinguish negative and positive numbers as in
Addition
Addition of two negative numbers is very similar to addition of two positive numbers. For example,
The idea is that two debts can be combined into a single debt of greater magnitude.
When adding together a mixture of positive and negative numbers, one can think of the negative numbers as positive quantities being subtracted. For example:
In the first example, a credit of is combined with a debt of , which yields a total credit of . If the negative number has greater magnitude, then the result is negative:
Here the credit is less than the debt, so the net result is a debt.
Subtraction
As discussed above, it is possible for the subtraction of two non-negative numbers to yield a negative answer:
In general, subtraction of a positive number yields the same result as the addition of a negative number of equal magnitude. Thus
and
On the other hand, subtracting a negative number yields the same result as the addition a positive number of equal magnitude. (The idea is that losing a debt is the same thing as gaining a credit.) Thus
and
Multiplication | Negative number | Wikipedia | 464 | 154616 | https://en.wikipedia.org/wiki/Negative%20number | Mathematics | Basics | null |
When multiplying numbers, the magnitude of the product is always just the product of the two magnitudes. The sign of the product is determined by the following rules:
The product of one positive number and one negative number is negative.
The product of two negative numbers is positive.
Thus
and
The reason behind the first example is simple: adding three 's together yields :
The reasoning behind the second example is more complicated. The idea again is that losing a debt is the same thing as gaining a credit. In this case, losing two debts of three each is the same as gaining a credit of six:
The convention that a product of two negative numbers is positive is also necessary for multiplication to follow the distributive law. In this case, we know that
Since , the product must equal .
These rules lead to another (equivalent) rule—the sign of any product a × b depends on the sign of a as follows:
if a is positive, then the sign of a × b is the same as the sign of b, and
if a is negative, then the sign of a × b is the opposite of the sign of b.
The justification for why the product of two negative numbers is a positive number can be observed in the analysis of complex numbers.
Division
The sign rules for division are the same as for multiplication. For example,
and
If dividend and divisor have the same sign, the result is positive, if they have different signs the result is negative.
Negation
The negative version of a positive number is referred to as its negation. For example, is the negation of the positive number . The sum of a number and its negation is equal to zero:
That is, the negation of a positive number is the additive inverse of the number.
Using algebra, we may write this principle as an algebraic identity:
This identity holds for any positive number . It can be made to hold for all real numbers by extending the definition of negation to include zero and negative numbers. Specifically:
The negation of 0 is 0, and
The negation of a negative number is the corresponding positive number.
For example, the negation of is . In general,
The absolute value of a number is the non-negative number with the same magnitude. For example, the absolute value of and the absolute value of are both equal to , and the absolute value of is .
Formal construction of negative integers | Negative number | Wikipedia | 487 | 154616 | https://en.wikipedia.org/wiki/Negative%20number | Mathematics | Basics | null |
In a similar manner to rational numbers, we can extend the natural numbers N to the integers Z by defining integers as an ordered pair of natural numbers (a, b). We can extend addition and multiplication to these pairs with the following rules:
We define an equivalence relation ~ upon these pairs with the following rule:
This equivalence relation is compatible with the addition and multiplication defined above, and we may define Z to be the quotient set N²/~, i.e. we identify two pairs (a, b) and (c, d) if they are equivalent in the above sense. Note that Z, equipped with these operations of addition and multiplication, is a ring, and is in fact, the prototypical example of a ring.
We can also define a total order on Z''' by writing
This will lead to an additive zero of the form (a, a), an additive inverse of (a, b) of the form (b, a), a multiplicative unit of the form (a + 1, a), and a definition of subtraction
This construction is a special case of the Grothendieck construction.
Uniqueness
The additive inverse of a number is unique, as is shown by the following proof. As mentioned above, an additive inverse of a number is defined as a value which when added to the number yields zero.
Let x be a number and let y be its additive inverse. Suppose y′ is another additive inverse of x. By definition,
And so, x + y′ = x + y. Using the law of cancellation for addition, it is seen that y′ = y. Thus y is equal to any other additive inverse of x. That is, y is the unique additive inverse of x.
History
For a long time, understanding of negative numbers was delayed by the impossibility of having a negative-number amount of a physical object, for example "minus-three apples", and negative solutions to problems were considered "false".
In Hellenistic Egypt, the Greek mathematician Diophantus in the 3rd century AD referred to an equation that was equivalent to (which has a negative solution) in Arithmetica, saying that the equation was absurd. For this reason Greek geometers were able to solve geometrically all forms of the quadratic equation which give positive roots, while they could take no account of others. | Negative number | Wikipedia | 484 | 154616 | https://en.wikipedia.org/wiki/Negative%20number | Mathematics | Basics | null |
Negative numbers appear for the first time in history in the Nine Chapters on the Mathematical Art (九章算術, Jiǔ zhāng suàn-shù), which in its present form dates from the Han period, but may well contain much older material. The mathematician Liu Hui (c. 3rd century) established rules for the addition and subtraction of negative numbers. The historian Jean-Claude Martzloff theorized that the importance of duality in Chinese natural philosophy made it easier for the Chinese to accept the idea of negative numbers. The Chinese were able to solve simultaneous equations involving negative numbers. The Nine Chapters used red counting rods to denote positive coefficients and black rods for negative. This system is the exact opposite of contemporary printing of positive and negative numbers in the fields of banking, accounting, and commerce, wherein red numbers denote negative values and black numbers signify positive values. Liu Hui writes:
The ancient Indian Bakhshali Manuscript carried out calculations with negative numbers, using "+" as a negative sign. The date of the manuscript is uncertain. LV Gurjar dates it no later than the 4th century, Hoernle dates it between the third and fourth centuries, Ayyangar and Pingree dates it to the 8th or 9th centuries, and George Gheverghese Joseph dates it to about AD 400 and no later than the early 7th century,
During the 7th century AD, negative numbers were used in India to represent debts. The Indian mathematician Brahmagupta, in Brahma-Sphuta-Siddhanta (written c. AD 630), discussed the use of negative numbers to produce a general form quadratic formula similar to the one in use today.
In the 9th century, Islamic mathematicians were familiar with negative numbers from the works of Indian mathematicians, but the recognition and use of negative numbers during this period remained timid. Al-Khwarizmi in his Al-jabr wa'l-muqabala (from which the word "algebra" derives) did not use negative numbers or negative coefficients. But within fifty years, Abu Kamil illustrated the rules of signs for expanding the multiplication , and al-Karaji wrote in his al-Fakhrī that "negative quantities must be counted as terms". In the 10th century, Abū al-Wafā' al-Būzjānī considered debts as negative numbers in A Book on What Is Necessary from the Science of Arithmetic for Scribes and Businessmen. | Negative number | Wikipedia | 497 | 154616 | https://en.wikipedia.org/wiki/Negative%20number | Mathematics | Basics | null |
By the 12th century, al-Karaji's successors were to state the general rules of signs and use them to solve polynomial divisions. As al-Samaw'al writes:
the product of a negative number—al-nāqiṣ (loss)—by a positive number—al-zāʾid (gain)—is negative, and by a negative number is positive. If we subtract a negative number from a higher negative number, the remainder is their negative difference. The difference remains positive if we subtract a negative number from a lower negative number. If we subtract a negative number from a positive number, the remainder is their positive sum. If we subtract a positive number from an empty power (martaba khāliyya), the remainder is the same negative, and if we subtract a negative number from an empty power, the remainder is the same positive number.
In the 12th century in India, Bhāskara II gave negative roots for quadratic equations but rejected them because they were inappropriate in the context of the problem. He stated that a negative value is "in this case not to be taken, for it is inadequate; people do not approve of negative roots."
Fibonacci allowed negative solutions in financial problems where they could be interpreted as debits (chapter 13 of Liber Abaci, 1202) and later as losses (in Flos, 1225).
In the 15th century, Nicolas Chuquet, a Frenchman, used negative numbers as exponents but referred to them as "absurd numbers".
Michael Stifel dealt with negative numbers in his 1544 AD Arithmetica Integra, where he also called them numeri absurdi (absurd numbers).
In 1545, Gerolamo Cardano, in his Ars Magna, provided the first satisfactory treatment of negative numbers in Europe. He did not allow negative numbers in his consideration of cubic equations, so he had to treat, for example, separately from (with in both cases). In all, Cardano was driven to the study of thirteen types of cubic equations, each with all negative terms moved to the other side of the = sign to make them positive. (Cardano also dealt with complex numbers, but understandably liked them even less.) | Negative number | Wikipedia | 467 | 154616 | https://en.wikipedia.org/wiki/Negative%20number | Mathematics | Basics | null |
In fluid dynamics, turbulence or turbulent flow is fluid motion characterized by chaotic changes in pressure and flow velocity. It is in contrast to laminar flow, which occurs when a fluid flows in parallel layers with no disruption between those layers.
Turbulence is commonly observed in everyday phenomena such as surf, fast flowing rivers, billowing storm clouds, or smoke from a chimney, and most fluid flows occurring in nature or created in engineering applications are turbulent. Turbulence is caused by excessive kinetic energy in parts of a fluid flow, which overcomes the damping effect of the fluid's viscosity. For this reason, turbulence is commonly realized in low viscosity fluids. In general terms, in turbulent flow, unsteady vortices appear of many sizes which interact with each other, consequently drag due to friction effects increases.
The onset of turbulence can be predicted by the dimensionless Reynolds number, the ratio of kinetic energy to viscous damping in a fluid flow. However, turbulence has long resisted detailed physical analysis, and the interactions within turbulence create a very complex phenomenon. Physicist Richard Feynman described turbulence as the most important unsolved problem in classical physics.
The turbulence intensity affects many fields, for examples fish ecology, air pollution, precipitation, and climate change.
Examples of turbulence | Turbulence | Wikipedia | 258 | 154664 | https://en.wikipedia.org/wiki/Turbulence | Physical sciences | Fluid mechanics | null |
Smoke rising from a cigarette. For the first few centimeters, the smoke is laminar. The smoke plume becomes turbulent as its Reynolds number increases with increases in flow velocity and characteristic length scale.
Flow over a golf ball. (This can be best understood by considering the golf ball to be stationary, with air flowing over it.) If the golf ball were smooth, the boundary layer flow over the front of the sphere would be laminar at typical conditions. However, the boundary layer would separate early, as the pressure gradient switched from favorable (pressure decreasing in the flow direction) to unfavorable (pressure increasing in the flow direction), creating a large region of low pressure behind the ball that creates high form drag. To prevent this, the surface is dimpled to perturb the boundary layer and promote turbulence. This results in higher skin friction, but it moves the point of boundary layer separation further along, resulting in lower drag.
Clear-air turbulence experienced during airplane flight, as well as poor astronomical seeing (the blurring of images seen through the atmosphere).
Most of the terrestrial atmospheric circulation.
The oceanic and atmospheric mixed layers and intense oceanic currents.
The flow conditions in many industrial equipment (such as pipes, ducts, precipitators, gas scrubbers, dynamic scraped surface heat exchangers, etc.) and machines (for instance, internal combustion engines and gas turbines).
The external flow over all kinds of vehicles such as cars, airplanes, ships, and submarines.
The motions of matter in stellar atmospheres.
A jet exhausting from a nozzle into a quiescent fluid. As the flow emerges into this external fluid, shear layers originating at the lips of the nozzle are created. These layers separate the fast moving jet from the external fluid, and at a certain critical Reynolds number they become unstable and break down to turbulence.
Biologically generated turbulence resulting from swimming animals affects ocean mixing.
Snow fences work by inducing turbulence in the wind, forcing it to drop much of its snow load near the fence.
Bridge supports (piers) in water. When river flow is slow, water flows smoothly around the support legs. When the flow is faster, a higher Reynolds number is associated with the flow. The flow may start off laminar but is quickly separated from the leg and becomes turbulent. | Turbulence | Wikipedia | 469 | 154664 | https://en.wikipedia.org/wiki/Turbulence | Physical sciences | Fluid mechanics | null |
In many geophysical flows (rivers, atmospheric boundary layer), the flow turbulence is dominated by the coherent structures and turbulent events. A turbulent event is a series of turbulent fluctuations that contain more energy than the average flow turbulence. The turbulent events are associated with coherent flow structures such as eddies and turbulent bursting, and they play a critical role in terms of sediment scour, accretion and transport in rivers as well as contaminant mixing and dispersion in rivers and estuaries, and in the atmosphere. | Turbulence | Wikipedia | 105 | 154664 | https://en.wikipedia.org/wiki/Turbulence | Physical sciences | Fluid mechanics | null |
In the medical field of cardiology, a stethoscope is used to detect heart sounds and bruits, which are due to turbulent blood flow. In normal individuals, heart sounds are a product of turbulent flow as heart valves close. However, in some conditions turbulent flow can be audible due to other reasons, some of them pathological. For example, in advanced atherosclerosis, bruits (and therefore turbulent flow) can be heard in some vessels that have been narrowed by the disease process.
Recently, turbulence in porous media became a highly debated subject.
Strategies used by animals for olfactory navigation, and their success, are heavily influenced by turbulence affecting the odor plume.
Features
Turbulence is characterized by the following features:
Irregularity Turbulent flows are always highly irregular. For this reason, turbulence problems are normally treated statistically rather than deterministically. Turbulent flow is chaotic. However, not all chaotic flows are turbulent.
Diffusivity The readily available supply of energy in turbulent flows tends to accelerate the homogenization (mixing) of fluid mixtures. The characteristic which is responsible for the enhanced mixing and increased rates of mass, momentum and energy transports in a flow is called "diffusivity".
Turbulent diffusion is usually described by a turbulent diffusion coefficient. This turbulent diffusion coefficient is defined in a phenomenological sense, by analogy with the molecular diffusivities, but it does not have a true physical meaning, being dependent on the flow conditions, and not a property of the fluid itself. In addition, the turbulent diffusivity concept assumes a constitutive relation between a turbulent flux and the gradient of a mean variable similar to the relation between flux and gradient that exists for molecular transport. In the best case, this assumption is only an approximation. Nevertheless, the turbulent diffusivity is the simplest approach for quantitative analysis of turbulent flows, and many models have been postulated to calculate it. For instance, in large bodies of water like oceans this coefficient can be found using Richardson's four-third power law and is governed by the random walk principle. In rivers and large ocean currents, the diffusion coefficient is given by variations of Elder's formula. | Turbulence | Wikipedia | 449 | 154664 | https://en.wikipedia.org/wiki/Turbulence | Physical sciences | Fluid mechanics | null |
Rotationality Turbulent flows have non-zero vorticity and are characterized by a strong three-dimensional vortex generation mechanism known as vortex stretching. In fluid dynamics, they are essentially vortices subjected to stretching associated with a corresponding increase of the component of vorticity in the stretching direction—due to the conservation of angular momentum. On the other hand, vortex stretching is the core mechanism on which the turbulence energy cascade relies to establish and maintain identifiable structure function. In general, the stretching mechanism implies thinning of the vortices in the direction perpendicular to the stretching direction due to volume conservation of fluid elements. As a result, the radial length scale of the vortices decreases and the larger flow structures break down into smaller structures. The process continues until the small scale structures are small enough that their kinetic energy can be transformed by the fluid's molecular viscosity into heat. Turbulent flow is always rotational and three dimensional. For example, atmospheric cyclones are rotational but their substantially two-dimensional shapes do not allow vortex generation and so are not turbulent. On the other hand, oceanic flows are dispersive but essentially non rotational and therefore are not turbulent.
Dissipation To sustain turbulent flow, a persistent source of energy supply is required because turbulence dissipates rapidly as the kinetic energy is converted into internal energy by viscous shear stress. Turbulence causes the formation of eddies of many different length scales. Most of the kinetic energy of the turbulent motion is contained in the large-scale structures. The energy "cascades" from these large-scale structures to smaller scale structures by an inertial and essentially inviscid mechanism. This process continues, creating smaller and smaller structures which produces a hierarchy of eddies. Eventually this process creates structures that are small enough that molecular diffusion becomes important and viscous dissipation of energy finally takes place. The scale at which this happens is the Kolmogorov length scale. | Turbulence | Wikipedia | 390 | 154664 | https://en.wikipedia.org/wiki/Turbulence | Physical sciences | Fluid mechanics | null |
Via this energy cascade, turbulent flow can be realized as a superposition of a spectrum of flow velocity fluctuations and eddies upon a mean flow. The eddies are loosely defined as coherent patterns of flow velocity, vorticity and pressure. Turbulent flows may be viewed as made of an entire hierarchy of eddies over a wide range of length scales and the hierarchy can be described by the energy spectrum that measures the energy in flow velocity fluctuations for each length scale (wavenumber). The scales in the energy cascade are generally uncontrollable and highly non-symmetric. Nevertheless, based on these length scales these eddies can be divided into three categories.
Integral time scale
The integral time scale for a Lagrangian flow can be defined as: | Turbulence | Wikipedia | 152 | 154664 | https://en.wikipedia.org/wiki/Turbulence | Physical sciences | Fluid mechanics | null |
where u′ is the velocity fluctuation, and is the time lag between measurements.
Integral length scales
Large eddies obtain energy from the mean flow and also from each other. Thus, these are the energy production eddies which contain most of the energy. They have the large flow velocity fluctuation and are low in frequency. Integral scales are highly anisotropic and are defined in terms of the normalized two-point flow velocity correlations. The maximum length of these scales is constrained by the characteristic length of the apparatus. For example, the largest integral length scale of pipe flow is equal to the pipe diameter. In the case of atmospheric turbulence, this length can reach up to the order of several hundreds kilometers.: The integral length scale can be defined as
where r is the distance between two measurement locations, and u′ is the velocity fluctuation in that same direction.
Kolmogorov length scales Smallest scales in the spectrum that form the viscous sub-layer range. In this range, the energy input from nonlinear interactions and the energy drain from viscous dissipation are in exact balance. The small scales have high frequency, causing turbulence to be locally isotropic and homogeneous.
Taylor microscales The intermediate scales between the largest and the smallest scales which make the inertial subrange. Taylor microscales are not dissipative scales, but pass down the energy from the largest to the smallest without dissipation. Some literatures do not consider Taylor microscales as a characteristic length scale and consider the energy cascade to contain only the largest and smallest scales; while the latter accommodate both the inertial subrange and the viscous sublayer. Nevertheless, Taylor microscales are often used in describing the term "turbulence" more conveniently as these Taylor microscales play a dominant role in energy and momentum transfer in the wavenumber space. | Turbulence | Wikipedia | 387 | 154664 | https://en.wikipedia.org/wiki/Turbulence | Physical sciences | Fluid mechanics | null |
Although it is possible to find some particular solutions of the Navier–Stokes equations governing fluid motion, all such solutions are unstable to finite perturbations at large Reynolds numbers. Sensitive dependence on the initial and boundary conditions makes fluid flow irregular both in time and in space so that a statistical description is needed. The Russian mathematician Andrey Kolmogorov proposed the first statistical theory of turbulence, based on the aforementioned notion of the energy cascade (an idea originally introduced by Richardson) and the concept of self-similarity. As a result, the Kolmogorov microscales were named after him. It is now known that the self-similarity is broken so the statistical description is presently modified.
A complete description of turbulence is one of the unsolved problems in physics. According to an apocryphal story, Werner Heisenberg was asked what he would ask God, given the opportunity. His reply was: "When I meet God, I am going to ask him two questions: Why relativity? And why turbulence? I really believe he will have an answer for the first." A similar witticism has been attributed to Horace Lamb in a speech to the British Association for the Advancement of Science: "I am an old man now, and when I die and go to heaven there are two matters on which I hope for enlightenment. One is quantum electrodynamics, and the other is the turbulent motion of fluids. And about the former I am rather more optimistic."
Onset of turbulence
The onset of turbulence can be, to some extent, predicted by the Reynolds number, which is the ratio of inertial forces to viscous forces within a fluid which is subject to relative internal movement due to different fluid velocities, in what is known as a boundary layer in the case of a bounding surface such as the interior of a pipe. A similar effect is created by the introduction of a stream of higher velocity fluid, such as the hot gases from a flame in air. This relative movement generates fluid friction, which is a factor in developing turbulent flow. Counteracting this effect is the viscosity of the fluid, which as it increases, progressively inhibits turbulence, as more kinetic energy is absorbed by a more viscous fluid. The Reynolds number quantifies the relative importance of these two types of forces for given flow conditions, and is a guide to when turbulent flow will occur in a particular situation. | Turbulence | Wikipedia | 491 | 154664 | https://en.wikipedia.org/wiki/Turbulence | Physical sciences | Fluid mechanics | null |
This ability to predict the onset of turbulent flow is an important design tool for equipment such as piping systems or aircraft wings, but the Reynolds number is also used in scaling of fluid dynamics problems, and is used to determine dynamic similitude between two different cases of fluid flow, such as between a model aircraft, and its full size version. Such scaling is not always linear and the application of Reynolds numbers to both situations allows scaling factors to be developed.
A flow situation in which the kinetic energy is significantly absorbed due to the action of fluid molecular viscosity gives rise to a laminar flow regime. For this the dimensionless quantity the Reynolds number () is used as a guide.
With respect to laminar and turbulent flow regimes:
laminar flow occurs at low Reynolds numbers, where viscous forces are dominant, and is characterized by smooth, constant fluid motion;
turbulent flow occurs at high Reynolds numbers and is dominated by inertial forces, which tend to produce chaotic eddies, vortices and other flow instabilities.
The Reynolds number is defined as
where:
is the density of the fluid (SI units: kg/m3)
is a characteristic velocity of the fluid with respect to the object (m/s)
is a characteristic linear dimension (m)
is the dynamic viscosity of the fluid (Pa·s or N·s/m2 or kg/(m·s)).
While there is no theorem directly relating the non-dimensional Reynolds number to turbulence, flows at Reynolds numbers larger than 5000 are typically (but not necessarily) turbulent, while those at low Reynolds numbers usually remain laminar. In Poiseuille flow, for example, turbulence can first be sustained if the Reynolds number is larger than a critical value of about 2040; moreover, the turbulence is generally interspersed with laminar flow until a larger Reynolds number of about 4000.
The transition occurs if the size of the object is gradually increased, or the viscosity of the fluid is decreased, or if the density of the fluid is increased.
Heat and momentum transfer
When flow is turbulent, particles exhibit additional transverse motion which enhances the rate of energy and momentum exchange between them thus increasing the heat transfer and the friction coefficient.
Assume for a two-dimensional turbulent flow that one was able to locate a specific point in the fluid and measure the actual flow velocity of every particle that passed through that point at any given time. Then one would find the actual flow velocity fluctuating about a mean value: | Turbulence | Wikipedia | 507 | 154664 | https://en.wikipedia.org/wiki/Turbulence | Physical sciences | Fluid mechanics | null |
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