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Alinea (2 species)
Aspronema (2 species)
Brasiliscincus (3 species)
Capitellum (3 species)
Chioninia (7 species)
Copeoglossum (5 species)
Dasia (10 species)
Eumecia (2 species)
Eutropis (48 species)
Exila (1 species)
Heremites (3 species)
Lubuya (1 species)
Mabuya (9 species)
Manciola (1 species)
Maracaiba (2 species)
Marisora (13 species)
Notomabuya (1 species)
Otosaurus (1 species)
Panopa (2 species)
Psychosaura (2 species)
Spondylurus (17 species)
Toenayar (1 species)
Trachylepis (87 species)
Varzea (2 species)
Vietnascincus (1 species)
Subfamily Sphenomorphinae (sphenomorphid skinks; 591 species in 41 genera) | Skink | Wikipedia | 199 | 323825 | https://en.wikipedia.org/wiki/Skink | Biology and health sciences | Reptiles | null |
Anomalopus (4 species)
Calorodius (1 species)
Calyptotis (4 species)
Coeranoscincus (2 species)
Coggeria (1 species)
Concinnia (7 species)
Ctenotus (103 species)
Eremiascincus (15 species)
Eulamprus (5 species)
Fojia (1 species)
Glaphyromorphus (11 species)
Gnypetoscincus (1 species)
Hemiergis (7 species)
Insulasaurus (4 species)
Isopachys (4 species)
Kaestlea (5 species)
Lankascincus (10 species)
Larutia (9 species)
Leptoseps (2 species)
Lerista (97 species)
Lipinia (28 species)
Nangura (1 species)
Notoscincus (2 species)
Ophioscincus (3 species)
Ornithuroscincus (9 species)
Orosaura (1 species)
Palaia (1 species)
Papuascincus (4 species)
Parvoscincus (24 species)
Pinoyscincus (5 species)
Praeteropus (4 species)
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Protoblepharus (3 species)
Ristella (4 species)
Saiphos (1 species)
Scincella (38 species)
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Silvascincus (2 species)
Sphenomorphus (113 species)
Tropidophorus (29 species)
Tumbunascincus (1 species)
Tytthoscincus (23 species)
Subfamily Scincinae (typical skinks; 294 species in 35 genera) | Skink | Wikipedia | 347 | 323825 | https://en.wikipedia.org/wiki/Skink | Biology and health sciences | Reptiles | null |
Amphiglossus (2 species)
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Chalcidoseps (1 species)
Eumeces (6 species)
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Feylinia (6 species)
Flexiseps (15 species)
Gongylomorphus (3 species)
Grandidierina (4 species)
Hakaria (1 species)
Janetaescincus (2 species)
Jarujinia (1 species)
Madascincus (12 species)
Melanoseps (8 species)
Mesoscincus (3 species)
Nessia (9 species)
Ophiomorus (12 species)
Pamelaescincus (1 species)
Paracontias (14 species)
Plestiodon (50 species)
Proscelotes (3 species)
Pseudoacontias (4 species)
Pygomeles (3 species)
Scelotes (22 species)
Scincopus (1 species)
Scincus (5 species)
Scolecoseps (4 species)
Sepsina (5 species)
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Gallery | Skink | Wikipedia | 274 | 323825 | https://en.wikipedia.org/wiki/Skink | Biology and health sciences | Reptiles | null |
Subsistence agriculture occurs when farmers grow crops on smallholdings to meet the needs of themselves and their families. Subsistence agriculturalists target farm output for survival and for mostly local requirements. Planting decisions occur principally with an eye toward what the family will need during the coming year, and only secondarily toward market prices. Tony Waters, a professor of sociology, defines "subsistence peasants" as "people who grow what they eat, build their own houses, and live without regularly making purchases in the marketplace".
Despite the self-sufficiency in subsistence farming, most subsistence farmers also participate in trade to some degree. Although their amount of trade as measured in cash is less than that of consumers in countries with modern complex markets, they use these markets mainly to obtain goods, not to generate income for food; these goods are typically not necessary for survival and may include sugar, iron roofing-sheets, bicycles, used clothing, and so forth. Many have important trade contacts and trade items that they can produce because of their special skills or special access to resources valued in the marketplace.
Subsistence farming today is most common in developing countries. Subsistence agriculture generally features: small capital/finance requirements, mixed cropping, limited use of agrochemicals (e.g. pesticides and fertilizer), unimproved varieties of crops and animals, little or no surplus yield for sale, use of crude/traditional tools (e.g. hoes, machetes, and cutlasses), mainly the production of crops, small scattered plots of land, reliance on unskilled labor (often family members), and (generally) low yields.
History
Subsistence agriculture was the dominant mode of production in the world until recently, when market-based capitalism became widespread.
Subsistence agriculture largely disappeared in Europe by the beginning of the twentieth century. It began to decrease in North America with the movement of sharecroppers and tenant farmers out of the American South and Midwest during the 1930s and 1940s. In Central and Eastern Europe, semi-subsistence agriculture reappeared within the transition economy after 1990 but declined in significance (or disappeared) in most countries by the accession to the EU in 2004 or 2007. | Subsistence agriculture | Wikipedia | 440 | 323964 | https://en.wikipedia.org/wiki/Subsistence%20agriculture | Technology | Forms | null |
Contemporary practices
Subsistence farming continues today in large parts of rural Africa, and parts of Asia and Latin America. In 2015, about 2 billion people (slightly more than 25% of the world's population) in 500 million households living in rural areas of developing nations survive as "smallholder" farmers, working less than 2 hectares (5 acres) of land. Around 98% of China's farmers work on small farms, and China accounts for around half of the total world farms. In India, 80% of the total farmers are smallholder farmers; Ethiopia and Asia have almost 90% being small; while Mexico and Brazil recorded 50% and 20% being small.
Areas where subsistence farming is largely practiced today, such as India and other regions in Asia, have seen a recent decline in the practice. This is due to processes such as urbanization, the transformation of land into rural areas, and integration of capitalist forms of farming. In India, the increase in industrialization and decrease in rural agriculture has led to rural unemployment and increased poverty for those in lower caste groups. Those that are able to live and work in urbanized areas are able to increase their income while those that remain in rural areas take large decreases, which is why there was no large decline in poverty. This effectively widens the income gap between lower and higher castes and makes it harder for those in rural areas to move up in caste ranking. This era has marked a time of increased farmer suicides and the "vanishing village". | Subsistence agriculture | Wikipedia | 301 | 323964 | https://en.wikipedia.org/wiki/Subsistence%20agriculture | Technology | Forms | null |
Adaptation to global warming
Most subsistence agriculture is practiced in developing countries located in tropical climates. Effects on crop production brought about by climate change will be more intense in these regions as extreme temperatures are linked to lower crop yields. Farmers have been forced to respond to increased temperatures through things such as increased land and labor inputs which threaten long-term productivity. Coping measures in response to variable climates can include reducing daily food consumption and selling livestock to compensate for the decreased productivity. These responses often threaten the future of household farms in the following seasons as many farmers will sell draft animals used for labor and will also consume seeds saved for planting. Measuring the full extent of future climate change impacts is difficult to determine as smallholder farms are complex systems with many different interactions. Different locations have different adaptation strategies available to them such as crop and livestock substitutions. Rates of production for cereal crops, such as wheat, oats, and maize have been declining largely due to heat's effects on crop fertility. This has forced many farmers to switch to more heat tolerant crops to maintain levels of productivity. Substitution of crops for heat tolerant alternatives limits the overall diversity of crops grown on smallholder farms. As many farmers farm to meet daily food needs, this can negatively impact nutrition and diet among many families practicing subsistence agriculture.
Water availability has a crucial role in determining the productivity of subsistence agriculture, especially in dryland regions. Rain-needed farming, common in many areas, relies only on natural precipitation. Because of this, dryland farming is particularly susceptible to the ill effects of climate change in areas where weather patterns are already very erratic.doi:10.3390/atmos11121287
Types of subsistence farming
Shifting agriculture | Subsistence agriculture | Wikipedia | 339 | 323964 | https://en.wikipedia.org/wiki/Subsistence%20agriculture | Technology | Forms | null |
In this type of farming, a patch of forest land is cleared by a combination of felling (chopping down) and burning, and crops are grown. After two–three years the fertility of the soil begins to decline, the land is abandoned and the farmer moves to clear a fresh piece of land elsewhere in the forest as the process continues. While the land is left fallow the forest regrows in the cleared area and soil fertility and biomass is restored. After a decade or more, the farmer may return to the first piece of land. This form of agriculture is sustainable at low population densities, but higher population loads require more frequent clearing which prevents soil fertility from recovering, opens up more of the forest canopy, and encourages scrub at the expense of large trees, eventually resulting in deforestation and soil erosion. Shifting cultivation is called dredd in India, ladang in Indonesia and jhumming in North East India.
Sedentary farming
While shifting agriculture's slash-and-burn technique may describe the method for opening new land, commonly the farmers in question have in existence at the same time smaller fields, sometimes merely gardens, near the homestead there they practice intensive "non-shifting" techniques. These farmers pair this with "slash and burn" techniques to clear additional land and (by the burning) provide fertilizer (ash). Such gardens near the homestead often regularly receive household refuse. The manure of any household chickens or goats are initially thrown into compost piles just to get them out of the way. However, such farmers often recognize the value of such compost and apply it regularly to their smaller fields. They also may irrigate part of such fields if they are near a source of water.
In some areas of tropical Africa, at least, such smaller fields may be ones in which crops are grown on raised beds. Thus farmers practicing "slash and burn" agriculture are often much more sophisticated agriculturalists than the term "slash and burn" subsistence farmers suggests. | Subsistence agriculture | Wikipedia | 402 | 323964 | https://en.wikipedia.org/wiki/Subsistence%20agriculture | Technology | Forms | null |
Nomadic herding
In this type of farming people migrate along with their animals from one place to another in search of fodder for their animals. Generally they rear cattle, sheep, goats, camels and/or yaks for milk, skin, meat and wool. This way of life is common in parts of central and western Asia, India, east and southwest Africa and northern Eurasia. Examples are the nomadic Bhotiyas and Gujjars of the Himalayas. They carry their belongings, such as tents, etc., on the backs of donkeys, horses, and camels. In mountainous regions, like Tibet and the Andes, yak and llama are reared. Reindeer are the livestock in arctic and sub-arctic areas. Sheep, goats, and camels are common animals, and cattle and horses are also important.
Intensive subsistence farming
In intensive subsistence agriculture, the farmer cultivates a small plot of land using simple tools and more labour. Climate with large number of days with sunshine and fertile soils, permits growing of more than one crop annually on the same plot. Farmers use their small land holdings to produce enough for their local consumption, while remaining produce is used for exchange against other goods. It results in much more food being produced per acre compared to other subsistence patterns. In the most intensive situation, farmers may even create terraces along steep hillsides to cultivate rice paddies. Such fields are found in densely populated parts of Asia, such as in the Philippines. They may also intensify by using manure, artificial irrigation and animal waste as fertilizer. Intensive subsistence farming is prevalent in the thickly populated areas of the monsoon regions of south, southwest, and southeast Asia.
Poverty alleviation
Subsistence agriculture can be used as a poverty alleviation strategy, specifically as a safety net for food-price shocks and for food security. Poor countries are limited in fiscal and institutional resources that would allow them to contain rises in domestic prices as well as to manage social assistance programs, which is often because they are using policy tools that are intended for middle- and high-income countries. Low-income countries tend to have populations in which 80% of poor are in rural areas. More than 90% of rural households have access to land, yet most of these poor have insufficient access to food. Subsistence agriculture can be used in low-income countries as a part of policy responses to a food crisis in the short and medium term and provide a safety net for the poor in these countries. | Subsistence agriculture | Wikipedia | 506 | 323964 | https://en.wikipedia.org/wiki/Subsistence%20agriculture | Technology | Forms | null |
Agriculture is more successful than non-agricultural jobs in combating poverty in countries with a larger population of people without education or who are unskilled. However, there are levels of poverty to be aware of to target agriculture towards the right audience. Agriculture is better at reducing poverty in those that have an income of $1 per day than those that have an income of $2 per day in Africa. People who make less income are more likely to be poorly educated and have fewer opportunities; therefore, they work more labor-intensive jobs, such as agriculture. People who make $2 have more opportunities to work in less labor-intensive jobs in non-agricultural fields. | Subsistence agriculture | Wikipedia | 133 | 323964 | https://en.wikipedia.org/wiki/Subsistence%20agriculture | Technology | Forms | null |
The Eurasian collared dove (Streptopelia decaocto), often simply just collared dove, is a dove species native to Europe, Asia, and northern Africa. It has also been introduced to Japan, North and Central America, and the islands in the Caribbean.
Taxonomy
The Hungarian naturalist Imre Frivaldszky first described the Eurasian collared dove with the scientific name Columba risoria varietas C. decaocto in 1838, considering it a wild variety of the domesticated barbary dove. The type locality is Plovdiv in Bulgaria. It is now placed in genus Streptopelia that was described in 1855 by the French ornithologist Charles Lucien Bonaparte.
The Burmese collared dove (S. xanthocycla) was formerly considered a subspecies of the Eurasian collared dove, but was split as a distinct species by the IOC in 2021. Two other subspecies were formerly sometimes accepted, S. d. stoliczkae from Turkestan in central Asia and S. d. intercedens from southern India and Sri Lanka; they are now considered junior synonyms of the species.
The Eurasian collared dove is also closely related to the Sunda collared dove of southeast Asia and the African collared dove of Sub-Saharan Africa, forming a superspecies with these. Identification from the African collared dove is very difficult with silent birds, with the African species being marginally smaller and paler, but the calls are very distinct, a soft purring "Cou'crrrrroouw" in the African collared dove quite unlike the Eurasian collared dove's three-note cooing. | Eurasian collared dove | Wikipedia | 348 | 323988 | https://en.wikipedia.org/wiki/Eurasian%20collared%20dove | Biology and health sciences | Columbimorphae | Animals |
Etymology
The generic name is from the Ancient Greek streptos meaning "collar" and peleia meaning "dove". The specific epithet, decaocto, is Greek for "eighteen". The association of the dove with the number eighteen has its roots in a Greek myth. A maid who worked hard for little money was unhappy that she was only paid 18 silver coins a year and begged the gods to let the world know how little she was rewarded by her mistress. Zeus, hearing her pleas, created the collared dove, which has called out "decaocto" ever since to tell the world of the maid's mistreatment. In several Balkan languages, the number 18 is a three-syllable word (e.g. tiz-en-nyolc in Frivaldszky's native Hungarian), so is ultimately onomatopoeic from the bird's call.
As most of its European range in the 19th century, including its type locality, was within the Turkish-controlled Ottoman Empire, its name in many European languages translates as Turkish dove, e.g. Danish Tyrkerdue, German Türkentaube, French Tourterelle turque.
Description | Eurasian collared dove | Wikipedia | 249 | 323988 | https://en.wikipedia.org/wiki/Eurasian%20collared%20dove | Biology and health sciences | Columbimorphae | Animals |
The Eurasian collared dove is a medium-sized dove, distinctly smaller than the wood pigeon, similar in length to a rock dove but slimmer and longer-tailed, and slightly larger than the related European turtle dove, with an average length of from tip of beak to tip of tail, with a wingspan of , and a weight of . It is grey-buff to pinkish-grey overall, a little darker above than below, with a blue-grey underwing patch. The tail feathers are grey-buff above, and dark grey and tipped white below; the outer tail feathers are also tipped whitish above. It has a black half-collar edged with white on its nape from which it gets its name. The short legs are red and the bill is black. The iris is red, but from a distance the eyes appear to be black, as the pupil is relatively large and only a narrow rim of reddish-brown iris can be seen around the black pupil. The eye is surrounded by a small area of bare skin, which is either white or yellow. The two sexes are virtually indistinguishable; juveniles differ in having a poorly developed collar, and a brown iris. The subspecies S. d. xanthocycla differs in having yellow rather than white eye-rings, darker grey on the head and the underparts a slightly darker pink.
The song is a three-syllable goo-GOO-goo, with stress placed on the second syllable. The Eurasian collared dove also makes a harsh loud screeching call lasting about two seconds, particularly in flight just before landing. A rough way to describe the screeching sound is a hah-hah.
Eurasian collared doves cooing in early spring are sometimes mistakenly reported as the calls of early-arriving common cuckoos and, as such, a mistaken sign of spring's return.
Distribution and habitat | Eurasian collared dove | Wikipedia | 383 | 323988 | https://en.wikipedia.org/wiki/Eurasian%20collared%20dove | Biology and health sciences | Columbimorphae | Animals |
The Eurasian collared dove is not migratory, but is strongly dispersive. Over the last century, it has been one of the great colonisers of the bird world, travelling far beyond its native range to colonise colder countries, becoming a permanent resident in several of them. Its original range at the end of the 19th century was warm temperate and subtropical Asia from Turkey east to southern China and south through India to Sri Lanka. In 1838 it was reported in Bulgaria, but not until the 20th century did it expand across Europe, appearing in parts of the Balkans between 1900 and 1920, and then spreading rapidly northwest, reaching Germany in 1945, Great Britain by 1953 (breeding for the first time in 1956), Ireland in 1959, and the Faroe Islands in the early 1970s. Subsequent spread was 'sideways' from this fast northwestern spread, reaching northeast to north of the Arctic Circle in Norway and east to the Ural Mountains in Russia, and southwest to the Canary Islands and northern Africa from Morocco to Egypt, by the end of the 20th century. In the east of its range, it has also spread northeast to most of central and northern China, and locally (probably introduced) in Japan. It has also reached Iceland as a vagrant (41 records up to 2006), but has not colonised successfully there.
Invasive status in North America
In 1974, fewer than 50 Eurasian collared doves escaped captivity in Nassau, New Providence, Bahamas. From the Bahamas, the species spread to Florida, and is now found in nearly every state in the U.S., as well as in Mexico. In Arkansas (the United States), the species was recorded first in 1989 and since then has grown in numbers and is now present in 42 of 75 counties in the state. It spread from the southeastern corner of the state in 1997 to the northwestern corner in five years, covering a distance of about at a rate of per year. This is more than double the rate of per year observed in Europe. As of 2012, few negative impacts have been demonstrated in Florida, where the species is most prolific. However, the species is known as an aggressive competitor and there is concern that as populations continue to grow, native birds will be out-competed by the invaders. One study, however, found that Eurasian collared doves are not more aggressive or competitive than native mourning doves, despite similar dietary preferences. | Eurasian collared dove | Wikipedia | 483 | 323988 | https://en.wikipedia.org/wiki/Eurasian%20collared%20dove | Biology and health sciences | Columbimorphae | Animals |
Population growth has ceased in areas where the species has long been established, such as Florida, and in these regions, recent observations suggest the population is in decline. The population is still growing exponentially in areas of more recent introduction; up to 2015, the Eurasian collared dove experienced a greater than 1.5% yearly population increase throughout nearly the entirety of its North American range. Carrying capacities appear to be highest in areas with higher temperatures and intermediate levels of development, such as suburban areas and some agricultural areas.
While the spread of disease to native species has not been recorded in a study, Eurasian collared doves are known carriers of the parasite Trichomonas gallinae and pigeon paramyxovirus type 1. Both Trichomonas gallinae and pigeon paramyxovirus type 1 can spread to native birds via commingling at feeders and by consumption of doves by predators. Pigeon paramyxovirus type 1 is an emergent disease and has the potential to affect domestic poultry, making the Eurasian collared dove a threat to not only native biodiversity, but a possible economic threat, as well.
Behaviour and ecology
Breeding
Eurasian collared doves typically breed close to human habitation wherever food resources are abundant and trees are available for nesting; almost all nests are within of inhabited buildings. The female lays two white eggs in a stick nest, which she incubates during the night and which the male incubates during the day. Incubation lasts between 14 and 18 days, with the young fledging after 15 to 19 days. Breeding occurs throughout the year when abundant food is available, though only rarely in winter in areas with cold winters such as northeastern Europe. Three to four broods per year are common, although up to six broods in a year have been recorded. Eurasian collared doves are a monogamous species, and share parental duties when caring for young.
The male's mating display is a ritual flight, which, as with many other pigeons, consists of a rapid, near-vertical climb to height followed by a long glide downward in a circle, with the wings held below the body in an inverted "V" shape. At all other times, flight is typically direct using fast and clipped wing beats and without use of gliding. | Eurasian collared dove | Wikipedia | 461 | 323988 | https://en.wikipedia.org/wiki/Eurasian%20collared%20dove | Biology and health sciences | Columbimorphae | Animals |
Food and feeding
The Eurasian collared dove is not wary and often feeds very close to human habitation, including visiting bird tables; the largest populations are typically found around farms where spilt grain is frequent around grain stores or where livestock are fed. It is a gregarious species and sizeable winter flocks form around food supplies such as grain (its main food), seeds, shoots, and insects. Flocks most commonly number between 10 and 50, but flocks of up to 10,000 have been recorded. | Eurasian collared dove | Wikipedia | 106 | 323988 | https://en.wikipedia.org/wiki/Eurasian%20collared%20dove | Biology and health sciences | Columbimorphae | Animals |
A cash crop, also called profit crop, is an agricultural crop which is grown to sell for profit. It is typically purchased by parties separate from a farm. The term is used to differentiate a marketed crop from a staple crop ("subsistence crop") in subsistence agriculture, which is one fed to the producer's own livestock or grown as food for the producer's family.
In earlier times, cash crops were usually only a small (but vital) part of a farm's total yield, while today, especially in developed countries and among smallholders almost all crops are mainly grown for revenue. In the least developed countries, cash crops are usually crops which attract demand in more developed nations, and hence have some export value.
Prices for major cash crops are set in international trade markets with global scope, with some local variation (termed as "basis") based on freight costs and local supply and demand balance. A consequence of this is that a nation, region, or individual producer relying on such a crop may suffer low prices should a bumper crop elsewhere lead to excess supply on the global markets. This system has been criticized by traditional farmers. Coffee is an example of a product that has been susceptible to significant commodity futures price variations.
Globalization
Issues involving subsidies and trade barriers on such crops have become controversial in discussions of globalization. Many developing countries take the position that the current international trade system is unfair because it has caused tariffs to be lowered in industrial goods while allowing for low tariffs and agricultural subsidies for agricultural goods. This makes it difficult for a developing nation to export its goods overseas, and forces developing nations to compete with imported goods which are exported from developed nations at artificially low prices. The practice of exporting at artificially low prices is known as dumping, and is illegal in most nations. Controversy over this issue led to the collapse of the Cancún trade talks in 2003, when the Group of 22 refused to consider agenda items proposed by the European Union unless the issue of agricultural subsidies was addressed.
Per climate zones
Arctic
The Arctic climate is generally not conducive for the cultivation of cash crops. However, one potential cash crop for the Arctic is Rhodiola rosea, a hardy plant used as a medicinal herb that grows in the Arctic. There is currently consumer demand for the plant, but the available supply is less than the demand (as of 2011). | Cash crop | Wikipedia | 478 | 323990 | https://en.wikipedia.org/wiki/Cash%20crop | Technology | Basics_2 | null |
Temperate
Cash crops grown in regions with a temperate climate include many cereals (wheat, rye, corn, barley, oats), oil-yielding crops (e.g. grapeseed, mustard seeds), vegetables (e.g. potatoes), lumber yielding trees (e.g. Spruce, Pines, Firs), tree fruit or top fruit (e.g. apples, cherries) and soft fruit (e.g. strawberries, raspberries).
Subtropical
In regions with a subtropical climate, oil-yielding crops (e.g. soybeans), cotton, rice, tobacco, indigo, citrus, pomegranates, and some vegetables and herbs are the predominant cash crops.
Tropical
In regions with a tropical climate, coffee, cocoa, sugar cane, bananas, oranges, cotton and jute are common cash crops. The oil palm is a tropical palm tree, and the fruit from it is used to make palm oil. The impact of climate change on the ranges of pests and diseasesespecially those of coffee, cocoa, and bananais commonly underestimated. Limiting temperature rise to is vital to maintaining productivity in the tropics.
By continent and country
Africa
Around 60 percent of African workers are employed in the agricultural sector, with about three-fifths of African farmers being subsistence farmers. For example, in Burkina Faso 85% of its residents (over two million people) are reliant upon cotton production for income, and over half of the country's population lives in poverty. Larger farms tend to grow cash crops such as coffee, tea, cotton, cocoa, fruit and rubber. These farms, typically operated by large corporations, cover dozens of square kilometres and employ large numbers of laborers. Subsistence farms provide a source of food and a relatively small income for families, but generally fail to produce enough to make re-investment possible.
The situation in which African nations export crops while a significant number of people on the continent struggle with hunger has been blamed on developed countries, including the United States, Japan and the European Union. These countries protect their own agricultural sectors, through high import tariffs and offer subsidies to their farmers, which some have contended is leading to the overproduction of commodities such as cotton, grain and milk. The result of this is that the global price of such products is continually reduced until Africans are unable to compete in world markets, except in cash crops that do not grow easily in temperate climates. | Cash crop | Wikipedia | 502 | 323990 | https://en.wikipedia.org/wiki/Cash%20crop | Technology | Basics_2 | null |
Africa has realized significant growth in biofuel plantations, many of which are on lands which were purchased by British companies. Jatropha curcas is a cash crop grown for biofuel production in Africa. Some have criticized the practice of raising non-food plants for export while Africa has problems with hunger and food shortages, and some studies have correlated the proliferation of land acquisitions, often for use to grow non-food cash crops with increasing hunger rates in Africa.
Australia
Australia produces significant amounts of lentils. It was estimated in 2010 that Australia would produce approximately 143,000 tons of lentils. Most of Australia's lentil harvest is exported to the Indian subcontinent and the Middle East.
Italy
Italy's Cassa per il Mezzogiorno in 1950 led to the government implementing incentives to grow cash crops such as tomatoes, tobacco and citrus fruits. As a result, they created an over abundance of these crops causing an over saturation of these crops on the global market. This caused these crops to depreciate.
United States
Cash cropping in the United States dates back to the colonial period with crops like tobacco, indigo, cotton and others farmed on massive scales on southern plantations primarily fueled by black slave labor, even after the end of slavery this system continued in some form with the share cropping system where farmers would live and work on large plantations for a share of the crop to sell themselves. Cash cropping of fruits rose to prominence after the baby boomer generation and the end of World War II. It was seen as a way to feed the large population boom and continues to be the main factor in having an affordable food supply in the United States. According to the 1997 U.S. Census of Agriculture, 90% of the farms in the United States are still owned by families, with an additional 6% owned by a partnership. Cash crop farmers have utilized precision agricultural technologies combined with time-tested practices to produce affordable food. Based upon United States Department of Agriculture (USDA) statistics for 2010, states with the highest fruit production quantities are California, Florida and Washington.
Vietnam
Coconut is a cash crop of Vietnam.
Global cash crops
Coconut palms are cultivated in more than 80 countries of the world, with a total production of 61 million tonnes per year. The oil and milk derived from it are commonly used in cooking and frying; coconut oil is also widely used in soaps and cosmetics. | Cash crop | Wikipedia | 486 | 323990 | https://en.wikipedia.org/wiki/Cash%20crop | Technology | Basics_2 | null |
Sustainability of cash crops
Approximately 70% of the world's food is produced by 500 million smallholder farmers. For their livelihood they depend on the production of cash crops, basic commodities that are hard to differentiate in the market. The great majority (80%) of the world's farms measure 2 hectares or less. These smallholder farmers are mainly found in developing countries and are often unorganized, illiterate or have only basic education. Smallholder farmers have little bargaining power and incomes are low, leading to a situation in which they cannot invest much in upscaling their businesses. In general, farmers lack access to agricultural inputs and finance, and do not have enough knowledge on good agricultural and business practices. These high level problems are in many cases threatening the future of agricultural sectors and theories start evolving on how to secure a sustainable future for agriculture. Sustainable market transformations are initiated in which industry leaders work together in a pre-competitive environment to change market conditions. Sustainable intensification focuses on facilitating entrepreneurial farmers. To stimulate farm investment, projects on access to finance for agriculture are also popping up. One example is the SCOPE methodology, an assessment tool that measures the management maturity and professionalism of producer organizations as to give financing organizations better insights in the risks involved in financing. Currently, agricultural finance is always considered risky and avoided by financial institutions.
Black market cash crops
Coca, opium poppies and cannabis are significant black market cash crops, the prevalence of which varies. In the United States, cannabis is considered by some to be the most valuable cash crop. In 2006, it was reported in a study by Jon Gettman, a marijuana policy researcher, that in contrast to government figures for legal crops such as corn and wheat and using the study's projections for U.S. cannabis production at that time, cannabis was cited as "the top cash crop in 12 states and among the top three cash crops in 30". The study also estimated cannabis production at the time (in 2006) to be valued at US$35.8 billion, which exceeded the combined value of corn at $23.3 billion and wheat at $7.5 billion. | Cash crop | Wikipedia | 433 | 323990 | https://en.wikipedia.org/wiki/Cash%20crop | Technology | Basics_2 | null |
In computer programming, a parameter or a formal argument is a special kind of variable used in a subroutine to refer to one of the pieces of data provided as input to the subroutine. These pieces of data are the values of the arguments (often called actual arguments or actual parameters) with which the subroutine is going to be called/invoked. An ordered list of parameters is usually included in the definition of a subroutine, so that, each time the subroutine is called, its arguments for that call are evaluated, and the resulting values can be assigned to the corresponding parameters.
Unlike argument in usual mathematical usage, the argument in computer science is the actual input expression passed/supplied to a function, procedure, or routine in the invocation/call statement, whereas the parameter is the variable inside the implementation of the subroutine. For example, if one defines the add subroutine as def add(x, y): return x + y, then x, y are parameters, while if this is called as add(2, 3), then 2, 3 are the arguments. Variables (and expressions thereof) from the calling context can be arguments: if the subroutine is called as a = 2; b = 3; add(a, b) then the variables a, b are the arguments, not the values 2, 3. See the Parameters and arguments section for more information.
The semantics for how parameters can be declared and how the (value of) arguments are passed to the parameters of subroutines are defined by the evaluation strategy of the language, and the details of how this is represented in any particular computer system depend on the calling convention of that system. In the most common case, call by value, a parameter acts within the subroutine as a new local variable initialized to the value of the argument (a local (isolated) copy of the argument if the argument is a variable), but in other cases, e.g. call by reference, the argument variable supplied by the caller can be affected by actions within the called subroutine.
Example
The following program in the C programming language defines a function that is named "SalesTax" and has one parameter named "price". The type of price is "double" (i.e. a double-precision floating point number). The function's return type is also a double.
double SalesTax(double price)
{
return 0.05 * price;
} | Parameter (computer programming) | Wikipedia | 507 | 324375 | https://en.wikipedia.org/wiki/Parameter%20%28computer%20programming%29 | Technology | Software development: General | null |
After the function has been defined, it can be invoked as follows:
SalesTax(10.00);
In this example, the function has been invoked with the argument 10.00. When this happens, 10.00 will be assigned to price, and the function begins calculating its result. The steps for producing the result are specified below, enclosed in {}. 0.05 * price indicates that the first thing to do is multiply 0.05 by the value of price, which gives 0.50. return means the function will produce the result of 0.05 * price. Therefore, the final result (ignoring possible round-off errors one encounters with representing decimal fractions as binary fractions) is 0.50.
Parameters and arguments
The terms parameter and argument may have different meanings in different programming languages. Sometimes they are used interchangeably, and the context is used to distinguish the meaning. The term parameter (sometimes called formal parameter) is often used to refer to the variable as found in the function declaration, while argument (sometimes called actual parameter) refers to the actual input supplied at a function call statement. For example, if one defines a function as def f(x): ..., then x is the parameter, and if it is called by a = ...; f(a) then a is the argument. A parameter is an (unbound) variable, while the argument can be a literal or variable or more complex expression involving literals and variables. In case of call by value, what is passed to the function is the value of the argument – for example, f(2) and a = 2; f(a) are equivalent calls – while in call by reference, with a variable as argument, what is passed is a reference to that variable - even though the syntax for the function call could stay the same. The specification for pass-by-reference or pass-by-value would be made in the function declaration and/or definition.
Parameters appear in procedure definitions; arguments appear in procedure calls. In the function definition f(x) = x*x the variable x is a parameter; in the function call f(2) the value 2 is the argument of the function. Loosely, a parameter is a type, and an argument is an instance. | Parameter (computer programming) | Wikipedia | 468 | 324375 | https://en.wikipedia.org/wiki/Parameter%20%28computer%20programming%29 | Technology | Software development: General | null |
A parameter is an intrinsic property of the procedure, included in its definition. For example, in many languages, a procedure to add two supplied integers together and calculate the sum would need two parameters, one for each integer. In general, a procedure may be defined with any number of parameters, or no parameters at all. If a procedure has parameters, the part of its definition that specifies the parameters is called its parameter list.
By contrast, the arguments are the expressions supplied to the procedure when it is called, usually one expression matching one of the parameters. Unlike the parameters, which form an unchanging part of the procedure's definition, the arguments may vary from call to call. Each time a procedure is called, the part of the procedure call that specifies the arguments is called the argument list.
Although parameters are also commonly referred to as arguments, arguments are sometimes thought of as the actual values or references assigned to the parameter variables when the subroutine is called at run-time. When discussing code that is calling into a subroutine, any values or references passed into the subroutine are the arguments, and the place in the code where these values or references are given is the parameter list. When discussing the code inside the subroutine definition, the variables in the subroutine's parameter list are the parameters, while the values of the parameters at runtime are the arguments. For example, in C, when dealing with threads it is common to pass in an argument of type void* and cast it to an expected type:
void ThreadFunction(void* pThreadArgument)
{
// Naming the first parameter 'pThreadArgument' is correct, rather than
// 'pThreadParameter'. At run time the value we use is an argument. As
// mentioned above, reserve the term parameter for when discussing
// subroutine definitions.
}
To better understand the difference, consider the following function written in C:
int Sum(int addend1, int addend2)
{
return addend1 + addend2;
}
The function Sum has two parameters, named addend1 and addend2. It adds the values passed into the parameters, and returns the result to the subroutine's caller (using a technique automatically supplied by the C compiler). | Parameter (computer programming) | Wikipedia | 475 | 324375 | https://en.wikipedia.org/wiki/Parameter%20%28computer%20programming%29 | Technology | Software development: General | null |
The code which calls the Sum function might look like this:
int value1 = 40;
int value2 = 2;
int sum_value = Sum(value1, value2);
The variables value1 and value2 are initialized with values. value1 and value2 are both arguments to the sum function in this context.
At runtime, the values assigned to these variables are passed to the function Sum as arguments. In the Sum function, the parameters addend1 and addend2 are evaluated, yielding the arguments 40 and 2, respectively. The values of the arguments are added, and the result is returned to the caller, where it is assigned to the variable sum_value.
Because of the difference between parameters and arguments, it is possible to supply inappropriate arguments to a procedure. The call may supply too many or too few arguments; one or more of the arguments may be a wrong type; or arguments may be supplied in the wrong order. Any of these situations causes a mismatch between the parameter and argument lists, and the procedure will often return an unintended answer or generate a runtime error.
Alternative convention in Eiffel
Within the Eiffel software development method and language, the terms argument and parameter have distinct uses established by convention. The term argument is used exclusively in reference to a routine's inputs, and the term parameter is used exclusively in type parameterization for generic classes.
Consider the following routine definition:
sum (addend1: INTEGER; addend2: INTEGER): INTEGER
do
Result := addend1 + addend2
end
The routine sum takes two arguments addend1 and addend2, which are called the routine's formal arguments. A call to sum specifies actual arguments, as shown below with value1 and value2.
sum_value: INTEGER
value1: INTEGER = 40
value2: INTEGER = 2
…
sum_value := sum (value1, value2)
Parameters are also thought of as either formal or actual. Formal generic parameters are used in the definition of generic classes. In the example below, the class HASH_TABLE is declared as a generic class which has two formal generic parameters, G representing data of interest and K representing the hash key for the data:
class HASH_TABLE [G, K -> HASHABLE]
… | Parameter (computer programming) | Wikipedia | 468 | 324375 | https://en.wikipedia.org/wiki/Parameter%20%28computer%20programming%29 | Technology | Software development: General | null |
When a class becomes a client to HASH_TABLE, the formal generic parameters are substituted with actual generic parameters in a generic derivation. In the following attribute declaration, my_dictionary is to be used as a character string based dictionary. As such, both data and key formal generic parameters are substituted with actual generic parameters of type STRING.
my_dictionary: HASH_TABLE [STRING, STRING]
Datatypes
In strongly typed programming languages, each parameter's type must be specified in the procedure declaration. Languages using type inference attempt to discover the types automatically from the function's body and usage. Dynamically typed programming languages defer type resolution until run-time. Weakly typed languages perform little to no type resolution, relying instead on the programmer for correctness.
Some languages use a special keyword (e.g. void) to indicate that the subroutine has no parameters; in formal type theory, such functions take an empty parameter list (whose type is not void, but rather unit).
Argument passing
The exact mechanism for assigning arguments to parameters, called argument passing, depends upon the evaluation strategy used for that parameter (typically call by value), which may be specified using keywords.
Default arguments
Some programming languages such as Ada, C++, Clojure, Common Lisp, Fortran 90, Python, Ruby, Tcl, and Windows PowerShell allow for a default argument to be explicitly or implicitly given in a subroutine's declaration. This allows the caller to omit that argument when calling the subroutine. If the default argument is explicitly given, then that value is used if it is not provided by the caller. If the default argument is implicit (sometimes by using a keyword such as Optional) then the language provides a well-known value (such as null, Empty, zero, an empty string, etc.) if a value is not provided by the caller.
PowerShell example:
function doc($g = 1.21) {
"$g gigawatts? $g gigawatts? Great Scott!"
}
PS > doc
1.21 gigawatts? 1.21 gigawatts? Great Scott!
PS > doc 88
88 gigawatts? 88 gigawatts? Great Scott!
Default arguments can be seen as a special case of the variable-length argument list. | Parameter (computer programming) | Wikipedia | 481 | 324375 | https://en.wikipedia.org/wiki/Parameter%20%28computer%20programming%29 | Technology | Software development: General | null |
Variable-length parameter lists
Some languages allow subroutines to be defined to accept a variable number of arguments. For such languages, the subroutines must iterate through the list of arguments.
PowerShell example:
function marty {
$args | foreach { "back to the year $_" }
}
PS > marty 1985
back to the year 1985
PS > marty 2015 1985 1955
back to the year 2015
back to the year 1985
back to the year 1955
Named parameters
Some programming languages—such as Ada and Windows PowerShell—allow subroutines to have named parameters. This allows the calling code to be more self-documenting. It also provides more flexibility to the caller, often allowing the order of the arguments to be changed, or for arguments to be omitted as needed.
PowerShell example:
function jennifer($adjectiveYoung, $adjectiveOld) {
"Young Jennifer: I'm $adjectiveYoung!"
"Old Jennifer: I'm $adjectiveOld!"
}
PS > jennifer 'fresh' 'experienced'
Young Jennifer: I'm fresh!
Old Jennifer: I'm experienced!
PS > jennifer -adjectiveOld 'experienced' -adjectiveYoung 'fresh'
Young Jennifer: I'm fresh!
Old Jennifer: I'm experienced!
Multiple parameters in functional languages
In lambda calculus, each function has exactly one parameter. What is thought of as functions with multiple parameters is usually represented in lambda calculus as a function which takes the first argument, and returns a function which takes the rest of the arguments; this is a transformation known as currying. Some programming languages, like ML and Haskell, follow this scheme. In these languages, every function has exactly one parameter, and what may look like the definition of a function of multiple parameters, is actually syntactic sugar for the definition of a function that returns a function, etc. Function application is left-associative in these languages as well as in lambda calculus, so what looks like an application of a function to multiple arguments is correctly evaluated as the function applied to the first argument, then the resulting function applied to the second argument, etc. | Parameter (computer programming) | Wikipedia | 434 | 324375 | https://en.wikipedia.org/wiki/Parameter%20%28computer%20programming%29 | Technology | Software development: General | null |
Output parameters
An output parameter, also known as an out parameter or return parameter, is a parameter used for output, rather than the more usual use for input. Using call by reference parameters, or call by value parameters where the value is a reference, as output parameters is an idiom in some languages, notably C and C++, while other languages have built-in support for output parameters. Languages with built-in support for output parameters include Ada (see Ada subprograms), Fortran (since Fortran 90; see Fortran "intent"), various procedural extensions to SQL, such as PL/SQL (see PL/SQL functions) and Transact-SQL, C# and the .NET Framework, Swift, and the scripting language TScript (see TScript function declarations).
More precisely, one may distinguish three types of parameters or parameter modes: s, output parameters, and s; these are often denoted in, out, and in out or inout. An input argument (the argument to an input parameter) must be a value, such as an initialized variable or literal, and must not be redefined or assigned to; an output argument must be an assignable variable, but it need not be initialized, any existing value is not accessible, and must be assigned a value; and an input/output argument must be an initialized, assignable variable, and can optionally be assigned a value. The exact requirements and enforcement vary between languages – for example, in Ada 83 output parameters can only be assigned to, not read, even after assignment (this was removed in Ada 95 to remove the need for an auxiliary accumulator variable). These are analogous to the notion of a value in an expression being an r-value (has a value), an l-value (can be assigned), or an r-value/l-value (has a value and can be assigned), respectively, though these terms have specialized meanings in C.
In some cases only input and input/output are distinguished, with output being considered a specific use of input/output, and in other cases only input and output (but not input/output) are supported. The default mode varies between languages: in Fortran 90 input/output is default, while in C# and SQL extensions input is default, and in TScript each parameter is explicitly specified as input or output. | Parameter (computer programming) | Wikipedia | 491 | 324375 | https://en.wikipedia.org/wiki/Parameter%20%28computer%20programming%29 | Technology | Software development: General | null |
Syntactically, parameter mode is generally indicated with a keyword in the function declaration, such as void f(out int x) in C#. Conventionally output parameters are often put at the end of the parameter list to clearly distinguish them, though this is not always followed. TScript uses a different approach, where in the function declaration input parameters are listed, then output parameters, separated by a colon (:) and there is no return type to the function itself, as in this function, which computes the size of a text fragment:
TextExtent(WString text, Font font : Integer width, Integer height)
Parameter modes are a form of denotational semantics, stating the programmer's intent and allowing compilers to catch errors and apply optimizations – they do not necessarily imply operational semantics (how the parameter passing actually occurs). Notably, while input parameters can be implemented by call by value, and output and input/output parameters by call by reference – and this is a straightforward way to implement these modes in languages without built-in support – this is not always how they are implemented. This distinction is discussed in detail in the Ada '83 Rationale, which emphasizes that the parameter mode is abstracted from which parameter passing mechanism (by reference or by copy) is actually implemented. For instance, while in C# input parameters (default, no keyword) are passed by value, and output and input/output parameters (out and ref) are passed by reference, in PL/SQL input parameters (IN) are passed by reference, and output and input/output parameters (OUT and IN OUT) are by default passed by value and the result copied back, but can be passed by reference by using the NOCOPY compiler hint.
A syntactically similar construction to output parameters is to assign the return value to a variable with the same name as the function. This is found in Pascal and Fortran 66 and Fortran 77, as in this Pascal example:
function f(x, y: integer): integer;
begin
f := x + y;
end;
This is semantically different in that when called, the function is simply evaluated – it is not passed a variable from the calling scope to store the output in. | Parameter (computer programming) | Wikipedia | 461 | 324375 | https://en.wikipedia.org/wiki/Parameter%20%28computer%20programming%29 | Technology | Software development: General | null |
Use
The primary use of output parameters is to return multiple values from a function, while the use of input/output parameters is to modify state using parameter passing (rather than by shared environment, as in global variables). An important use of returning multiple values is to solve the semipredicate problem of returning both a value and an error status – see Semipredicate problem: Multivalued return.
For example, to return two variables from a function in C, one may write:
int width
int height;
F(x, &width, &height);
where x is an input parameter and width and height are output parameters.
A common use case in C and related languages is for exception handling, where a function places the return value in an output variable, and returns a Boolean corresponding to whether the function succeeded or not. An archetypal example is the TryParse method in .NET, especially C#, which parses a string into an integer, returning true on success and false on failure. This has the following signature:
public static bool TryParse(string s, out int result)
and may be used as follows:
int result;
if (!Int32.TryParse(s, result)) {
// exception handling
}
Similar considerations apply to returning a value of one of several possible types, where the return value can specify the type and then value is stored in one of several output variables.
Drawbacks
Output parameters are often discouraged in modern programming, essentially as being awkward, confusing, and too low-level – commonplace return values are considerably easier to understand and work with. Notably, output parameters involve functions with side effects (modifying the output parameter) and are semantically similar to references, which are more confusing than pure functions and values, and the distinction between output parameters and input/output parameters can be subtle. Further, since in common programming styles most parameters are simply input parameters, output parameters and input/output parameters are unusual and hence susceptible to misunderstanding. | Parameter (computer programming) | Wikipedia | 404 | 324375 | https://en.wikipedia.org/wiki/Parameter%20%28computer%20programming%29 | Technology | Software development: General | null |
Output and input/output parameters prevent function composition, since the output is stored in variables, rather than in the value of an expression. Thus one must initially declare a variable, and then each step of a chain of functions must be a separate statement. For example, in C++ the following function composition:
Object obj = G(y, F(x));
when written with output and input/output parameters instead becomes (for F it is an output parameter, for G an input/output parameter):
Object obj;
F(x, &obj);
G(y, &obj);
In the special case of a function with a single output or input/output parameter and no return value, function composition is possible if the output or input/output parameter (or in C/C++, its address) is also returned by the function, in which case the above becomes:
Object obj;
G(y, F(x, &obj));
Alternatives
There are various alternatives to the use cases of output parameters.
For returning multiple values from a function, an alternative is to return a tuple. Syntactically this is clearer if automatic sequence unpacking and parallel assignment can be used, as in Go or Python, such as:
def f():
return 1, 2
a, b = f()
For returning a value of one of several types, a tagged union can be used instead; the most common cases are nullable types (option types), where the return value can be null to indicate failure. For exception handling, one can return a nullable type, or raise an exception. For example, in Python one might have either:
result = parse(s)
if result is None:
# exception handling
or, more idiomatically:
try:
result = parse(s)
except ParseError:
# exception handling
The micro-optimization of not requiring a local variable and copying the return when using output variables can also be applied to conventional functions and return values by sufficiently sophisticated compilers.
The usual alternative to output parameters in C and related languages is to return a single data structure containing all return values. For example, given a structure encapsulating width and height, one can write:
WidthHeight width_and_height = F(x); | Parameter (computer programming) | Wikipedia | 478 | 324375 | https://en.wikipedia.org/wiki/Parameter%20%28computer%20programming%29 | Technology | Software development: General | null |
In object-oriented languages, instead of using input/output parameters, one can often use call by sharing, passing a reference to an object and then mutating the object, though not changing which object the variable refers to. | Parameter (computer programming) | Wikipedia | 46 | 324375 | https://en.wikipedia.org/wiki/Parameter%20%28computer%20programming%29 | Technology | Software development: General | null |
Mortar is a workable paste which hardens to bind building blocks such as stones, bricks, and concrete masonry units, to fill and seal the irregular gaps between them, spread the weight of them evenly, and sometimes to add decorative colours or patterns to masonry walls. In its broadest sense, mortar includes pitch, asphalt, and soft clay, as those used between bricks, as well as cement mortar. The word "mortar" comes from the Old French word mortier, "builder's mortar, plaster; bowl for mixing." (13c.).
Cement mortar becomes hard when it cures, resulting in a rigid aggregate structure; however, the mortar functions as a weaker component than the building blocks and serves as the sacrificial element in the masonry, because mortar is easier and less expensive to repair than the building blocks. Bricklayers typically make mortars using a mixture of sand, a binder, and water. The most common binder since the early 20th century is Portland cement, but the ancient binder lime (producing lime mortar) is still used in some specialty new construction. Lime, lime mortar, and gypsum in the form of plaster of Paris are used particularly in the repair and repointing of historic buildings and structures, so that the repair materials will be similar in performance and appearance to the original materials. Several types of cement mortars and additives exist.
Ancient mortar
The first mortars were made of mud and clay, as demonstrated in the 10th millennia BCE buildings of Jericho, and the 8th millennia BCE of Ganj Dareh.
According to Roman Ghirshman, the first evidence of humans using a form of mortar was at the Mehrgarh of Baluchistan in what is today Pakistan, built of sun-dried bricks in 6500 BCE.
Gypsum mortar, also called plaster of Paris, was used in the construction of many ancient structures. It is made from gypsum, which requires a lower firing temperature. It is therefore easier to make than lime mortar and sets up much faster, which may be a reason it was used as the typical mortar in ancient, brick arch and vault construction. Gypsum mortar is not as durable as other mortars in damp conditions.
In the Indian subcontinent, multiple cement types have been observed in the sites of the Indus Valley civilization, with gypsum appearing at sites such as the Mohenjo-daro city-settlement, which dates to earlier than 2600 BCE. | Mortar (masonry) | Wikipedia | 501 | 324498 | https://en.wikipedia.org/wiki/Mortar%20%28masonry%29 | Technology | Building materials | null |
Gypsum cement that was "light grey and contained sand, clay, traces of calcium carbonate, and a high percentage of lime" was used in the construction of wells, drains, and on the exteriors of "important looking buildings." Bitumen mortar was also used at a lower-frequency, including in the Great Bath at Mohenjo-daro.
In early Egyptian pyramids, which were constructed during the Old Kingdom (~2600–2500 BCE), the limestone blocks were bound by a mortar of mud and clay, or clay and sand. In later Egyptian pyramids, the mortar was made of gypsum, or lime. Gypsum mortar was essentially a mixture of plaster and sand and was quite soft.
2nd millennia BCE Babylonian constructions used lime or pitch for mortar.
Historically, building with concrete and mortar next appeared in Greece. The excavation of the underground aqueduct of Megara revealed that a reservoir was coated with a pozzolanic mortar 12 mm thick. This aqueduct dates back to c. 500 BCE. Pozzolanic mortar is a lime based mortar, but is made with an additive of volcanic ash that allows it to be hardened underwater; thus it is known as hydraulic cement. The Greeks obtained the volcanic ash from the Greek islands Thira and Nisiros, or from the then Greek colony of Dicaearchia (Pozzuoli) near Naples, Italy. The Romans later improved the use and methods of making what became known as pozzolanic mortar and cement. Even later, the Romans used a mortar without pozzolana using crushed terra cotta, introducing aluminum oxide and silicon dioxide into the mix. This mortar was not as strong as pozzolanic mortar, but, because it was denser, it better resisted penetration by water.
Hydraulic mortar was not available in ancient China, possibly due to a lack of volcanic ash. Around 500 CE, sticky rice soup was mixed with slaked lime to make an inorganic−organic composite sticky rice mortar that had more strength and water resistance than lime mortar.
It is not understood how the art of making hydraulic mortar and cement, which was perfected and in such widespread use by both the Greeks and Romans, was then lost for almost two millennia. During the Middle Ages when the Gothic cathedrals were being built, the only active ingredient in the mortar was lime. Since cured lime mortar can be degraded by contact with water, many structures suffered over the centuries from wind-blown rain.
Ordinary Portland cement mortar | Mortar (masonry) | Wikipedia | 506 | 324498 | https://en.wikipedia.org/wiki/Mortar%20%28masonry%29 | Technology | Building materials | null |
Ordinary Portland cement mortar, commonly known as OPC mortar or just cement mortar, is created by mixing powdered ordinary Portland cement, fine aggregate and water.
It was invented in 1794 by Joseph Aspdin and patented on 18 December 1824, largely as a result of efforts to develop stronger mortars. It was made popular during the late nineteenth century, and had by 1930 became more popular than lime mortar as construction material. The advantages of Portland cement is that it sets hard and quickly, allowing a faster pace of construction. Furthermore, fewer skilled workers are required in building a structure with Portland cement.
As a general rule, however, Portland cement should not be used for the repair or repointing of older buildings built in lime mortar, which require the flexibility, softness and breathability of lime if they are to function correctly.
In the United States and other countries, five standard types of mortar (available as dry pre-mixed products) are generally used for both new construction and repair. Strengths of mortar change based on the mix ratio for each type of mortar, which are specified under the ASTM standards.
These premixed mortar products are designated by one of the five letters, M, S, N, O, and K. Type M mortar is the strongest, and Type K the weakest.
The mix ratio is always expressed by volume of .
These type letters are taken from the alternate letters of the words "MaSoN wOrK".
Polymer cement mortar
Polymer cement mortars (PCM) are the materials which are made by partially replacing the cement hydrate binders of conventional cement mortar with polymers. The polymeric admixtures include latexes or emulsions, redispersible polymer powders, water-soluble polymers, liquid thermoset resins and monomers. Although they increase cost of mortars when used as an additive, they enhance properties. Polymer mortar has low permeability that may be detrimental to moisture accumulation when used to repair a traditional brick, block or stone wall. It is mainly designed for repairing concrete structures. The use of recovered plastics in mortars is being researched and is gaining ground. Depolymerizing PET to use as a polymeric binder to enhance mortars is actively being studied.
Lime mortar | Mortar (masonry) | Wikipedia | 454 | 324498 | https://en.wikipedia.org/wiki/Mortar%20%28masonry%29 | Technology | Building materials | null |
The setting speed can be increased by using impure limestone in the kiln, to form a hydraulic lime that will set on contact with water. Such a lime must be stored as a dry powder. Alternatively, a pozzolanic material such as calcined clay or brick dust may be added to the mortar mix. Addition of a pozzolanic material will make the mortar set reasonably quickly by reaction with the water.
It would be problematic to use Portland cement mortars to repair older buildings originally constructed using lime mortar. Lime mortar is softer than cement mortar, allowing brickwork a certain degree of flexibility to adapt to shifting ground or other changing conditions. Cement mortar is harder and allows little flexibility. The contrast can cause brickwork to crack where the two mortars are present in a single wall.
Lime mortar is considered breathable in that it will allow moisture to freely move through and evaporate from the surface. In old buildings with walls that shift over time, cracks can be found which allow rain water into the structure. The lime mortar allows this moisture to escape through evaporation and keeps the wall dry. Re−pointing or rendering an old wall with cement mortar stops the evaporation and can cause problems associated with moisture behind the cement.
Pozzolanic mortar
Pozzolana is a fine, sandy volcanic ash. It was originally discovered and dug at Pozzuoli, nearby Mount Vesuvius in Italy, and was subsequently mined at other sites, too. The Romans learned that pozzolana added to lime mortar allowed the lime to set relatively quickly and even under water. Vitruvius, the Roman architect, spoke of four types of pozzolana. It is found in all the volcanic areas of Italy in various colours: black, white, grey and red. Pozzolana has since become a generic term for any siliceous and/or aluminous additive to slaked lime to create hydraulic cement.
Finely ground and mixed with lime it is a hydraulic cement, like Portland cement, and makes a strong mortar that will also set under water.
The fact that the materials involved in the creation of pozzolana are found in abundance within certain territories make its use more common there, with areas inside of Central Europe as well as inside of Southern Europe being an example (significantly because of the many European volcanoes of note). It has, as such, been commonly associated with a variety of large structures constructed by the Roman Empire. | Mortar (masonry) | Wikipedia | 497 | 324498 | https://en.wikipedia.org/wiki/Mortar%20%28masonry%29 | Technology | Building materials | null |
Radiocarbon dating
As the mortar hardens, the current atmosphere is encased in the mortar and thus provides a sample for analysis. Various factors affect the sample and raise the margin of error for the analysis.
Radiocarbon dating of mortar began as early as the 1960s, soon after the method was established (Delibrias and Labeyrie 1964; Stuiver and Smith 1965; Folk and Valastro 1976). The very first data were provided by van Strydonck et al. (1983), Heinemeier et al.(1997) and Ringbom and Remmer (1995). Methodological aspects were further developed by different groups (an international team headed by Åbo Akademi University, and teams from CIRCE, CIRCe, ETHZ, Poznań, RICH and Milano-Bicocca laboratory.
To evaluate the different anthropogenic carbon extraction methods for radiocarbon dating as well as to compare the different dating methods, i.e. radiocarbon and OSL, the first intercomparison study (MODIS) was set up and published in 2017. | Mortar (masonry) | Wikipedia | 224 | 324498 | https://en.wikipedia.org/wiki/Mortar%20%28masonry%29 | Technology | Building materials | null |
A mortar today is usually a simple, lightweight, man-portable, muzzle-loaded cannon, consisting of a smooth-bore (although some models use a rifled barrel) metal tube fixed to a base plate (to spread out the recoil) with a lightweight bipod mount and a sight. Mortars are typically used as indirect fire weapons for close fire support with a variety of ammunition. Historically mortars were heavy siege artillery. Mortars launch explosive shells (technically called bombs) in high-arching ballistic trajectories.
History
Mortars have been used for hundreds of years. The earliest reported use of mortars was in Korea in a 1413 naval battle when Korean gunsmiths developed the wan'gu (gourd-shaped mortar) (완구, 碗口). The earliest version of the wan'gu dates back to 1407. Ch'oe Hae-san (1380–1443), the son of Ch'oe Mu-sŏn (1325–1395), is generally credited with inventing the wan'gu. In the Ming dynasty, general Qi Jiguang recorded the use of a mini cannon called the hu dun pao that was similar to the mortar.
The first use in siege warfare was at the 1453 siege of Constantinople by Mehmed the Conqueror. An Italian account of the 1456 siege of Belgrade by Giovanni da Tagliacozzo states that the Ottoman Turks used seven mortars that fired "stone shots one Italian mile high". The time of flight of these was apparently long enough that casualties could be avoided by posting observers to give warning of their trajectories. | Mortar (weapon) | Wikipedia | 337 | 324499 | https://en.wikipedia.org/wiki/Mortar%20%28weapon%29 | Technology | Artillery and siege | null |
Early mortars, such as the Pumhart von Steyr, were large and heavy and could not be easily transported. Simply made, these weapons were no more than iron bowls reminiscent of the kitchen and apothecary mortars whence they drew their name. An early transportable mortar was invented by Baron Menno van Coehoorn in 1701. This mortar fired an exploding shell, which had a fuse that was lit by the hot gases when fired. The Coehorn mortar gained quick popularity, necessitating a new form of naval ship, the bomb vessel. Mortars played a significant role in the Venetian conquest of Morea, and in the course of this campaign an ammunition depot in the Parthenon was blown up. An early use of these more mobile mortars as field artillery (rather than siege artillery) was by British forces in the suppression of the Jacobite rising of 1719 at the Battle of Glen Shiel. High angle trajectory mortars held a great advantage over standard field guns in the rough terrain of the West Highlands of Scotland.
The mortar had fallen out of general use in Europe by the Napoleonic era, although Manby Mortars were widely used on the coast to launch lines to ships in distress, and interest in their use as a weapon was not revived until the beginning of the 20th century. Mortars were heavily used by both sides during the American Civil War. At the Siege of Vicksburg, General Ulysses S. Grant reported making mortars "by taking logs of the toughest wood that could be found, boring them out for shells and binding them with strong iron bands. These answered as Coehorns, and shells were successfully thrown from them into the trenches of the enemy".
During the Russo-Japanese War, Lieutenant General Leonid Gobyato of the Imperial Russian Army applied the principles of indirect fire from closed firing positions in the field; and with the collaboration of General Roman Kondratenko, he designed the first mortar that fired navy shells.
The German Army studied the Siege of Port Arthur, where heavy artillery had been unable to destroy defensive structures like barbed wire and bunkers. Consequently they developed a short-barrelled rifled muzzle-loading mortar called the Minenwerfer. Heavily used during World War I, they were made in three sizes: , , and .
Types
Stokes mortar | Mortar (weapon) | Wikipedia | 467 | 324499 | https://en.wikipedia.org/wiki/Mortar%20%28weapon%29 | Technology | Artillery and siege | null |
It was not until the Stokes mortar was devised by Sir Wilfred Stokes in 1915 during the First World War that the modern mortar transportable by one person was born. In the conditions of trench warfare, there was a great need for a versatile and easily portable weapon that could be manned by troops under cover in the trenches. Stokes' design was initially rejected in June 1915 because it was unable to use existing stocks of British mortar ammunition, and it took the intervention of David Lloyd George (at that time Minister of Munitions) and Lieutenant Colonel J. C. Matheson of the Trench Warfare Supply Department (who reported to Lloyd George) to expedite manufacture of the Stokes mortar. The weapon proved to be extremely useful in the muddy trenches of the Western Front, as a mortar round could be aimed to fall directly into trenches, where artillery shells, because of their low angle of flight, could not possibly go.
The Stokes mortar was a simple muzzle-loaded weapon, consisting of a smoothbore metal tube fixed to a base plate (to absorb recoil) with a lightweight bipod mount. When a mortar bomb was dropped into the tube, an impact sensitive primer in the base of the bomb would make contact with a firing pin at the base of the tube and detonate, firing the bomb towards the target. The Stokes mortar could fire as many as 25 bombs per minute and had a maximum range of , firing the original cylindrical unstabilised projectile.
A modified version of the mortar, which fired a modern fin-stabilised streamlined projectile and had a booster charge for longer range, was developed after World War I; this was in effect a new weapon. By World War II, it could fire as many as 30 bombs per minute and had a range of over with some shell types. The French developed an improved version of the Stokes mortar as the Brandt Mle 27, further refined as the Brandt Mle 31; this design was widely copied with and without license. These weapons were the prototypes for all subsequent light mortar developments around the world.
Mortar carrier | Mortar (weapon) | Wikipedia | 410 | 324499 | https://en.wikipedia.org/wiki/Mortar%20%28weapon%29 | Technology | Artillery and siege | null |
Mortar carriers are vehicles which carry a mortar as a primary weapon. Numerous vehicles have been used to mount mortars, from improvised civilian trucks used by insurgents, to modified infantry fighting vehicles, such as variants of the M3 half-track and M113 armored personnel carrier, to vehicles specifically intended to carry a mortar. Simpler vehicles carry a standard infantry mortar while in more complex vehicles the mortar is fully integrated into the vehicle and cannot be dismounted from the vehicle. Mortar carriers cannot be fired while on the move, and some must be dismounted to fire.
There are numerous armoured fighting vehicles and even main battle tanks that can be equipped with a mortar, either outside or inside of the cabin. The Israeli Merkava tank uses a mortar as a secondary armament. The Russian army uses the 2S4 Tyulpan self-propelled heavy mortar which is one of the largest mortars in current use.
Gun-mortars | Mortar (weapon) | Wikipedia | 181 | 324499 | https://en.wikipedia.org/wiki/Mortar%20%28weapon%29 | Technology | Artillery and siege | null |
Gun-mortars are breech-loaded mortars usually equipped with a hydraulic recoil mechanism, and sometimes equipped with an autoloader. They are usually mounted on an armoured vehicle and are capable of both direct fire and indirect fire. The archetypes are the Brandt Mle CM60A1 and Brandt 60 mm LR, which combine features of modern infantry mortars together with those of modern cannon. Such weapons are most commonly smoothbore, firing fin-stabilised rounds, using relatively small propellant charges in comparison to projectile weight. While some have been fitted with rifled barrels, such as the 2S31 Vena and 2S9 Nona. They have short barrels in comparison to guns and are much more lightly built than guns of a similar calibre – all characteristics of infantry mortars. This produces a hybrid weapon capable of engaging area targets with indirect high-angle fire, and also specific targets such as vehicles and bunkers with direct fire. Such hybrids are much heavier and more complicated than infantry mortars, superior to rocket-propelled grenades in the anti-armour and bunker-busting role, but have a reduced range compared to modern gun-howitzers and inferior anti-tank capability compared to modern anti-tank guided weapons. However, they do have a niche in, for example, providing a multi-role anti-personnel, anti-armour capability in light mobile formations. Such systems, like the Soviet 120 mm 2S9 Nona, are mostly self-propelled (although a towed variant exists). The AMOS (Advanced Mortar System) is an example of an even more advanced gun mortar system. It uses a 120 mm automatic twin-barrelled, breech-loaded mortar turret, which can be mounted on a variety of armoured vehicles and attack boats. A modern example of a gun-mortar is the 2B9 Vasilek.
Spigot mortar | Mortar (weapon) | Wikipedia | 383 | 324499 | https://en.wikipedia.org/wiki/Mortar%20%28weapon%29 | Technology | Artillery and siege | null |
A spigot mortar consists mainly of a solid rod or spigot, onto which a hollow tube in the projectile fits—inverting the normal tube-mortar arrangement. At the top of the tube in the projectile, a cavity contains propellant, such as cordite. There is usually a trigger mechanism built into the base of the spigot, with a long firing pin running up the length of the spigot activating a primer inside the projectile and firing the propellant charge. The advantage of a spigot mortar is that the firing unit (baseplate and spigot) is smaller and lighter than a conventional tube mortar of equivalent payload and range. It is also somewhat simpler to manufacture. Further, most spigot mortars have no barrel in the conventional sense, which means ammunition of almost any weight and diameter can be fired from the same mortar.
The disadvantage is that while most mortar bombs have a streamlined shape towards the back that fits a spigot mortar application well, using that space for the spigot mortar tube takes volume and mass away from the payload of the projectile. If a soldier is carrying only a few projectiles, the projectile weight disadvantage is not significant. However, the weight of a large quantity of the heavier and more complex spigot projectiles offsets the weight saved.
A near-silent mortar can operate using the spigot principle. Each round has a close-fitting sliding plug in the tube that fits over the spigot. When the round is fired, the projectile is pushed off the spigot, but before the plug clears the spigot it is caught by a constriction at the base of the tube. This traps the gases from the propelling charge and hence the sound of the firing. After World War II the Belgium Fly-K silent spigot mortar was accepted into French service as the TN-8111. | Mortar (weapon) | Wikipedia | 388 | 324499 | https://en.wikipedia.org/wiki/Mortar%20%28weapon%29 | Technology | Artillery and siege | null |
Spigot mortars generally fell out of favour after World War II and were replaced by smaller conventional mortars. Military applications of spigot mortars include:
The petard mortar used on the Churchill AVRE by Britain in World War II.
The Type 98 mortar used by Japan in World War II to some psychological effect in the battles of Iwo Jima and Okinawa
The Blacker Bombard and PIAT anti-tank launchers used by Britain in World War II.
The Hedgehog launcher, used from the deck of a ship, used 24 spigot mortars which fired a diamond pattern of anti-submarine projectiles into the sea ahead of the ship. A sinking projectile detonated if it struck a submarine, and the pattern was such that any submarine partly in the landing zone of the projectiles would be struck one or more times.
Non-military applications include the use of small-calibre spigot mortars to launch lightweight, low-velocity foam dummy targets used for training retriever dogs for bird hunting. Simple launchers use a separate small primer cap as the sole propellant (similar or identical to the cartridges used in industrial nail guns).
Improvised
Insurgent groups often use improvised, or "homemade" mortars to attack fortified military installations or terrorise civilians. They are usually constructed from heavy steel piping mounted on a steel frame. These weapons may fire standard mortar rounds, purpose-made shells, repurposed gas cylinders filled with explosives and shrapnel, or any other type of improvised explosive, incendiary or chemical munitions. These were called "barrack busters" by the Provisional Irish Republican Army (PIRA).
Syrian civil war
Improvised mortars used by insurgents in the Syrian civil war are known as hell cannons. Observers have noted that they are "wildly inaccurate" and responsible for hundreds of civilian deaths.
Sri Lankan civil war
Improvised mortars used in the Sri Lankan civil war by the rebel Tamil Tigers are known as "Pasilan 2000", also known as a "rocket mortar" or "Arti-mortar" like the cannon, successor to the Baba mortar used by the LTTE for ground operations since the 1980s. As Baba mortar rounds contained tar, they caused a fire when they hit the ground. The Baba, the prototype mortar, was crude. But with time the weapon has improved. | Mortar (weapon) | Wikipedia | 476 | 324499 | https://en.wikipedia.org/wiki/Mortar%20%28weapon%29 | Technology | Artillery and siege | null |
The Pasilan 2000, the improved version, has been developed with characteristics similar to a rocket launcher. The Pasilan 2000 was a heavy mortar fired from a mobile launcher mounted on a tractor. The shell does not emit constant muzzle flares like artillery or MBRL. This is ideal for LTTE's camouflage and conceals attacking style. Once a round is fired, forward observers/spies/civilian spotters can correct the fire. The way the tube is installed is similar to the positioning of rocket pods. The length and calibre of the barrel indicate Pasilan 2000 system has common features to the Chinese made Type 82 30-tube MLRS (introduced by the Palestinian Liberation Army (PLA) in the early 1980s) rather than rail-guided Katyusha variants such as the Qassam Rocket. The warhead weight is and it is filled with TNT. It had a range of . The rocket has since then undergone some modifications. The Pasilan 2000 was more lethal than Baba mortar. But it was not heavily used for ground attacks during the Eelam War IV.
Modern
Design
Most modern mortar systems consist of four main components: a barrel, a base plate, a bipod and a sight. Modern mortars normally range in calibre from 60 mm (2.36 in) to 120 mm (4.72 in). However, both larger and smaller mortars have been produced. The modern mortar is a muzzle-loaded weapon and relatively simple to operate. It consists of a barrel into which the gunners drop a mortar round. When the round reaches the base of the barrel it hits a fixed firing pin that fires the round. The barrel is generally set at an angle of between 45 and 85 degrees (800 to 1500 mils), with the higher angle producing a shorter horizontal trajectory. Some mortars have a moving firing pin, operated by a lanyard or trigger mechanism.
Ammunition
Ammunition for mortars generally comes in two main varieties: fin-stabilised and spin-stabilised. Examples of the former have short fins on their posterior portion, which control the path of the bomb in flight. Spin-stabilised mortar bombs rotate as they travel along and leave the mortar tube, which stabilises them in much the same way as a rifle bullet. Both types of rounds can be either illumination (infrared or visible illumination), smoke, high explosive, and training rounds. Mortar bombs are often referred to, incorrectly, as "mortars". | Mortar (weapon) | Wikipedia | 502 | 324499 | https://en.wikipedia.org/wiki/Mortar%20%28weapon%29 | Technology | Artillery and siege | null |
Operators may fire spin-stabilised rounds from either a smoothbore or a rifled barrel. Rifled mortars are more accurate but slower to load. Since mortars are generally muzzle-loaded, mortar bombs for rifled barrels usually have a pre-engraved band, called an obturator, that engages with the rifling of the barrel. Exceptions to this are the U.S. M2 4.2-inch mortar and M30 mortar, whose ammunition has a sub-calibre expandable ring that enlarged when fired. This allows the projectile to slide down the barrel freely but grip the rifling when fired. The system resembles the Minié ball for muzzle-loading rifles. For extra range, propellant rings (augmentation charges) are attached to the bomb's fins. The rings are usually easy to remove, because they have a major influence on the speed and thus the range of the bomb. Some mortar rounds can be fired without any augmentation charges, e.g., the 81 mm L16 mortar.
Precision guided
The XM395 Precision Guided Mortar Munition (PGMM) is a 120 mm guided mortar round developed by Alliant Techsystems. Based on Orbital ATK's Precision Guidance Kit for 155 mm artillery projectiles, XM395 combines GPS guidance and directional control surfaces into a package that replaces standard fuses, transforming existing 120 mm mortar bodies into precision-guided munitions. The XM395 munition consists of a GPS-guided kit fitted to standard 120 mm smoothbore mortar rounds that includes the fitting of a nose and tail subsystem containing the maneuvering parts.
The Strix mortar round is a Swedish endphase-guided projectile fired from a 120 mm mortar currently manufactured by Saab Bofors Dynamics. STRIX is fired like a conventional mortar round. The round contains an infrared imaging sensor that it uses to guide itself onto any tank or armoured fighting vehicle in the vicinity where it lands. The seeker is designed to ignore targets that are already burning. Launched from any 120 mm mortar, STRIX has a normal range of up to . The addition of a special sustainer motor increases the range to . | Mortar (weapon) | Wikipedia | 448 | 324499 | https://en.wikipedia.org/wiki/Mortar%20%28weapon%29 | Technology | Artillery and siege | null |
The GMM 120 (Guided Mortar Munition 120; known as Patzmi; also referred to as Morty) is a GPS and/or laser-guided mortar munition, which was developed by Israel Military Industries. Another Israeli guided mortar is Iron Sting, developed by Elbit. The Russian KM-8 Gran is also laser-guided.
Compared to long range artillery
Modern mortars and their ammunition are generally much smaller and lighter than long range artillery, such as field guns and howitzers, which allows light () and medium (/) mortars to be considered light weapons; i.e. capable of transport by personnel without vehicle assistance.
Mortars are short-range weapons and often more effective than long range artillery for many purposes within their shorter range. In particular, because of its high, parabolic trajectory with a near vertical descent, the mortar can land bombs on nearby targets, including those behind obstacles or in fortifications, such as light vehicles behind hills or structures, or infantry in trenches or spider holes. This also makes it possible to launch attacks from positions lower than the target of the attack. (For example, long-range artillery could not shell a target away and higher, a target easily accessible to a mortar.)
In trench warfare, mortars can use plunging fire directly into the enemy trenches, which is very hard or impossible to accomplish with long range artillery because of its much flatter trajectory. Mortars are also highly effective when used from concealed positions, such as the natural escarpments on hillsides or from woods, especially if forward observers are being employed in strategic positions to direct fire, an arrangement where the mortar is in relatively close proximity both to its forward observer and its target, allowing for fire to be quickly and accurately delivered with lethal effect. Mortars suffer from instability when used on snow or soft ground, because the recoil pushes them into the ground or snow unevenly. A Raschen bag addresses this problem. | Mortar (weapon) | Wikipedia | 395 | 324499 | https://en.wikipedia.org/wiki/Mortar%20%28weapon%29 | Technology | Artillery and siege | null |
Fin-stabilised mortar bombs do not have to withstand the rotational forces placed upon them by rifling or greater pressures, and can therefore carry a higher payload in a thinner skin than rifled artillery ammunition. Because of the difference in available volume, a smooth-bore mortar of a given diameter will have a greater explosive yield than a similarly sized artillery shell of a gun or howitzer. For example, a 120 mm mortar bomb has approximately the same explosive capability as a 152 mm/155 mm artillery shell. Also, fin-stabilised munitions fired from a smooth-bore, which do not rely on the spin imparted by a rifled bore for greater accuracy, do not have the drawback of veering in the direction of the spin.
Largest mortars
From the 17th to the mid-20th century, very heavy, relatively immobile siege mortars were used, of up to calibre, often made of cast iron and with an outside barrel diameter many times that of the bore diameter. An early example was Roaring Meg, with a barrel diameter and firing a hollow ball filled with gunpowder and used during the English Civil War in 1646.
The largest mortars ever developed were the Belgian "Monster Mortar" () developed by Henri-Joseph Paixhans in 1832, Mallet's Mortar () developed by Robert Mallet in 1857, and the "Little David" (() developed in the United States for use in World War II. Although the latter two had a calibre of , only the "Monster Mortar" was used in combat (at the Battle of Antwerp in 1832). The World War II German Karl-Gerät was a mortar and the largest to see combat in modern warfare. | Mortar (weapon) | Wikipedia | 347 | 324499 | https://en.wikipedia.org/wiki/Mortar%20%28weapon%29 | Technology | Artillery and siege | null |
The metatarsal bones or metatarsus (: metatarsi) are a group of five long bones in the midfoot, located between the tarsal bones (which form the heel and the ankle) and the phalanges (toes). Lacking individual names, the metatarsal bones are numbered from the medial side (the side of the great toe): the first, second, third, fourth, and fifth metatarsal (often depicted with Roman numerals). The metatarsals are analogous to the metacarpal bones of the hand. The lengths of the metatarsal bones in humans are, in descending order, second, third, fourth, fifth, and first. A bovine hind leg has two metatarsals.
Structure
The five metatarsals are dorsal convex long bones consisting of a shaft or body, a base (proximally), and a head (distally). The body is prismoid in form, tapers gradually from the tarsal to the phalangeal extremity, and is curved longitudinally, so as to be concave below, slightly convex above. The base or posterior extremity is wedge-shaped, articulating proximally with the tarsal bones, and by its sides with the contiguous metatarsal bones: its dorsal and plantar surfaces are rough for the attachment of ligaments. The head or distal extremity presents a convex articular surface, oblong from above downward, and extending farther backward below than above. Its sides are flattened, and on each is a depression, surmounted by a tubercle, for ligamentous attachment. Its plantar surface is grooved antero-posteriorly for the passage of the flexor tendons, and marked on either side by an articular eminence continuous with the terminal articular surface.
During growth, the growth plates are located distally on the metatarsals, except on the first metatarsal where it is located proximally. Yet it is quite common to have an accessory growth plate on the distal first metatarsal.
Articulations
The base of each metatarsal bone articulates with one or more of the tarsal bones at the tarsometatarsal joints, and the head with one of the first row of phalanges at the metatarsophalangeal joints. Their bases also articulate with each other at the intermetatarsal joints | Metatarsal bones | Wikipedia | 506 | 324681 | https://en.wikipedia.org/wiki/Metatarsal%20bones | Biology and health sciences | Skeletal system | Biology |
The first metatarsal articulates with the medial cuneiform, and to a small extent to the intermediate cuneiform.
the second with all three cuneiforms.
the third with the lateral cuneiform.
the fourth with the lateral cuneiform and the cuboid.
The fifth with the cuboid.
Muscle attachments
Clinical significance
Injuries
The metatarsal bones are often broken by association football (soccer) players. These and other recent cases have been attributed to the lightweight design of modern football boots, which provide less protection to the foot. In 2010 some football players began testing a new sock that incorporated a rubber silicone pad over the foot to provide protection to the top of the foot. Stress fractures are thought to account for 16% of injuries related to sports participation, and the metatarsals are the bones most often involved. These fractures are sometimes called march fractures, based on their traditional association with military recruits after long marches. The second and third metatarsals are fixed while walking, thus these metatarsals are common sites of injury. The fifth metatarsal may be fractured if the foot is oversupinated during locomotion.
Protection from injuries can be given by the use of safety footwear which can use built-in or removable metatarsal guards.
Additional images | Metatarsal bones | Wikipedia | 266 | 324681 | https://en.wikipedia.org/wiki/Metatarsal%20bones | Biology and health sciences | Skeletal system | Biology |
In human anatomy, the metacarpal bones or metacarpus, also known as the "palm bones", are the appendicular bones that form the intermediate part of the hand between the phalanges (fingers) and the carpal bones (wrist bones), which articulate with the forearm. The metacarpal bones are homologous to the metatarsal bones in the foot.
Structure
The metacarpals form a transverse arch to which the rigid row of distal carpal bones are fixed. The peripheral metacarpals (those of the thumb and little finger) form the sides of the cup of the palmar gutter and as they are brought together they deepen this concavity. The index metacarpal is the most firmly fixed, while the thumb metacarpal articulates with the trapezium and acts independently from the others. The middle metacarpals are tightly united to the carpus by intrinsic interlocking bone elements at their bases. The ring metacarpal is somewhat more mobile while the fifth metacarpal is semi-independent.
Each metacarpal bone consists of a body or shaft, and two extremities; the head at the distal or digital end (near the fingers), and the base at the proximal or carpal end (close to the wrist).
Body
The body (shaft) is prismoid in form, and curved, so as to be convex in the longitudinal direction behind, concave in front. It presents three surfaces: medial, lateral, and dorsal.
The medial and lateral surfaces are concave, for the attachment of the interosseus muscles, and separated from one another by a prominent anterior ridge.
The dorsal surface presents in its distal two-thirds a smooth, triangular, flattened area which is covered in by the tendons of the extensor muscles. This surface is bounded by two lines, which commence in small tubercles situated on either side of the digital extremity, and, passing upward, converge and meet some distance above the center of the bone and form a ridge which runs along the rest of the dorsal surface to the carpal extremity. This ridge separates two sloping surfaces for the attachment of the interossei dorsales.
To the tubercles on the digital extremities are attached the collateral ligaments of the metacarpophalangeal joints. | Metacarpal bones | Wikipedia | 487 | 324697 | https://en.wikipedia.org/wiki/Metacarpal%20bones | Biology and health sciences | Skeletal system | Biology |
Base
The base (basis) or carpal extremity is of a cuboidal form, and broader behind than in front. It articulates with the carpal bones and with the adjoining metacarpal bones while its dorsal and volar surfaces are rough, for the attachment of ligaments.
Head
The head (caput) or digital extremity presents an oblong surface markedly convex from before backward, less so transversely, and flattened from side to side; it articulates with the proximal phalanx. It is broader, and extends farther upward, on the volar than on the dorsal aspect, and is longer in the antero-posterior than in the transverse diameter. On either side of the head is a tubercle for the attachment of the collateral ligament of the metacarpophalangeal joint.
The dorsal surface, broad and flat, supports the tendons of the extensor muscles.
The volar surface is grooved in the middle line for the passage of the flexor tendons, and marked on either side by an articular eminence continuous with the terminal articular surface.
Neck
The neck, or subcapital segment, is the transition zone between the body and the head.
Articulations
Besides the metacarpophalangeal joints, the metacarpal bones articulate by carpometacarpal joints as follows:
the first with the trapezium;
the second with the trapezium, trapezoid, capitate and third metacarpal;
the third with the capitate and second and fourth metacarpals;
the fourth with the capitate, hamate, and third and fifth metacarpals;
and the fifth with the hamate and fourth metacarpal;
Insertions
Extensor Carpi Radialis Longus/Brevis: Both insert on the base of metacarpal II; Assist with wrist extension and radial flexion of the wrist
Extensor Carpi Ulnaris: Inserts on the base of metacarpal V; Extends and fixes wrist when digits are being flexed; assists with ulnar flexion of wrist
Abductor Pollicis Longus: Inserts on the trapezium and base of metacarpal I; Abducts thumb in frontal plane; extends thumb at carpometacarpal joint
Opponens Pollicis: Inserts on metacarpal I; flexes metacarpal I to oppose the thumb to the fingertips | Metacarpal bones | Wikipedia | 503 | 324697 | https://en.wikipedia.org/wiki/Metacarpal%20bones | Biology and health sciences | Skeletal system | Biology |
Opponens digiti minimi: Inserts on the medial surface of metacarpal V; Flexes metacarpal V at carpometacarpal joint when little finger is moved into opposition with tip of thumb; deepens palm of hand.
Clinical significance
Congenital disorders
The fourth and fifth metacarpal bones are commonly "blunted" or shortened, in pseudohypoparathyroidism and pseudopseudohypoparathyroidism.
A blunted fourth metacarpal, with normal fifth metacarpal, can signify Turner syndrome.
Blunted metacarpals (particularly the fourth metacarpal) are a symptom of nevoid basal-cell carcinoma syndrome.
Fracture
The neck of a metacarpal is a common location for a boxer's fracture, but all parts of the metacarpal bone (including head, body and base) are susceptible to fracture. During their lifetime, 2.5% of individuals will experience at least one metacarpal fracture. Bennett's fracture (base of the thumb) is the most common. Several types of treatment exist ranging from non-operative techniques, with or without immobilization, to operative techniques using closed or open reduction and internal fixation (ORIF). Generally, most fractures showing little or no displacement can be treated successfully without surgery. Intraarticular fracture-dislocations of the metacarpal head or base may require surgical fixation, as fragment displacement affecting the joint surface is rarely tolerated well.
Other animals
In four-legged animals, the metacarpals form part of the forefeet, and are frequently reduced in number, appropriate to the number of toes. In digitigrade and unguligrade animals, the metacarpals are greatly extended and strengthened, forming an additional segment to the limb, a feature that typically enhances the animal's speed. In both birds and bats, the metacarpals form part of the wing.
History | Metacarpal bones | Wikipedia | 403 | 324697 | https://en.wikipedia.org/wiki/Metacarpal%20bones | Biology and health sciences | Skeletal system | Biology |
Etymology
The Greek physician Galen used to refer to the as μετακάρπιον. The Latin form more truly resembles its Ancient Greek predecessor μετακάρπιον than metacarpus. Meta– is Greek for beyond and carpal from Ancient Greek καρπός (, “wrist”).
In anatomic Latin, adjectives like , , , , and can be found. The form is more true to the later Greek form μετακάρπιος. , as in in the current official Latin nomenclature, Terminologia Anatomica is a compound consisting of Latin and Greek parts. The usage of such hybrids in anatomic Latin is disapproved by some.
Additional images | Metacarpal bones | Wikipedia | 159 | 324697 | https://en.wikipedia.org/wiki/Metacarpal%20bones | Biology and health sciences | Skeletal system | Biology |
In mathematics, the modular group is the projective special linear group of matrices with integer coefficients and determinant 1. The matrices and are identified. The modular group acts on the upper-half of the complex plane by fractional linear transformations, and the name "modular group" comes from the relation to moduli spaces and not from modular arithmetic.
Definition
The modular group is the group of linear fractional transformations of the upper half of the complex plane, which have the form
where , , , are integers, and . The group operation is function composition.
This group of transformations is isomorphic to the projective special linear group , which is the quotient of the 2-dimensional special linear group over the integers by its center . In other words, consists of all matrices
where , , , are integers, , and pairs of matrices and are considered to be identical. The group operation is the usual multiplication of matrices.
Some authors define the modular group to be , and still others define the modular group to be the larger group .
Some mathematical relations require the consideration of the group of matrices with determinant plus or minus one. ( is a subgroup of this group.) Similarly, is the quotient group . A matrix with unit determinant is a symplectic matrix, and thus , the symplectic group of matrices.
Finding elements
To find an explicit matrix in , begin with two coprime integers , and solve the determinant equation(Notice the determinant equation forces to be coprime since otherwise there would be a factor such that , , hencewould have no integer solutions.) For example, if then the determinant equation readsthen taking and gives , henceis a matrix. Then, using the projection, these matrices define elements in .
Number-theoretic properties
The unit determinant of
implies that the fractions , , , are all irreducible, that is having no common factors (provided the denominators are non-zero, of course). More generally, if is an irreducible fraction, then
is also irreducible (again, provided the denominator be non-zero). Any pair of irreducible fractions can be connected in this way; that is, for any pair and of irreducible fractions, there exist elements
such that
Elements of the modular group provide a symmetry on the two-dimensional lattice. Let and be two complex numbers whose ratio is not real. Then the set of points | Modular group | Wikipedia | 503 | 325019 | https://en.wikipedia.org/wiki/Modular%20group | Mathematics | Abstract algebra | null |
is a lattice of parallelograms on the plane. A different pair of vectors and will generate exactly the same lattice if and only if
for some matrix in . It is for this reason that doubly periodic functions, such as elliptic functions, possess a modular group symmetry.
The action of the modular group on the rational numbers can most easily be understood by envisioning a square grid, with grid point corresponding to the fraction (see Euclid's orchard). An irreducible fraction is one that is visible from the origin; the action of the modular group on a fraction never takes a visible (irreducible) to a hidden (reducible) one, and vice versa.
Note that any member of the modular group maps the projectively extended real line one-to-one to itself, and furthermore bijectively maps the projectively extended rational line (the rationals with infinity) to itself, the irrationals to the irrationals, the transcendental numbers to the transcendental numbers, the non-real numbers to the non-real numbers, the upper half-plane to the upper half-plane, et cetera.
If and are two successive convergents of a continued fraction, then the matrix
belongs to . In particular, if for positive integers , , , with and then and will be neighbours in the Farey sequence of order . Important special cases of continued fraction convergents include the Fibonacci numbers and solutions to Pell's equation. In both cases, the numbers can be arranged to form a semigroup subset of the modular group.
Group-theoretic properties
Presentation
The modular group can be shown to be generated by the two transformations
so that every element in the modular group can be represented (in a non-unique way) by the composition of powers of and . Geometrically, represents inversion in the unit circle followed by reflection with respect to the imaginary axis, while represents a unit translation to the right.
The generators and obey the relations and . It can be shown that these are a complete set of relations, so the modular group has the presentation:
This presentation describes the modular group as the rotational triangle group (infinity as there is no relation on ), and it thus maps onto all triangle groups by adding the relation , which occurs for instance in the congruence subgroup .
Using the generators and instead of and , this shows that the modular group is isomorphic to the free product of the cyclic groups and :
Braid group | Modular group | Wikipedia | 499 | 325019 | https://en.wikipedia.org/wiki/Modular%20group | Mathematics | Abstract algebra | null |
The braid group is the universal central extension of the modular group, with these sitting as lattices inside the (topological) universal covering group . Further, the modular group has a trivial center, and thus the modular group is isomorphic to the quotient group of modulo its center; equivalently, to the group of inner automorphisms of .
The braid group in turn is isomorphic to the knot group of the trefoil knot.
Quotients
The quotients by congruence subgroups are of significant interest.
Other important quotients are the triangle groups, which correspond geometrically to descending to a cylinder, quotienting the coordinate modulo , as . is the group of icosahedral symmetry, and the triangle group (and associated tiling) is the cover for all Hurwitz surfaces.
Presenting as a matrix group
The group can be generated by the two matrices
since
The projection turns these matrices into generators of , with relations similar to the group presentation.
Relationship to hyperbolic geometry
The modular group is important because it forms a subgroup of the group of isometries of the hyperbolic plane. If we consider the upper half-plane model of hyperbolic plane geometry, then the group of all
orientation-preserving isometries of consists of all Möbius transformations of the form
where , , , are real numbers. In terms of projective coordinates, the group acts on the upper half-plane by projectivity:
This action is faithful. Since is a subgroup of , the modular group is a subgroup of the group of orientation-preserving isometries of .
Tessellation of the hyperbolic plane
The modular group acts on as a discrete subgroup of , that is, for each in we can find a neighbourhood of which does not contain any other element of the orbit of . This also means that we can construct fundamental domains, which (roughly) contain exactly one representative from the orbit of every in . (Care is needed on the boundary of the domain.)
There are many ways of constructing a fundamental domain, but a common choice is the region
bounded by the vertical lines and , and the circle . This region is a hyperbolic triangle. It has vertices at and , where the angle between its sides is , and a third vertex at infinity, where the angle between its sides is 0. | Modular group | Wikipedia | 464 | 325019 | https://en.wikipedia.org/wiki/Modular%20group | Mathematics | Abstract algebra | null |
There is a strong connection between the modular group and elliptic curves. Each point in the upper half-plane gives an elliptic curve, namely the quotient of by the lattice generated by 1 and .
Two points in the upper half-plane give isomorphic elliptic curves if and only if they are related by a transformation in the modular group. Thus, the quotient of the upper half-plane by the action of the modular group is the so-called moduli space of elliptic curves: a space whose points describe isomorphism classes of elliptic curves. This is often visualized as the fundamental domain described above, with some points on its boundary identified.
The modular group and its subgroups are also a source of interesting tilings of the hyperbolic plane. By transforming this fundamental domain in turn by each of the elements of the modular group, a regular tessellation of the hyperbolic plane by congruent hyperbolic triangles known as the V6.6.∞ Infinite-order triangular tiling is created. Note that each such triangle has one vertex either at infinity or on the real axis .
This tiling can be extended to the Poincaré disk, where every hyperbolic triangle has one vertex on the boundary of the disk. The tiling of the Poincaré disk is given in a natural way by the -invariant, which is invariant under the modular group, and attains every complex number once in each triangle of these regions.
This tessellation can be refined slightly, dividing each region into two halves (conventionally colored black and white), by adding an orientation-reversing map; the colors then correspond to orientation of the domain. Adding in and taking the right half of the region (where ) yields the usual tessellation. This tessellation first appears in print in , where it is credited to Richard Dedekind, in reference to .
The map of groups (from modular group to triangle group) can be visualized in terms of this tiling (yielding a tiling on the modular curve), as depicted in the video at right.
Congruence subgroups
Important subgroups of the modular group , called congruence subgroups, are given by imposing congruence relations on the associated matrices.
There is a natural homomorphism given by reducing the entries modulo . This induces a homomorphism on the modular group . The kernel of this homomorphism is called the principal congruence subgroup of level , denoted . We have the following short exact sequence: | Modular group | Wikipedia | 504 | 325019 | https://en.wikipedia.org/wiki/Modular%20group | Mathematics | Abstract algebra | null |
Being the kernel of a homomorphism is a normal subgroup of the modular group . The group is given as the set of all modular transformations
for which and .
It is easy to show that the trace of a matrix representing an element of cannot be −1, 0, or 1, so these subgroups are torsion-free groups. (There are other torsion-free subgroups.)
The principal congruence subgroup of level 2, , is also called the modular group . Since is isomorphic to , is a subgroup of index 6. The group consists of all modular transformations for which and are odd and and are even.
Another important family of congruence subgroups are the modular group defined as the set of all modular transformations for which , or equivalently, as the subgroup whose matrices become upper triangular upon reduction modulo . Note that is a subgroup of . The modular curves associated with these groups are an aspect of monstrous moonshine – for a prime number , the modular curve of the normalizer is genus zero if and only if divides the order of the monster group, or equivalently, if is a supersingular prime.
Dyadic monoid
One important subset of the modular group is the dyadic monoid, which is the monoid of all strings of the form for positive integers . This monoid occurs naturally in the study of fractal curves, and describes the self-similarity symmetries of the Cantor function, Minkowski's question mark function, and the Koch snowflake, each being a special case of the general de Rham curve. The monoid also has higher-dimensional linear representations; for example, the representation can be understood to describe the self-symmetry of the blancmange curve.
Maps of the torus
The group is the linear maps preserving the standard lattice , and is the orientation-preserving maps preserving this lattice; they thus descend to self-homeomorphisms of the torus (SL mapping to orientation-preserving maps), and in fact map isomorphically to the (extended) mapping class group of the torus, meaning that every self-homeomorphism of the torus is isotopic to a map of this form. The algebraic properties of a matrix as an element of correspond to the dynamics of the induced map of the torus.
Hecke groups
The modular group can be generalized to the Hecke groups, named for Erich Hecke, and defined as follows.
The Hecke group with , is the discrete group generated by | Modular group | Wikipedia | 509 | 325019 | https://en.wikipedia.org/wiki/Modular%20group | Mathematics | Abstract algebra | null |
where . For small values of , one has:
The modular group is isomorphic to and they share properties and applications – for example, just as one has the free product of cyclic groups
more generally one has
which corresponds to the triangle group . There is similarly a notion of principal congruence subgroups associated to principal ideals in .
History
The modular group and its subgroups were first studied in detail by Richard Dedekind and by Felix Klein as part of his Erlangen programme in the 1870s. However, the closely related elliptic functions were studied by Joseph Louis Lagrange in 1785, and further results on elliptic functions were published by Carl Gustav Jakob Jacobi and Niels Henrik Abel in 1827. | Modular group | Wikipedia | 140 | 325019 | https://en.wikipedia.org/wiki/Modular%20group | Mathematics | Abstract algebra | null |
Historical geology or palaeogeology is a discipline that uses the principles and methods of geology to reconstruct the geological history of Earth. Historical geology examines the vastness of geologic time, measured in billions of years, and investigates changes in the Earth, gradual and sudden, over this deep time. It focuses on geological processes, such as plate tectonics, that have changed the Earth's surface and subsurface over time and the use of methods including stratigraphy, structural geology, paleontology, and sedimentology to tell the sequence of these events. It also focuses on the evolution of life during different time periods in the geologic time scale.
Historical development
During the 17th century, Nicolas Steno was the first to observe and propose a number of basic principles of historical geology, including three key stratigraphic principles: the law of superposition, the principle of original horizontality, and the principle of lateral continuity.
18th-century geologist James Hutton contributed to an early understanding of the Earth's history by proposing the theory of uniformitarianism, which is now a basic principle in all branches of geology. Uniformitarianism describes an Earth formed by the same natural phenomena that are at work today, the product of slow and continuous geological changes. The theory can be summarized by the phrase "the present is the key to the past." Hutton also described the concept of deep time. The prevailing conceptualization of Earth history in 18th-century Europe, grounded in a literal interpretation of Christian scripture, was that of a young Earth shaped by catastrophic events. Hutton, however, depicted a very old Earth, shaped by slow, continuous change. Charles Lyell further developed the theory of uniformitarianism in the 19th century. Modern geologists have generally acknowledged that Earth's geological history is a product of both sudden, cataclysmic events (such as meteorite impacts and volcanic eruptions) and gradual processes (such as weathering, erosion, and deposition).
The discovery of radioactive decay in the late 19th century and the development of radiometric dating techniques in the 20th century provided a means of deriving absolute ages of events in geological history.
Use and importance
Geology is considered a historical science; accordingly, historical geology plays a prominent role in the field.
Historical geology covers much of the same subject matter as physical geology, the study of geological processes and the ways in which they shape the Earth's structure and composition. Historical geology extends physical geology into the past. | Historical geology | Wikipedia | 498 | 325030 | https://en.wikipedia.org/wiki/Historical%20geology | Physical sciences | Basics | Earth science |
Economic geology, the search for and extraction of fuel and raw materials, is heavily dependent on an understanding of the geological history of an area. Environmental geology, which examines the impacts of natural hazards such as earthquakes and volcanism, must rely on a detailed knowledge of geological history.
Methods
Stratigraphy
Layers of rock, or strata, represent a geologic record of Earth's history. Stratigraphy is the study of strata: their order, position, and age.
Structural geology
Structural geology is concerned with rocks' deformational histories.
Paleontology
Fossils are organic traces of Earth's history. In a historical geology context, paleontological methods can be used to study fossils and their environments, including surrounding rocks, and place them within the geologic time scale.
Sedimentology
Sedimentology is the study of the formation, transport, deposition, and diagenesis of sediments. Sedimentary rocks, including limestone, sandstone, and shale, serve as a record of Earth's history: they contain fossils and are transformed by geological processes, such as weathering, erosion, and deposition, through deep time.
Relative dating
Historical geology makes use of relative dating in order to establish the sequence of geological events in relation to each another, without determining their specific numerical ages or ranges.
Absolute dating
Absolute dating allows geologists to determine a more precise chronology of geological events, based on numerical ages or ranges. Absolute dating includes the use of radiometric dating methods, such as radiocarbon dating, potassium–argon dating, and uranium–lead dating. Luminescence dating, dendrochronology, and amino acid dating are other methods of absolute dating.
Plate tectonics
The theory of plate tectonics explains how the movement of lithospheric plates has structured the Earth throughout its geological history.
Weathering, erosion, and deposition
Weathering, erosion, and deposition are examples of gradual geological processes, taking place over large sections of the geologic time scale. In the rock cycle, rocks are continually broken down, transported, and deposited, cycling through three main rock types: sedimentary, metamorphic, and igneous.
Paleoclimatology
Paleoclimatology is the study of past climates recorded in geological time.
Brief geological history | Historical geology | Wikipedia | 446 | 325030 | https://en.wikipedia.org/wiki/Historical%20geology | Physical sciences | Basics | Earth science |
Tidal power or tidal energy is harnessed by converting energy from tides into useful forms of power, mainly electricity using various methods.
Although not yet widely used, tidal energy has the potential for future electricity generation. Tides are more predictable than the wind and the sun. Among sources of renewable energy, tidal energy has traditionally suffered from relatively high cost and limited availability of sites with sufficiently high tidal ranges or flow velocities, thus constricting its total availability. However many recent technological developments and improvements, both in design (e.g. dynamic tidal power, tidal lagoons) and turbine technology (e.g. new axial turbines, cross flow turbines), indicate that the total availability of tidal power may be much higher than previously assumed and that economic and environmental costs may be brought down to competitive levels.
Historically, tide mills have been used both in Europe and on the Atlantic coast of North America. Incoming water was contained in large storage ponds, and as the tide goes out, it turns waterwheels that use the mechanical power to mill grain. The earliest occurrences date from the Middle Ages, or even from Roman times. The process of using falling water and spinning turbines to create electricity was introduced in the U.S. and Europe in the 19th century.
Electricity generation from marine technologies increased an estimated 16% in 2018, and an estimated 13% in 2019. Policies promoting R&D are needed to achieve further cost reductions and large-scale development. The world's first large-scale tidal power plant was France's Rance Tidal Power Station, which became operational in 1966. It was the largest tidal power station in terms of output until Sihwa Lake Tidal Power Station opened in South Korea in August 2011. The Sihwa station uses sea wall defense barriers complete with 10 turbines generating 254 MW.
Principle
Tidal energy is taken from the Earth's oceanic tides. Tidal forces result from periodic variations in gravitational attraction exerted by celestial bodies. These forces create corresponding motions or currents in the world's oceans. This results in periodic changes in sea levels, varying as the Earth rotates. These changes are highly regular and predictable, due to the consistent pattern of the Earth's rotation and the Moon's orbit around the Earth. The magnitude and variations of this motion reflect the changing positions of the Moon and Sun relative to the Earth, the effects of Earth's rotation, and local geography of the seafloor and coastlines. | Tidal power | Wikipedia | 490 | 325060 | https://en.wikipedia.org/wiki/Tidal%20power | Technology | Power generation | null |
Tidal power is the only technology that draws on energy inherent in the orbital characteristics of the Earth–Moon system, and to a lesser extent in the Earth–Sun system. Other natural energies exploited by human technology originate directly or indirectly from the Sun, including fossil fuel, conventional hydroelectric, wind, biofuel, wave and solar energy. Nuclear energy makes use of Earth's mineral deposits of fissionable elements, while geothermal power utilizes the Earth's internal heat, which comes from a combination of residual heat from planetary accretion (about 20%) and heat produced through radioactive decay (80%).
A tidal generator converts the energy of tidal flows into electricity. Greater tidal variation and higher tidal current velocities can dramatically increase the potential of a site for tidal electricity generation. On the other hand, tidal energy has high reliability, excellent energy density, and high durability.
Because the Earth's tides are ultimately due to gravitational interaction with the Moon and Sun and the Earth's rotation, tidal power is practically inexhaustible, and is thus classified as a renewable energy resource. Movement of tides causes a loss of mechanical energy in the Earth-Moon system: this results from pumping of water through natural restrictions around coastlines and consequent viscous dissipation at the seabed and in turbulence. This loss of energy has caused the rotation of the Earth to slow in the 4.5 billion years since its formation. During the last 620 million years the period of rotation of the Earth (length of a day) has increased from 21.9 hours to 24 hours; in this period the Earth-Moon system has lost 17% of its rotational energy. While tidal power will take additional energy from the system, the effect is negligible and would not be noticeable in the foreseeable future.
Methods
Tidal power can be classified into four generating methods:
Tidal stream generator
Tidal stream generators make use of the kinetic energy of moving water to power turbines, in a similar way to wind turbines that use the wind to power turbines. Some tidal generators can be built into the structures of existing bridges or are entirely submersed, thus avoiding concerns over aesthetics or visual impact. Land constrictions such as straits or inlets can create high velocities at specific sites, which can be captured using turbines. These turbines can be horizontal, vertical, open, or ducted.
Tidal barrage | Tidal power | Wikipedia | 488 | 325060 | https://en.wikipedia.org/wiki/Tidal%20power | Technology | Power generation | null |
Tidal barrages use potential energy in the difference in height (or hydraulic head) between high and low tides. When using tidal barrages to generate power, the potential energy from a tide is seized through the strategic placement of specialized dams. When the sea level rises and the tide begins to come in, the temporary increase in tidal power is channeled into a large basin behind the dam, holding a large amount of potential energy. With the receding tide, this energy is then converted into mechanical energy as the water is released through large turbines that create electrical power through the use of generators. Barrages are essentially dams across the full width of a tidal estuary.
Tidal lagoon
A new tidal energy design option is to construct circular retaining walls embedded with turbines that can capture the potential energy of tides. The created reservoirs are similar to those of tidal barrages, except that the location is artificial and does not contain a pre-existing ecosystem.
The lagoons can also be in double (or triple) format without pumping or with pumping that will flatten out the power output. The pumping power could be provided by excess to grid demand renewable energy from for example wind turbines or solar photovoltaic arrays. Excess renewable energy rather than being curtailed could be used and stored for a later period of time. Geographically dispersed tidal lagoons with a time delay between peak production would also flatten out peak production providing near baseload production at a higher cost than other alternatives such as district heating renewable energy storage. The cancelled Tidal Lagoon Swansea Bay in Wales, United Kingdom would have been the first tidal power station of this type once built.
Dynamic tidal power
Dynamic tidal power (or DTP) is a theoretical technology that would exploit an interaction between potential and kinetic energies in tidal flows. It proposes that very long dams (for example: 30–50 km length) be built from coasts straight out into the sea or ocean, without enclosing an area. Tidal phase differences are introduced across the dam, leading to a significant water-level differential in shallow coastal seas – featuring strong coast-parallel oscillating tidal currents such as found in the UK, China, and Korea. | Tidal power | Wikipedia | 432 | 325060 | https://en.wikipedia.org/wiki/Tidal%20power | Technology | Power generation | null |
US and Canadian studies in the 20th century
The first study of large scale tidal power plants was by the US Federal Power Commission in 1924. If built, power plants would have been located in the northern border area of the US state of Maine and the southeastern border area of the Canadian province of New Brunswick, with various dams, powerhouses, and ship locks enclosing the Bay of Fundy and Passamaquoddy Bay (note: see map in reference). Nothing came of the study, and it is unknown whether Canada had been approached about the study by the US Federal Power Commission.
In 1956, utility Nova Scotia Light and Power of Halifax commissioned a pair of studies into commercial tidal power development feasibility on the Nova Scotia side of the Bay of Fundy. The two studies, by Stone & Webster of Boston and by Montreal Engineering Company of Montreal, independently concluded that millions of horsepower (i.e. gigawatts) could be harnessed from Fundy but that development costs would be commercially prohibitive.
There was also a report on the international commission in April 1961 entitled "Investigation of the International Passamaquoddy Tidal Power Project" produced by both the US and Canadian Federal Governments. According to benefit to costs ratios, the project was beneficial to the US but not to Canada.
A study was commissioned by the Canadian & Nova Scotian and New Brunswick governments (Reassessment of Fundy Tidal Power) to determine the potential for tidal barrages at Chignecto Bay and Minas Basin – at the end of the Fundy Bay estuary. There were three sites determined to be financially feasible: Shepody Bay (1550 MW), Cumberland Basin (1085 MW), and Cobequid Bay (3800 MW). These were never built despite their apparent feasibility in 1977. | Tidal power | Wikipedia | 364 | 325060 | https://en.wikipedia.org/wiki/Tidal%20power | Technology | Power generation | null |
US studies in the 21st century
The Snohomish PUD, a public utility district located primarily in Snohomish County, Washington State, began a tidal energy project in 2007. In April 2009 the PUD selected OpenHydro, a company based in Ireland, to develop turbines and equipment for eventual installation. The project as initially designed was to place generation equipment in areas of high tidal flow and operate that equipment for four to five years. After the trial period the equipment would be removed. The project was initially budgeted at a total cost of $10 million, with half of that funding provided by the PUD out of utility reserve funds, and half from grants, primarily from the US federal government. The PUD paid for part of this project from reserves and received a $900,000 grant in 2009 and a $3.5 million grant in 2010 in addition to using reserves to pay an estimated $4 million of costs. In 2010 the budget estimate was increased to $20 million, half to be paid by the utility, half by the federal government. The utility was unable to control costs on this project, and by October 2014, the costs had ballooned to an estimated $38 million and were projected to continue to increase. The PUD proposed that the federal government provide an additional $10 million towards this increased cost, citing a gentlemen's agreement. When the federal government refused to pay this, the PUD cancelled the project after spending nearly $10 million from reserves and grants. The PUD abandoned all tidal energy exploration after this project was cancelled and does not own or operate any tidal energy sources.
Rance tidal power plant in France
In 1966, Électricité de France opened the Rance Tidal Power Station, located on the estuary of the Rance River in Brittany. It was the world's first tidal power station. The plant was for 45 years the largest tidal power station in the world by installed capacity: Its 24 turbines reach peak output at 240 megawatts (MW) and average 57 MW, a capacity factor of approximately 24%. | Tidal power | Wikipedia | 416 | 325060 | https://en.wikipedia.org/wiki/Tidal%20power | Technology | Power generation | null |
Tidal power development in the UK
The world's first marine energy test facility was established in 2003 to start the development of the wave and tidal energy industry in the UK. Based in Orkney, Scotland, the European Marine Energy Centre (EMEC) has supported the deployment of more wave and tidal energy devices than at any other single site in the world. EMEC provides a variety of test sites in real sea conditions. Its grid connected tidal test site is located at the Fall of Warness, off the island of Eday, in a narrow channel which concentrates the tide as it flows between the Atlantic Ocean and North Sea. This area has a very strong tidal current, which can travel up to in spring tides. Tidal energy developers that have tested at the site include: Alstom (formerly Tidal Generation Ltd); ANDRITZ HYDRO Hammerfest; Atlantis Resources Corporation; Nautricity; OpenHydro; Scotrenewables Tidal Power; Voith. The resource could be 4 TJ per year. Elsewhere in the UK, annual energy of 50 TWh can be extracted if 25 GW capacity is installed with pivotable blades.
Current and future tidal power schemes | Tidal power | Wikipedia | 240 | 325060 | https://en.wikipedia.org/wiki/Tidal%20power | Technology | Power generation | null |
The Rance tidal power plant built over a period of six years from 1960 to 1966 at La Rance, France. It has 240 MW installed capacity.
254 MW Sihwa Lake Tidal Power Plant in South Korea is the largest tidal power installation in the world. Construction was completed in 2011.
The Jiangxia Tidal Power Station, south of Hangzhou in China has been operational since 1985, with current installed capacity of 3.2 MW. More tidal power is planned near the mouth of the Yalu River.
The first in-stream tidal current generator in North America (Race Rocks Tidal Power Demonstration Project) was installed at Race Rocks on southern Vancouver Island in September 2006. The Race Rocks project was shut down after operating for five years (2006–2011) because high operating costs produced electricity at a rate that was not economically feasible. The next phase in the development of this tidal current generator will be in Nova Scotia (Bay of Fundy).
A small project was built by the Soviet Union at Kislaya Guba on the Barents Sea. It has 0.4 MW installed capacity. In 2006 it was upgraded with a 1.2 MW experimental advanced orthogonal turbine.
Jindo Uldolmok Tidal Power Plant in South Korea is a tidal stream generation scheme planned to be expanded progressively to 90 MW of capacity by 2013. The first 1 MW was installed in May 2009.
A 1.2 MW SeaGen system became operational in late 2008 on Strangford Lough in Northern Ireland. It was decommissioned and removed in 2016.
The contract for an 812 MW tidal barrage near Ganghwa Island (South Korea) north-west of Incheon has been signed by Daewoo. Completion was planned for 2015 but project was retracted in 2013.
A 1,320 MW barrage was proposed by the South Korean government in 2009, to be built around islands west of Incheon. The project halted since 2012 due to environmental concerns.
The Scottish Government has approved plans for a 10 MW ''Òran na Mara'' array of tidal stream generators near Islay, Scotland, costing 40 million pounds, and consisting of 10 turbines – enough to power over 5,000 homes. The first turbine was expected to be in operation by 2013 and then once again announced in 2021, but as of 2023 none existed. | Tidal power | Wikipedia | 460 | 325060 | https://en.wikipedia.org/wiki/Tidal%20power | Technology | Power generation | null |
The Indian state of Gujarat was planning to host South Asia's first commercial-scale tidal power station. The company Atlantis Resources planned to install a 50 MW tidal farm in the Gulf of Kutch on India's west coast, with construction planned to start 2012, later withdrawn due to high costs.
Ocean Renewable Power Corporation was the first company to deliver tidal power to the US grid in September 2012 when its pilot TidGen system was successfully deployed in Cobscook Bay, near Eastport.
In New York City, Verdant Power successfully deployed and operated three tidal turbines in the East River near Roosevelt Island, on a single triangular base system, called a TriFrame. The Roosevelt Island Tidal Energy (RITE) Project generated over 300MWh of electricity to the local grid, an American marine energy record. The system's performance was independently confirmed by Scotland's European Marine Energy Centre (EMEC) under the new International Electrotechnical Commission (IEC) international standards. This is the first instance of a third-party verification of a tidal energy converter to an international standard.
The largest tidal energy project entitled MeyGen (398 MW) is currently in construction in the Pentland Firth in northern Scotland with 6 MW operational since 2018.
Construction of a 320 MW tidal lagoon power plant outside the city of Swansea in the UK was granted planning permission in June 2015, however it was later rejected by the UK government in 2018. If built it would have been the world's first tidal power plant based on a constructed lagoon.
Mersey Tidal Power, a proposed tidal range barrage within the channel of the Mersey Estuary with a capacity of up to 1 GW is undergoing local consultation by the Liverpool City Region Combined Authority.
Up to 240 MW of tidal stream generation is proposed at Morlais, Anglesey from multiple developers, with the first turbines expected to be installed in 2026. , a total of 38 MW of capacity has been awarded Contracts for Difference to supply power to the GB grid. | Tidal power | Wikipedia | 403 | 325060 | https://en.wikipedia.org/wiki/Tidal%20power | Technology | Power generation | null |
Issues and challenges
Environmental concerns
Tidal power can affect marine life. The turbines' rotating blades can accidentally kill swimming sea life. Projects such as the one in Strangford include a safety mechanism that turns off the turbine when marine animals approach. However, this feature causes a major loss in energy because of the amount of marine life that passes through the turbines. Some fish may avoid the area if threatened by a constantly rotating or noisy object. Marine life is a huge factor when siting tidal power energy generators, and precautions are taken to ensure that as few marine animals as possible are affected by it. In terms of global warming potential (i.e. carbon footprint), the impact of tidal power generation technologies ranges between 15 and 37 gCO2-eq/kWhe, with a median value of 23.8 gCO2-eq/kWhe. This is in line with the impact of other renewables like wind and solar power, and significantly better than fossil-based technologies. The Tethys database provides access to scientific literature and general information on the potential environmental effects of tidal energy.
Tidal turbines
The main environmental concern with tidal energy is associated with blade strike and entanglement of marine organisms as high-speed water increases the risk of organisms being pushed near or through these devices. As with all offshore renewable energies, there is also a concern about how the creation of electromagnetic fields and acoustic outputs may affect marine organisms. Because these devices are in the water, the acoustic output can be greater than those created with offshore wind energy. Depending on the frequency and amplitude of sound generated by the tidal energy devices, this acoustic output can have varying effects on marine mammals (particularly those who echolocate to communicate and navigate in the marine environment, such as dolphins and whales). Tidal energy removal can also cause environmental concerns such as degrading far-field water quality and disrupting sediment processes. Depending on the size of the project, these effects can range from small traces of sediment building up near the tidal device to severely affecting nearshore ecosystems and processes. | Tidal power | Wikipedia | 413 | 325060 | https://en.wikipedia.org/wiki/Tidal%20power | Technology | Power generation | null |
Tidal barrage
Installing a barrage may change the shoreline within the bay or estuary, affecting a large ecosystem that depends on tidal flats. Inhibiting the flow of water in and out of the bay, there may also be less flushing of the bay or estuary, causing additional turbidity (suspended solids) and less saltwater, which may result in the death of fish that act as a vital food source to birds and mammals. Migrating fish may also be unable to access breeding streams, and may attempt to pass through the turbines. The same acoustic concerns apply to tidal barrages. Decreasing shipping accessibility can become a socio-economic issue, though locks can be added to allow slow passage. However, the barrage may improve the local economy by increasing land access as a bridge. Calmer waters may also allow better recreation in the bay or estuary. In August 2004, a humpback whale swam through the open sluice gate of the Annapolis Royal Generating Station at slack tide, ending up trapped for several days before eventually finding its way out to the Annapolis Basin.
Tidal lagoon
Environmentally, the main concerns are blade strike on fish attempting to enter the lagoon, the acoustic output from turbines, and changes in sedimentation processes. However, all these effects are localized and do not affect the entire estuary or bay.
Corrosion
Saltwater causes corrosion in metal parts. It can be difficult to maintain tidal stream generators due to their size and depth in the water. The use of corrosion-resistant materials such as stainless steels, high-nickel alloys, copper-nickel alloys, nickel-copper alloys and titanium can greatly reduce, or eliminate corrosion damage. Composite materials could also be used, as composites do not corrode and could provide lightweight, durable structures for tidal power. Composite materials are being evaluated for tidal power.
Mechanical fluids, such as lubricants, can leak out, which may be harmful to the marine life nearby. Proper maintenance can minimize the number of harmful chemicals that may enter the environment.
Fouling
The biological events that happen when placing any structure in an area of high tidal currents and high biological productivity in the ocean will ensure that the structure becomes an ideal substrate for the growth of marine organisms. | Tidal power | Wikipedia | 440 | 325060 | https://en.wikipedia.org/wiki/Tidal%20power | Technology | Power generation | null |
Cost
Tidal energy has a high initial cost, which may be one of the reasons why it is not a popular source of renewable energy, although research has shown that the public is willing to pay for and support research and development of tidal energy devices. The methods of generating electricity from tidal energy are relatively new technology. Tidal energy is however still very early in the research process and it may be possible to reduce costs in future. The cost-effectiveness varies according to the site of the tidal generators. One indication of cost-effectiveness is the Gibrat ratio, which is the length of the barrage in metres divided by the annual energy production in kilowatt hours.
As tidal energy is reliable, it can reasonably be predicted how long it will take to pay off the high up-front cost of these generators. Due to the success of a greatly simplified design, the orthogonal turbine offers considerable cost savings. As a result, the production period of each generating unit is reduced, lower metal consumption is needed and technical efficiency is greater.
A possible risk is rising sea levels due to climate change, which may alter the characteristics of the local tides reducing future power generation.
Structural health monitoring
The high load factors resulting from the fact that water is around 800 times denser than air, and the predictable and reliable nature of tides compared with the wind, make tidal energy particularly attractive for electric power generation. Condition monitoring is the key for exploiting it cost-efficiently. | Tidal power | Wikipedia | 288 | 325060 | https://en.wikipedia.org/wiki/Tidal%20power | Technology | Power generation | null |
Domain theory is a branch of mathematics that studies special kinds of partially ordered sets (posets) commonly called domains. Consequently, domain theory can be considered as a branch of order theory. The field has major applications in computer science, where it is used to specify denotational semantics, especially for functional programming languages. Domain theory formalizes the intuitive ideas of approximation and convergence in a very general way and is closely related to topology.
Motivation and intuition
The primary motivation for the study of domains, which was initiated by Dana Scott in the late 1960s, was the search for a denotational semantics of the lambda calculus. In this formalism, one considers "functions" specified by certain terms in the language. In a purely syntactic way, one can go from simple functions to functions that take other functions as their input arguments. Using again just the syntactic transformations available in this formalism, one can obtain so-called fixed-point combinators (the best-known of which is the Y combinator); these, by definition, have the property that f(Y(f)) = Y(f) for all functions f.
To formulate such a denotational semantics, one might first try to construct a model for the lambda calculus, in which a genuine (total) function is associated with each lambda term. Such a model would formalize a link between the lambda calculus as a purely syntactic system and the lambda calculus as a notational system for manipulating concrete mathematical functions. The combinator calculus is such a model. However, the elements of the combinator calculus are functions from functions to functions; in order for the elements of a model of the lambda calculus to be of arbitrary domain and range, they could not be true functions, only partial functions.
Scott got around this difficulty by formalizing a notion of "partial" or "incomplete" information to represent computations that have not yet returned a result. This was modeled by considering, for each domain of computation (e.g. the natural numbers), an additional element that represents an undefined output, i.e. the "result" of a computation that never ends. In addition, the domain of computation is equipped with an ordering relation, in which the "undefined result" is the least element. | Domain theory | Wikipedia | 467 | 325077 | https://en.wikipedia.org/wiki/Domain%20theory | Mathematics | Order theory | null |
The important step to finding a model for the lambda calculus is to consider only those functions (on such a partially ordered set) that are guaranteed to have least fixed points. The set of these functions, together with an appropriate ordering, is again a "domain" in the sense of the theory. But the restriction to a subset of all available functions has another great benefit: it is possible to obtain domains that contain their own function spaces, i.e. one gets functions that can be applied to themselves.
Beside these desirable properties, domain theory also allows for an appealing intuitive interpretation. As mentioned above, the domains of computation are always partially ordered. This ordering represents a hierarchy of information or knowledge. The higher an element is within the order, the more specific it is and the more information it contains. Lower elements represent incomplete knowledge or intermediate results.
Computation then is modeled by applying monotone functions repeatedly on elements of the domain in order to refine a result. Reaching a fixed point is equivalent to finishing a calculation. Domains provide a superior setting for these ideas since fixed points of monotone functions can be guaranteed to exist and, under additional restrictions, can be approximated from below.
A guide to the formal definitions
In this section, the central concepts and definitions of domain theory will be introduced. The above intuition of domains being information orderings will be emphasized to motivate the mathematical formalization of the theory. The precise formal definitions are to be found in the dedicated articles for each concept. A list of general order-theoretic definitions, which include domain theoretic notions as well can be found in the order theory glossary. The most important concepts of domain theory will nonetheless be introduced below.
Directed sets as converging specifications
As mentioned before, domain theory deals with partially ordered sets to model a domain of computation. The goal is to interpret the elements of such an order as pieces of information or (partial) results of a computation, where elements that are higher in the order extend the information of the elements below them in a consistent way. From this simple intuition it is already clear that domains often do not have a greatest element, since this would mean that there is an element that contains the information of all other elements—a rather uninteresting situation. | Domain theory | Wikipedia | 455 | 325077 | https://en.wikipedia.org/wiki/Domain%20theory | Mathematics | Order theory | null |
A concept that plays an important role in the theory is that of a directed subset of a domain; a directed subset is a non-empty subset of the order in which any two elements have an upper bound that is an element of this subset. In view of our intuition about domains, this means that any two pieces of information within the directed subset are consistently extended by some other element in the subset. Hence we can view directed subsets as consistent specifications, i.e. as sets of partial results in which no two elements are contradictory. This interpretation can be compared with the notion of a convergent sequence in analysis, where each element is more specific than the preceding one. Indeed, in the theory of metric spaces, sequences play a role that is in many aspects analogous to the role of directed sets in domain theory.
Now, as in the case of sequences, we are interested in the limit of a directed set. According to what was said above, this would be an element that is the most general piece of information that extends the information of all elements of the directed set, i.e. the unique element that contains exactly the information that was present in the directed set, and nothing more. In the formalization of order theory, this is just the least upper bound of the directed set. As in the case of the limit of a sequence, the least upper bound of a directed set does not always exist.
Naturally, one has a special interest in those domains of computations in which all consistent specifications converge, i.e. in orders in which all directed sets have a least upper bound. This property defines the class of directed-complete partial orders, or dcpo for short. Indeed, most considerations of domain theory do only consider orders that are at least directed complete.
From the underlying idea of partially specified results as representing incomplete knowledge, one derives another desirable property: the existence of a least element. Such an element models that state of no information—the place where most computations start. It also can be regarded as the output of a computation that does not return any result at all. | Domain theory | Wikipedia | 421 | 325077 | https://en.wikipedia.org/wiki/Domain%20theory | Mathematics | Order theory | null |
Computations and domains
Now that we have some basic formal descriptions of what a domain of computation should be, we can turn to the computations themselves. Clearly, these have to be functions, taking inputs from some computational domain and returning outputs in some (possibly different) domain. However, one would also expect that the output of a function will contain more information when the information content of the input is increased. Formally, this means that we want a function to be monotonic.
When dealing with dcpos, one might also want computations to be compatible with the formation of limits of a directed set. Formally, this means that, for some function f, the image f(D) of a directed set D (i.e. the set of the images of each element of D) is again directed and has as a least upper bound the image of the least upper bound of D. One could also say that f preserves directed suprema. Also note that, by considering directed sets of two elements, such a function also has to be monotonic. These properties give rise to the notion of a Scott-continuous function. Since this often is not ambiguous one also may speak of continuous functions.
Approximation and finiteness
Domain theory is a purely qualitative approach to modeling the structure of information states. One can say that something contains more information, but the amount of additional information is not specified. Yet, there are some situations in which one wants to speak about elements that are in a sense much simpler (or much more incomplete) than a given state of information. For example, in the natural subset-inclusion ordering on some powerset, any infinite element (i.e. set) is much more "informative" than any of its finite subsets.
If one wants to model such a relationship, one may first want to consider the induced strict order < of a domain with order ≤. However, while this is a useful notion in the case of total orders, it does not tell us much in the case of partially ordered sets. Considering again inclusion-orders of sets, a set is already strictly smaller than another, possibly infinite, set if it contains just one less element. One would, however, hardly agree that this captures the notion of being "much simpler". | Domain theory | Wikipedia | 459 | 325077 | https://en.wikipedia.org/wiki/Domain%20theory | Mathematics | Order theory | null |
Way-below relation
A more elaborate approach leads to the definition of the so-called order of approximation, which is more suggestively also called the way-below relation. An element x is way below an element y, if, for every directed set D with supremum such that
,
there is some element d in D such that
.
Then one also says that x approximates y and writes
.
This does imply that
,
since the singleton set {y} is directed. For an example, in an ordering of sets, an infinite set is way above any of its finite subsets. On the other hand, consider the directed set (in fact, the chain) of finite sets
Since the supremum of this chain is the set of all natural numbers N, this shows that no infinite set is way below N.
However, being way below some element is a relative notion and does not reveal much about an element alone. For example, one would like to characterize finite sets in an order-theoretic way, but even infinite sets can be way below some other set. The special property of these finite elements x is that they are way below themselves, i.e.
.
An element with this property is also called compact. Yet, such elements do not have to be "finite" nor "compact" in any other mathematical usage of the terms. The notation is nonetheless motivated by certain parallels to the respective notions in set theory and topology. The compact elements of a domain have the important special property that they cannot be obtained as a limit of a directed set in which they did not already occur.
Many other important results about the way-below relation support the claim that this definition is appropriate to capture many important aspects of a domain.
Bases of domains
The previous thoughts raise another question: is it possible to guarantee that all elements of a domain can be obtained as a limit of much simpler elements? This is quite relevant in practice, since we cannot compute infinite objects but we may still hope to approximate them arbitrarily closely. | Domain theory | Wikipedia | 409 | 325077 | https://en.wikipedia.org/wiki/Domain%20theory | Mathematics | Order theory | null |
More generally, we would like to restrict to a certain subset of elements as being sufficient for getting all other elements as least upper bounds. Hence, one defines a base of a poset P as being a subset B of P, such that, for each x in P, the set of elements in B that are way below x contains a directed set with supremum x. The poset P is a continuous poset if it has some base. Especially, P itself is a base in this situation. In many applications, one restricts to continuous (d)cpos as a main object of study.
Finally, an even stronger restriction on a partially ordered set is given by requiring the existence of a base of finite elements. Such a poset is called algebraic. From the viewpoint of denotational semantics, algebraic posets are particularly well-behaved, since they allow for the approximation of all elements even when restricting to finite ones. As remarked before, not every finite element is "finite" in a classical sense and it may well be that the finite elements constitute an uncountable set.
In some cases, however, the base for a poset is countable. In this case, one speaks of an ω-continuous poset. Accordingly, if the countable base consists entirely of finite elements, we obtain an order that is ω-algebraic.
Special types of domains
A simple special case of a domain is known as an elementary or flat domain. This consists of a set of incomparable elements, such as the integers, along with a single "bottom" element considered smaller than all other elements.
One can obtain a number of other interesting special classes of ordered structures that could be suitable as "domains". We already mentioned continuous posets and algebraic posets. More special versions of both are continuous and algebraic cpos. Adding even further completeness properties one obtains continuous lattices and algebraic lattices, which are just complete lattices with the respective properties. For the algebraic case, one finds broader classes of posets that are still worth studying: historically, the Scott domains were the first structures to be studied in domain theory. Still wider classes of domains are constituted by SFP-domains, L-domains, and bifinite domains. | Domain theory | Wikipedia | 457 | 325077 | https://en.wikipedia.org/wiki/Domain%20theory | Mathematics | Order theory | null |
All of these classes of orders can be cast into various categories of dcpos, using functions that are monotone, Scott-continuous, or even more specialized as morphisms. Finally, note that the term domain itself is not exact and thus is only used as an abbreviation when a formal definition has been given before or when the details are irrelevant.
Important results
A poset D is a dcpo if and only if each chain in D has a supremum. (The 'if' direction relies on the axiom of choice.)
If f is a continuous function on a domain D then it has a least fixed point, given as the least upper bound of all finite iterations of f on the least element ⊥:
.
This is the Kleene fixed-point theorem. The symbol is the directed join.
Generalizations
A continuity space is a generalization of metric spaces and posets that can be used to unify the notions of metric spaces and domains. | Domain theory | Wikipedia | 196 | 325077 | https://en.wikipedia.org/wiki/Domain%20theory | Mathematics | Order theory | null |
Pollination management is the horticultural practices that accomplish or enhance pollination of a crop, to improve yield or quality, by understanding of the particular crop's pollination needs, and by knowledgeable management of pollenizers, pollinators, and pollination conditions.
While people think first of the European honey bee when pollination comes up, in fact there are many different means of pollination management that are used, both other insects and other mechanisms. There are other insects commercially available that are more efficient, like the blue orchard bee for fruit and nut trees, local bumblebees better specialized for some other crops, hand pollination that is essential for production of hybrid seeds and some greenhouse situations, and even pollination machines.
Pollinator decline
With the decline of both wild and domestic pollinator populations, pollination management is becoming an increasingly important part of horticulture. Factors that cause the loss of pollinators include pesticide misuse, unprofitability of beekeeping for honey, rapid transfer of pests and diseases to new areas of the globe, urban/suburban development, changing crop patterns, clearcut logging (particularly when mixed forests are replaced by monoculture pine), clearing of hedgerows and other wild areas, bad diet because of loss of floral biodiversity, and a loss of nectar corridors for migratory pollinators. With the declining habitat and resources available to sustain bee populations, populations are declining.
Importance
The increasing size of fields and orchards (monoculture) increase the importance of pollination management. Monoculture can cause a brief period when pollinators have more food resources than they can use (but monofloral diet can reduce their immune system) while other periods of the year can bring starvation or pesticide contamination of food sources. Most nectar source and pollen source throughout the growing season to build up their numbers. | Pollination management | Wikipedia | 373 | 325663 | https://en.wikipedia.org/wiki/Pollination%20management | Technology | Horticulture | null |
Crops that traditionally have had managed pollination include apple, almonds, pears, some plum and cherry varieties, blueberries, cranberries, cucumbers, cantaloupe, watermelon, alfalfa seeds, onion seeds, and many others. Some crops that have traditionally depended entirely on chance pollination by wild pollinators need pollination management nowadays to make a profitable crop. Many of these were at one time universally turning to honeybees, but as science has shown that honeybees are actually inefficient pollinators, demand for other managed pollinators has risen. While honeybees may visit dozens of different kinds of flowers, diluting the orchard pollen they carry, the Blue orchard bee will visit only the intended tree, producing a much higher fertilization rate. The focus on the specific tree also makes the orchard bee 100 times more efficient at pollinating, per bee.
Some crops, especially when planted in a monoculture situation, require a very high level of pollinators to produce economically viable crops, especially if depending on the more generalized honeybee. This may be because of lack of attractiveness of the blossoms, or from trying to pollinate with an alternative when the native pollinator is extinct or rare. These include crops such as alfalfa, cranberries, and kiwifruit. This technique is known as saturation pollination. In many such cases, various native bees are vastly more efficient at pollination (e.g., with blueberries), but the inefficiency of the honey bees is compensated for by using large numbers of hives, the total number of foragers thereby far exceeding the local abundance of native pollinators. In a very few cases, it has been possible to develop commercially viable pollination techniques that use the more efficient pollinators, rather than continued reliance on honey bees, as in the management of the alfalfa leafcutter bee.
In the case of the kiwifruit, its flowers do not even produce nectar, so that honeybees are reluctant to even visit them, unless present in such overwhelming numbers that they do so incidentally. This has led bumblebee pollination companies to begin offering their services for kiwifruit, as they appear to be far more efficient at the job than honeybees, even more efficient than hand pollination. | Pollination management | Wikipedia | 488 | 325663 | https://en.wikipedia.org/wiki/Pollination%20management | Technology | Horticulture | null |
It is estimated that about one hive per acre will sufficiently pollinate watermelons. In the 1950s when the woods were full of wild bee trees, and beehives were normally kept on most South Carolina farms, a farmer who grew ten acres (4 ha) of watermelons would be a large grower and probably had all the pollination needed. But today's grower may grow 200 acres (80 ha), and, if lucky, there might be one bee tree left within range. The only option in the current economy is to bring beehives to the field during blossom time.
Types of pollinators
Organisms that are currently being used as pollinators in managed pollination are honey bees, bumblebees, alfalfa leafcutter bees, and orchard mason bees. Other species are expected to be added to this list as this field develops. Humans also can be pollinators, as the gardener who hand pollinates her squash blossoms, or the Middle Eastern farmer, who climbs his date palms to pollinate them.
The Cooperative extension service recommends one honey bee hive per acre (2.5 hives per hectare) for standard watermelon varieties to meet this crop's pollination needs. In the past, when fields were small, pollination was accomplished by a mix of bees kept on farms, bumblebees, carpenter bees, feral honey bees in hollow trees and other insects. Today, with melons planted in large tracts, the grower may no longer have hives on the farm; he may have poisoned many of the pollinators by spraying blooming cotton; he may have logged off the woods, removing hollow trees that provided homes for bees, and pushed out the hedgerows that were home for solitary native bees and other pollinating insects.
Planning for improved pollination
Before pollination needs were understood, orchardists often planted entire blocks of apples of a single variety. Because apples are self-sterile, and different members of a single variety are genetic clones (equivalent to a single plant), this is not a good idea. Growers now supply pollenizers, by planting crab apples interspersed in the rows, or by grafting crab apple limbs on some trees. Pollenizers can also be supplied by putting drum bouquets of crab apples or a compatible apple variety in the orchard blocks. | Pollination management | Wikipedia | 475 | 325663 | https://en.wikipedia.org/wiki/Pollination%20management | Technology | Horticulture | null |
The field of pollination management cannot be placed wholly within any other field, because it bridges several fields. It draws from horticulture, apiculture, zoology (especially entomology), ecology, and botany.
Improving pollination with suboptimal bee densities
Growers’ demand for beehives far exceeds the available supply. The number of managed beehives in the US has steadily declined from close to 6 million after WWII, to less than 2.5 million today. In contrast, the area dedicated to growing bee-pollinated crops has grown over 300% in the same time period. To make matters worse, in the past five years we have seen a decline in winter managed beehives, which has reached an unprecedented rate near 30%. At present, there is an enormous demand for beehive rentals that cannot always be met. There is a clear need across the agricultural industry for a management tool to draw pollinators into cultivations and encourage them to preferentially visit and pollinate the flowering crop. By attracting pollinators like honeybees and increasing their foraging behavior, particularly in the center of large plots, we can increase grower returns and optimize yield from their plantings. | Pollination management | Wikipedia | 250 | 325663 | https://en.wikipedia.org/wiki/Pollination%20management | Technology | Horticulture | null |
In discrete mathematics, particularly in graph theory, a graph is a structure consisting of a set of objects where some pairs of the objects are in some sense "related". The objects are represented by abstractions called vertices (also called nodes or points) and each of the related pairs of vertices is called an edge (also called link or line). Typically, a graph is depicted in diagrammatic form as a set of dots or circles for the vertices, joined by lines or curves for the edges.
The edges may be directed or undirected. For example, if the vertices represent people at a party, and there is an edge between two people if they shake hands, then this graph is undirected because any person A can shake hands with a person B only if B also shakes hands with A. In contrast, if an edge from a person A to a person B means that A owes money to B, then this graph is directed, because owing money is not necessarily reciprocated.
Graphs are the basic subject studied by graph theory. The word "graph" was first used in this sense by J. J. Sylvester in 1878 due to a direct relation between mathematics and chemical structure (what he called a chemico-graphical image).
Definitions
Definitions in graph theory vary. The following are some of the more basic ways of defining graphs and related mathematical structures.
Graph
A graph (sometimes called an undirected graph to distinguish it from a directed graph, or a simple graph to distinguish it from a multigraph) is a pair , where is a set whose elements are called vertices (singular: vertex), and is a set of unordered pairs of vertices, whose elements are called edges (sometimes links or lines).
The vertices and of an edge are called the edge's endpoints. The edge is said to join and and to be incident on them. A vertex may belong to no edge, in which case it is not joined to any other vertex and is called isolated. When an edge exists, the vertices and are called adjacent.
A multigraph is a generalization that allows multiple edges to have the same pair of endpoints. In some texts, multigraphs are simply called graphs.
Sometimes, graphs are allowed to contain loops, which are edges that join a vertex to itself. To allow loops, the pairs of vertices in must be allowed to have the same node twice. Such generalized graphs are called graphs with loops or simply graphs when it is clear from the context that loops are allowed. | Graph (discrete mathematics) | Wikipedia | 508 | 325806 | https://en.wikipedia.org/wiki/Graph%20%28discrete%20mathematics%29 | Mathematics | Discrete mathematics | null |
Generally, the vertex set is taken to be finite (which implies that the edge set is also finite). Sometimes infinite graphs are considered, but they are usually viewed as a special kind of binary relation, because most results on finite graphs either do not extend to the infinite case or need a rather different proof.
An empty graph is a graph that has an empty set of vertices (and thus an empty set of edges). The order of a graph is its number of vertices, usually denoted by . The size of a graph is its number of edges, typically denoted by . However, in some contexts, such as for expressing the computational complexity of algorithms, the term size is used for the quantity (otherwise, a non-empty graph could have size 0). The degree or valency of a vertex is the number of edges that are incident to it; for graphs with loops, a loop is counted twice.
In a graph of order , the maximum degree of each vertex is (or if loops are allowed, because a loop contributes 2 to the degree), and the maximum number of edges is (or if loops are allowed).
The edges of a graph define a symmetric relation on the vertices, called the adjacency relation. Specifically, two vertices and are adjacent if is an edge. A graph is fully determined by its adjacency matrix , which is an square matrix, with specifying the number of connections from vertex to vertex . For a simple graph, is either 0, indicating disconnection, or 1, indicating connection; moreover because an edge in a simple graph cannot start and end at the same vertex. Graphs with self-loops will be characterized by some or all being equal to a positive integer, and multigraphs (with multiple edges between vertices) will be characterized by some or all being equal to a positive integer. Undirected graphs will have a symmetric adjacency matrix (meaning ).
Directed graph
A directed graph or digraph is a graph in which edges have orientations.
In one restricted but very common sense of the term, a directed graph is a pair comprising:
, a set of vertices (also called nodes or points);
, a set of edges (also called directed edges, directed links, directed lines, arrows, or arcs), which are ordered pairs of distinct vertices: .
To avoid ambiguity, this type of object may be called precisely a directed simple graph. | Graph (discrete mathematics) | Wikipedia | 488 | 325806 | https://en.wikipedia.org/wiki/Graph%20%28discrete%20mathematics%29 | Mathematics | Discrete mathematics | null |
In the edge directed from to , the vertices and are called the endpoints of the edge, the tail of the edge and the head of the edge. The edge is said to join and and to be incident on and on . A vertex may exist in a graph and not belong to an edge. The edge is called the inverted edge of . Multiple edges, not allowed under the definition above, are two or more edges with both the same tail and the same head.
In one more general sense of the term allowing multiple edges, a directed graph is sometimes defined to be an ordered triple comprising:
, a set of vertices (also called nodes or points);
, a set of edges (also called directed edges, directed links, directed lines, arrows or arcs);
, an incidence function mapping every edge to an ordered pair of vertices (that is, an edge is associated with two distinct vertices): .
To avoid ambiguity, this type of object may be called precisely a directed multigraph.
A loop is an edge that joins a vertex to itself. Directed graphs as defined in the two definitions above cannot have loops, because a loop joining a vertex to itself is the edge (for a directed simple graph) or is incident on (for a directed multigraph) which is not in . So to allow loops the definitions must be expanded. For directed simple graphs, the definition of should be modified to . For directed multigraphs, the definition of should be modified to . To avoid ambiguity, these types of objects may be called precisely a directed simple graph permitting loops and a directed multigraph permitting loops (or a quiver) respectively.
The edges of a directed simple graph permitting loops is a homogeneous relation ~ on the vertices of that is called the adjacency relation of . Specifically, for each edge , its endpoints and are said to be adjacent to one another, which is denoted .
Mixed graph
A mixed graph is a graph in which some edges may be directed and some may be undirected. It is an ordered triple for a mixed simple graph and for a mixed multigraph with , (the undirected edges), (the directed edges), and defined as above. Directed and undirected graphs are special cases.
Weighted graph
A weighted graph or a network is a graph in which a number (the weight) is assigned to each edge. Such weights might represent for example costs, lengths or capacities, depending on the problem at hand. Such graphs arise in many contexts, for example in shortest path problems such as the traveling salesman problem. | Graph (discrete mathematics) | Wikipedia | 512 | 325806 | https://en.wikipedia.org/wiki/Graph%20%28discrete%20mathematics%29 | Mathematics | Discrete mathematics | null |
Types of graphs
Oriented graph
One definition of an oriented graph is that it is a directed graph in which at most one of and may be edges of the graph. That is, it is a directed graph that can be formed as an orientation of an undirected (simple) graph.
Some authors use "oriented graph" to mean the same as "directed graph". Some authors use "oriented graph" to mean any orientation of a given undirected graph or multigraph.
Regular graph
A regular graph is a graph in which each vertex has the same number of neighbours, i.e., every vertex has the same degree. A regular graph with vertices of degree k is called a k‑regular graph or regular graph of degree k.
Complete graph
A complete graph is a graph in which each pair of vertices is joined by an edge. A complete graph contains all possible edges.
Finite graph
A finite graph is a graph in which the vertex set and the edge set are finite sets. Otherwise, it is called an infinite graph.
Most commonly in graph theory it is implied that the graphs discussed are finite. If the graphs are infinite, that is usually specifically stated.
Connected graph
In an undirected graph, an unordered pair of vertices is called connected if a path leads from x to y. Otherwise, the unordered pair is called disconnected.
A connected graph is an undirected graph in which every unordered pair of vertices in the graph is connected. Otherwise, it is called a disconnected graph.
In a directed graph, an ordered pair of vertices is called strongly connected if a directed path leads from x to y. Otherwise, the ordered pair is called weakly connected if an undirected path leads from x to y after replacing all of its directed edges with undirected edges. Otherwise, the ordered pair is called disconnected.
A strongly connected graph is a directed graph in which every ordered pair of vertices in the graph is strongly connected. Otherwise, it is called a weakly connected graph if every ordered pair of vertices in the graph is weakly connected. Otherwise it is called a disconnected graph.
A k-vertex-connected graph or k-edge-connected graph is a graph in which no set of vertices (respectively, edges) exists that, when removed, disconnects the graph. A k-vertex-connected graph is often called simply a k-connected graph.
Bipartite graph | Graph (discrete mathematics) | Wikipedia | 485 | 325806 | https://en.wikipedia.org/wiki/Graph%20%28discrete%20mathematics%29 | Mathematics | Discrete mathematics | null |
A bipartite graph is a simple graph in which the vertex set can be partitioned into two sets, W and X, so that no two vertices in W share a common edge and no two vertices in X share a common edge. Alternatively, it is a graph with a chromatic number of 2.
In a complete bipartite graph, the vertex set is the union of two disjoint sets, W and X, so that every vertex in W is adjacent to every vertex in X but there are no edges within W or X.
Path graph
A path graph or linear graph of order is a graph in which the vertices can be listed in an order v1, v2, …, vn such that the edges are the where i = 1, 2, …, n − 1. Path graphs can be characterized as connected graphs in which the degree of all but two vertices is 2 and the degree of the two remaining vertices is 1. If a path graph occurs as a subgraph of another graph, it is a path in that graph.
Planar graph
A planar graph is a graph whose vertices and edges can be drawn in a plane such that no two of the edges intersect.
Cycle graph
A cycle graph or circular graph of order is a graph in which the vertices can be listed in an order v1, v2, …, vn such that the edges are the where i = 1, 2, …, n − 1, plus the edge . Cycle graphs can be characterized as connected graphs in which the degree of all vertices is 2. If a cycle graph occurs as a subgraph of another graph, it is a cycle or circuit in that graph.
Tree
A tree is an undirected graph in which any two vertices are connected by exactly one path, or equivalently a connected acyclic undirected graph.
A forest is an undirected graph in which any two vertices are connected by at most one path, or equivalently an acyclic undirected graph, or equivalently a disjoint union of trees.
Polytree
A polytree (or directed tree or oriented tree or singly connected network) is a directed acyclic graph (DAG) whose underlying undirected graph is a tree.
A polyforest (or directed forest or oriented forest) is a directed acyclic graph whose underlying undirected graph is a forest. | Graph (discrete mathematics) | Wikipedia | 491 | 325806 | https://en.wikipedia.org/wiki/Graph%20%28discrete%20mathematics%29 | Mathematics | Discrete mathematics | null |
Advanced classes
More advanced kinds of graphs are:
Petersen graph and its generalizations;
perfect graphs;
cographs;
chordal graphs;
other graphs with large automorphism groups: vertex-transitive, arc-transitive, and distance-transitive graphs;
strongly regular graphs and their generalizations distance-regular graphs.
Properties of graphs
Two edges of a graph are called adjacent if they share a common vertex. Two edges of a directed graph are called consecutive if the head of the first one is the tail of the second one. Similarly, two vertices are called adjacent if they share a common edge (consecutive if the first one is the tail and the second one is the head of an edge), in which case the common edge is said to join the two vertices. An edge and a vertex on that edge are called incident.
The graph with only one vertex and no edges is called the trivial graph. A graph with only vertices and no edges is known as an edgeless graph. The graph with no vertices and no edges is sometimes called the null graph or empty graph, but the terminology is not consistent and not all mathematicians allow this object.
Normally, the vertices of a graph, by their nature as elements of a set, are distinguishable. This kind of graph may be called vertex-labeled. However, for many questions it is better to treat vertices as indistinguishable. (Of course, the vertices may be still distinguishable by the properties of the graph itself, e.g., by the numbers of incident edges.) The same remarks apply to edges, so graphs with labeled edges are called edge-labeled. Graphs with labels attached to edges or vertices are more generally designated as labeled. Consequently, graphs in which vertices are indistinguishable and edges are indistinguishable are called unlabeled. (In the literature, the term labeled may apply to other kinds of labeling, besides that which serves only to distinguish different vertices or edges.)
The category of all graphs is the comma category Set ↓ D where D: Set → Set is the functor taking a set s to s × s.
Examples | Graph (discrete mathematics) | Wikipedia | 435 | 325806 | https://en.wikipedia.org/wiki/Graph%20%28discrete%20mathematics%29 | Mathematics | Discrete mathematics | null |
The diagram is a schematic representation of the graph with vertices and edges
In computer science, directed graphs are used to represent knowledge (e.g., conceptual graph), finite-state machines, and many other discrete structures.
A binary relation R on a set X defines a directed graph. An element x of X is a direct predecessor of an element y of X if and only if xRy.
A directed graph can model information networks such as Twitter, with one user following another.
Particularly regular examples of directed graphs are given by the Cayley graphs of finitely-generated groups, as well as Schreier coset graphs
In category theory, every small category has an underlying directed multigraph whose vertices are the objects of the category, and whose edges are the arrows of the category. In the language of category theory, one says that there is a forgetful functor from the category of small categories to the category of quivers.
Graph operations
There are several operations that produce new graphs from initial ones, which might be classified into the following categories:
unary operations, which create a new graph from an initial one, such as:
edge contraction,
line graph,
dual graph,
complement graph,
graph rewriting;
binary operations, which create a new graph from two initial ones, such as:
disjoint union of graphs,
cartesian product of graphs,
tensor product of graphs,
strong product of graphs,
lexicographic product of graphs,
series–parallel graphs.
Generalizations
In a hypergraph, an edge can join any positive number of vertices.
An undirected graph can be seen as a simplicial complex consisting of 1-simplices (the edges) and 0-simplices (the vertices). As such, complexes are generalizations of graphs since they allow for higher-dimensional simplices.
Every graph gives rise to a matroid.
In model theory, a graph is just a structure. But in that case, there is no limitation on the number of edges: it can be any cardinal number, see continuous graph.
In computational biology, power graph analysis introduces power graphs as an alternative representation of undirected graphs.
In geographic information systems, geometric networks are closely modeled after graphs, and borrow many concepts from graph theory to perform spatial analysis on road networks or utility grids. | Graph (discrete mathematics) | Wikipedia | 471 | 325806 | https://en.wikipedia.org/wiki/Graph%20%28discrete%20mathematics%29 | Mathematics | Discrete mathematics | null |
Injection moulding (U.S. spelling: injection molding) is a manufacturing process for producing parts by injecting molten material into a mould, or mold. Injection moulding can be performed with a host of materials mainly including metals (for which the process is called die-casting), glasses, elastomers, confections, and most commonly thermoplastic and thermosetting polymers. Material for the part is fed into a heated barrel, mixed (using a helical screw), and injected into a mould cavity, where it cools and hardens to the configuration of the cavity. After a product is designed, usually by an industrial designer or an engineer, moulds are made by a mould-maker (or toolmaker) from metal, usually either steel or aluminium, and precision-machined to form the features of the desired part. Injection moulding is widely used for manufacturing a variety of parts, from the smallest components to entire body panels of cars. Advances in 3D printing technology, using photopolymers that do not melt during the injection moulding of some lower-temperature thermoplastics, can be used for some simple injection moulds.
Injection moulding uses a special-purpose machine that has three parts: the injection unit, the mould and the clamp. Parts to be injection-moulded must be very carefully designed to facilitate the moulding process; the material used for the part, the desired shape and features of the part, the material of the mould, and the properties of the moulding machine must all be taken into account. The versatility of injection moulding is facilitated by this breadth of design considerations and possibilities.
Applications
Injection moulding is used to create many things such as wire spools, packaging, bottle caps, automotive parts and components, toys, pocket combs, some musical instruments (and parts of them), one-piece chairs and small tables, storage containers, mechanical parts (including gears), and most other plastic products available today. Injection moulding is the most common modern method of manufacturing plastic parts; it is ideal for producing high volumes of the same object.
Process characteristics | Injection moulding | Wikipedia | 458 | 325831 | https://en.wikipedia.org/wiki/Injection%20moulding | Technology | Materials | null |
Injection moulding uses a ram or screw-type plunger to force molten plastic or rubber material into a mould cavity; this solidifies into a shape that has conformed to the contour of the mould. It is most commonly used to process both thermoplastic and thermosetting polymers, with the volume used of the former being considerably higher. Thermoplastics are prevalent due to characteristics that make them highly suitable for injection moulding, such as ease of recycling, versatility for a wide variety of applications, and ability to soften and flow on heating. Thermoplastics also have an element of safety over thermosets; if a thermosetting polymer is not ejected from the injection barrel in a timely manner, chemical crosslinking may occur causing the screw and check valves to seize and potentially damaging the injection moulding machine.
Injection moulding consists of the high pressure injection of the raw material into a mould, which shapes the polymer into the desired form. Moulds can be of a single cavity or multiple cavities. In multiple cavity moulds, each cavity can be identical and form the same parts or can be unique and form multiple different geometries during a single cycle. Moulds are generally made from tool steels, but stainless steels and aluminium moulds are suitable for certain applications. Aluminium moulds are typically ill-suited for high volume production or parts with narrow dimensional tolerances, as they have inferior mechanical properties and are more prone to wear, damage, and deformation during the injection and clamping cycles; however, aluminium moulds are cost-effective in low-volume applications, as mould fabrication costs and time are considerably reduced. Many steel moulds are designed to process well over a million parts during their lifetime and can cost hundreds of thousands of dollars to fabricate. | Injection moulding | Wikipedia | 386 | 325831 | https://en.wikipedia.org/wiki/Injection%20moulding | Technology | Materials | null |
When thermoplastics are moulded, typically pelletised raw material is fed through a hopper into a heated barrel with a reciprocating screw. Upon entrance to the barrel, the temperature increases and the Van der Waals forces that resist relative flow of individual chains are weakened as a result of increased space between molecules at higher thermal energy states. This process reduces its viscosity, which enables the polymer to flow with the driving force of the injection unit. The screw delivers the raw material forward, mixes and homogenises the thermal and viscous distributions of the polymer, and reduces the required heating time by mechanically shearing the material and adding a significant amount of frictional heating to the polymer. The material feeds forward through a check valve and collects at the front of the screw into a volume known as a shot. A shot is the volume of material that is used to fill the mould cavity, compensate for shrinkage, and provide a cushion (approximately 10% of the total shot volume, which remains in the barrel and prevents the screw from bottoming out) to transfer pressure from the screw to the mould cavity. When enough material has gathered, the material is forced at high pressure and velocity into the part forming cavity. The exact amount of shrinkage is a function of the resin being used, and can be relatively predictable. To prevent spikes in pressure, the process normally uses a transfer position corresponding to a 95–98% full cavity where the screw shifts from a constant velocity to a constant pressure control. Often injection times are well under 1 second. Once the screw reaches the transfer position the packing pressure is applied, which completes mould filling and compensates for thermal shrinkage, which is quite high for thermoplastics relative to many other materials. The packing pressure is applied until the gate (cavity entrance) solidifies. Due to its small size, the gate is normally the first place to solidify through its entire thickness. Once the gate solidifies, no more material can enter the cavity; accordingly, the screw reciprocates and acquires material for the next cycle while the material within the mould cools so that it can be ejected and be dimensionally stable. This cooling duration is dramatically reduced by the use of cooling lines circulating water or oil from an external temperature controller. Once the required temperature has been achieved, the mould opens and an array of pins, sleeves, strippers, etc. are driven forward to demould the article | Injection moulding | Wikipedia | 502 | 325831 | https://en.wikipedia.org/wiki/Injection%20moulding | Technology | Materials | null |
Then, the mould closes and the process is repeated | Injection moulding | Wikipedia | 11 | 325831 | https://en.wikipedia.org/wiki/Injection%20moulding | Technology | Materials | null |
For a two-shot mould, two separate materials are incorporated into one part. This type of injection moulding is used to add a soft touch to knobs, to give a product multiple colours, or to produce a part with multiple performance characteristics.
For thermosets, typically two different chemical components are injected into the barrel. These components immediately begin irreversible chemical reactions that eventually crosslinks the material into a single connected network of molecules. As the chemical reaction occurs, the two fluid components permanently transform into a viscoelastic solid. Solidification in the injection barrel and screw can be problematic and have financial repercussions; therefore, minimising the thermoset curing within the barrel is vital. This typically means that the residence time and temperature of the chemical precursors are minimised in the injection unit. The residence time can be reduced by minimising the barrel's volume capacity and by maximising the cycle times. These factors have led to the use of a thermally isolated, cold injection unit that injects the reacting chemicals into a thermally isolated hot mould, which increases the rate of chemical reactions and results in shorter time required to achieve a solidified thermoset component. After the part has solidified, valves close to isolate the injection system and chemical precursors, and the mould opens to eject the moulded parts. Then, the mould closes and the process repeats.
Pre-moulded or machined components can be inserted into the cavity while the mould is open, allowing the material injected in the next cycle to form and solidify around them. This process is known as insert moulding and allows single parts to contain multiple materials. This process is often used to create plastic parts with protruding metal screws so they can be fastened and unfastened repeatedly. This technique can also be used for In-mould labelling and film lids may also be attached to moulded plastic containers. | Injection moulding | Wikipedia | 405 | 325831 | https://en.wikipedia.org/wiki/Injection%20moulding | Technology | Materials | null |
A parting line, sprue, gate marks, and ejector pin marks are usually present on the final part. None of these features are typically desired, but are unavoidable due to the nature of the process. Gate marks occur at the gate that joins the melt-delivery channels (sprue and runner) to the part forming cavity. Parting line and ejector pin marks result from minute misalignments, wear, gaseous vents, clearances for adjacent parts in relative motion, and/or dimensional differences of the melting surfaces contacting the injected polymer. Dimensional differences can be attributed to non-uniform, pressure-induced deformation during injection, machining tolerances, and non-uniform thermal expansion and contraction of mould components, which experience rapid cycling during the injection, packing, cooling, and ejection phases of the process. Mould components are often designed with materials of various coefficients of thermal expansion. These factors cannot be simultaneously accounted for without astronomical increases in the cost of design, fabrication, processing, and quality monitoring. The skillful mould and part designer positions these aesthetic detriments in hidden areas if feasible.
History
In 1846 the British inventor Charles Hancock, a relative of Thomas Hancock, patented an injection molding machine.
American inventor John Wesley Hyatt, together with his brother Isaiah, patented one of the first injection moulding machines in 1872. This machine was relatively simple compared to machines in use today: it worked like a large hypodermic needle, using a plunger to inject plastic through a heated cylinder into a mould. The industry progressed slowly over the years, producing products such as collar stays, buttons, and hair combs (generally though, plastics, in its modern definition, are a more recent development ).
The German chemists Arthur Eichengrün and Theodore Becker invented the first soluble forms of cellulose acetate in 1903, which was much less flammable than cellulose nitrate. It was eventually made available in a powder form from which it was readily injection moulded. Arthur Eichengrün developed the first injection moulding press in 1919. In 1939, Arthur Eichengrün patented the injection moulding of plasticised cellulose acetate. | Injection moulding | Wikipedia | 459 | 325831 | https://en.wikipedia.org/wiki/Injection%20moulding | Technology | Materials | null |
The industry expanded rapidly in the 1940s because World War II created a huge demand for inexpensive, mass-produced products. In 1946, American inventor James Watson Hendry built the first screw injection machine, which allowed much more precise control over the speed of injection and the quality of articles produced. This machine also allowed material to be mixed before injection, so that coloured or recycled plastic could be added to virgin material and mixed thoroughly before being injected. In the 1970s, Hendry went on to develop the first gas-assisted injection moulding process, which permitted the production of complex, hollow articles that cooled quickly. This greatly improved design flexibility as well as the strength and finish of manufactured parts while reducing production time, cost, weight and waste. By 1979, plastic production overtook steel production, and by 1990, aluminium moulds were widely used in injection moulding. Today, screw injection machines account for the vast majority of all injection machines.
The plastic injection moulding industry has evolved over the years from producing combs and buttons to producing a vast array of products for many industries including automotive, medical, aerospace, consumer products, toys, plumbing, packaging, and construction.
Examples of polymers best suited for the process
Most polymers, sometimes referred to as resins, may be used, including all thermoplastics, some thermosets, and some elastomers. Since 1995, the total number of available materials for injection moulding has increased at a rate of 750 per year; there were approximately 18,000 materials available when that trend began. Available materials include alloys or blends of previously developed materials, so product designers can choose the material with the best set of properties from a vast selection. Major criteria for selection of a material are the strength and function required for the final part, as well as the cost, but also each material has different parameters for moulding that must be taken into account. Other considerations when choosing an injection moulding material include flexural modulus of elasticity, or the degree to which a material can be bent without damage, as well as heat deflection and water absorption. Common polymers like epoxy and phenolic are examples of thermosetting plastics while nylon, polyethylene, and polystyrene are thermoplastic. Until comparatively recently, plastic springs were not possible, but advances in polymer properties make them now quite practical. Applications include buckles for anchoring and disconnecting outdoor-equipment webbing.
Equipment | Injection moulding | Wikipedia | 506 | 325831 | https://en.wikipedia.org/wiki/Injection%20moulding | Technology | Materials | null |
Injection moulding machines consist of a material hopper, an injection ram or screw-type plunger, and a heating unit. Also known as platens, they hold the moulds in which the components are shaped. Presses are rated by tonnage, which expresses the amount of clamping force that the machine can exert. This force keeps the mould closed during the injection process. Tonnage can vary from less than 5 tons to over 9,000 tons, with the higher figures used in comparatively few manufacturing operations. The total clamp force needed is determined by the projected area of the part being moulded. This projected area is multiplied by a clamp force of from 1.8 to 7.2 tons for each square centimetre of the projected areas. As a rule of thumb, 4 or 5 tons/in2 can be used for most products. If the plastic material is very stiff, it requires more injection pressure to fill the mould, and thus more clamp tonnage to hold the mould closed. The required force can also be determined by the material used and the size of the part. Larger parts require higher clamping force.
Mould
Mould or die are the common terms used to describe the tool used to produce plastic parts in moulding. | Injection moulding | Wikipedia | 263 | 325831 | https://en.wikipedia.org/wiki/Injection%20moulding | Technology | Materials | null |
Since moulds have been expensive to manufacture, they were usually only used in mass production where thousands of parts were being produced. Typical moulds are constructed from hardened steel, pre-hardened steel, aluminium, and/or beryllium-copper alloy. The choice of material for the mold is not only based on cost considerations, but also has a lot to do with the product life cycle. In general, steel moulds cost more to construct, but their longer lifespan offsets the higher initial cost over a higher number of parts made before wearing out. Pre-hardened steel moulds are less wear-resistant and are used for lower volume requirements or larger components; their typical steel hardness is 38–45 on the Rockwell-C scale. Hardened steel moulds are heat treated after machining; these are by far superior in terms of wear resistance and lifespan. Typical hardness ranges between 50 and 60 Rockwell-C (HRC). Aluminium moulds can cost substantially less, and when designed and machined with modern computerised equipment can be economical for moulding tens or even hundreds of thousands of parts. Beryllium copper is used in areas of the mould that require fast heat removal or areas that see the most shear heat generated. The moulds can be manufactured either by CNC machining or by using electrical discharge machining processes.
Mould design
The mould consists of two primary components, the injection mould (A plate) and the ejector mould (B plate). These components are also referred to as moulder and mouldmaker. Plastic resin enters the mould through a sprue or gate in the injection mould; the sprue bushing is to seal tightly against the nozzle of the injection barrel of the moulding machine and to allow molten plastic to flow from the barrel into the mould, also known as the cavity. The sprue bushing directs the molten plastic to the cavity images through channels that are machined into the faces of the A and B plates. These channels allow plastic to run along them, so they are referred to as runners. The molten plastic flows through the runner and enters one or more specialised gates and into the cavity geometry to form the desired part. | Injection moulding | Wikipedia | 460 | 325831 | https://en.wikipedia.org/wiki/Injection%20moulding | Technology | Materials | null |
The amount of resin required to fill the sprue, runner and cavities of a mould comprises a "shot". Trapped air in the mould can escape through air vents that are ground into the parting line of the mould, or around ejector pins and slides that are slightly smaller than the holes retaining them. If the trapped air is not allowed to escape, it is compressed by the pressure of the incoming material and squeezed into the corners of the cavity, where it prevents filling and can also cause other defects. The air can even become so compressed that it ignites and burns the surrounding plastic material.
To allow for removal of the moulded part from the mould, the mould features must not overhang one another in the direction that the mould opens, unless parts of the mould are designed to move from between such overhangs when the mould opens using components called Lifters.
Sides of the part that appear parallel with the direction of draw (the axis of the cored position (hole) or insert is parallel to the up and down movement of the mould as it opens and closes) are typically angled slightly, called draft, to ease release of the part from the mould. Insufficient draft can cause deformation or damage. The draft required for mould release is primarily dependent on the depth of the cavity; the deeper the cavity, the more draft necessary. Shrinkage must also be taken into account when determining the draft required. If the skin is too thin, then the moulded part tends to shrink onto the cores that form while cooling and cling to those cores, or the part may warp, twist, blister or crack when the cavity is pulled away. | Injection moulding | Wikipedia | 348 | 325831 | https://en.wikipedia.org/wiki/Injection%20moulding | Technology | Materials | null |
A mould is usually designed so that the moulded part reliably remains on the ejector (B) side of the mould when it opens, and draws the runner and the sprue out of the (A) side along with the parts. The part then falls freely when ejected from the (B) side. Tunnel gates, also known as submarine or mould gates, are located below the parting line or mould surface. An opening is machined into the surface of the mould on the parting line. The moulded part is cut (by the mould) from the runner system on ejection from the mould. Ejector pins, also known as knockout pins, are circular pins placed in either half of the mould (usually the ejector half), which push the finished moulded product, or runner system out of a mould.The ejection of the article using pins, sleeves, strippers, etc., may cause undesirable impressions or distortion, so care must be taken when designing the mould.
The standard method of cooling is passing a coolant (usually water) through a series of holes drilled through the mould plates and connected by hoses to form a continuous pathway. The coolant absorbs heat from the mould (which has absorbed heat from the hot plastic) and keeps the mould at a proper temperature to solidify the plastic at the most efficient rate.
To ease maintenance and venting, cavities and cores are divided into pieces, called inserts, and sub-assemblies, also called inserts, blocks, or chase blocks. By substituting interchangeable inserts, one mould may make several variations of the same part.
More complex parts are formed using more complex moulds. These may have sections called slides, that move into a cavity perpendicular to the draw direction, to form overhanging part features. When the mould is opened, the slides are pulled away from the plastic part by using stationary “angle pins” on the stationary mould half. These pins enter a slot in the slides and cause the slides to move backward when the moving half of the mould opens. The part is then ejected and the mould closes. The closing action of the mould causes the slides to move forward along the angle pins. | Injection moulding | Wikipedia | 478 | 325831 | https://en.wikipedia.org/wiki/Injection%20moulding | Technology | Materials | null |
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