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Volcanic ash is further divided into fine ash, with particle sizes smaller than 0.0625 mm in diameter, and coarse ash, with particle sizes between 0.0625 mm and 2 mm in diameter. Tuff is correspondingly divided into coarse tuff (coarse ash tuff) and fine tuff (fine ash tuff or dust tuff). Consolidated tephra composed mostly of coarser particles is called lapillistone (particles 2 mm to 64 mm in diameter) or agglomerate or pyroclastic breccia (particles over 64 mm in diameter) rather than tuff.
Volcanic ash can vary greatly in composition, and so tuffs are further classified by the composition of the ash from which they formed. Ash from high-silica volcanism, particularly in ash flows, consists mainly of shards of volcanic glass, and tuff formed predominantly from glass shards is described as vitric tuff. The glass shards are typically either irregular in shape or are roughly triangular with convex sides. They are the shattered walls of countless small bubbles that formed in the magma as dissolved gases rapidly came out of solution.
Tuffs formed from ash consisting predominantly of individual crystals are described as crystal tuffs, while those formed from ash consisting predominantly of pulverized rock fragments are described as lithic tuffs.
The chemical composition of volcanic ash reflects the entire range of volcanic rock chemistry, from high-silica rhyolitic ash to low-silica basaltic ash, and tuffs are likewise described as rhyolitic, andesitic, basaltic, and so on.
Transport and lithification
The most straightforward way for volcanic ash to move away from the vent is as ash clouds that are part of an eruption column. These fall to the surface as fallout deposits that are characteristically well-sorted and tend to form a blanket of uniform thickness across terrain. Column collapse results in a more spectacular and destructive form of transport, which takes the form of pyroclastic flows and surges that characteristically are poorly sorted and pool in low terrain. Surge deposits sometimes show sedimentary structures typical of high-velocity flow, such as dunes and antidunes. Volcanic ash already deposited on the surface can be transported as mud flows (lahars) when mingled with water from rainfall or through eruption into a body of water or ice. | Tuff | Wikipedia | 474 | 44481 | https://en.wikipedia.org/wiki/Tuff | Physical sciences | Petrology | null |
Particles of volcanic ash that are sufficiently hot will weld together after settling to the surface, producing a welded tuff. Welding requires temperatures in excess of . If the rock contains scattered, pea-sized fragments or fiamme in it, it is called a welded lapilli tuff. Welded tuffs (and welded lapilli tuffs) can be of fallout origin, or deposited from ash flows, as in the case of ignimbrites. During welding, the glass shards and pumice fragments adhere together (necking at point contacts), deform, and compact together, resulting in a eutaxitic fabric. Welded tuff is commonly rhyolitic in composition, but examples of all compositions are known.
A sequence of ash flows may consist of multiple cooling units. These can be distinguished by the degree of welding. The base of a cooling unit is typically unwelded due to chilling from the underlying cold surface, and the degree of welding and of secondary reactions from fluids in the flow increases upwards towards the center of the flow. Welding decreases towards the top of the cooling unit, where the unit cools more rapidly. The intensity of welding may also decrease towards areas in which the deposit is thinner, and with distance from source.
Cooler pyroclastic flows are unwelded and the ash sheets deposited by them are relatively unconsolidated. However, cooled volcanic ash can quickly become lithified because it usually has a high content of volcanic glass. This is a thermodynamically unstable material that reacts rapidly with ground water or sea water, which leaches alkali metals and calcium from the glass. New minerals, such as zeolites, clays, and calcite, crystallize from the dissolved substances and cement the tuff.
Tuffs are further classified by their depositional environment, such as lacustrine tuff, subaerial tuff, or submarine tuff, or by the mechanism by which the ash was transported, such as fallout tuff or ash flow tuff. Reworked tuffs, formed by erosion and redeposition of ash deposits, are usually described by the transport agent, such as aeolian tuff or fluvial tuff.
Occurrences
Tuffs have the potential to be deposited wherever explosive volcanism takes place, and so have a wide distribution in location and age. | Tuff | Wikipedia | 482 | 44481 | https://en.wikipedia.org/wiki/Tuff | Physical sciences | Petrology | null |
High-silica volcanism
Rhyolite tuffs contain pumiceous, glassy fragments and small scoriae with quartz, alkali feldspar, biotite, etc. Iceland, Lipari, Hungary, the Basin and Range of the American southwest, and New Zealand are among the areas where such tuffs are prominent. In the ancient rocks of Wales, Charnwood, etc., similar tuffs are known, but in all cases, they are greatly changed by silicification (which has filled them with opal, chalcedony, and quartz) and by devitrification. The frequent presence of rounded corroded quartz crystals, such as occur in rhyolitic lavas, helps to demonstrate their real nature.
Welded ignimbrites can be highly voluminous, such as the Lava Creek Tuff erupted from Yellowstone Caldera in Wyoming 631,000 years ago. This tuff had an original volume of at least . Lava Creek tuff is known to be at least 1000 times as large as the deposits of the 1980 eruption of Mount St. Helens, and it had a Volcanic Explosivity Index (VEI) of 8, greater than any eruption known in the last 10,000 years. Ash flow tuffs cover of the North Island of New Zealand and about of Nevada. Ash flow tuffs are the only volcanic product with volumes rivaling those of flood basalts.
The Tioga Bentonite of the northeastern United States varies in composition from crystal tuff to tuffaceous shale. It was deposited as ash carried by wind that fell out over the sea and settled to the bottom. It is Devonian in age and likely came from a vent in central Virginia, where the tuff reaches its maximum thickness of about .
Alkaline volcanism
Trachyte tuffs contain little or no quartz, but much sanidine or anorthoclase and sometimes oligoclase feldspar, with occasional biotite, augite, and hornblende. In weathering, they often change to soft red or yellow claystones, rich in kaolin with secondary quartz. Recent trachyte tuffs are found on the Rhine (at Siebengebirge), in Ischia and near Naples. Trachyte-carbonatite tuffs have been identified in the East African Rift. Alkaline crystal tuffs have been reported from Rio de Janeiro. | Tuff | Wikipedia | 496 | 44481 | https://en.wikipedia.org/wiki/Tuff | Physical sciences | Petrology | null |
Intermediate volcanism
Andesitic tuffs are exceedingly common. They occur along the whole chain of the Cordilleras and Andes, in the West Indies, New Zealand, Japan, etc. In the Lake District, North Wales, Lorne, the Pentland Hills, the Cheviots, and many other districts of Great Britain, ancient rocks of exactly similar nature are abundant. In color, they are red or brown; their scoriae fragments are of all sizes from huge blocks down to minute granular dust. The cavities are filled with many secondary minerals, such as calcite, chlorite, quartz, epidote, or chalcedony; in microscopic sections, though, the nature of the original lava can nearly always be made out from the shapes and properties of the little crystals which occur in the decomposed glassy base. Even in the smallest details, these ancient tuffs have a complete resemblance to the modern ash beds of Cotopaxi, Krakatoa, and Mont Pelé.
Mafic volcanism
Mafic volcanism typically takes the form of Hawaiian eruptions that are nonexplosive and produce little ash. However, interaction between basaltic magma and groundwater or sea water results in hydromagmatic explosions that produce abundant ash. These deposit ash cones that subsequently can become cemented into tuff cones. Diamond Head, Hawaii, is an example of a tuff cone, as is the island of Ka'ula. The glassy basaltic ash produced in such eruptions rapidly alters to palagonite as part of the process of lithification.
Although conventional mafic volcanism produce little ash, such ash as is formed may accumulate locally as significant deposits. An example is the Pahala ash of Hawaii island, which locally is as thick as . These deposits also rapidly alter to palagonite, and eventually weather to laterite. | Tuff | Wikipedia | 391 | 44481 | https://en.wikipedia.org/wiki/Tuff | Physical sciences | Petrology | null |
Basaltic tuffs are also found in Skye, Mull, Antrim, and other places, where Paleogene volcanic rocks are found; in Scotland, Derbyshire, and Ireland among the Carboniferous strata, and among the still older rocks of the Lake District, the southern uplands of Scotland, and Wales. They are black, dark green, or red in colour; vary greatly in coarseness, some being full of round spongy bombs a foot or more in diameter; and being often submarine, may contain shale, sandstone, grit, and other sedimentary material, and are occasionally fossiliferous. Recent basaltic tuffs are found in Iceland, the Faroe Islands, Jan Mayen, Sicily, the Hawaiian Islands, Samoa, etc. When weathered, they are filled with calcite, chlorite, serpentine, and especially where the lavas contain nepheline or leucite, are often rich in zeolites, such as analcite, prehnite, natrolite, scolecite, chabazite, heulandite, etc.
Ultramafic volcanism
Ultramafic tuffs are extremely rare; their characteristic is the abundance of olivine or serpentine and the scarcity or absence of feldspar and quartz.
Kimberlites
Occurrences of ultramafic tuff include surface deposits of kimberlite at maars in the diamond-fields of southern Africa and other regions. The principal variety of kimberlite is a dark bluish-green, serpentine-rich breccia (blue-ground) which, when thoroughly oxidized and weathered, becomes a friable brown or yellow mass (the "yellow-ground"). These breccias were emplaced as gas–solid mixtures and are typically preserved and mined in diatremes that form intrusive pipe-like structures. At depth, some kimberlite breccias grade into root zones of dikes made of unfragmented rock. At the surface, ultramafic tuffs may occur in maar deposits. Because kimberlites are the most common igneous source of diamonds, the transitions from maar to diatreme to root-zone dikes have been studied in detail. Diatreme-facies kimberlite is more properly called an ultramafic breccia rather than a tuff. | Tuff | Wikipedia | 489 | 44481 | https://en.wikipedia.org/wiki/Tuff | Physical sciences | Petrology | null |
Komatiites
Komatiite tuffs are found, for example, in the greenstone belts of Canada and South Africa.
Folding and metamorphism
In course of time, changes other than weathering may overtake tuff deposits. Sometimes, they are involved in folding and become sheared and cleaved. Many of the green slates of the English Lake District are finely cleaved ashes. In Charnwood Forest also, the tuffs are slaty and cleaved. The green color is due to the large development of chlorite. Among the crystalline schists of many regions, green beds or green schists occur, which consist of quartz, hornblende, chlorite or biotite, iron oxides, feldspar, etc., and are probably recrystallized or metamorphosed tuffs. They often accompany masses of epidiorite and hornblende – schists which are the corresponding lavas and sills. Some chlorite-schists also are probably altered beds of volcanic tuff. The "Schalsteins" of Devon and Germany include many cleaved and partly recrystallized ash-beds, some of which still retain their fragmental structure, though their lapilli are flattened and drawn out. Their steam cavities are usually filled with calcite, but sometimes with quartz. The more completely altered forms of these rocks are platy, green chloritic schists; in these, however, structures indicating their original volcanic nature only sparingly occur. These are intermediate stages between cleaved tuffs and crystalline schists.
Importance
The primary economic value of tuff is as a building material. In the ancient world, tuff's relative softness meant that it was commonly used for construction where it was available.
Italy
Tuff is common in Italy, and the Romans used it for many buildings and bridges. For example, the whole port of the island of Ventotene (still in use), was carved from tuff. The Servian Wall, built to defend the city of Rome in the fourth century BC, is also built almost entirely from tuff. The Romans also cut tuff into small, rectangular stones that they used to create walls in a pattern known as opus reticulatum. | Tuff | Wikipedia | 477 | 44481 | https://en.wikipedia.org/wiki/Tuff | Physical sciences | Petrology | null |
Peperino has been used in Rome and Naples as a building stone, is a trachyte tuff. Pozzolana also is a decomposed tuff, but of basic character, originally obtained near Naples and used as a cement, but this name is now applied to a number of substances not always of identical character. In the historical architecture of Naples, Neapolitan yellow tuff is the most used building material. Piperno ignimbrite tuff was also used widely in Naples and Campania.
Germany
In the Eifel region of Germany, a trachytic, pumiceous tuff called trass has been extensively worked as a hydraulic mortar. Tuff of the Eifel region of Germany has been widely used for construction of railroad stations and other buildings in Frankfurt, Hamburg, and other large cities. Construction using the Rochlitz Porphyr, can be seen in the Mannerist-style sculpted portal outside the chapel entrance in Colditz Castle. The trade name Rochlitz Porphyr is the traditional designation for a dimension stone of Saxony with an architectural history over 1,000 years in Germany. The quarries are located near Rochlitz.
United States
Yucca Mountain nuclear waste repository, a U.S. Department of Energy terminal storage facility for spent nuclear reactor and other radioactive waste, is in tuff and ignimbrite in the Basin and Range Province in Nevada. In Napa Valley and Sonoma Valley, California, areas made of tuff are routinely excavated for storage of wine barrels.
Rapa Nui
Tuff from Rano Raraku was used by the Rapa Nui people of Easter Island to make the vast majority of their famous moai statues.
Armenia
Tuff is used extensively in Armenia and Armenian architecture. It is the dominant type of stone used in construction in Armenia's capital Yerevan, Gyumri, Armenia's second largest city, and Ani, the country's medieval capital, now in Turkey. A small village in Armenia was renamed Tufashen (literally "village of tuff") in 1946.
Tephrochronology | Tuff | Wikipedia | 433 | 44481 | https://en.wikipedia.org/wiki/Tuff | Physical sciences | Petrology | null |
Tuffs are deposited geologically instantaneously and often over a large region. This makes them highly useful as time-stratigraphic markers. The use of tuffs and other tephra deposits in this manner is known as tephrochronology and is particularly useful for Quaternary chronostratigraphy. Individual tuff beds can be "fingerprinted" by their chemical composition and phenocryst assemblages. Absolute ages for tuff beds can be determined by K-Ar, Ar-Ar, or carbon-14 dating. Zircon grains found in many tuffs are highly durable and can survive even metamorphism of the host tuff to schist, allowing absolute ages to be assigned to ancient metamorphic rocks. For example, dating of zircons in a metamorphosed tuff bed in the Pilar Formation provided some of the first evidence for the Picuris orogeny.
Etymology
The word tuff is derived from the Italian tufo. | Tuff | Wikipedia | 207 | 44481 | https://en.wikipedia.org/wiki/Tuff | Physical sciences | Petrology | null |
A linear motor is an electric motor that has had its stator and rotor "unrolled", thus, instead of producing a torque (rotation), it produces a linear force along its length. However, linear motors are not necessarily straight. Characteristically, a linear motor's active section has ends, whereas more conventional motors are arranged as a continuous loop.
A typical mode of operation is as a Lorentz-type actuator, in which the applied force is linearly proportional to the current and the magnetic field .
Linear motors are most commonly found in high accuracy engineering applications.
Many designs have been put forward for linear motors, falling into two major categories, low-acceleration and high-acceleration linear motors. Low-acceleration linear motors are suitable for maglev trains and other ground-based transportation applications. High-acceleration linear motors are normally rather short, and are designed to accelerate an object to a very high speed; for example, see the coilgun.
High-acceleration linear motors are typically used in studies of hypervelocity collisions, as weapons, or as mass drivers for spacecraft propulsion. They are usually of the AC linear induction motor (LIM) design with an active three-phase winding on one side of the air-gap and a passive conductor plate on the other side. However, the direct current homopolar linear motor railgun is another high acceleration linear motor design. The low-acceleration, high speed and high power motors are usually of the linear synchronous motor (LSM) design, with an active winding on one side of the air-gap and an array of alternate-pole magnets on the other side. These magnets can be permanent magnets or electromagnets. The motor for the Shanghai maglev train, for instance, is an LSM.
Types
Brushless
Brushless linear motors are members of the Synchronous motor family. They are typically used in standard linear stages or integrated into custom, high performance positioning systems. Invented in the late 1980s by Anwar Chitayat at Anorad Corporation, now Rockwell Automation, and helped improve the throughput and quality of industrial manufacturing processes.
Brush
Brushed linear motors were used in industrial automation applications prior to the invention of Brushless linear motors. Compared with three phase brushless motors, which are typically being used today, brush motors operate on a single phase. Brush linear motors have a lower cost since they do not need moving cables or three phase servo drives. However, they require higher maintenance since their brushes wear out. | Linear motor | Wikipedia | 510 | 44495 | https://en.wikipedia.org/wiki/Linear%20motor | Technology | Engines | null |
Synchronous
In this design the rate of movement of the magnetic field is controlled, usually electronically, to track the motion of the rotor. For cost reasons synchronous linear motors rarely use commutators, so the rotor often contains permanent magnets, or soft iron. Examples include coilguns and the motors used on some maglev systems, as well as many other linear motors. In high precision industrial automation linear motors are typically configured with a magnet stator and a moving coil. A Hall effect sensor is attached to the rotor to track the magnetic flux of the stator. The electric current is typically provided from a stationary servo drive to the moving coil by a moving cable inside a cable carrier.
Induction
In this design, the force is produced by a moving linear magnetic field acting on conductors in the field. Any conductor, be it a loop, a coil or simply a piece of plate metal, that is placed in this field will have eddy currents induced in it thus creating an opposing magnetic field, in accordance with Lenz's law. The two opposing fields will repel each other, thus creating motion as the magnetic field sweeps through the metal.
Homopolar
In this design a large current is passed through a metal sabot across sliding contacts that are fed by two rails. The magnetic field this generates causes the metal to be projected along the rails.
Tubular
Efficient and compact design applicable to the replacement of pneumatic cylinders.
Piezoelectric
Piezoelectric drive is often used to drive small linear motors.
History
Low acceleration
The history of linear electric motors can be traced back at least as far as the 1840s, to the work of Charles Wheatstone at King's College London, but Wheatstone's model was too inefficient to be practical. A feasible linear induction motor is described in (1905 - inventor Alfred Zehden of Frankfurt-am-Main), for driving trains or lifts. The German engineer Hermann Kemper built a working model in 1935. In the late 1940s, Dr. Eric Laithwaite of Manchester University, later Professor of Heavy Electrical Engineering at Imperial College in London developed the first full-size working model. | Linear motor | Wikipedia | 439 | 44495 | https://en.wikipedia.org/wiki/Linear%20motor | Technology | Engines | null |
In a single sided version the magnetic repulsion forces the conductor away from the stator, levitating it, and carrying it along in the direction of the moving magnetic field. He called the later versions of it magnetic river. The technologies would later be applied, in the 1984, Air-Rail Link shuttle, between Birmingham's airport and an adjacent train station.
Because of these properties, linear motors are often used in maglev propulsion, as in the Japanese Linimo magnetic levitation train line near Nagoya. However, linear motors have been used independently of magnetic levitation, as in the Bombardier Innovia Metro systems worldwide and a number of modern Japanese subways, including Tokyo's Toei Ōedo Line.
Similar technology is also used in some roller coasters with modifications but, at present, is still impractical on street running trams, although this, in theory, could be done by burying it in a slotted conduit.
Outside of public transportation, vertical linear motors have been proposed as lifting mechanisms in deep mines, and the use of linear motors is growing in motion control applications. They are also often used on sliding doors, such as those of low floor trams such as the Alstom Citadis and the Socimi Eurotram. Dual axis linear motors also exist. These specialized devices have been used to provide direct X-Y motion for precision laser cutting of cloth and sheet metal, automated drafting, and cable forming. Most linear motors in use are LIM (linear induction motor), or LSM (linear synchronous motor). Linear DC motors are not used due to their higher cost and linear SRM suffers from poor thrust. So for long runs in traction LIM is mostly preferred and for short runs LSM is mostly preferred.
High acceleration
High-acceleration linear motors have been suggested for a number of uses.
They have been considered for use as weapons, since current armour-piercing ammunition tends to consist of small rounds with very high kinetic energy, for which just such motors are suitable. Many amusement park launched roller coasters now use linear induction motors to propel the train at a high speed, as an alternative to using a lift hill. | Linear motor | Wikipedia | 439 | 44495 | https://en.wikipedia.org/wiki/Linear%20motor | Technology | Engines | null |
The United States Navy is also using linear induction motors in the Electromagnetic Aircraft Launch System that will replace traditional steam catapults on future aircraft carriers. They have also been suggested for use in spacecraft propulsion. In this context they are usually called mass drivers. The simplest way to use mass drivers for spacecraft propulsion would be to build a large mass driver that can accelerate cargo up to escape velocity, though RLV launch assist like StarTram to low Earth orbit has also been investigated.
High-acceleration linear motors are difficult to design for a number of reasons. They require large amounts of energy in very short periods of time. One rocket launcher design calls for 300 GJ for each launch in the space of less than a second. Normal electrical generators are not designed for this kind of load, but short-term electrical energy storage methods can be used. Capacitors are bulky and expensive but can supply large amounts of energy quickly. Homopolar generators can be used to convert the kinetic energy of a flywheel into electric energy very rapidly. High-acceleration linear motors also require very strong magnetic fields; in fact, the magnetic fields are often too strong to permit the use of superconductors. However, with careful design, this need not be a major problem.
Two different basic designs have been invented for high-acceleration linear motors: railguns and coilguns.
Usage
Linear motors are commonly used for actuating high performance industrial automation equipment. Their advantage, unlike any other commonly used actuator, such as a ball screw, timing belt, or rack and pinion, is that they provide any combination of high precision, high velocity, high force and long travel.
Linear motors are widely used. One of the major uses of linear motors is for propelling the shuttle in looms.
A linear motor has been used for sliding doors and various similar actuators. They have been used for baggage handling and even large-scale bulk materials transport.
Linear motors are sometimes used to create rotary motion. For example, they have been used at observatories to deal with the large radius of curvature.
Linear motors may also be used as an alternative to conventional chain-run lift hills for roller coasters. The coaster Maverick at Cedar Point uses one such linear motor in place of a chain lift.
A linear motor has been used to accelerate cars for crash tests. | Linear motor | Wikipedia | 475 | 44495 | https://en.wikipedia.org/wiki/Linear%20motor | Technology | Engines | null |
Industrial automation
The combination of high precision, high velocity, high force, and long travel makes brushless linear motors attractive for driving industrial automations equipment. They serve industries and applications such as semiconductor steppers, electronics surface-mount technology, automotive cartesian coordinate robots, aerospace chemical milling, optics electron microscope, healthcare laboratory automation, food and beverage pick and place.
Machine tools
Synchronous linear motor actuators, used in machine tools, provide high force, high velocity, high precision and high dynamic stiffness, resulting in high smoothness of motion and low settling time. They may reach velocities of 2 m/s and micron-level accuracies, with short cycle times and a smooth surface finish.
Train propulsion
Conventional rails
All of the following applications are in rapid transit and have the active part of the motor in the cars.
Bombardier Innovia Metro
Originally developed in the late 1970s by UTDC in Canada as the Intermediate Capacity Transit System (ICTS). A test track was constructed in Millhaven, Ontario, for extensive testing of prototype cars, after which three lines were constructed:
Line 3 Scarborough in Toronto (opened 1985; closed 2023)
Expo Line of the Vancouver SkyTrain (opened 1985 and extended in 1994)
Detroit People Mover in Detroit (opened 1987)
ICTS was sold to Bombardier Transportation in 1991 and later known as Advanced Rapid Transit (ART) before adopting its current branding in 2011. Since then, several more installations have been made:
Kelana Jaya Line in Kuala Lumpur (opened 1998 and extended in 2016)
Millennium Line of the Vancouver SkyTrain (opened 2002 and extended in 2016)
AirTrain JFK in New York (opened 2003)
Airport Express (Beijing Subway) (opened 2008)
Everline in Yongin, South Korea (opened 2013)
All Innovia Metro systems use third rail electrification. | Linear motor | Wikipedia | 373 | 44495 | https://en.wikipedia.org/wiki/Linear%20motor | Technology | Engines | null |
Japanese Linear Metro
One of the biggest challenges faced by Japanese railway engineers in the 1970s to the 1980s was the ever increasing construction costs of subways. In response, the Japan Subway Association began studying on the feasibility of the "mini-metro" for meeting urban traffic demand in 1979. In 1981, the Japan Railway Engineering Association studied on the use of linear induction motors for such small-profile subways and by 1984 was investigating on the practical applications of linear motors for urban rail with the Japanese Ministry of Land, Infrastructure, Transport and Tourism. In 1988, a successful demonstration was made with the Limtrain at Saitama and influenced the eventual adoption of the linear motor for the Nagahori Tsurumi-ryokuchi Line in Osaka and Toei Line 12 (present-day Toei Oedo Line) in Tokyo.
To date, the following subway lines in Japan use linear motors and use overhead lines for power collection:
Two Osaka Metro lines in Osaka:
Nagahori Tsurumi-ryokuchi Line (opened 1990)
Imazatosuji Line (opened 2006)
Toei Ōedo Line in Tokyo (opened 2000)
Kaigan Line of the Kobe Municipal Subway (opened 2001)
Nanakuma Line of the Fukuoka City Subway (opened 2005)
Yokohama Municipal Subway Green Line (opened 2008)
Sendai Subway Tōzai Line (opened 2015)
In addition, Kawasaki Heavy Industries has also exported the Linear Metro to the Guangzhou Metro in China; all of the Linear Metro lines in Guangzhou use third rail electrification:
Line 4 (opened 2005)
Line 5 (opened 2009).
Line 6 (opened 2013)
Monorail
There is at least one known monorail system which is not magnetically levitated, but nonetheless uses linear motors. This is the Moscow Monorail. Originally, traditional motors and wheels were to be used. However, it was discovered during test runs that the proposed motors and wheels would fail to provide adequate traction under some conditions, for example, when ice appeared on the rail. Hence, wheels are still used, but the trains use linear motors to accelerate and slow down. This is possibly the only use of such a combination, due to the lack of such requirements for other train systems.
The TELMAGV is a prototype of a monorail system that is also not magnetically levitated but uses linear motors.
Magnetic levitation | Linear motor | Wikipedia | 470 | 44495 | https://en.wikipedia.org/wiki/Linear%20motor | Technology | Engines | null |
High-speed trains:
Transrapid: first commercial use in Shanghai (opened in 2004)
SCMaglev, under construction in Japan (fastest train in the world, planned to open by 2027)
Rapid transit:
Birmingham Airport, UK (opened 1984, closed 1995)
M-Bahn in Berlin, Germany (opened in 1989, closed in 1991)
Daejeon EXPO, Korea (ran only 1993)
HSST: Linimo line in Aichi Prefecture, Japan (opened 2005)
Incheon Airport Maglev (opened July 2014)
Changsha Maglev Express (opened 2016)
S1 line of Beijing Subway (opened 2017)
Amusement rides
There are many roller coasters throughout the world that use LIMs to accelerate the ride vehicles. The first being Flight of Fear at Kings Island and Kings Dominion, both opening in 1996. Battlestar Galactica: Human VS Cylon & Revenge of the Mummy at Universal Studios Singapore opened in 2010. They both use LIMs to accelerate from certain point in the rides.
Revenge of the Mummy also located at Universal Studios Hollywood and Universal Studios Florida. The Incredible Hulk Coaster and VelociCoaster at Universal Islands of Adventure also use linear motors. At Walt Disney World, Rock 'n' Roller Coaster Starring Aerosmith at Disney's Hollywood Studios and Guardians of the Galaxy: Cosmic Rewind at Epcot both use LSM to launch their ride vehicles into their indoor ride enclosures.
In 2023 a hydraulic launch roller coaster, Top Thrill Dragster at Cedar Point in Ohio, USA, was renovated and the hydraulic launch replaced with a weaker multi-launch system using LSM, that creates less g-force.
Aircraft launching
Electromagnetic Aircraft Launch System
Proposed and research
Launch loop – A proposed system for launching vehicles into space using a linear motor powered loop
StarTram – Concept for a linear motor on extreme scale
Tether cable catapult system
Aérotrain S44 – A suburban commuter hovertrain prototype
Research Test Vehicle 31 – A hovercraft-type vehicle guided by a track
Hyperloop – a conceptual high-speed transportation system put forward by entrepreneur Elon Musk
Elevator
Lift
Magway - a UK freight delivery system under research and development that aims to deliver goods in pods via 90 cm diameter pipework under and over ground. | Linear motor | Wikipedia | 456 | 44495 | https://en.wikipedia.org/wiki/Linear%20motor | Technology | Engines | null |
Till or glacial till is unsorted glacial sediment.
Till is derived from the erosion and entrainment of material by the moving ice of a glacier. It is deposited some distance down-ice to form terminal, lateral, medial and ground moraines.
Till is classified into primary deposits, laid down directly by glaciers, and secondary deposits, reworked by fluvial transport and other processes.
Description
Till is a form of glacial drift, which is rock material transported by a glacier and deposited directly from the ice or from running water emerging from the ice. It is distinguished from other forms of drift in that it is deposited directly by glaciers without being reworked by meltwater.
Till is characteristically unsorted and unstratified, and is not usually consolidated. Most till consists predominantly of clay, silt, and sand, but with pebbles, cobbles, and boulders scattered through the till. The abundance of clay demonstrates lack of reworking by turbulent flow, which otherwise would winnow the clay. Typically, the distribution of particle sizes shows two peaks (it is bimodal) with pebbles predominating in the coarser peak.
The larger clasts (rock fragments) in till typically show a diverse composition, often including rock types from outcrops hundreds of kilometers away. Some clasts may be rounded, and these are thought to be stream pebbles entrained by the glacier. Many of the clasts are faceted, striated, or polished, all signs of glacial abrasion. The sand and silt grains are typically angular to subangular rather than rounded.
It has been known since the careful statistic work by geologist Chauncey D. Holmes in 1941 that elongated clasts in tills tend to align with the direction of ice flow. Clasts in till may also show slight imbrication, with the clasts dipping upstream.
Though till is generally unstratified, till high in clay may show lamination due to compaction under the weight of overlying ice. Till may also contain lenses of sand or gravel, indicating minor and local reworking by water transitional to non-till glacial drift. | Till | Wikipedia | 435 | 44545 | https://en.wikipedia.org/wiki/Till | Physical sciences | Sedimentology | Earth science |
The term till comes from an old Scottish name for coarse, rocky soil. It was first used to describe primary glacial deposits by Archibald Geikie in 1863. Early researchers tended to prefer the term boulder clay for the same kind of sediments, but this has fallen into disfavor. Where it is unclear whether a poorly sorted, unconsolidated glacial deposit was deposited directly from glaciers, it is described as diamict or (when lithified) as diamictite. Tillite is a sedimentary rock formed by lithification of till.
Processes
Erosional
Glacial till is mostly derived from subglacial erosion and from the entrainment by the moving ice of previously available unconsolidated sediments. Bedrock can be eroded through the action of glacial plucking and abrasion, and the resulting clasts of various sizes will be incorporated to the glacier's bed.
Glacial abrasion is the weathering of bedrock below a flowing glacier by fragmented rock on the basal layer of the glacier. The two mechanisms of glacial abrasion are striation of the bedrock by coarse grains moved by the glacier, thus gouging the rock below, and polishing of the bedrock by smaller grains such as silts. Glacial plucking is the removal of large blocks from the bed of a glacier.
Much of the silt in till is produced by glacial grinding, and the longer the till remains at the ice-bedrock interface, the more thoroughly it is crushed. However, the crushing process appears to stop with fine silt. Clay in till is likely eroded from bedrock rather than being created by glacial processes.
Depositional
The sediments carried by a glacier will eventually be deposited some distance down-ice from its source. This takes place in the ablation zone, which is the part of the glacier where the rate of ablation (removal of ice by evaporation, melting, or other processes) exceeds the rate of accumulation of new ice from snowfall. As ice is removed, debris are left behind as till. The deposition of glacial till is not uniform, and a single till plain can contain a wide variety of different types of tills due to the various erosional mechanisms and location of till with respect to the transporting glacier. | Till | Wikipedia | 455 | 44545 | https://en.wikipedia.org/wiki/Till | Physical sciences | Sedimentology | Earth science |
The different types of till can be categorized between subglacial (beneath) and supraglacial (surface) deposits. Subglacial deposits include lodgement, subglacial meltout, and deformation tills. Supraglacial deposits include supraglacial meltout and flow till. Supraglacial deposits and landforms are widespread in areas of glacial downwasting (vertical thinning of glaciers, as opposed to ice-retreat. They typically sit at the top of the stratigraphic sediment sequence, which has a major influence on land usage. Till is deposited as the terminal moraine, along the lateral and medial moraines and in the ground moraine of a glacier, and moraine is often conflated with till in older writings. Till may also be deposited as drumlins and flutes, though some drumlins consist of a core of stratified sediments with only a cover of till. Interpreting the glacial history of landforms can be difficult due to the tendency of overprinting landforms on top of each other.
As a glacier melts, large amounts of till are eroded and become a source of sediments for reworked glacial drift deposits. These include glaciofluvial deposits, such as outwash in sandurs, and as glaciolacustrine and glaciomarine deposits, such as varves (annual layers) in any proglacial lakes which may form. Erosion of till may take place even in the subglacial environment, such as in tunnel valleys.
Types of till
There are various types of classifying tills:
Primary deposits – Laid down directly by glacier action.
Secondary deposits – Reworked by fluvial transport, erosion, etc.
Traditionally (e.g. Dreimanis, 1988) a further set of divisions has been made to primary deposits, based upon the method of deposition. Van der Meer et al. 2003 have suggested that these till classifications are outdated and should instead be replaced with only one classification, that of deformation till. The reasons behind this are largely down to the difficulties in accurately classifying different tills, which are often based on inferences of the physical setting of the till rather than detailed analysis of the till fabric or particle size.
Subglacial till
Lodgement till | Till | Wikipedia | 468 | 44545 | https://en.wikipedia.org/wiki/Till | Physical sciences | Sedimentology | Earth science |
Subglacial lodgement tills are deposits beneath the glacier that are forced, or "lodged" into the bed below. As glaciers advance or retreat, the clasts that are deposited by the ice may have a lower velocity than the ice itself. When the friction between the clast and the bed exceeds the forces of the ice flowing above and around it, the clast will cease to move, and it will become a lodgement till.
Meltout till
Subglacial meltout tills are tills that are deposited via the melting of the ice lobe. Clasts are transported to the base of the glacier over time, and as basal melting continues, they are slowly deposited below the glacier. Since the rate of deposition is controlled by the rate of basal melting, it is worth considering the factors that contribute to melting. These can be the geothermal heat flux, frictional heat generated by sliding, ice thickness, and ice-surface temperature gradients.
Deformation till
Subglacial deformation tills refer to the homogenization of glacial sediments that occur when the stresses and shear forces from the moving glacier rework the topography of the bed. These contain preglacial sediments (non glacial or earlier glacial sediments), which have been run over and thus deformed by meltout processes or lodgement. The constant reworking of these deposited tills leads to a highly homogenized till.
Supraglacial till
Meltout till
Supraglacial meltout tills are similar to subglacial meltout tills. Rather than being the product of basal melting, however, supraglacial meltout tills are imposed on top of the glacier. These consist of clasts and debris that become exposed due to melting via solar radiation. These debris are either just debris that have a high relative position on the glacier, or clasts that have been transported up from the base of the glacier. Debris accumulation has a feedback-loop relationship with melting. Initially, the darker colored debris absorb more heat and thus accelerate the melting process. After a significant amount of melting has occurred, the thickness of the till insulates the ice sheet and slows the melting process. Supraglacial meltout tills typically end up forming moraines.
Flow till | Till | Wikipedia | 465 | 44545 | https://en.wikipedia.org/wiki/Till | Physical sciences | Sedimentology | Earth science |
Supraglacial flow tills refer to tills that are subject to a dense concentration of clasts and debris from meltout. These debris localities are then subsequently affected by ablation. Due to their unstable nature, they are subject to downslope flow, and thus named "flow till." Properties of flow tills vary, and can depend on factors such as water content, surface gradient, and debris characteristics. Generally, flow tills with a higher water content behave more fluidly, and thus are more susceptible to flow. There are three main types of flows, which are listed below.
Mobile flows: Thin, fluid, and rapid flows that significantly contribute to erosional processes. These cause strong clast orientation in the direction of flow.
Semi-plastic: Thick, slow moving "tongues" of debris. These are also erosive, and clast sorting is more organized than in mobile flows.
Creep: Very slow movement of debris, downslope in direction. Flow rate is slow enough not to be seen on relatively short timescales, as observed by humans. Particle orientation is often random and not associated with the direction of flow.
Tillite
In cases where till has been indurated or lithified by subsequent burial into solid rock, it is known as the sedimentary rock tillite. Matching beds of ancient tillites on opposite sides of the south Atlantic Ocean provided early evidence for continental drift. The same tillites also provide some support to the Precambrian Snowball Earth glaciation event hypothesis.
Economic resources
Tills sometimes contain placer deposits of valuable minerals such as gold. Diamonds have been found in glacial till in the north-central United States and in Canada. Till prospecting is a method of prospecting in which tills are sampled over a wide area to determine if they contain valuable minerals, such as gold, uranium, silver, nickel, or diamonds, and the flow direction indicated by the till is then used to trace the minerals back to their bedrock source. | Till | Wikipedia | 406 | 44545 | https://en.wikipedia.org/wiki/Till | Physical sciences | Sedimentology | Earth science |
A herbivore is an animal anatomically and physiologically evolved to feed on plants, especially upon vascular tissues such as foliage, fruits or seeds, as the main component of its diet. These more broadly also encompass animals that eat non-vascular autotrophs such as mosses, algae and lichens, but do not include those feeding on decomposed plant matters (i.e. detritivores) or macrofungi (i.e. fungivores).
As a result of their plant-based diet, herbivorous animals typically have mouth structures (jaws or mouthparts) well adapted to mechanically break down plant materials, and their digestive systems have special enzymes (e.g. amylase and cellulase) to digest polysaccharides. Grazing herbivores such as horses and cattles have wide flat-crowned teeth that are better adapted for grinding grass, tree bark and other tougher lignin-containing materials, and many of them evolved rumination or cecotropic behaviors to better extract nutrients from plants. A large percentage of herbivores also have mutualistic gut flora made up of bacteria and protozoans that help to degrade the cellulose in plants, whose heavily cross-linking polymer structure makes it far more difficult to digest than the protein- and fat-rich animal tissues that carnivores eat.
Etymology
Herbivore is the anglicized form of a modern Latin coinage, herbivora, cited in Charles Lyell's 1830 Principles of Geology. Richard Owen employed the anglicized term in an 1854 work on fossil teeth and skeletons. Herbivora is derived from Latin herba 'small plant, herb' and vora, from vorare 'to eat, devour'. | Herbivore | Wikipedia | 364 | 44568 | https://en.wikipedia.org/wiki/Herbivore | Biology and health sciences | Ethology | null |
Definition and related terms
Herbivory is a form of consumption in which an organism principally eats autotrophs such as plants, algae and photosynthesizing bacteria. More generally, organisms that feed on autotrophs in general are known as primary consumers.
Herbivory is usually limited to animals that eat plants. Insect herbivory can cause a variety of physical and metabolic alterations in the way the host plant interacts with itself and other surrounding biotic factors. Fungi, bacteria, and protists that feed on living plants are usually termed plant pathogens (plant diseases), while fungi and microbes that feed on dead plants are described as saprotrophs. Flowering plants that obtain nutrition from other living plants are usually termed parasitic plants. There is, however, no single exclusive and definitive ecological classification of consumption patterns; each textbook has its own variations on the theme.
Evolution of herbivory
The understanding of herbivory in geological time comes from three sources: fossilized plants, which may preserve evidence of defence (such as spines), or herbivory-related damage; the observation of plant debris in fossilised animal faeces; and the construction of herbivore mouthparts.
Although herbivory was long thought to be a Mesozoic phenomenon, fossils have shown that plants were being consumed by arthropods within less than 20 million years after the first land plants evolved. Insects fed on the spores of early Devonian plants, and the Rhynie chert also provides evidence that organisms fed on plants using a "pierce and suck" technique.
During the next 75 million years, plants evolved a range of more complex organs, such as roots and seeds. There is no evidence of any organism being fed upon until the middle-late Mississippian, . There was a gap of 50 to 100 million years between the time each organ evolved and the time organisms evolved to feed upon them; this may be due to the low levels of oxygen during this period, which may have suppressed evolution. Further than their arthropod status, the identity of these early herbivores is uncertain. Hole feeding and skeletonization are recorded in the early Permian, with surface fluid feeding evolving by the end of that period. | Herbivore | Wikipedia | 450 | 44568 | https://en.wikipedia.org/wiki/Herbivore | Biology and health sciences | Ethology | null |
Herbivory among four-limbed terrestrial vertebrates, the tetrapods, developed in the Late Carboniferous (307–299 million years ago). The oldest known example being Desmatodon hesperis. Early tetrapods were large amphibious piscivores. While amphibians continued to feed on fish and insects, some reptiles began exploring two new food types, tetrapods (carnivory) and plants (herbivory). The entire dinosaur order ornithischia was composed of herbivorous dinosaurs. Carnivory was a natural transition from insectivory for medium and large tetrapods, requiring minimal adaptation. In contrast, a complex set of adaptations was necessary for feeding on highly fibrous plant materials.
Arthropods evolved herbivory in four phases, changing their approach to it in response to changing plant communities. Tetrapod herbivores made their first appearance in the fossil record of their jaws near the Permio-Carboniferous boundary, approximately 300 million years ago. The earliest evidence of their herbivory has been attributed to dental occlusion, the process in which teeth from the upper jaw come in contact with teeth in the lower jaw is present. The evolution of dental occlusion led to a drastic increase in plant food processing and provides evidence about feeding strategies based on tooth wear patterns. Examination of phylogenetic frameworks of tooth and jaw morphologes has revealed that dental occlusion developed independently in several lineages tetrapod herbivores. This suggests that evolution and spread occurred simultaneously within various lineages.
Food chain
Herbivores form an important link in the food chain because they consume plants to digest the carbohydrates photosynthetically produced by a plant. Carnivores in turn consume herbivores for the same reason, while omnivores can obtain their nutrients from either plants or animals. Due to a herbivore's ability to survive solely on tough and fibrous plant matter, they are termed the primary consumers in the food cycle (chain). Herbivory, carnivory, and omnivory can be regarded as special cases of consumer–resource interactions.
Feeding strategies | Herbivore | Wikipedia | 452 | 44568 | https://en.wikipedia.org/wiki/Herbivore | Biology and health sciences | Ethology | null |
Two herbivore feeding strategies are grazing (e.g. cows) and browsing (e.g. moose). For a terrestrial mammal to be called a grazer, at least 90% of the forage has to be grass, and for a browser at least 90% tree leaves and twigs. An intermediate feeding strategy is called "mixed-feeding". In their daily need to take up energy from forage, herbivores of different body mass may be selective in choosing their food. "Selective" means that herbivores may choose their forage source depending on, e.g., season or food availability, but also that they may choose high quality (and consequently highly nutritious) forage before lower quality. The latter especially is determined by the body mass of the herbivore, with small herbivores selecting for high-quality forage, and with increasing body mass animals are less selective. Several theories attempt to explain and quantify the relationship between animals and their food, such as Kleiber's law, Holling's disk equation and the marginal value theorem (see below).
Kleiber's law describes the relationship between an animal's size and its feeding strategy, saying that larger animals need to eat less food per unit weight than smaller animals. Kleiber's law states that the metabolic rate (q0) of an animal is the mass of the animal (M) raised to the 3/4 power: q0=M3/4
Therefore, the mass of the animal increases at a faster rate than the metabolic rate.
Herbivores employ numerous types of feeding strategies. Many herbivores do not fall into one specific feeding strategy, but employ several strategies and eat a variety of plant parts.
Optimal foraging theory is a model for predicting animal behavior while looking for food or other resources, such as shelter or water. This model assesses both individual movement, such as animal behavior while looking for food, and distribution within a habitat, such as dynamics at the population and community level. For example, the model would be used to look at the browsing behavior of a deer while looking for food, as well as that deer's specific location and movement within the forested habitat and its interaction with other deer while in that habitat. | Herbivore | Wikipedia | 465 | 44568 | https://en.wikipedia.org/wiki/Herbivore | Biology and health sciences | Ethology | null |
This model has been criticized as circular and untestable. Critics have pointed out that its proponents use examples that fit the theory, but do not use the model when it does not fit the reality. Other critics point out that animals do not have the ability to assess and maximize their potential gains, therefore the optimal foraging theory is irrelevant and derived to explain trends that do not exist in nature.
Holling's disk equation models the efficiency at which predators consume prey. The model predicts that as the number of prey increases, the amount of time predators spend handling prey also increases, and therefore the efficiency of the predator decreases. In 1959, S. Holling proposed an equation to model the rate of return for an optimal diet: Rate (R )=Energy gained in foraging (Ef)/(time searching (Ts) + time handling (Th))
Where s=cost of search per unit time f=rate of encounter with items, h=handling time, e=energy gained per encounter.
In effect, this would indicate that a herbivore in a dense forest would spend more time handling (eating) the vegetation because there was so much vegetation around than a herbivore in a sparse forest, who could easily browse through the forest vegetation. According to the Holling's disk equation, a herbivore in the sparse forest would be more efficient at eating than the herbivore in the dense forest.
The marginal value theorem describes the balance between eating all the food in a patch for immediate energy, or moving to a new patch and leaving the plants in the first patch to regenerate for future use. The theory predicts that absent complicating factors, an animal should leave a resource patch when the rate of payoff (amount of food) falls below the average rate of payoff for the entire area. According to this theory, an animal should move to a new patch of food when the patch they are currently feeding on requires more energy to obtain food than an average patch. Within this theory, two subsequent parameters emerge, the Giving Up Density (GUD) and the Giving Up Time (GUT). The Giving Up Density (GUD) quantifies the amount of food that remains in a patch when a forager moves to a new patch. The Giving Up Time (GUT) is used when an animal continuously assesses the patch quality. | Herbivore | Wikipedia | 481 | 44568 | https://en.wikipedia.org/wiki/Herbivore | Biology and health sciences | Ethology | null |
Plant-herbivore interactions
Interactions between plants and herbivores can play a prevalent role in ecosystem dynamics such community structure and functional processes. Plant diversity and distribution is often driven by herbivory, and it is likely that trade-offs between plant competitiveness and defensiveness, and between colonization and mortality allow for coexistence between species in the presence of herbivores. However, the effects of herbivory on plant diversity and richness is variable. For example, increased abundance of herbivores such as deer decrease plant diversity and species richness, while other large mammalian herbivores like bison control dominant species which allows other species to flourish. Plant-herbivore interactions can also operate so that plant communities mediate herbivore communities. Plant communities that are more diverse typically sustain greater herbivore richness by providing a greater and more diverse set of resources.
Coevolution and phylogenetic correlation between herbivores and plants are important aspects of the influence of herbivore and plant interactions on communities and ecosystem functioning, especially in regard to herbivorous insects. This is apparent in the adaptations plants develop to tolerate and/or defend from insect herbivory and the responses of herbivores to overcome these adaptations. The evolution of antagonistic and mutualistic plant-herbivore interactions are not mutually exclusive and may co-occur. Plant phylogeny has been found to facilitate the colonization and community assembly of herbivores, and there is evidence of phylogenetic linkage between plant beta diversity and phylogenetic beta diversity of insect clades such as butterflies. These types of eco-evolutionary feedbacks between plants and herbivores are likely the main driving force behind plant and herbivore diversity. | Herbivore | Wikipedia | 346 | 44568 | https://en.wikipedia.org/wiki/Herbivore | Biology and health sciences | Ethology | null |
Abiotic factors such as climate and biogeographical features also impact plant-herbivore communities and interactions. For example, in temperate freshwater wetlands herbivorous waterfowl communities change according to season, with species that eat above-ground vegetation being abundant during summer, and species that forage below-ground being present in winter months. These seasonal herbivore communities differ in both their assemblage and functions within the wetland ecosystem. Such differences in herbivore modalities can potentially lead to trade-offs that influence species traits and may lead to additive effects on community composition and ecosystem functioning. Seasonal changes and environmental gradients such as elevation and latitude often affect the palatability of plants which in turn influences herbivore community assemblages and vice versa. Examples include a decrease in abundance of leaf-chewing larvae in the fall when hardwood leaf palatability decreases due to increased tannin levels which results in a decline of arthropod species richness, and increased palatability of plant communities at higher elevations where grasshoppers abundances are lower. Climatic stressors such as ocean acidification can lead to responses in plant-herbivore interactions in relation to palatability as well.
Herbivore offense
The myriad defenses displayed by plants means that their herbivores need a variety of skills to overcome these defenses and obtain food. These allow herbivores to increase their feeding and use of a host plant. Herbivores have three primary strategies for dealing with plant defenses: choice, herbivore modification, and plant modification.
Feeding choice involves which plants a herbivore chooses to consume. It has been suggested that many herbivores feed on a variety of plants to balance their nutrient uptake and to avoid consuming too much of any one type of defensive chemical. This involves a tradeoff however, between foraging on many plant species to avoid toxins or specializing on one type of plant that can be detoxified.
Herbivore modification is when various adaptations to body or digestive systems of the herbivore allow them to overcome plant defenses. This might include detoxifying secondary metabolites, sequestering toxins unaltered, or avoiding toxins, such as through the production of large amounts of saliva to reduce effectiveness of defenses. Herbivores may also utilize symbionts to evade plant defenses. For example, some aphids use bacteria in their gut to provide essential amino acids lacking in their sap diet. | Herbivore | Wikipedia | 501 | 44568 | https://en.wikipedia.org/wiki/Herbivore | Biology and health sciences | Ethology | null |
Plant modification occurs when herbivores manipulate their plant prey to increase feeding. For example, some caterpillars roll leaves to reduce the effectiveness of plant defenses activated by sunlight.
Plant defense
A plant defense is a trait that increases plant fitness when faced with herbivory. This is measured relative to another plant that lacks the defensive trait. Plant defenses increase survival and/or reproduction (fitness) of plants under pressure of predation from herbivores.
Defense can be divided into two main categories, tolerance and resistance. Tolerance is the ability of a plant to withstand damage without a reduction in fitness. This can occur by diverting herbivory to non-essential plant parts, resource allocation, compensatory growth, or by rapid regrowth and recovery from herbivory. Resistance refers to the ability of a plant to reduce the amount of damage it receives from herbivores. This can occur via avoidance in space or time, physical defenses, or chemical defenses. Defenses can either be constitutive, always present in the plant, or induced, produced or translocated by the plant following damage or stress.
Physical, or mechanical, defenses are barriers or structures designed to deter herbivores or reduce intake rates, lowering overall herbivory. Thorns such as those found on roses or acacia trees are one example, as are the spines on a cactus. Smaller hairs known as trichomes may cover leaves or stems and are especially effective against invertebrate herbivores. In addition, some plants have waxes or resins that alter their texture, making them difficult to eat. Also the incorporation of silica into cell walls is analogous to that of the role of lignin in that it is a compression-resistant structural component of cell walls; so that plants with their cell walls impregnated with silica are thereby afforded a measure of protection against herbivory.
Chemical defenses are secondary metabolites produced by the plant that deter herbivory. There are a wide variety of these in nature and a single plant can have hundreds of different chemical defenses. Chemical defenses can be divided into two main groups, carbon-based defenses and nitrogen-based defenses. | Herbivore | Wikipedia | 441 | 44568 | https://en.wikipedia.org/wiki/Herbivore | Biology and health sciences | Ethology | null |
Carbon-based defenses include terpenes and phenolics. Terpenes are derived from 5-carbon isoprene units and comprise essential oils, carotenoids, resins, and latex. They can have several functions that disrupt herbivores such as inhibiting adenosine triphosphate (ATP) formation, molting hormones, or the nervous system. Phenolics combine an aromatic carbon ring with a hydroxyl group. There are several different phenolics such as lignins, which are found in cell walls and are very indigestible except for specialized microorganisms; tannins, which have a bitter taste and bind to proteins making them indigestible; and furanocumerins, which produce free radicals disrupting DNA, protein, and lipids, and can cause skin irritation.
Nitrogen-based defenses are synthesized from amino acids and primarily come in the form of alkaloids and cyanogens. Alkaloids include commonly recognized substances such as caffeine, nicotine, and morphine. These compounds are often bitter and can inhibit DNA or RNA synthesis or block nervous system signal transmission. Cyanogens get their name from the cyanide stored within their tissues. This is released when the plant is damaged and inhibits cellular respiration and electron transport.
Plants have also changed features that enhance the probability of attracting natural enemies to herbivores. Some emit semiochemicals, odors that attract natural enemies, while others provide food and housing to maintain the natural enemies' presence, e.g. ants that reduce herbivory. A given plant species often has many types of defensive mechanisms, mechanical or chemical, constitutive or induced, which allow it to escape from herbivores.
Predator–prey theory
According to the theory of predator–prey interactions, the relationship between herbivores and plants is cyclic. When prey (plants) are numerous their predators (herbivores) increase in numbers, reducing the prey population, which in turn causes predator number to decline. The prey population eventually recovers, starting a new cycle. This suggests that the population of the herbivore fluctuates around the carrying capacity of the food source, in this case, the plant. | Herbivore | Wikipedia | 464 | 44568 | https://en.wikipedia.org/wiki/Herbivore | Biology and health sciences | Ethology | null |
Several factors play into these fluctuating populations and help stabilize predator-prey dynamics. For example, spatial heterogeneity is maintained, which means there will always be pockets of plants not found by herbivores. This stabilizing dynamic plays an especially important role for specialist herbivores that feed on one species of plant and prevents these specialists from wiping out their food source. Prey defenses also help stabilize predator-prey dynamics, and for more information on these relationships see the section on Plant Defenses. Eating a second prey type helps herbivores' populations stabilize. Alternating between two or more plant types provides population stability for the herbivore, while the populations of the plants oscillate. This plays an important role for generalist herbivores that eat a variety of plants. Keystone herbivores keep vegetation populations in check and allow for a greater diversity of both herbivores and plants. When an invasive herbivore or plant enters the system, the balance is thrown off and the diversity can collapse to a monotaxon system.
The back and forth relationship of plant defense and herbivore offense drives coevolution between plants and herbivores, resulting in a "coevolutionary arms race". The escape and radiation mechanisms for coevolution, presents the idea that adaptations in herbivores and their host plants, has been the driving force behind speciation.
Mutualism
While much of the interaction of herbivory and plant defense is negative, with one individual reducing the fitness of the other, some is beneficial. This beneficial herbivory takes the form of mutualisms in which both partners benefit in some way from the interaction. Seed dispersal by herbivores and pollination are two forms of mutualistic herbivory in which the herbivore receives a food resource and the plant is aided in reproduction. Plants can also be indirectly affected by herbivores through nutrient recycling, with plants benefiting from herbivores when nutrients are recycled very efficiently. Another form of plant-herbivore mutualism is physical changes to the environment and/or plant community structure by herbivores which serve as ecosystem engineers, such as wallowing by bison. Swans form a mutual relationship with the plant species that they forage by digging and disturbing the sediment which removes competing plants and subsequently allows colonization of other plant species.
Impacts | Herbivore | Wikipedia | 475 | 44568 | https://en.wikipedia.org/wiki/Herbivore | Biology and health sciences | Ethology | null |
Trophic cascades and environmental degradation
When herbivores are affected by trophic cascades, plant communities can be indirectly affected. Often these effects are felt when predator populations decline and herbivore populations are no longer limited, which leads to intense herbivore foraging which can suppress plant communities. With the size of herbivores having an effect on the amount of energy intake that is needed, larger herbivores need to forage on higher quality or more plants to gain the optimal amount of nutrients and energy compared to smaller herbivores. Environmental degradation from white-tailed deer (Odocoileus virginianus) in the US alone has the potential to both change vegetative communities through over-browsing and cost forest restoration projects upwards of $750 million annually. Another example of a trophic cascade involved plant-herbivore interactions are coral reef ecosystems. Herbivorous fish and marine animals are important algae and seaweed grazers, and in the absence of plant-eating fish, corals are outcompeted and seaweeds deprive corals of sunlight.
Economic impacts
Agricultural crop damage by the same species totals approximately $100 million every year. Insect crop damages also contribute largely to annual crop losses in the U.S. Herbivores also affect economics through the revenue generated by hunting and ecotourism. For example, the hunting of herbivorous game species such as white-tailed deer, cottontail rabbits, antelope, and elk in the U.S. contributes greatly to the billion-dollar annually, hunting industry. Ecotourism is a major source of revenue, particularly in Africa, where many large mammalian herbivores such as elephants, zebras, and giraffes help to bring in the equivalent of millions of US dollars to various nations annually. | Herbivore | Wikipedia | 368 | 44568 | https://en.wikipedia.org/wiki/Herbivore | Biology and health sciences | Ethology | null |
Big O notation is a mathematical notation that describes the limiting behavior of a function when the argument tends towards a particular value or infinity. Big O is a member of a family of notations invented by German mathematicians Paul Bachmann, Edmund Landau, and others, collectively called Bachmann–Landau notation or asymptotic notation. The letter O was chosen by Bachmann to stand for Ordnung, meaning the order of approximation.
In computer science, big O notation is used to classify algorithms according to how their run time or space requirements grow as the input size grows. In analytic number theory, big O notation is often used to express a bound on the difference between an arithmetical function and a better understood approximation; a famous example of such a difference is the remainder term in the prime number theorem. Big O notation is also used in many other fields to provide similar estimates.
Big O notation characterizes functions according to their growth rates: different functions with the same asymptotic growth rate may be represented using the same O notation. The letter O is used because the growth rate of a function is also referred to as the order of the function. A description of a function in terms of big O notation usually only provides an upper bound on the growth rate of the function.
Associated with big O notation are several related notations, using the symbols , and , to describe other kinds of bounds on asymptotic growth rates.
Formal definition
Let the function to be estimated, be a real or complex valued function, and let the comparison function, be a real valued function. Let both functions be defined on some unbounded subset of the positive real numbers, and be non-zero (often, but not necessarily, strictly positive) for all large enough values of One writes
and it is read " is big O of " or more often " is of the order of " if the absolute value of is at most a positive constant multiple of the absolute value of for all sufficiently large values of That is, if there exists a positive real number and a real number such that
In many contexts, the assumption that we are interested in the growth rate as the variable goes to infinity or to zero is left unstated, and one writes more simply that
The notation can also be used to describe the behavior of near some real number (often, ): we say
if there exist positive numbers and such that for all defined with
As is non-zero for adequately large (or small) values of both of these definitions can be unified using the limit superior:
if | Big O notation | Wikipedia | 511 | 44578 | https://en.wikipedia.org/wiki/Big%20O%20notation | Mathematics | Algorithms | null |
And in both of these definitions the limit point (whether or not) is a cluster point of the domains of and i. e., in every neighbourhood of there have to be infinitely many points in common. Moreover, as pointed out in the article about the limit inferior and limit superior, the (at least on the extended real number line) always exists.
In computer science, a slightly more restrictive definition is common: and are both required to be functions from some unbounded subset of the positive integers to the nonnegative real numbers; then if there exist positive integer numbers and such that for all
Example
In typical usage the notation is asymptotical, that is, it refers to very large . In this setting, the contribution of the terms that grow "most quickly" will eventually make the other ones irrelevant. As a result, the following simplification rules can be applied:
If is a sum of several terms, if there is one with largest growth rate, it can be kept, and all others omitted.
If is a product of several factors, any constants (factors in the product that do not depend on ) can be omitted.
For example, let , and suppose we wish to simplify this function, using notation, to describe its growth rate as approaches infinity. This function is the sum of three terms: , , and . Of these three terms, the one with the highest growth rate is the one with the largest exponent as a function of , namely . Now one may apply the second rule: is a product of and in which the first factor does not depend on . Omitting this factor results in the simplified form . Thus, we say that is a "big O" of . Mathematically, we can write . One may confirm this calculation using the formal definition: let and . Applying the formal definition from above, the statement that is equivalent to its expansion,
for some suitable choice of a real number and a positive real number and for all . To prove this, let and . Then, for all :
so
Use
Big O notation has two main areas of application:
In mathematics, it is commonly used to describe how closely a finite series approximates a given function, especially in the case of a truncated Taylor series or asymptotic expansion.
In computer science, it is useful in the analysis of algorithms.
In both applications, the function appearing within the is typically chosen to be as simple as possible, omitting constant factors and lower order terms. | Big O notation | Wikipedia | 502 | 44578 | https://en.wikipedia.org/wiki/Big%20O%20notation | Mathematics | Algorithms | null |
There are two formally close, but noticeably different, usages of this notation:
infinite asymptotics
infinitesimal asymptotics.
This distinction is only in application and not in principle, however—the formal definition for the "big O" is the same for both cases, only with different limits for the function argument.
Infinite asymptotics
Big O notation is useful when analyzing algorithms for efficiency. For example, the time (or the number of steps) it takes to complete a problem of size might be found to be . As grows large, the term will come to dominate, so that all other terms can be neglected—for instance when , the term is 1000 times as large as the term. Ignoring the latter would have negligible effect on the expression's value for most purposes. Further, the coefficients become irrelevant if we compare to any other order of expression, such as an expression containing a term or . Even if , if , the latter will always exceed the former once grows larger than , viz. . Additionally, the number of steps depends on the details of the machine model on which the algorithm runs, but different types of machines typically vary by only a constant factor in the number of steps needed to execute an algorithm. So the big O notation captures what remains: we write either
or
and say that the algorithm has order of time complexity. The sign "" is not meant to express "is equal to" in its normal mathematical sense, but rather a more colloquial "is", so the second expression is sometimes considered more accurate (see the "Equals sign" discussion below) while the first is considered by some as an abuse of notation.
Infinitesimal asymptotics
Big O can also be used to describe the error term in an approximation to a mathematical function. The most significant terms are written explicitly, and then the least-significant terms are summarized in a single big O term. Consider, for example, the exponential series and two expressions of it that are valid when is small:
The middle expression (the one with O(x3)) means the absolute-value of the error ex − (1 + x + x2/2) is at most some constant times x3 when x is close enough to 0.
Properties
If the function can be written as a finite sum of other functions, then the fastest growing one determines the order of . For example, | Big O notation | Wikipedia | 490 | 44578 | https://en.wikipedia.org/wiki/Big%20O%20notation | Mathematics | Algorithms | null |
In particular, if a function may be bounded by a polynomial in , then as tends to infinity, one may disregard lower-order terms of the polynomial. The sets and are very different. If is greater than one, then the latter grows much faster. A function that grows faster than for any is called superpolynomial. One that grows more slowly than any exponential function of the form is called subexponential. An algorithm can require time that is both superpolynomial and subexponential; examples of this include the fastest known algorithms for integer factorization and the function .
We may ignore any powers of inside of the logarithms. The set is exactly the same as . The logarithms differ only by a constant factor (since ) and thus the big O notation ignores that. Similarly, logs with different constant bases are equivalent. On the other hand, exponentials with different bases are not of the same order. For example, and are not of the same order.
Changing units may or may not affect the order of the resulting algorithm. Changing units is equivalent to multiplying the appropriate variable by a constant wherever it appears. For example, if an algorithm runs in the order of , replacing by means the algorithm runs in the order of , and the big O notation ignores the constant . This can be written as . If, however, an algorithm runs in the order of , replacing with gives . This is not equivalent to in general. Changing variables may also affect the order of the resulting algorithm. For example, if an algorithm's run time is when measured in terms of the number of digits of an input number , then its run time is when measured as a function of the input number itself, because .
Product
Sum
If and then . It follows that if and then . In other words, this second statement says that is a convex cone.
Multiplication by a constant
Let be a nonzero constant. Then . In other words, if , then
Multiple variables
Big O (and little o, Ω, etc.) can also be used with multiple variables. To define big O formally for multiple variables, suppose and are two functions defined on some subset of . We say
if and only if there exist constants and such that for all with for some
Equivalently, the condition that for some can be written , where denotes the Chebyshev norm. For example, the statement
asserts that there exist constants C and M such that | Big O notation | Wikipedia | 498 | 44578 | https://en.wikipedia.org/wiki/Big%20O%20notation | Mathematics | Algorithms | null |
whenever either or holds. This definition allows all of the coordinates of to increase to infinity. In particular, the statement
(i.e., ) is quite different from
(i.e., ).
Under this definition, the subset on which a function is defined is significant when generalizing statements from the univariate setting to the multivariate setting. For example, if and , then if we restrict and to , but not if they are defined on .
This is not the only generalization of big O to multivariate functions, and in practice, there is some inconsistency in the choice of definition.
Matters of notation
Equals sign
The statement " is " as defined above is usually written as . Some consider this to be an abuse of notation, since the use of the equals sign could be misleading as it suggests a symmetry that this statement does not have. As de Bruijn says, is true but is not. Knuth describes such statements as "one-way equalities", since if the sides could be reversed, "we could deduce ridiculous things like from the identities and ". In another letter, Knuth also pointed out that
"the equality sign is not symmetric with respect to such notations", [as, in this notation,] "mathematicians customarily use the '=' sign as they use the word 'is' in English: Aristotle is a man, but a man isn't necessarily Aristotle".
For these reasons, it would be more precise to use set notation and write (read as: " is an element of ", or " is in the set thinking of as the class of all functions such that for some positive real number . However, the use of the equals sign is customary.
Other arithmetic operators
Big O notation can also be used in conjunction with other arithmetic operators in more complicated equations. For example, denotes the collection of functions having the growth of h(x) plus a part whose growth is limited to that of f(x). Thus,
expresses the same as | Big O notation | Wikipedia | 414 | 44578 | https://en.wikipedia.org/wiki/Big%20O%20notation | Mathematics | Algorithms | null |
Example
Suppose an algorithm is being developed to operate on a set of n elements. Its developers are interested in finding a function T(n) that will express how long the algorithm will take to run (in some arbitrary measurement of time) in terms of the number of elements in the input set. The algorithm works by first calling a subroutine to sort the elements in the set and then perform its own operations. The sort has a known time complexity of O(n2), and after the subroutine runs the algorithm must take an additional steps before it terminates. Thus the overall time complexity of the algorithm can be expressed as . Here the terms are subsumed within the faster-growing O(n2). Again, this usage disregards some of the formal meaning of the "=" symbol, but it does allow one to use the big O notation as a kind of convenient placeholder.
Multiple uses
In more complicated usage, O(·) can appear in different places in an equation, even several times on each side. For example, the following are true for :
The meaning of such statements is as follows: for any functions which satisfy each O(·) on the left side, there are some functions satisfying each O(·) on the right side, such that substituting all these functions into the equation makes the two sides equal. For example, the third equation above means: "For any function f(n) = O(1), there is some function g(n) = O(en) such that nf(n) = g(n)." In terms of the "set notation" above, the meaning is that the class of functions represented by the left side is a subset of the class of functions represented by the right side. In this use the "=" is a formal symbol that unlike the usual use of "=" is not a symmetric relation. Thus for example does not imply the false statement .
Typesetting
Big O is typeset as an italicized uppercase "O", as in the following example: . In TeX, it is produced by simply typing O inside math mode. Unlike Greek-named Bachmann–Landau notations, it needs no special symbol. However, some authors use the calligraphic variant instead.
Orders of common functions | Big O notation | Wikipedia | 470 | 44578 | https://en.wikipedia.org/wiki/Big%20O%20notation | Mathematics | Algorithms | null |
Here is a list of classes of functions that are commonly encountered when analyzing the running time of an algorithm. In each case, c is a positive constant and n increases without bound. The slower-growing functions are generally listed first.
The statement is sometimes weakened to to derive simpler formulas for asymptotic complexity. For any and is a subset of for any so may be considered as a polynomial with some bigger order.
Related asymptotic notations
Big O is widely used in computer science. Together with some other related notations, it forms the family of Bachmann–Landau notations.
Little-o notation
Intuitively, the assertion " is " (read " is little-o of " or " is of inferior order to ") means that grows much faster than , or equivalently grows much slower than . As before, let f be a real or complex valued function and g a real valued function, both defined on some unbounded subset of the positive real numbers, such that g(x) is strictly positive for all large enough values of x. One writes
if for every positive constant there exists a constant such that
For example, one has
and both as
The difference between the definition of the big-O notation and the definition of little-o is that while the former has to be true for at least one constant M, the latter must hold for every positive constant , however small. In this way, little-o notation makes a stronger statement than the corresponding big-O notation: every function that is little-o of g is also big-O of g, but not every function that is big-O of g is little-o of g. For example, but
If g(x) is nonzero, or at least becomes nonzero beyond a certain point, the relation is equivalent to
(and this is in fact how Landau originally defined the little-o notation).
Little-o respects a number of arithmetic operations. For example,
if is a nonzero constant and then , and
if and then
It also satisfies a transitivity relation:
if and then
Big Omega notation
Another asymptotic notation is , read "big omega". There are two widespread and incompatible definitions of the statement
as ,
where a is some real number, , or , where f and g are real functions defined in a neighbourhood of a, and where g is positive in this neighbourhood. | Big O notation | Wikipedia | 487 | 44578 | https://en.wikipedia.org/wiki/Big%20O%20notation | Mathematics | Algorithms | null |
The Hardy–Littlewood definition is used mainly in analytic number theory, and the Knuth definition mainly in computational complexity theory; the definitions are not equivalent.
The Hardy–Littlewood definition
In 1914 G.H. Hardy and J.E. Littlewood introduced the new symbol which is defined as follows:
as if
Thus is the negation of
In 1916 the same authors introduced the two new symbols and defined as:
as if
as if
These symbols were used by E. Landau, with the same meanings, in 1924. Authors that followed Landau, however, use a different notation for the same definitions: The symbol has been replaced by the current notation with the same definition, and became
These three symbols as well as (meaning that and are both satisfied), are now currently used in analytic number theory.
Simple examples
We have
as
and more precisely
as
We have
as
and more precisely
as
however
as
The Knuth definition
In 1976 Donald Knuth published a paper to justify his use of the -symbol to describe a stronger property. Knuth wrote: "For all the applications I have seen so far in computer science, a stronger requirement ... is much more appropriate". He defined
with the comment: "Although I have changed Hardy and Littlewood's definition of , I feel justified in doing so because their definition is by no means in wide use, and because there are other ways to say what they want to say in the comparatively rare cases when their definition applies."
Family of Bachmann–Landau notations
The limit definitions assume for sufficiently large . The table is (partly) sorted from smallest to largest, in the sense that (Knuth's version of) on functions correspond to on the real line (the Hardy–Littlewood version of , however, doesn't correspond to any such description).
Computer science uses the big , big Theta , little , little omega and Knuth's big Omega notations. Analytic number theory often uses the big , small , Hardy's , Hardy–Littlewood's big Omega (with or without the +, − or ± subscripts) and notations. The small omega notation is not used as often in analysis.
Use in computer science | Big O notation | Wikipedia | 443 | 44578 | https://en.wikipedia.org/wiki/Big%20O%20notation | Mathematics | Algorithms | null |
Informally, especially in computer science, the big O notation often can be used somewhat differently to describe an asymptotic tight bound where using big Theta Θ notation might be more factually appropriate in a given context. For example, when considering a function T(n) = 73n3 + 22n2 + 58, all of the following are generally acceptable, but tighter bounds (such as numbers 2 and 3 below) are usually strongly preferred over looser bounds (such as number 1 below).
The equivalent English statements are respectively:
T(n) grows asymptotically no faster than n100
T(n) grows asymptotically no faster than n3
T(n) grows asymptotically as fast as n3.
So while all three statements are true, progressively more information is contained in each. In some fields, however, the big O notation (number 2 in the lists above) would be used more commonly than the big Theta notation (items numbered 3 in the lists above). For example, if T(n) represents the running time of a newly developed algorithm for input size n, the inventors and users of the algorithm might be more inclined to put an upper asymptotic bound on how long it will take to run without making an explicit statement about the lower asymptotic bound.
Other notation
In their book Introduction to Algorithms, Cormen, Leiserson, Rivest and Stein consider the set of functions f which satisfy
In a correct notation this set can, for instance, be called O(g), where
The authors state that the use of equality operator (=) to denote set membership rather than the set membership operator (∈) is an abuse of notation, but that doing so has advantages. Inside an equation or inequality, the use of asymptotic notation stands for an anonymous function in the set O(g), which eliminates lower-order terms, and helps to reduce inessential clutter in equations, for example: | Big O notation | Wikipedia | 410 | 44578 | https://en.wikipedia.org/wiki/Big%20O%20notation | Mathematics | Algorithms | null |
Extensions to the Bachmann–Landau notations
Another notation sometimes used in computer science is Õ (read soft-O), which hides polylogarithmic factors. There are two definitions in use: some authors use f(n) = Õ(g(n)) as shorthand for for some k, while others use it as shorthand for . When is polynomial in n, there is no difference; however, the latter definition allows one to say, e.g. that while the former definition allows for for any constant k. Some authors write O* for the same purpose as the latter definition. Essentially, it is big O notation, ignoring logarithmic factors because the growth-rate effects of some other super-logarithmic function indicate a growth-rate explosion for large-sized input parameters that is more important to predicting bad run-time performance than the finer-point effects contributed by the logarithmic-growth factor(s). This notation is often used to obviate the "nitpicking" within growth-rates that are stated as too tightly bounded for the matters at hand (since logk n is always o(nε) for any constant k and any ).
Also, the L notation, defined as
is convenient for functions that are between polynomial and exponential in terms of
Generalizations and related usages
The generalization to functions taking values in any normed vector space is straightforward (replacing absolute values by norms), where f and g need not take their values in the same space. A generalization to functions g taking values in any topological group is also possible.
The "limiting process" can also be generalized by introducing an arbitrary filter base, i.e. to directed nets f and g. The o notation can be used to define derivatives and differentiability in quite general spaces, and also (asymptotical) equivalence of functions,
which is an equivalence relation and a more restrictive notion than the relationship "f is Θ(g)" from above. (It reduces to lim f / g = 1 if f and g are positive real valued functions.) For example, 2x is Θ(x), but is not o(x).
History (Bachmann–Landau, Hardy, and Vinogradov notations) | Big O notation | Wikipedia | 468 | 44578 | https://en.wikipedia.org/wiki/Big%20O%20notation | Mathematics | Algorithms | null |
The symbol O was first introduced by number theorist Paul Bachmann in 1894, in the second volume of his book Analytische Zahlentheorie ("analytic number theory"). The number theorist Edmund Landau adopted it, and was thus inspired to introduce in 1909 the notation o; hence both are now called Landau symbols. These notations were used in applied mathematics during the 1950s for asymptotic analysis.
The symbol (in the sense "is not an o of") was introduced in 1914 by Hardy and Littlewood. Hardy and Littlewood also introduced in 1916 the symbols ("right") and ("left"), precursors of the modern symbols ("is not smaller than a small o of") and ("is not larger than a small o of"). Thus the Omega symbols (with their original meanings) are sometimes also referred to as "Landau symbols". This notation became commonly used in number theory at least since the 1950s.
The symbol , although it had been used before with different meanings, was given its modern definition by Landau in 1909 and by Hardy in 1910. Just above on the same page of his tract Hardy defined the symbol , where means that both and are satisfied. The notation is still currently used in analytic number theory. In his tract Hardy also proposed the symbol , where means that for some constant .
In the 1970s the big O was popularized in computer science by Donald Knuth, who proposed the different notation for Hardy's , and proposed a different definition for the Hardy and Littlewood Omega notation.
Two other symbols coined by Hardy were (in terms of the modern O notation)
and
(Hardy however never defined or used the notation , nor , as it has been sometimes reported).
Hardy introduced the symbols and (as well as the already mentioned other symbols) in his 1910 tract "Orders of Infinity", and made use of them only in three papers (1910–1913). In his nearly 400 remaining papers and books he consistently used the Landau symbols O and o.
Hardy's symbols and (as well as ) are not used anymore. On the other hand, in the 1930s, the Russian number theorist Ivan Matveyevich Vinogradov introduced his notation , which has been increasingly used in number theory instead of the notation. We have
and frequently both notations are used in the same paper. | Big O notation | Wikipedia | 477 | 44578 | https://en.wikipedia.org/wiki/Big%20O%20notation | Mathematics | Algorithms | null |
The big-O originally stands for "order of" ("Ordnung", Bachmann 1894), and is thus a Latin letter. Neither Bachmann nor Landau ever call it "Omicron". The symbol was much later on (1976) viewed by Knuth as a capital omicron, probably in reference to his definition of the symbol Omega. The digit zero should not be used. | Big O notation | Wikipedia | 84 | 44578 | https://en.wikipedia.org/wiki/Big%20O%20notation | Mathematics | Algorithms | null |
In vertebrate anatomy, ribs () are the long curved bones which form the rib cage, part of the axial skeleton. In most tetrapods, ribs surround the thoracic cavity, enabling the lungs to expand and thus facilitate breathing by expanding the thoracic cavity. They serve to protect the lungs, heart, and other vital organs of the thorax. In some animals, especially snakes, ribs may provide support and protection for the entire body.
Human anatomy
Rib details
Human ribs are flat bones that form part of the rib cage to help protect internal organs. Humans usually have 24 ribs, in 12 pairs. 1 in 500 people have an extra rib known as a cervical rib. People may have a cervical rib on the right, left or both sides. All are attached at the back to the thoracic vertebrae and are numbered from 1 to 12 according to the vertebrae to which they attach. The first rib is attached to thoracic vertebra 1 (T1). At the front of the body, most of the ribs are joined by costal cartilage to the sternum. Ribs connect to vertebrae at the costovertebral joints.
The parts of a rib includes the head, neck, body (or shaft), tubercle, and angle.
The head of the rib lies next to a vertebra. The ribs connect to the vertebrae with two costovertebral joints, one on the head and one on the neck. The head of the rib has a superior and an inferior articulating region, separated by a crest. These articulate with the superior and inferior costal facets on the connecting vertebrae. The crest gives attachment to the intra-articulate ligament that joins the rib to the vertebra of the same number, at the intervertebral disc. Another ligament, the radiate ligament joins the head of the rib to both the body of the upper vertebra and to the body of the lower vertebra. The smaller middle part of the ligament connects to the intervertebral disc. This plane joint is known as the articulation of the head of the rib.
The other costovertebral joint is that between the tubercle on the neck and the transverse process of the corresponding thoracic vertebra, known as the costotransverse joint. The superior costotransverse ligament attaches from the non-articular facet of the tubercle to the transverse process of the vertebra. | Rib | Wikipedia | 510 | 44593 | https://en.wikipedia.org/wiki/Rib | Biology and health sciences | Skeletal system | Biology |
The neck of the rib is a flattened part that extends laterally from the head. The neck is about 3 cm long. Its anterior surface is flat and smooth, whilst its posterior is perforated by numerous foramina and its surface rough, to give attachment to the ligament of the neck. Its upper border presents a rough crest (crista colli costae) for the attachment of the anterior costotransverse ligament; its lower border is rounded.
A tubercle of rib on the posterior surface of the neck of the rib, has two facets (surfaces) one articulating and one non-articulating. The articular facet, is small and oval and is the lower and more medial of the two, and connects to the transverse costal facet on the thoracic vertebra of the same rib number. The transverse costal facet is on the end of the transverse process of the lower of the two vertebrae to which the head is connected. The non-articular portion is a rough elevation and affords attachment to the ligament of the tubercle. The tubercle is much more prominent in the upper ribs than in the lower ribs.
Rib cage
The first seven sets of ribs, known as "true ribs", are attached to the sternum by the costal cartilages. The first rib is unique and easier to distinguish than other ribs. It is a short, flat, C-shaped bone, and attaches to the manubrium. The vertebral attachment can be found just below the neck at the first thoracic vertebra, and the majority of this bone can be found above the level of the clavicle. Ribs 2 through 7 then become longer and less curved as they progress downwards. The following five sets are known as "false ribs", three of these sharing a common cartilaginous connection to the sternum, while the last two (eleventh and twelfth ribs) are termed floating ribs. They are attached to the vertebrae only, and not to the sternum or cartilage coming off of the sternum.
In general, human ribs increase in length from ribs 1 through 7 and decrease in length again through rib 12. Along with this change in size, the ribs become progressively oblique (slanted) from ribs 1 through 9, then less slanted through rib 12. | Rib | Wikipedia | 479 | 44593 | https://en.wikipedia.org/wiki/Rib | Biology and health sciences | Skeletal system | Biology |
The rib cage is separated from the lower abdomen by the thoracic diaphragm which controls breathing. When the diaphragm contracts, the thoracic cavity is expanded, reducing intra-thoracic pressure and drawing air into the lungs. This happens through one of two actions (or a mix of the two): when the lower ribs the diaphragm connects to are stabilized by muscles and the central tendon is mobile, when the muscle contracts the central tendon is drawn down, compressing the cavity underneath and expanding the thoracic cavity downward. When the central tendon is stabilized and the lower ribs are mobile, a contraction of the diaphragm elevates the ribs, which works in conjunction with other muscles to expand the thoracic indent upward.
Development
Early in the developing embryo, somites form and soon subdivide into three mesodermal components – the myotome, dermatome, and the sclerotome. The vertebrae and ribs develop from the sclerotomes.
During the fourth week (fertilization age) costal processes have formed on the vertebral bodies. These processes are small, lateral protrusions of mesenchyme that develop in association with the vertebral arches. During the fifth week the costal processes on the thoracic vertebrae become longer to form the ribs. In the sixth week, the costovertebral joints begin to develop and separate the ribs from the vertebrae. The first seven pairs of ribs, the true ribs join at the front to the sternal bars. By the fetal stage the sternal bars have completely fused.
The ribs begin as cartilage that later ossifies – a process called endochondral ossification. Primary ossification centers are located near the angle of each rib, and ossification continues in the direction away from the head and neck. During adolescence secondary ossification centers are formed in the tubercles and heads of the ribs.
Other animals | Rib | Wikipedia | 415 | 44593 | https://en.wikipedia.org/wiki/Rib | Biology and health sciences | Skeletal system | Biology |
In jawed fish, there are often two sets of ribs attached to the vertebral column. One set, the dorsal ribs, are found in the dividing septum between the upper and lower parts of the main muscle segments, projecting roughly sideways from the vertebral column. The second set, the ventral ribs arise from the vertebral column just below the dorsal ribs, and enclose the lower body, often joining at the tips. Not all species possess both types of rib, with the dorsal ribs being most commonly absent. Sharks, for example, have no ventral ribs, and only very short dorsal ribs. In some teleosts, there may be additional rib-like bones within the muscle mass.
Tetrapods, however, only ever have a single set of ribs which are probably homologous with the dorsal ribs of fishes. In the earlier choanates, every vertebra bore a pair of ribs, although those on the thoracic vertebrae are typically the longest. The sacral ribs were stout and short, since they formed part of the pelvis, connecting the backbone to the hip bones.
In most true tetrapods, many of these early ribs have been lost, and in living amphibians and reptiles, there is great variation in rib structure and number. For example, turtles have only eight pairs of ribs, which are developed into a bony or cartilaginous carapace and plastron, while snakes have numerous ribs running along the full length of their trunk. Frogs typically have no ribs, aside from a sacral pair, which form part of the pelvis.
In birds, ribs are present as distinct bones only on the thoracic region, although small fused ribs are present on the cervical vertebrae. The thoracic ribs of birds possess a wide projection to the rear; this uncinate process is an attachment for the shoulder muscles.
Usually dogs have 26 ribs.
Mammals usually also only have distinct ribs on the thoracic vertebra, although fixed cervical ribs are also present in monotremes. In therian mammals, the cervical and lumbar ribs are found only as tiny remnants fused to the vertebrae, where they are referred to as transverse processes. In general, the structure and number of the true ribs in humans is similar to that in other mammals. Unlike reptiles, caudal ribs are never found in mammals.
Ribs as food | Rib | Wikipedia | 488 | 44593 | https://en.wikipedia.org/wiki/Rib | Biology and health sciences | Skeletal system | Biology |
Ribs as food are widely used from many animals. The ribs are the less meaty part of the meat chop and they are often cooked as part of a slab; five or more is known as a rack, as in a rack of lamb. Short ribs are ribs of beef either served singly or several as a plate. A rib steak from beef is a popular choice used in many cuisines. Pork ribs, including spare ribs are popular in European and Asian cuisine.
Animated images | Rib | Wikipedia | 96 | 44593 | https://en.wikipedia.org/wiki/Rib | Biology and health sciences | Skeletal system | Biology |
Positronium (Ps) is a system consisting of an electron and its anti-particle, a positron, bound together into an exotic atom, specifically an onium. Unlike hydrogen, the system has no protons. The system is unstable: the two particles annihilate each other to predominantly produce two or three gamma-rays, depending on the relative spin states. The energy levels of the two particles are similar to that of the hydrogen atom (which is a bound state of a proton and an electron). However, because of the reduced mass, the frequencies of the spectral lines are less than half of those for the corresponding hydrogen lines.
States
The mass of positronium is 1.022 MeV, which is twice the electron mass minus the binding energy of a few eV. The lowest energy orbital state of positronium is 1S, and like with hydrogen, it has a hyperfine structure arising from the relative orientations of the spins of the electron and the positron.
The singlet state, , with antiparallel spins (S = 0, Ms = 0) is known as para-positronium (p-Ps). It has a mean lifetime of and decays preferentially into two gamma rays with energy of each (in the center-of-mass frame). Para-positronium can decay into any even number of photons (2, 4, 6, ...), but the probability quickly decreases with the number: the branching ratio for decay into 4 photons is .
Para-positronium lifetime in vacuum is approximately
The triplet states, 3S1, with parallel spins (S = 1, Ms = −1, 0, 1) are known as ortho-positronium (o-Ps), and have an energy that is approximately 0.001 eV higher than the singlet. These states have a mean lifetime of , and the leading decay is three gammas. Other modes of decay are negligible; for instance, the five-photons mode has branching ratio of ≈.
Ortho-positronium lifetime in vacuum can be calculated approximately as:
However more accurate calculations with corrections to O(α2) yield a value of −1 for the decay rate, corresponding to a lifetime of . | Positronium | Wikipedia | 479 | 44596 | https://en.wikipedia.org/wiki/Positronium | Physical sciences | Atomic physics | Physics |
Positronium in the 2S state is metastable having a lifetime of against annihilation. The positronium created in such an excited state will quickly cascade down to the ground state, where annihilation will occur more quickly.
Measurements
Measurements of these lifetimes and energy levels have been used in precision tests of quantum electrodynamics, confirming quantum electrodynamics (QED) predictions to high precision.
Annihilation can proceed via a number of channels, each producing gamma rays with total energy of (sum of the electron and positron mass-energy), usually 2 or 3, with up to 5 gamma ray photons recorded from a single annihilation.
The annihilation into a neutrino–antineutrino pair is also possible, but the probability is predicted to be negligible. The branching ratio for o-Ps decay for this channel is (electron neutrino–antineutrino pair) and (for other flavour) in predictions based on the Standard Model, but it can be increased by non-standard neutrino properties, like relatively high magnetic moment. The experimental upper limits on branching ratio for this decay (as well as for a decay into any "invisible" particles) are < for p-Ps and < for o-Ps.
Energy levels
While precise calculation of positronium energy levels uses the Bethe–Salpeter equation or the Breit equation, the similarity between positronium and hydrogen allows a rough estimate. In this approximation, the energy levels are different because of a different effective mass, μ, in the energy equation (see electron energy levels for a derivation):
where:
is the charge magnitude of the electron (same as the positron),
is the Planck constant,
is the electric constant (otherwise known as the permittivity of free space),
is the reduced mass: where and are, respectively, the mass of the electron and the positron (which are the same by definition as antiparticles).
Thus, for positronium, its reduced mass only differs from the electron by a factor of 2. This causes the energy levels to also roughly be half of what they are for the hydrogen atom.
So finally, the energy levels of positronium are given by | Positronium | Wikipedia | 470 | 44596 | https://en.wikipedia.org/wiki/Positronium | Physical sciences | Atomic physics | Physics |
The lowest energy level of positronium () is . The next level is . The negative sign is a convention that implies a bound state. Positronium can also be considered by a particular form of the two-body Dirac equation; Two particles with a Coulomb interaction can be exactly separated in the (relativistic) center-of-momentum frame and the resulting ground-state energy has been obtained very accurately using finite element methods of Janine Shertzer. Their results lead to the discovery of anomalous states.
The Dirac equation whose Hamiltonian comprises two Dirac particles and a static Coulomb potential is not relativistically invariant. But if one adds the (or , where is the fine-structure constant) terms, where , then the result is relativistically invariant. Only the leading term is included. The contribution is the Breit term; workers rarely go to because at one has the Lamb shift, which requires quantum electrodynamics. | Positronium | Wikipedia | 204 | 44596 | https://en.wikipedia.org/wiki/Positronium | Physical sciences | Atomic physics | Physics |
Formation and decay in materials
After a radioactive atom in a material undergoes a β+ decay (positron emission), the resulting high-energy positron slows down by colliding with atoms, and eventually annihilates with one of the many electrons in the material. It may however first form positronium before the annihilation event. The understanding of this process is of some importance in positron emission tomography. Approximately:
~60% of positrons will directly annihilate with an electron without forming positronium. The annihilation usually results in two gamma rays. In most cases this direct annihilation occurs only after the positron has lost its excess kinetic energy and has thermalized with the material.
~10% of positrons form para-positronium, which then promptly (in ~0.12 ns) decays, usually into two gamma rays.
~30% of positrons form ortho-positronium but then annihilate within a few nanoseconds by 'picking off' another nearby electron with opposing spin. This usually produces two gamma rays. During this time, the very lightweight positronium atom exhibits a strong zero-point motion, that exerts a pressure and is able to push out a tiny nanometer-sized bubble in the medium.
Only ~0.5% of positrons form ortho-positronium that self-decays (usually into three gamma rays). This natural decay rate of ortho-positronium is relatively slow (~140 ns decay lifetime), compared to the aforementioned pick-off process, which is why the three-gamma decay rarely occurs.
History
The Croatian physicist Stjepan Mohorovičić predicted the existence of positronium in a 1934 article published in Astronomische Nachrichten, in which he called it the "electrum". Other sources incorrectly credit Carl Anderson as having predicted its existence in 1932 while at Caltech. It was experimentally discovered by Martin Deutsch at MIT in 1951 and became known as positronium. Many subsequent experiments have precisely measured its properties and verified predictions of quantum electrodynamics. | Positronium | Wikipedia | 462 | 44596 | https://en.wikipedia.org/wiki/Positronium | Physical sciences | Atomic physics | Physics |
A discrepancy known as the ortho-positronium lifetime puzzle persisted for some time, but was resolved with further calculations and measurements. Measurements were in error because of the lifetime measurement of unthermalised positronium, which was produced at only a small rate. This had yielded lifetimes that were too long. Also calculations using relativistic quantum electrodynamics are difficult, so they had been done to only the first order. Corrections that involved higher orders were then calculated in a non-relativistic quantum electrodynamics.
In 2024, the AEgIS collaboration at CERN was the first to cool positronium by laser light, leaving it available for experimental use. The substance was brought to using laser cooling.
Exotic compounds
Molecular bonding was predicted for positronium. Molecules of positronium hydride (PsH) can be made. Positronium can also form a cyanide and can form bonds with halogens or lithium.
The first observation of di-positronium () molecules—molecules consisting of two positronium atoms—was reported on 12 September 2007 by David Cassidy and Allen Mills from University of California, Riverside.
Unlike muonium, positronium does not have a nucleus analogue, because the electron and the positron have equal masses. Consequently, while muonium tends to behave like a light isotope of hydrogen, positronium shows large differences in size, polarisability, and binding energy from hydrogen.
Natural occurrence
The events in the early universe leading to baryon asymmetry predate the formation of atoms (including exotic varieties such as positronium) by around a third of a million years, so no positronium atoms occurred then.
Likewise, the naturally occurring positrons in the present day result from high-energy interactions such as in cosmic ray–atmosphere interactions, and so are too hot (thermally energetic) to form electrical bonds before annihilation. | Positronium | Wikipedia | 411 | 44596 | https://en.wikipedia.org/wiki/Positronium | Physical sciences | Atomic physics | Physics |
Chalcedony ( or ) is a cryptocrystalline form of silica, composed of very fine intergrowths of quartz and moganite. These are both silica minerals, but they differ in that quartz has a trigonal crystal structure, while moganite is monoclinic. Chalcedony's standard chemical structure (based on the chemical structure of quartz) is SiO2 (silicon dioxide).
Chalcedony has a waxy luster, and may be semitransparent or translucent. It can assume a wide range of colors, but those most commonly seen are white to gray, grayish-blue or a shade of brown ranging from pale to nearly black. The color of chalcedony sold commercially is often enhanced by dyeing or heating.
The name chalcedony comes from the Latin (alternatively spelled ) and is probably derived from the town of Chalcedon in Turkey. The name appears in Pliny the Elder's as a term for a translucent kind of jaspis. Another reference to a gem by the name of () is found in the Book of Revelation (21:19); however, it is a hapax legomenon, found nowhere else in the Bible, so it is hard to tell whether the precious gem mentioned in Revelation is the same as the mineral known by this name today. The term plasma is sometimes used to refer to green translucent chalcedony.
Varieties
Chalcedony occurs in a wide range of varieties. Many semi-precious gemstones are in fact forms of chalcedony. The more notable varieties of chalcedony are as follows:
Agate
Agate is a variety of chalcedony characterized by either transparency or color patterns, such as multi-colored curved or angular banding. Opaque varieties are sometimes referred to as jasper. Fire agate shows iridescent phenomena on a brown background; iris agate shows exceptional iridescence when light (especially pinpointed light) is shone through the stone. Landscape agate is chalcedony with a number of different mineral impurities making the stone resemble landscapes.
Carnelian
Carnelian (also spelled cornelian) is a clear-to-translucent reddish-brown variety of chalcedony. Its hue may vary from a pale orange to an intense almost-black coloration. Similar to carnelian is sard, which is brown rather than red.
Chrysoprase | Chalcedony | Wikipedia | 505 | 44599 | https://en.wikipedia.org/wiki/Chalcedony | Physical sciences | Silicate minerals | Earth science |
Chrysoprase (also spelled chrysophrase) is a green variety of chalcedony, which has been colored by nickel oxide. (The darker varieties of chrysoprase are also referred to as prase. However, the term prase is also used to describe green quartz and to a certain extent is a color-descriptor, rather than a rigorously defined mineral variety.)
Blue-colored chalcedony is sometimes referred to as "blue chrysoprase" if the color is sufficiently rich, though it derives its color from the presence of copper and is largely unrelated to nickel-bearing chrysoprase.
Fire agate
Fire agate is a variety of chalcedony with inclusions of goethite or limonite causing an iridescent effect. It can display a wide range of iridescent colors including red, orange, yellow, green, blue, and purple.
Heliotrope
Heliotrope is a green variety of chalcedony, containing red inclusions of iron oxide that resemble drops of blood, giving heliotrope its alternative name of bloodstone. In a similar variety known as plasma, the spots are yellow instead.
Moss agate
Moss agate contains green filament-like inclusions, giving it the superficial appearance of moss or blue cheese. There is also tree agate which is similar to moss agate except it is solid white with green filaments whereas moss agate usually has a transparent background, so the "moss" appears in 3D. It is not a true form of agate, as it lacks agate's defining feature of concentric banding.
Chrome chalcedony
Chrome chalcedony is a green variety of chalcedony, which is colored by chromium compounds. It is also known as "mtorolite" when found in Zimbabwe and "chiquitanita" when found in Bolivia.
Onyx
Onyx is a variant of agate with black and white banding. Similarly, agate with brown, orange, red and white banding is known as sardonyx.
Chalcedony ice-blue | Chalcedony | Wikipedia | 441 | 44599 | https://en.wikipedia.org/wiki/Chalcedony | Physical sciences | Silicate minerals | Earth science |
In Greenland, white to greyish chalcedony is known from volcanic strata of the Paleocene, in the Disko-Nuussuaq area (West Greenland) and from the Scoresby Sound area (East Greenland). A light blue variety of chalcedony is known from Illorsuit, formed in the volcanic rocks along the southern coast of the island. Because of its bluish, ice-like colour, it has the local name chalcedony "ice-blue".
History
Chalcedony was used in tool making as early as 32,000 BP in Central Australia where archaeological studies at sites in the Cleland Hills uncovered flakes from stone brought in from quarries many kilometres away. Pre-contact uses described in the twentieth century included ceremonial stone knives.
Chalcedony was used for green and yellow color in prehistoric cave paintings, for example at the Bhimbetka rock shelters. The chalcedony was ground to powder form then mixed with water and animal fat or tree resin or gum.
In the Bronze Age chalcedony was in use in the Mediterranean region; for example, on Minoan Crete at the Palace of Knossos, chalcedony seals have been recovered dating to circa 1800 BC. People living along the Central Asian trade routes used various forms of chalcedony, including carnelian, to carve intaglios, ring bezels (the upper faceted portion of a gem projecting from the ring setting), and beads that show strong Greco-Roman influence.
Fine examples of first century objects made from chalcedony, possibly Kushan, were found in recent years at Tillya-tepe in north-western Afghanistan. Hot wax would not stick to it so it was often used to make seal impressions.
The term chalcedony is derived from the name of the ancient Greek town Chalkedon in Asia Minor, in modern English usually spelled Chalcedon, today the Kadıköy district of Istanbul.
According to tradition, at least three varieties of chalcedony were used in the Jewish High Priest's Breastplate. (Jewish tradition states that Moses' brother Aaron wore the Breastplate, with inscribed gems representing the twelve tribes of Israel.) The Breastplate supposedly included jasper, chrysoprase and sardonyx, and there is some debate as to whether other agates were also used. | Chalcedony | Wikipedia | 489 | 44599 | https://en.wikipedia.org/wiki/Chalcedony | Physical sciences | Silicate minerals | Earth science |
In the 19th century, Idar-Oberstein, Germany, became the world's largest chalcedony processing center, working mostly on agates. Most of these agates were from Latin America, in particular Brazil. Originally the agate carving industry around Idar and Oberstein was driven by local deposits that were mined in the 15th century. Several factors contributed to the re-emergence of Idar-Oberstein as agate center of the world: ships brought agate nodules back as ballast, thus providing extremely cheap transport. In addition, cheap labor and a superior knowledge of chemistry allowed them to dye the agates in any color with processes that were kept secret. Each mill in Idar-Oberstein had four or five grindstones. These were of red sandstone, obtained from Zweibrücken; and two men ordinarily worked together at the same stone.
Geochemistry
Structure
Chalcedony was once thought to be a fibrous variety of cryptocrystalline quartz. More recently however, it has been shown to also contain a monoclinic polymorph of quartz, known as moganite. The fraction, by mass, of moganite within a typical chalcedony sample may vary from less than 5% to over 20%. The existence of moganite was once regarded as dubious, but it is now officially recognised by the International Mineralogical Association.
Solubility
Chalcedony is more soluble than quartz under low-temperature conditions, despite the two minerals being chemically identical. Possible reasons include the existence of the moganite component, defects caused by Brazil twinning, and small crystal size.
Solubility of quartz and chalcedony in pure water
This table gives equilibrium concentrations of total dissolved silicon as calculated by PHREEQC (PH REdox EQuilibrium (in C language, USGS)) using the llnl.dat database. | Chalcedony | Wikipedia | 394 | 44599 | https://en.wikipedia.org/wiki/Chalcedony | Physical sciences | Silicate minerals | Earth science |
Carnelian (also spelled cornelian) is a brownish-red mineral commonly used as a semiprecious stone. Similar to carnelian is sard, which is generally harder and darker; the difference is not rigidly defined, and the two names are often used interchangeably. Both carnelian and sard are varieties of the silica mineral chalcedony colored by impurities of iron oxide. The color can vary greatly, ranging from pale orange to an intense almost-black coloration. Significant localities include Yanacodo (Peru); Ratnapura (Sri Lanka); and Thailand. It has been found in Indonesia, Brazil, India, Russia (Siberia), and Germany. In the United States, the official State Gem of Maryland is also a variety of carnelian called Patuxent River stone.
History
The red variety of chalcedony has been known to be used as beads since the Early Neolithic in Bulgaria. The first faceted (with constant 16+16=32 facets on each side of the bead) carnelian beads are described from the Varna Chalcolithic necropolis (middle of the 5th millennium BC). The bow drill was used to drill holes into carnelian in Mehrgarh in the 4th–5th millennium BC.
Carnelian was recovered from Bronze Age Minoan layers at Knossos on Crete in a form that demonstrated its use in decorative arts; this use dates to approximately 1800 BC. Carnelian was used widely during Roman times to make engraved gems for signet or seal rings for imprinting a seal with wax on correspondence or other important documents, as hot wax does not stick to carnelian. Sard was used for Assyrian cylinder seals, Egyptian and Phoenician scarabs, and early Greek and Etruscan gems. The Hebrew odem (also translated as sardius), was the first stone in the High Priest's breastplate, a red stone, probably sard but perhaps red jasper. In Revelation 4:3, the One seated on the heavenly throne seen in the vision of John the apostle is said to "look like jasper and (sardius transliterated)." And likewise it is in Revelation 21:20 as one of the precious stones in the foundations of the wall of the heavenly city. | Carnelian | Wikipedia | 474 | 44600 | https://en.wikipedia.org/wiki/Carnelian | Physical sciences | Silicate minerals | Earth science |
There is a Neo-Assyrian seal made of carnelian in the Western Asiatic Seals collection of the British Museum that shows Ishtar-Gula as a star goddess. She is holding a ring of royal authority and is seated on a throne. She is shown with the spade of Marduk (his symbol), Sibbiti (seven) gods, the stylus of Nabu and a worshiper. An 8th century BC carnelian seal from the collection of the Ashmolean Museum in Oxford shows Ishtar-Gula with her dog facing the spade of Marduk and his red dragon.
Etymology
Although now the more common term, "carnelian" is a 16th-century corruption of the 14th-century word "cornelian" (and its associated orthographies corneline and cornalyn). Cornelian, cognate with similar words in several Romance languages, comes from the Mediaeval Latin , itself derived from the Latin word , the cornel cherry, whose translucent red fruits resemble the stone. The Oxford English Dictionary calls "carnelian" a perversion of "cornelian," by subsequent analogy with the Latin word ("flesh"). According to Pliny the Elder, sard derived its name from the city of Sardis in Lydia from which it came, and according to others, may ultimately be related to the Persian word (sered, "yellowish-red"). Another possible derivation is from the Greek σάρξ (sarx, "flesh"); compare the surer etymology of onyx, which comes from Greek ὄνυξ (onyx, "claw, fingernail"), presumably because onyx with flesh-colored and white bands can resemble a fingernail.
Distinction between carnelian and sard
The names carnelian and sard are often used interchangeably, but they can also be used to describe distinct subvarieties. The general differences are as follows:
All of these properties vary across a continuum, so the boundary between carnelian and sard is inherently blurry. | Carnelian | Wikipedia | 429 | 44600 | https://en.wikipedia.org/wiki/Carnelian | Physical sciences | Silicate minerals | Earth science |
Calcite is a carbonate mineral and the most stable polymorph of calcium carbonate (CaCO3). It is a very common mineral, particularly as a component of limestone. Calcite defines hardness 3 on the Mohs scale of mineral hardness, based on scratch hardness comparison. Large calcite crystals are used in optical equipment, and limestone composed mostly of calcite has numerous uses.
Other polymorphs of calcium carbonate are the minerals aragonite and vaterite. Aragonite will change to calcite over timescales of days or less at temperatures exceeding 300 °C, and vaterite is even less stable.
Etymology
Calcite is derived from the German , a term from the 19th century that came from the Latin word for lime, (genitive ) with the suffix -ite used to name minerals. It is thus a doublet of the word chalk.
When applied by archaeologists and stone trade professionals, the term alabaster is used not just as in geology and mineralogy, where it is reserved for a variety of gypsum; but also for a similar-looking, translucent variety of fine-grained banded deposit of calcite.
Unit cell and Miller indices
In publications, two different sets of Miller indices are used to describe directions in hexagonal and rhombohedral crystals, including calcite crystals: three Miller indices in the directions, or four Bravais–Miller indices in the directions, where is redundant but useful in visualizing permutation symmetries.
To add to the complications, there are also two definitions of unit cell for calcite. One, an older "morphological" unit cell, was inferred by measuring angles between faces of crystals, typically with a goniometer, and looking for the smallest numbers that fit. Later, a "structural" unit cell was determined using X-ray crystallography. The morphological unit cell is rhombohedral, having approximate dimensions and , while the structural unit cell is hexagonal (i.e. a rhombic prism), having approximate dimensions and . For the same orientation, must be multiplied by 4 to convert from morphological to structural units. As an example, calcite cleavage is given as "perfect on {1 0 1}" in morphological coordinates and "perfect on {1 0 4}" in structural units. In indices, these are {1 0 1} and {1 0 4}, respectively. Twinning, cleavage and crystal forms are often given in morphological units. | Calcite | Wikipedia | 505 | 44603 | https://en.wikipedia.org/wiki/Calcite | Physical sciences | Minerals | Earth science |
Properties
The diagnostic properties of calcite include a defining Mohs hardness of 3, a specific gravity of 2.71 and, in crystalline varieties, a vitreous luster. Color is white or none, though shades of gray, red, orange, yellow, green, blue, violet, brown, or even black can occur when the mineral is charged with impurities.
Crystal habits
Calcite has numerous habits, representing combinations of over 1000 crystallographic forms. Most common are scalenohedra, with faces in the hexagonal directions (morphological unit cell) or {2 1 4} directions (structural unit cell); and rhombohedral, with faces in the or directions (the most common cleavage plane). Habits include acute to obtuse rhombohedra, tabular habits, prisms, or various scalenohedra. Calcite exhibits several twinning types that add to the observed habits. It may occur as fibrous, granular, lamellar, or compact. A fibrous, efflorescent habit is known as lublinite. Cleavage is usually in three directions parallel to the rhombohedron form. Its fracture is conchoidal, but difficult to obtain.
Scalenohedral faces are chiral and come in pairs with mirror-image symmetry; their growth can be influenced by interaction with chiral biomolecules such as L- and D-amino acids. Rhombohedral faces are not chiral.
Optical
Calcite is transparent to opaque and may occasionally show phosphorescence or fluorescence. A transparent variety called "Iceland spar" is used for optical purposes. Acute scalenohedral crystals are sometimes referred to as "dogtooth spar" while the rhombohedral form is sometimes referred to as "nailhead spar". The rhombohedral form may also have been the "sunstone" whose use by Viking navigators is mentioned in the Icelandic Sagas. | Calcite | Wikipedia | 398 | 44603 | https://en.wikipedia.org/wiki/Calcite | Physical sciences | Minerals | Earth science |
Single calcite crystals display an optical property called birefringence (double refraction). This strong birefringence causes objects viewed through a clear piece of calcite to appear doubled. The birefringent effect (using calcite) was first described by the Danish scientist Rasmus Bartholin in 1669. At a wavelength of about 590 nm, calcite has ordinary and extraordinary refractive indices of 1.658 and 1.486, respectively. Between 190 and 1700 nm, the ordinary refractive index varies roughly between 1.9 and 1.5, while the extraordinary refractive index varies between 1.6 and 1.4.
Thermoluminescence
Calcite has thermoluminescent properties mainly due to manganese divalent (). An experiment was conducted by adding activators such as ions of Mn, Fe, Co, Ni, Cu, Zn, Ag, Pb, and Bi to the calcite samples to observe whether they emitted heat or light. The results showed that adding ions (, , , , , , , , ) did not react. However, a reaction occurred when both manganese and lead ions were present in calcite. By changing the temperature and observing the glow curve peaks, it was found that and acted as activators in the calcite lattice, but was much less efficient than .
Measuring mineral thermoluminescence experiments usually use x-rays or gamma-rays to activate the sample and record the changes in glowing curves at a temperature of 700–7500 K. Mineral thermoluminescence can form various glow curves of crystals under different conditions, such as temperature changes, because impurity ions or other crystal defects present in minerals supply luminescence centers and trapping levels. Observing these curve changes also can help infer geological correlation and age determination.
Chemical
Calcite, like most carbonates, dissolves in acids by the following reaction
The carbon dioxide released by this reaction produces a characteristic effervescence when a calcite sample is treated with an acid.
Due to its acidity, carbon dioxide has a slight solubilizing effect on calcite. The overall reaction is | Calcite | Wikipedia | 446 | 44603 | https://en.wikipedia.org/wiki/Calcite | Physical sciences | Minerals | Earth science |
If the amount of dissolved carbon dioxide drops, the reaction reverses to precipitate calcite. As a result, calcite can be either dissolved by groundwater or precipitated by groundwater, depending on such factors as the water temperature, pH, and dissolved ion concentrations. When conditions are right for precipitation, calcite forms mineral coatings that cement rock grains together and can fill fractures. When conditions are right for dissolution, the removal of calcite can dramatically increase the porosity and permeability of the rock, and if it continues for a long period of time, may result in the formation of caves. Continued dissolution of calcium carbonate-rich formations can lead to the expansion and eventual collapse of cave systems, resulting in various forms of karst topography.
Calcite exhibits an unusual characteristic called retrograde solubility: it is less soluble in water as the temperature increases. Calcite is also more soluble at higher pressures.
Pure calcite has the composition . However, the calcite in limestone often contains a few percent of magnesium. Calcite in limestone is divided into low-magnesium and high-magnesium calcite, with the dividing line placed at a composition of 4% magnesium. High-magnesium calcite retains the calcite mineral structure, which is distinct from that of dolomite, . Calcite can also contain small quantities of iron and manganese. Manganese may be responsible for the fluorescence of impure calcite, as may traces of organic compounds.
Distribution
Calcite is found all over the world, and its leading global distribution is as follows:
United States
Calcite is found in many different areas in the United States. One of the best examples is the Calcite Quarry in Michigan. The Calcite Quarry is the largest carbonate mine in the world and has been in use for more than 85 years. Large quantities of calcite can be mined from these sizeable open pit mines.
Canada
Calcite can also be found throughout Canada, such as in Thorold Quarry and Madawaska Mine, Ontario, Canada.
Mexico
Abundant calcite is mined in the Santa Eulalia mining district, Chihuahua, Mexico.
Iceland
Large quantities of calcite in Iceland are concentrated in the Helgustadir mine. The mine was once the primary mining location of "Iceland spar." However, it currently serves as a nature reserve, and calcite mining will not be allowed.
England
Calcite is found in parts of England, such as Alston Moor, Egremont, and Frizington, Cumbria.
Germany | Calcite | Wikipedia | 510 | 44603 | https://en.wikipedia.org/wiki/Calcite | Physical sciences | Minerals | Earth science |
St. Andreasberg, Harz Mountains, and Freiberg, Saxony can find calcite.
Use and applications
Ancient Egyptians carved many items out of calcite, relating it to their goddess Bast, whose name contributed to the term alabaster because of the close association. Many other cultures have used the material for similar carved objects and applications.
A transparent variety of calcite known as Iceland spar may have been used by Vikings for navigating on cloudy days. A very pure crystal of calcite can split a beam of sunlight into dual images, as the polarized light deviates slightly from the main beam. By observing the sky through the crystal and then rotating it so that the two images are of equal brightness, the rings of polarized light that surround the sun can be seen even under overcast skies. Identifying the sun's location would give seafarers a reference point for navigating on their lengthy sea voyages.
In World War II, high-grade optical calcite was used for gun sights, specifically in bomb sights and anti-aircraft weaponry. It was used as a polarizer (in Nicol prisms) before the invention of Polaroid plates and still finds use in optical instruments. Also, experiments have been conducted to use calcite for a cloak of invisibility.
Microbiologically precipitated calcite has a wide range of applications, such as soil remediation, soil stabilization and concrete repair. It also can be used for tailings management and is designed to promote sustainable development in the mining industry.
Calcite can help synthesize precipitated calcium carbonate (PCC) (mainly used in the paper industry) and increase carbonation. Furthermore, due to its particular crystal habit, such as rhombohedron, hexagonal prism, etc., it promotes the production of PCC with specific shapes and particle sizes.
Calcite, obtained from an 80 kg sample of Carrara marble, is used as the IAEA-603 isotopic standard in mass spectrometry for the calibration of δ18O and δ13C.
Calcite can be formed naturally or synthesized. However, artificial calcite is the preferred material to be used as a scaffold in bone tissue engineering due to its controllable and repeatable properties. | Calcite | Wikipedia | 470 | 44603 | https://en.wikipedia.org/wiki/Calcite | Physical sciences | Minerals | Earth science |
Calcite can be used to alleviate water pollution caused by the excessive growth of cyanobacteria. Lakes and rivers can lead to cyanobacteria blooms due to eutrophication, which pollutes water resources. Phosphorus (P) is the leading cause of excessive growth of cyanobacteria. As an active capping material, calcite can help reduce P release from sediments into the water, thus inhibiting cyanobacteria overgrowth.
Natural occurrence
Calcite is a common constituent of sedimentary rocks, limestone in particular, much of which is formed from the shells of dead marine organisms. Approximately 10% of sedimentary rock is limestone. It is the primary mineral in metamorphic marble. It also occurs in deposits from hot springs as a vein mineral; in caverns as stalactites and stalagmites; and in volcanic or mantle-derived rocks such as carbonatites, kimberlites, or rarely in peridotites.
Cacti contain Ca-oxalate biominerals. Their death releases these biominerals into the environment, which subsequently transform to calcite via a monohydrocalcite intermediate, sequestering carbon.
Calcite is often the primary constituent of the shells of marine organisms, such as plankton (such as coccoliths and planktic foraminifera), the hard parts of red algae, some sponges, brachiopods, echinoderms, some serpulids, most bryozoa, and parts of the shells of some bivalves (such as oysters and rudists). Calcite is found in spectacular form in the Snowy River Cave of New Mexico as mentioned above, where microorganisms are credited with natural formations. Trilobites, which became extinct a quarter billion years ago, had unique compound eyes that used clear calcite crystals to form the lenses. It also forms a substantial part of birds' eggshells, and the δC of the diet is reflected in the δC of the calcite of the shell.
The largest documented single crystal of calcite originated from Iceland, measured and and weighed about 250 tons. Classic samples have been produced at Madawaska Mine, near Bancroft, Ontario.
Bedding parallel veins of fibrous calcite, often referred to in quarrying parlance as beef, occur in dark organic rich mudstones and shales, these veins are formed by increasing fluid pressure during diagenesis.
Formation processes | Calcite | Wikipedia | 507 | 44603 | https://en.wikipedia.org/wiki/Calcite | Physical sciences | Minerals | Earth science |
Calcite formation can proceed by several pathways, from the classical terrace ledge kink model to the crystallization of poorly ordered precursor phases like amorphous calcium carbonate (ACC) via an Ostwald ripening process, or via the agglomeration of nanocrystals.
The crystallization of ACC can occur in two stages. First, the ACC nanoparticles rapidly dehydrate and crystallize to form individual particles of vaterite. Second, the vaterite transforms to calcite via a dissolution and reprecipitation mechanism, with the reaction rate controlled by the surface area of a calcite crystal. The second stage of the reaction is approximately 10 times slower.
However, crystallization of calcite has been observed to be dependent on the starting pH and concentration of magnesium in solution. A neutral starting pH during mixing promotes the direct transformation of ACC into calcite without a vaterite intermediate. But when ACC forms in a solution with a basic initial pH, the transformation to calcite occurs via metastable vaterite, following the pathway outlined above. Magnesium has a noteworthy effect on both the stability of ACC and its transformation to crystalline CaCO3, resulting in the formation of calcite directly from ACC, as this ion destabilizes the structure of vaterite.
Epitaxial overgrowths of calcite precipitated on weathered cleavage surfaces have morphologies that vary with the type of weathering the substrate experienced: growth on physically weathered surfaces has a shingled morphology due to Volmer-Weber growth, growth on chemically weathered surfaces has characteristics of Stranski-Krastanov growth, and growth on pristine cleavage surfaces has characteristics of Frank - van der Merwe growth. These differences are apparently due to the influence of surface roughness on layer coalescence dynamics.
Calcite may form in the subsurface in response to microorganism activity, such as sulfate-dependent anaerobic oxidation of methane, where methane is oxidized and sulfate is reduced, leading to precipitation of calcite and pyrite from the produced bicarbonate and sulfide. These processes can be traced by the specific carbon isotope composition of the calcites, which are extremely depleted in the 13C isotope, by as much as −125 per mil PDB (δ13C). | Calcite | Wikipedia | 477 | 44603 | https://en.wikipedia.org/wiki/Calcite | Physical sciences | Minerals | Earth science |
In Earth history
Calcite seas existed in Earth's history when the primary inorganic precipitate of calcium carbonate in marine waters was low-magnesium calcite (lmc), as opposed to the aragonite and high-magnesium calcite (hmc) precipitated today. Calcite seas alternated with aragonite seas over the Phanerozoic, being most prominent in the Ordovician and Jurassic periods. Lineages evolved to use whichever morph of calcium carbonate was favourable in the ocean at the time they became mineralised, and retained this mineralogy for the remainder of their evolutionary history. Petrographic evidence for these calcite sea conditions consists of calcitic ooids, lmc cements, hardgrounds, and rapid early seafloor aragonite dissolution. The evolution of marine organisms with calcium carbonate shells may have been affected by the calcite and aragonite sea cycle.
Calcite is one of the minerals that has been shown to catalyze an important biological reaction, the formose reaction, and may have had a role in the origin of life. Interaction of its chiral surfaces (see Form) with aspartic acid molecules results in a slight bias in chirality; this is one possible mechanism for the origin of homochirality in living cells.
Climate change
Climate change is exacerbating ocean acidification, possibly leading to lower natural calcite production. The oceans absorb large amounts of from fossil fuel emissions into the air. The total amount of artificial absorbed by the oceans is calculated to be 118 ± 19 Gt C. If a large amount of dissolves in the sea, it will cause the acidity of the seawater to increase, thereby affecting the pH value of the ocean. Calcifying organisms in the sea, such as molluscs foraminifera, crustaceans, echinoderms and corals, are susceptible to pH changes. Meanwhile, these calcifying organisms are also an essential source of calcite. As ocean acidification causes pH to drop, carbonate ion concentrations will decline, potentially reducing natural calcite production.
Gallery | Calcite | Wikipedia | 428 | 44603 | https://en.wikipedia.org/wiki/Calcite | Physical sciences | Minerals | Earth science |
Ultramarine is a deep blue color pigment which was originally made by grinding lapis lazuli into a powder. Its lengthy grinding and washing process makes the natural pigment quite valuable—roughly ten times more expensive than the stone it comes from and as expensive as gold.
The name ultramarine comes from the Latin . The word means 'beyond the sea', as the pigment was imported by Italian traders during the 14th and 15th centuries from mines in Afghanistan. Much of the expansion of ultramarine can be attributed to Venice which historically was the port of entry for lapis lazuli in Europe.
Ultramarine was the finest and most expensive blue used by Renaissance painters. It was often used for the robes of the Virgin Mary and symbolized holiness and humility. It remained an extremely expensive pigment until a synthetic ultramarine was invented in 1826.
Ultramarine is a permanent pigment when under ideal preservation conditions. Otherwise, it is susceptible to discoloration and fading.
Structure
The pigment consists primarily of a zeolite-based mineral containing small amounts of polysulfides. It occurs in nature as a proximate component of lapis lazuli containing a blue cubic mineral called lazurite. In the Colour Index International, the pigment of ultramarine is identified as P. Blue 29 77007.
The major component of lazurite is a complex sulfur-containing sodium-silicate (Na8–10Al6Si6O24S2–4), which makes ultramarine the most complex of all mineral pigments. Some chloride is often present in the crystal lattice as well. The blue color of the pigment is due to the radical anion, which contains an unpaired electron.
Visual properties
The best samples of ultramarine are a uniform deep blue while other specimens are of paler color.
Particle size distribution has been found to vary among samples of ultramarine from various workshops. Numerous grinding techniques used by painters have resulted in different pigment/medium ratios and particle size distributions. The grinding and purification process results in pigment with particles of various geometries. Different grades of pigment may have been used for different areas in a painting, a characteristic that is sometimes used in art authentication.
Shades and variations
International Klein Blue (IKB) a deep blue hue first mixed by the French artist Yves Klein.
Electric
Electric ultramarine is the tone of ultramarine that is halfway between blue and violet on the RGB (HSV) color wheel, the expression of the HSV color space of the RGB color model.
Production | Ultramarine | Wikipedia | 508 | 44633 | https://en.wikipedia.org/wiki/Ultramarine | Physical sciences | Colors | Physics |
Natural production
Historically, lapis lazuli stone was mined in Afghanistan and shipped overseas to Europe.
A method to produce ultramarine from lapis lazuli was introduced and later described by Cennino Cennini in the 15th century. This process consisted of grinding the lapis lazuli mineral, mixing the ground material with melted wax, resins, and oils, wrapping the resulting mass in a cloth, and then kneading it in a dilute lye solution, a potassium carbonate solution prepared by combining wood ash with water. The blue lazurite particles collect at the bottom of the pot, while the colorless crystalline material and other impurities remain at the top. This process was performed at least three times, with each successive extraction generating a lower quality material. The final extraction, consisting largely of colorless material as well as a few blue particles, brings forth ultramarine ash which is prized as a glaze for its pale blue transparency. This extensive process was specific to ultramarine because the mineral it comes from has a combination of both blue and colorless pigments. If an artist were to simply grind and wash lapis lazuli, the resulting powder would be a greyish-blue color that lacks purity and depth of color since lapis lazuli contains a high proportion of colorless material.
Although the lapis lazuli stone itself is relatively inexpensive, the lengthy process of pulverizing, sifting, and washing to produce ultramarine makes the natural pigment quite valuable and roughly ten times more expensive than the stone it comes from. The high cost of the imported raw material and the long laborious process of extraction combined has been said to make high-quality ultramarine as expensive as gold.
Synthetic production
In 1990, an estimated 20,000 tons of ultramarine were produced industrially. The raw materials used in the manufacture of synthetic ultramarine are the following:
white kaolin,
anhydrous sodium sulfate (Na2SO4),
anhydrous sodium carbonate (Na2CO3),
powdered sulfur,
powdered charcoal or relatively ash-free coal, or colophony in lumps. | Ultramarine | Wikipedia | 434 | 44633 | https://en.wikipedia.org/wiki/Ultramarine | Physical sciences | Colors | Physics |
The preparation is typically made in steps:
The first part of the process takes place at 700 to 750 °C in a closed furnace, so that sulfur, carbon and organic substances give reducing conditions. This yields a yellow-green product sometimes used as a pigment.
In the second step, air or sulfur dioxide at 350 to 450 °C is used to oxidize sulfide in the intermediate product to S2 and Sn chromophore molecules, resulting in the blue (or purple, pink or red) pigment.
The mixture is heated in a kiln, sometimes in brick-sized amounts.
The resultant solids are then ground and washed, as is the case in any other insoluble pigment's manufacturing process; the chemical reaction produces large amounts of sulfur dioxide. (Flue-gas desulfurization is thus essential to its manufacture where SO2 pollution is regulated.)
Ultramarine poor in silica is obtained by fusing a mixture of soft clay, sodium sulfate, charcoal, sodium carbonate, and sulfur. The product is at first white, but soon turns green "green ultramarine" when it is mixed with sulfur and heated. The sulfur burns, and a fine blue pigment is obtained. Ultramarine rich in silica is generally obtained by heating a mixture of pure clay, very fine white sand, sulfur, and charcoal in a muffle furnace. A blue product is obtained at once, but a red tinge often results. The different ultramarines—green, blue, red, and violet—are finely ground and washed with water.
Synthetic ultramarine is a more vivid blue than natural ultramarine, since the particles in synthetic ultramarine are smaller and more uniform than the particles in natural ultramarine and therefore diffuse light more evenly. Its color is unaffected by light nor by contact with oil or lime as used in painting. Hydrochloric acid immediately bleaches it with liberation of hydrogen sulfide. Even a small addition of zinc oxide to the reddish varieties especially causes a considerable diminution in the intensity of the color. Modern, synthetic ultramarine blue is a non-toxic, soft pigment that does not need much mulling to disperse into a paint formulation.
Structure and classification | Ultramarine | Wikipedia | 444 | 44633 | https://en.wikipedia.org/wiki/Ultramarine | Physical sciences | Colors | Physics |
Ultramarine is the aluminosilicate zeolite with a sodalite structure. Sodalite consists of interconnected aluminosilicate cages. Some of these cages contain polysulfide () groups that are the chromophore (color centre). The negative charge on these ions is balanced by ions that also occupy these cages.
The chromophore is proposed to be or S4.
History
Antiquity and Middle Ages
The name derives from Middle Latin , literally "beyond the sea" because it was imported from Asia by sea. In the past, it has also been known as azzurrum ultramarine, , , , . The current terminology for ultramarine includes natural ultramarine (English), (French), (German), (Italian), and (Spanish). The first recorded use of ultramarine as a color name in English was in 1598.
The first noted use of lapis lazuli as a pigment can be seen in 6th and 7th-century paintings in Zoroastrian and Buddhist cave temples in Afghanistan, near the most famous source of the mineral. Lapis lazuli has been identified in Chinese paintings from the 10th and 11th centuries, in Indian mural paintings from the 11th, 12th, and 17th centuries, and on Anglo-Saxon and Norman illuminated manuscripts from .
Ancient Egyptians used lapis lazuli in solid form for ornamental applications in jewelry, however, there is no record of them successfully formulating lapis lazuli into paint. Archaeological evidence and early literature reveal that lapis lazuli was used as a semi-precious stone and decorative building stone from early Egyptian times. The mineral is described by the classical authors Theophrastus and Pliny. There is no evidence that lapis lazuli was used ground as a painting pigment by ancient Greeks and Romans. Like ancient Egyptians, they had access to a satisfactory blue colorant in the synthetic copper silicate pigment, Egyptian blue.
Renaissance
Venice was central to both the manufacturing and distribution of ultramarine during the early modern period. The pigment was imported by Italian traders during the 14th and 15th centuries from mines in Afghanistan. Other European countries employed the pigment less extensively than in Italy; the pigment was not used even by wealthy painters in Spain at that time. | Ultramarine | Wikipedia | 460 | 44633 | https://en.wikipedia.org/wiki/Ultramarine | Physical sciences | Colors | Physics |
During the Renaissance, ultramarine was the finest and most expensive blue that could be used by painters. Color infrared photogenic studies of ultramarine in 13th and 14th-century Sienese panel paintings have revealed that historically, ultramarine has been diluted with white lead pigment in an effort to use the color more sparingly given its high price. The 15th century artist Cennino Cennini wrote in his painters' handbook: "Ultramarine blue is a glorious, lovely and absolutely perfect pigment beyond all the pigments. It would not be possible to say anything about or do anything to it which would not make it more so." Natural ultramarine is a difficult pigment to grind by hand, and for all except the highest quality of mineral, sheer grinding and washing produces only a pale grayish blue powder.
The pigment was most extensively used during the 14th through 15th centuries, as its brilliance complemented the vermilion and gold of illuminated manuscripts and Italian panel paintings. It was valued chiefly on account of its brilliancy of tone and its inertness in opposition to sunlight, oil, and slaked lime. It is, however, extremely susceptible to even minute and dilute mineral acids and acid vapors. Dilute HCl, HNO3, and H2SO4 rapidly destroy the blue color, producing hydrogen sulfide (H2S) in the process. Acetic acid attacks the pigment at a much slower rate than mineral acids.
Ultramarine was only used for frescoes when it was applied secco because frescoes' absorption rate made its use cost prohibitive. The pigment was mixed with a binding medium like egg to form a tempera and applied over dry plaster, such as in Giotto di Bondone's frescos in the Cappella degli Scrovegni or the Arena Chapel in Padua.
European artists used the pigment sparingly, reserving their highest quality blues for the robes of Mary and the Christ child, possibly in an effort to show piety, spending as a means of expressing devotion. As a result of the high price, artists sometimes economized by using a cheaper blue, azurite, for under painting. Most likely imported to Europe through Venice, the pigment was seldom seen in German art or art from countries north of Italy. Due to a shortage of azurite in the late 16th and 17th century, the price for the already-expensive ultramarine increased dramatically. | Ultramarine | Wikipedia | 491 | 44633 | https://en.wikipedia.org/wiki/Ultramarine | Physical sciences | Colors | Physics |
17th and 18th centuries
Johannes Vermeer made extensive use of ultramarine in his paintings. The turban of the Girl with a Pearl Earring is painted with a mixture of ultramarine and lead white, with a thin glaze of pure ultramarine over it. In Lady Standing at a Virginal, the young woman's dress is painted with a mixture of ultramarine and green earth, and ultramarine was used to add shadows in the flesh tones. Scientific analysis by the National Gallery in London of Lady Standing at a Virginal showed that the ultramarine in the blue seat cushion in the foreground had degraded and become paler with time; it would have been a deeper blue when originally painted.
19th century (invention of synthetic ultramarine)
The beginning of the development of artificial ultramarine blue is known from Goethe. In about 1787, he observed the blue deposits on the walls of lime kilns near Palermo in Sicily. He was aware of the use of these glassy deposits as a substitute for lapis lazuli in decorative applications. He did not mention if it was suitable to grind for a pigment.
In 1814, Tassaert observed the spontaneous formation of a blue compound, very similar to ultramarine, if not identical with it, in a lime kiln at St. Gobain. In 1824, this caused the to offer a prize for the artificial production of the precious color. Processes were devised by Jean Baptiste Guimet (1826) and by Christian Gmelin (1828), then professor of chemistry in Tübingen. While Guimet kept his process a secret, Gmelin published his, and became the originator of the "artificial ultramarine" industry.
Permanence
Easel paintings and illuminated manuscripts have revealed natural ultramarine in a perfect state of preservation even though the art may be several centuries old. In general, ultramarine is a permanent pigment. Although it is a sulfur-containing compound from which sulfur is readily emitted as H2S, historically, it has been mixed with lead white with no reported occurrences of the lead pigment blackening to become lead sulfide. | Ultramarine | Wikipedia | 422 | 44633 | https://en.wikipedia.org/wiki/Ultramarine | Physical sciences | Colors | Physics |
A plague known as "ultramarine sickness" has occasionally been observed among ultramarine oil paintings as a grayish or yellowish gray discoloration of the paint surface. This can occur with artificial ultramarine that is used industrially. The cause of this has been debated among experts, however, potential causes include atmospheric sulfur dioxide and moisture, acidity of an oil- or oleo-resinous paint medium, or slow drying of the oil during which time water may have been absorbed, creating swelling, opacity of the medium, and therefore whitening of the paint film.
Both natural and artificial ultramarine are stable to ammonia and caustic alkalis in ordinary conditions. Artificial ultramarine has been found to fade when in contact with lime when it is used to color concrete or plaster. These observations have led experts to speculate if the natural pigment's fading may be the result of contact with the lime plaster of fresco paintings.
Synthetic applications
Synthetic ultramarine, being very cheap, is used for wall painting, the printing of paper hangings, and calico. It also is used as a corrective for the yellowish tinge often present in things meant to be white, such as linen and paper. Bluing or "laundry blue" is a suspension of synthetic ultramarine, or the chemically different Prussian blue, that is used for this purpose when washing white clothes. It is often found in makeup such as mascaras or eye shadows.
Large quantities are used in the manufacture of paper, and especially for producing a kind of pale blue writing paper which was popular in Britain. During World War I, the RAF painted the outer roundels with a color made from ultramarine blue. This became BS 108(381C) aircraft blue. It was replaced in the 1960s by a new color made on phthalocyanine blue, called BS110(381C) roundel blue.
Terminology
Ultramarine is a blue made from natural lapis lazuli, or its synthetic equivalent which is sometimes called "French Ultramarine". More generally "ultramarine blue" can refer to a vivid blue.
The term ultramarine can also refer to other pigments. Variants of the pigment such as "ultramarine red," "ultramarine green," and "ultramarine violet" all resemble ultramarine with respect to their chemistry and crystal structure. | Ultramarine | Wikipedia | 474 | 44633 | https://en.wikipedia.org/wiki/Ultramarine | Physical sciences | Colors | Physics |
The term "ultramarine green" indicates a dark green while barium chromate is sometimes referred to as "ultramarine yellow". Ultramarine pigment has also been termed "Gmelin's Blue," "Guimet's Blue," "New blue," "Oriental Blue," and "Permanent Blue". | Ultramarine | Wikipedia | 67 | 44633 | https://en.wikipedia.org/wiki/Ultramarine | Physical sciences | Colors | Physics |
Lazurite, old name Azure spar is a tectosilicate mineral with sulfate, sulfur and chloride with formula . It is a feldspathoid and a member of the sodalite group. Lazurite crystallizes in the isometric system although well‐formed crystals are rare. It is usually massive and forms the bulk of the gemstone lapis lazuli.
Mineral
Lazurite is a deep‐blue to greenish‐blue. The colour is due to the presence of anions. It has a Mohs hardness of 5.0 to 5.5 and a specific gravity of 2.4. It is translucent with a refractive index of 1.50. It is fusible at 3.5 on Wolfgang Franz von Kobell's fusibility scale, and soluble in HCl. It commonly contains or is associated with grains of pyrite.
Lazurite is a product of contact metamorphism of limestone and is typically associated with calcite, pyrite, diopside, humite, forsterite, hauyne and muscovite.
Other blue minerals, such as the carbonate mineral, azurite, and the phosphate mineral, lazulite, may be confused with lazurite, but are easily distinguished with careful examination. At one time, lazurite was a synonym for azurite.
Lazurite was first described in 1890 for an occurrence in the Sar-e-Sang District, Koksha Valley, Badakhshan Province, Afghanistan. It has been mined for more than 6,000 years in the lapis lazuli district of Badakhshan. It has been used as a pigment in painting and cloth dyeing since at least the 6th or 7th century. It is also mined at Lake Baikal in Siberia; Mount Vesuvius; Burma; Canada; and the United States. The name is from the Persian for blue.
The most important mineral component of lapis lazuli is lazurite (25% to 40%)
Redefinition
Most lapis lazuli gets its blue color from Hauyne and almost none contain "true lazurite". This was changed in 2021, as lazurite was redefined so that it is enough for a quarter (instead of half) of the cages to contain sulfide. | Lazurite | Wikipedia | 472 | 44652 | https://en.wikipedia.org/wiki/Lazurite | Physical sciences | Silicate minerals | Earth science |
Structure
Lazurite and hauyne seem to have the same structure and both are sulfate-dominant minerals. Lazurite is a pigment (opalescent) and has a bright blue streak (especially as a component of the semiprecious stone lapis lazuli). Many hauynes have a white or pale blue streak and are translucent. The difference might be a consequence of the redox state (sulfate to sulfide ratio). | Lazurite | Wikipedia | 91 | 44652 | https://en.wikipedia.org/wiki/Lazurite | Physical sciences | Silicate minerals | Earth science |
Porcupines are large rodents with coats of sharp spines, or quills, that protect them against predation. The term covers two families of animals: the Old World porcupines of the family Hystricidae, and the New World porcupines of the family Erethizontidae. Both families belong to the infraorder Hystricognathi within the profoundly diverse order Rodentia and display superficially similar coats of rigid or semi-rigid quills, which are modified hairs composed of keratin. Despite this, the two groups are distinct from one another and are not closely related to each other within the Hystricognathi. The largest species of porcupine is the third-largest living rodent in the world, after the capybara and beaver.
The Old World porcupines (Hystricidae) live in Italy, Asia (western and southern), and most of Africa. They are large, terrestrial, and strictly nocturnal.
The New World porcupines (Erethizontidae) are indigenous to North America and northern South America. They live in wooded areas and can climb trees, where some species spend their entire lives. They are less strictly nocturnal than their Old World counterparts and generally smaller.
Most porcupines are about long, with a long tail. Weighing , they are rounded, large, and slow, and use an aposematic strategy of defence. Porcupines' colouration consists of various shades of brown, grey and white. Porcupines' spiny protection resembles that of the only distantly related erinaceomorph hedgehogs and Australian monotreme echidnas as well as tenrecid tenrecs.
Etymology
The word porcupine comes from the Latin + , from Old Italian porcospino, . A regional American name for the animal is quill-pig.
A baby porcupine is a porcupette. When born, a porcupette's quills are soft hair; they harden within a few days, forming the sharp quills of adults.
Evolution
Fossils belonging to the genus Hystrix date back to the late Miocene of the continent of Africa.
Species | Porcupine | Wikipedia | 447 | 44668 | https://en.wikipedia.org/wiki/Porcupine | Biology and health sciences | Rodents | null |
Taxonomy
A porcupine is any of 30 species of rodents belonging to the families Erethizontidae (genera: Coendou, Erethizon, and Chaetomys) or Hystricidae (genera: Atherurus, Hystrix, and Trichys). Porcupines vary in size considerably: Rothschild's porcupine of South America weighs less than a kilogram (2.2 lb); the crested porcupine found in Italy, North Africa, and sub-Saharan Africa can grow to well over . The two families of porcupines are quite different, and although both belong to the Hystricognathi branch of the vast order Rodentia, they are not closely related.
Old World compared with New World species
The 11 Old World porcupines tend to be fairly large and have spines grouped in clusters.
The two subfamilies of New World porcupines are mostly smaller (although the North American porcupine reaches about in length and ), have their quills attached singly rather than grouped in clusters, and are excellent climbers, spending much of their time in trees. The New World porcupines evolved their spines independently (through convergent evolution) and are more closely related to several other families of rodents than they are to the Old World porcupines.
Longevity
Porcupines have a relatively high longevity and hold the record for being the longest-living rodent, with one individual named Cooper living over 32 years.
Diet
The North American porcupine is a herbivore and often climbs trees for food; it eats leaves, herbs, twigs, and green plants such as clover. In the winter, it may eat bark. The African porcupine is not a climber; instead, it forages on the ground. It is mostly nocturnal but will sometimes forage for food during the day, eating bark, roots, fruits, berries, and farm crops. Porcupines have become a pest in Kenya and are eaten as a delicacy. | Porcupine | Wikipedia | 414 | 44668 | https://en.wikipedia.org/wiki/Porcupine | Biology and health sciences | Rodents | null |
Defence
Defensive behaviour displays in a porcupine depend on sight, scent, and sound. Often, these displays are shown when a porcupine becomes agitated or annoyed. There are four main displays seen in a porcupine: (in order from least to most aggressive) quill erection, teeth clattering, odour emission, and attack. A porcupine's colouring aids in part of its defence as most of the predators are nocturnal and colour-blind. A porcupine's markings are black and white. The dark body and coarse hair of the porcupine are dark brown/black and when quills are raised, present a white strip down its back mimicking the look of a skunk. This, along with the raising of the sharp quills, deters predators. Along with the raising of the quills, porcupines clatter their teeth to warn predators not to approach. The incisors vibrate against each other, the strike zone shifts back, and the cheek teeth clatter. This behaviour is often paired with body shivering, which is used to further display the dangerous quills. The rattling of quills is aided by the hollow quills at the back end of the porcupine. The use of odour is when the sight and sound have failed. An unpleasant scent is produced from the skin above the tail in times of stress and is often seen with a quill erection. If these processes fail, the porcupine will attack by running sideways or backwards into predators. A porcupine's tail can also be swung in the direction of the predator; if contact is made, the quills could be impaled into the predator causing injury or death.
Quills
Porcupines' quills, or spines, take on various forms, depending on the species, but all are modified hairs coated with thick plates of keratin, and embedded in the skin musculature. Old World porcupines have quills embedded in clusters, whereas in New World porcupines, single quills are interspersed with bristles, underfur, and hair.
Quills are released by contact or may drop out when the porcupine shakes its body. New quills grow to replace lost ones. Despite what is commonly believed, porcupines cannot launch their quills at range. | Porcupine | Wikipedia | 477 | 44668 | https://en.wikipedia.org/wiki/Porcupine | Biology and health sciences | Rodents | null |
There are some possible antibiotic properties within the quills, specifically associated with the free fatty acids coating the quills. The antibiotic properties are believed to aid a porcupine that has suffered from self-injury.
Uses by humans
Porcupines are seldom eaten in Western culture but are eaten often in Southeast Asia, particularly Vietnam, where the prominent use of them as a food source has contributed to declines in porcupine populations.
Naturalist William J. Long reported the taste of the North American porcupine as "vile" and "malodorous" and delightful only to a lover of strong cheese.
More commonly, their quills and guard hairs are used for traditional decorative clothing; for example, their guard hairs are used in the creation of the Native American "porky roach" headdress. The main quills may be dyed and then applied in combination with thread to embellish leather accessories, such as knife sheaths and leather bags. Lakota women would harvest the quills for quillwork by throwing a blanket over a porcupine and retrieving the quills left stuck in the blanket.
The presence of barbs, acting like anchors, causes increased pain when removing a quill that has pierced the skin. The shape of the barbs makes the quills effective for penetrating the skin and for remaining in place. The quills have inspired research for such applications as the design of hypodermic needles and surgical staples. In contrast to the current design for surgical staples, the porcupine quill and barb design would allow easy and painless insertion, as the staple would stay in the skin using the anchored barb design rather than being bent under the skin like traditional staples.
Porcupines are also sometimes kept as exotic pets.
Habitat
Porcupines occupy a small range of habitats in tropical and temperate parts of Asia, Southern Europe, Africa, and North and South America. They live in forests and deserts, rocky outcrops, and hillsides. Some New World porcupines live in trees, but Old World porcupines prefer a rocky environment. Porcupines can be found on rocky areas up to high. They are generally nocturnal but are occasionally active during daylight.
Classification
Porcupines are distributed into two evolutionarily independent groups within the suborder Hystricomorpha of the Rodentia. | Porcupine | Wikipedia | 477 | 44668 | https://en.wikipedia.org/wiki/Porcupine | Biology and health sciences | Rodents | null |
Infraorder Hystricognathi
Family Hystricidae: Old World porcupines
African brush-tailed porcupine, Atherurus africanus
African crested porcupine, Hystrix cristata
Asiatic brush-tailed porcupine, Atherurus macrourus
Cape porcupine, Hystrix africaeaustralis
Indian porcupine, Hystrix indicus
Malayan porcupine, Hystrix brachyura
Himalayan porcupine, Hystrix (brachyura) hodgsoni
Sunda porcupine, Hystrix javanica
Sumatran porcupine, Hystrix (Thecurus) sumatrae
Thick-spined porcupine, Hystrix (Thecurus) crassispinis
Philippine porcupine, Hystrix (Thecurus) pumilis
Long-tailed porcupine, Trichys fasciculata
Parvorder Phiomorpha sensu stricto
Family Thryonomyidae: cane rats
Family Petromuridae: Dassie rats
Family Bathyergidae: African mole-rats
Parvorder Caviomorpha
Superfamily Erethizontoidea
Family Erethizontidae: New World porcupines
North American porcupine, Erethizon dorsatum
Brazilian porcupine, Coendou prehensilis
Bicolored-spined porcupine, Coendou bicolor
Andean porcupine, Coendou quichua
Black dwarf (Koopman's) porcupine, Coendou nycthemera (koopmani)
Rothschild's porcupine, Coendou rothschildi
Santa Marta porcupine, Coendou sanctemartae
Mexican hairy dwarf porcupine, Coendou mexicanus
Paraguaian hairy dwarf porcupine, Coendou spinosus
Bahia porcupine, Coendou insidiosus
Brown hairy dwarf porcupine, Coendou vestitus
Streaked dwarf porcupine, Coendou ichillus
Black-tailed hairy dwarf porcupine, Coendou melanurus
Roosmalen's dwarf porcupine, Coendou roosmalenorum
Frosted hairy dwarf porcupine, Coendou pruinosus
Stump-tailed porcupine, Coendou rufescens
Bristle-spined porcupine, Chaetomys subspinosus (sometimes considered an echimyid)
Superfamily Cavioidea | Porcupine | Wikipedia | 511 | 44668 | https://en.wikipedia.org/wiki/Porcupine | Biology and health sciences | Rodents | null |
Family Hydrochaeridae: capybara
Family Caviidae: Guinea-pigs
Family Dasyproctidae: agoutis and acouchis
Superfamily Octodontoidea
Family Abrocomidae: chinchilla-rats
Family Octodontidae: degus
Family Ctenomyidae: tuco-tucos
Family Echimyidae: spiny rats
Family Myocastoridae: nutrias
Family Capromyidae: hutias
Superfamily Chinchilloidea
Family Chinchillidae: chinchillas and allies
Family Dinomyidae: pacaranas | Porcupine | Wikipedia | 118 | 44668 | https://en.wikipedia.org/wiki/Porcupine | Biology and health sciences | Rodents | null |
The CMYK color model (also known as process color, or four color) is a subtractive color model, based on the CMY color model, used in color printing, and is also used to describe the printing process itself. The abbreviation CMYK refers to the four ink plates used: cyan, magenta, yellow, and key (most often black).
The CMYK model works by partially or entirely masking colors on a lighter, usually white, background. The ink reduces the light that would otherwise be reflected. Such a model is called subtractive because inks subtract some colors from white light; in the CMY model, white light minus red leaves cyan, white light minus green leaves magenta, and white light minus blue leaves yellow.
In additive color models, such as RGB, white is the additive combination of all primary colored lights, and black is the absence of light. In the CMYK model, it is the opposite: white is the natural color of the paper or other background, and black results from a full combination of colored inks. To save cost on ink, and to produce deeper black tones, unsaturated and dark colors are produced by using black ink instead of or in addition to combinations of cyan, magenta, and yellow.
The CMYK printing process was invented in the 1890s, when newspapers began to publish color comic strips.
Halftoning
With CMYK printing, halftoning (also called screening) allows for less than full saturation of the primary colors; tiny dots of each primary color are printed in a pattern small enough that humans perceive a solid color. Magenta printed with a 20% halftone, for example, produces a pink color, because the eye perceives the tiny magenta dots on the large white paper as lighter and less saturated than the color of pure magenta ink. Halftoning allows for a continuous variability of each color, which enables continuous color mixing of the primaries. Without halftoning, each primary would be binary, i.e. on/off, which only allows for the reproduction of eight colors: white, the three primaries (cyan, magenta, yellow), the three secondaries (red, green, blue), and black.
Comparison to CMY | CMYK color model | Wikipedia | 464 | 44682 | https://en.wikipedia.org/wiki/CMYK%20color%20model | Physical sciences | Basics_7 | null |
The CMYK color model is based on the CMY color model, which omits the black ink. Four-color printing uses black ink in addition to subtractive primaries for several reasons:
In traditional preparation of color separations, a red keyline on the black line art marked the outline of solid or tint color areas. In some cases a black keyline was used when it served as both a color indicator and an outline to be printed in black because usually the black plate contained the keyline. The K in CMYK represents the keyline, or black, plate, also sometimes called the key plate.
Text is typically printed in black and includes fine detail (such as serifs). To avoid even slight blurring when reproducing text (or other finely detailed outlines) using three inks would require impractically accurate registration.
A combination of 100% cyan, magenta, and yellow inks soaks the paper with ink, making it slower to dry, causing bleeding, or (especially on low-quality paper such as newsprint) weakening the paper so much that it tears.
Although a combination of 100% cyan, magenta, and yellow inks would, in theory, completely absorb the entire visible spectrum of light and produce a perfect black, practical inks fall short of their ideal characteristics, and the result is a dark, muddy color that is not quite black. Black ink absorbs more light and yields much better blacks.
Black ink is less expensive than the combination of colored inks that makes black.
A black made with just CMY inks is sometimes called a composite black.
When a very dark area is wanted, a colored or gray CMY "bedding" is applied first, then a full black layer is applied on top, making a rich, deep black; this is called rich black.
The amount of black to use to replace amounts of the other inks is variable, and the choice depends on the technology, paper and ink in use. Processes called under color removal, under color addition, and gray component replacement are used to decide on the final mix; different CMYK recipes will be used depending on the printing task. | CMYK color model | Wikipedia | 442 | 44682 | https://en.wikipedia.org/wiki/CMYK%20color%20model | Physical sciences | Basics_7 | null |
Other printer color models
CMYK, as well as all other process color printing, is contrasted with spot color printing, in which specific colored inks are used to generate the colors seen. Some printing presses are capable of printing with both four-color process inks and additional spot color inks at the same time. High-quality printed materials, such as marketing brochures and books, often include photographs requiring process-color printing, other graphic effects requiring spot colors (such as metallic inks), and finishes such as varnish, which enhances the glossy appearance of the printed piece.
CMYK are the process printers which often have a relatively small color gamut. Processes such as Pantone's proprietary six-color (CMYKOG) Hexachrome considerably expand the gamut. Light, saturated colors often cannot be created with CMYK, and light colors in general may make visible the halftone pattern. Using a CcMmYK process, with the addition of light cyan and magenta inks to CMYK, can solve these problems, and such a process is used by many inkjet printers, including desktop models.
Comparison with RGB displays
Comparisons between RGB displays and CMYK prints can be difficult, since the color reproduction technologies and properties are very different. A computer monitor mixes shades of red, green, and blue light to create color images. A CMYK printer instead uses light-absorbing cyan, magenta, and yellow inks, whose colors are mixed using dithering, halftoning, or some other optical technique.
Similar to electronic displays, the inks used in printing produce color gamuts that are only a subsets of the visible spectrum, and the two color modes have their own specific ranges, each being capable of producing colors the other is not. As a result of this, an image rendered on an electronic display and rendered in print can vary in appearance. When designing images to be printed, designers work in RGB color spaces (electronic displays) capable of rendering colors a CMYK process cannot, and it is often difficult to accurately visualize a printed result that must fit into a different color space that both lacks some colors an electronic display can produce and includes colors it cannot. | CMYK color model | Wikipedia | 450 | 44682 | https://en.wikipedia.org/wiki/CMYK%20color%20model | Physical sciences | Basics_7 | null |
Spectrum of printed paper
To reproduce color, the CMYK color model codes for absorbing light rather than emitting it (as is assumed by RGB). The K component ideally absorbs all wavelengths and is therefore achromatic. The cyan, magenta, and yellow components are used for color reproduction and they may be viewed as the inverse of RGB: Cyan absorbs red, magenta absorbs green, and yellow absorbs blue (−R,−G,−B).
Conversion
Since RGB and CMYK spaces are both device-dependent spaces, there is no simple or general conversion formula that converts between them. Conversions are generally done through color management systems, using color profiles that describe the spaces being converted. An ICC profile defines the bidirectional conversion between a neutral "profile connection" color space (CIE XYZ or Lab) and a selected colorspace, in this case both RGB and CMYK. The precision of the conversion depends on the profile itself, the exact methodology, and because the gamuts do not generally match, the rendering intent and constraints such as ink limit.
ICC profiles, internally built out of lookup tables and other transformation functions, are capable of handling many effects of ink blending. One example is the dot gain, which show up as non-linear components in the color-to-density mapping. More complex interactions such as Neugebauer blending can be modelled in higher-dimension lookup tables.
The problem of computing a colorimetric estimate of the color that results from printing various combinations of ink has been addressed by many scientists. A general method that has emerged for the case of halftone printing is to treat each tiny overlap of color dots as one of 8 (combinations of CMY) or of 16 (combinations of CMYK) colors, which in this context are known as Neugebauer primaries. The resultant color would be an area-weighted colorimetric combination of these primary colors, except that the Yule–Nielsen effect of scattered light between and within the areas complicates the physics and the analysis; empirical formulas for such analysis have been developed, in terms of detailed dye combination absorption spectra and empirical parameters.
Standardization of printing practices allow for some profiles to be predefined. One of them is the US Specifications for Web Offset Publications, which has its ICC color profile built into some software including Microsoft Office (as Agfa RSWOP.icm). | CMYK color model | Wikipedia | 499 | 44682 | https://en.wikipedia.org/wiki/CMYK%20color%20model | Physical sciences | Basics_7 | null |
Leprosy, also known as Hansen's disease (HD), is a long-term infection by the bacteria Mycobacterium leprae or Mycobacterium lepromatosis. Infection can lead to damage of the nerves, respiratory tract, skin, and eyes. This nerve damage may result in a lack of ability to feel pain, which can lead to the loss of parts of a person's extremities from repeated injuries or infection through unnoticed wounds. An infected person may also experience muscle weakness and poor eyesight. Leprosy symptoms may begin within one year, but for some people symptoms may take 20 years or more to occur.
Leprosy is spread between people, although extensive contact is necessary. Leprosy has a low pathogenicity, and 95% of people who contract or who are exposed to M. leprae do not develop the disease. Spread is likely through a cough or contact with fluid from the nose of a person infected by leprosy. Genetic factors and immune function play a role in how easily a person catches the disease. Leprosy does not spread during pregnancy to the unborn child or through sexual contact. Leprosy occurs more commonly among people living in poverty. There are two main types of the disease – paucibacillary and multibacillary, which differ in the number of bacteria present. A person with paucibacillary disease has five or fewer poorly pigmented, numb skin patches, while a person with multibacillary disease has more than five skin patches. The diagnosis is confirmed by finding acid-fast bacilli in a biopsy of the skin.
Leprosy is curable with multidrug therapy. Treatment of paucibacillary leprosy is with the medications dapsone, rifampicin, and clofazimine for six months. Treatment for multibacillary leprosy uses the same medications for 12 months. Several other antibiotics may also be used. These treatments are provided free of charge by the World Health Organization. | Leprosy | Wikipedia | 422 | 44700 | https://en.wikipedia.org/wiki/Leprosy | Biology and health sciences | Infectious disease | null |
Leprosy is not highly contagious. People with leprosy can live with their families and go to school and work. In the 1980s, there were 5.2 million cases globally, but by 2020 this decreased to fewer than 200,000. Most new cases occur in one of 14 countries, with India accounting for more than half of all new cases. In the 20 years from 1994 to 2014, 16 million people worldwide were cured of leprosy. About 200 cases per year are reported in the United States. Central Florida accounted for 81% of cases in Florida and nearly 1 out of 5 leprosy cases nationwide. Separating people affected by leprosy by placing them in leper colonies is not supported by evidence but still occurs in some areas of India, China, Japan, Africa, and Thailand.
Leprosy has affected humanity for thousands of years. The disease takes its name from the Greek word (), from (; 'scale'), while the term "Hansen's disease" is named after the Norwegian physician Gerhard Armauer Hansen. Leprosy has historically been associated with social stigma, which continues to be a barrier to self-reporting and early treatment. Leprosy is classified as a neglected tropical disease. World Leprosy Day was started in 1954 to draw awareness to those affected by leprosy.
The study of leprosy and its treatment is known as leprology.
Signs and symptoms
Common symptoms present in the different types of leprosy include a runny nose; dry scalp; eye problems; skin lesions; muscle weakness; reddish skin; smooth, shiny, diffuse thickening of facial skin, ear, and hand; loss of sensation in fingers and toes; thickening of peripheral nerves; a flat nose from the destruction of nasal cartilages; and changes in phonation and other aspects of speech production. In addition, atrophy of the testes and impotence may occur. | Leprosy | Wikipedia | 395 | 44700 | https://en.wikipedia.org/wiki/Leprosy | Biology and health sciences | Infectious disease | null |
Leprosy can affect people in different ways. The average incubation period is five years. People may begin to notice symptoms within the first year or up to 20 years after infection. The first noticeable sign of leprosy is often the development of pale or pink coloured patches of skin that may be insensitive to temperature or pain. Patches of discolored skin are sometimes accompanied or preceded by nerve problems including numbness or tenderness in the hands or feet. Secondary infections (additional bacterial or viral infections) can result in tissue loss, causing fingers and toes to become shortened and deformed, as cartilage is absorbed into the body. A person's immune response differs depending on the form of leprosy.
Approximately 30% of people affected with leprosy experience nerve damage. The nerve damage sustained is reversible when treated early but becomes permanent when appropriate treatment is delayed by several months. Damage to nerves may cause loss of muscle function, leading to paralysis. It may also lead to sensation abnormalities or numbness, which may lead to additional infections, ulcerations, and joint deformities.
Cause
M. leprae and M. lepromatosis
Mycobacterioum leprae and Mycobacterium lepromatosis are the mycobacteria that cause leprosy. M. lepromatosis is a relatively newly identified mycobacterium isolated from a fatal case of diffuse lepromatous leprosy in 2008. M. lepromatosis is indistinguishable clinically from M. leprae. M. leprae is an aerobic, rod-shaped, acid-fast bacterium with a waxy cell envelope characteristic of the genus Mycobacterium. M. leprae and M. lepromatosis are obligate intracellular pathogens and cannot grow or be cultured outside of host tissues. However, they can be grown using research animals such as mice and armadillos. | Leprosy | Wikipedia | 411 | 44700 | https://en.wikipedia.org/wiki/Leprosy | Biology and health sciences | Infectious disease | null |
Naturally occurring infections have been reported in nonhuman primates (including the African chimpanzee, the sooty mangabey, and the cynomolgus macaque), armadillos, and red squirrels. Multilocus sequence typing of the armadillo M. leprae strains suggests that they were of human origin for at most a few hundred years. Thus, it is suspected that armadillos first acquired the organism incidentally from early European explorers of the Americas. This incidental transmission was sustained in the armadillo population, and it may be transmitted back to humans, making leprosy a zoonotic disease (spread between humans and animals).
Red squirrels (Sciurus vulgaris), a threatened species in Great Britain, were found to carry leprosy in November 2016. It has been suggested that the trade in red squirrel fur, highly prized in the medieval period and intensively traded, may have been responsible for the leprosy epidemic in medieval Europe. A pre-Norman era skull excavated in Hoxne, Suffolk, in 2017 was found to carry DNA from a strain of M. leprae which closely matched the strain carried by modern red squirrels on Brownsea Island.
Risk factors
The greatest risk factor for developing leprosy is contact with another person infected by leprosy. People who are exposed to a person who has leprosy are 5–8 times more likely to develop leprosy than members of the general population. Leprosy occurs more commonly among those living in poverty. Not all people who are infected with M. leprae develop symptoms.
Conditions that reduce immune function, such as malnutrition, other illnesses, or genetic mutations, may increase the risk of developing leprosy. Infection with HIV does not appear to increase the risk of developing leprosy. Certain genetic factors in the person exposed have been associated with developing lepromatous or tuberculoid leprosy.
Transmission
Transmission of leprosy occurs during close contact with those who are infected. Transmission of leprosy is through the upper respiratory tract. Older research suggested the skin as the main route of transmission, but research has increasingly favored the respiratory route. Transmission occurs through inhalation of bacilli present in upper airway secretion. | Leprosy | Wikipedia | 469 | 44700 | https://en.wikipedia.org/wiki/Leprosy | Biology and health sciences | Infectious disease | null |
Leprosy is not sexually transmitted and is not spread through pregnancy to the unborn child. The majority (95%) of people who are exposed to M. leprae do not develop leprosy; casual contact such as shaking hands and sitting next to someone with leprosy does not lead to transmission. People are considered non-infectious 72 hours after starting appropriate multi-drug therapy. Two exit routes of M. leprae from the human body that are often described are the skin and the nasal mucosa, although their relative importance is not clear. Lepromatous cases show large numbers of organisms deep in the dermis, but whether they reach the skin surface in sufficient numbers is doubtful. Leprosy may also be transmitted to humans by armadillos, although the mechanism is not fully understood.
Genetics
{| class="wikitable" style="float: right; margin-left:15px; text-align:center"
|-
! Name
! Locus
! OMIM
! Gene
|-
| LPRS1
| 10p13
|
|
|-
| LPRS2
| 6q25
|
| PARK2, PACRG
|-'
| LPRS3
| 4q32
|
| TLR2|-
| LPRS4
| 6p21.3
|
| LTA|-
| LPRS5
| 4p14
|
| TLR1|-
| LPRS6
| 13q14.11
|
|
|}
Not all people infected or exposed to M. leprae develop leprosy, and genetic factors are suspected to play a role in susceptibility to an infection. Cases of leprosy often cluster in families, and several genetic variants have been identified. In many who are exposed, the immune system can eliminate the leprosy bacteria during the early infection stage before severe symptoms develop. A genetic defect in cell-mediated immunity may cause a person to be susceptible to develop leprosy symptoms after exposure to the bacteria. The region of DNA responsible for this variability is also involved in Parkinson's disease, giving rise to current speculation that the two disorders may be linked at the biochemical level. | Leprosy | Wikipedia | 442 | 44700 | https://en.wikipedia.org/wiki/Leprosy | Biology and health sciences | Infectious disease | null |
Mechanism
Most leprosy complications are the result of nerve damage. The nerve damage occurs from direct invasion by the M. leprae bacteria and a person's immune response resulting in inflammation. The molecular mechanism underlying how M. leprae produces the symptoms of leprosy is not clear, but M. leprae has been shown to bind to Schwann cells, which may lead to nerve injury including demyelination and a loss of nerve function (specifically a loss of axonal conductance). Numerous molecular mechanisms have been associated with this nerve damage including the presence of a laminin-binding protein and the glycoconjugate (PGL-1) on the surface of M. leprae that can bind to laminin on peripheral nerves.
As part of the human immune response, white blood cell-derived macrophages may engulf M. leprae by phagocytosis. In the initial stages, small sensory and autonomic nerve fibers in the skin of a person with leprosy are damaged. This damage usually results in hair loss to the area, a loss of the ability to sweat, and numbness (decreased ability to detect sensations such as temperature and touch). Further peripheral nerve damage may result in skin dryness, more numbness, and muscle weaknesses or paralysis in the area affected. The skin can crack and if the skin injuries are not carefully cared for, there is a risk for a secondary infection that can lead to more severe damage.
Diagnosis
In countries where people are frequently infected, a person is considered to have leprosy if they have one of the following two signs:
Skin lesion consistent with leprosy and with definite sensory loss.
Positive skin smears. | Leprosy | Wikipedia | 354 | 44700 | https://en.wikipedia.org/wiki/Leprosy | Biology and health sciences | Infectious disease | null |
Skin lesions can be single or many, and usually hypopigmented, although occasionally reddish or copper-colored. The lesions may be flat (macules), raised (papules), or solid elevated areas (nodular). Experiencing sensory loss at the skin lesion is a feature that can help determine if the lesion is caused by leprosy or by another disorder such as tinea versicolor. Thickened nerves are associated with leprosy and can be accompanied by loss of sensation or muscle weakness, but muscle weakness without the characteristic skin lesion and sensory loss is not considered a reliable sign of leprosy. In some cases, the presence of acid-fast leprosy bacilli in skin smears is considered diagnostic; however, the diagnosis is typically made without laboratory tests, based on symptoms. If a person has a new leprosy diagnosis and already has a visible disability caused by leprosy, the diagnosis is considered late.
In countries or areas where leprosy is uncommon, such as the United States, diagnosis of leprosy is often delayed because healthcare providers are unaware of leprosy and its symptoms. Early diagnosis and treatment prevent nerve involvement, the hallmark of leprosy, and the disability it causes.U.S. Department of Health and Human Services, Health Resources and Services Administration. (n.d.). National Hansen's disease (leprosy) program Retrieved from There is no recommended test to diagnose latent leprosy in people without symptoms. Few people with latent leprosy test positive for anti PGL-1. The presence of M. leprae bacterial DNA can be identified using a polymerase chain reaction (PCR)-based technique. This molecular test alone is not sufficient to diagnose a person, but this approach may be used to identify someone who is at high risk of developing or transmitting leprosy such as those with few lesions or an atypical clinical presentation. New approaches propose tools to diagnose leprosy through artificial intelligence. | Leprosy | Wikipedia | 423 | 44700 | https://en.wikipedia.org/wiki/Leprosy | Biology and health sciences | Infectious disease | null |
Classification
Several different approaches for classifying leprosy exist. There are similarities between the classification approaches.
The World Health Organization (WHO) system distinguishes "paucibacillary" and "multibacillary" based on the proliferation of bacteria. ("pauci-" refers to a small quantity.)
The Ridley-Jopling scale provides five gradations.
The ICD-10, though developed by the WHO, uses Ridley-Jopling and not the WHO system. It also adds an indeterminate ("I") entry.
In MeSH, three groupings are used.
Leprosy may also occur with only neural involvement, without skin lesions.
Complications
Leprosy may cause the victim to lose limbs and digits but not directly. M. leprae attacks nerve endings and destroys the body's ability to feel pain and injury. Without feeling pain, people with leprosy have an increased risk of injuring themselves. Injuries become infected and result in tissue loss. Fingers, toes, and limbs become shortened and deformed as the tissue is absorbed into the body.
Prevention
Early disease detection is important, since physical and neurological damage may be irreversible even if cured. Medications can decrease the risk of those living with people who have leprosy from acquiring the disease and likely those with whom people with leprosy come into contact outside the home. The WHO recommends that preventive medicine be given to people who are in close contact with someone who has leprosy. The suggested preventive treatment is a single dose of rifampicin in adults and children over 2 years old who do not already have leprosy or tuberculosis. Preventive treatment is associated with a 57% reduction in infections within 2 years and a 30% reduction in infections within 6 years.
The Bacillus Calmette–Guérin (BCG) vaccine offers a variable amount of protection against leprosy in addition to its closely related target of tuberculosis. It appears to be 26% to 41% effective (based on controlled trials) and about 60% effective based on observational studies with two doses possibly working better than one. The WHO concluded in 2018 that the BCG vaccine at birth reduces leprosy risk and is recommended in countries with high incidence of TB and people who have leprosy. People living in the same home as a person with leprosy are suggested to take a BCG booster which may improve their immunity by 56%. Development of a more effective vaccine is ongoing. | Leprosy | Wikipedia | 506 | 44700 | https://en.wikipedia.org/wiki/Leprosy | Biology and health sciences | Infectious disease | null |
A novel vaccine called LepVax entered clinical trials in 2017 with the first encouraging results reported on 24 participants published in 2020. If successful, this would be the first leprosy-specific vaccine available.
Treatment
Several leprostatic agents are available for treatment. A three-drug regimen of rifampicin, dapsone, and clofazimine is recommended for all people with leprosy, for six months for paucibacillary leprosy and 12 months for multibacillary leprosy.
Multidrug therapy (MDT) remains highly effective, and people are no longer infectious after the first monthly dose. MDT is safe and easy to use under field conditions because it is available in calendar-labelled blister packs. Post-treatment relapse rates remain low. Resistance has been reported in several countries, although the number of cases is small. People with rifampicin-resistant leprosy may be treated with second-line medications such as fluoroquinolones, minocycline, or clarithromycin, but the treatment duration is 24 months because of their lower bactericidal activity. Evidence on the potential benefits and harms of alternative regimens for drug-resistant leprosy is not available.
For people with nerve damage, protective footwear may help prevent ulcers and secondary infection. Canvas shoes may be better than PVC boots. There may be no difference between double rocker shoes and below-knee plaster. Topical ketanserin seems to have a better effect on ulcer healing than clioquinol cream or zinc paste, but the evidence for this is weak. Phenytoin applied to the skin improves skin changes to a greater degree when compared to saline dressings. | Leprosy | Wikipedia | 364 | 44700 | https://en.wikipedia.org/wiki/Leprosy | Biology and health sciences | Infectious disease | null |
Outcomes
Although leprosy has been curable since the mid-20th century, left untreated it can cause permanent physical impairments and damage to a person's nerves, skin, eyes, and limbs. Despite leprosy not being very infectious and having a low pathogenicity, there is still significant stigma and prejudice associated with the disease. Because of this stigma, leprosy can affect a person's participation in social activities and may also affect the lives of their family and friends. People with leprosy are also at a higher risk for problems with their mental well-being. The social stigma may contribute to problems obtaining employment, financial difficulties, and social isolation. Efforts to reduce discrimination and reduce the stigma surrounding leprosy may help improve outcomes for people with leprosy.
Epidemiology
In 2018, there were 208,619 new cases of leprosy recorded, a slight decrease from 2017. In 2015, 94% of the new leprosy cases were confined to 14 countries. India reported the greatest number of new cases (60% of reported cases), followed by Brazil (13%) and Indonesia (8%). Although the number of cases worldwide continues to fall, there are parts of the world where leprosy is more common, including Brazil, South Asia (India, Nepal, Bhutan), some parts of Africa (Tanzania, Madagascar, Mozambique), and the western Pacific. About 150 to 250 cases are diagnosed in the United States each year.
In the 1960s, there were tens of millions of leprosy cases recorded when the bacteria started to develop resistance to dapsone, the most common treatment option at the time. International (e.g., the WHO's "Global Strategy for Reducing Disease Burden Due to Leprosy") and national (e.g., the International Federation of Anti-Leprosy Associations) initiatives have reduced the total number and the number of new cases of the disease. | Leprosy | Wikipedia | 400 | 44700 | https://en.wikipedia.org/wiki/Leprosy | Biology and health sciences | Infectious disease | null |
The number of new leprosy cases is difficult to measure and monitor because of leprosy's long incubation period, delays in diagnosis after the onset of the disease, and lack of medical care in affected areas. The registered prevalence of the disease is used to determine disease burden. Registered prevalence is a useful proxy indicator of the disease burden, as it reflects the number of active leprosy cases diagnosed with the disease and receiving treatment with MDT at a given point in time. The prevalence rate is defined as the number of cases registered for MDT treatment among the population in which the cases have occurred, again at a given point in time.
History
Historical distribution
Using comparative genomics, in 2005, geneticists traced the origins and worldwide distribution of leprosy from East Africa or the Near East along human migration routes. They found four strains of M. leprae with specific regional locations: Monot et al. (2005) determined that leprosy originated in East Africa or the Near East and traveled with humans along their migration routes, including those of trade in goods and slaves. The four strains of M. leprae are based in specific geographic regions where each predominantly occurs:
strain 1 in Asia, the Pacific region, and East Africa;
strain 2 in Ethiopia, Malawi, Nepal, north India, and New Caledonia;
strain 3 in Europe, North Africa, and the Americas;
strain 4 in West Africa and the Caribbean.
This confirms the spread of the disease along the migration, colonisation, and slave trade routes taken from East Africa to India, West Africa to the New World, and from Africa to Europe and vice versa.
Skeletal remains discovered in 2009 represent the oldest documented evidence for leprosy, dating to the 2nd millennium BC. Located at Balathal, Rajasthan, in northwest India, the discoverers suggest that if the disease did migrate from Africa to India during the 3rd millennium BC "at a time when there was substantial interaction among the Indus Civilization, Mesopotamia, and Egypt, there needs to be additional skeletal and molecular evidence of leprosy in India and Africa to confirm the African origin of the disease". A proven human case was verified by DNA taken from the shrouded remains of a man discovered by researchers from the Hebrew University of Jerusalem in a tomb in Akeldama, next to the Old City of Jerusalem dated by radiocarbon methods to the first half of the 1st century. | Leprosy | Wikipedia | 486 | 44700 | https://en.wikipedia.org/wiki/Leprosy | Biology and health sciences | Infectious disease | null |
The oldest strains of leprosy known from Europe are from Great Chesterford in southeast England and date back to AD 415–545. These findings suggest a different path for the spread of leprosy, meaning it may have originated in western Eurasia. This study also indicates that there were more strains in Europe at the time than previously determined.
Discovery and scientific progress
Literary attestation of leprosy is unclear because of the ambiguity of many early sources, including the Indian Atharvaveda and Kausika Sutra, the Egyptian Ebers Papyrus, and the Hebrew Bible's various sections regarding signs of impurity (tzaraath). Leprotic symptoms are attested in the Indian doctor Sushruta's Compendium, originally dating to c. 600 BC but only surviving in emended texts no earlier than the 5th century BC. Symptoms consistent with leprosy were possibly described by Hippocrates in 460 BC. However, Hansen's disease probably did not exist in Greece or the Middle East before the Common Era. In 1846, Francis Adams produced The Seven Books of Paulus Aegineta which included a commentary on all medical and surgical knowledge and descriptions and remedies to do with leprosy from the Romans, Greeks, and Arabs.Roman: Celsus, Pliny, Serenus Samonicus, Scribonius Largus, Caelius Aurelianus, Themison, Octavius Horatianus, Marcellus the Emperic; Greek: Aretaeus, Plutarch, Galen, Oribasius, Aetius (Aëtius of Amida or Sicamus Aëtius), Actuarius, Nonnus, Psellus, Leo, Myrepsus; Arabic: Scrapion, Avenzoar, Albucasis, Haly Abbas translated by Stephanus Antiochensis, Alsharavius, Rhases (Abū Bakr al-Rāzī), and Guido de Cauliaco.
Leprosy did not exist in the Americas before colonization by modern Europeans nor did it exist in Polynesia until the middle of the 19th century. The causative agent of leprosy, M. leprae, was discovered by Gerhard Armauer Hansen in Norway in 1873, making it one of the first species of pathogenic bacteria identified. | Leprosy | Wikipedia | 477 | 44700 | https://en.wikipedia.org/wiki/Leprosy | Biology and health sciences | Infectious disease | null |
Treatment
Chaulmoogra tree oil was used topically to manage Hansen's disease for centuries. Chaulmoogra oil could not be taken orally without causing nausea or injected without forming an abscess. Leprosy was once believed to be highly contagious and was treated with mercury, as was syphilis, which was first described in 1530. Many early cases thought to be leprosy could actually have been syphilis. In 1915, Alice Ball, the first black woman to graduate from the University of Hawai'i with a masters in chemistry, discovered how to make the oil water soluble. This technique led to marked improvements in patients with Hansen's disease who were treated in Hawai'i.
The first effective drug (promin) became available in the 1940s. In the 1950s, dapsone was introduced. The search for further effective antileprosy drugs led to the use of clofazimine and rifampicin in the 1960s and 1970s. Later, Indian scientist Shantaram Yawalkar and his colleagues formulated a combined therapy using rifampicin and dapsone, intended to mitigate bacterial resistance. Combining all three drugs was first recommended by the WHO in 1981. These three drugs are still used in the standard MDT regimens. Resistance has developed to initial treatment. Until the introduction of MDT in the early 1980s, leprosy could not be diagnosed and treated successfully within the community.
The importance of the nasal mucosa in the transmission of M. leprae was recognized as early as 1898 by Schäffer, in particular, that of the ulcerated mucosa. The mechanism of plantar ulceration in leprosy and its treatment was first described by Ernest W. Price.
Etymology
The word "leprosy" comes from the Greek word "λέπος (lépos) – skin" and "λεπερός (leperós) – scaly man".
Society and culture
Treatment cost
Between 1995 and 1999 the WHO, with the aid of the Nippon Foundation, supplied all endemic countries with free MDT in blister packs, channeled through ministries of health. This free provision was extended in 2000 and again in 2005, 2010, and 2015 with donations by the MDT manufacturer Novartis through the WHO. At the national level, non-governmental organizations (NGOs) affiliated with the national program will continue to be provided with an appropriate free supply. | Leprosy | Wikipedia | 509 | 44700 | https://en.wikipedia.org/wiki/Leprosy | Biology and health sciences | Infectious disease | null |
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