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Guan ware or Kuan ware ( Chinese : 官窯 ; pinyin : guān yáo ; Wade–Giles : kuan-yao ) is one of the Five Famous Kilns of Song dynasty China, making high-status stonewares , whose surface decoration relied heavily on crackled glaze , randomly crazed by a network of crack lines in the glaze.
Guan means "official" in Chinese and Guan ware was, most unusually for Chinese ceramics of the period, the result of an imperial initiative resulting from the loss of access to northern kilns such as those making Ru ware and Jun ware after the invasion of the north and the flight of a Song prince to establish the Southern Song at a new capital at Hangzhou , Zhejiang province . It is usually assumed that potters from the northern imperial kilns followed the court south to man the new kilns. [ 1 ]
In some Asian sources "Guan ware" may be used in the literally translated sense to cover any "official" wares ordered by the Imperial court. [ 2 ] In April 2015, Liu Yiqian paid US$14.7 million for a Guan ware vase from the Southern Song . [ 3 ]
The new Southern Song court was established in Hangzhou in 1127, but some time probably elapsed before the kiln was established; this may not have been until after hostilities with the invaders were concluded in 1141. According to Chinese historical sources, the first kiln was actually within or beside the palace precinct, described as in the "back park", and was called or was at "Xiuneisi". [ 4 ] Various places around the city have been explored, and ceramic remains found, but perhaps because of subsequent building on the site, the location of this kiln remained uncertain, and it is now thought that the name might refer to the controlling office rather than the actual kiln site. [ 5 ] Following excavations in starting in 1996 it is now thought that the site has been found, as the Laohudong or Tiger Cave Kiln [老虎洞窑] on the outskirts of the city. An old Yue ware dragon kiln had been revived, but the official wares were made in a northern-style mantou kiln , rare this far south. [ 6 ]
A second kiln was established later at Jiaotanxia ("Altar of Heaven" or "Suburban Altar"), on the outskirts of the new capital; this has been identified and excavated. In Chinese contemporary sources these wares were regarded as rather inferior to those from the first kiln, and the excavated sherds are very similar to those of the nearby Longquan celadon kilns. [ 7 ] Indeed, Longquan may have helped out when the Guan kilns could not fulfill orders by themselves. [ 8 ]
The end date of Guan ware is uncertain, but it probably persisted until 1400 or later, as the Ge Gu Yao Lun , a fourteenth century Ming dynasty manual on ceramics by Cao Zhao , seems to treat it as being still produced. [ 9 ]
Guan ware is not difficult to distinguish from the Ru ware which it perhaps tries to imitate, but wares from the second site can be very similar indeed to Longquan ware, and it has been suggested that some was made there. [ 10 ] Crackled glaze is usual, but perhaps was not at this time a desired effect, as it certainly became in imitations centuries later. [ 11 ] Alternatively it was originally produced accidentally, but within the Guan period became deliberate. [ 12 ] In surviving examples the effect is probably often more striking than it would have been originally, either because collectors have chemically enhanced them, through gradual oxidation over time, or from staining in use. [ 13 ]
Three qualities of the ware are recorded in old sources, and can be identified in surviving examples. The best had a grey-blue glaze on a thin body, with wide crackle, followed by a greener glaze with a denser crackle, then finally "almost a pale grey brown" with a "very dark close crackle on a dark grey body" that was rather thicker; all are illustrated here, with the types indicated by 1–3 (which is not a standard terminology). [ 14 ]
The crackle arises during cooling, when the coefficient of expansion differs between the glaze and the body. [ 15 ] There are several layers of glaze, and the glaze is often thicker than the clay body, as can be seen in sherds . [ 16 ] The crackle does not occur through all layers. Most shapes were wheel thrown , but moulds and slab-building were also used. [ 17 ] Less usual shapes include those derived from ancient ritual bronzes and jade congs . [ 18 ] Bowls and dishes often have "lobed or indented rims". [ 19 ]
Guan ware is "the most frequently copied of all Chinese wares", [ 20 ] and the imitations began immediately, at the many southern kilns producing Longquan celadon and other wares. Imitations in Jingdezhen porcelain seem to have begun under the Yuan dynasty and continue to the present day; these are often hard to date. [ 21 ] | https://en.wikipedia.org/wiki/Guan_ware |
Professor Guangzhao Mao is an American chemical engineer and an academic. She is professor and Head of the School of Engineering at the University of Edinburgh . [ 1 ] From 2020 to 2024 she served as the Head of the School of Chemical Engineering at the University of New South Wales . [ 2 ] She has held positions as chief investigator at the Australian Research Council (ARC) Centre of Excellence for Carbon Science and Innovation, the ARC Research Hub for Resilient Intelligent Infrastructure Systems, and the ARC Research Hub for Connected Sensors for Health. [ 3 ]
Mao is most known for her work on nanotechnology , primarily focusing on targeted drug delivery and electrochemistry for sensors .
Mao completed her BSc in chemistry from Nanjing University in 1988 and obtained her PhD in chemical engineering from the University of Minnesota in 1994. She then completed her postdoctoral fellowship at the same institution in 1995. [ 2 ]
Mao began her academic career in 1995 by joining Wayne State University as an assistant professor, promoted to full professor, and served until 2020. Since 2020, she has been serving as a professor at the school of chemical engineering at the University of New South Wales . [ 2 ]
Mao served as the director of the material science graduate program at Wayne State University from 2011 to 2015 and as the Chair of the Chemical Engineering and Material Science Department at Wayne State University from 2015 to 2020. From 2020 to 2024, she held the position of the Head of the School of Chemical Engineering at the University of New South Wales . [ 2 ] She joined the University of Edinburgh as Head of the School of Engineering in September 2024. [ 1 ]
Mao has been the chief investigator of the ARC Research Hub for Connected Sensors for Health [ 4 ] and the ARC Research Hub for Resilient Intelligent Infrastructure Systems, [ 5 ] and as of 2023, she has also been serving as the chief investigator of the ARC Centre of Excellence for Carbon Science and Innovation.
Mao has authored numerous publications spanning the areas of nanomanufacturing , nanofabrication, and nanochemistry , including articles in peer-reviewed journals. [ 6 ]
Centered on localized gene delivery, Mao's research proposed biodegradable polymer coatings for sequential DNA release from implantable devices. [ 7 ] This was built on her PhD research on the multilayer films. [ 8 ] In 2016, she and her team pioneered the idea of using retrograde transport proteins to specifically deliver drugs for treating respiratory issues linked to spinal cord injury. [ 9 ] In related research, she collaborated with Harry Goshgarian and Abdulghani Sankari to advance nanotherapeutics by integrating retrograde transport proteins, adenosine receptor antagonists, and nanoparticle carriers. [ 10 ] [ 11 ] Furthermore, she proposed a new technique for delivering drugs specifically to the central nervous system (CNS) using nanoparticles that are chemically attached to neural tract tracer proteins and can be transported along specific neural pathways, allowing them to bypass the blood–brain barrier and target the CNS directly. [ 12 ] Mao used human embryonic stem cells (hESCs) for assessing nanotoxicology, specifically, the effect of nanoparticle size on the viability, pluripotency, neuronal differentiation, and DNA methylation of hESCs. Her work revealed a type of gold nanoparticles to be highly toxic and demonstrated the potential of hESCs in predicting nanotoxicity. [ 13 ]
Mao's other nanotechnology research has focused on seed-mediated crystallization for nanosensor scale up. Her early research examined the potential of designing nucleation seeds to induce shape change in molecular crystals. In her investigation of the impact of seed size and surface chemistry, her study illustrated the capability of nanoparticles to effectively change the ordering pattern of molecular crystals nucleated on the nanoparticle. [ 14 ] Moreover, she examined the use of electrochemistry to deposit both the nanoparticle seeds and the molecular crystals on the seed to form a hybrid nanostructure. [ 15 ] In 2020, her research group introduced a method for manufacturing nanowire sensors by electrochemically depositing charge-transfer salt nanowire crystals on sensor substrates, demonstrating their gas sensing capabilities for detecting ammonia concentrations in the range of 1–100 ppm through electrical impedance measurements. [ 16 ] In 2023, Mao demonstrated the potential of electrochemistry for precise deposition and scale up of nanosensors. [ 17 ] She applied atomic force microscopy and surface forces measurement techniques for the study of colloidal and biomolecular interfaces including liposomes, [ 18 ] DNA nanoparticles, [ 19 ] and viral particles. [ 20 ] | https://en.wikipedia.org/wiki/Guangzhao_Mao |
Guanidine nitrate is the chemical compound with the formula [C(NH 2 ) 3 ]NO 3 . It is a colorless, water-soluble salt. It is produced on a large scale and finds use as precursor for nitroguanidine , [ 1 ] fuel in pyrotechnics and gas generators . Its correct name is guanidinium nitrate , but the colloquial term guanidine nitrate is widely used.
Although it is the salt formed by neutralizing guanidine with nitric acid , guanidine nitrate is produced industrially by the reaction of dicyandiamide (or calcium salt) and ammonium nitrate . [ 2 ]
It has been used as a monopropellant in the Jetex engine for model airplanes . It is attractive because it has a high gas output and low flame temperature. It has a relatively high monopropellant specific impulse of 177 seconds (1.7 kN·s/kg). [ note 1 ]
Guanidine nitrate's explosive decomposition is given by the following equation:
Guanidine nitrate is used as the gas generator in automobile airbags . [ 3 ] It is less toxic than the mixture used in older airbags of sodium azide , potassium nitrate and silica (NaN 3 , KNO 3 , and SiO 2 ), and it is less explosive and sensitive to moisture compared to the very cheap ammonium nitrate (NH 4 NO 3 ). [ 4 ]
The compound is a hazardous substance, being an explosive and containing an oxidant (nitrate). It is also harmful to the eyes, skin, and respiratory tract. [ 2 ] | https://en.wikipedia.org/wiki/Guanidine_nitrate |
In molecular biology, a guanine tetrad (also known as a G-tetrad or G-quartet ) is a structure composed of four guanine bases in a square planar array . [ 1 ] [ 2 ] They most prominently contribute to the structure of G-quadruplexes , where their hydrogen bonding stabilizes the structure. [ 3 ] [ 4 ] Usually, there are at least two guanine tetrads in a G-quadruplex, and they often feature Hoogsteen-style hydrogen bonding . [ 1 ]
Guanine tetrads are formed by sequences rich in guanine, such as GGGGC. [ 5 ] They may also play a role in the dimerization of non-endogenous RNAs to facilitate the replication of some viruses. [ 5 ] Guanine tetrads dimerize through their 5' ends since it is more energetically favorable . [ 6 ]
They can be stabilized by central cations , such as lithium, sodium, potassium, rubidium , or caesium . [ 7 ] [ 8 ] However, they still form a variety of different structures. [ 1 ] Guanine tetrads are not always stable, but the sugar-phosphate backbone of DNA can assist in stability of the guanine tetrads themselves. [ 1 ] Guanine tetrads are more stable when stacked, as intermolecular forces between each layers help stabilize them. [ 9 ]
Guanine tetrads can also influence recombination , replication, and transcription. [ 1 ] [ 2 ] For instance, guanine tetrads are found in the promoter region of the Myc family of oncogenes . [ 10 ] They also function in immunoglobulin class switching and may play a role in the genome of HIV . [ 11 ] Guanine tetrads appear frequently in the telomeric regions of DNA. [ 3 ] | https://en.wikipedia.org/wiki/Guanine_tetrad |
(p)ppGpp , guanosine pentaphosphate and tetraphosphate , also known as the "magic spot" nucleotides , [ 1 ] are alarmones involved in the stringent response in bacteria that cause the inhibition of RNA synthesis when there is a shortage of amino acids . This inhibition by (p)ppGpp decreases translation in the cell, conserving amino acids present. Furthermore, ppGpp and pppGpp cause the up-regulation of many other genes involved in stress response such as the genes for amino acid uptake (from surrounding media ) and biosynthesis . [ 2 ] (p)ppGpp is also conserved in plants , where it is known to play a role in regulating growth and developmental processes. [ 3 ]
ppGpp and pppGpp were first identified by Michael Cashel in 1969. [ 4 ] These nucleotides were found to accumulate rapidly in Escherichia coli cells starved for amino acids and inhibit synthesis of ribosomal and transfer RNAs. [ 5 ] It is now known that (p)ppGpp is also produced in response to other stressors including carbon and phosphate starvation. Historically, literature surrounding (p)ppGpp have given conflicting findings and information on its role in bacterial stress responses. [ 6 ]
E.coli are shown to be more sensitive to accumulations of guanosine tetraphosphate than guanosine pentaphosphate. [ 7 ] A complete absence of (p)ppGpp causes multiple amino acid requirements, poor survival of aged cultures, aberrant cell division, morphology, and immotility, as well as being locked in a growth mode during entry into starvation.
The synthesis and degradation of (p)ppGpp have been most extensively characterized in the bacterial model organism Escherichia coli.
(p)ppGpp is created via pppGpp synthase , also known as RelA, and is converted from pppGpp to ppGpp via pppGpp phosphohydrolase. RelA is associated with about every one in two hundred ribosomes and it becomes activated when an uncharged transfer RNA (tRNA) molecule enters the A site of the ribosome, due to the shortage of amino acid required by the tRNA. If a mutant bacterium is relA − it is said to be relaxed and no regulation of RNA production due to amino acid absence is seen.
E. coli produces a second protein responsible for degradation of (p)ppGpp, SpoT . When the amino acid balance in the cell is restored, (p)ppGpp is hydrolyzed by SpoT and returned to a more energetically favorable state. This protein also has the capacity to synthesize (p)ppGpp, and seems to be the primary synthase under certain conditions of stress. Most other bacteria encode a single protein that is responsible for both synthesis and degradation of (p)ppGpp, generally homologs of SpoT.
Targets of (p)ppGpp include rRNA operons , of which there are seven in E.coli , all of which have 2 promoters . When (p)ppGpp associates with the promoter it affects the RNA polymerase enzyme 's ability to bind and initiate transcription . It is thought that (p)ppGpp may affect the stability of the open complex formed by RNA polymerase on DNA and therefore affect promoter clearance. Its presence also leads to an increase in pausing during transcription elongation and it competes with nucleoside triphosphate substrates .
There is now a consensus that (p)ppGpp is a determinant of growth rate control rather than nucleoside triphosphate (NTP) substrate concentrations.
ppGpp inhibits IF2-mediated fMet-Phe initiation dipeptide formation, probably by interfering with 30S and 50S subunit interactions. E. coli accumulates more ppGpp than pppGpp during amino acid starvation, and ppGpp has about 8-fold greater efficiency than that of pppGpp. While B. subtilis accumulates more pppGpp than ppGpp.
In E. coli amino acid starvation inhibited DNA replication at the initiation stage at oriC, most probably owing to the lack of the DnaA replication initiation protein. In B. subtilis, the replication arrest due to (p)ppGpp accumulation is caused by the binding of an Rtp protein to specific sites about 100-200kb away from oriC in both directions. DNA primase (DnaG) was directly inhibited by (p)ppGpp. Unlike E. coli, B. subtilis accumulates more pppGpp than ppGpp; the more abundant nucleotide is a more-potent DnaG inhibitor. ppGpp can bind with Obg protein which belongs to the conserved, small GTPase protein family. Obg protein interacts with several regulators (RsbT, RsbW, RsbX) necessary for the stress activation of sigma B.
The (p)ppGpp levels of the host seem to act as a sensor for phage lambda development, primarily affecting transcription. Modest ppGpp levels inhibit pR and active pE, pI, and paQ promoters in vivo and have effects in vitro that seem to favor lysogeny. In contrast, absent or high concentrations of (p)ppGpp favor lysis. Modest ppGpp levels favor lysogeny by leading to low HflB (FtsH). When ppGpp is either absent or high, HflB protease levels are high; this leads to lower CII (a lysogeny-promoting phage protein)
and favors lysis.
One of the key elements of promoters inhibited by (p)ppGpp is the presence of a GC-rich discriminator, defined as a region between TATA-box (-10 box) and +1 nt (where +1 is the transcription start site). Promoters negatively regulated by ppGpp have a 16-bp linker, in contrast with the 17-bp consensus. Promoters activated by ppGpp seem to have an AT-rich discriminator and linger linkers (for example, the his promoter linker is 18 bp).
Genetic evidence suggesting that RNAP was the target of ppGpp came from the discovery that M+ mutants (also called stringent RNAP mutants) display in vitro and in vivo mimicry of physiology and transcription regulation conferred by (p)ppGpp, even in its absence. Cross-linking ppGpp to RNAP reinforced this notion. Structural details of an association between ppGpp and RNAP came from the analysis of cocrystals that positioned ppGpp in the secondary channel of RNAP near the catalytic center.
DksA is a 17-kDa protein, its structure is similar to GreA and GreB, which are well-characterized transcriptional elongation factors. GreA and GreB bind directly to RNAP rather than DNA and act by inserting their N-terminal coiled-coil finger domain through the RNAP secondary channel. Two conserved acidic residues at the tip of the finger domain are necessary to induce RNAP's intrinsic ability to cleave backtracked RNA. DksA also possesses two acidic residues at its finger tip, but it does not induce nucleolytic cleavage activity. Instead, these residues are proposed to stabilize ppGpp binding to RNAP by mutual coordination of an Mg2+ ion that is crucial for polymerization.
ppGpp directly inhibits transcription from ribosomal promoters. One model is ppGpp and DksA together and independently decrease the stability of the open complexes formed on DNA by RNAP. Another model is the trapping mechanism. In this model, RNAP is trapped by ppGpp in closed complexes and is unable to initiate transcription. Thus, ppGpp seems to act at many levels, and the mechanism of its action is a complex outcome of several factors, intrinsic promoter properties not being the least of them. The transcription activation by ppGpp can be direct or indirect. Direct activation occurs when RNAP interacts with effectors, such as ppGpp, DksA or both, to increase transcription from a given promoter. Indirect activation by these effectors of one promoter relies on inhibition of other (strong) promoters, leading to increased availability of RNAP that indirectly activates transcription initiation. The promoters that activated directly by ppGpp include P argI , P thrABC , P livJ , and P hisG . The indirectly activation promoters include these dependent on sigma factors: S, H, N, E. When strong promoters, such as rrn , are inhibited, there more RNAP are available for these alternative sigma factors.
When (p)ppGpp is absent, pathogenicity is compromised for reasons that vary with the organism studied. Deleting rel A and spo T genes, but not rel A alone, gave a (p)ppGpp 0 state that resulted in strong attenuation in mice and noninvasiveness in vitro. Vaccine tests reveal that 30 days after single immunization with the (p)ppGpp 0 strain, mice were protected from challenge with wild-type Salmonella at a dose 10 6 -fold above the established LD 50 .
It was proposed that increased synthesis of (p)ppGpp would cause polyphosphate (PolyP) accumulation in E. coli . [ 8 ] The alarmone could interact with exopolyphosphatase PPX , which would inhibit the hydrolysis of PolyP, thus causing its accumulation in bacteria. Although it has recently been shown that it is actually DksA and not (p)ppGpp that causes this buildup. [ 9 ] It has been shown in Pseudomonas aeruginosa that the phoU mutant ( phoU belongs to the Pho Regulon ) synthesizes more (p)ppGpp and this would be one of the reasons that it accumulates more polyphosphate. [ 10 ] | https://en.wikipedia.org/wiki/Guanosine_pentaphosphate |
Guanylurea dinitramide ( FOX-12 or GUDN ) is a novel insensitive high explosive .
GUDN was discovered by Abraham Langlet, a chemist at the Swedish Defence Research Agency , and patented in 1997. [ 1 ] The moniker FOX-12 stems from the Swedish-language acronym for the Agency, FOI, plus x for "explosive." [ 2 ]
GUDN is particularly valued for its extreme stability and insensitivity.
GUDN found its first major application when mixed with oxidizers such as potassium nitrate or copper nitrate in automotive airbag inflators. [ 3 ]
GUDN is also used in a 60/40 mix with RDX as a propellant in the UNIFLEX 2 IM modular artillery charge system fielded in the BAE 155mm /L52 Archer howitzer. [ 4 ]
Blended in equal parts with TNT , GUDN forms the a melt-castable explosive known as GUNTOL. A variation adding 15% Aluminum is known as GUNTONAL. [ 5 ]
Upon detonation , GUDN undergoes a thermal decomposition which is not entirely understood as of 2021. [ 6 ] The calculated detonation velocity is 8235 m/s, with a detonation pressure of 25.89 GPa , and a detonation temperature of 2887 K . [ 7 ]
GUDN is synthesized by a reaction of ammonium dinitramide and the sulfate salt of guanylurea [ de ] . [ 2 ] | https://en.wikipedia.org/wiki/Guanylurea_dinitramide |
Guar gum , also called guaran , is a galactomannan polysaccharide extracted from guar beans that has thickening and stabilizing properties useful in food, feed, and industrial applications. [ 1 ] The guar seeds are mechanically dehusked, hydrated, milled and screened according to application. [ 2 ] It is typically produced as a free-flowing, off-white powder.
The guar bean is principally grown in India , Pakistan , the United States , Australia and Africa . India is the largest producer, accounting for nearly 80% of world production. [ 3 ] In India, Rajasthan , Gujarat , and Haryana are the main producing regions. The US has produced 4,600 to 14,000 tonnes of guar over the last 5 years. [ 4 ] [ when? ] Texas acreage since 1999 has fluctuated from about 7,000 to 50,000 acres. [ 5 ] The world production for guar gum and its derivatives is about 1.0 million tonnes. Non-food guar gum accounts for about 40% of the total demand. [ 6 ]
Chemically, guar gum is an exo- polysaccharide composed of the sugars galactose and mannose . [ 7 ] The backbone is a linear chain of β 1,4-linked mannose residues to which galactose residues are 1,6-linked at every second mannose, forming short side-branches. Guar gum has the ability to withstand temperatures of 80 °C (176 °F) for five minutes. [ 8 ]
Guar gum is more soluble than locust bean gum due to its extra galactose branch points. Unlike locust bean gum, it is not self-gelling. [ 9 ] Either borax or calcium can cross-link guar gum, causing it to gel . In water, it is nonionic and hydrocolloidal . It is not affected by ionic strength or pH , but will degrade at extreme pH and temperature (e.g., pH 3 at 50 °C). [ 9 ] It remains stable in solution over pH range 5–7. Strong acids cause hydrolysis , and loss of viscosity and alkalis in strong concentration also tend to reduce viscosity. It is insoluble in most hydrocarbon solvents. The viscosity attained is dependent on time, temperature, concentration, pH, rate of agitation and particle size of the powdered gum used. The lower the temperature, the lower the rate at which viscosity increases, and the lower the final viscosity. Above 80°C, the final viscosity is slightly reduced. Finer guar powders swell more rapidly than larger particle size coarse powdered gum. [ citation needed ] [ 10 ]
Guar gum shows a clear low shear plateau on the flow curve and is strongly shear-thinning. The rheology of guar gum is typical for a random coil polymer. It does not show the very high low [ clarification needed ] shear plateau viscosities seen with more rigid polymer chains such as xanthan gum. It is very thixotropic above 1% concentration, but below 0.3%, the thixotropy is slight. Guar gum shows viscosity synergy with xanthan gum . [ clarification needed ] Guar gum and micellar casein mixtures can be slightly thixotropic if a biphase system forms. [ 9 ] [ 11 ]
One use of guar gum is as a thickening agent in foods and medicines for humans and animals. Because it is gluten-free, it is used as an additive to replace wheat flour in baked goods. [ 12 ] :41 It has been shown to reduce serum cholesterol and lower blood glucose levels. [ 13 ]
Guar gum is also economical because it has almost eight times the water-thickening ability of other agents (e.g., cornstarch ) and only a small quantity is needed for producing sufficient viscosity . [ clarification needed ] [ 14 ] Because less is required, costs are reduced.
In addition to guar gum's effects on viscosity, its high ability to flow, or deform , gives it favorable rheological [ clarification needed ] properties. It forms breakable [ clarification needed ] gels when cross-linked with boron [ citation needed ] . It is used in various multi-phase formulations for hydraulic fracturing, in some as an emulsifier because it helps prevent oil droplets from coalescing, [ citation needed ] and in others as a stabilizer to help prevent solid particles from settling and/or separating [ citation needed ] .
Fracking entails the pumping of sand-laden fluids into an oil or natural gas reservoir at high pressure and flow rate. This cracks the reservoir rock and then props the cracks open. Water alone is too thin to be effective at carrying proppant sand, so guar gum is one of the ingredients added to thicken the slurry mixture and improve its ability to carry proppant. There are several properties which are important 1. Thixotropic : the fluid should be thixotropic, meaning it should gel within a few hours. 2. Gelling and de-gelling: The desired viscosity changes over the course of a few hours. When the fracking slurry is mixed, it needs to be thin enough to make it easier to pump. Then as it flows down the pipe, the fluid needs to gel to support the proppant and flush it deep into the fractures. After that process, the gel has to break down so that it is possible to recover the fracking fluid but leave the proppant behind. This requires a chemical process which produces then breaks the gel cross-linking at a predictable rate. Guar+boron+proprietary chemicals can accomplish both of these goals at once. [ citation needed ]
Guar gum retards ice crystal growth by slowing mass transfer across the solid/liquid interface. It shows good stability during freeze-thaw cycles. Thus, it is used in egg-free ice cream. Guar gum has synergistic effects with locust bean gum and sodium alginate . May be synergistic with xanthan : together with xanthan gum, it produces a thicker product (0.5% guar gum / 0.35% xanthan gum), which is used in applications such as soups, which do not require clear results. [ 15 ]
Guar gum is a hydrocolloid, hence is useful for making thick pastes without forming a gel, and for keeping water bound in a sauce or emulsion. Guar gum can be used for thickening cold and hot liquids, to make hot gels, light foams and as an emulsion stabilizer. Guar gum can be used for cottage cheeses, curds, yoghurt, sauces, soups and frozen desserts. Guar gum is also a good source of fiber, with 80% soluble dietary fiber on a dry weight basis. [ 9 ]
Guar gum is analysed for
Guar gum powder standards are:
Depending upon the requirement of end product, various processing techniques are used. The commercial production of guar gum normally uses roasting, differential attrition, sieving, and polishing. Food-grade guar gum is manufactured in stages. Guar split selection is important in this process. The split is screened to clean it and then soaked to pre-hydrate it in a double-cone mixer. The prehydrating stage is very important because it determines the rate of hydration of the final product. The soaked splits, which have reasonably high moisture content, are passed through a flaker. The flaked guar split is ground and then dried. The powder is screened through rotary screens to deliver the required particle size. Oversize particles are either recycled to main ultra fine or reground in a separate regrind plant, according to the viscosity requirement. [ citation needed ]
This stage helps to reduce the load at the grinder. The soaked splits are difficult to grind. Direct grinding of those generates more heat in the grinder, which is not desired in the process, as it reduces the hydration of the product. Through the heating, grinding, and polishing process, the husk is separated from the endosperm halves and the refined guar split is obtained. Through the further grinding process, the refined guar split is then treated and converted into powder. The split manufacturing process yields husk and germ called “guar meal”, widely sold in the international market as cattle feed. It is high in protein and contains oil and albuminoids, about 50% in germ and about 25% in husks. The quality of the food-grade guar gum powder is defined from its particle size, rate of hydration, and microbial content. [ citation needed ]
Manufacturers define different grades and qualities of guar gum by the particle size, the viscosity generated with a given concentration, and the rate at which that viscosity develops. Coarse-mesh guar gums will typically, but not always, develop viscosity more slowly. They may achieve a reasonably high viscosity, but will take longer to achieve. On the other hand, they will disperse better than fine-mesh, all conditions being equal. A finer mesh, such as a 200 mesh , requires more effort to dissolve. [ citation needed ] Modified forms of guar gum are available commercially, including enzyme-modified, cationic and hydropropyl guar. [ 16 ]
Fracturing fluids normally consist of many additives that serve two main purposes, firstly to enhance fracture creation and proppant carrying capability and secondly to minimize formation damage. Viscosifiers, such as polymers and crosslinking agents, temperature stabilizers, pH control agents, and fluid loss control materials are among the additives that assist fracture creation. Formation damage is minimized by incorporating breakers, biocides, and surfactants. More appropriate gelling agents are linear polysaccharides, such as guar gum, cellulose, and their derivatives.
Guar gums are preferred as thickeners for enhanced oil recovery (EOR). Guar gum and its derivatives account for most of the gelled fracturing fluids. Guar is more water-soluble than other gums, and it is also a better emulsifier, because it has more galactose branch points. Guar gum shows high low-shear viscosity, but it is strongly shear-thinning. Being non-ionic, it is not affected by ionic strength or pH but will degrade at low pH at moderate temperature (pH 3 at 50 °C). Guar's derivatives demonstrate stability in high temperature and pH environments. Guar use allows for achieving exceptionally high viscosities, which improves the ability of the fracturing liquid to transport proppant. Guar hydrates fairly rapidly in cold water to give highly viscous pseudoplastic solutions of, generally, greater low-shear viscosity than other hydrocolloids. The colloidal solids present in guar make fluids more efficient by creating less filter cake. Proppant pack conductivity is maintained by utilizing a fluid that has excellent fluid loss control, such as the colloidal solids present in guar gum.
Guar has up to eight times the thickening power of starch. Derivatization of guar gum leads to subtle changes in properties, such as decreased hydrogen bonding, increased solubility in water-alcohol mixture, and improved electrolyte compatibility. These changes in properties result in increased use in different fields, like textile printing, explosives, and oil-water fracturing applications.
Guar molecules have a tendency to aggregate during the hydraulic fracturing process, mainly due to intermolecular hydrogen bonding. These aggregates are detrimental to oil recovery because they clog the fractures, restricting the flow of oil. Cross-linking guar polymer chains prevents aggregation by forming metal–hydroxyl complexes. The first crosslinked guar gels were developed in the late 1960s. Several metal additives have been used for crosslinking; among them are chromium, aluminium, antimony, zirconium, and the more commonly used boron. Boron, in the form of B(OH)4, reacts with the hydroxyl groups on the polymer in a two-step process to link two polymer strands together to form bis-diol complexes.
1:1 1,2 diol complex and a 1:1 1,3 diol complex, place the negatively charged borate ion onto the polymer chain as a pendant group. Boric acid itself does not apparently complex to the polymer so that all bound boron is negatively charged. The primary form of crosslinking may be due to ionic association between the anionic borate complex and adsorbed cations on the second polymer chain . The development of cross-linked gels was a major advance in fracturing fluid technology. Viscosity is enhanced by tying together the low molecular weight strands, effectively yielding higher molecular weight strands and a rigid structure. Cross-linking agents are added to linear polysaccharide slurries to provide higher proppant transport performance, relative to linear gels.
Lower concentrations of guar gelling agents are needed when linear guar chains are cross-linked. It has been determined that reduced guar concentrations provide better and more complete breaks in a fracture. The breakdown of cross-linked guar gel after the fracturing process restores formation permeability and allows increased production flow of petroleum products.
The largest market for guar gum is in the food industry . In the US, differing percentages are set for its allowable concentration in various food applications. [ 18 ] [ 19 ] In Europe, guar gum has EU food additive code E412. Xanthan gum and guar gum are the most frequently used gums in gluten-free recipes and gluten-free products.
Applications include:
Guar gum, as a water- soluble fiber , acts as a bulk-forming laxative . Several studies have found it decreases cholesterol levels. These decreases are thought to be a function of its high soluble fiber content. [ 23 ]
Moreover, its low digestibility lends its use in recipes as a filler, which can help to provide satiety or slow the digestion of a meal, thus lowering the glycemic index of that meal. In the late 1980s, guar gum was used and heavily promoted in several weight-loss drugs. The US Food and Drug Administration eventually recalled these due to reports of esophageal blockage from insufficient fluid intake, after one brand alone caused at least 10 users to be hospitalized, and a death. [ 24 ] For this reason, guar gum is no longer approved for use in over-the-counter weight loss drugs in the United States, although this restriction does not apply to supplements. Moreover, a meta-analysis found guar gum supplements were not effective in reducing body weight. [ 25 ]
Guar-based compounds, such as hydroxypropyl guar , have been used in artificial tears to treat dry eye . [ 26 ]
Some studies have found an allergic sensitivity to guar gum developed in a few individuals working in an industrial environment where airborne concentrations of the substance were present. In those affected by the inhalation of the airborne particles, common adverse reactions were occupational rhinitis and asthma. [ 27 ]
In July 2007, the European Commission issued a health warning to its member states after high levels of dioxins were detected in guar gum, which was used as a thickener in small quantities in meat, dairy, dessert and delicatessen products. The source was traced to guar gum from India that was contaminated with pentachlorophenol (PCP), a pesticide no longer in use. [ 28 ] PCP contains dioxins, which damage the human immune system. [ 29 ] | https://en.wikipedia.org/wiki/Guar_gum |
In computer programming , a guard is a Boolean expression that must evaluate to true if the execution of the program is to continue in the branch in question. Regardless of which programming language is used, a guard clause , guard code , or guard statement is a check of integrity preconditions used to avoid errors during execution.
The term guard clause is a Software design pattern attributed to Kent Beck who codified many often unnamed coding practices into named software design patterns, the practice of using this technique dates back to at least the early 1960's. The guard clause most commonly is added at the beginning of a procedure and is said to "guard" the rest of the procedure by handling edgecases upfront.
A typical example is checking that a reference about to be processed is not null, which avoids null-pointer failures.
Other uses include using a Boolean field for idempotence (so subsequent calls are nops ), as in the dispose pattern .
The guard provides an early exit from a subroutine , and is a commonly used deviation from structured programming , removing one level of nesting and resulting in flatter code: [ 1 ] replacing if guard { ... } with if not guard: return; ... .
Using guard clauses can be a refactoring technique to improve code. In general, less nesting is good, as it simplifies the code and reduces cognitive burden.
For example, in Python :
Another example, written in C :
The term is used with specific meaning in APL , Haskell , Clean , Erlang , occam , Promela , OCaml , Swift , [ 2 ] Python from version 3.10, and Scala programming languages. [ citation needed ] In Mathematica , guards are called constraints . Guards are the fundamental concept in Guarded Command Language , a language in formal methods . Guards can be used to augment pattern matching with the possibility to skip a pattern even if the structure matches. Boolean expressions in conditional statements usually also fit this definition of a guard although they are called conditions .
In the following Haskell example, the guards occur between each pair of "|" and "=":
This is similar to the respective mathematical notation:
f ( x ) = { 1 if x > 0 0 otherwise {\displaystyle f(x)=\left\{{\begin{matrix}1&{\mbox{if }}x>0\\0&{\mbox{otherwise}}\end{matrix}}\right.}
In this case the guards are in the "if" and "otherwise" clauses.
If there are several parallel guards, they are normally tried in a top-to-bottom order, and the branch of the first to pass is chosen. Guards in a list of cases are typically parallel.
However, in Haskell list comprehensions the guards are in series, and if any of them fails, the list element is not produced. This would be the same as combining the separate guards with logical AND , except that there can be other list comprehension clauses among the guards.
A simple conditional expression, already present in CPL in 1963, has a guard on first sub-expression, and another sub-expression to use in case the first one cannot be used. Some common ways to write this:
If the second sub-expression can be a further simple conditional expression, we can give more alternatives to try before the last fall-through :
In 1966 ISWIM had a form of conditional expression without an obligatory fall-through case, thus separating guard from the concept of choosing either-or. In the case of ISWIM, if none of the alternatives could be used, the value was to be undefined , which was defined to never compute into a value.
KRC , a "miniaturized version" [ 3 ] of SASL (1976), was one of the first programming languages to use the term "guard". Its function definitions could have several clauses, and the one to apply was chosen based on the guards that followed each clause:
Use of guard clauses, and the term "guard clause", dates at least to Smalltalk practice in the 1990s, as codified by Kent Beck . [ 1 ]
In 1996, Dyalog APL adopted an alternative pure functional style in which the guard is the only control structure. [ 4 ] This example, in APL, computes the parity of the input number:
In addition to a guard attached to a pattern, pattern guard can refer to the use of pattern matching in the context of a guard. In effect, a match of the pattern is taken to mean pass. This meaning was introduced in a proposal for Haskell by Simon Peyton Jones titled A new view of guards in April 1997 and was used in the implementation of the proposal. The feature provides the ability to use patterns in the guards of a pattern.
An example in extended Haskell:
This would read: "Clunky for an environment and two variables, in case the lookups of the variables from the environment produce values , is the sum of the values. ..." As in list comprehensions , the guards are in series, and if any of them fails the branch is not taken. | https://en.wikipedia.org/wiki/Guard_(computer_science) |
Guard theory is a branch of immunology which concerns the innate sensing of stereotypical consequences of a virulence factor or pathogen . [ 1 ] This is in contrast to the classical understanding of recognition by the innate immune system , which involves recognition of distinct microbial structures- pathogen-associated molecular patterns (PAMPs)- with pattern recognition receptors (PRRs) . Some of these stereotypical consequences of virulence factors and pathogens may include altered endosomal trafficking and changes in the cytoskeleton . [ 2 ] These recognition mechanisms would work to complement classical pattern recognition mechanisms. [ 3 ] [ 4 ]
In plants, guard theory is also known as indirect recognition. [ 5 ] This is because rather than direct recognition of a virulence factor or pathogen, there is instead recognition of the result of a process mediated by a virulence factor or pathogen. [ 6 ] In these cases, the virulence factor appears to target an accessory protein that is either a target or a structural mimic of the target of that virulence factor, [ 7 ] allowing for plant defences to respond to a specific strategy of pathogenesis rather structures that may evolve and change over time at a faster rate than the plant can adapt to. [ 8 ] The interaction between pathogen and accessory protein results in some modification of the accessory protein, which allows for recognition by plant NBS-LRR proteins, which monitor for infection. [ 9 ] This model is best illustrated by RIN4 protein in A. thaliana. [ 10 ] RIN4 forms a complex with the NB-LRR proteins RPM1 and RPS2. [ 11 ] [ 12 ] Protease effector AvrRpt2 is able to degrade RIN4, causing de-repression of RPS2. [ 13 ] On the other hand, AvrB or AvrRPM1-mediated phosphorylation of RIN4 results in activation of RPM1. [ 14 ] In short, this example elucidates how one NBS-LRR protein is able to recognize the effects of more than one virulence factor or effector. [ 15 ]
Little is known concerning guard receptors in humans. One example currently under speculation involves recognition of cysteine proteases secreted by helminths during infection. [ 16 ] It has been speculated that some allergies develop as a result of structural similarities between the allergen and high-activity cysteine proteases secreted by helminths during their infectious cycle. [ 17 ] One proposed mechanism by which this may take place is that proteases secreted by the helminths cleave proteins which act as detectors, and these detectors in turn activate sensors to alert the immune system. [ 18 ] | https://en.wikipedia.org/wiki/Guard_theory |
A guard tour patrol system is a system for logging the rounds of employees in a variety of situations such as security guards patrolling property, technicians monitoring climate-controlled environments, and correctional officers [ 1 ] checking prisoner living areas. It helps ensure that the employee makes their appointed rounds at the correct intervals and can offer a record for legal or insurance reasons. Such systems have existed for many years using mechanical watchclock -based systems (watchman clocks/guard tour clocks/patrol clocks). Computerized systems were first introduced in Europe in the early 1980s, and in North America in 1986. [ 2 ] Modern systems are based on handheld data loggers and RFID sensors.
The system provides a means to record the time when the employee reaches certain points on their tour. Checkpoints or watchstations are commonly placed at the extreme ends of the tour route and at critical points such as vaults , specimen refrigerators , vital equipment, and access points. Some systems are set so that the interval between stations is timed so if the employee fails to reach each point within a set time, other staff are dispatched to ensure the employee's well-being.
An example of a modern set-up might work as follows: the employee carries a portable electronic sensor (PES) or electronic data collector which is activated at each checkpoint. Checkpoints can consist of iButton semiconductors, magnetic strips, proximity microchips such as RFIDs or NFC- or optical barcodes . The data collector stores the serial number of the checkpoint with the date and time. Later, the information is downloaded from the collector into a computer where the checkpoint's serial number will have an assigned location (i.e. North Perimeter Fence, Cell Number 1, etc.). Data collectors can also be programmed to ignore duplicate checkpoint activations that occur sequentially or within a certain time period. Computer software used to compile the data from the collector can print out summaries that pinpoint missed checkpoints or patrols without the operator having to review all the data collected. Because devices can be subject to misuse, some have built-in microwave, g-force, and voltage detection.
It combines readers, tags and software.
The first Guard tour system were the touch readers with software. Upon further development, more working modes for the readers became available. Such as RFID and GPS . And the communication of readers and software was connected with USB cables or download stations. For USB connection, the Pogo Pin connection is very popular. Because the contacts with gold-plating are very stable and waterproof.
Newer, light-weight guard touring systems utilize QR codes or barcodes rather than expensive electronic components. A mobile phone app is used to scan (take a photo) of the QR code which creates a time stamp in the system.
The reader needs to read the tags to record the information, such as the time and tag's ID. Then upload the information to software to get the report.
There are three types of guard patrol software. They are desktop, local network client-server, and web-based versions.
The desktop version can only work on one computer.
The local network client server type can work using the local area network.
The web-based version can work everywhere with internet access.
In the analog age, the device used for this purpose was the watchclock. [ 3 ] Watchclocks often had a paper or light cardboard disk placed inside for each 24-hour period. The user would carry the clock to each checkpoint, where a numbered key could be found (typically chained in place). The key would be inserted into the clock where it would imprint the disk. At the end of the shift or 24-hour period an authorized person (usually a supervisor) would unlock the watchclock and retrieve the disk.
As development of guard tour system, the device can work with more functions. Such as send data real-time by GPRS to software and GPS location and tracking mode.
In software, we set up the Patrol Department, Patrol Route, Guard, Checkpoint, Event and Patrol Plan in general, depending on the software purchased. The software will then have specific tours set for officers to complete, being able to indicate whether the inspection was completed properly or not, with the ability to note a specific temperature of an inspection, or make any kind of notes necessary. Guard Tour software systems seem to be becoming the norm in tracking tours for officers.
New touring solutions rely on cloud-based Software as a Service (SaaS) combined with mobile or fixed on-site devices. These offer the advantages of lower installation and maintenance costs, forgoing the need for hardware, software upgrades, data backups and computer maintenance. On-site systems need all the usual software patches, backups and periodic hardware replacement. In operation, the role of the watchclock system, described above, has largely been replaced by some combination of GPS , RFID/NFC , or QR coded labels . Users prove that they have visited particular locations or performed tasks by scanning these tags or via GPS generated maps. These technologies result in lower costs, while increasing the flexibility of the systems to handle changes or new uses. This is important when routes change, or if a solution is needed on short notice. Tag-based touring systems typically utilize a mobile phone or tablet app to scan the tags and then upload that information along with a time stamp, phone's location information, and optionally other information the guard enters into the app on the phone. These systems provide instant access to tour information as it is uploaded by the application or device carried by the user, rather than requiring the officer to return to an upload station. | https://en.wikipedia.org/wiki/Guard_tour_patrol_system |
Guardian is the trademark name of a polymer originally manufactured by Securency International, [ 1 ] a joint venture between the Reserve Bank of Australia and Innovia Films Ltd . The latter completed acquisition of the former's stake in 2013.
Its production involves gravity feeding a molten polymer, composed of extruded polypropylene and other polyolefins , through a four-storey chamber. This creates sheets of the substrate used as the base material by many central banks in the printing of polymer banknotes .
Polypropylene is processed to create pellets. [ 2 ] These pellets are extruded from a core extruder in conjunction with polyolefin pellets from two "skin layer" extruders, and are combined into a molten polymer. [ 2 ] [ 3 ] [ 4 ] This consists of a 37.5 μm thick polypropylene sheet sandwiched between two 0.1 μm polyolefin sheets, [ 4 ] [ 3 ] creating a thin film 37.7 μm thick.
The molten polymer undergoes snap cooling as it passes by gravity feeding through a brass mandrel , which imparts on the thin film many properties, including its transparency . [ 2 ] The cast tube material is then reheated and blown into a large bubble using air pressure and temperature. [ 2 ] At the base of the four-storey chamber convergence rollers collapse the tube into a flat sheet consisting of two layers of the thin film. [ 4 ] [ 2 ] This creates the base biaxially-oriented polypropylene substrate of 75.4 μm thickness, called ClarityC by Innovia Films. [ 3 ] [ 5 ]
The base substrate is slit as it exits the convergence rollers. [ 2 ] [ 4 ] Four 3-micrometre (0.00012 in) thick layers of (usually white) opacifier are applied to the substrate, two on the upper surface and two on the lower surface. [ 3 ] [ 4 ] A mask prevents the deposition of the opacifier on parts of the substrate that are intended to remain transparent. [ 6 ] These overcoat layers protect the substrate from soiling and impart on it its characteristic texture, [ 7 ] and increase the overall thickness to 87.5 μm. The resulting product is the Guardian substrate. [ 4 ]
The opacifier conversion phase involves the use of resin and solvents , creating volatile organic compounds (VOCs) as by-products that are combusted in a thermal oxidizer . [ 5 ] The resulting polymer substrate then passes through a rotary printing press using chrome-plated copper cylinders. [ 5 ] After printing, the holographic security foil is incorporated into the base substrate. [ 5 ] This is then cut into sheets and transported to the banknote printing companies in wooden boxes as a secure shipment. [ 5 ] [ 8 ]
Guardian is a non-porous and non-fibrous substrate. [ 2 ] Because of this, it is "impervious to water and other liquids", and so remains clean for longer than a paper substrate. [ 2 ] It is difficult to initiate a tear on the substrate, which has higher tear initiation resistance than paper. [ 2 ]
Guardian is used in the printing of polymer banknotes by many central banks .
It is the base material used for currencies printed by:
In 1993, the Bank of Indonesia issued a commemorative Rp 50,000 banknote and the Central Bank of Kuwait issued a د.ك 1 banknote. [ 4 ] In 1998, the Bank Negara Malaysia issued a commemorative RM 50 banknote, [ 4 ] and the Central Bank of Sri Lanka issued a commemorative Rs 200 banknote. [ 27 ] In 1999, the Northern Bank of Northern Ireland issued a commemorative £ 5 banknote, [ 28 ] and the Central Bank of the Republic of China in Taiwan issued a commemorative NT$ 50 banknote. [ 29 ] [ 4 ] In 2000, the Central Bank of Brazil issued a commemorative R$ 10 banknote [ 30 ] and the People's Bank of China issued a commemorative ¥ 100 banknote. [ 4 ] In 2001, the Central Bank of Solomon Islands issued a commemorative SI$ 2 banknote. [ 31 ] In 2009, the Bank of Mexico issued a commemorative $ 100 banknote. [ 4 ] | https://en.wikipedia.org/wiki/Guardian_(polymer) |
The Guastavino tile arch system is a version of the Catalan vault introduced to the United States in 1885 by Spanish architect and builder Rafael Guastavino (1842–1908). [ 1 ] It was patented in the United States by Guastavino in 1892. [ 2 ]
Guastavino vaulting is a technique for constructing robust, self-supporting arches and architectural vaults using interlocking terracotta tiles and layers of mortar to form a thin skin, with the tiles following the curve of the roof as opposed to horizontally ( corbelling ), or perpendicular to the curve (as in Roman vaulting). This is known as timbrel vaulting , because of its supposed likeness to the skin of a timbrel or tambourine . It is also called Catalan vaulting (though Guastavino did not use this term) and "compression-only thin-tile vaulting". [ 3 ]
Guastavino tile is found in some of the most prominent Beaux-Arts structures in New York and Massachusetts, as well as in major buildings across the United States. [ 4 ] In New York City, these include the Grand Central Oyster Bar & Restaurant and the remnants of the Della Robbia Bar at the former Vanderbilt Hotel at 4 Park Avenue . [ 5 ] It is also found in some non-Beaux-Arts structures such as the crossing of the Cathedral of St. John the Divine . [ 6 ]
The Guastavino terracotta tiles are standardized, less than 1 inch (25 mm) thick, and about 6 by 12 inches (150 by 300 mm) across. They are usually set in three herringbone-pattern courses with a sandwich of thin layers of Portland cement . Unlike heavier stone construction, these tile domes could be built without centering . Supporting formwork was still required for structural arches which established a framework for the ceiling. The large openings framed by the support arches were then filled with thin Guastavino tiles fabricated into domed surfaces. Each ceiling tile was cantilevered out over the open space, relying only on the quick-drying cements developed by the company. Akoustolith , a special sound-absorbing tile, was one of several trade names used by Guastavino.
Guastavino tile has both structural and aesthetic significance.
Structurally, the timbrel vault was based on traditional vernacular vaulting techniques already very familiar to Mediterranean architects, but not well known in America. Terracotta free-span timbrel vaults were far more economical and structurally resilient than the ancient Roman vaulting alternatives.
Guastavino wrote extensively about his system of "Cohesive Construction". As the name suggests, he believed that these timbrel vaults represented an innovation in structural engineering . The tile system provided solutions that were impossible with traditional masonry arches and vaults. Subsequent research has shown the timbrel vault is simply a masonry vault, much less thick than traditional arches, that produces less horizontal thrust due to its lighter weight. This permits flatter arch profiles, which would produce unacceptable horizontal thrust if constructed in thicker, heavier masonry. [ 4 ]
In 2012, a group of students under supervision of MIT professor John Ochsendorf built a full-scale reproduction of a small Guastavino vault. The resulting structure was exhibited, as well as a time lapse video documenting the construction process. [ 7 ]
Ochsendorf also curated Palaces for the People , an exhibition featuring the history and legacy of Guastavino which was premiered in September 2012 at the Boston Public Library , Rafael Guastavino's first major architectural work in America. The exhibition then traveled to the National Building Museum in Washington DC, and an expanded version later appeared at the Museum of the City of New York . Ochsendorf, a winner of the MacArthur Foundation "genius grant", also wrote the book-length color-illustrated monograph Guastavino Vaulting: The Art of Structural Tile , [ 1 ] and an online exhibition coordinated with the traveling exhibits. [ 8 ]
In addition, Ochsendorf directs the Guastavino Project at MIT, which researches and maintains the Guastavino.net online archive of related materials. [ 9 ]
The Guastavino company was headquartered in Woburn, Massachusetts , in a building of their own design which still stands. [ 10 ] The records and drawings of the Guastavino Fireproof Construction Company are preserved by the Department of Drawings & Archives in the Avery Architectural and Fine Arts Library at Columbia University in New York City. | https://en.wikipedia.org/wiki/Guastavino_tile |
Guderley–Landau–Stanyukovich problem describes the time evolution of converging shock waves . The problem was discussed by G. Guderley in 1942 [ 1 ] and independently by Lev Landau and K. P. Stanyukovich in 1944, where the later authors' analysis was published in 1955. [ 2 ]
Consider a spherically converging shock wave that was initiated by some means at a radial location r = R 0 {\displaystyle r=R_{0}} and directed towards the center. As the shock wave travels towards the origin, its strength increases since the shock wave compresses lesser and lesser amount of mass as it propagates. The shock wave location r = R ( t ) {\displaystyle r=R(t)} thus varies with time. The self-similar solution to be described corresponds to the region r ∼ R ≪ R 0 {\displaystyle r\sim R\ll R_{0}} , that is to say, the shock wave has travelled enough to forget about the initial condition.
Since the shock wave in the self-similar region is strong, the pressure behind the wave p 1 {\displaystyle p_{1}} is very large in comparison with the pressure ahead of the wave p 0 {\displaystyle p_{0}} . According to Rankine–Hugoniot conditions , for strong waves, although p 1 ≫ p 0 {\displaystyle p_{1}\gg p_{0}} , ρ 1 ∼ ρ 0 {\displaystyle \rho _{1}\sim \rho _{0}} , where ρ {\displaystyle \rho } represents gas density; in other words, the density jump across the shock wave is finite. For the analysis, one can thus assume p 0 = 0 {\displaystyle p_{0}=0} and ρ 0 ≠ 0 {\displaystyle \rho _{0}\neq 0} , which in turn removes the velocity scale by setting c 0 = 0 {\displaystyle c_{0}=0} since c 0 2 = γ p 0 / ρ 0 {\displaystyle c_{0}^{2}=\gamma p_{0}/\rho _{0}} .
At this point, it is worth noting that the analogous problem in which a strong shock wave propagating outwards is known to be described by the Taylor–von Neumann–Sedov blast wave . The description for Taylor–von Neumann–Sedov blast wave utilizes ρ 0 {\displaystyle \rho _{0}} and the total energy content of the flow to develop a self-similar solution. Unlike this problem, the imploding shock wave is not self-similar throughout the entire region (the flow field near r = R 0 {\displaystyle r=R_{0}} depends on the manner in which the shock wave is generated) and thus the Guderley–Landau–Stanyukovich problem attempts to describe in a self-similar manner, the flow field only for r ∼ R ≪ R 0 {\displaystyle r\sim R\ll R_{0}} ; in this self-similar region, energy is not constant and in fact, will be shown to decrease with time (the total energy of the entire region is still constant). Since the self-similar region is small in comparison with the initial size of the shock wave region, only a small fraction of the total energy is accumulated in the self-similar region. The problem thus contains no length scale to use dimensional arguments to find out the self-similar description i.e., the dependence of R ( t ) {\displaystyle R(t)} on t {\displaystyle t} cannot be determined by dimensional arguments alone. The problems of these kind are described by the self-similar solution of the second kind .
For convenience, measure the time t {\displaystyle t} such that the converging shock wave reaches the origin at time t = 0 {\displaystyle t=0} . For t < 0 {\displaystyle t<0} , the converging shock approaches the origin and for t > 0 {\displaystyle t>0} , the reflected shock wave emerges from the origin. The location of shock wave r = R ( t ) {\displaystyle r=R(t)} is assumed to be described by the function
where α {\displaystyle \alpha } is the similarity index and A {\displaystyle A} is a constant. The reflected shock emerges with the same similarity index. The value of α {\displaystyle \alpha } is determined from the condition that a self-similar solution exists, whereas the constant A {\displaystyle A} cannot be described from the self-similar analysis; the constant A {\displaystyle A} contains information from the region r ∼ R 0 {\displaystyle r\sim R_{0}} and therefore can be determined only when the entire region of the flow is solved. The dimension of A {\displaystyle A} will be found only after solving for α {\displaystyle \alpha } . For Taylor–von Neumann–Sedov blast wave, dimensional arguments can be used to obtain α = 2 / 5. {\displaystyle \alpha =2/5.}
The shock-wave velocity is given by
According to Rankine–Hugoniot conditions the gas velocity v 1 {\displaystyle v_{1}} , pressure p 1 {\displaystyle p_{1}} and density ρ 1 {\displaystyle \rho _{1}} immediately behind the strong shock front, for an ideal gas are given by
These will serve as the boundary conditions for the flow behind the shock front.
The governing equations are
where ρ {\displaystyle \rho } is the density, p {\displaystyle p} is the pressure, s {\displaystyle s} is the entropy and v {\displaystyle v} is the radial velocity. In place of the pressure p ( r , t ) {\displaystyle p(r,t)} , we can use the sound speed c ( r , t ) {\displaystyle c(r,t)} using the relation c 2 = γ p / ρ {\displaystyle c^{2}=\gamma p/\rho } .
To obtain the self-similar equations, we introduce [ 3 ] [ 4 ] [ 5 ]
Note that since both t {\displaystyle t} and v {\displaystyle v} are negative, V > 0 {\displaystyle V>0} . Formally the solution has to be found for the range 1 < ξ < ∞ {\displaystyle 1<\xi <\infty } . The boundary conditions at ξ = 1 {\displaystyle \xi =1} are given by
The boundary conditions at ξ = ∞ {\displaystyle \xi =\infty } can be derived from the observation at the time of collapse t = 0 {\displaystyle t=0} , wherein ξ {\displaystyle \xi } becomes infinite. At the moment of collapse, the flow variables at any distance from the origin must be finite, that is to say, v {\displaystyle v} and c 2 {\displaystyle c^{2}} must be finite for t = 0 , r ≠ 0 {\displaystyle t=0,\,r\neq 0} . This is possible only if
Substituting the self-similar variables into the governing equations lead to
From here, we can easily solve for d ln G / d ln ξ {\displaystyle d\ln G/d\ln \xi } and d ln V / d ln ξ {\displaystyle d\ln V/d\ln \xi } (or, d ln Z / d ln ξ {\displaystyle d\ln Z/d\ln \xi } ) to find two equations. As a third equation, we could two of the equations by eliminating the variable ξ {\displaystyle \xi } . The resultant equations are
where Δ = Z − ( 1 − V ) 2 {\displaystyle \Delta =Z-(1-V)^{2}} and Δ 1 = [ 3 V − 2 ( 1 − α ) / α γ ] Z − V ( 1 − V ) ( 1 / α − V ) {\displaystyle \Delta _{1}=[3V-2(1-\alpha )/\alpha \gamma ]Z-V(1-V)(1/\alpha -V)} . It can be easily seen once the third equation is solved for Z = Z ( V ) {\displaystyle Z=Z(V)} , the first two equations can be integrated using simple quadratures.
The third equation is first-order differential equation for the function Z ( V ) {\displaystyle Z(V)} with the boundary condition Z ( 2 / ( γ + 1 ) ) = 2 γ ( γ − 1 ) / ( γ + 1 ) 2 {\displaystyle Z(2/(\gamma +1))=2\gamma (\gamma -1)/(\gamma +1)^{2}} pertaining to the condition behind the shock front. But there is another boundary condition that needs to be satisfied, i.e., Z ( 0 ) = 0 {\displaystyle Z(0)=0} pertaining to the condition found at ξ = ∞ {\displaystyle \xi =\infty } . This additional condition can be satisfied not for any arbitrary value of α {\displaystyle \alpha } , but there exists only one value of α {\displaystyle \alpha } for which the second condition can be satisfied. Thus α {\displaystyle \alpha } is obtained as an eigenvalue. This eigenvalue can be obtained numerically.
The condition that determines α {\displaystyle \alpha } can be explained by plotting the integral curve Z = Z ( V ) {\displaystyle Z=Z(V)} as shown in the figure as a solid curve. The point A {\displaystyle A} is the initial condition for the differential equation, i.e., A : ( V , Z ) = ( 2 / ( γ + 1 ) , 2 γ ( γ − 1 ) / ( γ + 1 ) 2 ) {\displaystyle A:(V,Z)=(2/(\gamma +1),2\gamma (\gamma -1)/(\gamma +1)^{2})} . The integral curve must end at the point O : ( V , Z ) = ( 0 , 0 ) {\displaystyle O:(V,Z)=(0,0)} . In the same figure, the parabola Z = ( 1 − V ) 2 {\displaystyle Z=(1-V)^{2}} corresponding to the condition Δ = 0 {\displaystyle \Delta =0} is also plotted as a dotted curve. It can be easily shown than the point A {\displaystyle A} always lies above this parabola. This means that the integral curve Z = Z ( V ) {\displaystyle Z=Z(V)} must intersect the parabola to reach the point O {\displaystyle O} . In all the three differential equation, the ratio Δ / Δ 1 {\displaystyle \Delta /\Delta _{1}} appears implying that this ratio vanishes at point B {\displaystyle B} where the integral curve intersects the parabola. The physical requirement for the functions V , G {\displaystyle V,\,G} and Z {\displaystyle Z} is that they must be single-valued functions of ξ {\displaystyle \xi } to get a unique solution. This means that the functions ξ ( V ) , ξ ( G ) {\displaystyle \xi (V),\,\xi (G)} and ξ ( Z ) {\displaystyle \xi (Z)} cannot have extrema anywhere inside the domain. But at the point B {\displaystyle B} , Δ / Δ 1 {\displaystyle \Delta /\Delta _{1}} can vanish, indicating that the aforementioned functions have extrema. The only way to avoid this situation is to make the ratio Δ / Δ 1 {\displaystyle \Delta /\Delta _{1}} at B {\displaystyle B} finite. That is to say, as Δ {\displaystyle \Delta } becomes zero, we require Δ 1 {\displaystyle \Delta _{1}} also to be zero in such a manner to obtain Δ / Δ 1 = 0 / 0 = finite {\displaystyle \Delta /\Delta _{1}=0/0={\text{finite}}} . At B {\displaystyle B} ,
Numerical integrations of the third equation provide α = 0.6883740859 {\displaystyle \alpha =0.6883740859} for γ = 5 / 3 {\displaystyle \gamma =5/3} and α = 0.7171745015 {\displaystyle \alpha =0.7171745015} for γ = 7 / 5 {\displaystyle \gamma =7/5} . These values for α {\displaystyle \alpha } may be compared with an approximate formula α = [ 1 + 2 γ / ( γ + 2 ) 2 ] − 1 {\displaystyle \alpha =[1+2\gamma /({\sqrt {\gamma }}+{\sqrt {2}})^{2}]^{-1}} , derived by Landau and Stanyukovich. It can be established that as γ → 1 {\displaystyle \gamma \rightarrow 1} , α → 1 {\displaystyle \alpha \rightarrow 1} . In general, the similarity index α {\displaystyle \alpha } is an irrational number . | https://en.wikipedia.org/wiki/Guderley–Landau–Stanyukovich_problem |
In mathematics, the Gudermannian function relates a hyperbolic angle measure ψ {\textstyle \psi } to a circular angle measure ϕ {\textstyle \phi } called the gudermannian of ψ {\textstyle \psi } and denoted gd ψ {\textstyle \operatorname {gd} \psi } . [ 1 ] The Gudermannian function reveals a close relationship between the circular functions and hyperbolic functions . It was introduced in the 1760s by Johann Heinrich Lambert , and later named for Christoph Gudermann who also described the relationship between circular and hyperbolic functions in 1830. [ 2 ] The gudermannian is sometimes called the hyperbolic amplitude as a limiting case of the Jacobi elliptic amplitude am ( ψ , m ) {\textstyle \operatorname {am} (\psi ,m)} when parameter m = 1. {\textstyle m=1.}
The real Gudermannian function is typically defined for − ∞ < ψ < ∞ {\textstyle -\infty <\psi <\infty } to be the integral of the hyperbolic secant [ 3 ]
The real inverse Gudermannian function can be defined for − 1 2 π < ϕ < 1 2 π {\textstyle -{\tfrac {1}{2}}\pi <\phi <{\tfrac {1}{2}}\pi } as the integral of the (circular) secant
The hyperbolic angle measure ψ = gd − 1 ϕ {\displaystyle \psi =\operatorname {gd} ^{-1}\phi } is called the anti-gudermannian of ϕ {\displaystyle \phi } or sometimes the lambertian of ϕ {\displaystyle \phi } , denoted ψ = lam ϕ . {\displaystyle \psi =\operatorname {lam} \phi .} [ 4 ] In the context of geodesy and navigation for latitude ϕ {\textstyle \phi } , k gd − 1 ϕ {\displaystyle k\operatorname {gd} ^{-1}\phi } (scaled by arbitrary constant k {\textstyle k} ) was historically called the meridional part of ϕ {\displaystyle \phi } ( French : latitude croissante ). It is the vertical coordinate of the Mercator projection .
The two angle measures ϕ {\textstyle \phi } and ψ {\textstyle \psi } are related by a common stereographic projection
and this identity can serve as an alternative definition for gd {\textstyle \operatorname {gd} } and gd − 1 {\textstyle \operatorname {gd} ^{-1}} valid throughout the complex plane :
We can evaluate the integral of the hyperbolic secant using the stereographic projection ( hyperbolic half-tangent ) as a change of variables : [ 5 ]
Letting ϕ = gd ψ {\textstyle \phi =\operatorname {gd} \psi } and s = tan 1 2 ϕ = tanh 1 2 ψ {\textstyle s=\tan {\tfrac {1}{2}}\phi =\tanh {\tfrac {1}{2}}\psi } we can derive a number of identities between hyperbolic functions of ψ {\textstyle \psi } and circular functions of ϕ . {\textstyle \phi .} [ 6 ]
These are commonly used as expressions for gd {\displaystyle \operatorname {gd} } and gd − 1 {\displaystyle \operatorname {gd} ^{-1}} for real values of ψ {\displaystyle \psi } and ϕ {\displaystyle \phi } with | ϕ | < 1 2 π . {\displaystyle |\phi |<{\tfrac {1}{2}}\pi .} For example, the numerically well-behaved formulas
(Note, for | ϕ | > 1 2 π {\displaystyle |\phi |>{\tfrac {1}{2}}\pi } and for complex arguments, care must be taken choosing branches of the inverse functions.) [ 7 ]
We can also express ψ {\textstyle \psi } and ϕ {\textstyle \phi } in terms of s : {\textstyle s\colon }
If we expand tan 1 2 {\textstyle \tan {\tfrac {1}{2}}} and tanh 1 2 {\textstyle \tanh {\tfrac {1}{2}}} in terms of the exponential , then we can see that s , {\textstyle s,} exp ϕ i , {\displaystyle \exp \phi i,} and exp ψ {\displaystyle \exp \psi } are all Möbius transformations of each-other (specifically, rotations of the Riemann sphere ):
For real values of ψ {\textstyle \psi } and ϕ {\textstyle \phi } with | ϕ | < 1 2 π {\displaystyle |\phi |<{\tfrac {1}{2}}\pi } , these Möbius transformations can be written in terms of trigonometric functions in several ways,
These give further expressions for gd {\displaystyle \operatorname {gd} } and gd − 1 {\displaystyle \operatorname {gd} ^{-1}} for real arguments with | ϕ | < 1 2 π . {\displaystyle |\phi |<{\tfrac {1}{2}}\pi .} For example, [ 8 ]
As a function of a complex variable , z ↦ w = gd z {\textstyle z\mapsto w=\operatorname {gd} z} conformally maps the infinite strip | Im z | ≤ 1 2 π {\textstyle \left|\operatorname {Im} z\right|\leq {\tfrac {1}{2}}\pi } to the infinite strip | Re w | ≤ 1 2 π , {\textstyle \left|\operatorname {Re} w\right|\leq {\tfrac {1}{2}}\pi ,} while w ↦ z = gd − 1 w {\textstyle w\mapsto z=\operatorname {gd} ^{-1}w} conformally maps the infinite strip | Re w | ≤ 1 2 π {\textstyle \left|\operatorname {Re} w\right|\leq {\tfrac {1}{2}}\pi } to the infinite strip | Im z | ≤ 1 2 π . {\textstyle \left|\operatorname {Im} z\right|\leq {\tfrac {1}{2}}\pi .}
Analytically continued by reflections to the whole complex plane, z ↦ w = gd z {\textstyle z\mapsto w=\operatorname {gd} z} is a periodic function of period 2 π i {\textstyle 2\pi i} which sends any infinite strip of "height" 2 π i {\textstyle 2\pi i} onto the strip − π < Re w ≤ π . {\textstyle -\pi <\operatorname {Re} w\leq \pi .} Likewise, extended to the whole complex plane, w ↦ z = gd − 1 w {\textstyle w\mapsto z=\operatorname {gd} ^{-1}w} is a periodic function of period 2 π {\textstyle 2\pi } which sends any infinite strip of "width" 2 π {\textstyle 2\pi } onto the strip − π < Im z ≤ π . {\textstyle -\pi <\operatorname {Im} z\leq \pi .} [ 9 ] For all points in the complex plane, these functions can be correctly written as:
For the gd {\textstyle \operatorname {gd} } and gd − 1 {\textstyle \operatorname {gd} ^{-1}} functions to remain invertible with these extended domains, we might consider each to be a multivalued function (perhaps Gd {\textstyle \operatorname {Gd} } and Gd − 1 {\textstyle \operatorname {Gd} ^{-1}} , with gd {\textstyle \operatorname {gd} } and gd − 1 {\textstyle \operatorname {gd} ^{-1}} the principal branch ) or consider their domains and codomains as Riemann surfaces .
If u + i v = gd ( x + i y ) , {\textstyle u+iv=\operatorname {gd} (x+iy),} then the real and imaginary components u {\textstyle u} and v {\textstyle v} can be found by: [ 10 ]
(In practical implementation, make sure to use the 2-argument arctangent , u = atan2 ( sinh x , cos y ) {\textstyle u=\operatorname {atan2} (\sinh x,\cos y)} .)
Likewise, if x + i y = gd − 1 ( u + i v ) , {\textstyle x+iy=\operatorname {gd} ^{-1}(u+iv),} then components x {\textstyle x} and y {\textstyle y} can be found by: [ 11 ]
Multiplying these together reveals the additional identity [ 8 ]
The two functions can be thought of as rotations or reflections of each-other, with a similar relationship as sinh i z = i sin z {\textstyle \sinh iz=i\sin z} between sine and hyperbolic sine : [ 12 ]
The functions are both odd and they commute with complex conjugation . That is, a reflection across the real or imaginary axis in the domain results in the same reflection in the codomain:
The functions are periodic , with periods 2 π i {\textstyle 2\pi i} and 2 π {\textstyle 2\pi } :
A translation in the domain of gd {\textstyle \operatorname {gd} } by ± π i {\textstyle \pm \pi i} results in a half-turn rotation and translation in the codomain by one of ± π , {\textstyle \pm \pi ,} and vice versa for gd − 1 : {\textstyle \operatorname {gd} ^{-1}\colon } [ 13 ]
A reflection in the domain of gd {\textstyle \operatorname {gd} } across either of the lines x ± 1 2 π i {\textstyle x\pm {\tfrac {1}{2}}\pi i} results in a reflection in the codomain across one of the lines ± 1 2 π + y i , {\textstyle \pm {\tfrac {1}{2}}\pi +yi,} and vice versa for gd − 1 : {\textstyle \operatorname {gd} ^{-1}\colon }
This is related to the identity
A few specific values (where ∞ {\textstyle \infty } indicates the limit at one end of the infinite strip): [ 14 ]
As the Gudermannian and inverse Gudermannian functions can be defined as the antiderivatives of the hyperbolic secant and circular secant functions, respectively, their derivatives are those secant functions:
By combining hyperbolic and circular argument-addition identities,
with the circular–hyperbolic identity ,
we have the Gudermannian argument-addition identities:
Further argument-addition identities can be written in terms of other circular functions, [ 15 ] but they require greater care in choosing branches in inverse functions. Notably,
which can be used to derive the per-component computation for the complex Gudermannian and inverse Gudermannian. [ 16 ]
In the specific case z = w , {\textstyle z=w,} double-argument identities are
The Taylor series near zero, valid for complex values z {\textstyle z} with | z | < 1 2 π , {\textstyle |z|<{\tfrac {1}{2}}\pi ,} are [ 17 ]
where the numbers E k {\textstyle E_{k}} are the Euler secant numbers , 1, 0, -1, 0, 5, 0, -61, 0, 1385 ... (sequences A122045 , A000364 , and A028296 in the OEIS ). These series were first computed by James Gregory in 1671. [ 18 ]
Because the Gudermannian and inverse Gudermannian functions are the integrals of the hyperbolic secant and secant functions, the numerators E k {\textstyle E_{k}} and | E k | {\textstyle |E_{k}|} are same as the numerators of the Taylor series for sech and sec , respectively, but shifted by one place.
The reduced unsigned numerators are 1, 1, 1, 61, 277, ... and the reduced denominators are 1, 6, 24, 5040, 72576, ... (sequences A091912 and A136606 in the OEIS ).
The function and its inverse are related to the Mercator projection . The vertical coordinate in the Mercator projection is called isometric latitude , and is often denoted ψ . {\textstyle \psi .} In terms of latitude ϕ {\textstyle \phi } on the sphere (expressed in radians ) the isometric latitude can be written
The inverse from the isometric latitude to spherical latitude is ϕ = gd ψ . {\textstyle \phi =\operatorname {gd} \psi .} (Note: on an ellipsoid of revolution , the relation between geodetic latitude and isometric latitude is slightly more complicated.)
Gerardus Mercator plotted his celebrated map in 1569, but the precise method of construction was not revealed. In 1599, Edward Wright described a method for constructing a Mercator projection numerically from trigonometric tables, but did not produce a closed formula. The closed formula was published in 1668 by James Gregory .
The Gudermannian function per se was introduced by Johann Heinrich Lambert in the 1760s at the same time as the hyperbolic functions . He called it the "transcendent angle", and it went by various names until 1862 when Arthur Cayley suggested it be given its current name as a tribute to Christoph Gudermann 's work in the 1830s on the theory of special functions. [ 19 ] Gudermann had published articles in Crelle's Journal that were later collected in a book [ 20 ] which expounded sinh {\textstyle \sinh } and cosh {\textstyle \cosh } to a wide audience (although represented by the symbols S i n {\textstyle {\mathfrak {Sin}}} and C o s {\textstyle {\mathfrak {Cos}}} ).
The notation gd {\textstyle \operatorname {gd} } was introduced by Cayley who starts by calling ϕ = gd u {\textstyle \phi =\operatorname {gd} u} the Jacobi elliptic amplitude am u {\textstyle \operatorname {am} u} in the degenerate case where the elliptic modulus is m = 1 , {\textstyle m=1,} so that 1 − m sin 2 ϕ {\textstyle {\sqrt {1-m\sin \!^{2}\,\phi }}} reduces to cos ϕ . {\textstyle \cos \phi .} [ 21 ] This is the inverse of the integral of the secant function . Using Cayley's notation,
He then derives "the definition of the transcendent",
observing that "although exhibited in an imaginary form, [it] is a real function of u {\textstyle u} ".
The Gudermannian and its inverse were used to make trigonometric tables of circular functions also function as tables of hyperbolic functions. Given a hyperbolic angle ψ {\textstyle \psi } , hyperbolic functions could be found by first looking up ϕ = gd ψ {\textstyle \phi =\operatorname {gd} \psi } in a Gudermannian table and then looking up the appropriate circular function of ϕ {\textstyle \phi } , or by directly locating ψ {\textstyle \psi } in an auxiliary gd − 1 {\displaystyle \operatorname {gd} ^{-1}} column of the trigonometric table. [ 22 ]
The Gudermannian function can be thought of mapping points on one branch of a hyperbola to points on a semicircle. Points on one sheet of an n -dimensional hyperboloid of two sheets can be likewise mapped onto a n -dimensional hemisphere via stereographic projection. The hemisphere model of hyperbolic space uses such a map to represent hyperbolic space. | https://en.wikipedia.org/wiki/Gudermannian_function |
In real algebraic geometry , Gudkov's conjecture , also called Gudkov’s congruence , (named after Dmitry Gudkov ) was a conjecture , and is now a theorem , which states that a M-curve of even degree 2 d {\displaystyle 2d} obeys the congruence
where p {\displaystyle p} is the number of positive ovals and n {\displaystyle n} the number of negative ovals of the M-curve. (Here, the term M-curve stands for "maximal curve"; it means a smooth algebraic curve over the reals whose genus is k − 1 {\displaystyle k-1} , where k {\displaystyle k} is the number of maximal components of the curve. [ 1 ] )
The theorem was proved by the combined works of Vladimir Arnold and Vladimir Rokhlin . [ 2 ] [ 3 ] [ 4 ] | https://en.wikipedia.org/wiki/Gudkov's_conjecture |
The Guerbet reaction , named after Marcel Guerbet (1861–1938), is an organic reaction that converts a primary alcohol into its β-alkylated dimer alcohol with loss of one equivalent of water. The process is of interest because it converts simple inexpensive feedstocks into more valuable products. Its main disadvantage is that the reaction produces mixtures. [ 1 ]
The original 1899 publication concerned the conversion of n -butanol to 2-ethylhexanol . [ 2 ] 2-ethylhexanol is however more easily prepared by alternative methods (from butyraldehyde by aldol condensation ).
Instead, the Guerbet reaction is mainly applied to fatty alcohols to afford oily products, which are called Guerbet alcohols . They are of commercial interest to as components of cosmetics, plasticizers, and related applications. The reaction is conducted in the temperature range 180-360 °C, often in a sealed reactor. The reaction requires alkali metal hydroxides or alkoxides . Catalysts such as Raney Nickel are required to facilitate the hydrogen transfer steps. [ 1 ]
While the Guerbet reaction is traditionally (and commercially) focused on fatty alcohols, it has been investigated for the dimerization of ethanol to butanol. [ 3 ]
Organometallic catalysts have been investigated. [ 4 ] A small amount of the diene 1,7-octadiene is required as a hydrogen acceptor.
The reaction mechanism for this reaction is a four-step sequence. In the first step the alcohol is oxidized to the aldehyde . These intermediates then react in an aldol condensation to the allyl aldehyde which the hydrogenation catalyst then reduces to the alcohol. [ 5 ]
The Cannizzaro reaction is a competing reaction when two aldehyde molecules react by disproportionation to form the corresponding alcohol and carboxylic acid . Another side reaction is the Tishchenko reaction . | https://en.wikipedia.org/wiki/Guerbet_reaction |
In Chinese astronomy , a guest star ( Chinese : 客星 ; pinyin : kèxīng ) is a star which has suddenly appeared in a place where no star had previously been observed and becomes invisible again after some time. The term is a literal translation from ancient Chinese astronomical records.
Modern astronomy recognizes that guest stars are manifestations of cataclysmic variable stars : novae and supernovae . The term "guest star" is used in the context of ancient records, since the exact classification of an astronomical event in question is based on interpretations of old records, including inference, rather than on direct observations.
In ancient Chinese astronomy, guest stars were one of the three types of highly transient objects (bright heavenly bodies). The other two were comets with tails ( Chinese : 彗星 ; pinyin : huìxīng ; lit. 'broom star') and comets without tails ( Chinese : 孛星 ; pinyin : beìxīng ; lit. 'fuzzy star'), with the former term being used for all comets in modern astronomy. [ 1 ] The earliest Chinese record of guest stars is contained in Han Shu (漢書), the history of Han dynasty (206 BC – AD 220), and all subsequent dynastic histories had such records. [ 1 ] These contain one of the clearest early descriptions consistent with a supernova, posited to be left over by object SN 185 , thus identified as a supernova remnant of the exact year AD 185. [ 2 ] Chronicles of the contemporary Europeans are more vague when consulted for supernovae candidates. [ 3 ] Whether this was due to the weather or other reasons, astronomers have questioned why the remnant attributed to Chinese observations of a guest star in AD 1054 (see SN 1054 ) is missing from the European records. [ 3 ] | https://en.wikipedia.org/wiki/Guest_star_(astronomy) |
Guha Research Conference (GRC) is a professional society set up by Indian scholars to develop the field of Biochemistry . It was established in 1960, and is named after Biresh Chandra Guha (1904-1962). [ 1 ]
The first four GRC meetings were held alongside the annual conference of the Indian Science Congress . Subsequently, under the guidance of Pushpa Mittra Bhargava , it was registered as a society with a convener elected annually, to organize the annual conference. According to Parthasarathi Benerjee, affiliation to GRC, "acts as the token, assuring easier access to prizes of several sorts." [ 2 ]
During its formative years (1960–65), GRC had 33 professionals from major national institutes such as AIIMS , CMC Vellore , IISc , Tata Memorial Centre , Indian Institute of Chemical Biology , Banaras Hindu University , Bhabha Atomic Research Centre , and TIFR . By 2004, the membership had grown to 114 members. [ 2 ] | https://en.wikipedia.org/wiki/Guha_Research_Conference |
Guide was a US technology startup company developing a newsreader app that translates text from online news sources, blogs and social media streams into streaming audio and video. The company's apps include animal character readers. [ 1 ] The company was founded in 2012 by chief executive officer Freddie A. Laker , and privately launched its mobile app in alpha in February 2013.
The company closed in 2014. [ citation needed ]
Guide is a visual newsreader app for personal computers, mobile devices and Smart TV , [ 2 ] [ 3 ] which uses text-to-speech and avatar technologies to turn text-based online news, blogs and social media updates into video content. [ 4 ] [ 5 ] [ 6 ] These technologies allow Guide to turn articles into news program-style episodes, incorporating video or images from the original source, while the text content of the article or blog post is read aloud by a virtual news anchor . [ 7 ] The app creates a "channel" for each site or news source, within which individual blog posts or news articles are separate episodes. [ 8 ]
Guide allows users to choose from three different virtual news anchors in the base application, [ 9 ] [ 10 ] and the company has stated it will offer additional avatars and newsroom backgrounds for purchase. [ 6 ] [ 8 ] An alpha version of the app, for iPad only, [ 2 ] was privately released on February 8, 2013. [ 4 ]
Freddie Laker, former vice president of strategy at Sapient Nitro and founder of digital agency iChameleon Group, [ 6 ] [ 2 ] developed the idea for Guide in 2011 after he noticed the rising trend in Smart TVs and Smart TV content at that year's CES . [ 8 ] He observed that the apps for Smart TV did not provide content in a TV-friendly format and decided to create an app that would provide a "TV experience". [ 11 ] In January 2013, Laker was joined at the company by chief operating officer Leslie Bradshaw . [ 12 ] The company is based in Miami, Florida, and has seven employees as of February 2013 [update] . [ 8 ] [ 13 ]
Guide closed its seed funding round in February 2013. It raised $1 million from investors including Sapient , the Knight Foundation , MTV founder Bob Pittman , founding Google team member Steve Schimmel , and actor Omar Epps . [ 3 ] [ 4 ] The company stated that the seed money will be used to focus on further development of the Guide app and pursuing patents for its technology. [ 3 ] [ 6 ] In February 2013, Guide was one of 65 companies out of 500 applicants selected to demonstrate its app in the annual South by Southwest (SXSW) Accelerator in Austin. [ 10 ] [ 14 ] | https://en.wikipedia.org/wiki/Guide_(software_company) |
The Guide to Available Mathematical Software (GAMS) is a project of the National Institute of Standards and Technology to classify mathematical software by the type of problem that it solves. GAMS became public in 1985. [ 1 ] It indexes Netlib and other packages, some of them public domain software and some proprietary software . [ 2 ] [ 3 ] [ 4 ] [ 5 ]
This article about a mathematical publication is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Guide_to_Available_Mathematical_Software |
The IUPHAR/BPS Guide to PHARMACOLOGY is an open-access website, acting as a portal to information on the biological targets of licensed drugs and other small molecules. The Guide to PHARMACOLOGY (with GtoPdb being the standard abbreviation) is developed as a joint venture between the International Union of Basic and Clinical Pharmacology (IUPHAR) and the British Pharmacological Society (BPS). This replaces and expands upon the original 2009 IUPHAR Database (standard abbreviation IUPHAR-DB). The Guide to PHARMACOLOGY aims to provide a concise overview of all pharmacological targets, accessible to all members of the scientific and clinical communities and the interested public, with links to details on a selected set of targets. The information featured includes pharmacological data, target, and gene nomenclature, as well as curated chemical information for ligands. Overviews and commentaries on each target family are included, with links to key references.
The Guide to PHARMACOLOGY was initially made available online in December 2011 with additional material released in July 2012. Maintained by a team of curators based at the University of Edinburgh, the Guide to PHARMACOLOGY is developed by an international network of contributors, including the editors of the Concise Guide to PHARMACOLOGY . As with the original IUPHAR-DB, the International Union of Basic and Clinical Pharmacology (IUPHAR) Committee on Receptor Nomenclature and Drug Classification (NC-IUPHAR), acts as the scientific advisory and editorial board for the database. Its network of over 500 specialist advisors (organized into ~90 subcommittees) contribute expertise and data. The current PI and Grant holder of the GtoPdb project is Prof. Jamie A. Davies . The development and release of the first version of the GtoPdb in 2012 were described in an editorial published in the British Journal of Pharmacology entitled 'Guide to Pharmacology.org- an update'. [ 2 ] The IUPHAR-DB is no longer being developed and all the information contained within this site is now available through the Guide to PHARMACOLOGY (IUPHAR-DB links should now re-direct).
The target groups currently included on the Guide to PHARMACOLOGY are:
Information for each target group is subdivided into families based on classification, with a separate data page for each family. Within each page, targets are arranged into lists of tables, with each table including the protein and gene nomenclature for the target with links to gene nomenclature databases, and listing selected ligands with activity at the target, including agonists, antagonists, inhibitors and radioligands. Pharmacological data and references are given and each ligand is hyperlinked to a ligand page displaying nomenclature and a chemical structure or peptide sequence, along with synonyms and relevant database links. The Guide to PHARMACOLOGY also includes a list of all ligand molecules included on the site, subdivided into categories including small organic molecules (including mammalian metabolites , hormones and neurotransmitters ), synthetic organic molecules, natural products , peptides , inorganic molecules and antibodies . A complete list of all the approved drugs included on the website is also available via the ligand list. The Guide to PHARMACOLOGY is being expanded to include clinical information on targets and ligands, in addition to educational resources.
Search features on the website include quick and advanced search options, and receptor and ligand searches, including support for ligand structures using chemical structures. Other features include 'Hot topic' news items and a recent receptor-ligand pairing list.
Between November 2015 and October 2018, the Wellcome Trust supported a project to develop the IUPHAR Guide to IMMUNOPHARMACOLOGY [ 3 ] (GtoImmuPdb), based on the GtoPdb schema. The GtoImmuPdb is an open-access resource that brings an immunological perspective to the high-quality, expert-curated pharmacological data found in the existing IUPHAR/BPS Guide to PHARMACOLOGY. Protein targets and ligands relevant to immunopharmacology have been tagged and curated into GtoImmuPdb. These have also been associated with new immunological data types such as immunological processes, cell types, and disease. GtoImmuPdb provides a knowledge base that connects immunology with pharmacology, bringing added value and supporting research and development of drugs targeted at modulating immune, inflammatory or infectious components of the disease. [ 4 ]
The Guide to PHARMACOLOGY includes an online, open-access database version of the Concise Guide to PHARMACOLOGY , previously "The Guide to Receptors and Channels" [ 5 ] available in HTML, PDF and printed formats. A hard copy summary of the online database is published as The Concise Guide to Pharmacology 2017/2018 [ 6 ] as a series of papers as a bi-annual supplement to the British Journal of Pharmacology .
The Guide to PHARMACOLOGY includes links to other relevant resources via target and ligand pages on both the concise and detailed view pages. Many of these resources maintain reciprocal links with the relevant Guide to PHARMACOLOGY pages.
Following funding from the Wellcome Trust , from 2012 to 2015 the Guide to PHARMACOLOGY was expanded to include the biological targets of all prescription drugs and other likely targets of future small molecule drugs. Overviews of the key features of a wide range of targets are provided on the summary view pages, with detailed view pages providing more in-depth information on the properties of a selected subset of targets. As of January 2018 the Medicines for Malaria Venture is supporting a new extension to develop the Guide to Malaria Pharmacology. [ 7 ] The core GtoPdb continues to be supported by the British Pharmacological Society . | https://en.wikipedia.org/wiki/Guide_to_Pharmacology |
A turbine ( / ˈ t ɜːr b aɪ n / or / ˈ t ɜːr b ɪ n / ) (from the Greek τύρβη , tyrbē , or Latin turbo , meaning vortex ) [ 1 ] [ 2 ] is a rotary mechanical device that extracts energy from a fluid flow and converts it into useful work . The work produced can be used for generating electrical power when combined with a generator . [ 3 ] A turbine is a turbomachine with at least one moving part called a rotor assembly, which is a shaft or drum with blades attached. Moving fluid acts on the blades so that they move and impart rotational energy to the rotor.
Gas , steam , and water turbines have a casing around the blades that contains and controls the working fluid. Modern steam turbines frequently employ both reaction and impulse in the same unit, typically varying the degree of reaction and impulse from the blade root to its periphery.
Hero of Alexandria demonstrated the turbine principle in an aeolipile in the first century AD and Vitruvius mentioned them around 70 BC.
Early turbine examples are windmills and waterwheels .
The word "turbine" was first applied to this kind of device in 1822 by the French mining engineer Claude Burdin in a memo, "Des turbines hydrauliques ou machines rotatoires à grande vitesse", which he submitted to the Académie royale des sciences in Paris. [ 4 ] The word derives from the Latin turbo , meaning " vortex " or " top ", and was in use in French to describe certain seashells. [ 5 ] However, it was not until 1824 that a committee of the Académie (composed of Prony, Dupin, and Girard) reported favorably on Burdin's memo. [ 6 ] Benoit Fourneyron , a former student of Claude Burdin, built the first practical water turbine.
Credit for invention of the steam turbine is given both to Anglo-Irish engineer Sir Charles Parsons (1854–1931) for invention of the reaction turbine, and to Swedish engineer Gustaf de Laval (1845–1913) for invention of the impulse turbine.
A working fluid contains potential energy (pressure head ) and kinetic energy (velocity head). The fluid may be compressible or incompressible . Several physical principles are employed by turbines to collect this energy:
Impulse turbines change the direction of flow of a high velocity fluid or gas jet. The resulting impulse spins the turbine and leaves the fluid flow with diminished kinetic energy. There is no pressure change of the fluid or gas in the turbine blades (the moving blades), as in the case of a steam or gas turbine, all the pressure drop takes place in the stationary blades (the nozzles). Before reaching the turbine, the fluid's pressure head is changed to velocity head by accelerating the fluid with a nozzle . Pelton wheels and de Laval turbines use this process exclusively. Impulse turbines do not require a pressure casement around the rotor since the fluid jet is created by the nozzle prior to reaching the blades on the rotor. Newton's second law describes the transfer of energy for impulse turbines. Impulse turbines are most efficient for use in cases where the flow is low and the inlet pressure is high. [ 3 ]
Reaction turbines develop torque by reacting to the gas or fluid's pressure or mass. The pressure of the gas or fluid changes as it passes through the turbine rotor blades. [ 3 ] A pressure casement is needed to contain the working fluid as it acts on the turbine stage(s) or the turbine must be fully immersed in the fluid flow (such as with wind turbines). The casing contains and directs the working fluid and, for water turbines, maintains the suction imparted by the draft tube . Francis turbines and most steam turbines use this concept. For compressible working fluids, multiple turbine stages are usually used to harness the expanding gas efficiently. Newton's third law describes the transfer of energy for reaction turbines. Reaction turbines are better suited to higher flow velocities or applications where the fluid head (upstream pressure) is low. [ 3 ]
In the case of steam turbines, such as would be used for marine applications or for land-based electricity generation, a Parsons-type reaction turbine would require approximately double the number of blade rows as a de Laval-type impulse turbine, for the same degree of thermal energy conversion. Whilst this makes the Parsons turbine much longer and heavier, the overall efficiency of a reaction turbine is slightly higher than the equivalent impulse turbine for the same thermal energy conversion.
In practice, modern turbine designs use both reaction and impulse concepts to varying degrees whenever possible. Wind turbines use an airfoil to generate a reaction lift from the moving fluid and impart it to the rotor. Wind turbines also gain some energy from the impulse of the wind, by deflecting it at an angle. Turbines with multiple stages may use either reaction or impulse blading at high pressure. Steam turbines were traditionally more impulse but continue to move towards reaction designs similar to those used in gas turbines. At low pressure the operating fluid medium expands in volume for small reductions in pressure. Under these conditions, blading becomes strictly a reaction type design with the base of the blade solely impulse. The reason is due to the effect of the rotation speed for each blade. As the volume increases, the blade height increases, and the base of the blade spins at a slower speed relative to the tip. This change in speed forces a designer to change from impulse at the base, to a high reaction-style tip.
Classical turbine design methods were developed in the mid 19th century. Vector analysis related the fluid flow with turbine shape and rotation. Graphical calculation methods were used at first. Formulae for the basic dimensions of turbine parts are well documented and a highly efficient machine can be reliably designed for any fluid flow condition . Some of the calculations are empirical or 'rule of thumb' formulae, and others are based on classical mechanics . As with most engineering calculations, simplifying assumptions were made.
Velocity triangles can be used to calculate the basic performance of a turbine stage. Gas exits the stationary turbine nozzle guide vanes at absolute velocity V a1 . The rotor rotates at velocity U . Relative to the rotor, the velocity of the gas as it impinges on the rotor entrance is V r1 . The gas is turned by the rotor and exits, relative to the rotor, at velocity V r2 . However, in absolute terms the rotor exit velocity is V a2 . The velocity triangles are constructed using these various velocity vectors. Velocity triangles can be constructed at any section through the blading (for example: hub, tip, midsection and so on) but are usually shown at the mean stage radius. Mean performance for the stage can be calculated from the velocity triangles, at this radius, using the Euler equation :
Hence:
where:
The turbine pressure ratio is a function of Δ h T {\displaystyle {\frac {\Delta h}{T}}} and the turbine efficiency.
Modern turbine design carries the calculations further. Computational fluid dynamics dispenses with many of the simplifying assumptions used to derive classical formulas and computer software facilitates optimization. These tools have led to steady improvements in turbine design over the last forty years.
The primary numerical classification of a turbine is its specific speed . This number describes the speed of the turbine at its maximum efficiency with respect to the power and flow rate. The specific speed is derived to be independent of turbine size. Given the fluid flow conditions and the desired shaft output speed, the specific speed can be calculated and an appropriate turbine design selected.
The specific speed, along with some fundamental formulas can be used to reliably scale an existing design of known performance to a new size with corresponding performance.
Off-design performance is normally displayed as a turbine map or characteristic.
The number of blades in the rotor and the number of vanes in the stator are often two different prime numbers in order to reduce the harmonics and maximize the blade-passing frequency. [ 7 ]
A large proportion of the world's electrical power is generated by turbo generators .
Turbines are used in gas turbine engines on land, sea and air.
Turbochargers are used on piston engines.
Gas turbines have very high power densities (i.e. the ratio of power to mass, or power to volume) because they run at very high speeds. The Space Shuttle main engines used turbopumps (machines consisting of a pump driven by a turbine engine) to feed the propellants (liquid oxygen and liquid hydrogen) into the engine's combustion chamber. The liquid hydrogen turbopump is slightly larger than an automobile engine (weighing approximately 700 lb) with the turbine producing nearly 70,000 hp (52.2 MW ).
Turboexpanders are used for refrigeration in industrial processes. | https://en.wikipedia.org/wiki/Guide_vane |
Guided local search is a metaheuristic search method. A meta-heuristic method is a method that sits on top of a local search algorithm to change its behavior.
Guided local search builds up penalties during a search. It uses penalties to help local search algorithms escape from local minima and plateaus. When the given local search algorithm settles in a local optimum, GLS modifies the objective function using a specific scheme (explained below). Then the local search will operate using an augmented objective function, which is designed to bring the search out of the local optimum. The key is in the way that the objective function is modified.
The method in its current form was developed by Dr Christos Voudouris and detailed in his PhD Thesis. [ 1 ] GLS was inspired by and extended GENET, a neural network architecture for solving Constraint Satisfaction Problems, which was developed by Chang Wang, Edward Tsang and Andrew Davenport. Both GLS's and GENET's mechanism for escaping from local minima resembles reinforcement learning .
To apply GLS, solution features must be defined for the given problem. Solution features are defined to distinguish between solutions with different characteristics, so that regions of similarity around local optima can be recognized and avoided. The choice of solution features depends on the type of problem, and also to a certain extent on the local search algorithm. For each feature f i {\displaystyle f_{i}} a cost function c i {\displaystyle c_{i}} is defined.
Each feature is also associated with a penalty p i {\displaystyle p_{i}} (initially set to 0) to record the number of occurrences of the feature in local minima.
The features and costs often come directly from the objective function. For example, in the traveling salesman problem, “whether the tour goes directly from city X to city Y” can be defined to be a feature. The distance between X and Y can be defined to be the cost. In the SAT and weighted MAX-SAT problems, the features can be “whether clause C satisfied by the current assignments”.
At the implementation level, we define for each feature i {\displaystyle i} an Indicator Function I i {\displaystyle I_{i}} indicating whether the feature is present in the current solution or not. I i {\displaystyle I_{i}} is 1 when solution x {\displaystyle x} exhibits property i {\displaystyle i} , 0 otherwise.
GLS computes the utility of penalising each feature. When the local search algorithm returns a local minimum x, GLS penalizes all those features (through increments to the penalty of the features) present in that solution which have maximum utility, util ( x , i ) {\displaystyle \operatorname {util} (x,i)} , as defined below.
The idea is to penalise features that have high costs, although the utility of doing so decreases as the feature is penalised more and more often.
GLS uses an augmented cost function (defined below), to allow it to guide the local search algorithm out of the local minimum, through penalising features present in that local minimum. The idea is to make the local minimum more costly than the surrounding search space, where these features are not present.
The parameter λ may be used to alter the intensification of the search for solutions. A higher value for λ will result in a more diverse search, where plateaus and basins are searched more coarsely; a low value will result in a more intensive search for the solution, where the plateaus and basins in the search landscape are searched in finer detail. The coefficient a {\displaystyle a} is used to make the penalty part of the objective function balanced relative to changes in the objective function and is problem specific. A simple heuristic for setting a {\displaystyle a} is simply to record the average change in objective function up until the first local minimum, and then set a {\displaystyle a} to this value divided by the number of GLS features in the problem instance.
Mills (2002) has described an extended guided local search (EGLS) which utilises random moves and an aspiration criterion designed specifically for penalty based schemes. The resulting algorithm improved the robustness of GLS over a range of parameter settings, particularly in the case of the quadratic assignment problem . A general version of the GLS algorithm, using a min-conflicts based hill climber (Minton et al. 1992) and based partly on GENET for constraint satisfaction and optimisation, has also been implemented in the Computer-Aided Constraint Programming project.
Alsheddy (2011) extended guided local search to multi-objective optimization , and demonstrated its use in staff empowerment in scheduling [ citation needed ] .
GLS was built on GENET, which was developed by Chang Wang, Edward Tsang and Andrew Davenport.
The breakout method is very similar to GENET. It was designed for constraint satisfaction .
Tabu search is a class of search methods which can be instantiated to specific methods. GLS can be seen as a special case of Tabu search .
By sitting GLS on top of genetic algorithm , Tung-leng Lau introduced the guided genetic programming (GGA) algorithm. It was successfully applied to the general assignment problem (in scheduling), processors configuration problem (in electronic design) and a set of radio-link frequency assignment problems (an abstracted military application).
Choi et al. cast GENET as a Lagrangian search. | https://en.wikipedia.org/wiki/Guided_local_search |
A remotely guided rat, popularly called a ratbot or robo-rat , is a rat with electrodes implanted in the medial forebrain bundle (MFB) and sensorimotor cortex of its brain. They were developed in 2002 by Sanjiv Talwar and John Chapin at the State University of New York Downstate Medical Center . The rats wear a small electronics backpack containing a radio receiver and electrical stimulator. The rat receives remote stimulation in the sensorimotor cortex via its backpack that causes the rat to feel a sensation in its left or right whiskers , and stimulation in the MFB that is interpreted as a reward or pleasure.
After a period of training and conditioning using MFB stimulation as a reward, the rats can be remotely directed to move left, right, and forward in response to whisker stimulation signals. It is possible to roughly guide the animal along an obstacle course, jumping small gaps and scaling obstacles.
Concerns have been raised by animal rights groups about the use of animals in this context, particularly due to a concern about the removal of autonomy from an independent creature. For example, a spokesman of the Dr Hadwen Trust , a group funding alternatives to animal research in medicine, has said that the experiments are an "appalling example of how the human species instrumentalizes other species." [ 1 ]
Researchers tend to liken the training mechanism of the robo-rat to standard operant conditioning techniques. Talwar himself has acknowledged the ethical issues apparent in the development of the robo-rat, but points out that the research meets standards for animal treatment laid down by the National Institute of Health . [ 2 ] Moreover, the researchers emphasize that the animals are trained, not coerced, into particular behaviors. Because the rats are encouraged to act via the reward of pleasure, not muscularly compelled to behave in a particular manner, their behavior under MFB stimulation is likened to a carrot-and-stick model of encouraged behavior versus a system of mind control . It seems unlikely that the rats could be persuaded to knowingly risk their lives even with this stimulation. "Our animals were completely happy and treated well," Talwar stated. [ 1 ]
The technology is reminiscent of experiments performed in 1965 by Dr. Jose Delgado , a controversial scientist who was able to pacify a charging bull via electrodes fitted in its brain. He was also said to control cats and monkeys like "electronic toys." [ 3 ] Doctor Robert Galbraith Heath also placed electrodes deep into the brains of patients and wrote hundreds of medical papers on his work. | https://en.wikipedia.org/wiki/Guided_rat |
Guido Bargellini (1879–1963) was an Italian organic chemist . He specialized in natural product chemistry, in particular, flavonoid dyes and coumarins , and the compound santonin . He was admitted to the Accademia dei Lincei in 1946. The Bargellini reaction is named for him.
This biographical article about a chemist is a stub . You can help Wikipedia by expanding it .
This Italian scientist article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Guido_Bargellini |
A guild (or ecological guild ) is any group of species that exploit the same resources, or that exploit different resources in related ways. [ 1 ] [ 2 ] [ 3 ] It is not necessary that the species within a guild occupy the same, or even similar, ecological niches . [ a ]
Guilds are defined according to the locations, attributes, or activities of their component species. For example, the mode of acquiring nutrients, the mobility, and the habitat zones that the species occupy or exploit can be used to define a guild. The number of guilds occupying an ecosystem is termed its disparity . [ 5 ] Members of a guild within a given ecosystem could be competing for resources, such as space or light, while cooperating in resisting wind stresses, attracting pollinators, or detecting predators, such as happens among savannah-dwelling antelope and zebra .
A guild does not typically have strict, or even clearly defined boundaries, nor does it need to be taxonomically cohesive. A broadly defined guild will almost always have constituent guilds; for example, grazing guilds will have some species that concentrate on coarse, plentiful forage, while others concentrate on low-growing, finer plants. Each of those two sub-guilds may be regarded as guilds in appropriate contexts, and they might, in turn, have sub-guilds in more closely selective contexts. Some authorities even speak of guilds in terms of a fractal resource model. [ 6 ] This concept arises in several related contexts, such as the metabolic theory of ecology , the scaling pattern of occupancy , and spatial analysis in ecology, all of which are fundamental concepts in defining guilds.
An ecological guild is not to be confused with a taxocene , a group of phylogenetically related organisms in a community that do not necessarily share the same or similar niches (for example, "the insect community"). Nor is a guild the same as a trophic species , which is a functional group of taxa sharing the same set of predators and prey within a food web. [ 7 ]
Some authors have used the term guild to analyze microbial communities. However, precisely because of the pointed lack of concretion in the original definition, it has been used with different connotations. Recently, some effort has been made to address this issue. [ 8 ] Some authors have proposed a formal definition for guilds that avoids this inherent ambiguity of niche exploitation, and a quantification method considering the problems arising from degeneracy in protein functions. [ 9 ] According to the authors, any organism that performs a function, regardless of its phylogenetic lineage, its environmental preferences or how it carries it out, would be regarded as a representative member of the guild. This contrasts with the definitions used for the study of macro organisms, where membership demanded that the different forms of exploitation of the resource were related or similar.
The term guild is a broad term to describe the relationship between different species using the same resource. Since it is difficult to classify a guild it can be broken down into two more specific categories, alpha guilds and beta guilds.
Alpha guild is specifically related to species that share a resource used within the same community. [ 10 ] Species in an alpha guild do not typically coexist in the same area, as the competitive exclusion principle prevents this. If species are grouped into an alpha guild together one of them will need to change the way they use this resource or change the resources they use to survive.
Beta guild is specifically related to species that are found in the same environmental conditions. [ 10 ] Species in a beta guild are typically found in the same space and time together, as their environmental range is the same. Species grouped into the same beta guild still may use the same resources but not competitively. | https://en.wikipedia.org/wiki/Guild_(ecology) |
Guillaume François Antoine, Marquis de l'Hôpital [ 1 ] ( French: [ɡijom fʁɑ̃swa ɑ̃twan maʁki də lopital] ; sometimes spelled L'Hospital ; 7 June 1661 – 2 February 1704) [ a ] was a French mathematician . His name is firmly associated with l'Hôpital's rule for calculating limits involving indeterminate forms 0/0 and ∞/∞. Although the rule did not originate with l'Hôpital, it appeared in print for the first time in his 1696 treatise on the infinitesimal calculus , entitled Analyse des Infiniment Petits pour l'Intelligence des Lignes Courbes . [ 3 ] This book was a first systematic exposition of differential calculus . Several editions and translations to other languages were published and it became a model for subsequent treatments of calculus .
L'Hôpital was born into a military family. His father was Anne-Alexandre de l'Hôpital, a Lieutenant-General of the King's army, Comte de Saint-Mesme and the first squire of Gaston, Duke of Orléans . His mother was Elisabeth Gobelin, a daughter of Claude Gobelin, Intendant in the King's Army and Councilor of the State.
L'Hôpital abandoned a military career due to poor eyesight and pursued his interest in mathematics , [ 4 ] which was apparent since his childhood. For a while, he was a member of Nicolas Malebranche 's circle in Paris and it was there that in 1691 he met young Johann Bernoulli , who was visiting France and agreed to supplement his Paris talks on infinitesimal calculus with private lectures to l'Hôpital at his estate at Oucques . In 1693, l'Hôpital was elected to the French academy of sciences and even served twice as its vice-president. [ 5 ] Among his accomplishments were the determination of the arc length of the logarithmic graph, [ 6 ] one of the solutions to the brachistochrone problem , and the discovery of a turning point singularity on the involute of a plane curve near an inflection point . [ 7 ]
L'Hôpital exchanged ideas with Pierre Varignon and corresponded with Gottfried Leibniz , Christiaan Huygens , and Jacob and Johann Bernoulli . His Traité analytique des sections coniques et de leur usage pour la résolution des équations dans les problêmes tant déterminés qu'indéterminés ("Analytic treatise on conic sections ") was published posthumously in Paris in 1707.
In 1696 l'Hôpital published his book Analyse des Infiniment Petits pour l'Intelligence des Lignes Courbes ("Infinitesimal calculus with applications to curved lines"). This was the first textbook on infinitesimal calculus and it presented the ideas of differential calculus and their applications to differential geometry of curves in a lucid form and with numerous figures; however, it did not consider integration .
The history leading to the book's publication became a subject of a protracted controversy. In a letter from 17 March 1694, l'Hôpital made the following proposal to Johann Bernoulli : in exchange for an annual payment of 300 Francs, Bernoulli would inform l'Hôpital of his latest mathematical discoveries, withholding them from correspondence with others, including Varignon . Bernoulli's immediate response has not been preserved, but he must have agreed soon, as the subsequent letters show. L'Hôpital may have felt fully justified in describing these results in his book, after acknowledging his debt to Leibniz and the Bernoulli brothers, "especially the younger one" (Johann). Johann Bernoulli grew increasingly unhappy with the accolades bestowed on l'Hôpital's work and complained in private correspondence about being sidelined. After l'Hôpital's death, he publicly revealed their agreement and claimed credit for the statements and portions of the text of Analyse , which were supplied to l'Hôpital in letters. Over a period of many years, Bernoulli made progressively stronger allegations about his role in the writing of Analyse , culminating in the publication of his old work on integral calculus in 1742: he remarked that this is a continuation of his old lectures on differential calculus, which he discarded since l'Hôpital had already included them in his famous book. For a long time, these claims were not regarded as credible by many historians of mathematics, because l'Hôpital's mathematical talent was not in doubt, while Bernoulli was involved in several other priority disputes. For example, both H. G. Zeuthen and Moritz Cantor , writing at the cusp of the 20th century, dismissed Bernoulli's claims on these grounds. However, in 1921 Paul Schafheitlin discovered a manuscript of Bernoulli's lectures on differential calculus from 1691 to 1692 in the Basel University library. The text showed remarkable similarities to l'Hôpital's writing, substantiating Bernoulli's account of the book's origin.
L'Hôpital married Marie-Charlotte de Romilley de La Chesnelaye , also a mathematician and a member of the nobility, and inheritor of large estates in Brittany . Together, they had one son and three daughters. [ 8 ] L'Hôpital passed away at the age of 42. The exact cause of his death is not widely recorded, and historical sources do not provide specific details regarding the circumstances of his passing. | https://en.wikipedia.org/wiki/Guillaume_de_l'Hôpital |
Guillemin effect is one of the magnetomechanical effects . It is connected with the tendency of a previously bent rod, made of magnetostrictive material, to be straightened, when subjected to magnetic field applied in the direction of rod's axis.
This electromagnetism -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Guillemin_effect |
Guillermo Carlos Bazan is an American chemist , material scientist , and academic .
Bazan earned a B.Sc with Honors in chemistry from the University of Ottawa in 1986, and a Ph.D in Inorganic Chemistry from Massachusetts Institute of Technology in 1991. From 1992 to 1998 he was on the faculty of the University of Rochester . In 1998 he was appointed as a professor in the Chemistry & Biochemistry Department and the Materials Department at the University of California, Santa Barbara . In January 2020, he took a position at the National University of Singapore , joining the faculty of the Institute for Functional Intelligent Materials [ 1 ] initiated by Professor Konstantin Novoselov . [ 2 ] In March 2024, he became director of IDMxS, [ 3 ] a research centre of excellence at Nanyang Technological University , becoming a professor at the School of Chemistry, Chemical Engineering & Biotechnology (CCEB).
Bazan has over 670 publications, an h -index of 120, and his work has been recognized by the Arthur C. Cope Scholar Award of the American Chemical Society (2007) [ 4 ] and the Bessel Award of the Humboldt Foundation. [ 5 ] He is a fellow of the American Association for the Advancement of Science . [ 6 ] | https://en.wikipedia.org/wiki/Guillermo_Bazan |
Guillermo Rein (born May 1975) is a professor of fire science in the Department of Mechanical Engineering at Imperial College London . His research is focused on fire , combustion , and heat transfer . He is the editor-in-chief of the journal Fire Technology and Fellow of the Combustion Institute .
Rein is best known for his contributions to smouldering combustion research in the field of fire science. [ 2 ]
Rein obtained his Industrial Engineering degree at the ICAI School of Engineering in 1999. He studied mechanical engineering at the University of California, Berkeley , and obtained an MSc in 2003 and a PhD. in 2005. He taught at the School of Engineering of the University of Edinburgh (2006–2012), where he was a senior lecturer before moving to Imperial College in 2012. [ 3 ]
His research meanly focus on heat transfer , combustion , fire and wildfire . [ 4 ] He is best known in three areas: polymer and wood ignition; design of fire-resistant structures; and wildfire spread and mitigation.
Rein, together with his research group and collaborators, has edited two books, published six book chapters and over 200 journal publications. [ 5 ] His current h-index is above 60 and citation count is over 12,000 on Google Scholar . [ 6 ]
Rein has been editor-in-chief of the journal Fire Technology since 2012. [ 7 ] [ 8 ] He was associate editor of Proceedings of the Combustion Institute from 2013 to 2019 ; [ 9 ] associate editor of Thermal and Mass Transport ( Frontiers of Mechanical Engineering ) from 2016 ; [ 10 ] and is on the editorial board of Safety Science [ 11 ] and the advisory board of International Journal of Wildland Fire since 2016. [ 12 ] He was also on the editorial board of Fire Safety Journal from 2014 to 2017. | https://en.wikipedia.org/wiki/Guillermo_Rein |
Guillermo Rojas Bazan is an aviation model maker and researcher from Argentina. He is internationally renowned and considered unique and innovative in the field of museum quality airplane modeling in metal. [ 1 ] [ 2 ] His work has had a significant impact in the development of highly detailed model aircraft. [ 3 ] [ 4 ] Rojas Bazan has developed his own modeling techniques and is one of the only aircraft model builders to use aluminum. [ 5 ] [ 3 ] He is a true scratch builder, working completely by hand, foregoing electrical machines, except for a small compressor used for his airbrush. [ 6 ] [ 7 ]
During the first forty-five years of his career, while living and working in four different countries, he made more than 200 custom models for museums, art galleries, scale model companies, and collectors. [ 6 ] He has been called the greatest aircraft model maker in the world by various sources. [ 8 ]
Guillermo Rojas Bazan was born in 1949 in Buenos Aires, Argentina. [ 9 ] Rojas Bazan received his education in both a technical engineering school and an art school. [ 10 ] From 1981 to 1988, Rojas Bazan worked for the Instituto Aeronaval (Naval Air Institute) and the Argentine Air Force. [ 6 ] During that time, he worked as a technical draftsman, aircraft illustrator, and designer. [ 6 ] Additionally, he was commissioned to build all of the aircraft used in Argentina's Naval history, [ 11 ] [ 12 ] resulting in ninety-nine aircraft models built that are still currently on display. [ 3 ] [ 13 ]
In 1988, he left Argentina for Spain, where he built models for an aviation art gallery in London and produced replicas for collectors in the United States and Europe. [ 6 ] While working for the London gallery, Rojas Bazan was able to choose which models he built, and made several of what he describes as non-commercial models, that all sold despite not being ordered. [ 3 ]
In 1994, he moved to the U.S. and was hired by Fine Art Models, a company located in Royal Oak, Michigan. [ 14 ] [ 15 ] During his years working for Fine Art Models, he made models in 1/15 scale that were copied in Eastern Europe and sold in limited editions. [ 14 ] [ 16 ] In recent years, he has worked as a freelance artist for collectors and museums. [ 6 ]
Rojas Bazan's models are known for their high detail and weathering, giving the aircraft models their realism. [ 10 ] [ 14 ] Ann Cooper, a writer for Private Pilot magazine, explained that Rojas Bazan "doesn't just assemble parts and finish the exterior surfaces of his models, he loads them, inside and out, with rich, realistic detail work." [ 10 ] Furthermore, there is a precision to details that are microscopic. [ 17 ] Kelly Shaw of the magazine Fine Scale Modeler stated that "His all-metal scratch-builds are memorable for their undulating surfaces, variation in riveting, overlapping panels, and stressed skin. In photos, it's easy to mistake his models for real aircraft." Also noting that despite his success as a model maker, he has continued to strive for perfection. [ 14 ] Moreover, Rojas Bazan’s models were lauded in letters by the University of Notre Dame, Christie's, and the U.S. Air Force and were referred to as the "Tiffany of Models," further explaining that his work is taking scale modeling around the world into a new dimension. [ 18 ]
To make sure his models are accurate, Rojas Bazan relies on extensive research before beginning work on a model. This process takes a longer period of time when an aircraft has a greater complexity. [ 10 ] [ 14 ] Rojas Bazan’s research has involved construction plans, material samples, test samples, and talking to former pilots. [ 3 ] His Junkers G 24 model was built despite the fact that none of those aircraft still exist, using photos and original publications. [ 5 ] Rojas Bazan has explained how "a lot of kits get it wrong." [ 14 ] He primarily specializes in models of aircraft built between 1925-1945. [ 6 ] In 1995, Mike Knepper, a writer for Cigar Aficionado magazine named Rojas Bazan the "Mozart of Modeling." [ 9 ]
Rojas Bazan built eighty-seven models for Argentina’s National Museum of the Nation as a result of being commissioned to build every aircraft used in Argentina’s Naval history. [ 11 ] [ 3 ] He built an additional twelve models that were displayed in different locations in Argentina. [ 13 ] At Fine Art Models, he built numerous models including the F-4UD Corsair, which was recognized as a masterpiece by the German magazine IQ. [ 3 ] [ 19 ] When discussing Rojas Bazan’s P-51 Mustang model, a former World War II pilot of that aircraft, said that the details in the model are the best that he has ever seen. [ 10 ] When asked about which are his favorite models, Rojas Bazan said, 'I do not have only one favorite model, I have several. Many of them are planes from the period between 1920 and 1939, before WWII (golden age of aviation). These include the Northrop Gamma, Boeing B-15, Boeing YB-17 (prototypes on the great B-17), Martin B-10, Vought Vindicator, Curtiss Hawk III, Junkers G-38, Junkers G-24, Heinkel He70, Fairey Battle, etc. Many of these aircraft were not good machines, or have not been very popular, but I like them aesthetically.' [ 6 ] One model that was built in Rojas Bazan's most recent freelancer era is a Mitsubishi A6M Zero that now resides in Japan and was promoted there as the best Zero replica ever built. [ 6 ] [ 20 ] Another model completed in recent years is a Ju 87 B-1 Stuka, which is featured in one of his YouTube videos. In that video, he explains the archeological labor that he undergoes to complete his models in the most realistic way possible. [ 21 ] His last completed model is a Consolidated B-24H Liberator. [ 22 ] It was commissioned by the 467th Bombardment Group (H) Association and will be displayed at the historic Wendover airfield. [ 23 ] | https://en.wikipedia.org/wiki/Guillermo_Rojas_Bazan |
In safety engineering, a Guillotine Test simulates an arc fault condition between parallel conductors or a cut wire, replicating the conditions that result from arc faults and which can lead to fires in adjacent material and wires, for example during accidents. [ 1 ] Based upon a dry arc test method used for testing wire insulation material, this test was originally developed for arc-fault circuit interrupters . Here is a sample test schematic, showing the logic flow of one guillotine test. It shows the guidelines on whether to retest or if the test was passed or failed.
Testing of this type plays an important role in helping researchers who are looking into wiring faults in aircraft, submarine communication cables, etc. [ 2 ] This can lead to products that are able to quickly identify and locate these wiring faults for easier and less costly repairs and an overall safer environment. | https://en.wikipedia.org/wiki/Guillotine_test |
A Guinier–Preston zone , or GP-zone , is a fine-scale metallurgical phenomenon, involving early stage precipitation. [ 1 ] [ 2 ]
GP-zones are associated with the phenomenon of age hardening , whereby room-temperature reactions continue to occur within a material through time, resulting in changing physical properties. In particular, this occurs in several aluminium series, such as the 6000 and 7000 series alloys.
Physically, GP zones are extremely fine-scaled (on the order of 3–10 nm in size) solute enriched regions of the material, which offer physical obstructions to the motion of dislocations , above that of the solid solution strengthening of the solute components. In 7075 aluminium for example, [ 3 ] Zn–Mg clusters precede the formation of equilibrium MgZn 2 precipitates.
The zone is named after André Guinier and George Dawson Preston who independently identified the zones in 1938. [ 4 ] [ 5 ] | https://en.wikipedia.org/wiki/Guinier–Preston_zone |
A guitar technician (or guitar tech ) is a member of a music ensemble's road crew who maintains and sets up the musical equipment for one or more guitarists . Depending on the type and size of band, the guitar tech may be responsible for stringing, tuning, and adjusting electric guitars and acoustic guitars , and maintaining and setting up guitar amplifiers and other related electronic equipment such as effect pedals .
Once the guitar equipment has been set up onstage, the guitar tech does a soundcheck to ensure that the equipment is working well. If there are any problems, the guitar tech replaces or repairs the faulty components or equipment. Since guitar techs need to soundcheck the instruments and amplifiers, they must have basic guitar-playing skills, a musical "ear" for tuning, and a familiarity with the way guitars, amplifiers, and effect pedals are supposed to sound in the style of music of their band.
Guitar techs learn their craft either "on the job", by working in a range of music, sound engineering, and instrument repair jobs; by completing a guitar repair program at a college or lutherie school; or from a combination of these two routes. The salaries and conditions of work for guitar techs vary widely, depending on whether a guitar tech is working for a minor or regional touring bar band or a major international touring act.
The duties of a guitar technician depend on the type of band they are working for, and on a range of other factors such as the size and nature of the stage show and the length of the show. Guitar technicians who work for an acoustic band, such as a folk group or bluegrass ensemble may be responsible for setting up and stringing, and tuning a range of stringed, fretted instruments including acoustic guitars, dobros , and mandolins. A guitar tech for a heavy metal band, on the other hand, may focus mainly on electric guitars, guitar amplifiers, and effects pedals. A guitar tech may change the sequence of effects pedals or alter the settings on effects pedals during the show, to assist the guitarist in creating different tone colours or sounds. For example, a guitarist may ask the guitar tech to connect a chorus effect and reverb before a guitar solo . In an indie rock band, a guitar technician would likely configure the equipment to evoke through tone a modern yet historically evocative sound. In an acid rock band, a guitar tech might have to manipulate the controls on a ring modulator or a rotating Leslie speaker cabinet to create unusual sounds while the guitarist is performing.
Once the guitars have been tuned with an electronic tuner and strummed to ensure that they are in tune, the guitar tech usually sets up the different guitars on guitar racks, ensures that the leather or nylon straps are properly connected, and that the patch cords are plugged in properly. During the show, the guitar tech hands instruments to the guitarist or guitarists according to the types of guitar that are required in the songs that they are playing. For example, a hard rock guitarist may use a "flying-V" guitar for a fast song, and then switch to an acoustic 12-string guitar for a soft ballad. The guitar tech retunes all of the instruments before they are used, because even if an instrument was perfectly in tune during the soundcheck, the heat from stage lights and the humidity from the stage conditions may render the instrument slightly out of tune.
After each guitar is used, the guitar tech cleans the strings with a cloth and replaces the instrument on a rack. During the show, the tech stands ready to replace any guitars in case a string breaks or if there is an equipment malfunction. The guitar tech may hand fresh towels to the guitarist so that the guitarist can remove sweat from the hands and ensure that the guitarist has ready access to bottles of cool water or other beverages . If a guitar technician is working for a guitarist who uses picks , the guitar tech may lay out a variety of picks on a guitar amplifier or tape the picks to the mic stands with double-sided tape, so that they are within easy reach. At the end of the show, the guitar tech disconnects all of the patch cords, cleans the instruments and puts them back into their cases.
The guitar tech also might perform any of a variety of maintenance tasks, such as checking that the string height of the guitars is set properly, modifying ("dressing") the height and arc of the frets, adjusting the intonation of the instruments , checking that tubes (valves) on tube amplifiers are working properly, and that cables are in good condition and free from crackles and hum caused by nicks and abrasions in the shielding or cable insulation. Techs also check the batteries on "outboard" devices — effects boxes, tuners, and pre-amps — and wireless transmitters, and change them as necessary. Depending on the size of a band's road crew, the guitar tech may either do this maintenance him- or herself, or, in a large touring act, delegate tasks to more-junior personnel.
The guitar tech does a basic soundcheck with the different guitars, amplifiers, and effects, to ensure that the equipment is functioning properly and that all of the connections between the equipment (which are made with patch cords ) are plugged in correctly. This may be as simple as plugging an electric guitar into an amplifier or plugging an acoustic guitar into a DI box and preamp/equalizer. On the other hand, a tech may have to set up ten or more electric guitars, a variety of amplifiers, and connect them to an intricate sequence of effects pedals.
When all of the instruments and equipment are set up and soundchecked , if there are problems — crackles, hum, no signal from the guitar, no sound from an amplifier — the tech may have responsibility for troubleshooting to determine the cause or causes. Common problems include damaged patch cords, ground loops in connection between instruments and amplifiers, weak batteries in effects boxes or on-board preamps, bad vacuum tubes in tube amplifiers or overdrive effects, broken electrical connectors or solder joints, speaker voice coils damaged from the previous concert, or equipment damaged during transport. Tuning problems may come from old or dirty strings, damaged or worn machine heads or frets, or mis-adjusted bridges.
A guitar tech is often a "jack of all trades," expected to make simple repairs: resolder a loose wiring connection inside a guitar, replace an amplifier tube, swap out a damaged speaker for a new one, reglue a loose part on an acoustic guitar, or adjust a truss rod . In cases where there is either not enough time to make the repair, or if the equipment is damaged beyond repair, the guitar tech may be responsible for finding a replacement instrument or part, either by purchasing or renting it from a local music store or by borrowing it from another band. While another member of the road crew may be dispatched to pick up an item, the tech usually writes down which models or brands are acceptable replacements.
On rare occasions, guitar technicians may be asked to fill in for the guitarist they are teching for.
The conditions of work for guitar techs vary widely. Some guitar techs for small touring acts may set up guitars for all of the stringed-instrument performers—rhythm guitar, lead guitar, bass, and so on; they may even take on a large variety of tasks beyond guitar tech work, such as helping to set up sound equipment or soundcheck the microphones. On the other hand, guitar techs for major touring bands may be part of a large road crew team that includes amplifier technicians, guitar technicians for each guitarist (rhythm guitarist and lead guitarist), and a variety of people who set up the stage equipment. In a major touring band, a guitar tech's duties might be more narrowly circumscribed. They might only have to set up the guitars for a single performer, and there might be other staff who set up and maintain the amplifiers, effects, and guitar stands, and electronics technicians who solder and repair connections and wiring.
The salary, benefits, and accommodations of guitar techs vary widely. The first jobs that a guitar tech does may be on a volunteer basis in a garage band or amateur group, to gain experience, or alternatively the guitar tech might work in return for a small cash payment that is more of a symbolic honorarium than a real salary. In regional-level bar bands or minor touring acts, the guitar techs may be paid on a contractual basis during the weeks or months that the group is on tour, and there may not be health or dental benefits. A guitar tech working for this type of band must find other work to fill in months when the band is not on tour. On the other hand, a major touring act may hire a guitar technician as a permanent employee and provide them with a range of benefits.
Accommodations depend on conditions set out in the contract, and the level and status of the group. A guitar tech traveling with a regional-level band may stay in inexpensive motels and receive a modest per diem for restaurant meals. A guitar tech traveling with a major touring band, however, may stay at the same first-class hotels as the star performers and eat catered buffet or restaurant meals. Some bands with substantial road crews may have their own catering crew. Guitar techs for the most famous international guitarists such as Jimmy Page or Tony Iommi can become minor celebrities within the guitar fan community because of their proximity to famous musicians and insider knowledge of how a certain guitarist's unique tone is created.
Guitar technicians must have a broad knowledge of the musical equipment used in the types of bands they work with. At a minimum, this must consist of familiarity with setting up and tuning guitars and making simple adjustments and repairs. As well, guitar techs are often expected to set up, repair, and adjust electronic effects, tuners, pre-amplifiers, amplifiers, and pedalboards. To do these tasks, guitar techs must know about a range of audio engineering and electronics concepts—such as impedance , signal phase (for speakers and microphone wiring), and input voltage for pre-amps and effects. To do simple repairs on electronic gear, a guitar tech may have to know how to use a soldering iron and a multitester , and how to do basic electronics troubleshooting.
As well, since guitar techs need to soundcheck the instruments and amplifiers, they must have a knowledge of the way guitars and amplifiers are supposed to sound in the style of music of the band. This means that the guitar tech must have an ear for music, and for musical tones and sounds. A guitar tech for a heavy metal band must be able to tell whether distortion from a heavily over-driven tube amp is desirable tube clipping or distortion from a blown speaker or damaged power amp. The distinctions a guitar tech must make can be subtle. For example, a guitar tech replacing a blown tube with a new one may have to ensure that the tube amplifier still has the same "color" or "warmth" when chords are played through it.
To check guitar tuning, a guitar tech must be able to play major, minor, and other chords in a variety of keys. Even if the guitar has been tuned with an electronic tuner, the tuning still must be checked by ear, because the equal tempered tuning of a guitar can involve compromise. Guitar tuning can be affected by fret placement and wear, the angle of bridge angle, string age, and other factors. Thus, even if an electronic tuner indicates that a guitar is 100% "in tune," it may still need minor adjustments which are made by ear.
The training of guitar technicians varies widely. Some guitar technicians have studied music, guitar repair, amplifier maintenance, or electronics repair in college or university. On the other hand, some techs learned these skills informally on the job, or by working their way up through the ranks in a range of musical jobs, from a roadie and sound engineer to a sideman in a bar band. Guitar techs trained on the job may learn their skills by playing in amateur or semi-professional bands as a guitarist or bassist, working for music stores as a guitar repairperson, for clubs or bars as a sound engineer, or by maintaining equipment for PA system rental companies.
A typical career path for becoming a guitar technician via on the job training is to begin by volunteering in a bar band and then working for low wages in a regional touring act or a minor touring act. As they gain experience and add skills, they may seek out better-paying jobs with higher-status touring bands. Once a guitar technician has joined the road crew of a major touring act, they may seek out promotions within this organization, to jobs with greater responsibilities and higher pay. For example, a guitar tech who works as an assistant technician could try to get promoted to a guitar technician for the lead guitarist. A guitar tech who completes a guitar repair program at a college or lutherie school may be able to enter midway up the guitar tech career ladder.
In the early part of a guitar tech's career, there might be a great deal of mobility between different types of bands and technician roles. While working for minor or regional acts, a guitar tech may be able to work for a country rock bar band and then immediately switch to being the bass tech for a hard rock tribute band , because the tasks are fairly uniform. Career mobility of guitar technicians tends to become more constrained, though, when guitar techs begin to get jobs with high-status professional touring acts from specific genres. When a regional bar band looks for a guitar tech for a summer nightclub tour, there may many guitar techs who could meet the skill requirements. However, if an internationally known 1960s-style acid rock touring act with a celebrity lead guitarist goes on a major tour, there may be only a handful of guitar techs who have the unique combination of skills for this position. [ 1 ]
Bass guitar technicians (or "bass techs") perform the same functions for a bass guitar player. The bass guitar is a variety of electric guitar pitched below a regular electric guitar, typically by one octave. Many basic elements of the two types of instruments are similar enough—magnetic pickups routed to an electronic amplifier—that a guitar technician is usually able to work as a bass guitar technician if they become familiar with the unique aspects of the electric bass. The electric bass differs from the electric guitar in several respects. To become a bass tech, a person must learn how to set up the string action (height) and adjust the height of the pickups so that the bassist is able to create the tones associated with different bass styles. Depending on the band, these styles might include such as slap and pop , tapping , or upright bass -style playing with the thumb.
As with guitar techs, a bass tech also sets up the amplification equipment and effects pedals. Due to the lower pitch of the bass guitar, this instrument is amplified with specialized bass instrument amplifiers . While bass guitarists do not usually use as many effects pedals as most guitarists (e.g., reverb, chorus, flanger, etc.), most professional bassists may use a few "sound conditioner" effects such as a compressor , limiter , or equalizer . Some bassists also use octave pedals to generate extremely low pitches or bass overdrive pedals that produce a fuzzy, distorted sound. Although these effects function in the same way as regular electric guitar effects, a bass tech must be familiar with the settings and the resulting sounds and tones that are most often used by bass guitarists. A guitar tech who is in the first stages of learning to become a bass tech may know how to set up the bass effects from a technical point of view, but it may take a little longer for them to learn which compressor settings, for example, are associated with different funk or metal styles.
In some country, rockabilly , or jazz bands, the bass tech might also be responsible for setting up, tuning, and maintaining an upright bass or electric upright bass . In some folk or acoustic bands, the bass technician may also be responsible for maintaining an acoustic bass guitar , which is a larger, bass version of a standard acoustic guitar . More rarely, some bass techs might have to set up a bass synth (e.g., as used by the bassists in some alternative bands) or bass pedal keyboard such as a Moog Taurus pedal, as used by Sting or Led Zeppelin . Both upright basses and acoustic bass guitars usually use piezoelectric pickups rather than magnetic pickups, and in some cases, the instruments may use condenser mics to pick up the higher range sounds. To amplify instruments with piezo transducers and condenser mics, specialized impedance-matching preamplifiers are often required. Also, since both piezoelectric transducers and microphones are more prone to unwanted feedback than magnetic pickups, the bass tech may have to set up a notch filter with a parametric equalizer to reduce the frequency that is feeding back. | https://en.wikipedia.org/wiki/Guitar_tech |
A gul (also written gol , göl and gül ) is a medallion-like design element typical of traditional hand- woven carpets from Central and West Asia . In Turkmen weavings they are often repeated to form the pattern in the main field.
Gul are medallions, often octagonal , and often somewhat angular on a generally octagonal plan, though they can be somewhat rounded within the constraints of carpet-weaving, and some are lozenge-shaped ( rhombuses ). They usually have either twofold rotational symmetry or mirror reflection symmetry (often both left/right and up/down). [ 1 ]
Gul were historically described in the West as being elephant's foot motifs. Other Western guesses held that the gul was a drawing of a round Turkmen tent, with lines between tents representing irrigation canals; or that the emblem was a totemic bird. None of these descriptions have any basis in weaving tradition or culture. [ 2 ]
The term gul , gol , göl or gül is used widely across Central and West Asia, and among carpet specialists in the West. It is derived from the Persian word gol (گل) which means flower or rose. [ 3 ] [ 4 ]
In Turkmen weavings, such as bags and rugs, guls are often repeated to form the basic pattern in the main field (excluding the border). [ 4 ] [ 5 ]
The different Turkmen tribes such as Tekke , Salor , Ersari and Yomut traditionally wove a variety of guls, some of ancient design, but gul designs were often used by more than one tribe, and by non-Turkmens. [ 4 ] [ 5 ]
Western authors have used comparison of the "design vocabulary" of tribal guls, reproduced on traditional rugs, in studying the ethnogenesis of Asian peoples. [ 6 ]
Western artists including Hans Memling depicted oriental carpets from Turkish Anatolia with guls in several of his paintings, to the extent that these are known as Memling carpets . These guls often contain star or (hooked) dragon motifs as found on 15th century Konya carpets. [ 7 ] The presence of the hooked motif defines a "Memling carpet". [ 8 ] The artists Lorenzo Lotto and Hans Holbein who similarly depicted Anatolian carpets also have the varieties they painted named after them. [ 9 ] | https://en.wikipedia.org/wiki/Gul_(design) |
Gul Bahao is an environmental non-governmental organization based in Karachi , Sindh , Pakistan . It has received international recognition for its work on environmental research in the country. [ 1 ] [ 2 ] [ 3 ] Along with its research activities, has provided practical solutions for low cost housing, water sanitation, and garbage disposal. [ 4 ] [ 5 ] [ 6 ] [ 7 ]
Nargis Latif runs Gul Bahao which is situated in Karachi . The city produces 12,000 tonnes of garbage every day, Nargis Latif's team has established a recycling system there. Gul Bahao recycle garbage and create houses, water reservoirs and swimming pools out of it. Blocks created by Chandi technology are used for the construction of houses. [ 8 ]
This article about an organization in Pakistan is a stub . You can help Wikipedia by expanding it .
This environment -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Gul_Bahao |
The Gulf Petrochemicals and Chemicals Association ( GPCA ) represents the downstream hydrocarbon industry in the Arab states of the Persian Gulf . Established in 2006, the association voices the common interests of more than 230 member companies from the chemical and allied industries, accounting for over 95% of chemical output in the Persian Gulf region. The industry makes up the second largest manufacturing sector in the region, producing up to US$97.3 billion worth of products a year.
The association supports the region's petrochemical and chemical industry through advocacy, networking and thought leadership initiatives.
The GPCA manages six working committees – Plastics , Supply Chain , Fertilizers , International Trade, Research and Innovation, and Responsible Care – and organizes six conferences each year. The association also publishes an annual report, regular newsletters and reports.
The Chairman of Gulf Petrochemicals and Chemicals Association (GPCA) is Yousef Al-Benyan, Vice Chairman & CEO SABIC.
This article about a chemistry organization is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Gulf_Petrochemicals_and_Chemicals_Association |
The Gulf of St. Lawrence lowland forests are a temperate broadleaf and mixed forest ecoregion of Eastern Canada , as defined by the World Wildlife Fund (WWF) categorization system. [ 2 ]
Located on the Gulf of Saint Lawrence , the world's largest estuary, this ecoregion covers all of Prince Edward Island , the Les Îles-de-la-Madeleine of Quebec, most of east-central New Brunswick , the Annapolis Valley , Minas Basin and the Northumberland Strait coast of Nova Scotia . This area has a coastal climate of warm summers and cold and snowy winters with an average annual temperature of around 5 °C going up to 15 °C in summer, the coast is warmer than the islands or the sheltered inland valleys. [ 3 ]
The colder climate allows more hardwood trees to grow in the Gulf of St Lawrence than in most of this part of northeast North America. Trees of the region include eastern hemlock ( Tsuga canadensis ), balsam fir ( Abies balsamea ), American elm ( Ulmus americana ), black ash ( Fraxinus nigra ), eastern white pine ( Pinus strobus ), red maple ( Acer rubrum ), northern red oak ( Quercus rubra ), black spruce ( Picea mariana ), red spruce ( Picea rubens ) and white spruce ( Picea glauca ).
The forests are home to a variety of wildlife including American black bear ( Ursus americanus ), moose ( Alces alces ), white-tailed deer ( Odocoileus virginianus ), red fox ( Vulpes vulpes ), snowshoe hare ( Lepus americanus ), North American porcupine ( Erithyzon dorsatum ), fisher ( Martes pennanti ), North American beaver ( Castor canadensis ), bobcat ( Lynx rufus ), American marten ( Martes americana ), raccoon ( Procyon lotor ) and muskrat ( Ondatra zibethica ). The area is habitat for maritime ringlet butterflies ( Coenonympha nipisiquit ) and other invertebrates. Birds include many seabirds, a large colony of great blue heron ( Ardea herodias ), the largest remaining population of the endangered piping plover , and one of the largest colonies of double-crested cormorant ( Phalacrocorax auritus ) in the world.
Most of this ecoregion has been altered by logging and clearance for agriculture with only 3% of the original habitat remaining and that highly fragmented. The only large block of intact habitat remains in the area around Kouchibouguac National Park in New Brunswick, although even here logging is ongoing. | https://en.wikipedia.org/wiki/Gulf_of_St._Lawrence_lowland_forests |
A gully is a landform created by running water , mass movement , or both, which erodes soil to a sharp angle, typically on a hillside or in river floodplains or terraces . [ 1 ]
Gullies resemble large ditches or small valleys , but are metres to tens of metres in depth and width, are characterized by a distinct 'headscarp' or ' headwall ' and progress by headward (i.e., upstream) erosion . Gullies are commonly related to intermittent or ephemeral water flow, usually associated with localised intense or protracted rainfall events or snowmelt.
Gullies can be formed and accelerated by cultivation practices on hillslopes (often gentle gradients) in farmland , and they can develop rapidly in rangelands from existing natural erosion forms subject to vegetative cover removal and livestock activity. [ 2 ]
The earliest known usage of the term is from 1657. It originates from the French word goulet , a diminutive form of goule which means throat . The term may be connected to the name of a type of knife used at the time, a gully-knife. [ citation needed ]
Water erosion is more likely to occur on steep terrain because of erosive pressures, splashes, scour, and transport. Slope characteristics, such as slope length and amounts proportionate to slope length, affect soil erosion. Relief and soil erosion are positively correlated in southeast Nigeria. [ 3 ] There are three types of topography: mountains, cuesta landscapes, and plains and lowlands. While highlands with stable lithology avoid gullying yet allow for vigorous runoff, uplands with friable sandstones are more prone to erosion. [ citation needed ]
Gully erosion can progress through a variety and combination of processes. The erosion processes include incision and bank erosion by water flow, mass movement of saturated or unsaturated bank or wall material, groundwater seepage - sapping the overlying material, collapse of soil pipes or tunnels in dispersive soils, or a combination of these to a greater or lesser degree. Hillsides are more prone to gully erosion when they are cleared of vegetation cover through deforestation , over-grazing , or other means. Gullies in rangelands can be initiated by concentrated water flow down tracks worn by livestock or vehicle tracks. The flowing water easily carries the eroded soil after being dislodged from the ground, typically when rainfall falls during short, intense storms such as thunderstorms .
A gully may grow in length through headward (i.e., upstream) erosion at a knick point . This erosion can result from interflow and soil piping ( internal erosion ) as well as surface runoff . Gully erosion may also advance laterally through similar methods, including mass movement, acting on the gully walls (banks), and the development of 'branches' (a type of tributary ).
Gullies reduce the productivity of farmlands where they incise into the land and produce sediment that may choke downstream waterbodies and reduce water quality within the drainage system and lake or coastal system. Because of this, much effort is invested into the study of gullies within the scope of geomorphology and soil science , in the prevention of gully erosion, and the in remediation and rehabilitation of gullied landscapes. The total soil loss from gully formation and subsequent downstream river sedimentation can be substantial, especially from unstable soil materials prone to dispersion .
When water is directed over exposed ground, gully erosion removes soil near drainage lines. This may result in divided properties, loss of arable land, diminished amenities, and decreased property values. Additionally, it can lead to sedimentation, discoloration of the water supply, and creating a haven for rodents. [ 4 ]
Water rushing over exposed, naked soil creates gullies and ridges that erode rock and soil. When water rushes across exposed terrain, it erodes or pushes dirt away, creating rills. Gravity causes rift erosion on a downward slope, with steeper slopes generating greater water flow. Sandier terrains are more commonly affected by rills most prevalent during the rainier months. Gullies develop when a rill is neglected for an extended time, thickening and expanding as soil erosion persists. [ 5 ]
The factors influencing gully erosion were investigated in Zaria, Kaduna state, Nigeria, utilizing SRTM data, soil samples, rainfall data, and satellite imagery. The findings indicated that the factors that had the biggest effects on gully erosion were slope (56%) and rainfall (26%), land cover (12%), and soil (6%). The investigation concluded that each particular component significantly influenced soil loss. [ 6 ]
The loss of fertile farmland due to gully erosion is a severe environmental problem that lowers crop quality and may cause famine and food shortages. It also causes the soil to lose organic content, which has an impact on plant viability. As items washed from fields end up in rivers, streams, or vacant land, erosion also contaminates the ecosystem. Because of increased population expansion and increasing land demand, erosion also threatens the natural ecosystem, encroaching on natural forests. Important assets including homes, power poles, and water pipelines may also be destroyed. [ 7 ]
Effective land management techniques can prevent gullies. These techniques include keeping vegetation along drainage lines, using more water, classifying drainage lines as distinct land classes, stabilizing erosion, preventing vermin, distributing runoff evenly, keeping soil organic matter levels high, and avoiding over-cultivation. These tactics guarantee uniform rates of penetration and robust plant coverage. [ 4 ]
One serious environmental problem endangering sustainable development is gully erosion. Gullying prevention and control methods are dispersed and lacking, and they have low success and efficacy rates. [ 8 ] This review attempts to make a valuable contribution to effective gully prevention and management techniques by combining information from previous research. It is possible to stop the creation of gullies by changing how land is used, conserving water and soil, or implementing specific actions in areas with concentrated flow. [ 9 ] Plant leftovers and other vegetation barriers can prevent erosion, although their usefulness is limited. The biophysical environment, terrain, climate, and geomorphology are examples of external elements that affect gully prevention and control. [ 10 ]
Stabilizing gullies entails altering water flow to lessen scouring, sediment buildup, and revegetation. Water can be securely moved from the natural level to the gully floor using a variety of structures, including drop structures, pipe structures, grass chutes, and rock chutes. Structural modifications can be required along steep gully floors. Vegetation can reestablish itself thanks to sediments deposited over flatter gradients. Until the restoration is finished, damaged areas should be walled off. [ 11 ]
Eastern Nigeria's people and ecology are seriously threatened by gully erosion. A research project focused on 370 families and nine risk regions evaluated the region's gully erosion issues. [ 12 ] The greatest perceived problem, according to the results, was biodiversity loss. In contrast, damage to properties, roads, and walkways was ranked as the least important issue. This implies a notable variation in the average evaluations across impacted individuals, underscoring the necessity for long-term repair approaches. Reducing soil loss, raising public knowledge of environmental issues, passing environmental legislation, and giving residents funds to strengthen their coping mechanisms are all advised by the study. [ 13 ]
In Agulu-Nanka, Southeast Nigeria, a study examined the geoenvironmental causes driving gully erosion. It focuses on catchment management for gully erosion and geotechnical analysis. [ 14 ] Through fieldwork, data was gathered utilizing GIS and GPS methods. According to the study, gully erosion occurs throughout, with Nanka/Oko having the highest concentration. The gully characteristic map shows variations in length and depth, emphasizing the necessity of considering gully vulnerability and giving erosion hazards immediate attention. [ 15 ]
Gullies can be formed or enlarged by several human activities.
Artificial gullies are formed during hydraulic mining when jets or streams of water are projected onto soft alluvial deposits to extract gold or tin ore . The remains of such mining methods are very visible landform features in old goldfields such as in California and northern Spain. The badlands at Las Medulas , for example, was created during the Roman period by hushing or hydraulic mining of the gold-rich alluvium with water supplied by numerous aqueducts tapping nearby rivers. [ 16 ] Each aqueduct produced large gullies below by erosion of the soft deposits. The effluvium was carefully washed with smaller streams of water to extract the nuggets and gold dust. [ citation needed ]
Gully initiation results from localized erosion by surface runoff, often focusing on areas where forest cover has been removed for agricultural purposes, uneven compaction of surface soils by foot and wheeled traffic, and poorly designed road culverts and gutters. [ 17 ] Termination of gully processes requires water-resource management, soil conservation, and community migration. Gully erosion is localized in the Coastal Plain Sands, Nanka Sands, and Nsukka Sandstone of the Anambra-Imo basin region. The most affected deposits are unconsolidated or poorly consolidated and have short dispersion times. Public education is essential for a sustainable termination strategy, and collaboration between the government, donors, the private sector, and rural people is crucial. [ 18 ]
Gullies are widespread at mid-to-high latitudes on the surface of Mars and are some of the youngest features observed on that planet, probably forming within the last few 100,000 years. There, they are one of the best lines of evidence for the presence of liquid water on Mars in the recent geological past, probably resulting from the slight melting of snowpacks on the surface [ 19 ] or ice in the shallow subsurface [ 20 ] on the warmest days of the Martian year. Flow as springs from deeper seated liquid water aquifers in the deeper subsurface is also a possible explanation for the formation of some Martian gullies. [ 21 ] | https://en.wikipedia.org/wiki/Gully |
Gummed film refers to a technique used to measure nuclear fallout . It involves the use of a sheet of plastic ( cellulose acetate ) or paper substrate coated on one side with an adhesive (e.g., rubber cement ). [ 1 ] The sheet is exposed (adhesive-side up) to the environment to be monitored, where fallout particles land on (and thus adhere to) the gummed film. After some period, the films are collected and analyzed for radioactivity. [ 2 ]
This radioactivity –related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Gummed_film |
Gun-type fission weapons are fission -based nuclear weapons whose design assembles their fissile material into a supercritical mass by the use of the "gun" method: shooting one piece of sub-critical material into another. Although this is sometimes pictured as two sub-critical hemispheres driven together to make a supercritical sphere, typically a hollow projectile is shot onto a spike, which fills the hole in its center. Its name is a reference to the fact that it is shooting the material through an artillery barrel as if it were a projectile.
Since it is a slow and asymmetrical method of assembly, weapons-grade plutonium cannot be used. The presence of the isotope 240 Pu , with its high spontaneous fission rate, causes predetonation . It is extremely impractical to produce plutonium of the required isotopic purity in a reactor. Additionally, the required amount of highly enriched uranium is relatively large, and thus the overall efficiency is relatively low. The main reason for this is the fissile material does not undergo compression (and resulting density increase) as does the implosion design. Instead, gun-type bombs assemble the supercritical mass by amassing such a large quantity of uranium that the overall distance through which daughter neutrons must travel has so many mean free paths it becomes very probable most neutrons will find uranium nuclei to collide with, before escaping the supercritical mass.
The first time gun-type fission weapons were discussed was as part of the British Tube Alloys nuclear bomb development program, the world's first nuclear bomb development program. [ 1 ] The British MAUD Report [ 2 ] of 1941 laid out how "an effective uranium bomb which, containing some 25 lb of active material, would be equivalent as regards destructive effect to 1,800 tons of T.N.T". [ 3 ] The bomb would use the gun-type design "to bring the two halves together at high velocity and it is proposed to do this by firing them together with charges of ordinary explosive in a form of double gun". [ 4 ]
The method was applied in four known US programs. First, the " Little Boy " weapon which was detonated over Hiroshima and several additional units of the same design prepared after World War II, in 40 Mark 8 bombs, and their replacement, 40 Mark 11 bombs. Both the Mark 8 and Mark 11 designs were intended for use as earth-penetrating bombs (see nuclear bunker buster ), for which the gun-type method was preferred for a time by designers who were less than certain that early implosion-type weapons would successfully detonate following an impact. The second program was a family of 11-inch (280 mm) nuclear artillery shells, the W9 and its derivative W19 , plus a repackaged W19 in a 16-inch (406 mm) shell for US Navy battleships, the W23 . The third family was an 8-inch (203 mm) artillery shell, the W33 .
South Africa also developed six nuclear bombs based on the gun-type principle, and was working on missile warheads using the same basic design – See South Africa and weapons of mass destruction .
There are currently no known gun-type weapons in service: advanced nuclear weapon states tended to abandon the design in favor of the implosion-type weapons , boosted fission weapons , and thermonuclear weapons . New nuclear weapon states tend to develop boosted fission and thermonuclear weapons only. All known gun-type nuclear weapons previously built worldwide have been dismantled.
The "gun" method is roughly how the Little Boy weapon, which was detonated over Hiroshima , worked, using uranium-235 as its fissile material. In the Little Boy design, the U-235 "bullet" had a mass of around 86 pounds (39 kg), and it was 7 inches (17.8 cm) long, with a diameter of 6.25 inches (15.9 cm). The hollow cylindrical shape made it subcritical. It was powered by a cordite charge. The uranium target spike was about 57.3 pounds (26 kg). Both the bullet and the target consisted of multiple rings stacked together.
The use of "rings" had two advantages: it allowed the larger bullet to confidently remain subcritical (the hollow column served to keep the material from having too much contact with other material), and it allowed sub-critical assemblies to be tested using the same bullet but with just one ring.
The barrel had an inside diameter of 6.5 inches (16.5 cm). Its length was 70.8 inches (1.8 m), which allowed the bullet to accelerate to its final speed of about 1,000 feet per second (300 m/s) [ 5 ] before coming into contact with the target.
When the bullet is at a distance of 9.8 inches (25 cm), the combination becomes critical. This means that some free neutrons may cause the chain reaction to take place before the material could be fully joined (see nuclear chain reaction ).
Typically the chain reaction takes less than 1 μs (100 shakes ), during which time the bullet travels only 0.3 mm ( 1 ⁄ 85 inch). Although the chain reaction is slower when the supercriticality is low, it still happens in a time so brief that the bullet hardly moves in that time.
This could cause a fizzle , a predetonation which would blow the material apart before creating much of an explosion. Thus, it is important that the frequency at which free neutrons occur is kept low, compared with the assembly time from this point. This also means that the speed of the projectile must be sufficiently high; its speed can be increased but this requires a longer and heavier barrel, or a higher pressure of the propellant gas for greater acceleration of the bullet subcritical mass.
In the case of Little Boy, the 20% 238 U in the uranium had 70 spontaneous fissions per second. With the fissionable material in a supercritical state, each gave a large probability of detonation: each fission creates on average 2.52 neutrons, which each have a probability of more than 1:2.52 of creating another fission. During the 1.35 ms of supercriticality prior to full assembly, there was a 10% probability of a fission, with somewhat less probability of pre-detonation.
Initially the Manhattan Project gun-type effort was directed at making a gun weapon that used plutonium as its source of fissile material, known as the " Thin Man " because of its extreme length. It was thought that if a plutonium gun-type bomb could be created, then the uranium gun-type bomb would be very easy to make by comparison. However, it was discovered in April 1944 that reactor -bred plutonium ( Pu-239 ) is contaminated with another isotope of plutonium, Pu-240 , which increases the material's spontaneous neutron-release rate, making pre-detonation inevitable. For this reason, a gun-type bomb is thought to only be usable with enriched uranium fuel. It is unknown though possible to make a composite design using high grade plutonium in the bullet only.
After it was discovered that the "Thin Man" program would not be successful, Los Alamos redirected its efforts into creating the implosion-type plutonium weapon: " Fat Man ". The gun program switched completely over to developing a uranium bomb.
Although in Little Boy 132 pounds (60 kg) of 80%-grade 235 U was used (hence 106 pounds or 48 kilograms), the minimum is about 44 to 55 pounds (20 to 25 kg), versus 33 pounds (15 kg) for the implosion method.
Little Boy's target subcritical mass was enclosed in a neutron reflector made of tungsten carbide (WC). The presence of a neutron reflector reduced neutron losses during the chain reaction, and so reduced the quantity of uranium fuel needed. A more effective reflector material would be metallic beryllium, but this was not known until the postwar years when Ted Taylor developed an implosion design known as "Scorpion".
The scientists who designed the "Little Boy" weapon were confident enough of its success that they did not field-test a design before using it in war (though scientists such as Louis Slotin did perform non-destructive tests with sub-critical assemblies, dangerous experiments nicknamed " tickling the dragon's tail "). In any event, it could not be tested before being deployed, as there was only sufficient U-235 available for one device. Even though the design was never proof-tested, there was thought to be no risk of the device being captured by an enemy if it malfunctioned.
Even a "fizzle" would have completely disintegrated the device, while the multiple redundancies built into the "Little Boy" design meant there was negligible, if any, potential for the device to strike the ground without detonating at all.
For a quick start of the chain reaction at the right moment a neutron trigger/initiator is used. An initiator is not strictly necessary for an effective gun design, [ 6 ] [ 5 ] as long as the design uses "target capture" (in essence, ensuring that the two subcritical masses, once fired together, cannot come apart until they explode). Considering the 70 spontaneous fissions per second, this only causes a delay of a few times 1/70 second, which in this case does not matter. Initiators were only added to Little Boy late in its design.
With regard to the risk of proliferation and use by terrorists , the relatively simple design is a concern, as it does not require as much fine engineering or manufacturing as other methods. With enough highly enriched uranium, nations or groups with relatively low levels of technological sophistication could create an inefficient—though still quite powerful—gun-type nuclear weapon.
For technologically advanced states the gun-type method is now essentially obsolete, for reasons of efficiency and safety (discussed above).
The gun type method was largely abandoned by the United States as soon as the implosion technique was perfected, though it was retained in the specialised role of nuclear artillery for a time. Other nuclear powers, such as the United Kingdom and Soviet Union , never built an example of this type of weapon. Besides requiring the use of highly enriched U-235, the technique has other severe limitations. The implosion technique is much better suited to the various methods employed to reduce the mass of the weapon and increase the proportion of material which fissions. Apartheid South Africa built around five gun-type weapons, and no implosion-type weapons. They later abandoned their nuclear weapon program altogether. They were unique in their abandonment of nuclear weapons, and probably also by building gun-type weapons rather than implosion-type weapons.
There are also safety problems with gun-type weapons. For example, it is inherently dangerous to have a weapon containing a quantity and shape of fissile material that can form a critical mass through a relatively simple accident. Furthermore, if the weapon is dropped from an aircraft into the sea, then the moderating effect of the seawater can also cause a criticality accident without the weapon even being physically damaged. Neither can happen with an implosion-type weapon, since there is normally insufficient fissile material to form a critical mass without the correct detonation of the explosive lenses.
The gun method has also been applied for nuclear artillery shells, since the simpler design can be more easily engineered to withstand the rapid acceleration and g-forces imparted by an artillery gun, and since the smaller diameter of the gun-type design can be relatively easily fitted to projectiles that can be fired from existing artillery.
A US gun-type nuclear artillery weapon, the W9 , was tested on May 25, 1953, at the Nevada Test Site . Fired as part of Operation Upshot–Knothole and codenamed Shot GRABLE , a 280 mm (11 in) shell was fired 10,000 m (33,000 ft) and detonated 160 m (520 ft) above the ground with an estimated yield of 15 kilotons . This is approximately the same yield as Little Boy , although the W9 had less than 1 ⁄ 10 of Little Boy's weight (365 kg vs. 4,000 kg, or 805 lbs vs. 8,819 lbs). The shell was 1,384 mm (54.5 in) long.
This was the only nuclear artillery shell ever actually fired (from an artillery gun) in the US test program. It was fired from a specially built artillery piece, nicknamed Atomic Annie . Eighty shells were produced from 1952 to 1953. It was retired in 1957.
The W19 was also a 280 mm gun-type nuclear shell, a longer version of the W-9. Eighty warheads were produced and the system was retired in 1963.
The W33 was a smaller, 8 inch (203 mm) gun-type nuclear artillery shell, which was produced starting in 1957 and in service until 1992. Two were test fired (detonated, not fired from an artillery gun), one hung under a balloon in the open air, and one in a tunnel. [ 7 ]
Later versions were based on the implosion design. | https://en.wikipedia.org/wiki/Gun-type_fission_weapon |
Gunda I. Georg is a chemist who is currently the Professor and Head of the Department of Medicinal Chemistry, [ 1 ] Regents Professor, [ 2 ] McKnight Presidential Chair, Robert Vince Endowed Chair at University of Minnesota and a former Co-Editor-in-Chief of American Chemical Society 's Journal of Medicinal Chemistry . [ 3 ] Her research interests are total synthesis and semisynthesis as well as evaluating biologically active agents. [ 4 ] A cited expert in her field, [ 5 ] she was elected to the American Association for the Advancement of Science in 1996 [ 6 ] and inducted in the Medicinal Chemistry Hall of Fame in 2017. [ 7 ] In 2019, she was announced as the 2020 winner and first woman to receive the Alfred Burger Award in Medicinal Chemistry (established by GlaxoSmithKline, now sponsored by Gilead [ 8 ] ). [ 9 ] She along with chemists, Shameem Syeda and Gustavo Blanco, are leading researchers in male contraception. [ 10 ] Dr Georg also works with her research groups to conduct research on Alzheimer's disease, epilepsy and cancer experimental therapeutics. [ 11 ]
She earned her B.S. in 1975 and Ph.D. in 1980 from Philipps Universitat Marburg . [ 12 ]
Georg is the Principal Investigator for a National Institutes of Health Center grant [ 13 ] for the Contraceptive Discovery, Development and Behavioral Research Center funded from 2017 to 2021. The grant work is in five interdisciplinary groups that are working on the discovery and development of non-hormonal male contraceptive agents and the investigation of contraceptive use. [ 14 ]
Georg's work is described in over 250 peer-reviewed publications [ 15 ] and she holds a number of patents.
She co-authored a book with Lednicer and Mitscher (RIP).
Her medical contributions include polishing off Gamendazole , Lonidamine and Pregnenolyne derivatives. | https://en.wikipedia.org/wiki/Gunda_Georg |
The Gunderson Do-All Machine is a colorful, interconnected network of dozens of machines that have been cross-sectioned to reveal their internal operating mechanisms. It was designed by Mark Gunderson to illustrate mechanical concepts.
The Gunderson Do-All Machine includes more than 30 individual machines that are linked together by an array of belts, gears, pulleys, and transmissions. Collectively, they operate in a continuous chain reaction on the power of one 10-horsepower (7.5 kW) Whitte gas oil well engine, forming a kinetic sculpture . The entire network is mounted on a 15-foot (4.6 m) flat bed trailer platform, so that it can be transported to engine shows, educational venues, and county fairs. The combined weight of the trailer and all components is about 6000 pounds.
The Do-All's layout and design allows one to follow the chain reaction from machine to machine while observing the internal cogs , gears , and other components that make them work. The variety of machines include an automatically reversing worm gear , a water pump impellar, a governor/gas valve from a 20- horsepower (HP) JC engine, a blacksmith blower/bubble maker, the main line shaft and pulley from an antique corn grinder, a floating gear, a DC 110- volt generator and lights, a 38-to-1 gear reducer, a bicycle light generator , and a fan blower painted to look like a clown. Recent additions include a penny press that creates a commemorative Do-All Machine coin and a rotating satellite dish with sun and moon images painted on opposite sides.
The Gunderson Do-All includes the following major engines that have been cut away to reveal their inner workings in action: | https://en.wikipedia.org/wiki/Gunderson_Do-All_Machine |
Gunnar Aksnes (8 August 1926 in Kvam , Hardanger – 31 January 2010 in Bergen , Hordaland ) was a Norwegian chemist and poet, [ 1 ] [ 2 ] the brother of the astronomer Kaare Aksnes , [ 3 ] married to Milly Aksnes (b. 1928) [ 4 ]
Aksnes started his studies in 1945 at the University of Oslo where he completed Mag.Scient exam in 1951. He was then employed by the Norwegian Forsvarets Forskningsinstitutt (FFI), and where he worked with problem related to chemical warfare agent until 1960. Then turning his Heimatt to the West Coast, to assistant professor of organic chemistry at the Department of Chemistry at the University of Bergen (UiB). In 1962 Aksnes defended his Dr.Philos. degree, and was appointed Professor of Organic Chemistry at the UiB in 1966, a position he filled with relish until he resigned in August 1993. Some years after this he was still active at the Department of Chemistrywith holding a senior scholarship from 'Norges Allmennvitenskapelige Forskningsråd' (NAVF). [ 1 ] [ 2 ]
His academic interests ranged wide. Through his work on nerve gases at FFI he was attracted to the phosphorus chemistry. This was his major research field in which he published articles through the years, including many important scientific works that made his name well known in the scientific community world wide. In the late 1970s he started to work with chemical problems connected to environmental issues. As one of the first chemists in Norway, he recognized the importance of inter-disciplinary cooperation when scientists work on solving multi-disciplinary problems. He took a strong interest in NAVF major Research program on marine pollution and built up a team of specialists in oil chemistry at the University of Bergen, together with younger employees. Later he focused on pollution of lakes, and here his knowledge of chemistry came to its right, when he extracted new knowledge from the previously published data. [ 1 ]
Aksnes was a popular lecturer, and all his students at the basic course in organic chemistry remember his loudly, involved explanations about organic molecule that moves and reacts. As a student mentor, he was always interested in the work of the students, and he asked critical questions that helped developing critical thinking and expanded the mind of the student. He also raised critical questions in popular scientific articles in professional magazines, the last concerning the mercury of the German U-boat in the fjord off Fedje. Through articles and interviews in the press, and through several popular books on environmental issues for nonscientists, he showed his engagement throughout his lifetime. He served in several administrative tasks, not only on at the Faculty of Mathematics and Natural Sciences (Dean 1969-72) and head of the Chemical institute (1991–93) at UiB, but also as a member of Council of Natural Sciences at NAVF (1970–76, as leader 1970–71). [ 1 ]
Aksnes also wrote poems, and in 2001 he published the book Med penn og pensel i Hardanger (With pen and brush in Hardanger) with the publisher 'Hardangerforlaget' in Øystese . The book was richly illustrated by his wife Milly Aksnes. The poems in the book were written in the period from 1970 to 2001, and the illustrations are inspired by the scenery of Hardanger. [ 4 ] | https://en.wikipedia.org/wiki/Gunnar_Aksnes |
Gunnar Hägg (December 14, 1903 in Stockholm – May 28, 1986 in Uppsala ) [ 1 ] was a Swedish chemist and crystallographer. [ 2 ]
Hägg studied chemistry at Stockholm University from 1922, was a Ramsay Fellow at the University of London in 1926, studying under Frederick G. Donnan . [ 3 ] He obtained his PhD in Stockholm in 1929 under Arne Westgren for the work X-ray studies on the binary systems of iron with nitrogen, phosphorus, arsenic, antimony and bismuth . After that he became a lecturer at the Stockholm University and in 1930 at the University of Jena , Germany. In 1937 he became professor of inorganic and general chemistry at Uppsala University . He retired in 1969.
Hägg's research dealt with nitrides, borides, carbides and hydrides of transition metals and determined their crystal structure with X-ray diffraction. He also developed X-ray cameras and calculating machines for this purpose. His investigations into phases and phase transformations in steel had practical applications. In Sweden he is known for his university chemistry textbooks. [ 2 ]
He was a member of the Royal Society of Sciences in Uppsala (1940), the Royal Swedish Academy of Sciences (1942), the Royal Physiographic Society in Lund (1943) and the Royal Swedish Academy of Engineering Sciences , from which he received the Great Gold Medal in 1969. In 1960 he also became a member of the German National Academy of Sciences Leopoldina . A room in Uppsala University 's Ångstrom Laboratory is named after him. In 1968 he received the Oscar Carlson Medal and in 1997 the Gunnar Starck Medal from the Swedish Chemical Society . [ 4 ] From 1965 to 1976 he was a member of the Nobel Committee for Chemistry (and chairman in 1976). [ 5 ] | https://en.wikipedia.org/wiki/Gunnar_Hägg |
In astronomical spectroscopy , the Gunn–Peterson trough is a feature of the spectra of bright high redshift sources, particularly quasars and gamma-ray burst afterglows, due to the presence of neutral hydrogen in the Intergalactic medium (IGM) before the epoch of reionization . The trough is characterized by suppression of electromagnetic emission from the source at wavelengths just below that of a redshifted Lyman series line. As the radiation came towards us and was progressively redshifted, photons at wavelengths higher than that line were never absorbed by the hydrogen because they did not have enough energy to cause the ground-state hydrogen to jump to the higher state corresponding to the line, whereas photons of somewhat higher energy were absorbed when they got redshifted to the wavelength of the line (for instance 91 nanometres for the Lyman alpha line). Photons of even higher energy did not get redshifted to the appropriate wavelength until after the hydrogen of the intergaalactic medium was reionized, and so were not absorbed. The trough is thus the span of wavelengths where absorption did take place. The low-wavelength end of the trough is at a redshift of about 6 from the true Lyman wavelength, since reioonization occurred around the time corresponding to that redshift, whereas the high-wavelength end of the trough is at the redshift of the source, greater than 6.
This effect was originally predicted in 1965 by James E. Gunn and Bruce Peterson , [ 1 ] and independently by Peter Scheuer . [ 2 ]
For over three decades after the prediction, no objects had been found distant enough to show the Gunn–Peterson trough. It was not until 2001, with the discovery of a quasar with a redshift z = 6.28 by Robert Becker and others [ 3 ] using data from the Sloan Digital Sky Survey , that a Gunn–Peterson trough was finally observed. The article also included quasars at redshifts of z = 5.82 and z = 5.99, and, while each of these exhibited absorption of photons with energies just above that of the Lyman-alpha transition (or, wavelengths just to the blue side of the transition), there were numerous spikes in flux as well, indicating having traversed pockets of space with negligible neutral hydrogen. The flux of the quasar at z = 6.28, however, was effectively zero at energies just above that of Lyman-alpha transition, meaning that the neutral hydrogen fraction in the IGM must have been larger than ~10 −3 .
In the present day universe, the intergalactic medium (IGM; the space between galaxies) contains very low density plasma . Very early in the history of the universe, prior to the formation of the first stars, electrons and protons first became bound as neutral hydrogen atoms during an epoch known as recombination . The period during which the first objects in the universe started emitting light and energy that would drive the transition from neutral to ionized matter in the IGM is known as reionization . The study of objects with Gunn–Peterson troughs in their spectra provide a means for studying the late phases of this epoch of reionization.
The discovery of the Gunn–Peterson trough in a z = 6.28 quasar indicated that the universe still had an appreciable, if small, neutral hydrogen fraction at that time. As photons with energies near that of the Lyman-alpha transition have scattering cross sections with neutral hydrogen that are very high, even a small fraction of neutral hydrogen will make the optical depth of the IGM high enough to cause the suppression of emission. [ 4 ] Meanwhile, the absence of the trough in quasars detected at redshifts just below z = 6 presented evidence for the process of reionization having completed by about z = 6. [ 3 ] Subsequent to the original discovery of a Gunn–Peterson trough, detection of a trough as low as z ≈ 5.6 suggests that reionization of the universe is inhomogeneous and incomplete at z = 5.6. [ 5 ]
Following the first release of data from the WMAP spacecraft in 2003, the determination by Becker that the end of reionization occurred at z ≈ 6 appeared to conflict with estimates made from the WMAP measurement of the electron column density. [ 6 ] However, the WMAP III data released in 2006 now seems to be in much better agreement with the limits on reionization placed by observation of the Gunn–Peterson trough. [ 7 ]
Recent observations of quasi-stellar objects have shown strong absorption gaps in regions with redshifts as low as z ≈ 5.3 indicating that reionization was not uniformly spread through the IGM. [ 8 ] Simulations have shown that low-mass galaxies could have initially contributed to reionization until their star formation was radiatively suppressed, potentially explaining these islands of neutral hydrogen persisting at lower redshifts. [ 9 ]
It has also been shown that islands of neutral hydrogen cannot account for absorption gaps alone, leading to investigation of dense systems within ionized regions of the IGM referred to as Lyman Limit Systems or small scale absorbers. This is supported by the abundance of these systems in the post-reionization era as neutral hydrogen disappears. [ 10 ] | https://en.wikipedia.org/wiki/Gunn–Peterson_trough |
Gundam Plastic models , Gundam Plamo , or Gunpla ( ガンプラ , Ganpura ) [ 1 ] are model kits depicting the mecha machinery and characters of the fictional Gundam multiverse by Bandai Spirits .
These kits became popular among mecha anime fans and model enthusiasts in Japan and nearby Asian countries beginning in the 1980s. Gundam modeling spread in the 1990s with North America and Europe being exposed to Gundam through anime and manga .
The name Gunpla derives from an abbreviation of " Gun dam pla stic model" phrase, since most kits are made of plastic.
Bandai sold over 100 million Gundam plastic model units between 1980 and 1984, and over 300 million units by May 1999. [ 2 ] Recently, Bandai had sold an estimated 450 million units worldwide across nearly 2,000 different Gundam models. [ 3 ] As of March 2021 [update] , Bandai Namco has sold 714.84 million Gundam plastic model units, including 538.24 million standard Gundam units (since 1980) and 176.6 million SD Gundam units (since 1987). [ 2 ]
Gundam models are based on the Mobile Suit Gundam franchise, which debuted in 1979 as a television show. The show was not highly successful, and the toys produced by Clover did not sell well.
In 1980, Bandai obtained the rights to produce models based on the Gundam franchise. While Clover's models were produced in the style of most children's toys - fully assembled and ready for play - Bandai designed theirs as plastic kits to be assembled, similar to military vehicle models. [ 4 ] While Clover's products targeted children, Bandai's approach was more appealing to the teenage and adult consumers that were more typical of Mobile Suit Gundam's audience, and was received extremely well. [ 5 ]
Nearly every mecha in the series was made into a model kit, from mobile suits to support aircraft and space battleships. Parts came in up to three different cast-in colors. These early kits are distinguished by their lack of articulation and low detail and, unlike later generations, require glue to assemble.
A later development was System Injection , a technique which permitted a single "part" to be cast in multiple colors of plastic simultaneously, minimizing the need to paint the finished model. [ 6 ]
In 1985, Bandai introduced use of poly-caps (soft plastic, typically Polyethylene ) as connectors for better articulation of joints.
The 1987 model line for Gundam Sentinel introduced snap-fit models, which needed little or no glue to assemble. This would become standard in 1988, after which all kits use snap-fit assembly and no glue is needed.
In 1990, Bandai introduced the High Grade (HG) line, which began an ongoing process of increasing model quality, and the creation of a grade system to describe the detail and quality of each kit. HG kits had much higher detail and articulation, as well as features normally found in larger-scale models, despite being 1:144 scale . One example is the 'Gundam Core Block System', in which the pilot sits in a "Core" which can be removed from the Gundam to become a distinct vehicle, and the Zeta Gundam 's transformation feature.
In 1993, a unified set of poly-cap joints was created for smaller scale models that allowed easy mass production of models that all shared the same basic skeletal frame. This standardization allowed Bandai to release more models over a shorter period. As a result, the Gundam shows of the 1990s usually received sizable 1:144 model lines.
In 1995, the 1:100 scale Master Grade (MG) line was introduced. This line featured more parts, better detail and improved articulation than past kits of the same scale.
In 1998, Bandai introduced the 1:60 Perfect Grade (PG) line. This line features extensive detail and articulation, light-up features, and a "body on frame" skeletal system in which the exterior panels of the model are separate components attached to a completely functional, articulated internal frame. [ 7 ] This design element would later appear (sometimes in a limited form) in lower-grade models. [ 8 ] The PG line is typically the most expensive among all Gunpla kits, and only a select few mobile suits have been released in this line.
In 1999, to celebrate the 20th anniversary of the franchise, Bandai released 1:144 First Grade (FG) kits of mobile suits from the original series. Marketed as budget models, these snap-fit kits featured the simplicity of the original kits, but with more modern designs based upon the corresponding Perfect Grade kits.
For the Mobile Suit Gundam SEED models a new type of non-graded (NG) 1:144 model was introduced, with a completely different design plan. While these still feature snap-fit and color molding, they omit major joints, opting instead to only allow critical pieces to move—typically the neck, hips, shoulders, and feet. These are budget models, usually retailing much lower than other models; and this line was extensive, covering nearly every machine to be featured in that TV series.
Gundam SEED also featured non graded 1:100 models, identical in quality to Bandai's High Grade offerings.
It was also during this decade that the term "Gunpla" was coined by Bandai.
In 2010, Bandai released the 1:48 Mega Size Model RX-78-2 Gundam kit as part of the franchise's 30th anniversary campaign. This kit features many innovations that make it easy to assemble for first-time Gunpla collectors. For example, the parts are attached to sprue gates thin enough to break without the need to use of plastic cutters, and excess gate plastic can be removed from the parts without using a hobby knife . Some sprues have been designed to snap together for easy and quick removal of assembled parts. [ 9 ]
In the same year, Bandai introduced the 1:144 Real Grade (RG) line, which takes design elements from the MG line such as an inner skeletal frame to improve upon the HG line.
Both Mega Size Model and RG variants of the RX-78-2 Gundam were patterned after the 1/1 scale Gundam statue on display in Odaiba . Bandai also released Ecopla, a series of High Grade Universal Century (HGUC) and super deformed (SD) kits molded in black and made entirely out of recycled sprues.
In 2011, Bandai released the Entry Grade (EG) line, a low-cost model series similar to the 1:144 NG and FG lines, sold only in parts of Asia. Unlike other kits of the same scale, the first line of EG kits were made in China and the series was initially discontinued until the line was rebooted in 2020 with kits from non-Gundam franchises.
Also in 2011, Bandai introduced the Advanced Grade (AG) line, a budget line that focuses more on the arrangement of colored parts, thus sacrificing more articulation than the previous budget lines. The AG line incorporates a microchip that enables collectors to use the kit in the Gage-ing arcade game. [ 10 ]
In 2014, as part of the 35th anniversary celebration of Gundam , Bandai released the MG RX-78-2 Gundam ver. 3.0, which incorporates the engineering techniques used in the MG 2.0 and RG kits.
In 2015, Bandai introduced a sub-line of the HG called "HG Revive", which consists of re-engineered 1:144 scale kits of the RX-78-2 Gundam and other classic mobile suit designs.
From late 2016 onwards, every Bandai produced model kit, including Gunpla, were made with Japanese and English text on the box and manuals.
In 2017, Bandai began the Gundam Evolution Project, which sought to improve Gunpla technology with various groundbreaking kits, such as the adoption of a new joint system or a new LED system for large-scale kits. This was in preparation for the 40th anniversary of Gunpla in 2020.
Gundam model kits come in many varieties, but the majority made from the late 80s on - standard "plastic" kits - are manufactured and assembled similarly. Kits come as a collection of plastic parts, decals , and sometimes other decorative accessories which the purchaser assembles by hand into the finished model.
The plastic parts are delivered in the exact form they exit the injection molding machine , [ 11 ] on a " sprue tree" - a grid of interconnecting plastic rods, called runners, created by the channels in the mold that carried the molten plastic into the cavities that create each part. Each part is connected to the runners by a small plastic nub called a " gate " where the runner connected to the cavity.
The kit builder must cut away this excess plastic - e.g. with a pair of side cutting pliers - to free each part, then (optionally, but usually) clip, carve or sand away the remaining plastic tip where the gates attached to leave a clean surface.
Once the parts have been freed, the builder must then snap them together to assemble the model. Early kits required glue, but from the late 80s onward all kits assemble without special tools or materials.
Some kits use an internal frame - a complete "skeleton," fully articulated and able to stand on its own - to which panels are then attached to finish the appearance of the mecha.
When it comes time to assemble the panels making up the external appearance of the model, the builder may choose to customize the model in a wide variety of ways. [ 12 ] The most basic is simply to paint the model, which allows for a large amount of personal creativity. Applying decals is also a common technique - decals are included with most models, but are also available as separate products for customization.
Every conceivable modification is possible, with some more common options including:
All of these are optional, and the model can be assembled and displayed using nothing more than a side-cutter.
Most models, once assembled, are poseable to some degree. Many are "fully poseable," with a wide latitude of motion. To help hold models in "dynamic" poses, Gunpla can be mounted on a stand, with some recent models having a dedicated attachment point for this purpose.
Over the decades, Gundam plastic models have been available in many forms, with many levels of intricacy and functionality, from immobile display units that are static once assembled, to fully poseable, highly articulated models with interchangeable parts (weapons, shields, etc.) and complex mechanical engineering.
All parts fit together with a variety of glueless, toolless joints, such as ball-and-socket pivots, or posts on one component that fit tightly into holes on another. While models are designed to be posed for display, these joints are not intended to hold up to action figure-style play; even during gentle pose adjustments, it is possible for parts to come loose and need to be pushed back together.
Components are made of plastic materials selected to fit the needs of each part. A given unit, like a foot or leg, may use parts made of multiple different materials. Bandai casts colored pigment into each part to provide a basic color scheme for the finished model, so the builder does not need to paint it if undesired.
The picture above illustrates the detail level of a higher end (Real Grade, 2011) model. This is one part of the model's "foot", less than an inch across, which not only has many details in a very small component, but is built around a very small doubly-articulated hinge. The fully assembled leg unit uses many more parts which allow it to bend at two major joints, and also has trim panels which slide apart as the leg is bent to allow the motion.
Gundam model kits can be made of several materials.
The typical mass-market kit is made from thermoplastics , such as ABS , polypropylene or polystyrene . These are referred to in the community simply as "plastic" models, and use the snap-fit assembly method described in this article.
Plastic Gundam model kits are manufactured in Japan or China by Bandai , which has an exclusive license in manufacturing and marketing them around the world.
A less common type, known as a garage kit or resin kit , is made from a thermoset resin , typically polyurethane , often simply referred to as "resin." [ 13 ] These are not assembled with the snap-fit approach, and the builder must assemble them with glue. Many other assertions of this article will also not apply to resin kits, since they make up a very small minority of the product line.
Garage kits were originally made by amateur or small-scale manufacturers (hence the name,) a cottage industry that predates Gunpla, [ 14 ] but Bandai has released some first-party Gundam resin kits under a separate marque, B-Club . These models are made of unpainted resin with no decals provided and often require touch-up work by the builder due to the inherent limitations of the manufacturing process.
While comparably more expensive (some surpassing $400) and more complex to assemble compared to plastic kits, they offer higher detail for the dedicated and experienced model builder.
A few select kits have also been manufactured from metal. These kits are offered by several different manufacturers and most commonly will result in a finished model of about MG level. These types of models usually take days to build.
As with hobby models based on real-world military equipment, Gundam models are intended to be "scaled down" replicas of realistic designs, based on the dimensions given in the fiction. These scales are given in terms of the ratio of actual model size to the size the machine would have if it were actually built. 1:60, for instance, means that every inch of the models height is equivalent to 60 inches of the machines height if it was real.
Generally, finished model heights range from 4~5 inches for small-scale models, 6~8 inches for mid-scale models, and 12 inches for large-scale models. Common scales, and the grades typically associated with them, [ 15 ] include:
Bandai uses a naming convention called grade to denote its scale and detail, with 4 main model lines and several spinoff lines. Each line evolves with improved modelmaking technology over time, so a High Grade kit released in the 2020s will trounce the 2000s releases. In addition, singular Mobile Suits will be released in multiple lines several times with new designs. For example, the RX-78-2 Gundam has releases in almost every model line, commemorating the anniversary of the series and to display new technology.
With minor exceptions such as plastic mold damage, Gunpla kits are almost never officially discontinued.
The original 1980 line of Gundam models does not have an associated grade, since this terminology was not introduced until 1990. These kits are limited in articulation, some require glue to assemble, and they must be painted for a correct appearance. Model Kits released to coincide with a show or movie usually that did not have a grade associated with them are generally referred to as No Grade kits. These were released in 1/144, 1/100, or 1/60 scale (some 1/100 models used the High Grade name on their boxes).
After the adoption of the grade nomenclature, Bandai rereleased the designs of the RX-78-2 and Zaku II with minimal updates as First Grade (FG) starting in 1999. Four mobile suits from Gundam 00 were also given First Grade Models, with limited color separation.
Reissues of the original 1980 line are sometimes referred to as the Best Mecha Collection (BMC). For the 45th Anniversary of Gundam in 2024, a modern remake of the original RX-78-2 kit was released in October, called the BMC Revival version, which now features modern Gunpla techniques such as color separation and snap-fit parts while retaining it's limited articulation.
HG models were introduced in 1990. The original kits featured full snap-fit assembly, an articulated internal frame (for the first two kits, which provides better range of motion and is more poseable), and utilized the molding technique known as System Injection, wherein multiple colors would be cast on the same part. In 1999, the High Grade Universal Century Line was introduced, which collected mobile suits from the Universal Century Timeline. In 2010, the line was expanded to include mobile suits from Future Century, After Colony, After War, Correct Century, and Cosmic Era, and Gundam series that did not fit in those timeline (Like Gundam AGE or Iron Blooded Orphans) received their own HG lines.
In 2015, HG Revive, a subline within the HGUC line was introduced, which gave older HGUC kits redesigns that adhered to modern HG standards in terms of detail and articulation. The High Grade line is not exclusive to Gundam, as other mecha series, such as Mazinger , Kyoukai Senki , and Evangelion receiving HG kits of their own. HG Amplified IMGN was a subline introduced in 2022, which redesigned smaller robots (namely those from the Wataru series) with more humanoid proportions. A vast majority of HGs use polycaps , but Bandai has started to abandon the technology with the release of Witch From Mercury and Gundam SEED Freedom kits for better stability.
In 2010, Real Grade (RG) was released to celebrate the 30th anniversary of Gunpla. Real Grade kits are differentiated from HG kits by a number of features previously found only in larger scale kits, including near perfect color accuracy without the use of color-correcting stickers, a full inner frame, high part counts, advanced articulation, and extensive decals. These kits have also been redesigned to appear more "realistic" by adding additional surface detail, color separation and mechanical detail. Most RG kits use a technology called the Advanced MS Joint, where the inner frame for the chest, arms, legs, and feet are prebuilt and fully articulated, requiring the other parts to be attached to it. The rubbery nature of the prebuilt parts leads to the model deteriorating in stability if too much weight is put on the prebuilt parts. Later RG kits use the more stable Advanced MS Framework that combines limited use of prebuilt parts alongside traditional inner frame technology, or use the MS Joints exclusively in lightweight areas such as accessories or weapons.
For the 45th Anniversary of Gundam in 2024, the RX-78-2 Gundam Ver.2.0 was announced for August 2024, with a focus on realistic inner frame detailing and high articulation. It is also the first kit to abandon the MS Joint technology altogether.
The Real Grade line has also hosted mechas from Neon Genesis Evangelion and The King of Braves Gaogaigar . These do not use MS joints and emphasize other aspects of their design (The Evangelions use a universal inner frame and high color separation and the Gaogaigar features a complex combining design)
MG models were first introduced in the summer of 1995, designed and made to higher standards than most other models. These kits take longer to construct and are often more expensive than their lower-grade counterparts. [ 16 ] More recent Master Grade plastic models typically feature a movable inner frame system which enables extensive movement and bending of joints, as well as including standing and seating miniature figures of the pilots of each Gundam model.
Beginning in 2005 with the Zeta Gundam and Gundam Mk-II, Older MG Kits would be redesigned under the Ver.2.0 moniker with features such as improved articulation and a full inner frame. The RX-78-2 Gundam has had multiple MG iterations, including a Ver.1.5 that uses a mix of old and new parts, a Ver.2.0 that is more faithful to the original anime, a Ver.3.0 that is modeled after the life size statue similar to the Real Grade version, a version based on its appearance in Gundam The Origin , as well as a Ver.Ka and Ver.OYW (One Year War) version released to coincide with the video game of the same name.
The Master Grade line is not Gundam exclusive as a few Master Grade offerings have come from mechas in Patlabor and Dunbine . Bandai also released a line featuring a series of character figures from Dragon Ball Z , Kamen Rider , and Tiger & Bunny [ 17 ] under the name of MG Figure-rise .
In 2002, a new line of Master Grade kits subtitled "Ver. Ka" was released, which are Master Grades (re)designed by mecha designer Hajime Katoki . Mobile suits chosen to become Ver. Ka kits are chosen by annual fan votes. Ver. Ka kits are known for their highly realistic and complex gimmicks and designs, as well as an abundance of decals.
In 2020 a new line, Master Grade Extreme (abbreviated as MGEX), released as luxury-grade redesigns of Master Grades that contained additional gimmicks, called "Extreme Points", that exaggerate and amplify key appeals of the featured mobile suit. The first model kit of this line, the Unicorn Gundam Ver. Ka, contained an LED light strip that ran across the mobile suit, changing colors between the normal Unicorn and Destroy Mode. The second, Strike Freedom Gundam, released in November 2022 and uses metallic coated and plated parts for the inner frame, as well as the highest amount of joint part interactivity.
PG is the highest grade line of Bandai kits. The first PG Gunpla kit was a RX 78-2 Gundam model released in 1998, but an Evangelion Unit-01 kit labeled as Perfect Grade released the year prior. Only 19 kits have been released as 1/60 Perfect Grade since then. A Perfect Grade Millennium Falcon kit released in 2017 and was 1/72 scale instead of 1/60 scale. The first PG Unleashed kit was a RX 78-2 Gundam model released in December 2020.
As the name suggests, Perfect Grade Gunpla kits attempt to represent the Gundam as perfectly as possible within real world and design limitations. These limitations result in the Perfect Grade line sometimes taking several years between releases to wait for advances in model making technology. Perfect Grade Unleashed is an updated version of Perfect Grade that uses more advanced technology and concepts, such as the return of Advanced MS Joints, the use of LEDs, hard plastic stickers and metallic etched parts, multiple points of articulation in the same limb, and the Evolution Link System, where the construction is separated into multiple phases (starts with the bare inner frame, then the extra detail within the frame with metallic parts, then the armor attached to the frame) to simulate building a real mecha, with the final phase displaying the detail of the inner frame using multiple hatches.
Features like metal joints, increased detail in plastic molding and plastic quality, opening hatch gimmicks, as well as LED lighting kits are signatures of the PG line. [ 18 ]
Not based on any particular scale, the super-deformed style features comically proportioned models, the most noticeable features of which are their very large heads. Super Deformed Gundam kits are often very easy to construct and contain original gimmicks but offer very limited articulation and require paint and detailing.
The most famous line is BB Senshi (BB Warriors in English), which ran from 1987 to 2018. Various other SD gundam lines have run alongside and replaced it, including:
In 2011, Bandai released the Entry Grade (EG) line in Southeast Asia. Originally manufactured in China, the EG line contained fewer parts than the FG kits, thus having very limited articulation. Only four Gundams were released in the line. Bandai later rebooted the Entry Grade line in 2020 to be released worldwide. While most releases were static figurines from other franchises, the RX-78-2 Gundam was the starting Gundam model, with the kit having articulation and proportions similar to the High Grade kits and advanced color separated parts without the need of stickers or tools (for example, the silhouette in the eye that would normally be a sticker is done through shadow).
A smaller line beginning in 2023 as part of the Fun to Build GUNPLA campaign. The models can be assembled as a figure or on a faux runner for display. Gunpla-kun demonstrated the use of Limestone -based LIMEX plastic while the event-exclusive Zakupla-kun used plastic made from green tea leaves. The latter was released later using standard plastic in 2025.
A 1/100 scale model line focusing on replicating surface detail and complex "gimmick points" without the use of an inner frame like Master Grades. The line debuted in 2016 to coincide with the second season of Iron-Blooded Orphans before relaunching in 2021 with suits from Mobile Suit Gundam SEED and The Witch From Mercury.
A line of character figure model kits primarily focused on various anime, manga, and tokusatsu hero franchises like Dragon Ball, Ultraman, and Kamen Rider . The line also features characters owned by Bandai Namco, including human characters from the Gundam franchise.
A 1/144 scale accessory line consisting primarily of rereleases of older accessories under a new label, with new releases being designed to attach to most modern 1/144 scale kits.
Bandai's Shokugan division of candy toys releases Minipla models for combining mecha in the Super Sentai series. Each part of the mecha is sold in an individual box, or a full set can be purchased by individuals and vendors. Super Minipla (later renamed Shokugan Modeling Project and abbreviated as SMP) is a line containing higher-quality redesigns of older Super Sentai Models as well as combining mecha from other series.
A line of display bases that allow a Gundam model to be displayed in mid-air poses. 8 variations of the Action Base, meant for 1/144 scale, 1/100 scale, and SD kits have been released since 2006, and some models will have an action base included, although it is uncommon. With the exception of weight considerations, there is no strict rule as to what base can be used as long as it fits within the included adapter or x-millimeter peg on the bottom of most models.
Mega Size Model was a line released in 2010 to commemorate the franchises' 30th anniversary. The line was released in 1/48 scale, 3 times the size of their High Grade counterparts, and included simplified building techniques such as a parts separator and joint parts that can be connected without removing them from the runner. They also come with water decals and guides on customizing finished models. 5 suits were released throughout 2010 and 2011, with a Unicorn Gundam model being released in 2017.
Iropla was released in 1983 as a budget line. 4 kits were released in 1/250 scale and it was the first to use multi-colored runners for better color separation.
Haropla is a line of model kits based on Haro , a robot helper that appears in various Gundam timelines.
Speed Grade uses a scale of 1:200 and had parts prepainted on the runners.
Advanced Grade , released to coincide with Gundam AGE , had limited articulation (restricted to the head and shoulders) and came with microchips and trading cards for use with a Gundam AGE arcade game.
Gundam Collection is a line of 1/400 scale battleships and mobile armors released between 2003 and 2007 alongside a blind box figure line, utilizing painted parts instead of color molding.
High Grade Mechanics was a 1/550 scale line depicting 3 mobile armors from Gundam 0083: Stardust Memory.
EX Model is a line depicting support units in 1/144 and 1/100 scale and battleships in 1/1700 scale. These are similar to traditional vehicle models, requiring paint and glue for a complete appearance. This series is not Gundam-exclusive, having models from other series including Sentō Yōsei Yukikaze , Patlabor , and Batman .
HI-Resolution Models are 1/100 scale and, in addition to redesigning the mobile suit, included a pre-built inner frame similar to an action figure.
Hyper Hybrid Models (HY2Ms) include 1/100 scale Gundam heads modified to incorporate LED units or 1/60 scale models that have LED units across the body and require knowledge on electronics to make.
Reborn 1/100 kits are 1/100 scale and cover more obscure mobile suits and those that would be too large to make into a standard MG model. As such, these kits are less complicated than a typical MG kit.
Universal Century HardGraph (UCHG) was a 1/35 scale line focusing on military vehicles and dioramas that would be seen during the One Year War. Some releases include to-scale mecha parts, such as a Zaku head or a severed GM arm. The High Grade UC Hardgraph subline features 1/144 scale mobile suits and vehicle models.
A non-Gundam line that began in 2019, the 30 Minutes Label focuses on easy-to-build, highly customizable model kits. The line gets its name from its assembly system that enables modelers to complete the kit in as fast as 30 minutes. In addition to simplified joint structure allowing for the combination of multiple kits, the armor includes various 3mm holes to allow the use of multiple different weapon and armor sets. The 30 Minutes Label consists of four lines: [ 19 ] [ 20 ]
Gundam model building as a hobby is a worldwide phenomenon. [ 21 ] Participation ranges from simply assembling kits as sold, to mild personalization with paint and decals, to creating nearly original works with parts from multiple kits, additional custom-made components and in-depth, highly detailed multi-layer paint jobs.
Like any hobby, Gunpla building can be extremely involved and expensive, but with model kits starting at less than US$20 [ 22 ] and requiring no special tools or materials, barrier to entry is low.
Some hobbyists build dioramas around finished models [ 23 ] using techniques shared with other miniature model-based hobbies such as model railroading and wargaming. A diorama could depict a mecha in combat, undergoing maintenance or even destroyed on the battlefield.
Bandai holds an annual international contest, Gunpla Builders World Cup, [ 24 ] in at least 16 countries. Winners are awarded trophies and model kits. [ 25 ]
Gundam models are divided into series according to the media they are derived from.
Since 1999, the High Grade series uses various names to separate them from line to line.
The Gundam FIX Figuration [ 26 ] (aka G.F.F.) series of collectible figures was started based on the Gundam mechanical designs of Hajime Katoki and his 'Gundam FIX' illustration artbook and are released by Tamashii Nations , a Bandai 's characters based toys line. These figures share similar features as those found in the MSiA series, but are considerably more detailed and often include more accessories.
Changeable parts and variant models are often utilized throughout the line, offering the collector a wide variety of display abilities. The collectible figures use PVC (with some ABS plastic) for construction materials, and a recently introduced expansion to the line use metal in the skeleton of the figure. Gundam FIX figures are designed to be true to Hajime Katoki's vision, and as such often adopt design elements and styling found throughout his artwork. The Fix series caters to Gundam fans who enjoy the scale, possibility and durability of the MSiA line, but seek the extensive details and variations that can often only be found in the Master Grade Gundam model-kits.
The G.F.F. line does carry a higher price than the MSIA and MSIA Extended lines, which can represent a concern for some collectors. However, overall the G.F.F. represent a more "high-end" line of collectibles, which often contain better detail, more accessories, and the option to build multiple variations in the same box.
As the series has progressed, G.F.F. collectibles have been improved. Changes include sharper-more precise part casting resulting in better detail, improved articulation, and improved durability. [ citation needed ]
The G.F.F.N. line up is a significantly better than the old G.F.F. series, though usually sporting a considerably higher price due to materials, production and shipping. The quality has improved thanks to a new durable plastic that is distinctively reminiscent to the Gundam Model plastic (HG, HGUC, MG, PG) thus replacing the resin that shrank while curing. There is also little, or no casting lines, professionally cast heads, and considerably less of the brittle gray-ish plastic that plagued the G.F.F. series. Rubber is now being used sparsely, often to be used for the hands to allow ease of swapping weapons or spare hands without breaking or warping the joint socket.
There are very few toys in the line-up, with some costing between $70–$150 or more (the price of a Perfect Grade, or large Master Grade.)
Bandai also created similar toy lines:
Over the years, Bandai releases special limited editions of various kits, usually as competition (such as the yearly Bandai Action Kits Asia (now Universal) Cup held in Hong Kong) prizes, or as an event-limited (such as Japanese toy expos, movie launch premieres) item, although sometimes these kits are sold as limited web-shop items or discreetly sold by Bandai.
These kits usually come in clear plastic, metal-plated (certain kits are in so-called 24-k gold finish), "gloss-finish", "pearl-finish", "titanium-finish", or any combination of these. Their prices are usually much higher than their regular-release counterparts.
For trade shows and toy fairs, Bandai displays some extremely large models in 1:6 or 1:12 scale. True to the scaling, some of these models are well over 5 feet (1.50 m) tall.
Although most of these are one off promotional models used for display purposes, Bandai has produced a few of these for commercial purposes under their HY2M line. Notably, these are MS-06S "Zaku II Commander Type" (Char Aznable custom), which is now out of production, and the RX-78-2 "Gundam". These generally retail for approximately $2,000 and are intended to be sold primarily to store owners as display fronts.
As part of the 30th Anniversary of the Gundam series, the company officially announced a project on March 11, 2009, called Real-G planning to build a 1:1 real size scale Gundam in Japan, it was completed on June 9, 2009, and displayed in a Tokyo park. [ 32 ] [ 33 ] The 18-meter tall statue was later moved and reconstructed in Shizuoka City , where it stayed from July 2010 to March 2011 [ 34 ] [ 35 ] when in August it was dismantled only to reopen in Odaiba, Tokyo on April 19, 2012. [ 36 ] [ 37 ] It stood in front of a gift shop, "Gundam Front Tokyo", until 2017 when it was replaced by the titular mobile suit of Mobile Suit Gundam Unicorn .
In April 2010, Bandai sued two Chinese toy manufacturers for manufacturing and selling counterfeit Gunpla kits. The lawsuit states that Bandai demands 3.69 million RMB (roughly US$540,000) compensation from the companies. [ 38 ]
Bootleg Gunpla companies include Daban, TT Hongli, Model GD, Elyn Hobby, and Dragon Momoko. [ 39 ] [ 40 ] [ 41 ]
Four Gundam Media series titles focus primarily on Gunpla kits: Plamo-Kyoshiro (1982), Model Suit Gunpla Builders Beginning G (2010), and Gundam Build Fighters (2013) and its sequel Gundam Build Fighters Try (2014) and later the spiritual successor Gundam Build Divers (2018) as well as its sequel series, Gundam Build Divers Re:Rise (2019–2020).
In the manga/anime series Sgt. Frog , an addiction to Gundam models is the only thing stopping Keroro from invading Earth, since he reasons that if the Keronians invade Earth, all of the Gundam models will be destroyed, and there will be no one to make new ones. He loves the models so much, if any harm comes to them, he will react violently (such as going Super Saiyan ). He is prepared for such events, though, since he keeps spare kits in the Hinata family's attic. Because the anime is made by Sunrise (the makers of the Gundam anime), and because Bandai is the show's primary sponsor, the show is able to refer to Gundam models directly without legal issues.
In the manga/anime series Genshiken , Soichiro Tanaka teaches Kanako Ohno and Kanji Sasahara how to build Gundam models in Chapter 13 (adapted as episode 8 of the anime, where the pseudonym " Gungal " is used). Saki Kasukabe accidentally breaks Ohno's model and has to make it up to her by doing cosplay. | https://en.wikipedia.org/wiki/Gunpla |
Gunpowder , also commonly known as black powder to distinguish it from modern smokeless powder , is the earliest known chemical explosive . It consists of a mixture of sulfur , charcoal (which is mostly carbon ), and potassium nitrate (saltpeter) . The sulfur and charcoal act as fuels while the saltpeter is an oxidizer . [ 1 ] [ 2 ] Gunpowder has been widely used as a propellant in firearms , artillery , rocketry , and pyrotechnics , including use as a blasting agent for explosives in quarrying , mining , building pipelines , tunnels , [ 3 ] and roads .
Gunpowder is classified as a low explosive because of its relatively slow decomposition rate, low ignition temperature and consequently low brisance (breaking/shattering) . Low explosives deflagrate (i.e., burn at subsonic speeds), whereas high explosives detonate , producing a supersonic shockwave . Ignition of gunpowder packed behind a projectile generates enough pressure to force the shot from the muzzle at high speed, but usually not enough force to rupture the gun barrel . It thus makes a good propellant but is less suitable for shattering rock or fortifications with its low-yield explosive power. Nonetheless, it was widely used to fill fused artillery shells (and used in mining and civil engineering projects) until the second half of the 19th century, when the first high explosives were put into use.
Gunpowder is one of the Four Great Inventions of China. [ 4 ] Originally developed by Taoists for medicinal purposes, it was first used for warfare around AD 904. [ 5 ] Its use in weapons has declined due to smokeless powder replacing it, whilst its relative inefficiency led to newer alternatives such as dynamite and ammonium nitrate/fuel oil replacing it in industrial applications. [ 6 ]
Gunpowder is a low explosive : it does not detonate , but rather deflagrates (burns quickly). This is an advantage in a propellant device, where one does not desire a shock that would shatter the gun and potentially harm the operator; however, it is a drawback when an explosion is desired. In that case, the propellant (and most importantly, gases produced by its burning) must be confined. Since it contains its own oxidizer and additionally burns faster under pressure, its combustion is capable of bursting containers such as a shell, grenade, or improvised " pipe bomb " or "pressure cooker" casings to form shrapnel .
In quarrying, high explosives are generally preferred for shattering rock. However, because of its low brisance , gunpowder causes fewer fractures and results in more usable stone compared to other explosives, making it useful for blasting slate , which is fragile, [ 7 ] or monumental stone such as granite and marble . Gunpowder is well suited for blank rounds , signal flares , burst charges , and rescue-line launches. It is also used in fireworks for lifting shells, in rockets as fuel, and in certain special effects .
Combustion converts less than half the mass of gunpowder to gas; most of it turns into particulate matter. Some of it is ejected, wasting propelling power, fouling the air, and generally being a nuisance (giving away a soldier's position, generating fog that hinders vision, etc.). Some of it ends up as a thick layer of soot inside the barrel, where it also is a nuisance for subsequent shots, and a cause of jamming an automatic weapon. Moreover, this residue is hygroscopic , and with the addition of moisture absorbed from the air forms a corrosive substance . The soot contains potassium oxide or sodium oxide that turns into potassium hydroxide , or sodium hydroxide , which corrodes wrought iron or steel gun barrels. Gunpowder arms therefore require thorough and regular cleaning to remove the residue. [ 8 ]
Gunpowder loads can be used in modern firearms as long as they are not gas-operated . [ Footnote 1 ] The most compatible modern guns are smoothbore-barreled shotguns that are long-recoil operated with chrome-plated essential parts such as barrels and bores. Such guns have minimal fouling and corrosion and are easier to clean. [ 15 ]
The first confirmed reference to what can be considered gunpowder in China occurred in the 9th century during the Tang dynasty , first in a formula contained in the Taishang Shengzu Jindan Mijue ( Chinese : 太上聖祖金丹秘訣 ) in 808, and then about 50 years later in a Daoist text known as the Zhenyuan miaodao yaolüe ( 真元妙道要略 ). [ 16 ] The Taishang Shengzu Jindan Mijue mentions a formula composed of six parts sulfur to six parts saltpeter to one part birthwort herb. [ 16 ] According to the Zhenyuan miaodao yaolüe , "Some have heated together sulfur, realgar and saltpeter with honey ; smoke and flames result, so that their hands and faces have been burnt, and even the whole house where they were working burned down." [ 17 ] Based on these Taoist texts, the invention of gunpowder by Chinese alchemists was likely an accidental byproduct from experiments seeking to create the elixir of life . [ 18 ] This experimental medicine origin is reflected in its Chinese name huoyao ( Chinese : 火药/火藥 ; pinyin : huǒ yào /xuo jɑʊ/ ), which means "fire medicine". [ 19 ] Saltpeter was known to the Chinese by the mid-1st century AD and was primarily produced in the provinces of Sichuan , Shanxi , and Shandong . [ 20 ] There is strong evidence of the use of saltpeter and sulfur in various medicinal combinations. [ 21 ] A Chinese alchemical text dated 492 noted saltpeter burnt with a purple flame, providing a practical and reliable means of distinguishing it from other inorganic salts, thus enabling alchemists to evaluate and compare purification techniques; the earliest Latin accounts of saltpeter purification are dated after 1200. [ 22 ]
The earliest chemical formula for gunpowder appeared in the 11th century Song dynasty text, Wujing Zongyao ( Complete Essentials from the Military Classics ), written by Zeng Gongliang between 1040 and 1044. [ 23 ] The Wujing Zongyao provides encyclopedia references to a variety of mixtures that included petrochemicals—as well as garlic and honey. A slow match for flame-throwing mechanisms using the siphon principle and for fireworks and rockets is mentioned. The mixture formulas in this book contain at most 50% saltpeter — not enough to create an explosion, they produce an incendiary instead. [ 23 ] The Essentials was written by a Song dynasty court bureaucrat and there is little evidence that it had any immediate impact on warfare; there is no mention of its use in the chronicles of the wars against the Tanguts in the 11th century, and China was otherwise mostly at peace during this century. However, it had already been used for fire arrows since at least the 10th century. Its first recorded military application dates its use to 904 in the form of incendiary projectiles. [ 5 ] In the following centuries various gunpowder weapons such as bombs , fire lances , and the gun appeared in China. [ 24 ] [ 25 ] Explosive weapons such as bombs have been discovered in a shipwreck off the shore of Japan dated from 1281, during the Mongol invasions of Japan. [ 26 ]
By 1083 the Song court was producing hundreds of thousands of fire arrows for their garrisons. [ 27 ] Bombs and the first proto-guns, known as "fire lances", became prominent during the 12th century and were used by the Song during the Jin-Song Wars . Fire lances were first recorded to have been used at the Siege of De'an in 1132 by Song forces against the Jin . [ 28 ] In the early 13th century the Jin used iron-casing bombs. [ 29 ] Projectiles were added to fire lances, and re-usable fire lance barrels were developed, first out of hardened paper, and then metal. By 1257 some fire lances were firing wads of bullets. [ 30 ] [ 31 ] In the late 13th century metal fire lances became 'eruptors', proto-cannons firing co-viative projectiles (mixed with the propellant, rather than seated over it with a wad), and by 1287 at the latest, had become true guns, the hand cannon . [ 32 ]
According to Iqtidar Alam Khan, the Mongols introduced gunpowder in their invasion of Persia and Mesopotamia . [ 33 ] The Muslims acquired knowledge of gunpowder sometime between 1240 and 1280, by which point the Syrian Hasan al-Rammah had written recipes, instructions for the purification of saltpeter, and descriptions of gunpowder incendiaries. It is implied by al-Rammah's usage of "terms that suggested he derived his knowledge from Chinese sources" and his references to saltpeter as "Chinese snow" ( Arabic : ثلج الصين thalj al-ṣīn ), fireworks as "Chinese flowers", and rockets as "Chinese arrows", that knowledge of gunpowder arrived from China. [ 34 ] However, because al-Rammah attributes his material to "his father and forefathers", Ahmad Y. al-Hassan argues that gunpowder became prevalent in Syria and Egypt by "the end of the twelfth century or the beginning of the thirteenth". [ 35 ] In Persia saltpeter was known as "Chinese salt" ( Persian : نمک چینی} , romanized : namak-i chīnī ) [ 36 ] [ 37 ] or "salt from Chinese salt marshes" ( نمک شوره چینی namak-i shūra-yi chīnī ). [ 38 ] [ 39 ]
Hasan al-Rammah included 107 gunpowder recipes in The Book of Military Horsemanship and Ingenious War Devices ( Arabic : الـفـروسـيـة و الـمـنـاصـب الـحـربـيـة , romanized : al-Furūsiyya wal-Manāsib al-Ḥarbiyya ), 22 of which are for rockets. The median of 17 of these 22 compositions for rockets (75% nitrates, 9.06% sulphur, and 15.94% charcoal) are nearly identical to the modern reported ideal recipe of 75% potassium nitrate, 10% sulphur, and 15% charcoal. [ 35 ] The text also mentions fuses, incendiary bombs, naphtha pots, fire lances, and an illustration and description of the earliest torpedo . The torpedo was called the "egg which moves itself and burns". [ 40 ] Two iron sheets were fastened together and tightened using felt. The flattened, pear-shaped vessel was filled with gunpowder, metal filings, "good mixtures", two rods, and a large rocket for propulsion. Judging by the illustration, it was supposed to glide across the water. [ 40 ] [ 41 ] [ 42 ] Fire lances were used in battles between the Muslims and Mongols in 1299 and 1303. [ 43 ]
Al-Hassan claims that in the Battle of Ain Jalut of 1260, the Mamluk Sultanate used "the first cannon in history" against the Mongols, utilizing a formula with near-identical ideal composition ratios for explosive gunpowder. [ 35 ] Other historians urge caution regarding claims of Islamic firearms use in the 1204–1324 period, as late medieval Arabic texts used the same word for gunpowder, naft , that they used for an earlier incendiary, naphtha . [ 44 ] [ 45 ]
The earliest surviving documentary evidence for cannons in the Islamic world is from an Arabic manuscript dated to the early 14th century. [ 46 ] [ 47 ] The author's name is uncertain but may have been Shams al-Din Muhammad, who died in 1350. [ 40 ] Dating from around 1320–1350, the illustrations show gunpowder weapons such as gunpowder arrows, bombs, fire tubes, and fire lances or proto-guns. [ 42 ] The manuscript describes a type of gunpowder weapon called a midfa which uses gunpowder to shoot projectiles out of a tube at the end of a stock. [ 48 ] Some consider this a cannon, while others do not. The problem with identifying cannons in early 14th-century Arabic texts is the term midfa , which appears from 1342 to 1352 but cannot be proven to be true hand-guns or bombards. Contemporary accounts of a metal-barrel cannon in the Islamic world do not occur until 1365. [ 49 ] Needham believes that in its original form the term midfa refers to the tube or cylinder of a naphtha projector ( flamethrower ). After the invention of gunpowder, it meant the tube of fire lances, and eventually it applied to the cylinder of hand-guns and cannons. [ 50 ]
According to Paul E. J. Hammer, the Mamluk Sultanate certainly used cannons by 1342. [ 51 ] According to J. Lavin, cannons were used by Moors at the siege of Algeciras in 1343. Shihab al-Din Abu al-Abbas al-Qalqashandi described a metal cannon firing an iron ball between 1365 and 1376. [ 49 ]
The musket appeared in the Ottoman Empire by 1465. [ 52 ] In 1598, Chinese writer Zhao Shizhen described Turkish muskets as being superior to European muskets. [ 53 ] The Chinese military work Wubei Zhi (1621) later described Turkish muskets that used a rack and pinion mechanism, which was not known to have been used in European or Chinese firearms at the time. [ 54 ]
The state-controlled manufacture of gunpowder by the Ottoman Empire through early supply chains to obtain nitre, sulphur and high-quality charcoal from oaks in Anatolia contributed significantly to its expansion between the 15th and 18th centuries. It was not until later in the 19th century that the systemic production of Turkish gunpowder was reduced considerably, coinciding with the decline of its military might. [ 55 ]
The earliest Western accounts of gunpowder appear in texts written by English philosopher Roger Bacon in 1267 called Opus Majus and Opus Tertium . [ 56 ] The oldest written recipes in continental Europe were recorded under the name Marcus Graecus or Mark the Greek between 1280 and 1300 in the Liber Ignium , or Book of Fires . [ 57 ]
Some sources mention possible gunpowder weapons being deployed by the Mongols against European forces at the Battle of Mohi in 1241. [ 58 ] [ 59 ] [ 60 ] Professor Kenneth Warren Chase credits the Mongols for introducing into Europe gunpowder and its associated weaponry. [ 61 ] However, there is no clear route of transmission, [ 62 ] and while the Mongols are often pointed to as the likeliest vector, Timothy May points out that "there is no concrete evidence that the Mongols used gunpowder weapons on a regular basis outside of China." [ 63 ] May also states, "however [, ...] the Mongols used the gunpowder weapon in their wars against the Jin, the Song and in their invasions of Japan." [ 63 ]
Records show that, in England, gunpowder was being made in 1346 at the Tower of London ; a powder house existed at the Tower in 1461, and in 1515 three King's gunpowder makers worked there. [ 64 ] Gunpowder was also being made or stored at other royal castles, such as Portchester . [ 65 ] The English Civil War (1642–1645) led to an expansion of the gunpowder industry, with the repeal of the Royal Patent in August 1641. [ 64 ]
In late 14th century Europe, gunpowder was improved by corning , the practice of drying it into small clumps to improve combustion and consistency. [ 66 ] During this time, European manufacturers also began regularly purifying saltpeter, using wood ashes containing potassium carbonate to precipitate calcium from their dung liquor, and using ox blood, alum , and slices of turnip to clarify the solution. [ 66 ]
During the Renaissance, two European schools of pyrotechnic thought emerged, one in Italy and the other at Nuremberg, Germany. [ 67 ] In Italy, Vannoccio Biringuccio , born in 1480, was a member of the guild Fraternita di Santa Barbara but broke with the tradition of secrecy by setting down everything he knew in a book titled De la pirotechnia , written in vernacular. It was published posthumously in 1540, with 9 editions over 138 years, and also reprinted by MIT Press in 1966. [ 66 ]
By the mid-17th century fireworks were used for entertainment on an unprecedented scale in Europe, being popular even at resorts and public gardens. [ 68 ] With the publication of Deutliche Anweisung zur Feuerwerkerey (1748), methods for creating fireworks were sufficiently well-known and well-described that "Firework making has become an exact science." [ 69 ] In 1774 Louis XVI ascended to the throne of France at age 20. After he discovered that France was not self-sufficient in gunpowder, a Gunpowder Administration was established; to head it, the lawyer Antoine Lavoisier was appointed. Although from a bourgeois family, after his degree in law Lavoisier became wealthy from a company set up to collect taxes for the Crown; this allowed him to pursue experimental natural science as a hobby. [ 70 ]
Without access to cheap saltpeter (controlled by the British), for hundreds of years France had relied on saltpetremen with royal warrants, the droit de fouille or "right to dig", to seize nitrous-containing soil and demolish walls of barnyards, without compensation to the owners. [ 71 ] This caused farmers, the wealthy, or entire villages to bribe the petermen and the associated bureaucracy to leave their buildings alone and the saltpeter uncollected. Lavoisier instituted a crash program to increase saltpeter production, revised (and later eliminated) the droit de fouille , researched best refining and powder manufacturing methods, instituted management and record-keeping, and established pricing that encouraged private investment in works. Although saltpeter from new Prussian-style putrefaction works had not been produced yet (the process taking about 18 months), in only a year France had gunpowder to export. A chief beneficiary of this surplus was the American Revolution . By careful testing and adjusting the proportions and grinding time, powder from mills such as at Essonne outside Paris became the best in the world by 1788, and inexpensive. [ 71 ] [ 72 ]
Two British physicists, Andrew Noble and Frederick Abel , worked to improve the properties of gunpowder during the late 19th century. This formed the basis for the Noble-Abel gas equation for internal ballistics . [ 73 ]
The introduction of smokeless powder in the late 19th century led to a contraction of the gunpowder industry. After the end of World War I , the majority of the British gunpowder manufacturers merged into a single company, "Explosives Trades limited", and a number of sites were closed down, including those in Ireland. This company became Nobel Industries Limited, and in 1926 became a founding member of Imperial Chemical Industries . The Home Office removed gunpowder from its list of Permitted Explosives . Shortly afterwards, on 31 December 1931, the former Curtis & Harvey 's Glynneath gunpowder factory at Pontneddfechan in Wales closed down. The factory was demolished by fire in 1932. [ 74 ] The last remaining gunpowder mill at the Royal Gunpowder Factory, Waltham Abbey was damaged by a German parachute mine in 1941 and it never reopened. [ 64 ] This was followed by the closure and demolition of the gunpowder section at the Royal Ordnance Factory , ROF Chorley , at the end of World War II , and of ICI Nobel 's Roslin gunpowder factory which closed in 1954. [ 64 ] [ 75 ] This left ICI Nobel's Ardeer site in Scotland , which included a gunpowder factory, as the only factory in Great Britain producing gunpowder. The gunpowder area of the Ardeer site closed in October 1976. [ 64 ]
Gunpowder and gunpowder weapons were transmitted to India through the Mongol invasions of India . [ 76 ] [ 77 ] The Mongols were defeated by Alauddin Khalji of the Delhi Sultanate , and some of the Mongol soldiers remained in northern India after their conversion to Islam. [ 77 ] It was written in the Tarikh-i Firishta (1606–1607) that Nasiruddin Mahmud the ruler of the Delhi Sultanate presented the envoy of the Mongol ruler Hulegu Khan with a dazzling pyrotechnics display upon his arrival in Delhi in 1258. Nasiruddin Mahmud tried to express his strength as a ruler and tried to ward off any Mongol attempt similar to the Siege of Baghdad (1258) . [ 78 ] Firearms known as top-o-tufak also existed in many Muslim kingdoms in India by as early as 1366. [ 78 ] From then on the employment of gunpowder warfare in India was prevalent, with events such as the "Siege of Belgaum " in 1473 by Sultan Muhammad Shah Bahmani. [ 79 ]
The shipwrecked Ottoman Admiral Seydi Ali Reis is known to have introduced the earliest type of matchlock weapons, which the Ottomans used against the Portuguese during the Siege of Diu (1531) . After that, a diverse variety of firearms, large guns in particular, became visible in Tanjore , Dacca , Bijapur , and Murshidabad . [ 80 ] Guns made of bronze were recovered from Calicut (1504)- the former capital of the Zamorins [ 81 ]
The Mughal emperor Akbar mass-produced matchlocks for the Mughal Army . Akbar is personally known to have shot a leading Rajput commander during the Siege of Chittorgarh . [ 82 ] The Mughals began to use bamboo rockets (mainly for signalling) and employ sappers : special units that undermined heavy stone fortifications to plant gunpowder charges.
The Mughal Emperor Shah Jahan is known to have introduced much more advanced matchlocks, their designs were a combination of Ottoman and Mughal designs. Shah Jahan also countered the British and other Europeans in his province of Gujarāt , which supplied Europe saltpeter for use in gunpowder warfare during the 17th century. [ 83 ] Bengal and Mālwa participated in saltpeter production. [ 83 ] The Dutch, French, Portuguese, and English used Chhapra as a center of saltpeter refining. [ 83 ]
Ever since the founding of the Sultanate of Mysore by Hyder Ali , French military officers were employed to train the Mysore Army. Hyder Ali and his son Tipu Sultan were the first to introduce modern cannons and muskets , their army was also the first in India to have official uniforms. During the Second Anglo-Mysore War Hyder Ali and his son Tipu Sultan unleashed the Mysorean rockets at their British opponents effectively defeating them on various occasions. The Mysorean rockets inspired the development of the Congreve rocket , which the British widely used during the Napoleonic Wars and the War of 1812 . [ 84 ]
Cannons were introduced to Majapahit when Kublai Khan's Chinese army under the leadership of Ike Mese sought to invade Java in 1293. History of Yuan mentioned that the Mongol used cannons (Chinese: 炮— Pào ) against Daha forces. [ 85 ] : 1–2 [ 86 ] [ 87 ] : 220 Cannons were used by the Ayutthaya Kingdom in 1352 during its invasion of the Khmer Empire . [ 88 ] Within a decade large quantities of gunpowder could be found in the Khmer Empire . [ 88 ] By the end of the century firearms were also used by the Trần dynasty . [ 89 ]
Even though the knowledge of making gunpowder-based weapons was known after the failed Mongol invasion of Java, and the predecessor of firearms, the pole gun ( bedil tombak ), is recorded as being used by Java in 1413, [ 90 ] [ 91 ] : 245 the knowledge of making "true" firearms came much later, after the middle of the 15th century. It was brought by the Islamic nations of West Asia, most probably the Arabs . The precise year of introduction is unknown, but it may be safely concluded to be no earlier than 1460. [ 92 ] : 23 Before the arrival of the Portuguese in Southeast Asia, the natives already possessed primitive firearms, the Java arquebus . [ 93 ] Portuguese influence to local weaponry after the capture of Malacca (1511) resulted in a new type of hybrid tradition matchlock firearm, the istinggar . [ 94 ] [ 95 ] : 53
When the Portuguese came to the archipelago, they referred to the breech-loading swivel gun as berço , while the Spaniards call it verso . [ 96 ] : 151 By the early 16th century, the Javanese already locally producing large guns, some of them still survived until the present day and dubbed as "sacred cannon" or "holy cannon". These cannons varied between 180- and 260-pounders, weighing anywhere between 3 and 8 tons, length of them between 3 and 6 m. [ 97 ]
Saltpeter harvesting was recorded by Dutch and German travelers as being common in even the smallest villages and was collected from the decomposition process of large dung hills specifically piled for the purpose. The Dutch punishment for possession of non-permitted gunpowder appears to have been amputation. [ 98 ] : 180–181 Ownership and manufacture of gunpowder was later prohibited by the colonial Dutch occupiers. [ 99 ] According to colonel McKenzie quoted in Sir Thomas Stamford Raffles ', The History of Java (1817), the purest sulfur was supplied from a crater from a mountain near the straits of Bali . [ 98 ] : 180–181
On the origins of gunpowder technology, historian Tonio Andrade remarked, "Scholars today overwhelmingly concur that the gun was invented in China." [ 100 ] Gunpowder and the gun are widely believed by historians to have originated from China due to the large body of evidence that documents the evolution of gunpowder from a medicine to an incendiary and explosive, and the evolution of the gun from the fire lance to a metal gun, whereas similar records do not exist elsewhere. [ 101 ] As Andrade explains, the large amount of variation in gunpowder recipes in China relative to Europe is "evidence of experimentation in China, where gunpowder was at first used as an incendiary and only later became an explosive and a propellant... in contrast, formulas in Europe diverged only very slightly from the ideal proportions for use as an explosive and a propellant, suggesting that gunpowder was introduced as a mature technology." [ 62 ]
However, the history of gunpowder is not without controversy. A major problem confronting the study of early gunpowder history is ready access to sources close to the events described. Often the first records potentially describing use of gunpowder in warfare were written several centuries after the fact, and may well have been colored by the contemporary experiences of the chronicler. [ 102 ] Translation difficulties have led to errors or loose interpretations bordering on artistic licence . Ambiguous language can make it difficult to distinguish gunpowder weapons from similar technologies that do not rely on gunpowder. A commonly cited example is a report of the Battle of Mohi in Eastern Europe that mentions a "long lance" sending forth "evil-smelling vapors and smoke", which has been variously interpreted by different historians as the "first-gas attack upon European soil" using gunpowder, "the first use of cannon in Europe", or merely a "toxic gas" with no evidence of gunpowder. [ 103 ] It is difficult to accurately translate original Chinese alchemical texts, which tend to explain phenomena through metaphor, into modern scientific language with rigidly defined terminology in English. [ 34 ] Early texts potentially mentioning gunpowder are sometimes marked by a linguistic process where semantic change occurred. [ 104 ] For instance, the Arabic word naft transitioned from denoting naphtha to denoting gunpowder, and the Chinese word pào changed in meaning from trebuchet to a cannon . [ 105 ] This has led to arguments on the exact origins of gunpowder based on etymological foundations. Science and technology historian Bert S. Hall makes the observation that, "It goes without saying, however, that historians bent on special pleading, or simply with axes of their own to grind, can find rich material in these terminological thickets." [ 104 ]
Another major area of contention in modern studies of the history of gunpowder is regarding the transmission of gunpowder. While the literary and archaeological evidence supports a Chinese origin for gunpowder and guns, the manner in which gunpowder technology was transferred from China to the West is still under debate. [ 100 ] It is unknown why the rapid spread of gunpowder technology across Eurasia took place over several decades whereas other technologies such as paper, the compass, and printing did not reach Europe until centuries after they were invented in China. [ 62 ]
Gunpowder is a granular mixture of:
Potassium nitrate is the most important ingredient in terms of both bulk and function because the combustion process releases oxygen from the potassium nitrate, promoting the rapid burning of the other ingredients. [ 106 ] To reduce the likelihood of accidental ignition by static electricity , the granules of modern gunpowder are typically coated with graphite , which prevents the build-up of electrostatic charge.
Charcoal does not consist of pure carbon; rather, it consists of partially pyrolyzed cellulose , in which the wood is not completely decomposed. Carbon differs from ordinary charcoal . Whereas charcoal's autoignition temperature is relatively low, carbon's is much greater. Thus, a gunpowder composition containing pure carbon would burn similarly to a match head, at best. [ 107 ]
The current standard composition for the gunpowder manufactured by pyrotechnicians was adopted as long ago as 1780. Proportions by weight are 75% potassium nitrate (known as saltpeter or saltpetre), 15% softwood charcoal, and 10% sulfur. [ 108 ] These ratios have varied over the centuries and by country, and can be altered somewhat depending on the purpose of the powder. For instance, power grades of black powder, unsuitable for use in firearms but adequate for blasting rock in quarrying operations, are called blasting powder rather than gunpowder with standard proportions of 70% nitrate, 14% charcoal, and 16% sulfur; blasting powder may be made with the cheaper sodium nitrate substituted for potassium nitrate and proportions may be as low as 40% nitrate, 30% charcoal, and 30% sulfur. [ 109 ] In 1857, Lammot du Pont solved the main problem of using cheaper sodium nitrate formulations when he patented DuPont "B" blasting powder. After manufacturing grains from press-cake in the usual way, his process tumbled the powder with graphite dust for 12 hours. This formed a graphite coating on each grain that reduced its ability to absorb moisture. [ 110 ]
Neither the use of graphite nor sodium nitrate was new. Glossing gunpowder corns with graphite was already an accepted technique in 1839, [ 111 ] and sodium nitrate-based blasting powder had been made in Peru for many years using the sodium nitrate mined at Tarapacá (now in Chile). [ 112 ] Also, in 1846, two plants were built in south-west England to make blasting powder using this sodium nitrate. [ 113 ] The idea may well have been brought from Peru by Cornish miners returning home after completing their contracts. Another suggestion is that it was William Lobb , the plant collector, who recognised the possibilities of sodium nitrate during his travels in South America. Lammot du Pont would have known about the use of graphite and probably also knew about the plants in south-west England. In his patent he was careful to state that his claim was for the combination of graphite with sodium nitrate-based powder, rather than for either of the two individual technologies.
French war powder in 1879 used the ratio 75% saltpeter, 12.5% charcoal, 12.5% sulfur. English war powder in 1879 used the ratio 75% saltpeter, 15% charcoal, 10% sulfur. [ 114 ] The British Congreve rockets used 62.4% saltpeter, 23.2% charcoal and 14.4% sulfur, but the British Mark VII gunpowder was changed to 65% saltpeter, 20% charcoal and 15% sulfur. [ citation needed ] The explanation for the wide variety in formulation relates to usage. Powder used for rocketry can use a slower burn rate since it accelerates the projectile for a much longer time—whereas powders for weapons such as flintlocks, cap-locks, or matchlocks need a higher burn rate to accelerate the projectile in a much shorter distance. Cannons usually used lower burn-rate powders, because most would burst with higher burn-rate powders.
Besides black powder, there are other historically important types of gunpowder. "Brown gunpowder" is cited as composed of 79% nitre, 3% sulfur, and 18% charcoal per 100 of dry powder, with about 2% moisture. Prismatic Brown Powder is a large-grained product the Rottweil Company introduced in 1884 in Germany, which was adopted by the British Royal Navy shortly thereafter. The French navy adopted a fine, 3.1 millimeter, not prismatic grained product called Slow Burning Cocoa (SBC) or "cocoa powder". These brown powders reduced burning rate even further by using as little as 2 percent sulfur and using charcoal made from rye straw that had not been completely charred, hence the brown color. [ 115 ]
Lesmok powder was a product developed by DuPont in 1911, [ 116 ] one of several semi-smokeless products in the industry containing a mixture of black and nitrocellulose powder. It was sold to Winchester and others primarily for .22 and .32 small calibers. Its advantage was that it was believed at the time to be less corrosive than smokeless powders then in use. It was not understood in the U.S. until the 1920s that the actual source of corrosion was the potassium chloride residue from potassium chlorate sensitized primers. The bulkier black powder fouling better disperses primer residue. Failure to mitigate primer corrosion by dispersion caused the false impression that nitrocellulose-based powder caused corrosion. [ 117 ] Lesmok had some of the bulk of black powder for dispersing primer residue, but somewhat less total bulk than straight black powder, thus requiring less frequent bore cleaning. [ 118 ] It was last sold by Winchester in 1947.
The development of smokeless powders, such as cordite , in the late 19th century created the need for a spark-sensitive priming charge , such as gunpowder. However, the sulfur content of traditional gunpowders caused corrosion problems with Cordite Mk I and this led to the introduction of a range of sulfur-free gunpowders, of varying grain sizes. [ 64 ] They typically contain 70.5% of saltpeter and 29.5% of charcoal. [ 64 ] Like black powder, they were produced in different grain sizes. In the United Kingdom, the finest grain was known as sulfur-free mealed powder ( SMP ). Coarser grains were numbered as sulfur-free gunpowder (SFG n): 'SFG 12', 'SFG 20', 'SFG 40' and 'SFG 90', for example where the number represents the smallest BSS sieve mesh size, which retained no grains.
Sulfur's main role in gunpowder is to decrease the ignition temperature. A sample reaction for sulfur-free gunpowder would be:
The term black powder was coined in the late 19th century, primarily in the United States, to distinguish prior gunpowder formulations from the new smokeless powders and semi-smokeless powders. Semi-smokeless powders featured bulk volume properties that approximated black powder, but had significantly reduced amounts of smoke and combustion products. Smokeless powder has different burning properties (pressure vs. time) and can generate higher pressures and work per gram. This can rupture older weapons designed for black powder. Smokeless powders ranged in color from brownish tan to yellow to white. Most of the bulk semi-smokeless powders ceased to be manufactured in the 1920s. [ 119 ] [ 118 ] [ 120 ]
The original dry-compounded powder used in 15th-century Europe was known as "Serpentine", either a reference to Satan [ 37 ] or to a common artillery piece that used it. [ 121 ] The ingredients were ground
together with a mortar and pestle, perhaps for 24 hours, [ 121 ] resulting in a fine flour. Vibration during transportation could cause the components to separate again, requiring remixing in the field. Also if the quality of the saltpeter was low (for instance if it was contaminated with highly hygroscopic calcium nitrate ), or if the powder was simply old (due to the mildly hygroscopic nature of potassium nitrate), in humid weather it would need to be re-dried. The dust from "repairing" powder in the field was a major hazard.
Loading cannons or bombards before the powder-making advances of the Renaissance was a skilled art. Fine powder loaded haphazardly or too tightly would burn incompletely or too slowly. Typically, the breech-loading powder chamber in the rear of the piece was filled only about half full, the serpentine powder neither too compressed nor too loose, a wooden bung pounded in to seal the chamber from the barrel when assembled, and the projectile placed on. A carefully determined empty space was necessary for the charge to burn effectively. When the cannon was fired through the touchhole, turbulence from the initial surface combustion caused the rest of the powder to be rapidly exposed to the flame. [ 121 ]
The advent of much more powerful and easy to use corned powder changed this procedure, but serpentine was used with older guns into the 17th century. [ 122 ]
For propellants to oxidize and burn rapidly and effectively, the combustible ingredients must be reduced to the smallest possible particle sizes, and be as thoroughly mixed as possible. Once mixed, however, for better results in a gun, makers discovered that the final product should be in the form of individual dense grains that spread the fire quickly from grain to grain, much as straw or twigs catch fire more quickly than a pile of sawdust .
In late 14th century Europe and China, [ 123 ] gunpowder was improved by wet grinding; liquid such as distilled spirits [ 66 ] were added during the grinding-together of the ingredients and the moist paste dried afterwards. The principle of wet mixing to prevent the separation of dry ingredients, invented for gunpowder, is used today in the pharmaceutical industry. [ 124 ] It was discovered that if the paste was rolled into balls before drying the resulting gunpowder absorbed less water from the air during storage and traveled better. The balls were then crushed in a mortar by the gunner immediately before use, with the old problem of uneven particle size and packing causing unpredictable results. If the right size particles were chosen, however, the result was a great improvement in power. Forming the damp paste into corn -sized clumps by hand or with the use of a sieve instead of larger balls produced a product after drying that loaded much better, as each tiny piece provided its own surrounding air space that allowed much more rapid combustion than a fine powder. This "corned" gunpowder was from 30% to 300% more powerful. An example is cited where 15 kilograms (34 lb) of serpentine was needed to shoot a 21-kilogram (47 lb) ball, but only 8.2 kilograms (18 lb) of corned powder. [ 66 ]
Because the dry powdered ingredients must be mixed and bonded together for extrusion and cut into grains to maintain the blend, size reduction and mixing is done while the ingredients are damp, usually with water. After 1800, instead of forming grains by hand or with sieves, the damp mill-cake was pressed in molds to increase its density and extract the liquid, forming press-cake . The pressing took varying amounts of time, depending on conditions such as atmospheric humidity. The hard, dense product was broken again into tiny pieces, which were separated with sieves to produce a uniform product for each purpose: coarse powders for cannons, finer grained powders for muskets, and the finest for small hand guns and priming. [ 122 ] Inappropriately fine-grained powder often caused cannons to burst before the projectile could move down the barrel, due to the high initial spike in pressure. [ 125 ] Mammoth powder with large grains, made for Rodman's 15-inch cannon , reduced the pressure to only 20 percent as high as ordinary cannon powder would have produced. [ 126 ]
In the mid-19th century, measurements were made determining that the burning rate within a grain of black powder (or a tightly packed mass) is about 6 cm/s (0.20 feet/s), while the rate of ignition propagation from grain to grain is around 9 m/s (30 feet/s), over two orders of magnitude faster. [ 122 ]
Modern corning first compresses the fine black powder meal into blocks with a fixed density (1.7 g/cm 3 ). [ 127 ] In the United States, gunpowder grains were designated F (for fine) or C (for coarse). Grain diameter decreased with a larger number of Fs and increased with a larger number of Cs, ranging from about 2 mm ( 1 ⁄ 16 in) for 7F to 15 mm ( 9 ⁄ 16 in) for 7C. Even larger grains were produced for artillery bore diameters greater than about 17 cm (6.7 in). The standard DuPont Mammoth powder developed by Thomas Rodman and Lammot du Pont for use during the American Civil War had grains averaging 15 mm (0.6 in) in diameter with edges rounded in a glazing barrel. [ 126 ] Other versions had grains the size of golf and tennis balls for use in 20-inch (51 cm) Rodman guns . [ 128 ] In 1875 DuPont introduced Hexagonal powder for large artillery, which was pressed using shaped plates with a small center core—about 38 mm ( 1 + 1 ⁄ 2 in) diameter, like a wagon wheel nut, the center hole widened as the grain burned. [ 115 ] By 1882 German makers also produced hexagonal grained powders of a similar size for artillery. [ 115 ]
By the late 19th century manufacturing focused on standard grades of black powder from Fg used in large bore rifles and shotguns, through FFg (medium and small-bore arms such as muskets and fusils), FFFg (small-bore rifles and pistols), and FFFFg (extreme small bore, short pistols and most commonly for priming flintlocks ). [ 129 ] A coarser grade for use in military artillery blanks was designated A-1. These grades were sorted on a system of screens with oversize retained on a mesh of 6 wires per inch, A-1 retained on 10 wires per inch, Fg retained on 14, FFg on 24, FFFg on 46, and FFFFg on 60. Fines designated FFFFFg were usually reprocessed to minimize explosive dust hazards. [ 130 ] In the United Kingdom , the main service gunpowders were classified RFG (rifle grained fine) with diameter of one or two millimeters and RLG (rifle grained large) for grain diameters between two and six millimeters. [ 128 ] Gunpowder grains can alternatively be categorized by mesh size: the BSS sieve mesh size , being the smallest mesh size, which retains no grains. Recognized grain sizes are Gunpowder G 7, G 20, G 40, and G 90.
Owing to the large market of antique and replica black-powder firearms in the US, modern black powder substitutes like Pyrodex , Triple Seven and Black Mag3 [ 118 ] pellets have been developed since the 1970s. These products, which should not be confused with smokeless powders, aim to produce less fouling (solid residue), while maintaining the traditional volumetric measurement system for charges. Claims of less corrosiveness of these products have been controversial however. New cleaning products for black-powder guns have also been developed for this market. [ 129 ]
A simple, commonly cited, chemical equation for the combustion of gunpowder is:
A balanced, but still simplified, equation is: [ 131 ]
The exact percentages of ingredients varied greatly through the medieval period as the recipes were developed by trial and error, and needed to be updated for changing military technology. [ 132 ]
Gunpowder does not burn as a single reaction, so the byproducts are not easily predicted. One study [ 133 ] showed that it produced (in order of descending quantities) 55.91% solid products: potassium carbonate , potassium sulfate , potassium sulfide , sulfur , potassium nitrate , potassium thiocyanate , carbon , ammonium carbonate and 42.98% gaseous products: carbon dioxide , nitrogen , carbon monoxide , hydrogen sulfide , hydrogen , methane , 1.11% water.
Gunpowder made with less-expensive and more plentiful sodium nitrate instead of potassium nitrate (in appropriate proportions) works just as well. Gunpowder releases 3 megajoules per kilogram and contains its own oxidant. [ citation needed ] This is less than TNT (4.7 megajoules per kilogram), or gasoline (47.2 megajoules per kilogram in combustion, but gasoline requires an oxidant; for instance, an optimized gasoline and O 2 mixture releases 10.4 megajoules per kilogram, taking into account the mass of the oxygen).
Gunpowder also has a low energy density [ how much? ] compared to modern "smokeless" powders, and thus to achieve high energy loadings, large amounts are needed with heavy projectiles. [ 134 ]
For the most powerful black powder, meal powder , a wood charcoal is used. The best wood for the purpose is Pacific willow , [ 135 ] but others such as alder or buckthorn can be used. In Great Britain between the 15th and 19th centuries charcoal from alder buckthorn was greatly prized for gunpowder manufacture; cottonwood was used by the American Confederate States . [ 136 ] The ingredients are reduced in particle size and mixed as intimately as possible. Originally, this was with a mortar-and-pestle or a similarly operating stamping-mill, using copper, bronze or other non-sparking materials, until supplanted by the rotating ball mill principle with non-sparking bronze or lead . Historically, a marble or limestone edge runner mill, running on a limestone bed, was used in Great Britain; however, by the mid 19th century this had changed to either an iron-shod stone wheel or a cast iron wheel running on an iron bed. [ 108 ] The mix was dampened with alcohol or water during grinding to prevent accidental ignition. This also helps the extremely soluble saltpeter to mix into the microscopic pores of the very high surface-area charcoal.
Around the late 14th century, European powdermakers first began adding liquid during grinding to improve mixing, reduce dust, and with it the risk of explosion. [ 137 ] The powder-makers would then shape the resulting paste of dampened gunpowder, known as mill cake, into corns, or grains, to dry. Not only did corned powder keep better because of its reduced surface area, gunners also found that it was more powerful and easier to load into guns. Before long, powder-makers standardized the process by forcing mill cake through sieves instead of corning powder by hand.
The improvement was based on reducing the surface area of a higher density composition. At the beginning of the 19th century, makers increased density further by static pressing. They shoveled damp mill cake into a two-foot square box, placed this beneath a screw press and reduced it to half its volume. "Press cake" had the hardness of slate . They broke the dried slabs with hammers or rollers, and sorted the granules with sieves into different grades. In the United States, Eleuthere Irenee du Pont , who had learned the trade from Lavoisier, tumbled the dried grains in rotating barrels to round the edges and increase durability during shipping and handling. (Sharp grains rounded off in transport, producing fine "meal dust" that changed the burning properties.)
Another advance was the manufacture of kiln charcoal by distilling wood in heated iron retorts instead of burning it in earthen pits. Controlling the temperature influenced the power and consistency of the finished gunpowder. In 1863, in response to high prices for Indian saltpeter, DuPont chemists developed a process using potash or mined potassium chloride to convert plentiful Chilean sodium nitrate to potassium nitrate. [ 138 ]
The following year (1864) the Gatebeck Low Gunpowder Works in Cumbria (Great Britain) started a plant to manufacture potassium nitrate by essentially the same chemical process. [ 139 ] This is nowadays called the 'Wakefield Process', after the owners of the company. It would have used potassium chloride from the Staßfurt mines, near Magdeburg, Germany, which had recently become available in industrial quantities. [ 140 ]
During the 18th century, gunpowder factories became increasingly dependent on mechanical energy. [ 141 ] Despite mechanization, production difficulties related to humidity control, especially during the pressing, were still present in the late 19th century. A paper from 1885 laments that "Gunpowder is such a nervous and sensitive spirit, that in almost every process of manufacture it changes under our hands as the weather changes." Pressing times to the desired density could vary by a factor of three depending on the atmospheric humidity. [ 142 ]
The United Nations Recommendations on the Transport of Dangerous Goods and national transportation authorities, such as United States Department of Transportation , have classified gunpowder (black powder) as a Group A: Primary explosive substance for shipment because it ignites so easily. Complete manufactured devices containing black powder are usually classified as Group D: Secondary detonating substance, or black powder, or article containing secondary detonating substance , such as firework, class D model rocket engine, etc., for shipment because they are harder to ignite than loose powder. As explosives, they all fall into the category of Class 1.
Besides its use as a propellant in firearms and artillery, black powder's other main use has been as a blasting powder in quarrying, mining, and road construction (including railroad construction). During the 19th century, outside of war emergencies such as the Crimean War or the American Civil War, more black powder was used in these industrial uses than in firearms and artillery. Dynamite gradually replaced it for those uses. Today, industrial explosives for such uses are still a huge market, but most of the market is in newer explosives rather than black powder.
Beginning in the 1930s, gunpowder or smokeless powder was used in rivet guns , stun guns for animals, cable splicers and other industrial construction tools. [ 143 ] The "stud gun", a powder-actuated tool , drove nails or screws into solid concrete, a function not possible with hydraulic tools, and today is still an important part of various industries, but the cartridges usually use smokeless powders. Industrial shotguns have been used to eliminate persistent material rings in operating rotary kilns (such as those for cement, lime, phosphate, etc.) and clinker in operating furnaces, and commercial tools make the method more reliable. [ 144 ]
Gunpowder has occasionally been employed for other purposes besides weapons, mining, fireworks and construction:
Gunpowder had originally been produced for medicinal purposes. It was eaten, in hopes of curing digestive ailments; inhaled, for respiratory disorders; and, as mentioned, rubbed onto skin level disorders like rashes or burns. | https://en.wikipedia.org/wiki/Gunpowder |
Gunzberg's test is a chemical test used for detecting the presence of hydrochloric acid . Gunzberg's reagent is made by dissolving two grams of phloroglucinol and one gram of vanillin in 100 millilitres of 95% ethanol . Hydrochloric acid catalyses Gunzberg's reagent to form a red complex. [ 1 ] [ 2 ]
Two drops of gastric juice are mixed with two drops of Gunzberg's reagent in an evaporating dish. The mixture is evaporated and if red is seen, free hydrochloric acid is present. [ 3 ]
This article about analytical chemistry is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Gunzberg's_test |
Guowang [ 1 ] [ 2 ] and also referred to as Hulianwang and Xingwang , [ 3 ] is a planned Chinese low-Earth orbit satellite internet megaconstellation to create a system of worldwide internet coverage . It was created by SatNet, a firm backed by the CAST . The project was started in 2022 as a rival to the Starlink satellite constellation installed by SpaceX , and plans to be constituted of over 13,000 satellites by the project's end.
Since April 2025, the program has launched 14 Hulianwang Jishu Shiyan satellites, [ 4 ] 3 Hulianwang Gaogui satellites [ 5 ] and 29 Operational Hulianwang Satellites. [ 6 ] [ 7 ] Hulianwang Jishu Shiyan satellites are for Testing Technology for the Operational Hulianwang satellites and Hulianwang Gaogui satellites are a GEO variant of Guowang satellite constellation.
09:30 | https://en.wikipedia.org/wiki/Guowang |
The Gurney equations are a set of mathematical formulas used in explosives engineering to relate how fast an explosive will accelerate an adjacent layer of metal or other material when the explosive detonates. This determines how fast fragments are released by military explosives, how quickly shaped charge explosives accelerate their liners inwards, and in other calculations such as explosive welding where explosives force two metal sheets together and bond them. [ 1 ]
The equations were first developed in the 1940s by Ronald Gurney [ 2 ] and have been expanded on and added to significantly since that time. The original paper by Gurney analyzed the situation of an exploding shell or bomb, a mass of explosives surrounded by a solid shell. Other researchers have extended similar methods of analysis to other geometries. All of the equations derived based on Gurney's methods are collectively called "Gurney equations".
When an explosive adjacent to a layer of a metallic or other solid material detonates, the layer is accelerated both by the initial detonation shock wave and by the pressure of the detonation gas products. Gurney developed a simple and convenient formula based on the conservation laws of momentum and energy that model how energy was distributed between the metal shell and the detonation gases that is remarkably accurate in many cases.
A key simplifying assumption Gurney made was that there is a linear velocity gradient in the explosive detonation product gases; in situations where this is strongly violated, such as implosions, the accuracy of the equations is low. In the most common situations encountered in ordnance (shells surrounding explosives) this works remarkably well though. In such cases the approximations are within 10% of experimental or detailed numerical results over a wide range of metal mass (M) to explosive charge mass (C) ratios (0.1 < M/C < 10.0). This is due to offsetting errors in the simplified model. Ignoring rarefaction waves in the detonation gases causes the calculated velocity to be too high; the assumption of an initial constant gas density rather than the actual one of the gases being densest next the accelerated layer causes the value to be low, cancelling each other out. In consequence attempts to improve the accuracy of the Gurney model by making more realistic assumptions about one aspect or another may not actually improve the accuracy of the result. [ 3 ] [ 4 ]
The Gurney equations relate the following quantities:
For imploding systems, where a hollow explosive charge accelerates an inner mass towards the center, the calculations additionally take into account:
As a simple approximate equation, the physical value of 2 E {\displaystyle {\sqrt {2E}}} is usually very close to 1/3 of the detonation velocity of the explosive material for standard explosives. [ 1 ] For a typical set of military explosives, the value of D 2 E {\displaystyle {\frac {D}{\sqrt {2E}}}} ranges from between 2.32 for Tritonal and 3.16 for PAX-29n.
m m μ s {\displaystyle {\frac {mm}{\mu s}}} is equal to kilometers per second, a more familiar unit for many applications.
The commonly quoted values for 2 E {\displaystyle {\sqrt {2E}}} are what are called the terminal values , the limiting case of acceleration in the cylinder expansion tests used to measure it (at 19–26 mm expansion). There is also a prompt value that may be measured for smaller expansion radii (5–7 mm). When no clarification is given in the literature, it is normally the limiting value. [ 5 ]
The Gurney equations give a result that assumes the shell or sheet of material remains intact throughout a large portion of the explosive-gas expansion such that work can performed upon it. For some configurations and materials this is true; explosive welding, for example, uses a thin sheet of explosive to evenly accelerate flat plates of metal and collide them, the plates remaining solid throughout. However, for many configurations where materials, brittle materials in particular, are accelerated outwards, the expanding shell fractures due to stretching. When it fractures, it typically breaks into many small fragments due to the combined effects of ongoing expansion of the shell and stress relief waves moving into the material from fracture points. [ 1 ] This phenomenon allows the detonation gases to stream around the fragments or bypass them, reducing effective drive.
Thus for metal shells that are brittle or have low ultimate strain, fragment velocities are typically about 80% of the value predicted by the Gurney formulas.
The basic Gurney equations for flat sheets assume that the sheet of material is a large diameter.
Small explosive charges, where the explosive's diameter is not significantly larger than its thickness, have reduced effectiveness as gas and energy are lost to the sides. [ 1 ]
This loss is empirically modeled as reducing the effective explosive charge mass C to an effective value C eff which is the volume of explosives contained within a 60° cone with its base on the explosives/flyer boundary.
Putting a cylindrical tamper around the explosive charge reduces that side loss effectively, as analyzed by Benham.
In 1996, Hirsch described a performance region, for relatively small ratios of M C {\displaystyle {\frac {M}{C}}} in which the Gurney equations misrepresent the actual physical behavior. [ 6 ]
The range of values for which the basic Gurney equations generated anomalous values is described by (for flat asymmetrical and open-faced sandwich configurations):
M C [ ( 4 N C ) + 1 ] < 1 2 {\displaystyle {\frac {M}{C}}\left[\left(4{\frac {N}{C}}\right)+1\right]<{\frac {1}{2}}}
For an open-faced sandwich configuration (see below), this corresponds to values of M C {\displaystyle {\frac {M}{C}}} of 0.5 or less. For a sandwich with tamper mass equal to explosive charge mass ( N C ≥ 1.0 {\displaystyle {\frac {N}{C}}\geq 1.0} ) a flyer plate mass of 0.1 or less of the charge mass will be anomalous.
This error is due to the configuration exceeding one of the underlying simplifying assumptions used in the Gurney equations, that there is a linear velocity gradient in the explosive product gases. For values of M C {\displaystyle {\frac {M}{C}}} outside the anomalous region, this is a good assumption. Hirsch demonstrated that as the total energy partition between the flyer plate and gases exceeds unity, the assumption breaks down, and the Gurney equations become less accurate as a result.
Complicating factors in the anomalous region include detailed gas behavior of the explosive products, including the reaction products' heat capacity ratio , γ.
Modern explosives engineering utilizes computational analysis methods which avoid this problem.
For the simplest case, a long hollow cylinder of metal is filled completely with explosives. The cylinder's walls are accelerated outwards as described by: [ 1 ]
V 2 E = ( M C + 1 2 ) − 1 / 2 {\displaystyle {\frac {V}{\sqrt {2E}}}=\left({\frac {M}{C}}+{\frac {1}{2}}\right)^{-1/2}}
This configuration is a first-order approximation for most military explosive devices, including artillery shells , bombs , and most missile warheads . These use mostly cylindrical explosive charges.
A spherical charge, initiated at its center, will accelerate a surrounding flyer shell as described by: [ 1 ]
V 2 E = ( M C + 3 5 ) − 1 / 2 {\displaystyle {\frac {V}{\sqrt {2E}}}=\left({\frac {M}{C}}+{\frac {3}{5}}\right)^{-1/2}}
This model approximates the behavior of military grenades , and some cluster bomb submunitions.
A flat layer of explosive with two identical heavy flat flyer plates on each side will accelerate the plates as described by: [ 1 ]
V 2 E = ( 2 M C + 1 3 ) − 1 / 2 {\displaystyle {\frac {V}{\sqrt {2E}}}=\left(2{\frac {M}{C}}+{\frac {1}{3}}\right)^{-1/2}}
Symmetrical sandwiches are used in some Reactive armor applications, on heavily armored vehicles such as main battle tanks . The inward-firing flyer will impact the vehicle main armor, causing damage if the armor is not thick enough, so these can only be used on heavier armored vehicles. Lighter vehicles use open-face sandwich reactive armor (see below). However, the dual moving plate method of operation of a symmetrical sandwich offers the best armor protection.
A flat layer of explosive with two flat flyer plates of different masses will accelerate the plates as described by: [ 1 ] [ 7 ] [ 8 ]
Let: A = 1 + 2 M C 1 + 2 N C {\displaystyle A={\frac {1+2{\frac {M}{C}}}{1+2{\frac {N}{C}}}}}
V M 2 E = ( 1 + A 3 3 ( 1 + A ) + A 2 N C + M C ) − 1 / 2 {\displaystyle {\frac {V_{M}}{\sqrt {2E}}}=\left({\frac {1+A^{3}}{3(1+A)}}+A^{2}{\frac {N}{C}}+{\frac {M}{C}}\right)^{-1/2}}
When a flat layer of explosive is placed on a practically infinitely thick supporting surface, and topped with a flyer plate of material, the flyer plate will be accelerated as described by: [ 1 ]
V M 2 E = ( M C + 1 3 ) − 1 / 2 {\displaystyle {\frac {V_{M}}{\sqrt {2E}}}=\left({\frac {M}{C}}+{\frac {1}{3}}\right)^{-1/2}}
A single flat sheet of explosives with a flyer plate on one side, known as an "open-faced sandwich", is described by: [ 1 ]
Since:
N = 0 {\displaystyle N=0}
then:
A = 1 + 2 ( M C ) {\displaystyle A=1+2\left({\frac {M}{C}}\right)}
which gives:
V 2 E = [ 1 + ( 1 + 2 M C ) 3 6 ( 1 + M C ) + M C ] − 1 / 2 {\displaystyle {\frac {V}{\sqrt {2E}}}=\left[{\frac {1+\left(1+2{\frac {M}{C}}\right)^{3}}{6\left(1+{\frac {M}{C}}\right)}}+{\frac {M}{C}}\right]^{-1/2}}
Open-faced sandwich configurations are used in Explosion welding and some other metalforming operations.
It is also a configuration commonly used in reactive armour on lightly armored vehicles, with the open face down towards the vehicle's main armor plate. This minimizes the reactive armor units damage to the vehicle structure during firing.
A hollow cylinder of explosive, initiated evenly around its surface, with an outer tamper and inner hollow shell which is then accelerated inwards (" imploded ") rather than outwards is described by the following equations. [ 9 ]
Unlike other forms of the Gurney equation, implosion forms (cylindrical and spherical) must take into account the shape of the control volume of the detonating shell of explosives and the distribution of momentum and energy within the detonation product gases. For cylindrical implosions, the geometry involved is simplified to include the inner and outer radii of the explosive charge, R i and R o .
β = R o R i {\displaystyle \beta ={\frac {R_{o}}{R_{i}}}}
a = 1 {\displaystyle a=1}
A = V o V i = ( M C + a ( M C ) ( β − 1 ) + β + 2 3 ( β + 1 ) ) ( N C + 2 β + 1 3 ( β + 1 ) ) {\displaystyle A={\frac {V_{o}}{V_{i}}}={\frac {\left({\frac {M}{C}}+a\left({\frac {M}{C}}\right)\left(\beta -1\right)+{\frac {\beta +2}{3\left(\beta +1\right)}}\right)}{\left({\frac {N}{C}}+{\frac {2\beta +1}{3\left(\beta +1\right)}}\right)}}}
V m 2 E = {\displaystyle {\frac {V_{m}}{\sqrt {2E}}}=} [ A { ( M C + β + 3 6 ( β + 1 ) ) A + A ( N C + 3 β + 1 6 ( β + 1 ) ) − 1 / 3 } ] − 1 / 2 {\displaystyle \left[A\left\{{\frac {\left({\frac {M}{C}}+{\frac {\beta +3}{6\left(\beta +1\right)}}\right)}{A}}+A\left({\frac {N}{C}}+{\frac {3\beta +1}{6\left(\beta +1\right)}}\right)-1/3\right\}\right]^{-1/2}}
While the imploding cylinder equations are fundamentally similar to the general equation for asymmetrical sandwiches, the geometry involved (volume and area within the explosive's hollow shell, and expanding shell of detonation product gases pushing inwards and out) is more complicated, as the equations demonstrate.
The constant a {\displaystyle a} was experimentally and analytically determined to be 1.0.
A special case is a hollow sphere of explosives, initiated evenly around its surface, with an outer tamper and inner hollow shell which is then accelerated inwards ("imploded") rather than outwards, is described by: [ 9 ]
β = R o R i {\displaystyle \beta ={\frac {R_{o}}{R_{i}}}}
a = 1 {\displaystyle a=1}
A = V o V i = [ M C + ( a M C ) ( β 2 − 1 ) + β 2 + 2 β + 3 4 ( β 2 + β + 1 ) ] ( N C + 3 β 2 + 2 β + 1 4 ( β 2 + β + 1 ) ) {\displaystyle A={\frac {V_{o}}{V_{i}}}={\frac {\left[{\frac {M}{C}}+\left(a{\frac {M}{C}}\right)\left(\beta ^{2}-1\right)+{\frac {\beta ^{2}+2\beta +3}{4\left(\beta ^{2}+\beta +1\right)}}\right]}{\left({\frac {N}{C}}+{\frac {3\beta ^{2}+2\beta +1}{4\left(\beta ^{2}+\beta +1\right)}}\right)}}}
V m 2 E = {\displaystyle {\frac {V_{m}}{\sqrt {2E}}}=} [ A { ( M C + β 2 + 3 β + 6 10 ( β 2 + β + 1 ) ) A + A ( N C + 6 β 2 + 3 β + 1 10 ( β 2 + β + 1 ) ) − 3 β 2 + 4 β + 3 10 ( β 2 + β + 1 ) } ] − 1 / 2 {\displaystyle \left[A\left\{{\frac {\left({\frac {M}{C}}+{\frac {\beta ^{2}+3\beta +6}{10\left(\beta ^{2}+\beta +1\right)}}\right)}{A}}+A\left({\frac {N}{C}}+{\frac {6\beta ^{2}+3\beta +1}{10\left(\beta ^{2}+\beta +1\right)}}\right)-{\frac {3\beta ^{2}+4\beta +3}{10\left(\beta ^{2}+\beta +1\right)}}\right\}\right]^{-1/2}}
The spherical Gurney equation has applications in early nuclear weapons design . | https://en.wikipedia.org/wiki/Gurney_equations |
Guru Meditation is an error notice originally displayed by the Amiga computer when it crashes . It is now also used by Varnish , [ 1 ] a software component used by many content-heavy websites. This has led to many internet users seeing a "Guru Meditation" message (or the variant "Guru Mediation") [ 2 ] when these websites suffer crashes or other issues. It is analogous to the " Blue Screen of Death " in Microsoft Windows operating systems , or a kernel panic in Unix .
It has also been used as a message for unrecoverable errors in software packages such as VirtualBox [ 3 ] and other operating systems (see Legacy section below).
The term "Guru Meditation Error" originated as an in-house joke in Amiga's early days. The company had a product called the Joyboard for the Atari 2600 home video game console , a game controller much like a joystick but operated by the feet, similar to the Wii Balance Board . Early in the development of the Amiga computer operating system, the company's developers became so frustrated with the system's frequent crashes that, as a relaxation technique, a game was developed where a person would sit cross-legged on the Joyboard, resembling an Indian guru . [ 4 ] The player tried to remain extremely still; the winner was the player who stayed still the longest. If the player moved too much, a "guru meditation" error occurred. [ 5 ]
The alert occurred when there was a fatal problem with the system. If the system had no means of recovery, it could display the alert, even in systems with numerous critical flaws. In extreme cases, the alert could even be displayed if the system's memory was completely exhausted.
The text of the alert messages was completely baffling to most users. Only highly technically adept Amiga users would know, for example, that exception 3 was an address error, and meant the program was accessing a word on an unaligned boundary. Users without this specialized knowledge would have no recourse but to look for a "Guru" or to simply reboot the machine and hope for the best.
When a Guru Meditation is displayed, the options are to reboot by pressing the left mouse button, or to invoke ROMWack by pressing the right mouse button or to manually reboot. ROMWack is a minimalist debugger built into the operating system which is accessible by connecting a 9600 bit /s terminal to the serial port .
The alert itself appears as a black rectangular box located in the upper portion of the screen. Its border and text are red for a normal Guru Meditation, or green/yellow for a Recoverable Alert, another kind of Guru Meditation. The screen may go black, but the power LEDs always alternates between full and half-brightness for a few seconds before the alert appears. In AmigaOS 1.x, programmed in ROMs known as Kickstart 1.1, 1.2 and 1.3, the errors are always red. In AmigaOS 2.x and 3.x, recoverable alerts are yellow, except for some very early versions of 2.x where they were green.
Dead-end alerts are always red and terminal in all OS versions except in a rare series of events, as in when a deprecated Kickstart (example: 1.1) program conditionally boots from disk on a more advanced Kickstart 3.x ROM Amiga running in compatibility mode (therefore eschewing the on-disk OS) and crashes with a red Guru Meditation but subsequently restores itself by pressing the left mouse button, the newer Kickstart recognizing an inadvised low level chipset call for the older ROM directly poking the hardware, and addressing it.
The error is displayed as two fields , separated by a period. The format is #0000000x.yyyyyyyy in case of a CPU error, or #aabbcccc.dddddddd in case of a system software error. The first field is either the Motorola 68000 exception number that occurred (if a CPU error occurs) or an internal error identifier (such as an "Out of Memory" code), in case of a system software error. The second can be the address of a Task structure, or the address of a memory block whose allocation or deallocation failed. It is never the address of the code that caused the error. If the cause of the crash is uncertain, this number is rendered as 48454C50 , which stands for "HELP" in hexadecimal ASCII characters (48=H, 45=E, 4C=L, 50=P).
There was a commercially available error handler for AmigaOS, before version 2.04, called GOMF (Get Outta My Face) made by Hypertek/Silicon Springs Development corp. It was able to deal with many kinds of errors and gave the user a choice to either remove the offending process and associated screen, or allow the machine to show the Guru Meditation. In many cases, removal of the offending process gave one the choice to save one's data and exit running programs before rebooting the system. When the damage was not extensive, one was able to continue using the machine. However, it did not save the user from all errors, as one may have still seen this error occasionally.
Recoverable Alerts are non-critical crashes in the computer system. In most cases, it is possible to resume work and save files after a Recoverable Alert, while a normal, red Guru Meditation always results in an immediate reboot.
It is, however, still recommended to reboot as soon as possible after encountering a Recoverable Alert, because the system may be in an unpredictable state that can cause data corruption. [ citation needed ]
The first byte specifies the area of the system affected. The top bit will be set if the error is a dead end alert. [ citation needed ] | https://en.wikipedia.org/wiki/Guru_Meditation |
In coding theory , list decoding is an alternative to unique decoding of error-correcting codes in the presence of many errors. If a code has relative distance δ {\displaystyle \delta } , then it is possible in principle to recover an encoded message when up to δ / 2 {\displaystyle \delta /2} fraction of the codeword symbols are corrupted. But when error rate is greater than δ / 2 {\displaystyle \delta /2} , this will not in general be possible. List decoding overcomes that issue by allowing the decoder to output a short list of messages that might have been encoded. List decoding can correct more than δ / 2 {\displaystyle \delta /2} fraction of errors.
There are many polynomial-time algorithms for list decoding. In this article, we first present an algorithm for Reed–Solomon (RS) codes which corrects up to 1 − 2 R {\displaystyle 1-{\sqrt {2R}}} errors and is due to Madhu Sudan . Subsequently, we describe the improved Guruswami – Sudan list decoding algorithm, which can correct up to 1 − R {\displaystyle 1-{\sqrt {R}}} errors.
Here is a plot of the rate R and distance δ {\displaystyle \delta } for different algorithms.
https://wiki.cse.buffalo.edu/cse545/sites/wiki.cse.buffalo.edu.cse545/files/81/Graph.jpg
Input : A field F {\displaystyle F} ; n distinct pairs of elements ( x i , y i ) i = 1 n {\displaystyle {(x_{i},y_{i})_{i=1}^{n}}} in F × F {\displaystyle F\times F} ; and integers d {\displaystyle d} and t {\displaystyle t} .
Output: A list of all functions f : F → F {\displaystyle f:F\to F} satisfying
f ( x ) {\displaystyle f(x)} is a polynomial in x {\displaystyle x} of degree at most d {\displaystyle d}
To understand Sudan's Algorithm better, one may want to first know another algorithm which can be considered as the earlier version or the fundamental version of the algorithms for list decoding RS codes - the Berlekamp–Welch algorithm .
Welch and Berlekamp initially came with an algorithm which can solve the problem in polynomial time with best threshold on t {\displaystyle t} to be t ≥ ( n + d + 1 ) / 2 {\displaystyle t\geq (n+d+1)/2} .
The mechanism of Sudan's Algorithm is almost the same as the algorithm of Berlekamp–Welch Algorithm, except in the step 1, one wants to compute a bivariate polynomial of bounded ( 1 , k ) {\displaystyle (1,k)} degree. Sudan's list decoding algorithm for Reed–Solomon code which is an improvement on Berlekamp and Welch algorithm, can solve the problem with t = ( 2 n d ) {\displaystyle t=({\sqrt {2nd}})} . This bound is better than the unique decoding bound 1 − ( R 2 ) {\displaystyle 1-\left({\frac {R}{2}}\right)} for R < 0.07 {\displaystyle R<0.07} .
Definition 1 (weighted degree)
For weights w x , w y ∈ Z + {\displaystyle w_{x},w_{y}\in \mathbb {Z} ^{+}} , the ( w x , w y ) {\displaystyle (w_{x},w_{y})} – weighted degree of monomial q i j x i y j {\displaystyle q_{ij}x^{i}y^{j}} is i w x + j w y {\displaystyle iw_{x}+jw_{y}} . The ( w x , w y ) {\displaystyle (w_{x},w_{y})} – weighted degree of a polynomial Q ( x , y ) = ∑ i j q i j x i y j {\displaystyle Q(x,y)=\sum _{ij}q_{ij}x^{i}y^{j}} is the maximum, over the monomials with non-zero coefficients, of the ( w x , w y ) {\displaystyle (w_{x},w_{y})} – weighted degree of the monomial.
For example, x y 2 {\displaystyle xy^{2}} has ( 1 , 3 ) {\displaystyle (1,3)} -degree 7
Algorithm:
Inputs: n , d , t {\displaystyle n,d,t} ; { ( x 1 , y 1 ) ⋯ ( x n , y n ) {\displaystyle (x_{1},y_{1})\cdots (x_{n},y_{n})} } /* Parameters l,m to be set later. */
Step 1: Find a non-zero bivariate polynomial Q : F 2 ↦ F {\displaystyle Q:F^{2}\mapsto F} satisfying
Step 2. Factor Q into irreducible factors.
Step 3. Output all the polynomials f {\displaystyle f} such that ( y − f ( x ) ) {\displaystyle (y-f(x))} is a factor of Q and f ( x i ) = y i {\displaystyle f(x_{i})=y_{i}} for at least t values of i ∈ [ n ] {\displaystyle i\in [n]}
One has to prove that the above algorithm runs in polynomial time and outputs the correct result. That can be done by proving following set of claims.
Claim 1:
If a function Q : F 2 → F {\displaystyle Q:F^{2}\to F} satisfying (2) exists, then one can find it in polynomial time.
Proof:
Note that a bivariate polynomial Q ( x , y ) {\displaystyle Q(x,y)} of ( 1 , d ) {\displaystyle (1,d)} -weighted degree at most D {\displaystyle D} can be uniquely written as Q ( x , y ) = ∑ j = 0 l ∑ k = 0 m + ( l − j ) d q k j x k y j {\displaystyle Q(x,y)=\sum _{j=0}^{l}\sum _{k=0}^{m+(l-j)d}q_{kj}x^{k}y^{j}} . Then one has to find the coefficients q k j {\displaystyle q_{kj}} satisfying the constraints ∑ j = 0 l ∑ k = 0 m + ( l − j ) d q k j x i k y i j = 0 {\displaystyle \sum _{j=0}^{l}\sum _{k=0}^{m+(l-j)d}q_{kj}x_{i}^{k}y_{i}^{j}=0} , for every i ∈ [ n ] {\displaystyle i\in [n]} . This is a linear set of equations in the unknowns { q k j {\displaystyle q_{kj}} }. One can find a solution using Gaussian elimination in polynomial time.
Claim 2:
If ( m + 1 ) ( l + 1 ) + d ( l + 1 2 ) > n {\displaystyle (m+1)(l+1)+d{\begin{pmatrix}l+1\\2\end{pmatrix}}>n} then there exists a function Q ( x , y ) {\displaystyle Q(x,y)} satisfying (2)
Proof:
To ensure a non zero solution exists, the number of coefficients in Q ( x , y ) {\displaystyle Q(x,y)} should be greater than the number of constraints. Assume that the maximum degree d e g x ( Q ) {\displaystyle deg_{x}(Q)} of x {\displaystyle x} in Q ( x , y ) {\displaystyle Q(x,y)} is m and the maximum degree d e g y ( Q ) {\displaystyle deg_{y}(Q)} of y {\displaystyle y} in Q ( x , y ) {\displaystyle Q(x,y)} is l {\displaystyle l} . Then the degree of Q ( x , y ) {\displaystyle Q(x,y)} will be at most m + l d {\displaystyle m+ld} . One has to see that the linear system is homogeneous. The setting q j k = 0 {\displaystyle q_{jk}=0} satisfies all linear constraints. However this does not satisfy (2), since the solution can be identically zero. To ensure that a non-zero solution exists, one has to make sure that number of unknowns in the linear system to be ( m + 1 ) ( l + 1 ) + d ( l + 1 2 ) > n {\displaystyle (m+1)(l+1)+d{\begin{pmatrix}l+1\\2\end{pmatrix}}>n} , so that one can have a non zero Q ( x , y ) {\displaystyle Q(x,y)} . Since this value is greater than n, there are more variables than constraints and therefore a non-zero solution exists.
Claim 3:
If Q ( x , y ) {\displaystyle Q(x,y)} is a function satisfying (2) and f ( x ) {\displaystyle f(x)} is function satisfying (1) and t > m + l d {\displaystyle t>m+ld} , then ( y − f ( x ) ) {\displaystyle (y-f(x))} divides Q ( x , y ) {\displaystyle Q(x,y)}
Proof:
Consider a function p ( x ) = Q ( x , f ( x ) ) {\displaystyle p(x)=Q(x,f(x))} . This is a polynomial in x {\displaystyle x} , and argue that it has degree at most m + l d {\displaystyle m+ld} . Consider any monomial q j k x k y j {\displaystyle q_{jk}x^{k}y^{j}} of Q ( x ) {\displaystyle Q(x)} . Since Q {\displaystyle Q} has ( 1 , d ) {\displaystyle (1,d)} -weighted degree at most m + l d {\displaystyle m+ld} , one can say that k + j d ≤ m + l d {\displaystyle k+jd\leq m+ld} . Thus the term q k j x k f ( x ) j {\displaystyle q_{kj}x^{k}f(x)^{j}} is a polynomial in x {\displaystyle x} of degree at most k + j d ≤ m + l d {\displaystyle k+jd\leq m+ld} . Thus p ( x ) {\displaystyle p(x)} has degree at most m + l d {\displaystyle m+ld}
Next argue that p ( x ) {\displaystyle p(x)} is identically zero. Since Q ( x i , f ( x i ) ) {\displaystyle Q(x_{i},f(x_{i}))} is zero whenever y i = f ( x i ) {\displaystyle y_{i}=f(x_{i})} , one can say that p ( x i ) {\displaystyle p(x_{i})} is zero for strictly greater than m + l d {\displaystyle m+ld} points. Thus p {\displaystyle p} has more zeroes than its degree and hence is identically zero, implying Q ( x , f ( x ) ) ≡ 0 {\displaystyle Q(x,f(x))\equiv 0}
Finding optimal values for m {\displaystyle m} and l {\displaystyle l} .
Note that m + l d < t {\displaystyle m+ld<t} and ( m + 1 ) ( l + 1 ) + d ( l + 1 2 ) > n {\displaystyle (m+1)(l+1)+d{\begin{pmatrix}l+1\\2\end{pmatrix}}>n} For a given value l {\displaystyle l} , one can compute the smallest m {\displaystyle m} for which the second condition holds
By interchanging the second condition one can get m {\displaystyle m} to be at most ( n + 1 − d ( l + 1 2 ) ) / 2 − 1 {\displaystyle (n+1-d{\begin{pmatrix}l+1\\2\end{pmatrix}})/2-1} Substituting this value into first condition one can get t {\displaystyle t} to be at least n + 1 l + 1 + d l 2 {\displaystyle {\frac {n+1}{l+1}}+{\frac {dl}{2}}} Next minimize the above equation of unknown parameter l {\displaystyle l} . One can do that by taking derivative of the equation and equating that to zero
By doing that one will get, l = 2 ( n + 1 ) d − 1 {\displaystyle l={\sqrt {\frac {2(n+1)}{d}}}-1} Substituting back the l {\displaystyle l} value into m {\displaystyle m} and t {\displaystyle t} one will get m ≥ ( n + 1 ) d 2 − ( n + 1 ) d 2 + d 2 − 1 = d 2 − 1 {\displaystyle m\geq {\sqrt {\frac {(n+1)d}{2}}}-{\sqrt {\frac {(n+1)d}{2}}}+{\frac {d}{2}}-1={\frac {d}{2}}-1} t > 2 ( n + 1 ) d 2 d − d 2 − 1 {\displaystyle t>{\sqrt {\frac {2(n+1)d^{2}}{d}}}-{\frac {d}{2}}-1} t > 2 ( n + 1 ) d − d 2 − 1 {\displaystyle t>{\sqrt {2(n+1)d}}-{\frac {d}{2}}-1}
Consider a ( n , k ) {\displaystyle (n,k)} Reed–Solomon code over the finite field F = G F ( q ) {\displaystyle \mathbb {F} =GF(q)} with evaluation set ( α 1 , α 2 , … , α n ) {\displaystyle (\alpha _{1},\alpha _{2},\ldots ,\alpha _{n})} and a positive integer r {\displaystyle r} , the Guruswami-Sudan List Decoder accepts a vector β = ( β 1 , β 2 , … , β n ) {\displaystyle \beta =(\beta _{1},\beta _{2},\ldots ,\beta _{n})} ∈ {\displaystyle \in } F n {\displaystyle \mathbb {F} ^{n}} as input, and outputs a list of polynomials of degree ≤ k {\displaystyle \leq k} which are in 1 to 1 correspondence with codewords.
The idea is to add more restrictions on the bi-variate polynomial Q ( x , y ) {\displaystyle Q(x,y)} which results in the increment of constraints along with the number of roots.
A bi-variate polynomial Q ( x , y ) {\displaystyle Q(x,y)} has a zero of multiplicity r {\displaystyle r} at ( 0 , 0 ) {\displaystyle (0,0)} means that Q ( x , y ) {\displaystyle Q(x,y)} has no term of degree ≤ r {\displaystyle \leq r} , where the x -degree of f ( x ) {\displaystyle f(x)} is defined as the maximum degree of any x term in f ( x ) {\displaystyle f(x)} {\displaystyle \qquad } d e g x f ( x ) {\displaystyle deg_{x}f(x)} = {\displaystyle =} max i ∈ I { i } {\displaystyle \max _{i\in I}\{i\}}
For example:
Let Q ( x , y ) = y − 4 x 2 {\displaystyle Q(x,y)=y-4x^{2}} .
https://wiki.cse.buffalo.edu/cse545/sites/wiki.cse.buffalo.edu.cse545/files/76/Fig1.jpg
Hence, Q ( x , y ) {\displaystyle Q(x,y)} has a zero of multiplicity 1 at (0,0).
Let Q ( x , y ) = y + 6 x 2 {\displaystyle Q(x,y)=y+6x^{2}} .
https://wiki.cse.buffalo.edu/cse545/sites/wiki.cse.buffalo.edu.cse545/files/76/Fig2.jpg
Hence, Q ( x , y ) {\displaystyle Q(x,y)} has a zero of multiplicity 1 at (0,0).
Let Q ( x , y ) = ( y − 4 x 2 ) ( y + 6 x 2 ) = y 2 + 6 x 2 y − 4 x 2 y − 24 x 4 {\displaystyle Q(x,y)=(y-4x^{2})(y+6x^{2})=y^{2}+6x^{2}y-4x^{2}y-24x^{4}}
https://wiki.cse.buffalo.edu/cse545/sites/wiki.cse.buffalo.edu.cse545/files/76/Fig3.jpg
Hence, Q ( x , y ) {\displaystyle Q(x,y)} has a zero of multiplicity 2 at (0,0).
Similarly, if Q ( x , y ) = [ ( y − β ) − 4 ( x − α ) 2 ) ] [ ( y − β ) + 6 ( x − α ) 2 ) ] {\displaystyle Q(x,y)=[(y-\beta )-4(x-\alpha )^{2})][(y-\beta )+6(x-\alpha )^{2})]} Then, Q ( x , y ) {\displaystyle Q(x,y)} has a zero of multiplicity 2 at ( α , β ) {\displaystyle (\alpha ,\beta )} .
Q ( x , y ) {\displaystyle Q(x,y)} has r {\displaystyle r} roots at ( α , β ) {\displaystyle (\alpha ,\beta )} if Q ( x , y ) {\displaystyle Q(x,y)} has a zero of multiplicity r {\displaystyle r} at ( α , β ) {\displaystyle (\alpha ,\beta )} when ( α , β ) ≠ ( 0 , 0 ) {\displaystyle (\alpha ,\beta )\neq (0,0)} .
Let the transmitted codeword be ( f ( α 1 ) , f ( α 2 ) , … , f ( α n ) ) {\displaystyle (f(\alpha _{1}),f(\alpha _{2}),\ldots ,f(\alpha _{n}))} , ( α 1 , α 2 , … , α n ) {\displaystyle (\alpha _{1},\alpha _{2},\ldots ,\alpha _{n})} be the support set of the transmitted codeword & the received word be ( β 1 , β 2 , … , β n ) {\displaystyle (\beta _{1},\beta _{2},\ldots ,\beta _{n})}
The algorithm is as follows:
• Interpolation step
For a received vector ( β 1 , β 2 , … , β n ) {\displaystyle (\beta _{1},\beta _{2},\ldots ,\beta _{n})} , construct a non-zero bi-variate polynomial Q ( x , y ) {\displaystyle Q(x,y)} with ( 1 , k ) − {\displaystyle (1,k)-} weighted degree of at most d {\displaystyle d} such that Q {\displaystyle Q} has a zero of multiplicity r {\displaystyle r} at each of the points ( α i , β i ) {\displaystyle (\alpha _{i},\beta _{i})} where 1 ≤ i ≤ n {\displaystyle 1\leq i\leq n}
• Factorization step
Find all the factors of Q ( x , y ) {\displaystyle Q(x,y)} of the form y − p ( x ) {\displaystyle y-p(x)} and p ( α i ) = β i {\displaystyle p(\alpha _{i})=\beta _{i}} for at least t {\displaystyle t} values of i {\displaystyle i}
where 0 ≤ i ≤ n {\displaystyle 0\leq i\leq n} & p ( x ) {\displaystyle p(x)} is a polynomial of degree ≤ k {\displaystyle \leq k}
Recall that polynomials of degree ≤ k {\displaystyle \leq k} are in 1 to 1 correspondence with codewords. Hence, this step outputs the list of codewords.
Lemma: Interpolation step implies ( r + 1 2 ) {\displaystyle {\begin{pmatrix}r+1\\2\end{pmatrix}}} constraints on the coefficients of a i {\displaystyle a_{i}}
Let Q ( x , y ) = ∑ i = 0 , j = 0 i = m , j = p a i , j x i y j {\displaystyle Q(x,y)=\sum _{i=0,j=0}^{i=m,j=p}a_{i,j}x^{i}y^{j}} where deg x Q ( x , y ) = m {\displaystyle \deg _{x}Q(x,y)=m} and deg y Q ( x , y ) = p {\displaystyle \deg _{y}Q(x,y)=p}
Then, Q ( x + α , y + β ) {\displaystyle Q(x+\alpha ,y+\beta )} = {\displaystyle =} ∑ u = 0 , v = 0 r {\displaystyle \sum _{u=0,v=0}^{r}} Q u , v {\displaystyle Q_{u,v}} ( α , β ) {\displaystyle (\alpha ,\beta )} x u {\displaystyle x^{u}} y v {\displaystyle y^{v}} ........................(Equation 1)
where Q u , v {\displaystyle Q_{u,v}} ( x , y ) {\displaystyle (x,y)} = {\displaystyle =} ∑ i = 0 , j = 0 i = m , j = p {\displaystyle \sum _{i=0,j=0}^{i=m,j=p}} ( i u ) {\displaystyle {\begin{pmatrix}i\\u\end{pmatrix}}} ( j v ) {\displaystyle {\begin{pmatrix}j\\v\end{pmatrix}}} a i , j {\displaystyle a_{i,j}} x i − u {\displaystyle x^{i-u}} y j − v {\displaystyle y^{j-v}}
Proof of Equation 1:
Proof of Lemma:
The polynomial Q ( x , y ) {\displaystyle Q(x,y)} has a zero of multiplicity r {\displaystyle r} at ( α , β ) {\displaystyle (\alpha ,\beta )} if
∑ v = 0 r − 1 r − v {\displaystyle \sum _{v=0}^{r-1}{r-v}} = {\displaystyle =} ( r + 1 2 ) {\displaystyle {\begin{pmatrix}r+1\\2\end{pmatrix}}}
Thus, ( r + 1 2 ) {\displaystyle {\begin{pmatrix}r+1\\2\end{pmatrix}}} number of selections can be made for ( u , v ) {\displaystyle (u,v)} and each selection implies constraints on the coefficients of a i {\displaystyle a_{i}}
Proposition:
Q ( x , p ( x ) ) ≡ 0 {\displaystyle Q(x,p(x))\equiv 0} if y − p ( x ) {\displaystyle y-p(x)} is a factor of Q ( x , y ) {\displaystyle Q(x,y)}
Proof:
Since, y − p ( x ) {\displaystyle y-p(x)} is a factor of Q ( x , y ) {\displaystyle Q(x,y)} , Q ( x , y ) {\displaystyle Q(x,y)} can be represented as
Q ( x , y ) = L ( x , y ) ( y − p ( x ) ) {\displaystyle Q(x,y)=L(x,y)(y-p(x))} + {\displaystyle +} R ( x ) {\displaystyle R(x)}
where, L ( x , y ) {\displaystyle L(x,y)} is the quotient obtained when Q ( x , y ) {\displaystyle Q(x,y)} is divided by y − p ( x ) {\displaystyle y-p(x)} R ( x ) {\displaystyle R(x)} is the remainder
Now, if y {\displaystyle y} is replaced by p ( x ) {\displaystyle p(x)} , Q ( x , p ( x ) ) {\displaystyle Q(x,p(x))} ≡ {\displaystyle \equiv } 0 {\displaystyle 0} , only if R ( x ) {\displaystyle R(x)} ≡ {\displaystyle \equiv } 0 {\displaystyle 0}
Theorem:
If p ( α ) = β {\displaystyle p(\alpha )=\beta } , then ( x − α ) r {\displaystyle (x-\alpha )^{r}} is a factor of Q ( x , p ( x ) ) {\displaystyle Q(x,p(x))}
Proof:
Q ( x , y ) {\displaystyle Q(x,y)} = {\displaystyle =} ∑ u , v {\displaystyle \sum _{u,v}} Q u , v {\displaystyle Q_{u,v}} ( α , β ) {\displaystyle (\alpha ,\beta )} ( x − α ) u {\displaystyle (x-\alpha )^{u}} ( y − β ) v {\displaystyle (y-\beta )^{v}} ...........................From Equation 2
Q ( x , p ( x ) ) {\displaystyle Q(x,p(x))} = {\displaystyle =} ∑ u , v {\displaystyle \sum _{u,v}} Q u , v {\displaystyle Q_{u,v}} ( α , β ) {\displaystyle (\alpha ,\beta )} ( x − α ) u {\displaystyle (x-\alpha )^{u}} ( p ( x ) − β ) v {\displaystyle (p(x)-\beta )^{v}}
Given, p ( α ) {\displaystyle p(\alpha )} = {\displaystyle =} β {\displaystyle \beta } ( p ( x ) − β ) {\displaystyle (p(x)-\beta )} mod ( x − α ) {\displaystyle (x-\alpha )} = {\displaystyle =} 0 {\displaystyle 0}
Hence, ( x − α ) u {\displaystyle (x-\alpha )^{u}} ( p ( x ) − β ) v {\displaystyle (p(x)-\beta )^{v}} mod ( x − α ) u + v {\displaystyle (x-\alpha )^{u+v}} = {\displaystyle =} 0 {\displaystyle 0}
Thus, ( x − α ) r {\displaystyle (x-\alpha )^{r}} is a factor of Q ( x , p ( x ) ) {\displaystyle Q(x,p(x))} .
As proved above,
t ⋅ r > D {\displaystyle t\cdot r>D}
t > D r {\displaystyle t>{\frac {D}{r}}}
D ( D + 2 ) 2 ( k − 1 ) > n ( r + 1 2 ) {\displaystyle {\frac {D(D+2)}{2(k-1)}}>n{\begin{pmatrix}r+1\\2\end{pmatrix}}} where LHS is the upper bound on the number of coefficients of Q ( x , y ) {\displaystyle Q(x,y)} and RHS is the earlier proved Lemma.
Therefore, t = ⌈ k n ( 1 − 1 r ) ⌉ {\displaystyle t=\left\lceil {\sqrt {kn(1-{\frac {1}{r}})}}\right\rceil }
Substitute r = 2 k n {\displaystyle r=2kn} ,
Hence proved, that Guruswami–Sudan List Decoding Algorithm can list decode Reed-Solomon codes up to 1 − R {\displaystyle 1-{\sqrt {R}}} errors. | https://en.wikipedia.org/wiki/Guruswami–Sudan_list_decoding_algorithm |
In cosmology , the Gurzadyan theorem , proved by Vahe Gurzadyan , [ 1 ] states the most general functional form for the force satisfying the condition of identity of the gravity of the sphere and of a point mass located in the sphere's center. This theorem thus refers to the first statement of Isaac Newton ’s [ 2 ] shell theorem (the identity mentioned above) but not the second one, namely, the absence of gravitational force inside a shell. [ 3 ]
The theorem had entered and its importance for cosmology outlined in several papers [ 4 ] [ 5 ] as well as in shell theorem .
The formula for the force derived in [ 1 ] has the form
where G {\displaystyle G} and Λ {\displaystyle \Lambda } are constants. The first term is the familiar law of universal gravitation, the second one corresponds to the cosmological constant term in general relativity and McCrea-Milne cosmology. [ 6 ] Then the field is force-free only in the center of a shell but the confinement (oscillator) term does not change the initial O ( 4 ) {\displaystyle O(4)} symmetry of the Newtonian field. Also, this field corresponds to the only field possessing the property of the Newtonian one: the closing of orbits at any negative value of energy, i.e. the coincidence of the period of variation of the value of the radius vector with that of its revolution by 2 π {\displaystyle 2\pi } (resonance principle) .
Einstein named the cosmological constant as a universal constant, introducing it to define the static cosmological model. [ 7 ] [ 8 ] Einstein has stated: [ 9 ] “I should have initially set λ = 0 {\displaystyle \lambda =0} in Newton's sense. But the new considerations speak for a non-zero λ {\displaystyle \lambda } , which strives to bring about a non-zero mean density ρ 0 {\displaystyle \rho _{0}} of matter.” This theorem solves that contradiction between “non-zero λ {\displaystyle \lambda } ” and Newton's law.
From this theorem the cosmological constant Λ {\displaystyle \Lambda } emerges as additional constant of gravity along with the Newton's gravitational constant G {\displaystyle G} . Then, the cosmological constant is dimension independent and matter-uncoupled and hence can be considered even more universal than Newton's gravitational constant. [ 10 ]
For Λ {\displaystyle \Lambda } joining the set of fundamental constants ( G , c , ℏ ) {\displaystyle (G,c,\hbar )} , the gravitational
Newton's constant, the speed of light and the Planck constant , yields
and a dimensionless quantity emerges for the 4-constant set ( G , Λ , c , ℏ ) {\displaystyle (G,\Lambda ,c,\hbar )} [ 11 ]
where a {\displaystyle a} is a real number. Note, no dimensionless quantity is possible to construct from the 3 constants G , c , ℏ {\displaystyle G,c,\hbar } .
This within a numerical factor, a = 1 {\displaystyle a=1} , coincides with the information (or entropy ) of de Sitter event horizon [ 12 ]
and the Bekenstein Bound [ 13 ]
Within the conformal cyclic cosmology [ 14 ] [ 15 ] this theorem implies that, in each aeon of an initial value of Λ {\displaystyle \Lambda } , the values of the 3 physical constants will be eligible for rescaling fulfilling the dimensionless ratio of invariants with respect to the conformal transformation [ 11 ]
Then the ratio yields
for all physical quantities in Planck (initial) and de Sitter (final) eras of the aeons, remaining invariant under conformal transformations.
This theorem, in the context of nonlocal effects in a system of gravitating particles, leads to the inhomogeneous Dirichlet boundary problem for the Poisson equation [ 16 ]
where R Ω {\displaystyle R_{\Omega }} is the radius of the region,
Its solution can be expressed in terms of the double layer potential , which leads to an inhomogeneous nonlinear Hammerstein integral equation for the gravitational potential
This leads to a linear inhomogeneous 2nd kind Fredholm equation
Its solution can be expressed in terms of the resolvent Γ {\displaystyle \Gamma } of the integral kernel and the non-linear (repulsive) term
The dynamics of groups and clusters of galaxies are claimed to fit the theorem, [ 10 ] [ 17 ] see also. [ 18 ] The possibility of two Hubble flows, a local one, determined by that formula, and a global one, described by Friedmannian cosmological equations was stated in. [ 19 ] | https://en.wikipedia.org/wiki/Gurzadyan_theorem |
Gustaaf Van Tendeloo (born 1950), or Staf Van Tendeloo [ 1 ] is a Belgian physicist known for his contributions to electron microscopy, electron crystallography , and the physics of materials. [ 2 ] [ 3 ] In 2011, his group reported the first atomically resolved reconstruction of a nanoparticle in 3D. [ 4 ]
Van Tendeloo was born in Lier, Belgium . He obtained his licentiate in physics from the Vrije Universiteit Brussel (VUB; 'Free University of Brussels') in 1972, followed by his doctorate from the University of Antwerp in 1974 under the supervision of Severin Amelinckx. He received an aggregation from the VUB in 1981. Since 1972, Van Tendeloo has been associated with the University of Antwerp, where he is the professor of solid-state physics . Additionally, he serves as Professor of the Physics of Materials at the University of Antwerp. In 1986 he became part-time professor at the VUB and since 1994 he has been a full professor at the University of Antwerp. Since 2003, he has been the head of the EMAT (Electron Microscopy of Materials) laboratory on electron microscopy. [ 2 ] [ 5 ]
Throughout his career, Van Tendeloo has undertaken significant research endeavors both domestically and internationally, including research stints at the University of California, Berkeley, University of Illinois Urbana-Champaign and the Université de Caen . [ 2 ] He is a member of the Royal Flemish Academy of Belgium for Science and the Arts since 2010. [ 6 ] [ 7 ] He received the Dr. De Leeuw-Damry-Bourlart Prize from the Research Foundation – Flanders (FWO) in 2015. [ 8 ] In 2023, He received an honorary doctorate degree from the University of Zaragoza . [ 5 ] | https://en.wikipedia.org/wiki/Gustaaf_Van_Tendeloo |
Gustav Heinrich Johann Apollon Tammann (9 June [ O.S. 28 May] 1861 – 17 December 1938) [ 1 ] was a prominent Baltic German chemist-physicist who made important contributions in the fields of glassy and solid solutions , heterogeneous equilibria, crystallization, and metallurgy . [ 2 ] He first predicted the order-disorder transition in alloys .
Tammann was born in Yamburg (now Kingisepp , Leningrad Oblast ). His father, Heinrich Tammann (1833–1864) was of Estonian peasant origin and his mother, Matilda Schünmann, was of German origin. [ 2 ] Tammann graduated from University of Dorpat in chemistry. [ 3 ] He went to Göttingen University in 1903 where he established the first Institute of Inorganic Chemistry in Germany. In 1908 he was appointed director of the Physico-Chemical Institute.
Tammann died in Göttingen at age 77. [ citation needed ]
In 1900, he discovered the phases of ice , now known as ice II and ice III. [ 4 ]
Later, his interests focused on the physics and physical chemistry of metals and alloys ( metallurgy ). He was also known for the Vogel–Fulcher–Tammann equation , and the Tait–Tammann equation of state which seeks to account for the compressibility of liquids. [ 5 ]
in 1919, Tammann predicted the order-disorder transition that is found in alloys at low temperatures. [ 6 ] Tamman and Otto Heusler also observed an anomaly in the specific heat of a bronze alloy in 1926, related to the critical points of the disorder-order transition. [ 6 ] This transition was demonstrated in 1929 by C. H. Johannsen and J. O Linde using x-ray diffraction . [ 6 ]
In 1925, Tammann was awarded Liebig Medal . On 28 May 1936, Tammann was awarded the Eagle Shield of the German Empire ( Adlerschild des Deutschen Reiches ), [ 7 ] with dedication "The Doyen of German Metallurgy". [ 8 ]
Tammann was awarded the following prizes:
The Tammann Commemorative Medal of the Deutsche Gesellschaft für Materialkunde is named after him. [ 10 ] | https://en.wikipedia.org/wiki/Gustav_Heinrich_Tammann |
Gustavo R. Paz-Pujalt (born 1954) is a Peruvian American scientist and inventor . He holds 45 US patents [ 1 ] and 59 international patents mainly in the areas of remote sensing, [ 2 ] thin films, sensors, and upconversion materials. [ 3 ]
Paz-Pujalt was born August 9, 1954, in Arequipa , Peru . He is of Galician and Welsh descent on his father's side and Catalan and Basque on his mother's. He graduated from San Andrés (Colegio) , an Anglo Peruvian college preparatory school in Lima, Peru. He graduated with honors and received the Miller Prize for accomplishments in English. Paz-Pujalt did his undergraduate work at the University of Wisconsin-Eau Claire and completed his Ph.D. in physical chemistry at the University of Wisconsin–Milwaukee . His doctoral adviser was George Keulks. He was also mentored by the distinguished professor W. Keith Hall. [ 4 ] During this time he studied surface science under Gert Ertl , winner of the Nobel Prize in Chemistry . Additionally, Paz-Pujalt has received numerous executive level diplomas from MIT and Wharton.
He was the Eastman Kodak Company 's Senior Research Associate from 1986 to 2004, the Director of Technology for IPValue at Xerox from 2004 to 2007, and is currently the CEO of Idealurgy, a knowledge company, which currently serves the needs of Fortune 500 corporations, International Industry Consortia, and major international research universities. Paz-Pujalt's patents are seminal to the formation of Frintz.com, an industry changing advertising medium.
This article about a Peruvian scientist is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Gustavo_R._Paz-Pujalt |
Gustavs Vanags (10 March 1891 — 8 May 1965) was a Soviet and Latvian organic chemist, full member of Latvian SSR Academy of Sciences . He was also one of the signers of the Memorandum of Latvian Central Council in 1944.
Gustavs Vanags was born in "Rungas" house of the Schnicken (Sniķeru) manor (now in Ukri Parish , Auce Municipality ). He received primary education in the Mitau Classic Gymnasium , and in 1910 enrolled Riga Polytechnic Institute. During the First World War, he, among many, went in evacuation to the inner regions of Russian Empire; after returning from it in 1921, he completed his education in the new-founded University of Latvia and worked at the Faculty of Chemistry, raising to the position of the chair of the Department of organic chemistry. He received his habilitation in 1932.
After Riga Polytechnic Institute was reestablished in 1958, G. Vanags moved to it, serving in the same position as the department chair until 1965. Simultaneously he also worked in the State Institute of Organic Synthesis, where he carried out his research in the chemistry of cyclic β- diketones . He was founder of Riga scholl of organic chemists specializing on β-diketones, which continues up to day (2020). Gustavs Vanags, along with his students, designed and synthesized several compounds of notable application in medicine, agriculture and chemical analysis (omefin, bindon, [ 1 ] nitroindandione, [ 2 ] rhodenticide diphenadione or ratindan).
Gustavs Vanags died in a sudden death on May 8, 1965, in Riga. He was buried in the Forest Cemetery . [ 3 ]
Latvian Academy of Sciences named a biannual prize for advances in chemistry in Gustavs Vanags' name.
A commemorative plaque with bas-relief of G. Vanags is installed in the hall of Riga Technical University Faculty of Chemistry . A commemorative stone is erected at the place where his native house of "Rungas" once stood. [ 4 ] | https://en.wikipedia.org/wiki/Gustavs_Vanags |
Gut microbiota , gut microbiome , or gut flora are the microorganisms , including bacteria , archaea , fungi , and viruses , that live in the digestive tracts of animals . [ 1 ] [ 2 ] The gastrointestinal metagenome is the aggregate of all the genomes of the gut microbiota . [ 3 ] [ 4 ] The gut is the main location of the human microbiome . [ 5 ] The gut microbiota has broad impacts, including effects on colonization , resistance to pathogens , maintaining the intestinal epithelium , metabolizing dietary and pharmaceutical compounds, controlling immune function, and even behavior through the gut–brain axis . [ 4 ]
The microbial composition of the gut microbiota varies across regions of the digestive tract. The colon contains the highest microbial density of any human-associated microbial community studied so far, representing between 300 and 1000 different species . [ 6 ] Bacteria are the largest and to date, best studied component and 99% of gut bacteria come from about 30 or 40 species. [ 7 ] About 55% of the dry mass of feces is bacteria. [ 8 ] Over 99% of the bacteria in the gut are anaerobes , but in the cecum , aerobic bacteria reach high densities. [ 5 ] It is estimated that the human gut microbiota has around a hundred times as many genes as there are in the human genome .
In humans, the gut microbiota has the highest numbers and species of bacteria compared to other areas of the body. [ 9 ] The approximate number of bacteria composing the gut microbiota is about 10 13 –10 14 (10,000 to 100,000 billion). [ 10 ] In humans, the gut flora is established at birth and gradually transitions towards a state resembling that of adults by the age of two, [ 11 ] coinciding with the development and maturation of the intestinal epithelium and intestinal mucosal barrier . This barrier is essential for supporting a symbiotic relationship with the gut flora while providing protection against pathogenic organisms. [ 12 ] [ 13 ]
The relationship between some gut microbiota and humans is not merely commensal (a non-harmful coexistence), but rather a mutualistic relationship. [ 5 ] : 700 Some human gut microorganisms benefit the host by fermenting dietary fiber into short-chain fatty acids (SCFAs), such as acetic acid and butyric acid , which are then absorbed by the host. [ 9 ] [ 14 ] Intestinal bacteria also play a role in synthesizing certain B vitamins and vitamin K as well as metabolizing bile acids , sterols , and xenobiotics . [ 5 ] [ 14 ] The systemic importance of the SCFAs and other compounds they produce are like hormones and the gut flora itself appears to function like an endocrine organ . [ 14 ] Dysregulation of the gut flora has been correlated with a host of inflammatory and autoimmune conditions. [ 9 ] [ 15 ]
The composition of human gut microbiota changes over time, when the diet changes, and as overall health changes. [ 9 ] [ 15 ] A systematic review from 2016 examined the preclinical and small human trials that have been conducted with certain commercially available strains of probiotic bacteria and identified those that had the most potential to be useful for certain central nervous system disorders . [ 16 ] It should also be highlighted that the Mediterranean diet, rich in vegetables and fibers, stimulates the activity and growth of beneficial bacteria for the brain. [ 17 ]
The microbial composition of the gut microbiota varies across the digestive tract. In the stomach and small intestine , relatively few species of bacteria are generally present. [ 6 ] [ 18 ] Fungi , protists , archaea , and viruses are also present in the gut flora, but less is known about their activities. [ 19 ]
Many species in the gut have not been studied outside of their hosts because they cannot be cultured . [ 18 ] [ 7 ] [ 20 ] While there are a small number of core microbial species shared by most individuals, populations of microbes can vary widely. [ 21 ] Within an individual, their microbial populations stay fairly constant over time, with some alterations occurring due to changes in lifestyle, diet and age. [ 6 ] [ 22 ] The Human Microbiome Project has set out to better describe the microbiota of the human gut and other body locations. [ citation needed ]
The four dominant bacterial phyla in the human gut are Bacillota (Firmicutes), Bacteroidota , Actinomycetota , and Pseudomonadota . [ 23 ] Most bacteria belong to the genera Bacteroides , Clostridium , Faecalibacterium , [ 6 ] [ 7 ] Eubacterium , Ruminococcus , Peptococcus , Peptostreptococcus , and Bifidobacterium . [ 6 ] [ 7 ] Other genera, such as Escherichia and Lactobacillus , are present to a lesser extent. [ 6 ] Species from the genus Bacteroides alone constitute about 30% of all bacteria in the gut, suggesting that this genus is especially important in the functioning of the host. [ 18 ]
Fungal genera that have been detected in the gut include Candida , Saccharomyces , Aspergillus , Penicillium , Rhodotorula , Trametes , Pleospora , Sclerotinia , Bullera , and Galactomyces , among others. [ 24 ] [ 25 ] Rhodotorula is most frequently found in individuals with inflammatory bowel disease while Candida is most frequently found in individuals with hepatitis B cirrhosis and chronic hepatitis B. [ 24 ]
Archaea constitute another large class of gut flora which are important in the metabolism of the bacterial products of fermentation.
Industrialization is associated with changes in the microbiota and the reduction of diversity could drive certain species to extinction; in 2018, researchers proposed a biobank repository of human microbiota. [ 26 ]
An enterotype is a classification of living organisms based on its bacteriological ecosystem in the human gut microbiome not dictated by age, gender, body weight, or national divisions. [ 27 ] There are indications that long-term diet influences enterotype. [ 28 ] Three human enterotypes have been proposed, [ 27 ] [ 29 ] but their value has been questioned. [ 30 ]
Due to the high acidity of the stomach , most microorganisms cannot survive there. The main bacteria of the gastric microbiota belong to five major phyla: Firmicutes , Bacteroidetes , Actinobacteria , Fusobacteriota , and Proteobacteria . The dominant genera are Prevotella , Streptococcus , Veillonella , Rothia , and Haemophilus . [ 31 ] The interaction between the pre-existing gastric microbiota with the introduction of H. pylori may influence disease progression . [ 31 ] When there is a presence of H. pylori it becomes the dominant species of the microbiota. [ 32 ]
The small intestine contains a trace amount of microorganisms due to the proximity and influence of the stomach. Gram-positive cocci and rod-shaped bacteria are the predominant microorganisms found in the small intestine. [ 5 ] However, in the distal portion of the small intestine alkaline conditions support gram-negative bacteria of the Enterobacteriaceae . [ 5 ] The bacterial flora of the small intestine aid in a wide range of intestinal functions. The bacterial flora provide regulatory signals that enable the development and utility of the gut. Overgrowth of bacteria in the small intestine can lead to intestinal failure. [ 34 ] In addition the large intestine contains the largest bacterial ecosystem in the human body. [ 5 ] About 99% of the large intestine and feces flora are made up of obligate anaerobes such as Bacteroides and Bifidobacterium. [ 35 ] Factors that disrupt the microorganism population of the large intestine include antibiotics, stress, and parasites. [ 5 ]
Bacteria make up most of the flora in the colon [ 36 ] and accounts for 60% of fecal nitrogen. [ 6 ] This fact makes feces an ideal source of gut flora for any tests and experiments by extracting the nucleic acid from fecal specimens, and bacterial 16S rRNA gene sequences are generated with bacterial primers. This form of testing is also often preferable to more invasive techniques, such as biopsies.
Five phyla dominate the intestinal microbiota: Bacteroidota , Bacillota (Firmicutes), Actinomycetota , Pseudomonadota , and Verrucomicrobiota – with Bacteroidota and Bacillota constituting 90% of the composition. [ 37 ] Somewhere between 300 [ 6 ] and 1000 different species live in the gut, [ 18 ] with most estimates at about 500. [ 38 ] [ 39 ] However, it is probable that 99% of the bacteria come from about 30 or 40 species, with Faecalibacterium prausnitzii (phylum firmicutes) being the most common species in healthy adults. [ 7 ] [ 40 ]
Research suggests that the relationship between gut flora and humans is not merely commensal (a non-harmful coexistence), but rather is a mutualistic , symbiotic relationship. [ 18 ] Though people can survive with no gut flora, [ 38 ] the microorganisms perform a host of useful functions, such as fermenting unused energy substrates, training the immune system via end products of metabolism like propionate and acetate , preventing growth of harmful species, regulating the development of the gut, producing vitamins for the host (such as biotin and vitamin K ), and producing hormones to direct the host to store fats. [ 5 ] Extensive modification and imbalances of the gut microbiota and its microbiome or gene collection are associated with obesity. [ 41 ] However, in certain conditions, some species are thought to be capable of causing disease by causing infection or increasing cancer risk for the host. [ 6 ] [ 36 ]
Fungi also make up a part of the gut flora, but less is known about their activities. [ 42 ]
Due to the prevalence of fungi in the natural environment, determining which genera and species are permanent members of the gut mycobiome is difficult. [ 43 ] [ 44 ] Research is underway as to whether Penicillium is a permanent or transient member of the gut flora, obtained from dietary sources such as cheese , though several species in the genus are known to survive at temperatures around 37 °C, about the same as the core body temperature . [ 44 ] Saccharomyces cerevisiae , brewer's yeast, is known to reach the intestines after being ingested and can be responsible for the condition auto-brewery syndrome in cases where it is overabundant, [ 44 ] [ 45 ] [ 46 ] while Candida albicans is likely a permanent member, and is believed to be acquired at birth through vertical transmission . [ 47 ] [ medical citation needed ]
The human virome includes all viruses associated with the human body, ranging from viruses that infect native cells to bacteriophages that infect bacteria in the microbiome. Among these, bacteriophages are by far the most numerous. [ 48 ]
There are common patterns of microbiome composition evolution during life. [ 49 ] In general, the diversity of microbiota composition of fecal samples is significantly higher in adults than in children, although interpersonal differences are higher in children than in adults. [ 50 ] Much of the maturation of microbiota into an adult-like configuration happens during the first three years of life. [ 50 ]
As the microbiome composition changes, so does the composition of bacterial proteins produced in the gut. In adult microbiomes, a high prevalence of enzymes involved in fermentation , methanogenesis and the metabolism of arginine , glutamate , aspartate and lysine have been found. In contrast, in infant microbiomes the dominant enzymes are involved in cysteine metabolism and fermentation pathways. [ 50 ]
Gut microbiome composition depends on the geographic origin of populations. Variations in a trade-off of Prevotella , the representation of the urease gene, and the representation of genes encoding glutamate synthase/degradation or other enzymes involved in amino acids degradation or vitamin biosynthesis show significant differences between populations from the US, Malawi , or Amerindian origin. [ 50 ]
The US population has a high representation of enzymes encoding the degradation of glutamine and enzymes involved in vitamin and lipoic acid biosynthesis; whereas Malawi and Amerindian populations have a high representation of enzymes encoding glutamate synthase and they also have an overrepresentation of α-amylase in their microbiomes. As the US population has a diet richer in fats than Amerindian or Malawian populations which have a corn-rich diet, the diet is probably the main determinant of the gut bacterial composition. [ 50 ]
Further studies have indicated a large difference in the composition of microbiota between European and rural African children. The fecal bacteria of children from Florence were compared to that of children from the small rural village of Boulpon in Burkina Faso . The diet of a typical child living in this village is largely lacking in fats and animal proteins and rich in polysaccharides and plant proteins. The fecal bacteria of European children were dominated by Firmicutes and showed a marked reduction in biodiversity, while the fecal bacteria of the Boulpon children was dominated by Bacteroidetes . The increased biodiversity and different composition of the gut microbiome in African populations may aid in the digestion of normally indigestible plant polysaccharides and also may result in a reduced incidence of non-infectious colonic diseases. [ 51 ]
On a smaller scale, it has been shown that sharing numerous common environmental exposures in a family is a strong determinant of individual microbiome composition. This effect has no genetic influence and it is consistently observed in culturally different populations. [ 50 ]
Malnourished children have less mature and less diverse gut microbiota than healthy children, and changes in the microbiome associated with nutrient scarcity can in turn be a pathophysiological cause of malnutrition. [ 52 ] [ 53 ] Malnourished children also typically have more potentially pathogenic gut flora, and more yeast in their mouths and throats. [ 54 ] Altering diet may lead to changes in gut microbiota composition and diversity. [ 55 ]
Researchers with the American Gut Project and Human Microbiome Project found that twelve microbe families varied in abundance based on the race or ethnicity of the individual. The strength of these associations is limited by the small sample size: the American Gut Project collected data from 1,375 individuals, 90% of whom were white. [ 56 ] The Healthy Life in an Urban Setting (HELIUS) study in Amsterdam found that those of Dutch ancestry had the highest level of gut microbiota diversity, while those of South Asian and Surinamese descent had the lowest diversity. The study results suggested that individuals of the same race or ethnicity have more similar microbiomes than individuals of different racial backgrounds. [ 56 ]
As of 2020, at least two studies have demonstrated a link between an individual's socioeconomic status (SES) and their gut microbiota. A study in Chicago found that individuals in higher SES neighborhoods had greater microbiota diversity. People from higher SES neighborhoods also had more abundant Bacteroides bacteria. Similarly, a study of twins in the United Kingdom found that higher SES was also linked with a greater gut diversity. [ 56 ]
As of 2023, a study suggests that antibiotics, especially those used in the treatment of broad-spectrum bacterial infections, have negative effects on the gut microbiota. [ 57 ] The study also states that there are many experts on intestinal health concerned that antibody usage has reduced the diversity of the gut microbiota, many of the strains are lost, and if there is a re-emergence of the bacteria, is gradual and long-term. [ 57 ]
When the study of gut flora began in 1995, [ 58 ] it was thought to have three key roles: direct defense against pathogens , fortification of host defense by its role in developing and maintaining the intestinal epithelium and inducing antibody production there, and metabolizing otherwise indigestible compounds in food. Subsequent work discovered its role in training the developing immune system, and yet further work focused on its role in the gut–brain axis . [ 59 ] The gut microbiota not only influences intestinal health but also plays a role in systemic immune regulation, including interactions with the pulmonary immune environment through what is known as the 'gut–lung axis'. [ 60 ]
The gut flora community plays a direct role in defending against pathogens by fully colonising the space, making use of all available nutrients, and by secreting compounds known as cytokines that kill or inhibit unwelcome organisms that would compete for nutrients with it. [ 61 ] Different strains of gut bacteria cause the production of different cytokines. Cytokines are chemical compounds produced by our immune system for initiating the inflammatory response against infections. Disruption of the gut flora allows competing organisms like Clostridioides difficile to become established that otherwise are kept in abeyance. [ 61 ]
Gut flora in infants becomes similar to an adult within one to two years of birth. [ 12 ] As the gut flora establishes, the lining of the intestines – the intestinal epithelium and the intestinal mucosal barrier that it secretes – develop a symbiosis with microorganisms. [ 12 ] Specifically, goblet cells that produce the mucosa proliferate, and the mucosa layer thickens, providing an outside mucosal layer in which favorable microorganisms can anchor and feed, and an inner layer that these organisms cannot penetrate. [ 12 ] [ 13 ] Additionally, the development of gut-associated lymphoid tissue (GALT), which forms part of the intestinal epithelium and which detects and reacts to pathogens, develops during the time that the gut flora becomes established. [ 12 ] The GALT that develops is tolerant to gut flora species, but not to other microorganisms. [ 12 ] GALT also normally becomes tolerant to food the infant consumes, and the gut flora metabolites (molecules formed from metabolism) produced from food. [ 12 ]
The human immune system creates cytokines that can drive the immune system to produce inflammation in order to protect itself, and that can tamp down the immune response to maintain homeostasis and allow healing after insult or injury. [ 12 ] Different bacterial species that appear in gut flora have been shown to be able to drive the immune system to create cytokines selectively; for example Bacteroides fragilis and some Clostridia species appear to drive an anti-inflammatory response, while some segmented filamentous bacteria drive the production of inflammatory cytokines. [ 12 ] [ 62 ] Gut flora can also regulate the production of antibodies by the immune system. [ 12 ] [ 63 ] One function of this regulation is to cause B cells to class switch to IgA . In most cases B cells need activation from T helper cells to induce class switching ; however, in another pathway, gut flora cause NF-kB signaling by intestinal epithelial cells which results in further signaling molecules being secreted. [ 64 ] These signaling molecules interact with B cells to induce class switching to IgA. [ 64 ] IgA is an important type of antibody that is used in mucosal environments like the gut. It has been shown that IgA can help diversify the gut community and helps in getting rid of bacteria that cause inflammatory responses. [ 65 ] Ultimately, IgA maintains a healthy environment between the host and gut bacteria. [ 65 ] These cytokines and antibodies can have effects outside the gut, in the lungs and other tissues. [ 12 ]
A 2022 review indicated that various mechanisms are under preliminary research to assess how gut microbes may modulate vaccine immunogenicity , including effects on antigen presentation and cytokine profiles. [ 66 ]
Without gut flora, the human body would be unable to utilize some of the undigested carbohydrates it consumes, because some types of gut flora have enzymes that human cells lack for breaking down certain polysaccharides . [ 14 ] Rodents raised in a sterile environment and lacking in gut flora need to eat 30% more calories just to remain the same weight as their normal counterparts. [ 14 ] Carbohydrates that humans cannot digest without bacterial help include certain starches , fiber , oligosaccharides , and sugars that the body failed to digest and absorb like lactose in the case of lactose intolerance and sugar alcohols , mucus produced by the gut, and proteins. [ 9 ] [ 14 ]
Bacteria turn carbohydrates they ferment into short-chain fatty acids by a form of fermentation called saccharolytic fermentation . [ 39 ] Products include acetic acid , propionic acid and butyric acid . [ 7 ] [ 39 ] These materials can be used by host cells, providing a major source of energy and nutrients. [ 39 ] Gases (which are involved in signaling [ 71 ] and may cause flatulence ) and organic acids , such as lactic acid , are also produced by fermentation. [ 7 ] Acetic acid is used by muscle , propionic acid facilitates liver production of ATP , and butyric acid provides energy to gut cells. [ 39 ]
Gut flora also synthesize vitamins like biotin and folate , and facilitate absorption of dietary minerals , including magnesium, calcium, and iron. [ 6 ] [ 22 ] Methanobrevibacter smithii is unique because it is not a species of bacteria, but rather a member of domain Archaea , and is the most abundant methane -producing archaeal species in the human gastrointestinal microbiota. [ 72 ]
Gut microbiota also serve as a source of vitamins K and B 12 , which are not produced by the body or produced in little amount. [ 73 ] [ 74 ]
Bacteria that degrade cellulose (such as Ruminococcus ) are prevalent among great apes , ancient human societies, hunter-gatherer communities, and even modern rural populations. However, they are rare in industrialized societies. Human-associated strains have acquired genes that can degrade specific plant fibers such as maize , rice , and wheat . Bacterial strains found in primates can also degrade chitin , a polymer abundant in insects, which are part of the diet of many nonhuman primates . The decline of these bacteria in the human gut were likely influenced by the shift toward western lifestyles. [ 75 ]
The human metagenome (i.e., the genetic composition of an individual and all microorganisms that reside on or within the individual's body) varies considerably between individuals. [ 76 ] [ 77 ] Since the total number of microbial cells in the human body (over 100 trillion) greatly outnumbers Homo sapiens cells (tens of trillions), [ note 1 ] [ 76 ] [ 78 ] there is considerable potential for interactions between drugs and an individual's microbiome, including: drugs altering the composition of the human microbiome , drug metabolism by microbial enzymes modifying the drug's pharmacokinetic profile, and microbial drug metabolism affecting a drug's clinical efficacy and toxicity profile. [ 76 ] [ 77 ] [ 79 ]
Apart from carbohydrates, gut microbiota can also metabolize other xenobiotics such as drugs, phytochemicals , and food toxicants. More than 30 drugs have been shown to be metabolized by gut microbiota. [ 80 ] The microbial metabolism of drugs can sometimes inactivate the drug. [ 81 ]
The gut microbiota is an enriched community that contains diverse genes with huge biochemical capabilities to modify drugs, especially those taken by mouth. [ 82 ] Gut microbiota can affect drug metabolism via direct and indirect mechanisms. [ 83 ] The direct mechanism is mediated by the microbial enzymes that can modify the chemical structure of the administered drugs. [ 84 ] Conversely, the indirect pathway is mediated by the microbial metabolites which affect the expression of host metabolizing enzymes such as cytochrome P450 . [ 85 ] [ 83 ] The effects of the gut microbiota on the pharmacokinetics and bioavailability of the drug have been investigated a few decades ago. [ 86 ] [ 87 ] [ 88 ] These effects can be varied; it could activate the inactive drugs such as lovastatin, [ 89 ] inactivate the active drug such as digoxin [ 90 ] or induce drug toxicity as in irinotecan . [ 91 ] Since then, the impacts of the gut microbiota on the pharmacokinetics of many drugs were heavily studied. [ 92 ] [ 82 ]
The human gut microbiota plays a crucial role in modulating the effect of the administered drugs on the human. Directly, gut microbiota can synthesize and release a series of enzymes with the capability to metabolize drugs such as microbial biotransformation of L-dopa by decarboxylase and dehydroxylase enzymes. [ 84 ] On the contrary, gut microbiota may also alter the metabolism of the drugs by modulating the host drug metabolism. This mechanism can be mediated by microbial metabolites or by modifying host metabolites which in turn change the expression of host metabolizing enzymes. [ 85 ]
A large number of studies have demonstrated the metabolism of over 50 drugs by the gut microbiota. [ 92 ] [ 83 ] For example, lovastatin (a cholesterol-lowering agent) which is a lactone prodrug is partially activated by the human gut microbiota forming active acid hydroxylated metabolites. [ 89 ] Conversely, digoxin (a drug used to treat Congestive Heart Failure) is inactivated by a member of the gut microbiota (i.e. Eggerthella lanta ). [ 93 ] Eggerthella lanta has a cytochrome-encoding operon up-regulated by digoxin and associated with digoxin-inactivation. [ 93 ] Gut microbiota can also modulate the efficacy and toxicity of chemotherapeutic agents such as irinotecan. [ 94 ] This effect is derived from the microbiome-encoded β-glucuronidase enzymes which recover the active form of the irinotecan causing gastrointestinal toxicity. [ 95 ]
This microbial community in the gut has a huge biochemical capability to produce distinct secondary metabolites that are sometimes produced from the metabolic conversion of dietary foods such as fibers , endogenous biological compounds such as indole or bile acids . [ 96 ] [ 97 ] [ 98 ] Microbial metabolites especially short chain fatty acids (SCFAs) and secondary bile acids (BAs) play important roles for the human in health and disease states. [ 99 ] [ 100 ] [ 101 ]
One of the most important bacterial metabolites produced by the gut microbiota is secondary bile acids (BAs). [ 98 ] These metabolites are produced by the bacterial biotransformation of the primary bile acids such as cholic acid (CA) and chenodeoxycholic acid (CDCA) into secondary bile acids (BAs) lithocholic acid (LCA) and deoxy cholic acid (DCA) respectively. [ 102 ] Primary bile acids which are synthesized by hepatocytes and stored in the gall bladder possess hydrophobic characters. These metabolites are subsequently metabolized by the gut microbiota into secondary metabolites with increased hydrophobicity. [ 102 ] Bile salt hydrolases (BSH) which are conserved across gut microbiota phyla such as Bacteroides , Firmicutes , and Actinobacteria responsible for the first step of secondary bile acids metabolism. [ 102 ] Secondary bile acids (BAs) such as DCA and LCA have been demonstrated to inhibit both Clostridioides difficile germination and outgrowth. [ 101 ]
The gut microbiota is important for maintaining homeostasis in the intestine. Development of intestinal cancer is associated with an imbalance in the natural microflora (dysbiosis). [ 103 ] The secondary bile acid deoxycholic acid is associated with alterations of the microbial community that lead to increased intestinal carcinogenesis. [ 103 ] Increased exposure of the colon to secondary bile acids resulting from dysbiosis can cause DNA damage , and such damage can produce carcinogenic mutations in cells of the colon. [ 104 ] The high density of bacteria in the colon (about 10 12 per ml.) that are subject to dysbiosis compared to the relatively low density in the small intestine (about 10 2 per ml.) may account for the greater than 10-fold higher incidence of cancer in the colon compared to the small intestine. [ 104 ]
The gut microbiota contributes to digestion and immune modulation, as it plays a role in the gut-brain axis, where microbial metabolites such as short-chain fatty acids and neurotransmitters influence brain function and behavior. The gut–brain axis is the biochemical signaling that takes place between the gastrointestinal tract and the central nervous system . [ 59 ] That term has been expanded to include the role of the gut flora in the interplay; the term "microbiome––brain axis" is sometimes used to describe paradigms explicitly including the gut flora. [ 59 ] [ 105 ] [ 106 ] Broadly defined, the gut-brain axis includes the central nervous system, neuroendocrine and neuroimmune systems including the hypothalamic–pituitary–adrenal axis (HPA axis), sympathetic and parasympathetic arms of the autonomic nervous system including the enteric nervous system , the vagus nerve , and the gut microbiota . [ 59 ] [ 106 ]
A 2016 systematic review of preclinical studies and small human trials conducted with certain commercially available strains of probiotic bacteria found that Bifidobacterium and Lactobacillus genera ( B. longum , B. breve , B. infantis , L. helveticus , L. rhamnosus , L. plantarum , and L. casei ), were of interest for certain central nervous system disorders . [ 16 ]
Altering the numbers of gut bacteria, for example by taking broad-spectrum antibiotics , may affect the host's health and ability to digest food. [ 107 ] Antibiotics can cause antibiotic-associated diarrhea by irritating the bowel directly, changing the levels of microbiota, or allowing pathogenic bacteria to grow. [ 7 ] Another harmful effect of antibiotics is the increase in numbers of antibiotic-resistant bacteria found after their use, which, when they invade the host, cause illnesses that are difficult to treat with antibiotics. [ 107 ]
Changing the numbers and species of gut microbiota can reduce the body's ability to ferment carbohydrates and metabolize bile acids and may cause diarrhea . Carbohydrates that are not broken down may absorb too much water and cause runny stools, or lack of SCFAs produced by gut microbiota could cause diarrhea. [ 7 ]
A reduction in levels of native bacterial species also disrupts their ability to inhibit the growth of harmful species such as C. difficile and Salmonella Kedougou, and these species can get out of hand, though their overgrowth may be incidental and not be the true cause of diarrhea. [ 6 ] [ 7 ] [ 107 ] Emerging treatment protocols for C. difficile infections involve fecal microbiota transplantation of donor feces (see Fecal transplant ). [ 108 ] Initial reports of treatment describe success rates of 90%, with few side effects. Efficacy is speculated to result from restoring bacterial balances of bacteroides and firmicutes classes of bacteria. [ 109 ]
The composition of the gut microbiome also changes in severe illnesses, due not only to antibiotic use but also to such factors as ischemia of the gut, failure to eat, and immune compromise . Negative effects from this have led to interest in selective digestive tract decontamination , a treatment to kill only pathogenic bacteria and allow the re-establishment of healthy ones. [ 110 ]
Antibiotics alter the population of the microbiota in the gastrointestinal tract , and this may change the intra-community metabolic interactions, modify caloric intake by using carbohydrates, and globally affect host metabolic, hormonal, and immune homeostasis. [ 111 ]
There is reasonable evidence that taking probiotics containing Lactobacillus species may help prevent antibiotic-associated diarrhea and that taking probiotics with Saccharomyces (e.g., Saccharomyces boulardii ) may help to prevent Clostridioides difficile infection following systemic antibiotic treatment. [ 112 ]
The gut microbiota of a woman changes as pregnancy advances, with the changes similar to those seen in metabolic syndromes such as diabetes. The change in gut microbiota causes no ill effects. The newborn's gut microbiota resemble the mother's first-trimester samples. The diversity of the microbiome decreases from the first to third trimester, as the numbers of certain species go up. [ 113 ] [ 114 ]
Probiotics contain live microorganisms . When consumed, they are believed to provide health benefits by altering the microbiome composition. [ 115 ] [ 116 ] [ 117 ] Current research explores using probiotics as a way to restore the microbial balance of the intestine by stimulating the immune system and inhibiting pro-inflammatory cytokines . [ 115 ]
With regard to gut microbiota, prebiotics are typically non-digestible, fiber compounds that pass undigested through the upper part of the gastrointestinal tract and stimulate the growth or activity of advantageous gut flora by acting as substrate for them. [ 39 ] [ 118 ]
Synbiotics refers to food ingredients or dietary supplements combining probiotics and prebiotics in a form of synergism . [ 119 ]
The term "pharmabiotics" is used in various ways, to mean: pharmaceutical formulations (standardized manufacturing that can obtain regulatory approval as a drug) of probiotics, prebiotics , or synbiotics ; [ 120 ] probiotics that have been genetically engineered or otherwise optimized for best performance (shelf life, survival in the digestive tract, etc.); [ 121 ] and the natural products of gut flora metabolism (vitamins, etc.). [ 122 ]
There is some evidence that treatment with some probiotic strains of bacteria may be effective in treatment of irritable bowel syndrome , inflammatory bowel disease , and abdominal bloating . [ 123 ] [ 124 ] [ 125 ] [ 126 ] Those organisms most likely to result in a decrease of symptoms have included:
Tests for whether non-antibiotic drugs may impact human gut-associated bacteria were performed by in vitro analysis on more than 1000 marketed drugs against 40 gut bacterial strains, demonstrating that 24% of the drugs inhibited the growth of at least one of the bacterial strains. [ 127 ]
Bacteria in the digestive tract can contribute to and be affected by disease in various ways. The presence or overabundance of some kinds of bacteria may contribute to inflammatory disorders such as inflammatory bowel disease . [ 6 ] Additionally, metabolites from certain members of the gut flora may influence host signalling pathways, contributing to disorders such as obesity and colon cancer . [ 6 ] Some gut bacteria may also cause infections and sepsis , for example when they are allowed to pass from the gut into the rest of the body . [ 6 ]
Helicobacter pylori infection can initiate formation of stomach ulcers when the bacteria penetrate the stomach epithelial lining, then causing an inflammatory phagocytotic response . [ 128 ] In turn, the inflammation damages parietal cells which release excessive hydrochloric acid into the stomach and produce less of the protective mucus. [ 129 ] Injury to the stomach lining, leading to ulcers , develops when gastric acid overwhelms the defensive properties of cells and inhibits endogenous prostaglandin synthesis, reduces mucus and bicarbonate secretion, reduces mucosal blood flow, and lowers resistance to injury. [ 129 ] Reduced protective properties of the stomach lining increase vulnerability to further injury and ulcer formation by stomach acid, pepsin , and bile salts. [ 128 ] [ 129 ]
Normally- commensal bacteria can harm the host if they extrude from the intestinal tract. [ 12 ] [ 13 ] Translocation , which occurs when bacteria leave the gut through its mucosal lining, can occur in a number of different diseases. [ 13 ] If the gut is perforated, bacteria invade the interstitium , causing a potentially fatal infection . [ 5 ] : 715
The two main types of inflammatory bowel diseases , Crohn's disease and ulcerative colitis , are chronic inflammatory disorders of the gut; the causes of these diseases are unknown and issues with the gut flora and its relationship with the host have been implicated in these conditions. [ 15 ] [ 130 ] [ 131 ] [ 132 ] Additionally, it appears that interactions of gut flora with the gut–brain axis have a role in IBD, with physiological stress mediated through the hypothalamic–pituitary–adrenal axis driving changes to intestinal epithelium and the gut flora in turn releasing factors and metabolites that trigger signaling in the enteric nervous system and the vagus nerve . [ 4 ]
The diversity of gut flora appears to be significantly diminished in people with inflammatory bowel diseases compared to healthy people; additionally, in people with ulcerative colitis, Proteobacteria and Actinobacteria appear to dominate; in people with Crohn's, Enterococcus faecium and several Proteobacteria appear to be over-represented. [ 4 ]
There is reasonable evidence that correcting gut flora imbalances by taking probiotics with Lactobacilli and Bifidobacteria can reduce visceral pain and gut inflammation in IBD. [ 112 ]
Irritable bowel syndrome is a result of stress and chronic activation of the HPA axis; its symptoms include abdominal pain, changes in bowel movements, and an increase in proinflammatory cytokines. Overall, studies have found that the luminal and mucosal microbiota are changed in irritable bowel syndrome individuals, and these changes can relate to the type of irritation such as diarrhea or constipation . Also, there is a decrease in the diversity of the microbiome with low levels of fecal Lactobacilli and Bifidobacteria, high levels of facultative anaerobic bacteria such as Escherichia coli , and increased ratios of Firmicutes: Bacteroidetes. [ 106 ]
With asthma, two hypotheses have been posed to explain its rising prevalence in the developed world. The hygiene hypothesis posits that children in the developed world are not exposed to enough microbes and thus may contain lower prevalence of specific bacterial taxa that play protective roles. [ 133 ] The second hypothesis focuses on the Western pattern diet , which lacks whole grains and fiber and has an overabundance of simple sugars . [ 15 ] Both hypotheses converge on the role of short-chain fatty acids (SCFAs) in immunomodulation . These bacterial fermentation metabolites are involved in immune signalling that prevents the triggering of asthma and lower SCFA levels are associated with the disease. [ 133 ] [ 134 ] Lacking protective genera such as Lachnospira , Veillonella , Rothia and Faecalibacterium has been linked to reduced SCFA levels. [ 133 ] Further, SCFAs are the product of bacterial fermentation of fiber, which is low in the Western pattern diet. [ 15 ] [ 134 ] SCFAs offer a link between gut flora and immune disorders, and as of 2016, this was an active area of research. [ 15 ] Similar hypotheses have also been posited for the rise of food and other allergies. [ 135 ]
The connection between the gut microbiota and diabetes mellitus type 1 has also been linked to SCFAs, such as butyrate and acetate. Diets yielding butyrate and acetate from bacterial fermentation show increased T reg expression. [ 136 ] T reg cells downregulate effector T cells , which in turn reduces the inflammatory response in the gut. [ 137 ] Butyrate is an energy source for colon cells. butyrate-yielding diets thus decrease gut permeability by providing sufficient energy for the formation of tight junctions . [ 138 ] Additionally, butyrate has also been shown to decrease insulin resistance, suggesting gut communities low in butyrate-producing microbes may increase chances of acquiring diabetes mellitus type 2 . [ 139 ] Butyrate-yielding diets may also have potential colorectal cancer suppression effects. [ 138 ]
The gut flora have been implicated in obesity and metabolic syndrome due to a key role in the digestive process; the Western pattern diet appears to drive and maintain changes in the gut flora that in turn change how much energy is derived from food and how that energy is used. [ 132 ] [ 140 ] One aspect of a healthy diet that is often lacking in the Western-pattern diet is fiber and other complex carbohydrates that a healthy gut flora require flourishing; changes to gut flora in response to a Western-pattern diet appear to increase the amount of energy generated by the gut flora which may contribute to obesity and metabolic syndrome. [ 112 ] There is also evidence that microbiota influence eating behaviours based on the preferences of the microbiota, which can lead to the host consuming more food eventually resulting in obesity. It has generally been observed that with higher gut microbiome diversity, the microbiota will spend energy and resources on competing with other microbiota and less on manipulating the host. The opposite is seen with lower gut microbiome diversity, and these microbiotas may work together to create host food cravings. [ 55 ]
Additionally, the liver plays a dominant role in blood glucose homeostasis by maintaining a balance between the uptake and storage of glucose through the metabolic pathways of glycogenesis and gluconeogenesis . Intestinal lipids regulate glucose homeostasis involving a gut–brain–liver axis. The direct administration of lipids into the upper intestine increases the long chain fatty acyl-coenzyme A (LCFA-CoA) levels in the upper intestines and suppresses glucose production even under subdiaphragmatic vagotomy or gut vagal deafferentation . This interrupts the neural connection between the brain and the gut and blocks the upper intestinal lipids' ability to inhibit glucose production. The gut–brain–liver axis and gut microbiota composition can regulate the glucose homeostasis in the liver and provide potential therapeutic methods to treat obesity and diabetes. [ 141 ]
Just as gut flora can function in a feedback loop that can drive the development of obesity, there is evidence that restricting intake of calories (i.e., dieting ) can drive changes to the composition of the gut flora. [ 132 ]
The composition of the human gut microbiome is similar to that of the other great apes. However, humans' gut biota has decreased in diversity and changed in composition since our evolutionary split from Pan . [ 142 ] Humans display increases in Bacteroidetes, a bacterial phylum associated with diets high in animal protein and fat, and decreases in Methanobrevibacter and Fibrobacter, groups that ferment complex plant polysaccharides. [ 142 ] These changes are the result of the combined dietary, genetic, and cultural changes humans have undergone since evolutionary divergence from Pan (chimpanzees and bonobos). [ citation needed ]
In addition to humans and vertebrates, some insects also have complex and diverse gut microbiota that play key nutritional roles. [ 2 ] Microbial communities associated with termites can constitute a majority of the weight of the individuals and perform important roles in the digestion of lignocellulose and nitrogen fixation . [ 143 ] It is known that the disruption of gut microbiota of termites using agents like antibiotics [ 144 ] or boric acid [ 145 ] (a common agent used in preventative treatment) causes severe damage to digestive function and leads to the rise of opportunistic pathogens. [ 145 ] These communities are host-specific, and closely related insect species share comparable similarities in gut microbiota composition. [ 146 ] [ 147 ] In cockroaches , gut microbiota have been shown to assemble in a deterministic fashion, irrespective of the inoculum ; [ 148 ] the reason for this host-specific assembly remains unclear. Bacterial communities associated with insects like termites and cockroaches are determined by a combination of forces, primarily diet, but there is some indication that host phylogeny may also be playing a role in the selection of lineages. [ 146 ] [ 147 ]
For more than 51 years it has been known that the administration of low doses of antibacterial agents promotes the growth of farm animals to increase weight gain. [ 111 ]
In a study carried out on mice the ratio of Firmicutes and Lachnospiraceae was significantly elevated in animals treated with subtherapeutic doses of different antibiotics. By analyzing the caloric content of faeces and the concentration of small chain fatty acids (SCFAs) in the GI tract, it was concluded that the changes in the composition of microbiota lead to an increased capacity to extract calories from otherwise indigestible constituents, and to an increased production of SCFAs. These findings provide evidence that antibiotics perturb not only the composition of the GI microbiome but also its metabolic capabilities, specifically with respect to SCFAs. [ 111 ] | https://en.wikipedia.org/wiki/Gut_microbiota |
The gut–brain axis is the two-way biochemical signaling that takes place between the gastrointestinal tract (GI tract) and the central nervous system (CNS). [ 2 ] The term " microbiota–gut–brain axis " highlights the role of gut microbiota in these biochemical signaling . [ 3 ] [ 2 ] Broadly defined, the gut–brain axis includes the central nervous system , neuroendocrine system, neuroimmune systems , the hypothalamic–pituitary–adrenal axis (HPA axis), sympathetic and parasympathetic arms of the autonomic nervous system , the enteric nervous system , vagus nerve , and the gut microbiota. [ 2 ]
Chemicals released by the gut microbiome can influence brain development, starting from birth. A review from 2015 states that the gut microbiome influences the CNS by "regulating brain chemistry and influencing neuro-endocrine systems associated with stress response, anxiety and memory function". [ 4 ] The gut, sometimes referred to as the "second brain", may use the same type of neural network as the CNS, suggesting why it could have a role in brain function and mental health . [ 5 ]
The bidirectional communication is done by immune , endocrine , humoral and neural connections between the gastrointestinal tract and the central nervous system. [ 4 ] More research suggests that the gut microbiome influence the function of the brain by releasing the following chemicals: cytokines , neurotransmitters , neuropeptides , chemokines , endocrine messengers and microbial metabolites such as "short-chain fatty acids, branched chain amino acids, and peptidoglycans ". [ 6 ] These chemical signals are then transported to the brain via the blood , neuropod cells , nerves , endocrine cells , [ 7 ] [ 8 ] where they impact different metabolic processes. Studies have confirmed that gut microbiome contribute to range of brain functions controlled by the hippocampus , prefrontal cortex and amygdala (responsible for emotions and motivation ) and act as a key node in the gut-brain behavioral axis. [ 9 ]
While Irritable bowel syndrome (IBS) is the only disease confirmed to be directly influenced by the gut microbiome, many disorders (such as anxiety , autism , depression and schizophrenia ) have been reportedly linked to the gut-brain axis as well. [ 6 ] [ 10 ] [ 7 ] According to a study from 2017, " probiotics have the ability to restore normal microbial balance, and therefore have a potential role in the treatment and prevention of anxiety and depression". [ 11 ]
The first of the brain–gut interactions shown, was the cephalic phase of digestion , in the release of gastric and pancreatic secretions in response to sensory signals, such as the smell and sight of food. This was first demonstrated by Pavlov through Nobel prize winning research in 1904. [ 12 ] [ 13 ]
As of October 2016, most of the work done on the role of gut microbiota in the gut–brain axis had been conducted in animals, or on characterizing the various neuroactive compounds that gut microbiota can produce. Studies with humans – measuring variations in gut microbiota between people with various psychiatric and neurological conditions or when stressed, or measuring effects of various probiotics (dubbed " psychobiotics " in this context) – had generally been small and were just beginning to be generalized. [ 14 ] Whether changes to the gut microbiota are a result of disease, a cause of disease, or both in any number of possible feedback loops in the gut–brain axis, remain unclear. [ 15 ]
The enteric nervous system is one of the main divisions of the nervous system and consists of a mesh-like system of neurons that governs the function of the gastrointestinal system ; it has been described as a "second brain" for several reasons. The enteric nervous system can operate autonomously. It normally communicates with the central nervous system (CNS) through the parasympathetic (e.g., via the vagus nerve ) and sympathetic (e.g., via the prevertebral ganglia ) nervous systems. However, vertebrate studies show that when the vagus nerve is severed, the enteric nervous system continues to function. [ 16 ]
In vertebrates, the enteric nervous system includes efferent neurons , afferent neurons , and interneurons , all of which make the enteric nervous system capable of carrying reflexes in the absence of CNS input. The sensory neurons report on mechanical and chemical conditions. Through intestinal muscles, the motor neurons control peristalsis and churning of intestinal contents. Other neurons control the secretion of enzymes . The enteric nervous system also makes use of more than 30 neurotransmitters , most of which are identical to the ones found in CNS, such as acetylcholine , dopamine , and serotonin . More than 90% of the body's serotonin lies in the gut, as well as about 50% of the body's dopamine; the dual function of these neurotransmitters is an active part of gut–brain research. [ 17 ] [ 18 ] [ 19 ]
The first of the gut–brain interactions was shown to be between the sight and smell of food and the release of gastric secretions, known as the cephalic phase , or cephalic response of digestion. [ 12 ] [ 13 ]
The gut microbiota is the complex community of microorganisms that live in the digestive tracts of humans and other animals. The gut metagenome is the aggregate of all the genomes of gut microbiota. [ 24 ] The gut is one niche that human microbiota inhabit. [ 25 ]
In humans, the gut microbiota has the largest quantity of bacteria and the greatest number of species, compared to other areas of the body. [ 26 ] In humans, the gut flora is established at one to two years after birth; by that time, the intestinal epithelium and the intestinal mucosal barrier that it secretes have co-developed in a way that is tolerant to, and even supportive of, the gut flora and that also provides a barrier to pathogenic organisms . [ 27 ] [ 28 ]
The relationship between gut microbiota and humans is not merely commensal (a non-harmful coexistence), but rather a mutualistic relationship. [ 25 ] Human gut microorganisms benefit the host by collecting the energy from the fermentation of undigested carbohydrates and the subsequent absorption of short-chain fatty acids (SCFAs), acetate , butyrate , and propionate . [ 26 ] [ 29 ] Intestinal bacteria also play a role in synthesizing vitamin B and vitamin K as well as metabolizing bile acids , sterols , and xenobiotics . [ 25 ] [ 29 ] The systemic importance of the SCFAs and other compounds they produce are like hormones and the gut flora itself appears to function like an endocrine organ ; [ 29 ] dysregulation of the gut flora has been correlated with a host of inflammatory and autoimmune conditions. [ 26 ] [ 30 ]
The composition of human gut microbiota changes over time, when the diet changes, and as overall health changes. [ 26 ] [ 30 ] In general, the average human has over 1000 species of bacteria in their gut microbiome, with Bacteroidetes and Firmicutes being the dominant phyla. Diets higher in processed foods and unnatural chemicals can negatively alter the ratios of these species, while diets high in whole foods can positively alter the ratios. [ citation needed ] Additional health factors that may skew the composition of the gut microbiota are antibiotics and probiotics . Antibiotics have severe impacts on gut microbiota, ridding of both good and bad bacteria. Without proper rehabilitation, it can be easy for harmful bacteria to become dominant. [ citation needed ] Probiotics may help to mitigate this by supplying healthy bacteria into the gut and replenishing the richness and diversity of the gut microbiota. There are many strains of probiotics that can be administered depending on the needs of a specific individual. [ 31 ]
The gut–brain axis, a bidirectional neurohumoral communication system, is important for maintaining homeostasis and is regulated through the central and enteric nervous systems and the neural, endocrine, immune, and metabolic pathways, and especially including the hypothalamic–pituitary–adrenal axis (HPA axis). [ 2 ] That term has been expanded to include the role of the gut microbiota as part of the "microbiome-gut-brain axis", a linkage of functions including the gut microbiota. [ 2 ]
Interest in the field was sparked by a 2004 study (Nobuyuki Sudo and Yoichi Chida) showing that germ-free mice (genetically homogeneous laboratory mice, birthed and raised in an antiseptic environment) showed an exaggerated HPA axis response to stress, compared to non-GF laboratory mice. [ 2 ]
The gut microbiota can produce a range of neuroactive molecules, such as acetylcholine , catecholamines , γ-aminobutyric acid , histamine , melatonin , and serotonin , which are essential for regulating peristalsis and sensation in the gut. [ 32 ] Changes in the composition of the gut microbiota due to diet, drugs, or disease correlate with changes in levels of circulating cytokines , some of which can affect brain function. [ 32 ] The gut microbiota also release molecules that can directly activate the vagus nerve , which transmits information about the state of the intestines to the brain. [ 32 ]
Likewise, chronic or acutely stressful situations activate the hypothalamic–pituitary–adrenal axis , causing changes in the gut microbiota and intestinal epithelium , and possibly having systemic effects . [ 32 ] Additionally, the cholinergic anti-inflammatory pathway , signaling through the vagus nerve, affects the gut epithelium and microbiota. [ 32 ] Hunger and satiety are integrated in the brain, and the presence or absence of food in the gut and types of food present also affect the composition and activity of gut microbiota. [ 32 ]
Most of the work that has been done on the role of gut microbiota in the gut–brain axis has been conducted in animals, including the highly artificial germ-free mice. As of 2016, studies with humans measuring changes to gut microbiota in response to stress, or measuring effects of various probiotics, have generally been small and cannot be generalized; whether changes to gut microbiota are a result of disease, a cause of disease, or both in any number of possible feedback loops in the gut–brain axis, remains unclear. [ 15 ]
The concept is of special interest in autoimmune diseases such as multiple sclerosis . [ 33 ] This process is thought to be regulated via the gut microbiota, which ferment indigestible dietary fibre and resistant starch; the fermentation process produces short chain fatty acids (SCFAs) such as propionate, butyrate, and acetate. [ 34 ] The history of ideas about a relationship between the gut and the mind dates from the nineteenth century. [ 35 ]
The gut-brain axis is a complex communication network linking the gastrointestinal tract and the central nervous system, playing a pivotal role in maintaining physiological homeostasis. Disruptions in this axis have been implicated in various illnesses, highlighting the significance of gut microbiota in disease pathogenesis.
While Irritable bowel syndrome (IBS) is the only disease confirmed to be directly influenced by the gut microbiome, many disorders such as anxiety , autism , depression and schizophrenia have been linked to the gut-brain axis as well. [ 6 ] [ 36 ] [ 7 ] Below is an overview of several ailments associated with gut-brain axis dysfunction:
Skin conditions such as acne were proposed as early as 1930, [ 37 ] to be related to emotional states which altered the gut microbiome leading to systemic inflammation . According to one article, "...there appears to be more than enough supportive evidence to suggest that gut microbes, and the integrity of the gastrointestinal tract itself, are contributing factors in the acne process." [ 38 ] Studies have shown overlapping mechanisms in psoriasis and depression; psoriasis causing disturbances in the gut microbiota that reflect in the brain causing depression that in turn can cause the stress that affects the microbiome. [ 39 ]
Irritable Bowel Syndrome (IBS) is a functional gastrointestinal disorder characterized by abdominal pain and altered bowel habits. The pathogenesis of IBS is complex, involving gut-brain axis dysfunction, altered gut motility, and visceral hypersensitivity. [ 40 ] Irritable bowel syndrome (IBS) can cause many abdominal issues such as symptoms of constipation, diarrhea, gas, bloating, and abdominal pain. IBS can be stress-induced and flare-ups are associated with bouts of stress. The gut-brain axis may explain this. The use of probiotics has been shown to help to restore a balance of helpful and harmful bacteria. [ 41 ]
Brain function is dependent on multiple neuropeptides including dopamine , GABA and serotonin , that are controlled in the gut microbiota. Imbalances in the gut microbiota intensifies anxiety as both the immune and metabolic pathways are affected. Specific microbes can lead to increased anxiety due to the activation of c-Fos proteins. These proteins serve as indicators of neuronal activation. "However, the therapeutic benefits of probiotics on mental health have not yet been thoroughly examined despite a wealth of preclinical data." [ 42 ]
Autism Spectrum Disorder (ASD) is a neurodevelopmental condition with emerging evidence linking it to gut microbiota alterations. Research indicates that individuals with ASD often exhibit gastrointestinal issues and distinct microbial profiles.These microbial changes may affect the gut-brain axis, influencing neurodevelopment and behavior. [ 43 ] Studies have shown that children with autism are four times more likely to develop gastrointestinal disorders. The severity of their behavioral symptoms is proportional to the severity of their gastrointestinal issues. Many children with autism have high focal levels of HMGB1 . [ 44 ] [ 45 ]
Alzheimer's disease (AD) has been associated with changes in gut microbiota composition, which may influence neuroinflammatory processes and amyloid beta accumulation. Studies have identified specific microbial patterns in AD patients, suggesting that gut dysbiosis could contribute to disease progression. Targeting the gut microbiome through dietary interventions or probiotics presents a potential strategy for modulating AD risk and progression. [ 46 ]
Some research has suggested that the gut microbiota plays a role in the development and progression of depression by influencing neurotransmitter regulation , inflammation , and the stress response. The gut microbiota contributes to the synthesis of key neuroactive compounds, including serotonin , dopamine , and gamma-amino butyric acid (GABA), which are essential for mood regulation. Approximately 90% of the body’s serotonin is produced in the gut by enterochromaffin cell , with microbial metabolites influencing its availability and signaling. Dysbiosis , or microbial imbalance, has been linked to altered serotonin production, which may contribute to depressive symptoms. Gut microbiota significantly influence the Hypothalamic–pituitary–adrenal axis (HPA), the body’s central stress response system, with dysbiosis leading to HPA hyperactivation and increased cortisol levels, a common feature in major depressive disorder (MDD). Additionally, an imbalance in gut bacteria can trigger chronic low-grade inflammation through the release of lipopolysaccharide (LPS) from Gram-negative bacteria, stimulating an immune response that elevates pro-inflammatory cytokines such as Interleukin 6 (IL-6) and tumor necrosis factor-alpha (TNF-a ). [ 47 ] [ 48 ] These inflammatory mediators can disrupt neurotransmitter function and impair neuroplasticity, contributing to depressive symptoms. Emerging research highlights the therapeutic potential of probiotics and microbiota-targeted interventions, with strains like Lactobacillus and Bifidobacterium shown to reduce inflammation, restore neurotransmitter balance, and improve mood-related behaviors in both animal models and human trials. Given these findings, microbiota-based therapies are being explored as adjunctive treatments for depression. [ 49 ] Further evidence suggests that changes in the composition of gut bacteria can also increase intestinal permeability and stimulate immune system activity, contributing to the persistence of depressive symptoms. Therapeutic approaches aimed at modulating the gut microbiota, including the use of probiotics, specific diets, and fecal transplants, are being actively investigated for their potential to reduce inflammation and improve emotional regulation. [ 50 ]
Different neurotrophins play a role in schizophrenia. One of the main ones is called Brain-Derived Neurotrophic Factor (BDNF). BDNF has been associated with schizophrenia and is believed to be a part of the molecular mechanism that has to do with cognitive dysfunction during neurodevelopmental changes. Those who have been diagnosed with schizophrenia tend to exhibit lower levels of BDNF in blood and levels of BDNF are also lower in the cerebral cortex and hippocampus . Levels of butyric acid have also been shown to be different between schizophrenic patients and non-schizophrenic patients. It is important to note that studies regarding the link between the gut-brain axis and schizophrenia are limited and further studies are underway. [ 51 ]
Braak's theory proposed that gut dysbiosis in Parkinson's causes the aggregation of alpha-synuclein in the gastrointestinal tract before its spreading to the brain. [ 52 ]
The gut-brain microbiota abnormalities that contribute to Parkinson's disease, supports the idea that it originates in the gut and spreads. The route would be from the gut to the central nervous system, through the vagus nerve. Gastrointestinal syndromes are known to be dysphagia , gastroparesis , and constipation among others, contributing to the risk of Parkinson's disease. From the understanding of these diseases, the disease modifying therapies are known to be aspects that help prevent the progress of these diseases that focus on the gut-brain axis. Relevant therapies are the vagus nerve stimulation , the fecal microbiota transplantation , the use of Rifaximin and other drugs directed towards the gut. [ 53 ]
Microbial derived secondary bile acids produced in the gut may influence cognitive function. [ 54 ] Altered bile acid profiles occur in cases of mild cognitive impairment and Alzheimer's disease with an increase in cytotoxic secondary bile acids and a decrease in primary bile acids. [ 55 ] These findings suggest a role of the gut microbiome in the progression to Alzheimer's disease. [ 55 ] In contrast to the cytotoxic effect of secondary bile acids, the bile acid tauroursodeoxycholic acid may be beneficial in the treatment of neurodegenerative diseases . [ 56 ]
As more bile acids are absorbed via apical sodium-bile acid transporters, there is a significant increase in age-related cognitive impairment. Levels of serum conjugated primary bile acids were monitored and increased levels revealed ammonia accumulation in the brain. These increased levels of ammonia led to hippocampal synapse loss. Because the hippocampus is largely responsible for memory, the loss of these synapses can have profound impacts on the memories of those affected. [ 57 ] | https://en.wikipedia.org/wiki/Gut–brain_axis |
Guy Bertrand , born on July 17, 1952, at Limoges is a chemistry professor at the University of California, San Diego . [ 1 ]
Bertrand obtained his B.Sc. from the University of Montpellier in 1975 and his Ph.D. from the Paul Sabatier University , Toulouse , in 1979. He was a postdoctoral researcher at Sanofi Research , France , in 1981. [ 1 ]
The research interests of Bertrand and his co-workers lie mainly in the chemistry of with main group elements from group 13 to 16, at the border between organic, organometallic and inorganic chemistry; especially their use in stabilizing carbenes , nitrenes , phosphinidenes, radicals and biradicals , 1,3-dipoles , anti-aromatic heterocycles , and more. He has directed the synthesis of some original persistent carbenes , including bis(diisopropylamino)cyclopropenylidene , the first example of a carbene with all-carbon environment that is stable at room-temperature. [ 2 ]
Guy Bertrand is an honorific member or fellow of several scientific societies, such as the AAAS (2006), the French Academy of Sciences (2004), the European Academy of Sciences (2003), Academia Europaea (2002), and the recipient of various prizes and awards.
Questioning the current dogma is a design feature of Guy Bertrand's research program. He has made many important contributions to the chemistry of main group elements and new binding systems in inorganic , organometallic and organic chemistry. Throughout his career, he has isolated a variety of species [ 3 ] [ 4 ] [ 5 ] [ 6 ] [ 7 ] that were supposed to be only transitional intermediates, and are now powerful tools for chemists.
Its best-known contribution was the discovery in 1988 of the first stable carbene , a (phosphino)(silyl)carbene, [ 8 ] three years before Arduengo's report on a stable N-heterocyclic carbene . Guy Bertrand is at the origin of the chemistry of stable carbenes . Since then, he has made several revolutionary discoveries that have allowed us to better understand the stability of carbenes. He was the first to isolate cyclopropenylidenes , [ 2 ] mesoionic carbenes that cannot dimerize, resulting in a relaxation of steric requirements for their isolation [ 9 ] [ 10 ] More importantly, he discovered cyclic (alkyl) (amino) (amino) carbenes ( CAACs ), [ 11 ] including the recently published six-membered version. CAACs are even richer in electrons than NHCs and phosphines, but at the same time, due to the presence of a single pair of free electrons on nitrogen , CAACs are more accepting than NHCs. [ 12 ] The electronic properties of CAACs stabilize highly reactive species, including organic and major group radicals , as well as paramagnetic metal species, such as gold complexes (0), which were completely unknown. CAACs have also allowed the isolation of bis(copper)acetylide complexes, [ 13 ] which are key catalytic intermediates in the famous "Click Reaction", and which were supposed to be only transient species. He also used CAACs to prepare and isolate the first isoelectronic nucleophilic tricoordinated organoborane from amines. [ 14 ] [ 15 ] These recent developments appear paradoxical since they consist in using carbenes long considered as prototypic reactive intermediates to isolate otherwise unstable molecules. Among the large-scale applications already known of CAACs are their use as a ligand for transition metal catalysts. For example, in collaboration with Grubbs, Guy Bertrand has shown that ruthenium catalysts bearing a CAAC are extremely active in the ethenolysis of methyl oleate. [ 16 ] This is the first time that a series of metathesis catalysts have performed so well in cross-metathesis reactions using ethylene gas, with sufficient activity to make ethenolysis applicable to the industrial production of linear alpha-olefins (LAOs) and other olefinic end products from biomass.
Today, hundreds of academic and industrial groups use Guy Bertrand's CAACs and other carbenes in transition metal catalysis, [ 17 ] but also for other purposes. The most recent developments cover a wide range from nanoparticle stabilization to the antibacterial and anti-cancer properties of silver (I) and gold (I) complexes. A CAAC- copper complex even allows OLEDs to be used with a quantum efficiency close to 100% at high brightness. [ 18 ] The discovery of stable carbenes was a breakthrough for fundamental chemistry, a real paradigm shift, but its importance also comes, and perhaps more importantly, from applications. In his review article on "N-heterocyclic carbenes", a terminology that includes carbenes, Glorius et al. [ 19 ] wrote: "The discovery and development of N-heterocyclic carbenes is undoubtedly one of the greatest successes of recent chemical research", "N-heterocyclic carbenes are today among the most powerful tools in organic chemistry, with many applications in commercially important processes", "the meteoric rise of NHC is far from over".
Guy Bertrand's contribution is not limited to carbenes. Recent highlights include the isolation of the first stable nitrenes [ 20 ] and phosphinidenes . [ 21 ] He showed that the first can be used to transfer a nitrogen atom to organic fragments, a difficult task for nitrido complexes of transition metals. For the second, it has recently demonstrated that it mimics the behaviour of transition metals, just like carbenes. [ 22 ]
He was awarded the CNRS silver medal in 1998. He is a member of the French Academy of Technology (2000), [ 23 ] the Academia Europaea (2002), [ 24 ] the European Academy of Sciences (2003), [ 24 ] the French Academy of Sciences (2004) [ 25 ] and the American Association for Advancement of Sciences (2006). [ 26 ] He was recently awarded the Sir Ronald Nyholm Medal from the SRC (2009), the Grand Prix Le Bel from the French Chemical Society (2010), the ACS Prize in Inorganic Chemistry (2014), the Sir Geoffrey Wilkinson Prize from the SRC (2016) and the Sacconi Medal from the Italian Chemical Society (2017). He is one of the associate editors of Chemical Reviews and a member of the editorial boards of several journals.
He is Chevalier of the Légion d'Honneur . [ 27 ] | https://en.wikipedia.org/wiki/Guy_Bertrand_(chemist) |
Guy Terjanian is a French mathematician who has worked on algebraic number theory . He achieved his Ph.D. under Claude Chevalley in 1970, [ 1 ] and at that time published a counterexample [ 2 ] to the original form of a conjecture of Emil Artin , which suitably modified had just been proved as the Ax-Kochen theorem .
In 1977, he proved that if p is an odd prime number, and the natural numbers x , y and z satisfy x 2 p + y 2 p = z 2 p {\displaystyle x^{2p}+y^{2p}=z^{2p}} , then 2p must divide x or y . [ 3 ]
This article about a French mathematician is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Guy_Terjanian |
Gye Nyame is one of the Adinkra symbols of the Akan people of Ghana . [ 1 ] It is translated into English literally as 'Except God' or 'Except for God' where the Akan name for God - nyame is used. [ 2 ] [ 3 ] [ 4 ]
Gye Nyame, according to the Akan belief, is interpreted as the belief of the existence of an omnipotent supreme deity that is to be revered above all others. [ 2 ] [ 3 ] Other interpretations of this symbol speak to a belief of a supreme deity that existed before creation who would continue to exist after everything no longer exists. This second interpretation speaks to the cultivation of humility in the human race. [ 5 ]
The Adinkra symbol Gye Nyame originates from the Akan language, specifically the Twi dialect. The phrase translates to "Except for God" or "Only God," emphasizing the supreme authority and omnipotence of the divine in all aspects of life. This expression underscores the Akan belief that no event occurs without God's will, reflecting their deep spiritual ethos. The symbol visually represents the notion that God is the ultimate protector and authority, reinforcing the idea that nothing is beyond divine intervention. [ 6 ]
Gye Nyame as an Adinkra symbol is considered one of the widely used Adinkra symbols in the Ghanaian culture and government. It is a part of the symbols found on the wall of the Ghanaian embassy in Washington DC , United States . [ 7 ] It is also found as one of the security features of the 200 ghana cedi note - highest denomination of the Ghanaian currency issued by the Bank of Ghana as official Ghanaian currency in 2019. [ 8 ] [ 9 ] [ 10 ] It is also used widely in the design of textiles, jewelry, decorations and artwork. It was included as one of the Adinkra symbols on the attire of John Mahama , worn for his swearing-in ceremony as president of Ghana in 2025. [ 11 ] [ 12 ] [ 13 ] [ 14 ] [ 15 ] It also was used in the design of a carved stool presented to Queen Elizabeth II , Queen of the United Kingdom . [ 16 ]
The phrase Gye Nyame is also widely used in the Ghanaian context. The phrase is seen on the 50, 200, 100, 500 and 5000 cedis notes issued by the Bank of Ghana as official Ghanaian currency between 1972 and 1994. [ 17 ] It is also used as the name of a gas field located 60 km offshore Takoradi in the Western region of Ghana. [ 18 ]
[ 19 ] The Gye Nyame symbol is featured in the logos of the University of Cape Coast , a public university, and the Catholic University College , a private institution. [ 20 ] | https://en.wikipedia.org/wiki/Gye_Nyame_(Adinkra) |
Gymnochrome E is a cytotoxic phenanthroperylenequinone isolated from a deep-water crinoid called Holopus rangii . [ 1 ]
This article about an organic compound is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Gymnochrome_E |
Gynaecologic cytology , also gynecologic cytology , is a field of pathology concerned with the investigation of disorders of the female genital tract . [ 1 ]
The most common investigation in this field is the Pap test , which is used to screen for potentially precancerous lesions of the cervix . Cytology can also be used to investigate disorders of the ovaries , uterus , vagina and vulva .
Gynaecologic cytology makes frequent use of the Bethesda system in order to grade the results of HPV testing . [ 2 ]
This article related to pathology is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Gynaecologic_cytology |
Gynodioecy / ˌ dʒ ɪ n oʊ d aɪ ˈ iː s i / is a rare breeding system that is found in certain flowering plant species in which female and hermaphroditic plants coexist within a population. Gynodioecy is the evolutionary intermediate between hermaphroditism (exhibiting both female and male parts) and dioecy (having two distinct morphs: male and female).
Gynodioecy is sometimes considered a mixed mating system comparable with trioecy and androdioecy . [ 1 ] It is also considered a dimorphic sexual system alongside dioecy and androdioecy . [ 2 ]
Gynodioecy occurs as a result of transmission of nuclear (nuclear male sterility) or, more commonly, [ 3 ] extra-nuclear (e.g. cytoplasmic male sterility ) mutated alleles, which prevents pollen production, while keeping the female reproductive parts intact; other members of the species population don't inherit the mutated alleles, thus remaining hermaphrodites. In some cases, a combination of both nuclear and extra-nuclear mechanisms is observed in determining the sterile phenotype. Gynodioecy is extremely rare, with fewer than 1% of angiosperm species exhibiting the breeding system. Some notable taxa that exhibit a gynodioecious mating system include Beta vulgaris (wild beet), Lobelia siphilitica , Silene , and Lamiaceae .
The word gynodioecy comes from Greek ; gyne (woman), di (twice or double), and okios (house). The term was first used by Charles Darwin in 1877 when writing about plant morphology . [ 4 ]
Gynodioecy is often referred to as the evolutionary intermediate state between hermaphroditism and dioecy, however there is no evidence it is an intermediate state in animals. [ 5 ] Gynodioecy has been investigated by biologists dating as far back as to Charles Darwin . [ 6 ]
Gynodioecy can evolve from hermaphroditism due to certain environmental factors. If enough resources in a population are allocated to the female functions in a hermaphroditic species, gynodioecy will ensue. On the other hand, if more of those resources favor a hermaphrodite's male functions, androdioecy will result. A high rate of self-pollination in a population facilitates the maintenance of gynodioecy by increasing the inbreeding costs for hermaphrodites. [ 7 ] Thus, as the rate of inbreeding increases in a population, the more likely gynodioecy is to occur.
Hermaphroditic plants may be able to reproduce on their own but in many species they are self-incompatible . [ 8 ] Research has shown that a species can be either gynodioecious or self-incompatible, but very rarely is there a co-occurrence between the two. Therefore, gynodioecy and self-incompatibility tend to prevent each other's maintenance. Self-incompatibility of plants helps maintain androdioecy in plants, since males are in competition with only hermaphrodites to fertilize ovules. Self-incompatibility leads to a loss in gynodioecy, since neither hermaphrodites nor females have to deal with inbreeding depression . [ 9 ]
Two scenarios have been proposed to explain the evolutionary dynamics of the maintenance of gynodioecy. The first scenario, known as the balancing selection theory, considers the genetic factors that control gynodioecy over long evolutionary time scales. The balancing selection leads to cycles that explain the normal sex ratios in gynodioecious populations. The second scenario, known as epidemic dynamics, involves the arrival and loss of new cytoplasmic male sterility genes in new populations. These are the same genes that invade hermaphrodite populations and eventually result in gynodioecy. [ 6 ]
Gynodioecy is determined as a result of a genetic mutation that stops a plant from producing pollen, but still allows normal female reproductive features. [ 10 ] In plants, nuclear genes are inherited from both parents, but all the cytoplasmic genes come from the mother. This allows male gametes to be smaller and more motile while female gametes are larger. It makes sense for most plants to be hermaphrodites, since they are sessile and unable to find mates as easily as animals can. [ 11 ]
Cytoplasmic male sterility genes, usually found in the mitochondrial genome, show up and are established when female fertility is just slightly more than the hermaphroditic fertility. The female only needs to make slightly more or better seeds than hermaphrodites since the mitochondrial genome is maternally inherited. [ 12 ] Research done on plants has shown that hermaphroditic plants are in constant battles against organelle genes trying to kill their male parts. In over 140 plant species, these “male killer” genes have been observed. Male sterility genes cause plants to grow anthers that are stunted or withered and as a result, do not produce pollen. In most plants, there are nuclear fertility restoring genes that counteract the work of the male sterility genes, maintaining the hermaphroditic state of the plant. However, in some species of plants, the male sterility genes win the battle over the nuclear fertility restoring genes, and gynodioecy occurs. [ 11 ]
Maize farmers take advantage of gynodioecy to produce favorable hybrid maize seeds. The farmers deliberately make use of the gynodioecy that develops in the maize, resulting in a population of male-sterile and female-fertile individuals. They then introduce a new strain of male-sterile individuals and the breeders are able to collect the more favorable hybrid seeds. [ 11 ]
Gynodioecy is a rare, but widely distributed sexual system in angiosperm species. Gynodioecy is found in at least 81 different angiosperm families but less than 1% of the angiosperms species on Earth are gynodioecious. [ 13 ] One likely explanation for its rarity is due to its limited evolution. Since females are at a disadvantage when compared with hermaphrodites, they will never be able to evolve as quickly. In addition, gynodioecy is rare because the mechanisms that favor females and cause gynodioecy in some populations only operate in some plant lineages, but not others.
The reason for this variation in the rarity of gynodioecy stems from certain phenotypic traits or ecological factors that promote and favor the presence of female plants in a population. For example, a herbaceous growth form is much more highly favored in gynodioecious species of Lamiaceae when compared with woody lineages. [ 13 ] Herbaceous growth form is also associated with a reduced pollen limitation [ clarification needed ] and increased self-fertilization. A reduced pollen limitation may decrease seed quantity and quality. Woody growth form Lamiaceae are more pollen-limited and thus produce fewer seeds and seeds of lower quality, thus favoring the female herbaceous growth form. [ 13 ] Gynodioecy is rare because some sexual systems are more evolutionarily liable to change in certain lineages in comparison with others. [ citation needed ]
It has been estimated that gynodioecy occurs in 13.3% of Silene species. [ 14 ]
Theoretically, hermaphrodites should have the evolutionary and reproductive advantage over females in a population because they naturally can produce more offspring. Hermaphrodites can transmit their genes through both pollen and ovules, whereas females can only transmit genes via ovules. Thus, in order for females to remain viable in a population, they would have to be twice as successful as hermaphrodites.
It would appear that gynodioecy should not persist. In order for it to be maintained, the females need to have some sort of a reproductive advantage over the hermaphroditic population, known as female compensation or female advantage. [ 6 ] Female advantage includes an increase in saved energy from not producing pollen and making seedlings of higher quality, since hermaphrodite seedlings are susceptible to homozygous deleterious alleles. Additional advantages include more flowers, higher fruit set, higher total seed production, heavier seeds, and better germination rates.
Inbreeding depression was found to be an important factor in the maintenance of gynodioecy in an endemic Hawaiian shrub Schiedea adamantis occurring in a single population in Diamond Head Crater Oahu. [ 15 ] Inbreeding depression, due to selfing in the hermaphrodites , was considered to be caused by the presence of many mutations of small effect. [ 15 ]
The following species and higher taxa have been observed to exhibit a gynodioecious breeding system: | https://en.wikipedia.org/wiki/Gynodioecy |
Gynogenesis , a form of parthenogenesis , is a system of asexual reproduction that requires the presence of sperm without the actual contribution of its DNA for completion. The paternal DNA dissolves or is destroyed before it can fuse with the egg. [ 1 ] The egg cell of the organism is able to develop, unfertilized, into an adult using only maternal genetic material. Gynogenesis is often termed " sperm parasitism " in reference to the somewhat pointless role of male gametes. [ 2 ] Gynogenetic species, "gynogens" for short, are unisexual , meaning they must mate with males from a closely related bisexual species that normally reproduces sexually. [ 3 ]
Gynogenesis is a disadvantageous mating system for males, as they are unable to pass on their DNA. The question as to why this reproductive mode exists, given that it appears to combine the disadvantages of both asexual and sexual reproduction, remains unsolved in the field of evolutionary biology. The male equivalent to this process is androgenesis where the father is the sole contributor of DNA. [ 4 ]
Most gynogenetic species are fishes or amphibians. [ 3 ] Among the fishes, Amazon mollies ( Poecilia formosa ) require the sperm of closely related male Poecilia latipinna to engage in gynogenesis. P. latipinna males prefer to mate with females of their own species. [ 5 ] This presents a problem for P. formosa , as they must compete for males who do not favour them. However, those P. formosa successful in finding a mate make up the deficit by producing twice as many female offspring as their competitors. [ 5 ] Among salamanders, the Ambystoma platineum , a unisexual mole salamander , is hybrid of sexually reproducing A. jeffersonianum and A. laterale . [ 6 ] A. platineum individuals normally live in proximity to either of these parent species, so as to access their sperm. [ 6 ]
The ant Myrmecia impaternata is a hybrid of M. banksi and M. pilosula . [ 7 ] In ants, sex is determined by the haplodiploidy system: unfertilized eggs result in haploid males, while fertilized eggs result in diploid females. In this species – its specific epithet impaternata meaning 'fatherless' – the queen reproduces through sexual interaction, yet not fertilization, with gynogenetically produced females, and males reared from fatherless eggs. Since these males are haploid, they are genetically identical to one of the two parent species, but are produced by a queen of M. impaternata . The queens therefore have no need to mate parasitically with males of either parent species. This situation is unique. [ 7 ]
Two evolutionary pathways may be considered to explain how and why gynogenesis evolved. The single-step pathway involves multiple changes taking place simultaneously: meiosis must be interrupted, one gender's gametes eradicated, and a unisexual gender formation must arise. [ 2 ] The second option involves multiple steps: a sexual generation is formed with a strongly biased sex ratio , and because of Haldane's rule the species evolves towards loss of sexuality, with selection preferential towards the gynogen. [ 2 ] Experimenters who attempted unsuccessfully to induce P. formosa by hybridizing its genetic ancestors concluded that the evolutionary origin of P. formosa was not from the simple hybridization of two specific genomes, but the movement of certain alleles. [ 8 ] | https://en.wikipedia.org/wiki/Gynogenesis |
Gypsum is a soft sulfate mineral composed of calcium sulfate dihydrate , with the chemical formula CaSO 4 ·2H 2 O . [ 4 ] It is widely mined and is used as a fertilizer and as the main constituent in many forms of plaster , drywall and blackboard or sidewalk chalk . [ 5 ] [ 6 ] [ 7 ] [ 8 ] Gypsum also crystallizes as translucent crystals of selenite . It forms as an evaporite mineral and as a hydration product of anhydrite . The Mohs scale of mineral hardness defines gypsum as hardness value 2 based on scratch hardness comparison .
Fine-grained white or lightly tinted forms of gypsum known as alabaster have been used for sculpture by many cultures including Ancient Egypt , Mesopotamia , Ancient Rome , the Byzantine Empire , and the Nottingham alabasters of Medieval England .
The word gypsum is derived from the Greek word γύψος ( gypsos ), "plaster". [ 9 ] Because the quarries of the Montmartre district of Paris have long furnished burnt gypsum ( calcined gypsum) used for various purposes, this dehydrated gypsum became known as plaster of Paris . Upon adding water, after a few dozen minutes, plaster of Paris becomes regular gypsum (dihydrate) again, causing the material to harden or "set" in ways that are useful for casting and construction. [ 10 ]
Gypsum was known in Old English as spærstān , "spear stone", referring to its crystalline projections. Thus, the word spar in mineralogy, by comparison to gypsum, refers to any non- ore mineral or crystal that forms in spearlike projections. In the mid-18th century, the German clergyman and agriculturalist Johann Friderich Mayer investigated and publicized gypsum's use as a fertilizer. [ 11 ] Gypsum may act as a source of sulfur for plant growth, and in the early 19th century, it was regarded as an almost miraculous fertilizer. American farmers were so anxious to acquire it that a lively smuggling trade with Nova Scotia evolved, resulting in the so-called "Plaster War" of 1820. [ 12 ]
Gypsum is moderately water-soluble (~2.0–2.5 g/L at 25 °C) [ 13 ] and, in contrast to most other salts, it exhibits retrograde solubility , becoming less soluble at higher temperatures. When gypsum is heated in air it loses water and converts first to calcium sulfate hemihydrate ( bassanite , often simply called "plaster") and, if heated further, to anhydrous calcium sulfate ( anhydrite ). As with anhydrite , the solubility of gypsum in saline solutions and in brines is also strongly dependent on sodium chloride (common table salt) concentration. [ 13 ]
The structure of gypsum consists of layers of calcium (Ca 2+ ) and sulfate ( SO 2− 4 ) ions tightly bound together. These layers are bonded by sheets of anion water molecules via weaker hydrogen bonding , which gives the crystal perfect cleavage along the sheets (in the {010} plane). [ 4 ] [ 14 ]
Gypsum occurs in nature as flattened and often twinned crystals , and transparent, cleavable masses called selenite . Selenite contains no significant selenium ; rather, both substances were named for the ancient Greek word for the Moon .
Selenite may also occur in a silky, fibrous form, in which case it is commonly called "satin spar". Finally, it may also be granular or quite compact. In hand-sized samples, it can be anywhere from transparent to opaque. A very fine-grained white or lightly tinted variety of gypsum, called alabaster , is prized for ornamental work of various sorts. In arid areas, gypsum can occur in a flower-like form, typically opaque, with embedded sand grains called desert rose . It also forms some of the largest crystals found in nature, up to 12 m (39 ft) long, in the form of selenite. [ 15 ]
Gypsum is a common mineral, with thick and extensive evaporite beds in association with sedimentary rocks . Deposits are known to occur in strata from as far back as the Archaean eon . [ 16 ] Gypsum is deposited from lake and sea water, as well as in hot springs , from volcanic vapors, and sulfate solutions in veins . Hydrothermal anhydrite in veins is commonly hydrated to gypsum by groundwater in near-surface exposures. It is often associated with the minerals halite and sulfur . Gypsum is the most common sulfate mineral. [ 17 ] Pure gypsum is white, but other substances found as impurities may give a wide range of colors to local deposits.
Because gypsum dissolves over time in water, gypsum is rarely found in the form of sand. However, the unique conditions of the White Sands National Park in the US state of New Mexico have created a 710 km 2 (270 sq mi) expanse of white gypsum sand, enough to supply the US construction industry with drywall for 1,000 years. [ 18 ] Commercial exploitation of the area, strongly opposed by area residents, was permanently prevented in 1933 when President Herbert Hoover declared the gypsum dunes a protected national monument .
Gypsum is also formed as a by-product of sulfide oxidation , amongst others by pyrite oxidation , when the sulfuric acid generated reacts with calcium carbonate . Its presence indicates oxidizing conditions. Under reducing conditions, the sulfates it contains can be reduced back to sulfide by sulfate-reducing bacteria . This can lead to accumulation of elemental sulfur in oil-bearing formations, [ 19 ] such as salt domes, [ 20 ] where it can be mined using the Frasch process [ 21 ] Electric power stations burning coal with flue gas desulfurization produce large quantities of gypsum as a byproduct from the scrubbers.
Orbital pictures from the Mars Reconnaissance Orbiter (MRO) have indicated the existence of gypsum dunes in the northern polar region of Mars, [ 22 ] which were later confirmed at ground level by the Mars Exploration Rover (MER) Opportunity . [ 23 ]
Commercial quantities of gypsum are found in the cities of Araripina and Grajaú in Brazil; in Pakistan, Jamaica, Iran (world's second largest producer), Thailand, Spain (the main producer in Europe), Germany, Italy, England, Ireland, Canada [ 25 ] and the United States. Large open pit quarries are located in many places including Fort Dodge, Iowa , which sits on one of the largest deposits of gypsum in the world, [ 26 ] and Plaster City, California , United States, and East Kutai , Kalimantan , Indonesia. Several small mines also exist in places such as Kalannie in Western Australia , where gypsum is sold to private buyers for additions of calcium and sulfur as well as reduction of aluminium toxicities on soil for agricultural purposes. [ 27 ] [ 28 ]
Crystals of gypsum up to 11 m (36 ft) long have been found in the caves of the Naica Mine of Chihuahua , Mexico. The crystals thrived in the cave's extremely rare and stable natural environment. Temperatures stayed at 58 °C (136 °F), and the cave was filled with mineral-rich water that drove the crystals' growth. The largest of those crystals weighs 55 tonnes (61 short tons) and is around 500,000 years old. [ 29 ]
Synthetic gypsum is produced as a waste product or by-product in a range of industrial processes.
Flue gas desulfurization gypsum (FGDG) is recovered at some coal-fired power plants. The main contaminants are Mg, K, Cl, F, B, Al, Fe, Si, and Se. They come both from the limestone used in desulfurization and from the coal burned. This product is pure enough to replace natural gypsum in a wide variety of fields including drywalls, water treatment, and cement set retarder. Improvements in flue gas desulfurization have greatly reduced the amount of toxic elements present. [ 30 ]
Gypsum precipitates onto brackish water membranes , a phenomenon known as mineral salt scaling , such as during brackish water desalination of water with high concentrations of calcium and sulfate . Scaling decreases membrane life and productivity. [ 31 ] This is one of the main obstacles in brackish water membrane desalination processes, such as reverse osmosis or nanofiltration . Other forms of scaling, such as calcite scaling, depending on the water source, can also be important considerations in distillation , as well as in heat exchangers , where either the salt solubility or concentration can change rapidly.
A new study has suggested that the formation of gypsum starts as tiny crystals of a mineral called bassanite (2CaSO 4 ·H 2 O). [ 32 ] This process occurs via a three-stage pathway:
The production of phosphate fertilizers requires breaking down calcium-containing phosphate rock with acid, producing calcium sulfate waste known as phosphogypsum (PG). This form of gypsum is contaminated by impurities found in the rock, namely fluoride , silica , radioactive elements such as radium , and heavy metal elements such as cadmium . [ 33 ] Similarly, production of titanium dioxide produces titanium gypsum (TG) due to neutralization of excess acid with lime . The product is contaminated with silica, fluorides, organic matters, and alkalis. [ 34 ]
Impurities in refinery gypsum waste have, in many cases, prevented them from being used as normal gypsum in fields such as construction. As a result, waste gypsum is stored in stacks indefinitely, with significant risk of leaching their contaminants into water and soil. [ 33 ] To reduce the accumulation and ultimately clear out these stacks, research is underway to find more applications for such waste products. [ 34 ]
People can be exposed to gypsum in the workplace by breathing it in, skin contact, and eye contact. Calcium sulfate per se is nontoxic and is even approved as a food additive, [ 36 ] but as powdered gypsum, it can irritate skin and mucous membranes. [ 37 ]
The Occupational Safety and Health Administration (OSHA) has set the legal limit ( permissible exposure limit ) for gypsum exposure in the workplace as TWA 15 mg/m 3 for total exposure and TWA 5 mg/m 3 for respiratory exposure over an eight-hour workday. The National Institute for Occupational Safety and Health (NIOSH) has set a recommended exposure limit (REL) of TWA 10 mg/m 3 for total exposure and TWA 5 mg/m 3 for respiratory exposure over an eight-hour workday. [ 37 ]
Gypsum is used in a wide variety of applications: | https://en.wikipedia.org/wiki/Gypsum |
In geometry, a gyration is a rotation in a discrete subgroup of symmetries of the Euclidean plane such that the subgroup does not also contain a reflection symmetry whose axis passes through the center of rotational symmetry . In the orbifold corresponding to the subgroup, a gyration corresponds to a rotation point that does not lie on a mirror , called a gyration point . [ 1 ]
For example, having a sphere rotating about any point that is not the center of the sphere, the sphere is gyrating. If it was rotating about its center, the rotation would be symmetrical and it would not be considered gyration.
This geometry-related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Gyration |
In physics , the gyration tensor is a tensor that describes the second moments of position of a collection of particles
where r m ( i ) {\displaystyle r_{m}^{(i)}} is the m t h {\displaystyle \mathrm {m^{th}} } Cartesian coordinate of the position vector r ( i ) {\displaystyle \mathbf {r} ^{(i)}} of the i t h {\displaystyle \mathrm {i^{th}} } particle. The origin of the coordinate system has been chosen such that
i.e. in the system of the center of mass r C M {\displaystyle r_{CM}} . Where
Another definition, which is mathematically identical but gives an alternative calculation method, is:
Therefore, the x-y component of the gyration tensor for particles in Cartesian coordinates would be:
In the continuum limit ,
where ρ ( r ) {\displaystyle \rho (\mathbf {r} )} represents the number density of particles at position r {\displaystyle \mathbf {r} } .
Although they have different units, the gyration tensor is related to the moment of inertia tensor . The key difference is that the particle positions are weighted by mass in the inertia tensor, whereas the gyration tensor depends only on the particle positions; mass plays no role in defining the gyration tensor.
Since the gyration tensor is a symmetric 3x3 matrix , a Cartesian coordinate system can be found in which it is diagonal
where the axes are chosen such that the diagonal elements are ordered λ x 2 ≤ λ y 2 ≤ λ z 2 {\displaystyle \lambda _{x}^{2}\leq \lambda _{y}^{2}\leq \lambda _{z}^{2}} .
These diagonal elements are called the principal moments of the gyration tensor.
The principal moments can be combined to give several parameters that describe the distribution of particles. The squared radius of gyration is the sum of the principal moments:
The asphericity b {\displaystyle b} is defined by
which is always non-negative and zero only when the three principal moments are equal, λ x = λ y = λ z . This zero condition is met when the distribution of particles is spherically symmetric (hence the name asphericity ) but also whenever the particle distribution is symmetric with respect to the three coordinate axes, e.g., when the particles are distributed uniformly on a cube , tetrahedron or other Platonic solid .
Similarly, the acylindricity c {\displaystyle c} is defined by
which is always non-negative and zero only when the two principal moments are equal, λ x = λ y .
This zero condition is met when the distribution of particles is cylindrically symmetric (hence the name, acylindricity ), but also whenever the particle distribution is symmetric with respect to the two coordinate axes, e.g., when the particles are distributed uniformly on a regular prism .
Finally, the relative shape anisotropy κ 2 {\displaystyle \kappa ^{2}} is defined
which is bounded between zero and one. κ 2 {\displaystyle \kappa ^{2}} = 0 only occurs if all points are spherically symmetric, and κ 2 {\displaystyle \kappa ^{2}} = 1 only occurs if all points lie on a line. | https://en.wikipedia.org/wiki/Gyration_tensor |
Gyratory equipment , used in mechanical screening and sieving is based on a circular motion of the machine . Unlike other methods, gyratory screen operates in a gentler manner and is more suited to handle fragile things, enabling it to produce finer products. [ 1 ] This method is applicable for both wet and dry screening.
A distinct difference to other techniques is that the gyratory motion applied here depends on eccentric weights instead of vibrations , [ 2 ] which can be varied based on individual process requirement.
In the early 1930s, most vibratory separators had a rectangular or square design employing simple reciprocating movement. After the introduction of machines utilizing gyratory motion with orbital movements, there was a huge change in machinery industry due to the much greater screen area usage and capacity per unit mesh area. [ 3 ]
The gyratory equipment contains decks of cards on top of each other with the coarsest screen on top and the finest below. The feed is inserted from the top and gyratory motion triggers the penetration of particles into the next deck through screen openings. [ 4 ]
Casings are inclined at relatively low angles (< 15°) to the horizontal plane, with gyrations occurring in the vertical plane. [ 5 ] The eccentric masses can be varied in such as the increase of top eccentric mass leads to an increase in horizontal throw, promoting the discharge of oversize materials. Increment in bottom eccentric mass boosts the material turn over on the screen surface, maximizing the quantity of undersize-material penetration. [ 6 ] Oversize materials are discharged via tangential outlet.
The option to select number of decks enables gyratory equipment to accurately separate materials consisting particles that are very close in size. This advantage is unrivalled and proves to be significant in the powder processing industry where fine materials are involved. High separating efficiency and ease of maintenance puts gyratory screening ahead compared to other processes in terms of product quality. [ 5 ]
Existing gyratory equipment designs are already on the market, more to come with further development. Recent studies have shown that potential improvements are available for cost-saving and effective separation process. [ 7 ]
Common applications include separation used in the process industry , food industry , chemical industry and pharmaceuticals . This includes screening, classification, sifting, fiber recovery, filtration, and scalping. Gyratory screening is capable of separating finer materials as compared to other methods, and is therefore more suitable to treat fragile materials. Several applications in respective industries are shown in the table [ 8 ] below.
General and industrial heavy duty models are available for gyratory equipment, with wooden frames for general models aiming to save cost. Industrial heavy duty models are constructed with carbon steel or stainless steel. Screen capacities vary with model sizes over a huge range to satisfy individual application requirements such as material size, bulk density, moisture contamination, etc. Models consist up to seven decks with screenings up to 325 meshes, allowing it to perform accurate separations for the finest materials. This feature comes in handy in the powder processing industry where fine powders with relatively close sizes are involved. Screens openings for different decks are to be calculated accurately to ensure accurate separation.
General models, installed with wooden frames indicating lesser reinforcements, are used for applications involving materials with distinct difference in sizes. An example for this is the removal of impurities from wood chips for biomass fuel production. In this case, the desired product will be discharged at the coarsest screen, leaving smaller impurities to sink to the bottom frames. These models are selected for more economical purposes and are less common.
The low amount of power required to run a gyratory screener enables an overall low cost of operation for this machine. This is due to the relatively lower energy required for gyratory motion compared to vibrating a massive frame. The low running cost as well as the low purchasing cost of gyratory equipment make it one of the more commonly used machines for solid-solid mechanical separation. [ 9 ]
As a gyratory screening machine employs the use of smaller stacked screen frames, the screens can be accurately placed to the precise requirements of each separation. This puts a gyratory screener at an advantage over a number of other mechanical screening devices, as many other devices would require the use of additional equipment to cope with a different type of feed. [ 10 ]
A gyratory screener can be used in many situations, regardless of whether the solid-solid mixture to be separated consists of a binary mixture, or a multi-fraction mixture. This is because the flexibility of usage of the gyratory sifter screens eliminates the need for excess screen materials, cleaners or other forms of additional apparatus. [ 10 ]
The lack of vertical motion in the mechanism of a gyratory sifter, coupled with its relatively gentle motion enables a higher accuracy in the separation of materials in the solid-solid mixture. The longer stroke involved in gyratory machines allows the finer particles to settle down and spread out. This, coupled with the horizontal motion used maximises the opportunity for the finer particles to pass, thus enhancing the quality and efficiency of separation. [ 11 ]
Most modern day gyratory screening machines employ the use of screen cleaners, which act to prevent any clogging of the gyratory sifters. The motion and mechanism of a gyratory screener enables more energy to be imparted onto the cleaners, thus actively preventing the occurrence of build-up on the gyratory sifters. In the long run, the prevention of build-up in the sifters would enable the gyratory screener to have a longer lifespan. [ 9 ]
Vibration at the vertical component by the bottom eccentric weight significantly reduces screen blinding. Additional ball trays and Kleen rings can further reduce screen blinding. [ citation needed ]
The large area of the gyratory screen requires a large floor space to be reserved. This may cause logistical problems in cases where space needs to be optimised and efficiently used. [ 9 ]
The gyratory sifter has a complex flow pattern, as well a complex drive mechanism, which is more complex than most other sifters. This could pose problems, as the complexity of the operating mechanism makes the unit harder to operate. [ 11 ]
The gyratory sifter operates at a gentle pace, and has a non-robust motion during operation. The gentle motion involved will not break up any lumps or agglomerates found in the feed. Thus, the lumps in the feed would be discarded in the top frame discharge, along with other large particles. [ 9 ]
Gyratory equipment is divided to a top and a bottom unit. The unit on top consists of screening frames supported with rugged springs attached to the circular base, which allows free vibration of the top unit. Secondary support springs are attached to for heavy duty operation, preventing the vibration of the top unit from reaching the floor. The base of the machine (bottom unit) consists of top and bottom eccentric weights attached to a heavy duty motor. Minimum energy is consumed with the installation of double extended shafts on the motors, which are attached to both the top and bottom eccentric weights. Screen decks can be mounted on top of another within the machine assembly with spacing frames connected together via stainless steel quick release clamps. [ 12 ]
There are large amounts of gyratory equipment designs available with some possible design characteristics include: [ 13 ] [ 14 ]
Gyratory equipment is capable of handling feeds of 500 tons/(h·m 2 ) with separation efficiency up to 98% for dry processes, with feed materials to be separated not below a diameter of 4 μm.
Wet processes in the other hand can only manage a relatively high efficiency (85%) if the moisture content is above 70%.
Eccentric weights can be varied accordingly to obtain desired ratio of coarse vs fine products.
Separation efficiency factor is given by the equation: [ 15 ]
where m o {\displaystyle m_{\text{o}}} is the fraction of undersize in oversize and M o {\displaystyle M_{\text{o}}} is the mass of oversize in feed.
However, correction coefficient factor is to be included in the event of multiple decks are involved, as stated in the table [ 15 ] below.
This is due to the error carried forward for every deck. Efficiency factor is multiplied by the correction factor to obtain a more accurate estimate.
The degree of removal of wet processes is lower than their dry counterparts, which is explained by the change in physico-mechanical properties of the body.
The trend of the curve displays that feed materials with a moisture content above 70% is more suited for gyratory screening.
Both top and bottom eccentric weights play a big role in sorting a ratio of coarse versus fine products. Kinetic moment produced by the additional eccentric weights changes the oscillation swing, hence producing outputs of different rates and compositions. Increasing the upper eccentric weight promotes discharge of the coarse material. An increase in the lower eccentric weight maximizes the quantity discharged below. The relationships are demonstrated in the table below for a fixed design:
The kinetic moment is linked to eccentric weights with the equations: [ 17 ]
where θ {\displaystyle \theta } is the lower or upper wheel position (rad), ϕ {\displaystyle \phi } is the phase angle (rad), m {\displaystyle m} is the mass of wheel, N {\displaystyle N} is the motor shaft input speed (rpm) and η {\displaystyle \eta } is the force transfer coefficient.
Gyratory equipment is only invalid if two or more materials to be separated are finer than 4 μm , which varies with different machine dimensions. The proposed value of 4 μm was calculated using the dimensions of the largest available model with the largest possible gyration radius. The critical velocity, which cannot be exceeded by the materials or else the operation fails, is given by the equation: [ 5 ] [ 18 ] [ 19 ]
where D a {\displaystyle D_{\text{a}}} is the length of side of aperture and d p {\displaystyle d_{\text{p}}} is the particle diameter.
Gyration inertia formulae allow the calculations for different models with different dimensions.
Typical gyratory equipment operation circulates around eccentric weight and screen frames. Materials are distributed along the screen surface and undersize materials are allowed to penetrate the screen. A rule of thumb is to be followed for high separation efficiency and smooth operation:
Screening can be carried out in dry or wet basis. Wet screening often requires post treatment, drying as a preparation for the downstream process. In most cases, drying is often used in the final stage of the process, however this can be varied due to the need of the process. Drying process involves the removal of water or other solutes, whereby most of the process are done by vaporization with the aid of heat supply. Thus, efficiency of heat supply equipment plays an important role to optimize the drying process.
Furthermore, this treatment can be applied on the waste stream prior the disposal. Drying greatly reduce the total volume mass of the solid waste, which simplify the handling process and reduce the transportation cost.
The list below states the examples of dryers available for industrial process: [ 23 ]
Gyratory screener separates solids from liquid or other dry solids according to the particle sizes. Screening is one of the crucial pre-treatment to several industries, such as chemical, food, mining, pharmaceutical, and waste. [ 8 ]
The table above presents the waste stream for several processes that are commonly use in different industries. The example given for chemical industry is the powdered detergent production where gyratory screener is used to filter out the oversized granules found in end product to improve product appearance and dissolve rate. Citrus juice production is the example of food industry. Gyratory screener available in multi-layered planes eliminates all the wastes in several stages. Juice sacs are the desirable element to produce citrus juice. Screening in food industry significantly increases the product quality. Among the ore processing, gyratory screener is used after crushing to filter out the oversized ore particles. These unfavourable particles can be regarded as waste or recycle back to the process. Similarly, in pharmaceutical industry, gyratory screener removes undissolved particles from liquid pharmaceuticals or fine powder that stick on the capsule surface to ease the capsule stamp. As for wastewater treatment, removal of coarse solid wastes from the wastewater stream is exclusively to protect the downstream equipment from damages. Fine solid waste removal acts as pre-treatment for the process, more specifically a primary clarification. The overall screening process enhances system performance, minimize the cost and reduce the need for cleaning of the filter in other equipment. [ 24 ]
The waste materials usually travel through a discharge chute for disposal depending on the design of the gyratory screener. There will be at least one outlet for every deck of gyratory screener. [ 25 ] | https://en.wikipedia.org/wiki/Gyratory_equipment |
The gyrator–capacitor model [ 1 ] - sometimes also the capacitor-permeance model [ 2 ] - is a lumped-element model for magnetic circuits , that can be used in place of the more common resistance–reluctance model . The model makes permeance elements analogous to electrical capacitance ( see magnetic capacitance section ) rather than electrical resistance ( see magnetic reluctance ). Windings are represented as gyrators , interfacing between the electrical circuit and the magnetic model.
The primary advantage of the gyrator–capacitor model compared to the magnetic reluctance model is that the model preserves the correct values of energy flow, storage and dissipation. [ 3 ] [ 4 ] The gyrator–capacitor model is an example of a group of analogies that preserve energy flow across energy domains by making power conjugate pairs of variables in the various domains analogous. It fills the same role as the impedance analogy for the mechanical domain.
Magnetic circuit may refer to either the physical magnetic circuit or the model magnetic circuit. Elements and dynamical variables that are part of the model magnetic circuit have names that start with the adjective magnetic , although this convention is not strictly followed. Elements or dynamical variables in the model magnetic circuit may not have a one to one correspondence with components in the physical magnetic circuit. Symbols for elements and variables that are part of the model magnetic circuit may be written with a subscript of M. For example, C M {\displaystyle C_{M}} would be a magnetic capacitor in the model circuit.
Electrical elements in an associated electrical circuit may be brought into the magnetic model for ease of analysis. Model elements in the magnetic circuit that represent electrical elements are typically the electrical dual of the electrical elements. This is because transducers between the electrical and magnetic domains in this model are usually represented by gyrators. A gyrator will transform an element into its dual. For example, a magnetic inductance may represent an electrical capacitance.
The following table summarizes the mathematical analogy between electrical circuit theory and magnetic circuit theory.
newton / weber
newton / coulomb
A gyrator is a two-port element used in network analysis. The gyrator is the complement of the transformer ; whereas in a transformer, a voltage on one port will transform to a proportional voltage on the other port, in a gyrator, a voltage on one port will transform to a current on the other port, and vice versa.
The role gyrators play in the gyrator–capacitor model is as transducers between the electrical energy domain and the magnetic energy domain. An emf in the electrical domain is analogous to an mmf in the magnetic domain, and a transducer doing such a conversion would be represented as a transformer. However, real electro-magnetic transducers usually behave as gyrators. A transducer from the magnetic domain to the electrical domain will obey Faraday's law of induction , that is, a rate of change of magnetic flux (a magnetic current in this analogy) produces a proportional emf in the electrical domain. Similarly, a transducer from the electrical domain to the magnetic domain will obey Ampère's circuital law , that is, an electric current will produce a mmf.
A winding of N turns is modeled by a gyrator with a gyration resistance of N ohms. [ 1 ] : 100
Transducers that are not based on magnetic induction may not be represented by a gyrator. For instance, a Hall effect sensor is modelled by a transformer.
Magnetic voltage , v m {\displaystyle v_{m}} , is an alternate name for magnetomotive force (mmf), F {\displaystyle {\mathcal {F}}} ( SI unit : A or amp-turn ), which is analogous to electrical voltage in an electric circuit. [ 4 ] : 42 [ 3 ] : 5 Not all authors use the term magnetic voltage . The magnetomotive force applied to an element between point A and point B is equal to the line integral through the component of the magnetic field strength, H {\displaystyle \mathbf {H} } . v m = F = − ∫ A B H ⋅ d l {\displaystyle v_{m}={\mathcal {F}}=-\int _{A}^{B}\mathbf {H} \cdot d\mathbf {l} } The resistance–reluctance model uses the same equivalence between magnetic voltage and magnetomotive force.
Magnetic current , i m {\displaystyle i_{m}} , is an alternate name for the time rate of change of flux , Φ ˙ {\displaystyle {\dot {\Phi }}} ( SI unit : Wb /sec or volts ), which is analogous to electrical current in an electric circuit. [ 2 ] : 2429 [ 4 ] : 37 In the physical circuit, Φ ˙ {\displaystyle {\dot {\Phi }}} , is magnetic displacement current . [ 4 ] : 37 The magnetic current flowing through an element of cross section, S {\displaystyle S} , is the area integral of the magnetic flux density B {\displaystyle \mathbf {B} } .
i m = Φ ˙ = d d t ∫ S B ⋅ d S {\displaystyle i_{m}={\dot {\Phi }}={\frac {d}{dt}}\int _{S}\mathbf {B} \cdot d\mathbf {S} } The resistance–reluctance model uses a different equivalence, taking magnetic current to be an alternate name for flux, Φ {\displaystyle \Phi } . This difference in the definition of magnetic current is the fundamental difference between the gyrator-capacitor model and the resistance–reluctance model. The definition of magnetic current and magnetic voltage imply the definitions of the other magnetic elements. [ 4 ] : 35
Magnetic capacitance is an alternate name for permeance , ( SI unit : H ). It is represented by a capacitance in the model magnetic circuit. Some authors use C M {\displaystyle C_{\mathrm {M} }} to denote magnetic capacitance while others use P {\displaystyle P} and refer to the capacitance as a permeance. Permeance of an element is an extensive property defined as the magnetic flux, Φ {\displaystyle \Phi } , through the cross sectional surface of the element divided by the magnetomotive force , F {\displaystyle {\mathcal {F}}} , across the element' [ 3 ] : 6 C M = P = ∫ B ⋅ d S ∫ H ⋅ d l = Φ F {\displaystyle C_{\mathrm {M} }=P={\frac {\int \mathbf {B} \cdot d\mathbf {S} }{\int \mathbf {H} \cdot d\mathbf {l} }}={\frac {\Phi }{\mathcal {F}}}}
For a bar of uniform cross-section, magnetic capacitance is given by, C M = P = μ r μ 0 S l {\displaystyle C_{\mathrm {M} }=P=\mu _{\mathrm {r} }\mu _{0}{\frac {S}{l}}} where:
For phasor analysis , the magnetic permeability [ 5 ] and the permeance are complex values. [ 5 ] [ 6 ]
Permeance is the reciprocal of reluctance .
In the context of the gyrator-capacitor model of a magnetic circuit, magnetic inductance L M {\displaystyle L_{\mathrm {M} }} ( SI unit : F ) is the analogy to inductance in an electrical circuit.
For phasor analysis the magnetic inductive reactance is: x L = ω L M {\displaystyle x_{\mathrm {L} }=\omega L_{\mathrm {M} }} where:
In the complex form it is a positive imaginary number: j x L = j ω L M {\displaystyle jx_{\mathrm {L} }=j\omega L_{\mathrm {M} }}
The magnetic potential energy sustained by magnetic inductance varies with the frequency of oscillations in electric fields. The average power in a given period is equal to zero. Due to its dependence on frequency, magnetic inductance is mainly observable in magnetic circuits which operate at VHF and/or UHF frequencies. [ citation needed ]
The notion of magnetic inductance is employed in analysis and computation of circuit behavior in the gyrator–capacitor model in a way analogous to inductance in electrical circuits.
A magnetic inductor can represent an electrical capacitor. [ 4 ] : 43 A shunt capacitance in the electrical circuit, such as intra-winding capacitance can be represented as a series inductance in the magnetic circuit.
This example shows a three-phase transformer modeled by the gyrator-capacitor approach. The transformer in this example has three primary windings and three secondary windings. The magnetic circuit is split into seven reluctance or permeance elements. Each winding is modeled by a gyrator. The gyration resistance of each gyrator is equal to the number of turns on the associated winding. Each permeance element is modeled by a capacitor. The value of each capacitor in farads is the same as the inductance of the associated permeance in henrys .
N 1 , N 2 , and N 3 are the number of turns in the three primary windings. N 4 , N 5 , and N 6 are the number of turns in the three secondary windings. Φ 1 , Φ 2 , and Φ 3 are the fluxes in the three vertical elements. Magnetic flux in each permeance element in webers is numerically equal to the charge in the associated capacitance in coulombs . The energy in each permeance element is the same as the energy in the associated capacitor.
The schematic shows a three phase generator and a three phase load in addition to the schematic of the transformer model.
The gyrator-capacitor approach can accommodate leakage inductance and air gaps in the magnetic circuit. Gaps and leakage flux have a permeance which can be added to the equivalent circuit as capacitors. The permeance of the gap is computed in the same way as the substantive elements, except a relative permeability of unity is used. The permeance of the leakage flux may be difficult to compute due to complex geometry. It may be computed from other considerations such as measurements or specifications.
C PL and C SL represent the primary and secondary leakage inductance respectively. C GAP represents the air gap permeance.
Magnetic complex impedance , also called full magnetic resistance, is the quotient of a complex sinusoidal magnetic tension ( magnetomotive force , F {\displaystyle {\mathcal {F}}} ) on a passive magnetic circuit and the resulting complex sinusoidal magnetic current ( Φ ˙ {\displaystyle {\dot {\Phi }}} ) in the circuit. Magnetic impedance is analogous to electrical impedance .
Magnetic complex impedance ( SI unit : S ) is determined by: Z M = F Φ ˙ = z M e j ϕ {\displaystyle Z_{M}={\frac {\mathcal {F}}{\dot {\Phi }}}=z_{M}e^{j\phi }} where z M {\displaystyle z_{M}} is the modulus of Z M {\displaystyle Z_{M}} and ϕ {\displaystyle \phi } is its phase. The argument of a complex magnetic impedance is equal to the difference of the phases of the magnetic tension and magnetic current.
Complex magnetic impedance can be presented in following form: Z M = z M e j ϕ = z M cos ϕ + j z M sin ϕ = r M + j x M {\displaystyle Z_{M}=z_{M}e^{j\phi }=z_{M}\cos \phi +jz_{M}\sin \phi =r_{M}+jx_{M}} where r M = z M cos ϕ {\displaystyle r_{M}=z_{M}\cos \phi } is the real part of the complex magnetic impedance, called the effective magnetic resistance, and x M = z M sin ϕ {\displaystyle x_{M}=z_{M}\sin \phi } is the imaginary part of the complex magnetic impedance, called the reactive magnetic resistance.
The magnetic impedance is equal to z M = r M 2 + x M 2 , {\displaystyle z_{M}={\sqrt {r_{M}^{2}+x_{M}^{2}}},} ϕ = arctan x M r M {\displaystyle \phi =\arctan {\frac {x_{M}}{r_{M}}}}
Magnetic effective resistance is the real component of complex magnetic impedance. This causes a magnetic circuit to lose magnetic potential energy. [ 7 ] [ 8 ] Active power in a magnetic circuit equals the product of magnetic effective resistance r M {\displaystyle r_{\mathrm {M} }} and magnetic current squared I M 2 {\displaystyle I_{\mathrm {M} }^{2}} .
P = r M I M 2 {\displaystyle P=r_{\mathrm {M} }I_{\mathrm {M} }^{2}}
The magnetic effective resistance on a complex plane appears as the side of the resistance triangle for magnetic circuit of an alternating current. The effective magnetic resistance is bounding with the effective magnetic conductance g M {\displaystyle g_{\mathrm {M} }} by the expression g M = r M z M 2 {\displaystyle g_{\mathrm {M} }={\frac {r_{\mathrm {M} }}{z_{\mathrm {M} }^{2}}}} where z M {\displaystyle z_{\mathrm {M} }} is the full magnetic impedance of a magnetic circuit.
Magnetic reactance is the parameter of a passive magnetic circuit, or an element of the circuit, which is equal to the square root of the difference of squares of the magnetic complex impedance and magnetic effective resistance to a magnetic current, taken with the sign plus, if the magnetic current lags behind the magnetic tension in phase, and with the sign minus, if the magnetic current leads the magnetic tension in phase.
Magnetic reactance [ 7 ] [ 6 ] [ 8 ] is the component of magnetic complex impedance of the alternating current circuit, which produces the phase shift between a magnetic current and magnetic tension in the circuit. It is measured in units of 1 Ω {\displaystyle {\tfrac {1}{\Omega }}} and is denoted by x {\displaystyle x} (or X {\displaystyle X} ). It may be inductive x L = ω L M {\displaystyle x_{L}=\omega L_{M}} or capacitive x C = 1 ω C M {\displaystyle x_{C}={\tfrac {1}{\omega C_{M}}}} , where ω {\displaystyle \omega } is the angular frequency of a magnetic current, L M {\displaystyle L_{M}} is the magnetic inductiance of a circuit, C M {\displaystyle C_{M}} is the magnetic capacitance of a circuit. The magnetic reactance of an undeveloped circuit with the inductance and the capacitance which are connected in series, is equal: x = x L − x C = ω L M − 1 ω C M {\textstyle x=x_{L}-x_{C}=\omega L_{M}-{\frac {1}{\omega C_{M}}}} . If x L = x C {\displaystyle x_{L}=x_{C}} , then the net reactance x = 0 {\displaystyle x=0} and resonance takes place in the circuit. In the general case x = z 2 − r 2 {\textstyle x={\sqrt {z^{2}-r^{2}}}} . When an energy loss is absent ( r = 0 {\displaystyle r=0} ), x = z {\displaystyle x=z} . The angle of the phase shift in a magnetic circuit ϕ = arctan x r {\textstyle \phi =\arctan {\frac {x}{r}}} . On a complex plane, the magnetic reactance appears as the side of the resistance triangle for circuit of an alternating current.
The limitations of this analogy between magnetic circuits and electric circuits include the following; | https://en.wikipedia.org/wiki/Gyrator–capacitor_model |
Gyrochronology is a method for estimating the age of a low-mass (cool) main sequence star (spectral class F8 V or later) from its rotation period . The term is derived from the Greek words gyros, chronos and logos , roughly translated as rotation, age , and study respectively. It was coined in 2003 by Sydney Barnes [ 1 ] to describe the associated procedure for deriving stellar ages, and developed extensively in empirical form in 2007. [ 2 ]
Gyrochronology builds on a work of Andrew Skumanich, [ 3 ] who found that the average value of ( v sin i ) for several open clusters was inversely proportional to the square root of the cluster's age. In the expression ( v sin i ), ( v ) is the velocity on the star's equator and ( i ) is the inclination angle of the star's axis of rotation , which is generally an unmeasurable quantity. The gyrochronology method depends on the relationship between the rotation period and the mass of low mass main-sequence stars of the same age, which was verified by early work on the Hyades open cluster . [ 4 ] The associated age estimate for a star is known as the gyrochronological age.
The basic idea underlying gyrochronology is that the rotation period P, of a cool main-sequence star is a deterministic function of its age t and its mass M (or a suitable substitute such as color ). Although main sequence stars of a given mass form with a range of rotation periods, their periods increase rapidly and converge to a well defined value as they lose angular momentum through magnetically channelled stellar winds. Therefore, their periods converge to a certain function of age and mass, mathematically denoted by P=P(t,M). Consequently, cool stars do not occupy the entire 3-dimensional parameter space of (mass, age, period), but instead define a 2-dimensional surface in this P-t-M space. Therefore, measuring two of these variables yields the third. Of these quantities, the mass (color) and the rotation period are the easier variables to measure, providing access to the star's age, otherwise difficult to obtain.
In order to determine the shape of this P=P(t,M) surface, the rotation periods and photometric colors (mass) of stars in clusters of known age are measured. Data has been accumulated from several clusters younger than one billion years (Gyr) of age and one cluster with an age of 2.5 Gyr. Another data point on the surface is from the Sun with an age of 4.56 Gyr and a rotation period of 25 days. Using these results, the ages of a large number of cool galactic field stars can be derived with 10% precision.
Magnetic stellar wind breaking increases the rotation period of the star and it is important in stars with convective envelopes. Stars with a color index greater than about (B-V)=0.47 mag (the Sun has a color index of 0.66 mag) have convective envelopes, but more massive stars have radiative envelopes. Also, these lower mass stars spend a considerable amount of time on a pre main sequence Hayashi track where they are nearly fully convective. [ 5 ] | https://en.wikipedia.org/wiki/Gyrochronology |
A gyrocompass is a type of non-magnetic compass which is based on a fast-spinning disc and the rotation of the Earth (or another planetary body if used elsewhere in the universe) to find geographical direction automatically. A gyrocompass makes use of one of the seven fundamental ways to determine the heading of a vehicle. [ 1 ] A gyroscope is an essential component of a gyrocompass, but they are different devices; a gyrocompass is built to use the effect of gyroscopic precession , which is a distinctive aspect of the general gyroscopic effect . [ 2 ] [ 3 ] Gyrocompasses, such as the fibre optic gyrocompass are widely used to provide a heading for navigation on ships . [ 4 ] [ 5 ] This is because they have two significant advantages over magnetic compasses : [ 3 ]
Aircraft commonly use gyroscopic instruments (but not a gyrocompass) for navigation and attitude monitoring; for details, see flight instruments (specifically the heading indicator ) and gyroscopic autopilot .
The first, not yet practical, [ 6 ] form of gyrocompass was patented in 1885 by Marinus Gerardus van den Bos. [ 6 ] A usable gyrocompass was invented in 1906 in Germany by Hermann Anschütz-Kaempfe , and after successful tests in 1908 became widely used in the German Imperial Navy. [ 2 ] [ 6 ] [ 7 ] Anschütz-Kaempfe founded the company Anschütz & Co. in Kiel , to mass produce gyrocompasses; the company is today Raytheon Anschütz GmbH. [ 8 ] The gyrocompass was an important invention for nautical navigation because it allowed accurate determination of a vessel’s location at all times regardless of the vessel’s motion, the weather and the amount of steel used in the construction of the ship. [ 9 ]
In the United States, Elmer Ambrose Sperry produced a workable gyrocompass system (1908: U.S. patent 1,242,065 ), and founded the Sperry Gyroscope Company . The unit was adopted by the U.S. Navy (1911 [ 3 ] ), and played a major role in World War I. The Navy also began using Sperry's "Metal Mike": the first gyroscope-guided autopilot steering system. In the following decades, these and other Sperry devices were adopted by steamships such as the RMS Queen Mary , airplanes, and the warships of World War II. After his death in 1930, the Navy named the USS Sperry after him.
Meanwhile, in 1913, C. Plath (a Hamburg, Germany-based manufacturer of navigational equipment including sextants and magnetic compasses) developed the first gyrocompass to be installed on a commercial vessel. C. Plath sold many gyrocompasses to the Weems’ School for Navigation in Annapolis, MD, and soon the founders of each organization formed an alliance and became Weems & Plath. [ 10 ]
Before the success of the gyrocompass, several attempts had been made in Europe to use a gyroscope instead. By 1880, William Thomson (Lord Kelvin) tried to propose a gyrostat to the British Navy. In 1889, Arthur Krebs adapted an electric motor to the Dumoulin-Froment marine gyroscope, for the French Navy. That gave the Gymnote submarine the ability to keep a straight line while underwater for several hours, and it allowed her to force a naval block in 1890.
In 1923 Max Schuler published his paper containing his observation that if a gyrocompass possessed Schuler tuning such that it had an oscillation period of 84.4 minutes (which is the orbital period of a notional satellite orbiting around the Earth at sea level), then it could be rendered insensitive to lateral motion and maintain directional stability. [ 11 ]
A gyroscope , not to be confused with a gyrocompass, is a spinning wheel mounted on a set of gimbals so that its axis is free to orient itself in any way. [ 3 ] When it is spun up to speed with its axis pointing in some direction, due to the law of conservation of angular momentum , such a wheel will normally maintain its original orientation to a fixed point in outer space (not to a fixed point on Earth). Since the Earth rotates, it appears to a stationary observer on Earth that a gyroscope's axis is completing a full rotation once every 24 hours. [ note 1 ] Such a rotating gyroscope is used for navigation in some cases, for example on aircraft, where it is known as heading indicator or directional gyro, but cannot ordinarily be used for long-term marine navigation. The crucial additional ingredient needed to turn a gyroscope into a gyrocompass, so it would automatically position to true north, [ 2 ] [ 3 ] is some mechanism that results in an application of torque whenever the compass's axis is not pointing north.
One method uses friction to apply the needed torque: [ 9 ] the gyroscope in a gyrocompass is not completely free to reorient itself; if for instance a device connected to the axis is immersed in a viscous fluid, then that fluid will resist reorientation of the axis. This friction force caused by the fluid results in a torque acting on the axis, causing the axis to turn in a direction orthogonal to the torque (that is, to precess ) along a line of longitude . Once the axis points toward the celestial pole, it will appear to be stationary and won't experience any more frictional forces. This is because true north (or true south) is the only direction for which the gyroscope can remain on the surface of the earth and not be required to change. This axis orientation is considered to be a point of minimum potential energy .
Another, more practical, method is to use weights to force the axis of the compass to remain horizontal (perpendicular to the direction of the center of the Earth), but otherwise allow it to rotate freely within the horizontal plane. [ 2 ] [ 3 ] In this case, gravity will apply a torque forcing the compass's axis toward true north. Because the weights will confine the compass's axis to be horizontal with respect to the Earth's surface, the axis can never align with the Earth's axis (except on the Equator) and must realign itself as the Earth rotates. But with respect to the Earth's surface, the compass will appear to be stationary and pointing along the Earth's surface toward the true North Pole.
Since the gyrocompass's north-seeking function depends on the rotation around the axis of the Earth that causes torque-induced gyroscopic precession , it will not orient itself correctly to true north if it is moved very fast in an east to west direction, thus negating the Earth's rotation. However, aircraft commonly use heading indicators or directional gyros , which are not gyrocompasses and do not align themselves to north via precession, but are periodically aligned manually to magnetic north. [ 12 ] [ 13 ]
A gyrocompass is subject to certain errors. These include steaming error, where rapid changes in course, speed and latitude cause deviation before the gyro can adjust itself. [ 14 ] On most modern ships the GPS or other navigational aids feed data to the gyrocompass allowing a small computer to apply a correction.
Alternatively a design based on a strapdown architecture (including a triad of fibre optic gyroscopes , ring laser gyroscopes or hemispherical resonator gyroscopes and a triad of accelerometers) will eliminate these errors, as they do not depend upon mechanical parts to determinate rate of rotation. [ 15 ]
We consider a gyrocompass as a gyroscope which is free to rotate about one of its symmetry axes, also the whole rotating gyroscope is free to rotate on the horizontal plane about the local vertical. Therefore there are two independent local rotations. In addition to these rotations we consider the rotation of the Earth about its north-south (NS) axis, and we model the planet as a perfect sphere. We neglect friction and also the rotation of the Earth about the Sun.
In this case a non-rotating observer located at the center of the Earth can be approximated as being an inertial frame. We establish cartesian coordinates ( X 1 , Y 1 , Z 1 ) {\displaystyle (X_{1},Y_{1},Z_{1})} for such an observer (whom we name as 1-O), and the barycenter of the gyroscope is located at a distance R {\displaystyle R} from the center of the Earth.
Consider another (non-inertial) observer (the 2-O) located at the center of the Earth but rotating about the NS-axis by Ω . {\displaystyle \Omega .} We establish coordinates attached to this observer as ( X 2 Y 2 Z 2 ) = ( cos Ω t sin Ω t 0 − sin Ω t cos Ω t 0 0 0 1 ) ( X 1 Y 1 Z 1 ) {\displaystyle {\begin{pmatrix}X_{2}\\Y_{2}\\Z_{2}\end{pmatrix}}={\begin{pmatrix}\cos \Omega t&\sin \Omega t&0\\-\sin \Omega t&\cos \Omega t&0\\0&0&1\end{pmatrix}}{\begin{pmatrix}X_{1}\\Y_{1}\\Z_{1}\end{pmatrix}}} so that the unit X ^ 1 {\displaystyle {\hat {X}}_{1}} versor ( X 1 = 1 , Y 1 = 0 , Z 1 = 0 ) T {\displaystyle (X_{1}=1,Y_{1}=0,Z_{1}=0)^{T}} is mapped to the point ( X 2 = cos Ω t , Y 2 = − sin Ω t , Z 2 = 0 ) T {\displaystyle (X_{2}=\cos \Omega t,Y_{2}=-\sin \Omega t,Z_{2}=0)^{T}} . For the 2-O neither the Earth nor the barycenter of the gyroscope is moving. The rotation of 2-O relative to 1-O is performed with angular velocity Ω → = ( 0 , 0 , Ω ) T {\displaystyle {\vec {\Omega }}=(0,0,\Omega )^{T}} . We suppose that the X 2 {\displaystyle X_{2}} axis denotes points with zero longitude (the prime, or Greenwich, meridian).
We now rotate about the Z 2 {\textstyle Z_{2}} axis, so that the X 3 {\textstyle X_{3}} -axis has the longitude of the barycenter. In this case we have ( X 3 Y 3 Z 3 ) = ( cos Φ sin Φ 0 − sin Φ cos Φ 0 0 0 1 ) ( X 2 Y 2 Z 2 ) . {\displaystyle {\begin{pmatrix}X_{3}\\Y_{3}\\Z_{3}\end{pmatrix}}={\begin{pmatrix}\cos \Phi &\sin \Phi &0\\-\sin \Phi &\cos \Phi &0\\0&0&1\end{pmatrix}}{\begin{pmatrix}X_{2}\\Y_{2}\\Z_{2}\end{pmatrix}}.}
With the next rotation (about the axis Y 3 {\textstyle Y_{3}} of an angle δ {\textstyle \delta } , the co-latitude) we bring the Z 3 {\textstyle Z_{3}} axis along the local zenith ( Z 4 {\textstyle Z_{4}} -axis) of the barycenter. This can be achieved by the following orthogonal matrix (with unit determinant) ( X 4 Y 4 Z 4 ) = ( cos δ 0 − sin δ 0 1 0 sin δ 0 cos δ ) ( X 3 Y 3 Z 3 ) , {\displaystyle {\begin{pmatrix}X_{4}\\Y_{4}\\Z_{4}\end{pmatrix}}={\begin{pmatrix}\cos \delta &0&-\sin \delta \\0&1&0\\\sin \delta &0&\cos \delta \end{pmatrix}}{\begin{pmatrix}X_{3}\\Y_{3}\\Z_{3}\end{pmatrix}},}
so that the Z ^ 3 {\textstyle {\hat {Z}}_{3}} versor ( X 3 = 0 , Y 3 = 0 , Z 3 = 1 ) T {\textstyle (X_{3}=0,Y_{3}=0,Z_{3}=1)^{T}} is mapped to the point ( X 4 = − sin δ , Y 4 = 0 , Z 4 = cos δ ) T . {\textstyle (X_{4}=-\sin \delta ,Y_{4}=0,Z_{4}=\cos \delta )^{T}.}
We now choose another coordinate basis whose origin is located at the barycenter of the gyroscope. This can be performed by the following translation along the zenith axis ( X 5 Y 5 Z 5 ) = ( X 4 Y 4 Z 4 ) − ( 0 0 R ) , {\displaystyle {\begin{pmatrix}X_{5}\\Y_{5}\\Z_{5}\end{pmatrix}}={\begin{pmatrix}X_{4}\\Y_{4}\\Z_{4}\end{pmatrix}}-{\begin{pmatrix}0\\0\\R\end{pmatrix}},}
so that the origin of the new system, ( X 5 = 0 , Y 5 = 0 , Z 5 = 0 ) T {\displaystyle (X_{5}=0,Y_{5}=0,Z_{5}=0)^{T}} is located at the point ( X 4 = 0 , Y 4 = 0 , Z 4 = R ) T , {\displaystyle (X_{4}=0,Y_{4}=0,Z_{4}=R)^{T},} and R {\displaystyle R} is the radius of the Earth. Now the X 5 {\displaystyle X_{5}} -axis points towards the south direction.
Now we rotate about the zenith Z 5 {\displaystyle Z_{5}} -axis so that the new coordinate system is attached to the structure of the gyroscope, so that for an observer at rest in this coordinate system, the gyrocompass is only rotating about its own axis of symmetry. In this case we find ( X 6 Y 6 Z 6 ) = ( cos α sin α 0 − sin α cos α 0 0 0 1 ) ( X 5 Y 5 Z 5 ) . {\displaystyle {\begin{pmatrix}X_{6}\\Y_{6}\\Z_{6}\end{pmatrix}}={\begin{pmatrix}\cos \alpha &\sin \alpha &0\\-\sin \alpha &\cos \alpha &0\\0&0&1\end{pmatrix}}{\begin{pmatrix}X_{5}\\Y_{5}\\Z_{5}\end{pmatrix}}.}
The axis of symmetry of the gyrocompass is now along the X 6 {\displaystyle X_{6}} -axis.
The last rotation is a rotation on the axis of symmetry of the gyroscope as in ( X 7 Y 7 Z 7 ) = ( 1 0 0 0 cos ψ sin ψ 0 − sin ψ cos ψ ) ( X 6 Y 6 Z 6 ) . {\displaystyle {\begin{pmatrix}X_{7}\\Y_{7}\\Z_{7}\end{pmatrix}}={\begin{pmatrix}1&0&0\\0&\cos \psi &\sin \psi \\0&-\sin \psi &\cos \psi \end{pmatrix}}{\begin{pmatrix}X_{6}\\Y_{6}\\Z_{6}\end{pmatrix}}.}
Since the height of the gyroscope's barycenter does not change (and the origin of the coordinate system is located at this same point), its gravitational potential energy is constant. Therefore its Lagrangian L {\displaystyle {\mathcal {L}}} corresponds to its kinetic energy K {\displaystyle K} only. We have L = K = 1 2 ω → T I ω → + 1 2 M v → C M 2 , {\displaystyle {\mathcal {L}}=K={\frac {1}{2}}{\vec {\omega }}^{T}I{\vec {\omega }}+{\frac {1}{2}}M{\vec {v}}_{\rm {CM}}^{2},} where M {\displaystyle M} is the mass of the gyroscope, and v → C M 2 = Ω 2 R 2 sin 2 δ = c o n s t a n t {\displaystyle {\vec {v}}_{\rm {CM}}^{2}=\Omega ^{2}R^{2}\sin ^{2}\delta ={\rm {constant}}} is the squared inertial speed of the origin of the coordinates of the final coordinate system (i.e. the center of mass). This constant term does not affect the dynamics of the gyroscope and it can be neglected. On the other hand, the tensor of inertia is given by I = ( I 1 0 0 0 I 2 0 0 0 I 2 ) {\displaystyle I={\begin{pmatrix}I_{1}&0&0\\0&I_{2}&0\\0&0&I_{2}\end{pmatrix}}} and ω → = ( 1 0 0 0 cos ψ sin ψ 0 − sin ψ cos ψ ) ( ψ ˙ 0 0 ) + ( 1 0 0 0 cos ψ sin ψ 0 − sin ψ cos ψ ) ( cos α sin α 0 − sin α cos α 0 0 0 1 ) ( 0 0 α ˙ ) + ( 1 0 0 0 cos ψ sin ψ 0 − sin ψ cos ψ ) ( cos α sin α 0 − sin α cos α 0 0 0 1 ) ( cos δ 0 − sin δ 0 1 0 sin δ 0 cos δ ) ( cos Φ sin Φ 0 − sin Φ cos Φ 0 0 0 1 ) ( cos Ω t sin Ω t 0 − sin Ω t cos Ω t 0 0 0 1 ) ( 0 0 Ω ) = ( ψ ˙ 0 0 ) + ( 0 α ˙ sin ψ α ˙ cos ψ ) + ( − Ω sin δ cos α Ω ( sin δ sin α cos ψ + cos δ sin ψ ) Ω ( − sin δ sin α sin ψ + cos δ cos ψ ) ) {\displaystyle {\begin{aligned}{\vec {\omega }}&={\begin{pmatrix}1&0&0\\0&\cos \psi &\sin \psi \\0&-\sin \psi &\cos \psi \end{pmatrix}}{\begin{pmatrix}{\dot {\psi }}\\0\\0\end{pmatrix}}+{\begin{pmatrix}1&0&0\\0&\cos \psi &\sin \psi \\0&-\sin \psi &\cos \psi \end{pmatrix}}{\begin{pmatrix}\cos \alpha &\sin \alpha &0\\-\sin \alpha &\cos \alpha &0\\0&0&1\end{pmatrix}}{\begin{pmatrix}0\\0\\{\dot {\alpha }}\end{pmatrix}}\\&\qquad +{\begin{pmatrix}1&0&0\\0&\cos \psi &\sin \psi \\0&-\sin \psi &\cos \psi \end{pmatrix}}{\begin{pmatrix}\cos \alpha &\sin \alpha &0\\-\sin \alpha &\cos \alpha &0\\0&0&1\end{pmatrix}}{\begin{pmatrix}\cos \delta &0&-\sin \delta \\0&1&0\\\sin \delta &0&\cos \delta \end{pmatrix}}{\begin{pmatrix}\cos \Phi &\sin \Phi &0\\-\sin \Phi &\cos \Phi &0\\0&0&1\end{pmatrix}}{\begin{pmatrix}\cos \Omega t&\sin \Omega t&0\\-\sin \Omega t&\cos \Omega t&0\\0&0&1\end{pmatrix}}{\begin{pmatrix}0\\0\\\Omega \end{pmatrix}}\\&={\begin{pmatrix}{\dot {\psi }}\\0\\0\\\end{pmatrix}}+{\begin{pmatrix}0\\{\dot {\alpha }}\sin \psi \\{\dot {\alpha }}\cos \psi \end{pmatrix}}+{\begin{pmatrix}-\Omega \sin \delta \cos \alpha \\\Omega (\sin \delta \sin \alpha \cos \psi +\cos \delta \sin \psi )\\\Omega (-\sin \delta \sin \alpha \sin \psi +\cos \delta \cos \psi )\end{pmatrix}}\end{aligned}}}
Therefore we find L = 1 2 [ I 1 ω 1 2 + I 2 ( ω 2 2 + ω 3 2 ) ] = 1 2 I 1 ( ψ ˙ − Ω sin δ cos α ) 2 + 1 2 I 2 { [ α ˙ sin ψ + Ω ( sin δ sin α cos ψ + cos δ sin ψ ) ] 2 + [ α ˙ cos ψ + Ω ( − sin δ sin α sin ψ + cos δ cos ψ ) ] 2 } = 1 2 I 1 ( ψ ˙ − Ω sin δ cos α ) 2 + 1 2 I 2 { α ˙ 2 + Ω 2 ( cos 2 δ + sin 2 α sin 2 δ ) + 2 α ˙ Ω cos δ } {\displaystyle {\begin{aligned}{\mathcal {L}}&={\frac {1}{2}}\left[I_{1}\omega _{1}^{2}+I_{2}\left(\omega _{2}^{2}+\omega _{3}^{2}\right)\right]\\&={\frac {1}{2}}I_{1}\left({\dot {\psi }}-\Omega \sin \delta \cos \alpha \right)^{2}+{\frac {1}{2}}I_{2}\left\{\left[{\dot {\alpha }}\sin \psi +\Omega (\sin \delta \sin \alpha \cos \psi +\cos \delta \sin \psi )\right]^{2}+\left[{\dot {\alpha }}\cos \psi +\Omega (-\sin \delta \sin \alpha \sin \psi +\cos \delta \cos \psi )\right]^{2}\right\}\\&={\frac {1}{2}}I_{1}\left({\dot {\psi }}-\Omega \sin \delta \cos \alpha \right)^{2}+{\frac {1}{2}}I_{2}\left\{{\dot {\alpha }}^{2}+\Omega ^{2}\left(\cos ^{2}\delta +\sin ^{2}\alpha \sin ^{2}\delta \right)+2{\dot {\alpha }}\Omega \cos \delta \right\}\end{aligned}}}
The Lagrangian can be rewritten as L = L 1 + 1 2 I 2 Ω 2 cos 2 δ + d d t ( I 2 α Ω cos δ ) , {\displaystyle {\mathcal {L}}={\mathcal {L}}_{1}+{\frac {1}{2}}I_{2}\Omega ^{2}\cos ^{2}\delta +{\frac {d}{dt}}(I_{2}\alpha \Omega \cos \delta ),} where L 1 = 1 2 I 1 ( ψ ˙ − Ω sin δ cos α ) 2 + 1 2 I 2 ( α ˙ 2 + Ω 2 sin 2 α sin 2 δ ) {\displaystyle {\mathcal {L}}_{1}={\frac {1}{2}}I_{1}\left({\dot {\psi }}-\Omega \sin \delta \cos \alpha \right)^{2}+{\frac {1}{2}}I_{2}\left({\dot {\alpha }}^{2}+\Omega ^{2}\sin ^{2}\alpha \sin ^{2}\delta \right)} is the part of the Lagrangian responsible for the dynamics of the system. Then, since ∂ L 1 / ∂ ψ = 0 {\displaystyle \partial {\mathcal {L}}_{1}/\partial \psi =0} , we find L x ≡ ∂ L 1 ∂ ψ ˙ = I 1 ( ψ ˙ − Ω sin δ cos α ) = c o n s t a n t . {\displaystyle L_{x}\equiv {\frac {\partial {\mathcal {L}}_{1}}{\partial {\dot {\psi }}}}=I_{1}\left({\dot {\psi }}-\Omega \sin \delta \cos \alpha \right)=\mathrm {constant} .}
Since the angular momentum L → {\displaystyle {\vec {L}}} of the gyrocompass is given by L → = I ω → , {\displaystyle {\vec {L}}=I{\vec {\omega }},} we see that the constant L x {\displaystyle L_{x}} is the component of the angular momentum about the axis of symmetry. Furthermore, we find the equation of motion for the variable α {\displaystyle \alpha } as d d t ( ∂ L 1 ∂ α ˙ ) = ∂ L 1 ∂ α , {\displaystyle {\frac {d}{dt}}\left({\frac {\partial {\mathcal {L}}_{1}}{\partial {\dot {\alpha }}}}\right)={\frac {\partial {\mathcal {L}}_{1}}{\partial \alpha }},} or I 2 α ¨ = I 1 Ω ( ψ ˙ − Ω sin δ cos α ) sin δ sin α + 1 2 I 2 Ω 2 sin 2 δ sin 2 α = L x Ω sin δ sin α + 1 2 I 2 Ω 2 sin 2 δ sin 2 α {\displaystyle {\begin{aligned}I_{2}{\ddot {\alpha }}&=I_{1}\Omega \left({\dot {\psi }}-\Omega \sin \delta \cos \alpha \right)\sin \delta \sin \alpha +{\frac {1}{2}}I_{2}\Omega ^{2}\sin ^{2}\delta \sin 2\alpha \\&=L_{x}\Omega \sin \delta \sin \alpha +{\frac {1}{2}}I_{2}\Omega ^{2}\sin ^{2}\delta \sin 2\alpha \end{aligned}}}
At the poles we find sin δ = 0 , {\displaystyle \sin \delta =0,} and the equations of motion become L x = I 1 ψ ˙ = c o n s t a n t I 2 α ¨ = 0 {\displaystyle {\begin{aligned}L_{x}&=I_{1}{\dot {\psi }}=\mathrm {constant} \\I_{2}{\ddot {\alpha }}&=0\end{aligned}}}
This simple solution implies that the gyroscope is uniformly rotating with constant angular velocity in both the vertical and symmetrical axis.
Let us suppose now that sin δ ≠ 0 {\displaystyle \sin \delta \neq 0} and that α ≈ 0 {\displaystyle \alpha \approx 0} , that is the axis of the gyroscope is approximately along the north-south line, and let us find the parameter space (if it exists) for which the system admits stable small oscillations about this same line. If this situation occurs, the gyroscope will always be approximately aligned along the north-south line, giving direction. In this case we find L x ≈ I 1 ( ψ ˙ − Ω sin δ ) I 2 α ¨ ≈ ( L x Ω sin δ + I 2 Ω 2 sin 2 δ ) α {\displaystyle {\begin{aligned}L_{x}&\approx I_{1}\left({\dot {\psi }}-\Omega \sin \delta \right)\\I_{2}{\ddot {\alpha }}&\approx \left(L_{x}\Omega \sin \delta +I_{2}\Omega ^{2}\sin ^{2}\delta \right)\alpha \end{aligned}}}
Consider the case that L x < 0 , {\displaystyle L_{x}<0,} and, further, we allow for fast gyro-rotations, that is | ψ ˙ | ≫ Ω . {\displaystyle \left|{\dot {\psi }}\right|\gg \Omega .}
Therefore, for fast spinning rotations, L x < 0 {\displaystyle L_{x}<0} implies ψ ˙ < 0. {\displaystyle {\dot {\psi }}<0.} In this case, the equations of motion further simplify to L x ≈ − I 1 | ψ ˙ | ≈ c o n s t a n t I 2 α ¨ ≈ − I 1 | ψ ˙ | Ω sin δ α {\displaystyle {\begin{aligned}L_{x}&\approx -I_{1}\left|{\dot {\psi }}\right|\approx \mathrm {constant} \\I_{2}{\ddot {\alpha }}&\approx -I_{1}\left|{\dot {\psi }}\right|\Omega \sin \delta \alpha \end{aligned}}}
Therefore we find small oscillations about the north-south line, as α ≈ A sin ( ω ~ t + B ) {\displaystyle \alpha \approx A\sin({\tilde {\omega }}t+B)} , where the angular velocity of this harmonic motion of the axis of symmetry of the gyrocompass about the north-south line is given by ω ~ = I 1 sin δ I 2 | ψ ˙ | Ω , {\displaystyle {\tilde {\omega }}={\sqrt {\frac {I_{1}\sin \delta }{I_{2}}}}{\sqrt {\left|{\dot {\psi }}\right|\Omega }},} which corresponds to a period for the oscillations given by T = 2 π | ψ ˙ | Ω I 2 I 1 sin δ . {\displaystyle T={\frac {2\pi }{\sqrt {\left|{\dot {\psi }}\right|\Omega }}}{\sqrt {\frac {I_{2}}{I_{1}\sin \delta }}}.}
Therefore ω ~ {\displaystyle {\tilde {\omega }}} is proportional to the geometric mean of the Earth and spinning angular velocities. In order to have small oscillations we have required ψ ˙ < 0 {\displaystyle {\dot {\psi }}<0} , so that the North is located along the right-hand-rule direction of the spinning axis, that is along the negative direction of the X 7 {\displaystyle X_{7}} -axis, the axis of symmetry. As a side result, on measuring T {\displaystyle T} (and knowing ψ ˙ {\displaystyle {\dot {\psi }}} ), one can deduce the local co-latitude δ . {\displaystyle \delta .} | https://en.wikipedia.org/wiki/Gyrocompass |
Gyrokinetic ElectroMagnetic (GEM) is a gyrokinetic plasma turbulence simulation that uses the δ f {\displaystyle \delta f} particle-in-cell method. It is used to study waves, instabilities and nonlinear behavior of tokamak fusion plasmas. Information about GEM can be found at the GEM web page. [ 1 ] There are two versions of GEM, one is a flux-tube version [ 2 ] and the other one is a global general geometry
version. [ 3 ] Both versions of GEM use a field-aligned coordinate system. Ions are treated kinetically, but averaged over their gyro-obits and electrons are treated as drift-kinetic.
GEM solves the electromagnetic gyrokinetic equations which are the appropriate equations for well magnetized plasmas. The plasma is treated statistically as a kinetic distribution function. The distribution function depends on the three-dimensional position, the energy and magnetic moment. The time evolution of the distribution function is described by gyrokinetic theory which simply averages the Vlasov-Maxwell system of equations over the fast gyromotion associated with particles exhibiting cyclotron motion about the magnetic field lines. This eliminates fast time scales associated with the gyromotion and reduces the dimensionality of the problem from six down to five.
GEM uses the delta-f particle-in-cell (PIC) plasma simulation method. An expansion about an adiabatic response is made for electrons to overcome the limit of small time step, which is caused by the fast motion of electrons. GEM uses a novel electromagnetic algorithm allowing direct numerical simulation of the electromagnetic problem at high plasma pressures. GEM uses a two-dimensional domain decomposition (see domain decomposition method ) of the grid and particles to obtain good performance on massively parallel computers. A Monte Carlo method is used to model small angle Coulomb collisions .
GEM is used to study nonlinear physics associated with tokamak plasma turbulence and transport. Tokamak turbulence driven by ion-temperature-gradient modes, electron-temperature gradient modes, trapped electron modes and micro-tearing modes has been investigated using GEM. It is also being used to look at energetic particle driven magnetohydrodynamic (see magnetohydrodynamics ) eigenmodes.
This computational physics -related article is a stub . You can help Wikipedia by expanding it .
This plasma physics –related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Gyrokinetic_ElectroMagnetic |
Gyrokinetics is a theoretical framework to study plasma behavior on perpendicular spatial scales comparable to the gyroradius and frequencies much lower than the particle cyclotron frequencies . [ 1 ] These particular scales have been experimentally shown to be appropriate for modeling plasma turbulence. [ 2 ] The trajectory of charged particles in a magnetic field is a helix that winds around the field line . This trajectory can be decomposed into a relatively slow motion of the guiding center along the field line and a fast circular motion, called gyromotion. For most plasma behavior, this gyromotion is irrelevant. Averaging over this gyromotion reduces the equations to six dimensions (3 spatial, 2 velocity, and time) rather than the seven (3 spatial, 3 velocity, and time). Because of this simplification, gyrokinetics governs the evolution of charged rings with a guiding center position, instead of gyrating charged particles.
Fundamentally, the gyrokinetic model assumes the plasma is strongly magnetized ( ρ i ≪ L plasma {\displaystyle \rho _{i}\ll L_{\text{plasma}}} ), the perpendicular spatial scales are comparable to the gyroradius ( k ⊥ ρ i ∼ 1 {\displaystyle k_{\perp }\rho _{i}\sim 1} ), and the behavior of interest has low frequencies ( ω ≪ Ω i ≪ Ω e {\displaystyle \omega \ll \Omega _{i}\ll \Omega _{e}} ). We must also expand the distribution function , f s = f s 0 + f s 1 + ⋯ {\displaystyle f_{s}=f_{s0}+f_{s1}+\cdots } , and assume the perturbation is small compared to the background ( f s 1 ≪ f s 0 {\displaystyle f_{s1}\ll f_{s0}} ). [ 3 ] The starting point is the Fokker–Planck equation and Maxwell's equations . The first step is to change spatial variables from the particle position r {\displaystyle \mathbf {r} } to the guiding center position R {\displaystyle \mathbf {R} } . Then, we change velocity coordinates from ( v x , v y , v z ) {\displaystyle (v_{x},v_{y},v_{z})} to the velocity parallel v ∥ ≡ v ⋅ b ^ {\displaystyle v_{\parallel }\equiv \mathbf {v} \cdot {\hat {\mathbf {b} }}} , the magnetic moment μ ≡ m s v ⊥ 2 2 B {\displaystyle \mu \equiv {\frac {m_{s}v_{\perp }^{2}}{2B}}} , and the gyrophase angle φ {\displaystyle \varphi } . Here parallel and perpendicular are relative to b ≡ B / B {\displaystyle \mathbf {b} \equiv \mathbf {B} /B} , the direction of the magnetic field, and m s {\displaystyle m_{s}} is the mass of the particle. Now, we can average over the gyrophase angle at constant guiding center position, denoted by ⟨ … ⟩ φ {\displaystyle \left\langle \ldots \right\rangle _{\varphi }} , yielding the gyrokinetic equation.
The electrostatic gyrokinetic equation, in the absence of large plasma flow, is given by [ 4 ]
∂ h s ∂ t + ( v ∥ b ^ + V d s + ⟨ V ϕ ⟩ φ ) ⋅ ∇ R h s − ∑ s ′ ⟨ C [ h s , h s ′ ] ⟩ φ = Z s e f s 0 T s ∂ ⟨ ϕ ⟩ φ ∂ t − ∂ f s 0 ∂ ψ ⟨ V ϕ ⟩ φ ⋅ ∇ ψ . {\displaystyle {\frac {\partial h_{s}}{\partial t}}+\left(v_{\parallel }{\hat {\mathbf {b} }}+\mathbf {V} _{ds}+\left\langle \mathbf {V} _{\phi }\right\rangle _{\varphi }\right)\cdot {\boldsymbol {\nabla }}_{\mathbf {R} }h_{s}-\sum _{s'}\left\langle C\left[h_{s},h_{s'}\right]\right\rangle _{\varphi }={\frac {Z_{s}ef_{s0}}{T_{s}}}{\frac {\partial \left\langle \phi \right\rangle _{\varphi }}{\partial t}}-{\frac {\partial f_{s0}}{\partial \psi }}\left\langle \mathbf {V} _{\phi }\right\rangle _{\varphi }\cdot {\boldsymbol {\nabla }}\psi .}
Here the first term represents the change in the perturbed distribution function, h s ≡ f s 1 + Z s e ϕ T s f s 0 {\displaystyle h_{s}\equiv f_{s1}+{\frac {Z_{s}e\phi }{T_{s}}}f_{s0}} , with time. The second term represents particle streaming along the magnetic field line. The third term contains the effects of cross-field particle drifts, including the curvature drift , the grad-B drift , and the lowest order E-cross-B drift . The fourth term represents the nonlinear effect of the perturbed E × B {\displaystyle \mathbf {E} \times \mathbf {B} } drift interacting with the distribution function perturbation. The fifth term uses a collision operator to include the effects of collisions between particles. The sixth term represents the Maxwell–Boltzmann response to the perturbed electric potential . The last term includes temperature and density gradients of the background distribution function, which drive the perturbation. These gradients are only significant in the direction across flux surfaces, parameterized by ψ {\displaystyle \psi } , the magnetic flux .
The gyrokinetic equation, together with gyro-averaged Maxwell's equations, give the distribution function and the perturbed electric and magnetic fields. In the electrostatic case we only require Gauss's law (which takes the form of the quasineutrality condition), given by [ 5 ]
∑ s Z s e B ∫ d v ∥ d μ d φ h s ( R ) = ∑ s Z s 2 e 2 n s ϕ T s . {\displaystyle \sum _{s}Z_{s}eB\int dv_{\parallel }\,d\mu \,d\varphi \,h_{s}\left(\mathbf {R} \right)=\sum _{s}{\frac {Z_{s}^{2}e^{2}n_{s}\phi }{T_{s}}}.}
Usually solutions are found numerically with the help of supercomputers , but in simplified situations analytic solutions are possible. | https://en.wikipedia.org/wiki/Gyrokinetics |
In physics , the gyromagnetic ratio (also sometimes known as the magnetogyric ratio [ 1 ] in other disciplines) of a particle or system is the ratio of its magnetic moment to its angular momentum , and it is often denoted by the symbol γ , gamma. Its SI unit is the radian per second per tesla (rad⋅s −1 ⋅T −1 ) or, equivalently, the coulomb per kilogram (C⋅kg −1 ).
The g -factor of a particle is related to its gyromagnetic ratio by a constant multiplier that is related to the system, and is dimensionless .
Consider a nonconductive charged body rotating about an axis of symmetry. According to the laws of classical physics, it has both a magnetic dipole moment due to the movement of charge and an angular momentum due to the movement of mass arising from its rotation. It can be shown that as long as its charge and mass densities and currents are distributed identically and rotationally symmetric, its gyromagnetic ratio is
where q {\displaystyle q} is its charge, and m {\displaystyle m} is its mass.
The derivation of this relation is as follows. It suffices to demonstrate this for an infinitesimally narrow circular ring within the body, as the general result then follows from an integration . Suppose the ring has radius r , area A = πr 2 , mass m , charge q , and angular momentum L = mvr . Then the magnitude of the magnetic dipole moment is
An isolated electron has an angular momentum and a magnetic moment resulting from its spin . While an electron's spin is sometimes visualized as a literal rotation about an axis, it cannot be attributed to mass distributed identically to the charge. The above classical relation does not hold, giving the wrong result by the absolute value of the electron's g -factor, which is denoted g e : γ e = − e 2 m e | g e | = g e μ B ℏ , {\displaystyle \gamma _{\text{e}}={\frac {-e}{2m_{\text{e}}}}\,|g_{\mathrm {e} }|={\frac {g_{\text{e}}\mu _{\text{B}}}{\hbar }},} where μ B is the Bohr magneton .
The gyromagnetic ratio due to electron spin is twice that due to the orbiting of an electron.
In the framework of relativistic quantum mechanics, g e = − 2 ( 1 + α 2 π + ⋯ ) , {\displaystyle g_{\text{e}}=-2\left(1+{\frac {\alpha }{2\pi }}+\cdots \right),} where α {\displaystyle \alpha } is the fine-structure constant . Here the small corrections to the relativistic result g = 2 come from the quantum field theory calculations of the anomalous magnetic dipole moment . The electron g -factor is known to twelve decimal places by measuring the electron magnetic moment in a one-electron cyclotron: [ 2 ] g e = − 2.002 319 304 361 18 ( 27 ) . {\displaystyle g_{\text{e}}=-2.002\,319\,304\,361\,18(27).}
The electron gyromagnetic ratio is [ 3 ] [ 4 ] [ 5 ] γ e = − 1.760 859 630 23 ( 53 ) × 10 11 rad ⋅ s − 1 ⋅ T − 1 , {\displaystyle \gamma _{\text{e}}=-1.760\,859\,630\,23(53)\times 10^{11}~{\text{rad}}\cdot {\text{s}}^{-1}\cdot {\text{T}}^{-1},} γ e 2 π = − 28 024.951 4242 ( 85 ) MHz ⋅ T − 1 . {\displaystyle {\frac {\gamma _{\text{e}}}{2\pi }}=-28\,024.951\,4242(85)~{\text{MHz}}\cdot {\text{T}}^{-1}.}
The electron g -factor and γ are in excellent agreement with theory; see Precision tests of QED for details. [ 6 ]
Since a gyromagnetic factor equal to 2 follows from Dirac's equation, it is a frequent misconception to think that a g -factor 2 is a consequence of relativity; it is not. The factor 2 can be obtained from the linearization of both the Schrödinger equation (known as Lévy-Leblond equation ) and the relativistic Klein–Gordon equation (which leads to Dirac's). In both cases a 4- spinor is obtained and for both linearizations the g -factor is found to be equal to 2. Therefore, the factor 2 is a consequence of the minimal coupling and of the fact of having the same order of derivatives for space and time. [ 7 ]
Physical spin- 1 / 2 particles which cannot be described by the linear gauged Dirac equation satisfy the gauged Klein–Gordon equation extended by the g e / 4 σ μν F μν term according to, [ 8 ]
Here, 1 / 2 σ μν and F μν stand for the Lorentz group generators in the Dirac space, and the electromagnetic tensor respectively, while A μ is the electromagnetic four-potential . An example for such a particle [ 8 ] is the spin 1 / 2 companion to spin 3 / 2 in the D (½,1) ⊕ D (1,½) representation space of the Lorentz group . This particle has been shown to be characterized by g = − + 2 / 3 and consequently to behave as a truly quadratic fermion.
Protons , neutrons, and many nuclei carry nuclear spin , which gives rise to a gyromagnetic ratio as above. The ratio is conventionally written in terms of the proton mass and charge, even for neutrons and for other nuclei, for the sake of simplicity and consistency. The formula is:
where μ N {\displaystyle \mu _{\text{N}}} is the nuclear magneton , and g n {\displaystyle g_{\text{n}}} is the g -factor of the nucleon or nucleus in question. The ratio γ n 2 π g n = μ N / h = 7.622593285 ( 47 ) {\displaystyle {\frac {\gamma _{n}}{2\pi \,g_{\text{n}}}}=\mu _{\text{N}}/h=7.622593285(47)} MHz/T. [ 9 ]
The gyromagnetic ratio of a nucleus plays a role in nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI). These procedures rely on the fact that bulk magnetization due to nuclear spins precess in a magnetic field at a rate called the Larmor frequency , which is simply the product of the gyromagnetic ratio with the magnetic field strength. With this phenomenon, the sign of γ determines the sense (clockwise vs counterclockwise) of precession.
Most common nuclei such as 1 H and 13 C have positive gyromagnetic ratios. [ 10 ] [ 11 ] Approximate values for some common nuclei are given in the table below. [ 12 ] [ 13 ]
A full list can be found in the external link section below.
Any free system with a constant gyromagnetic ratio, such as a rigid system of charges, a nucleus , or an electron , when placed in an external magnetic field B (measured in teslas) that is not aligned with its magnetic moment , will precess at a frequency f (measured in hertz ) proportional to the external field:
For this reason, values of γ / 2 π , in units of hertz per tesla (Hz/T), are often quoted instead of γ .
The derivation of this ratio is as follows: First we must prove the torque resulting from subjecting a magnetic moment m {\displaystyle \mathbf {m} } to a magnetic field B {\displaystyle \mathbf {B} } is T = m × B . {\displaystyle {\boldsymbol {\mathrm {T} }}=\mathbf {m} \times \mathbf {B} .} The identity of the functional form of the stationary electric and magnetic fields has led to defining the magnitude of the magnetic dipole moment equally well as m = I π r 2 {\displaystyle m=I\pi r^{2}} , or in the following way, imitating the moment p of an electric dipole: The magnetic dipole can be represented by a needle of a compass with fictitious magnetic charges ± q m {\displaystyle \pm q_{\text{m}}} on the two poles and vector distance between the poles d {\displaystyle \mathbf {d} } under the influence of the magnetic field of earth B . {\displaystyle \mathbf {B} .} By classical mechanics the torque on this needle is T = q m ( d × B ) . {\displaystyle {\boldsymbol {\mathrm {T} }}=q_{\text{m}}(\mathbf {d} \times \mathbf {B} ).} But as previously stated q m d = I π r 2 d ^ = m , {\displaystyle q_{\text{m}}\mathbf {d} =I\pi r^{2}{\hat {\mathbf {d} }}=\mathbf {m} ,} so the desired formula comes up. d ^ {\displaystyle {\hat {\mathbf {d} }}} is the unit distance vector.
The spinning electron model here is analogous to a gyroscope. For any rotating body the rate of change of the angular momentum J {\displaystyle \mathbf {J} } equals the applied torque T {\displaystyle \mathbf {T} } :
Note as an example the precession of a gyroscope. The earth's gravitational attraction applies a force or torque to the gyroscope in the vertical direction, and the angular momentum vector along the axis of the gyroscope rotates slowly about a vertical line through the pivot. In place of a gyroscope, imagine a sphere spinning around the axis with its center on the pivot of the gyroscope, and along the axis of the gyroscope two oppositely directed vectors both originated in the center of the sphere, upwards J {\displaystyle \mathbf {J} } and downwards m . {\displaystyle \mathbf {m} .} Replace the gravity with a magnetic flux density B . {\displaystyle \mathbf {B} .}
d J d t {\displaystyle {\frac {d\mathbf {J} }{dt}}} represents the linear velocity of the pike of the arrow J {\displaystyle \mathbf {J} } along a circle whose radius is J sin ϕ , {\displaystyle J\sin {\phi },} where ϕ {\displaystyle \phi } is the angle between J {\displaystyle \mathbf {J} } and the vertical. Hence the angular velocity of the rotation of the spin is
Consequently, f = γ 2 π B , q.e.d. {\displaystyle f={\frac {\gamma }{2\pi }}\,B,\quad {\text{q.e.d.}}}
This relationship also explains an apparent contradiction between the two equivalent terms, gyromagnetic ratio versus magnetogyric ratio: whereas it is a ratio of a magnetic property (i.e. dipole moment) to a gyric (rotational, from Greek : γύρος , "turn") property (i.e. angular momentum ), it is also a ratio between the angular precession frequency (another gyric property) ω = 2 πf and the magnetic field .
The angular precession frequency has an important physical meaning: It is the angular cyclotron frequency , the resonance frequency of an ionized plasma being under the influence of a static finite magnetic field, when we superimpose a high frequency electromagnetic field. | https://en.wikipedia.org/wiki/Gyromagnetic_ratio |
The gyroscopic autopilot was a type of autopilot system developed primarily for aviation uses in the early 20th century. Since then, the principles of this autopilot has been the basis of many different aircraft control systems, both military and civilian.
The Sperry Corporation developed the original gyroscopic autopilot in 1912. The device was called a “gyroscopic stabilizer apparatus,” and its purpose was to improve stability and control of aircraft. It utilized the inputs from several other instruments to allow an aircraft to automatically maintain a desired compass heading and altitude. [ 1 ]
The key feature of the gyroscopic stabilizer apparatus was that it incorporated a gyroscope to regulate the control surfaces of the aircraft. [ 1 ] Lawrence Sperry managed to design a smaller and lighter version of a gyroscope, [ 1 ] and the device was integrated into an aircraft's hydraulic control system. Using a negative feedback loop, the gyroscope automatically adjusted the control surfaces of an aircraft to maintain straight and level flight. [ 1 ]
Lawrence Sperry's autopilot was first demonstrated in France on June 18, 1914. Sperry was participating in an exhibition in which 57 planes were fitted with new improvements and innovations. Sperry's aircraft, a Curtiss C-2 , was the only one equipped with a gyroscopic stabilizer. Sperry, along with his assistant Emil Cachin, made three passes in front of a grandstand full of spectators and military observers. On his first pass, Sperry engaged the autopilot and flew past the grandstand with his hands held high off of the controls. On the second pass, Cachin climbed out onto the starboard wing seven feet away from the fuselage with Sperry's hands still off the controls. When the aircraft banked due to the shift in weight, the autopilot immediately stabilized the wings. On his final pass, Sperry climbed out onto the opposite wing, leaving the pilot seat empty. The observers were amazed at the aircraft's ability to maintain level flight without a pilot manually controlling it. Sperry also gave Joseph Barres, Commandant of the French Army Air Corps, a ride to demonstrate his device's ability to perform an unassisted takeoff and landing. [ 1 ]
Wiley Post became famous after his record setting trip around the world on June 23, 1931. In his aircraft, a Lockheed Vega nicknamed “ Winnie Mae ,” he managed to travel around the world in eight days 15 hours and 51 minutes. He accomplished this with the help of Harold Gatty , who served as his navigator and copilot. Two years later he set out to beat his previous record by flying around the world by himself. He wanted to prove that one man could accomplish the same trip without a copilot. In order to accomplish this, he equipped the Winnie Mae with a Sperry gyroscope autopilot and a radio direction finder . Although he experienced some problems with the autopilot, he completed the trip in seven days, 18 hours and 49 minutes. The use of the autopilot and radio direction finder is credited for making the task of navigating the aircraft much easier and more efficient. The use of an autopilot reduced the physical and mental demands on Post as he flew around the world. [ 2 ]
The U.S. Army Air Corps and the U.S. Navy experimented with autopilots on military aircraft before and during World War II. Straight and level flight had become a necessity for new level bombing techniques that were being developed at the time. The Sperry Gyroscope Company developed many autopilot systems for use on military aircraft. When the Boeing B-17 Flying Fortress was delivered in the late 1930s, it came equipped a commercial Sperry A-3 Autopilot. The A-3 was a simple autopilot and only corrected angular deviations in the aircraft's straight and level course. It utilized pneumatic hydraulic servos, which had a tendency to react slowly to inputs, and this often led to overcompensation of the aircraft's corrected course. This caused navigation and control issues when pilots were flying in poor weather or rough air. [ 3 ]
To fix these problems, the Sperry A-5 autopilot was developed. This was the first all electric autopilot. This new autopilot used three dual-element vacuum tube amplifiers and high-speed gyros. Each amplifier was associated with a different axis: Yaw, pitch, and roll. The high-speed gyros were more sensitive and established a base reference level of the aircraft's level flight path. Whenever the aircraft deviated from the base reference level, the autopilot adjusted for the amount of time that occurred between the changes in reference levels. This allowed the autopilot to detect the velocity and acceleration of the change. The calculated change was then communicated quickly to the control surfaces by independent electro-hydraulic servos. This led to faster, more stable corrections of the aircraft. [ 3 ]
The faster stabilization of the aircraft by the A-5 autopilot made it possible for new bombsights to be used on military aircraft. The Norden Bombsight and Sperry Bombsight were both used onboard Army and Navy bombers during the war. Both bombsights used gyroscopes, telescopes and analog computers to calculate the release point for bombers to drop their payloads accurately onto ground targets. The A-5 had the ability to be integrated with these bombsights. Once the bombardier found the target and adjusted the bombsight, the autopilot would be engaged to fly the aircraft straight and level to the target, where the bombsight would automatically calculate the release point of the bombs. [ 3 ]
The German V-1 Buzz Bomb also used an autopilot system for guidance. It used a pendulum system that was damped by a gyroscope, similar to the ones used in Sperry autopilots. It also used radio direction-finding to maintain course. [ 4 ] The use of autopilot on unmanned weapons can be seen as the precursor to modern cruise missiles. | https://en.wikipedia.org/wiki/Gyroscopic_autopilot |
A gyrovector space is a mathematical concept proposed by Abraham A. Ungar for studying hyperbolic geometry in analogy to the way vector spaces are used in Euclidean geometry . [ 1 ] Ungar introduced the concept of gyrovectors that have addition based on gyrogroups instead of vectors which have addition based on groups . Ungar developed his concept as a tool for the formulation of special relativity as an alternative to the use of Lorentz transformations to represent compositions of velocities (also called boosts – "boosts" are aspects of relative velocities , and should not be conflated with " translations "). This is achieved by introducing "gyro operators"; two 3d velocity vectors are used to construct an operator, which acts on another 3d velocity.
Gyrogroups are weakly associative group-like structures. Ungar proposed the term gyrogroup for what he called a gyrocommutative-gyrogroup, with the term gyrogroup being reserved for the non-gyrocommutative case, in analogy with groups vs. abelian groups . Gyrogroups are a type of Bol loop . Gyrocommutative gyrogroups are equivalent to K-loops [ 2 ] although defined differently. The terms Bruck loop [ 3 ] and dyadic symset [ 4 ] are also in use.
A gyrogroup ( G , ⊕ {\displaystyle \oplus } ) consists of an underlying set G and a binary operation ⊕ {\displaystyle \oplus } satisfying the following axioms:
The first pair of axioms are like the group axioms. The last pair present the gyrator axioms and the middle axiom links the two pairs.
Since a gyrogroup has inverses and an identity it qualifies as a quasigroup and a loop .
Gyrogroups are a generalization of groups . Every group is an example of a gyrogroup with gyr[ a , b ] defined as the identity map for all a and b in G .
An example of a finite gyrogroup is given in [ 5 ] .
Some identities which hold in any gyrogroup ( G , ⊕ {\displaystyle \oplus } ) are:
Furthermore, one may prove the Gyration inversion law, which is the motivation for the definition of gyrocommutativity below:
Some additional theorems satisfied by the Gyration group of any gyrogroup include:
More identities given on page 50 of [ 6 ] . One particularly useful consequence of the above identities is that Gyrogroups satisfy the left Bol property
A gyrogroup (G, ⊕ {\displaystyle \oplus } ) is gyrocommutative if its binary operation obeys the gyrocommutative law: a ⊕ {\displaystyle \oplus } b = gyr[ a , b ]( b ⊕ {\displaystyle \oplus } a ). For relativistic velocity addition, this formula showing the role of rotation relating a + b and b + a was published in 1914 by Ludwik Silberstein . [ 7 ] [ 8 ]
In every gyrogroup, a second operation can be defined called coaddition : a ⊞ {\displaystyle \boxplus } b = a ⊕ {\displaystyle \oplus } gyr[ a , ⊖ {\displaystyle \ominus } b ] b for all a , b ∈ G . Coaddition is commutative if the gyrogroup addition is gyrocommutative.
Relativistic velocities can be considered as points in the Beltrami–Klein model of hyperbolic geometry and so vector addition in the Beltrami–Klein model can be given by the velocity addition formula. In order for the formula to generalize to vector addition in hyperbolic space of dimensions greater than 3, the formula must be written in a form that avoids use of the cross product in favour of the dot product .
In the general case, the Einstein velocity addition of two velocities u {\displaystyle \mathbf {u} } and v {\displaystyle \mathbf {v} } is given in coordinate-independent form as:
where γ u {\displaystyle \gamma _{\mathbf {u} }} is the gamma factor given by the equation γ u = 1 1 − | u | 2 c 2 {\displaystyle \gamma _{\mathbf {u} }={\frac {1}{\sqrt {1-{\frac {|\mathbf {u} |^{2}}{c^{2}}}}}}} .
Using coordinates this becomes:
where γ u = 1 1 − u 1 2 + u 2 2 + u 3 2 c 2 {\displaystyle \gamma _{\mathbf {u} }={\frac {1}{\sqrt {1-{\frac {u_{1}^{2}+u_{2}^{2}+u_{3}^{2}}{c^{2}}}}}}} .
Einstein velocity addition is commutative and associative only when u {\displaystyle \mathbf {u} } and v {\displaystyle \mathbf {v} } are parallel . In fact
and
where "gyr" is the mathematical abstraction of Thomas precession into an operator called Thomas gyration and given by
for all w . Thomas precession has an interpretation in hyperbolic geometry as the negative hyperbolic triangle defect.
If the 3 × 3 matrix form of the rotation applied to 3-coordinates is given by gyr[ u , v ], then the 4 × 4 matrix rotation applied to 4-coordinates is given by:
The composition of two Lorentz boosts B( u ) and B( v ) of velocities u and v is given by: [ 9 ] [ 10 ]
This fact that either B( u ⊕ {\displaystyle \oplus } v ) or B( v ⊕ {\displaystyle \oplus } u ) can be used depending whether you write the rotation before or after explains the velocity composition paradox .
The composition of two Lorentz transformations L( u ,U) and L( v ,V) which include rotations U and V is given by: [ 11 ]
In the above, a boost can be represented as a 4 × 4 matrix. The boost matrix B( v ) means the boost B that uses the components of v , i.e. v 1 , v 2 , v 3 in the entries of the matrix, or rather the components of v / c in the representation that is used in the section Lorentz transformation#Matrix forms . The matrix entries depend on the components of the 3-velocity v , and that's what the notation B( v ) means. It could be argued that the entries depend on the components of the 4-velocity because 3 of the entries of the 4-velocity are the same as the entries of the 3-velocity, but the usefulness of parameterizing the boost by 3-velocity is that the resultant boost you get from the composition of two boosts uses the components of the 3-velocity composition u ⊕ {\displaystyle \oplus } v in the 4 × 4 matrix B( u ⊕ {\displaystyle \oplus } v ). But the resultant boost also needs to be multiplied by a rotation matrix because boost composition (i.e. the multiplication of two 4 × 4 matrices) results not in a pure boost but a boost and a rotation, i.e. a 4 × 4 matrix that corresponds to the rotation Gyr[ u , v ] to get B( u )B( v ) = B( u ⊕ {\displaystyle \oplus } v )Gyr[ u , v ] = Gyr[ u , v ]B( v ⊕ {\displaystyle \oplus } u ).
Let s be any positive constant, let (V,+,.) be any real inner product space and let V s ={ v ∈ V :| v |<s}. An Einstein gyrovector space ( V s , ⊕ {\displaystyle \oplus } , ⊗ {\displaystyle \otimes } ) is an Einstein gyrogroup ( V s , ⊕ {\displaystyle \oplus } ) with scalar multiplication given by r ⊗ {\displaystyle \otimes } v = s tanh( r tanh −1 (| v |/ s )) v /| v | where r is any real number, v ∈ V s , v ≠ 0 and r ⊗ {\displaystyle \otimes } 0 = 0 with the notation v ⊗ {\displaystyle \otimes } r = r ⊗ {\displaystyle \otimes } v .
Einstein scalar multiplication does not distribute over Einstein addition except when the gyrovectors are colinear (monodistributivity), but it has other properties of vector spaces: For any positive integer n and for all real numbers r , r 1 , r 2 and v ∈ V s :
The Möbius transformation of the open unit disc in the complex plane is given by the polar decomposition
To generalize this to higher dimensions the complex numbers are considered as vectors in the plane R 2 {\displaystyle \mathbf {\mathrm {R} } ^{2}} , and Möbius addition is rewritten in vector form as:
This gives the vector addition of points in the Poincaré ball model of hyperbolic geometry where radius s=1 for the complex unit disc now becomes any s>0.
Let s be any positive constant, let (V,+,.) be any real inner product space and let V s ={ v ∈ V :| v |<s}. A Möbius gyrovector space ( V s , ⊕ {\displaystyle \oplus } , ⊗ {\displaystyle \otimes } ) is a Möbius gyrogroup ( V s , ⊕ {\displaystyle \oplus } ) with scalar multiplication given by r ⊗ {\displaystyle \otimes } v = s tanh( r tanh −1 (| v |/ s )) v /| v | where r is any real number, v ∈ V s , v ≠ 0 and r ⊗ {\displaystyle \otimes } 0 = 0 with the notation v ⊗ {\displaystyle \otimes } r = r ⊗ {\displaystyle \otimes } v .
Möbius scalar multiplication coincides with Einstein scalar multiplication (see section above) and this stems from Möbius addition and Einstein addition coinciding for vectors that are parallel.
A proper velocity space model of hyperbolic geometry is given by proper velocities with vector addition given by the proper velocity addition formula: [ 6 ] [ 12 ] [ 13 ]
where β w {\displaystyle \beta _{\mathbf {w} }} is the beta factor given by β w = 1 1 + | w | 2 c 2 {\displaystyle \beta _{\mathbf {w} }={\frac {1}{\sqrt {1+{\frac {|\mathbf {w} |^{2}}{c^{2}}}}}}} .
This formula provides a model that uses a whole space compared to other models of hyperbolic geometry which use discs or half-planes.
A proper velocity gyrovector space is a real inner product space V, with the proper velocity gyrogroup addition ⊕ U {\displaystyle \oplus _{U}} and with scalar multiplication defined by r ⊗ {\displaystyle \otimes } v = s sinh( r sinh −1 (| v |/ s )) v /| v | where r is any real number, v ∈ V , v ≠ 0 and r ⊗ {\displaystyle \otimes } 0 = 0 with the notation v ⊗ {\displaystyle \otimes } r = r ⊗ {\displaystyle \otimes } v .
A gyrovector space isomorphism preserves gyrogroup addition and scalar multiplication and the inner product.
The three gyrovector spaces Möbius, Einstein and Proper Velocity are isomorphic.
If M, E and U are Möbius, Einstein and Proper Velocity gyrovector spaces respectively with elements v m , v e and v u then the isomorphisms are given by:
From this table the relation between ⊕ E {\displaystyle \oplus _{E}} and ⊕ M {\displaystyle \oplus _{M}} is given by the equations:
u ⊕ E v = 2 ⊗ ( 1 2 ⊗ u ⊕ M 1 2 ⊗ v ) {\displaystyle \mathbf {u} \oplus _{E}\mathbf {v} =2\otimes \left({{\frac {1}{2}}\otimes \mathbf {u} \oplus _{M}{\frac {1}{2}}\otimes \mathbf {v} }\right)}
u ⊕ M v = 1 2 ⊗ ( 2 ⊗ u ⊕ E 2 ⊗ v ) {\displaystyle \mathbf {u} \oplus _{M}\mathbf {v} ={\frac {1}{2}}\otimes \left({2\otimes \mathbf {u} \oplus _{E}2\otimes \mathbf {v} }\right)}
This is related to the connection between Möbius transformations and Lorentz transformations .
Gyrotrigonometry is the use of gyroconcepts to study hyperbolic triangles .
Hyperbolic trigonometry as usually studied uses the hyperbolic functions cosh, sinh etc., and this contrasts with spherical trigonometry which uses the Euclidean trigonometric functions cos, sin, but with spherical triangle identities instead of ordinary plane triangle identities . Gyrotrigonometry takes the approach of using the ordinary trigonometric functions but in conjunction with gyrotriangle identities.
The study of triangle centers traditionally is concerned with Euclidean geometry, but triangle centers can also be studied in hyperbolic geometry. Using gyrotrigonometry, expressions for trigonometric barycentric coordinates can be calculated that have the same form for both euclidean and hyperbolic geometry. In order for the expressions to coincide, the expressions must not encapsulate the specification of the anglesum being 180 degrees. [ 14 ] [ 15 ] [ 16 ]
Using gyrotrigonometry, a gyrovector addition can be found which operates according to the gyroparallelogram law. This is the coaddition to the gyrogroup operation. Gyroparallelogram addition is commutative.
The gyroparallelogram law is similar to the parallelogram law in that a gyroparallelogram is a hyperbolic quadrilateral the two gyrodiagonals of which intersect at their gyromidpoints, just as a parallelogram is a Euclidean quadrilateral the two diagonals of which intersect at their midpoints. [ 17 ]
Bloch vectors which belong to the open unit ball of the Euclidean 3-space, can be studied with Einstein addition [ 18 ] or Möbius addition. [ 6 ]
A review of one of the earlier gyrovector books [ 19 ] says the following:
"Over the years, there have been a handful of attempts to promote the non-Euclidean style for use in problem solving in relativity and electrodynamics, the failure of which to attract any substantial following, compounded by the absence of any positive results must give pause to anyone considering a similar undertaking. Until recently, no one was in a position to offer an improvement on the tools available since 1912. In his new book, Ungar furnishes the crucial missing element from the panoply of the non-Euclidean style: an elegant nonassociative algebraic formalism that fully exploits the structure of Einstein’s law of velocity composition." [ 20 ] | https://en.wikipedia.org/wiki/Gyrovector_space |
Gyula Pál (27 June 1881 – 6 September 1946) was a noted Hungarian - Danish mathematician . [ 1 ] He is known for his work on Jordan curves both in plane and space, and on the Kakeya problem . He proved that every locally connected planar continuum with at least two points is the orthogonal projection of a closed Jordan curve of the Euclidean 3-space.
He was born as Gyula Perl but hungaricized his surname to Pál in 1909. Fleeing the post-war chaos of Hungary after World War I he moved to Denmark in 1919, possibly by the invitation of Harald Bohr , where he spent the rest of his life and westernized his name to Julius Pal . [ 1 ]
This article about a Hungarian scientist is a stub . You can help Wikipedia by expanding it .
This article about a European mathematician is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Gyula_Pál |
Gyula Strommer (8 May 1920 – 28 August 1995) was a Hungarian mathematician and astronomer. [ 1 ] [ 2 ]
He discovered an asteroid, 1537 Transylvania , on 27 August 1940. This was his first scientific success. From 1942, he was a teaching assistant at the Descriptive Geometry Department of the Technical University of Budapest . In 1952, he became the head of the Descriptive Geometry Department. In 1972, he was appointed a university professor. Between 1981 and 1987, he was the dean of the Faculty of Mechanical Engineering.
His research topics: the foundations of geometry, Bolyai-Lobachevsky geometry . | https://en.wikipedia.org/wiki/Gyula_Strommer |
György Hajós (February 21, 1912, Budapest – March 17, 1972, Budapest ) was a Hungarian mathematician who worked in group theory , graph theory , and geometry . [ 1 ] [ 2 ]
Hajós was born February 21, 1912, in Budapest ; his great-grandfather, Adam Clark , was the famous Scottish engineer who built the Chain Bridge in Budapest. He earned a teaching degree from the University of Budapest in 1935. He then took a position at the Technical University of Budapest , where he stayed from 1935 to 1949. While at the Technical University of Budapest, he earned a doctorate in 1938. He became a professor at the Eötvös Loránd University in 1949 and remained there until his death in 1972. Additionally he was president of the János Bolyai Mathematical Society from 1963 to 1972. [ 1 ] [ 2 ]
Hajós's theorem is named after Hajós, and concerns factorizations of Abelian groups into Cartesian products of subsets of their elements. [ 3 ] This result in group theory has consequences also in geometry: Hajós used it to prove a conjecture of Hermann Minkowski that, if a Euclidean space of any dimension is tiled by hypercubes whose positions form a lattice , then some pair of hypercubes must meet face-to-face. Hajós used similar group-theoretic methods to attack Keller's conjecture on whether cube tilings (without the lattice constraint) must have pairs of cubes that meet face to face; his work formed an important step in the eventual disproof of this conjecture. [ 4 ]
Hajós's conjecture is a conjecture made by Hajós that every graph with chromatic number k contains a subdivision of a complete graph K k . However, it is now known to be false: in 1979, Paul A. Catlin found a counterexample for k = 8 , [ 5 ] and Paul Erdős and Siemion Fajtlowicz later observed that it fails badly for random graphs . [ 6 ] The Hajós construction is a general method for constructing graphs with a given chromatic number , also due to Hajós. [ 7 ]
Hajós was a member of the Hungarian Academy of Sciences , first as a corresponding member beginning in 1948 and then as a full member in 1958. In 1965 he was elected to the Romanian Academy of Sciences , and in 1967 to the German Academy of Sciences Leopoldina . He won the Gyula König Prize in 1942, and the Kossuth Prize in 1951 and again in 1962. [ 1 ] [ 2 ] | https://en.wikipedia.org/wiki/György_Hajós |
In the south German language (of the Alemannic -speaking area, or in Switzerland ), a gäu landscape ( gäulandschaft ) refers to an area of open, level countryside. These regions typically have fertile soils resulting from depositions of loess (an exception is the Arme Gäue ["Poor Gäus"] of the Baden-Württemberg Gäu ).
The intensive use of the Gäu regions for crops has displaced the originally wooded countryside (→ climax vegetation – in contrast with the steppe heath theory and disputed megaherbivore hypothesis). The North German equivalent of such landscapes is börde . | https://en.wikipedia.org/wiki/Gäu |
In mathematics , Gårding's inequality is a result that gives a lower bound for the bilinear form induced by a real linear elliptic partial differential operator . The inequality is named after Lars Gårding .
Let Ω {\displaystyle \Omega } be a bounded , open domain in n {\displaystyle n} - dimensional Euclidean space and let H k ( Ω ) {\displaystyle H^{k}(\Omega )} denote the Sobolev space of k {\displaystyle k} -times weakly differentiable functions u : Ω → R {\displaystyle u\colon \Omega \rightarrow \mathbb {R} } with weak derivatives in L 2 ( Ω ) {\displaystyle L^{2}(\Omega )} . Assume that Ω {\displaystyle \Omega } satisfies the k {\displaystyle k} -extension property, i.e., that there exists a bounded linear operator E : H k ( Ω ) → H k ( R n ) {\displaystyle E\colon H^{k}(\Omega )\rightarrow H^{k}(\mathbb {R} ^{n})} such that E u | Ω = u {\displaystyle Eu\vert _{\Omega }=u} for all u ∈ H k ( Ω ) {\displaystyle u\in H^{k}(\Omega )} .
Let L be a linear partial differential operator of even order 2k , written in divergence form
and suppose that L is uniformly elliptic, i.e., there exists a constant θ > 0 such that
Finally, suppose that the coefficients A αβ are bounded , continuous functions on the closure of Ω for | α | = | β | = k and that
Then Gårding's inequality holds: there exist constants C > 0 and G ≥ 0
where
is the bilinear form associated to the operator L .
Be careful, in this application, Garding's Inequality seems useless here as the final result is a direct consequence of Poincaré's Inequality, or Friedrich Inequality. (See talk on the article).
As a simple example, consider the Laplace operator Δ. More specifically, suppose that one wishes to solve, for f ∈ L 2 (Ω) the Poisson equation
where Ω is a bounded Lipschitz domain in R n . The corresponding weak form of the problem is to find u in the Sobolev space H 0 1 (Ω) such that
where
The Lax–Milgram lemma ensures that if the bilinear form B is both continuous and elliptic with respect to the norm on H 0 1 (Ω), then, for each f ∈ L 2 (Ω), a unique solution u must exist in H 0 1 (Ω). The hypotheses of Gårding's inequality are easy to verify for the Laplace operator Δ, so there exist constants C and G ≥ 0
Applying the Poincaré inequality allows the two terms on the right-hand side to be combined, yielding a new constant K > 0 with
which is precisely the statement that B is elliptic. The continuity of B is even easier to see: simply apply the Cauchy–Schwarz inequality and the fact that the Sobolev norm is controlled by the L 2 norm of the gradient. | https://en.wikipedia.org/wiki/Gårding's_inequality |
The Géotechnique lecture is an biennial lecture on the topic of soil mechanics , organised by the British Geotechnical Association named after its major scientific journal Géotechnique .
This should not be confused with the annual BGA Rankine Lecture . | https://en.wikipedia.org/wiki/Géotechnique_Lecture |
Gérard Férey (14 July 1941 – 19 August 2017) [ 1 ] was a French chemist who was a member of the French Academy of Sciences and a professor at the University of Versailles Saint-Quentin-en-Yvelines . He specialized in the physical chemistry of solids and materials. He focused on the crystal chemistry of inorganic fluorides [ 2 ] and on porous solids. [ 3 ]
In September 2010, he received the CNRS Gold medal , the highest French scientific distinction. [ 4 ]
Gerard Férey was a lecturer at the University of Maine . In 1968, he founded the Department of Chemistry at the University Institutes of Technology of Le Mans . [ 5 ] He argued his doctoral thesis at the Pierre-and-Marie-Curie University in 1977.
He was a teacher at the University of Maine from 1981 to 1996 and then at the Versailles Saint-Quentin-en-Yvelines University since that date, where he founded the Lavoisier Institute. [ 6 ] From 1988 to 1992 he was deputy director of the Department of Chemistry at the French National Centre for Scientific Research .
He was elected to the French Academy of Sciences 18 November 2003. In 2007, he was vice-president of the Société Chimique de France . He was a member of the Institut Universitaire de France . He was also at the initiative of the Chemistry Ambition, a group that includes seven players in chemistry of France aimed at enhancing the image of the discipline to the public. [ 7 ]
Gerard Férey published 605 articles in international journals, including the Journal of Solid State Chemistry, the Solid State Sciences, the Chemistry of Materials , Angewandte Chemie International Edition , the Journal of the American Chemical Society , four book chapters and one book (Crystal Chemistry, World Scientific Publishing, 2016). He gave more than 100 plenary lectures in international symposia, and deposited 14 international patents. [ 8 ] | https://en.wikipedia.org/wiki/Gérard_Férey |
Gérard Vergnaud (8 February 1933 – 6 June 2021) was a French mathematician, philosopher, educator, and psychologist. He earned his doctorate from the International Center for Genetic Epistemology in Geneva under the supervision of Jean Piaget . Vergnaud was a professor emeritus of the Centre national de la recherche scientifique in Paris , where he was a researcher in mathematics. Among his most significant work has been the development of the Theory of Conceptual Fields , which describes how children develop an understanding of mathematics. [ 1 ]
Gérard Vergnaud graduated from HEC Paris in 1956 and from the University of Geneva in 1968. [ 2 ]
This article about a French mathematician is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Gérard_Vergnaud |
Gödel's completeness theorem is a fundamental theorem in mathematical logic that establishes a correspondence between semantic truth and syntactic provability in first-order logic .
The completeness theorem applies to any first-order theory : If T is such a theory, and φ is a sentence (in the same language) and every model of T is a model of φ, then there is a (first-order) proof of φ using the statements of T as axioms. One sometimes says this as "anything true in all models is provable". (This does not contradict Gödel's incompleteness theorem , which is about a formula φ u that is unprovable in a certain theory T but true in the "standard" model of the natural numbers: φ u is false in some other, "non-standard" models of T . [ 1 ] )
The completeness theorem makes a close link between model theory , which deals with what is true in different models, and proof theory , which studies what can be formally proven in particular formal systems .
It was first proved by Kurt Gödel in 1929. It was then simplified when Leon Henkin observed in his Ph.D. thesis that the hard part of the proof can be presented as the Model Existence Theorem (published in 1949). [ 2 ] Henkin's proof was simplified by Gisbert Hasenjaeger in 1953. [ 3 ]
There are numerous deductive systems for first-order logic, including systems of natural deduction and Hilbert-style systems . Common to all deductive systems is the notion of a formal deduction . This is a sequence (or, in some cases, a finite tree ) of formulae with a specially designated conclusion . The definition of a deduction is such that it is finite and that it is possible to verify algorithmically (by a computer , for example, or by hand) that a given sequence (or tree) of formulae is indeed a deduction.
A first-order formula is called logically valid if it is true in every structure for the language of the formula (i.e. for any assignment of values to the variables of the formula). To formally state, and then prove, the completeness theorem, it is necessary to also define a deductive system. A deductive system is called complete if every logically valid formula is the conclusion of some formal deduction, and the completeness theorem for a particular deductive system is the theorem that it is complete in this sense. Thus, in a sense, there is a different completeness theorem for each deductive system. A converse to completeness is soundness , the fact that only logically valid formulas are provable in the deductive system.
If some specific deductive system of first-order logic is sound and complete, then it is "perfect" (a formula is provable if and only if it is logically valid), thus equivalent to any other deductive system with the same quality (any proof in one system can be converted into the other). [ citation needed ]
We first fix a deductive system of first-order predicate calculus, choosing any of the well-known equivalent systems. Gödel's original proof assumed the Hilbert-Ackermann proof system.
The completeness theorem says that if a formula is logically valid then there is a finite deduction (a formal proof) of the formula.
Thus, the deductive system is "complete" in the sense that no additional inference rules are required to prove all the logically valid formulae. A converse to completeness is soundness , the fact that only logically valid formulae are provable in the deductive system. Together with soundness (whose verification is easy), this theorem implies that a formula is logically valid if and only if it is the conclusion of a formal deduction.
The theorem can be expressed more generally in terms of logical consequence . We say that a sentence s is a syntactic consequence of a theory T , denoted T ⊢ s {\displaystyle T\vdash s} , if s is provable from T in our deductive system. We say that s is a semantic consequence of T , denoted T ⊨ s {\displaystyle T\models s} , if s holds in every model of T . The completeness theorem then says that for any first-order theory T with a well-orderable language, and any sentence s in the language of T ,
Since the converse (soundness) also holds, it follows that T ⊨ s {\displaystyle T\models s} if and only if T ⊢ s {\displaystyle T\vdash s} , and thus that syntactic and semantic consequence are equivalent for first-order logic.
This more general theorem is used implicitly, for example, when a sentence is shown to be provable from the axioms of group theory by considering an arbitrary group and showing that the sentence is satisfied by that group.
Gödel's original formulation is deduced by taking the particular case of a theory without any axiom.
The completeness theorem can also be understood in terms of consistency , as a consequence of Henkin's model existence theorem . We say that a theory T is syntactically consistent if there is no sentence s such that both s and its negation ¬ s are provable from T in our deductive system. The model existence theorem says that for any first-order theory T with a well-orderable language,
Another version, with connections to the Löwenheim–Skolem theorem , says:
Given Henkin's theorem, the completeness theorem can be proved as follows: If T ⊨ s {\displaystyle T\models s} , then T ∪ ¬ s {\displaystyle T\cup \lnot s} does not have models. By the contrapositive of Henkin's theorem, then T ∪ ¬ s {\displaystyle T\cup \lnot s} is syntactically inconsistent. So a contradiction ( ⊥ {\displaystyle \bot } ) is provable from T ∪ ¬ s {\displaystyle T\cup \lnot s} in the deductive system. Hence ( T ∪ ¬ s ) ⊢ ⊥ {\displaystyle (T\cup \lnot s)\vdash \bot } , and then by the properties of the deductive system, T ⊢ s {\displaystyle T\vdash s} .
The model existence theorem and its proof can be formalized in the framework of Peano arithmetic . Precisely, we can systematically define a model of any consistent effective first-order theory T in Peano arithmetic by interpreting each symbol of T by an arithmetical formula whose free variables are the arguments of the symbol. (In many cases, we will need to assume, as a hypothesis of the construction, that T is consistent, since Peano arithmetic may not prove that fact.) However, the definition expressed by this formula is not recursive (but is, in general, Δ 2 ).
An important consequence of the completeness theorem is that it is possible to recursively enumerate the semantic consequences of any effective first-order theory, by enumerating all the possible formal deductions from the axioms of the theory, and use this to produce an enumeration of their conclusions.
This comes in contrast with the direct meaning of the notion of semantic consequence, that quantifies over all structures in a particular language, which is clearly not a recursive definition.
Also, it makes the concept of "provability", and thus of "theorem", a clear concept that only depends on the chosen system of axioms of the theory, and not on the choice of a proof system.
Gödel's incompleteness theorems show that there are inherent limitations to what can be proven within any given first-order theory in mathematics. The "incompleteness" in their name refers to another meaning of complete (see model theory – Using the compactness and completeness theorems ): A theory T {\displaystyle T} is complete (or decidable) if every sentence S {\displaystyle S} in the language of T {\displaystyle T} is either provable ( T ⊢ S {\displaystyle T\vdash S} ) or disprovable ( T ⊢ ¬ S {\displaystyle T\vdash \neg S} ).
The first incompleteness theorem states that any T {\displaystyle T} which is consistent , effective and contains Robinson arithmetic (" Q ") must be incomplete in this sense, by explicitly constructing a sentence S T {\displaystyle S_{T}} which is demonstrably neither provable nor disprovable within T {\displaystyle T} . The second incompleteness theorem extends this result by showing that S T {\displaystyle S_{T}} can be chosen so that it expresses the consistency of T {\displaystyle T} itself.
Since S T {\displaystyle S_{T}} cannot be proven in T {\displaystyle T} , the completeness theorem implies the existence of a model of T {\displaystyle T} in which S T {\displaystyle S_{T}} is false. In fact, S T {\displaystyle S_{T}} is a Π 1 sentence , i.e. it states that some finitistic property is true of all natural numbers; so if it is false, then some natural number is a counterexample. If this counterexample existed within the standard natural numbers, its existence would disprove S T {\displaystyle S_{T}} within T {\displaystyle T} ; but the incompleteness theorem showed this to be impossible, so the counterexample must not be a standard number, and thus any model of T {\displaystyle T} in which S T {\displaystyle S_{T}} is false must include non-standard numbers .
In fact, the model of any theory containing Q obtained by the systematic construction of the arithmetical model existence theorem, is always non-standard with a non-equivalent provability predicate and a non-equivalent way to interpret its own construction, so that this construction is non-recursive (as recursive definitions would be unambiguous).
Also, if T {\displaystyle T} is at least slightly stronger than Q (e.g. if it includes induction for bounded existential formulas), then Tennenbaum's theorem shows that it has no recursive non-standard models.
The completeness theorem and the compactness theorem are two cornerstones of first-order logic. While neither of these theorems can be proven in a completely effective manner, each one can be effectively obtained from the other.
The compactness theorem says that if a formula φ is a logical consequence of a (possibly infinite) set of formulas Γ then it is a logical consequence of a finite subset of Γ. This is an immediate consequence of the completeness theorem, because only a finite number of axioms from Γ can be mentioned in a formal deduction of φ, and the soundness of the deductive system then implies φ is a logical consequence of this finite set. This proof of the compactness theorem is originally due to Gödel.
Conversely, for many deductive systems, it is possible to prove the completeness theorem as an effective consequence of the compactness theorem.
The ineffectiveness of the completeness theorem can be measured along the lines of reverse mathematics . When considered over a countable language, the completeness and compactness theorems are equivalent to each other and equivalent to a weak form of choice known as weak Kőnig's lemma , with the equivalence provable in RCA 0 (a second-order variant of Peano arithmetic restricted to induction over Σ 0 1 formulas). Weak Kőnig's lemma is provable in ZF, the system of Zermelo–Fraenkel set theory without axiom of choice, and thus the completeness and compactness theorems for countable languages are provable in ZF. However the situation is different when the language is of arbitrary large cardinality since then, though the completeness and compactness theorems remain provably equivalent to each other in ZF, they are also provably equivalent to a weak form of the axiom of choice known as the ultrafilter lemma . In particular, no theory extending ZF can prove either the completeness or compactness theorems over arbitrary (possibly uncountable) languages without also proving the ultrafilter lemma on a set of the same cardinality.
The completeness theorem is a central property of first-order logic that does not hold for all logics. Second-order logic , for example, does not have a completeness theorem for its standard semantics (though does have the completeness property for Henkin semantics ), and the set of logically valid formulas in second-order logic is not recursively enumerable. The same is true of all higher-order logics. It is possible to produce sound deductive systems for higher-order logics, but no such system can be complete.
Lindström's theorem states that first-order logic is the strongest (subject to certain constraints) logic satisfying both compactness and completeness.
A completeness theorem can be proved for modal logic or intuitionistic logic with respect to Kripke semantics .
Gödel's original proof of the theorem proceeded by reducing the problem to a special case for formulas in a certain syntactic form, and then handling this form with an ad hoc argument.
In modern logic texts, Gödel's completeness theorem is usually proved with Henkin 's proof, rather than with Gödel's original proof. Henkin's proof directly constructs a term model for any consistent first-order theory. James Margetson (2004) developed a computerized formal proof using the Isabelle theorem prover. [ 4 ] Other proofs are also known. | https://en.wikipedia.org/wiki/Gödel's_completeness_theorem |
In mathematics , Gödel's speed-up theorem , proved by Gödel ( 1936 ), shows that there are theorems whose proofs can be drastically shortened by working in more powerful axiomatic systems.
Kurt Gödel showed how to find explicit examples of statements in formal systems that are provable in that system but whose shortest proof is unimaginably long. For example, the statement:
is provable in Peano arithmetic (PA) but the shortest proof has at least a googolplex symbols, by an argument similar to the proof of Gödel's first incompleteness theorem : If PA is consistent , then it cannot prove the statement in fewer than a googolplex symbols, because the existence of such a proof would itself be a theorem of PA, a contradiction . But simply enumerating all strings of length up to a googolplex and checking that each such string is not a proof (in PA) of the statement, yields a proof of the statement (which is necessarily longer than a googolplex symbols).
The statement has a short proof in a more powerful system: in fact the proof given in the previous paragraph is a proof in the system of Peano arithmetic plus the statement "Peano arithmetic is consistent" (which, per the incompleteness theorem, cannot be proved in Peano arithmetic).
In this argument, Peano arithmetic can be replaced by any more powerful consistent system, and a googolplex can be replaced by any number that can be described concisely in the system.
Harvey Friedman found some explicit natural examples of this phenomenon, giving some explicit statements in Peano arithmetic and other formal systems whose shortest proofs are ridiculously long ( Smoryński 1982 ). For example, the statement
is provable in Peano arithmetic, but the shortest proof has length at least A (1000), where A (0) = 1 and A ( n +1) = 2 A ( n ) . The statement is a special case of Kruskal's theorem and has a short proof in second order arithmetic .
If one takes Peano arithmetic together with the negation of the statement above, one obtains an inconsistent theory whose shortest known contradiction is equivalently long. | https://en.wikipedia.org/wiki/Gödel's_speed-up_theorem |
In mathematical logic , Gödel's β function is a function used to permit quantification over finite sequences of natural numbers in formal theories of arithmetic. The β function is used, in particular, in showing that the class of arithmetically definable functions is closed under primitive recursion, and therefore includes all primitive recursive functions .
The β function was introduced without the name in the proof of the first of Gödel's incompleteness theorems (Gödel 1931). The β function lemma given below is an essential step of that proof. Gödel gave the β function its name in (Gödel 1934).
The β {\displaystyle \beta } function takes three natural numbers as arguments. It is defined as
where r e m ( x , y ) {\displaystyle \mathrm {rem} (x,y)} denotes the remainder after integer division of x {\displaystyle x} by y {\displaystyle y} (Mendelson 1997:186).
The β function is arithmetically definable in an obvious way, because it uses only arithmetic operations and the remainder function which is arithmetically definable. It is therefore representable in Robinson arithmetic and stronger theories such as Peano arithmetic . By fixing the first two arguments appropriately, one can arrange that the values obtained by varying the final argument from 0 to n run through any specified ( n +1)-tuple of natural numbers (the β lemma described in detail below). This allows simulating the quantification over sequences of natural numbers of arbitrary length, which cannot be done directly in the language of arithmetic, by quantification over just two numbers, to be used as the first two arguments of the β function.
For example, if f is a function defined by primitive recursion on a recursion variable n , say by f (0) = c and f ( n +1) = g ( n , f ( n )), then to express f ( n ) = y one would like to say: there exists a sequence a 0 , a 1 , ..., a n such that a 0 = c , a n = y and for all i < n one has g ( i , a i ) = a i +1 . While that is not possible directly, one can say instead: there exist natural numbers a and b such that β ( a , b ,0) = c , β ( a , b , n ) = y and for all i < n one has g ( i , β ( a , b , i )) = β ( a , b , i +1).
The primitive recursion schema as given may be replaced by one which makes use of fewer parameters. Let w {\displaystyle w} be an elementary pairing function, and π 1 , π 2 {\displaystyle \pi _{1},\pi _{2}} be its projection functions for inversion.
Theorem: Any function constructible via the clauses of primitive recursion using the standard primitive recursion schema is constructible when the schema is replaced with the following.
This is proven by providing two intermediate schemata for primitive recursion, starting with a function defined via the standard schema, and translating the definition into terms of each intermediate schema and finally into terms of the above schema. The first intermediate schemata is as follows:
Translation of the standard definition of a primitive recursive function to the intermediate schema is done inductively, where an elementary pairing function w {\displaystyle w} is used to reinterpret the definition of a k + 1 {\displaystyle k+1} -ary primitive recursive function into a k {\displaystyle k} -ary primitive recursive function, terminating the induction at k = 1 {\displaystyle k=1} .
The second intermediate schema is as follows, with the x {\displaystyle x} parameter eliminated.
Translation to it is accomplished by pairing x {\displaystyle x} and f 1 ( x , y ) {\displaystyle f_{1}(x,y)} together to use one parameter for handling both, namely by setting g 2 ( x ) = w ( x , g 1 ( x ) ) {\displaystyle g_{2}(x)=w(x,g_{1}(x))} , h 2 ( x , z ) = w ( π 1 z , h 1 ( π 1 z , x , π 2 z ) ) {\displaystyle h_{2}(x,z)=w(\pi _{1}z,h_{1}(\pi _{1}z,x,\pi _{2}z))} , and recovering f 1 ( x , y ) {\displaystyle f_{1}(x,y)} from these paired images by taking π 2 ( f 2 ( x , y ) ) {\displaystyle \pi _{2}(f_{2}(x,y))} .
Finally, translation of the intermediate schema into the parameter-eliminated schema is done with a similar pairing and unpairing of y {\displaystyle y} and f 2 ( x , y ) {\displaystyle f_{2}(x,y)} . Composing these three translations gives a definition in the original parameter-free schema. [ 1 ]
This allows primitive recursion to be formalized in Peano arithmetic, due to its lack of extra n -ary function symbols. [ citation needed ]
The utility of the β function comes from the following result (Gödel 1931, Hilfssatz 1, p. 192-193), which is the purpose of the β function in Gödel's incompleteness proof. This result is explained in more detail than in Gödel's proof in (Mendelson 1997:186) and (Smith 2013:113-118).
As an example, the sequence (2,0,2,1) can be encoded by b = 3 412 752 and c =24, since
The proof of the β function lemma makes use of the Chinese remainder theorem . | https://en.wikipedia.org/wiki/Gödel's_β_function |
In mathematical logic , a Gödel logic , sometimes referred to as Dummett logic or Gödel–Dummett logic , [ 1 ] is a member of a family of finite- or infinite-valued logics in which the sets of truth values V are closed subsets of the unit interval [0,1] containing both 0 and 1. Different such sets V in general determine different Gödel logics. The concept is named after Kurt Gödel . [ 2 ] [ 3 ]
In 1959, Michael Dummett showed that infinite-valued propositional Gödel logic can be axiomatised by adding the axiom schema
to intuitionistic propositional logic . [ 1 ] [ 4 ]
This mathematical logic -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Gödel_logic |
The Gödel metric , also known as the Gödel solution or Gödel universe , is an exact solution , found in 1949 by Kurt Gödel , [ 1 ] of the Einstein field equations in which the stress–energy tensor contains two terms: the first representing the matter density of a homogeneous distribution of swirling dust particles (see dust solution ), and the second associated with a negative cosmological constant (see Lambdavacuum solution ).
This solution has many unusual properties—in particular, the existence of closed time-like curves that would allow time travel in a universe described by the solution. Its definition is somewhat artificial, since the value of the cosmological constant must be carefully chosen to correspond to the density of the dust grains, but this spacetime is an important pedagogical example.
Like any other Lorentzian spacetime , the Gödel solution represents the metric tensor in terms of a local coordinate chart . It may be easiest to understand the Gödel universe using the cylindrical coordinate system (see below), but this article uses the chart originally used by Gödel. In this chart, the metric (or, equivalently, the line element ) is
where ω {\displaystyle \omega } is a non-zero real constant that gives the angular velocity of the surrounding dust grains about the y -axis, measured by a "non-spinning" observer riding on one of the dust grains. "Non-spinning" means that the observer does not feel centrifugal forces, but in this coordinate system, it would rotate about an axis parallel to the y -axis. In this rotating frame, the dust grains remain at constant values of x , y , and z . Their density in this coordinate diagram increases with x , but their density in their own frames of reference is the same everywhere.
To investigate the properties of the Gödel solution, the frame field can be assumed (dual to the co-frame read from the metric as given above),
This framework defines a family of inertial observers that are 'comoving with the dust grains'. The computation of the Fermi–Walker derivatives with respect to e → 0 {\displaystyle {\vec {e}}_{0}} shows that the spatial frames are spinning about e → 2 {\displaystyle {\vec {e}}_{2}} with the angular velocity − ω {\displaystyle -\omega } . It follows that the 'non spinning inertial frame' comoving with the dust particles is
The components of the Einstein tensor (with respect to either frame above) are
Here, the first term is characteristic of a Lambdavacuum solution and the second term is characteristic of a pressureless perfect fluid or dust solution. The cosmological constant is carefully chosen to partially cancel the matter density of the dust.
The Gödel spacetime is a rare example of a regular (singularity-free) solution of the Einstein field equations . Gödel's original chart is geodesically complete and free of singularities. Therefore, it is a global chart, and the spacetime is homeomorphic to R 4 , and therefore, simply connected.
In any Lorentzian spacetime, the fourth rank Riemann tensor is a multilinear operator on the four-dimensional space of tangent vectors (at some event), but a linear operator on the six-dimensional space of bivectors at that event. Accordingly, it has a characteristic polynomial , whose roots are the eigenvalues . In Gödelian spacetime, these eigenvalues are very simple:
This spacetime admits a five-dimensional Lie algebra of Killing vectors , which can be generated by ' time translation ' ∂ t {\displaystyle \partial _{t}} , two 'spatial translations' ∂ y , ∂ z {\displaystyle \partial _{y},\;\partial _{z}} , plus two further Killing vector fields:
and
The isometry group acts 'transitively' (since we can translate into t , y , z {\displaystyle t,y,z} , and with the fourth vector we can move along x {\displaystyle x} ), so spacetime is 'homogeneous'. However, it is not 'isotropic', as can be seen.
The given demonstrators show that the slices x = x 0 {\displaystyle x=x_{0}} admit a transitive abelian three-dimensional transformation group , so that a quotient of the solution can be reinterpreted as a stationary cylindrically symmetric solution. The slices y = y 0 {\displaystyle y=y_{0}} allow for an SL(2, R ) action, and the slices t = t 0 {\displaystyle t=t_{0}} admit a Bianchi III (cf. the fourth Killing vector field). This can be rewritten as the symmetry group containing three-dimensional subgroups with examples of Bianchi types I, III, and VIII. Four of the five Killing vectors, as well as the curvature tensor do not depend on the coordinate y. The Gödel solution is the Cartesian product of a factor R with a three-dimensional Lorentzian manifold ( signature −++).
It can be shown that, except for the local isometry , the Gödel solution is the only perfect fluid solution of the Einstein field equation which admits a five-dimensional Lie algebra of the Killing vectors.
The Weyl tensor of the Gödel solution has Petrov type D . This means that for an appropriately chosen observer, the tidal forces are very close to those that would be felt from a point mass in Newtonian gravity.
To study the tidal forces in more detail, the Bel decomposition of the Riemann tensor can be computed into three pieces, the tidal or electrogravitic tensor (which represents tidal forces), the magnetogravitic tensor (which represents spin-spin forces on spinning test particles and other gravitational effects analogous to magnetism), and the topogravitic tensor (which represents the spatial sectional curvatures).
Observers comoving with the dust particles would observe that the tidal tensor (with respect to u → = e → 0 {\displaystyle {\vec {u}}={\vec {e}}_{0}} , which components evaluated in our frame) has the form
That is, they measure isotropic tidal tension orthogonal to the distinguished direction ∂ y {\displaystyle \partial _{y}} .
The gravitomagnetic tensor vanishes identically
This is an artifact of the unusual symmetries of this spacetime, and implies that the putative "rotation" of the dust does not have the gravitomagnetic effects usually associated with the gravitational field produced by rotating matter.
The principal Lorentz invariants of the Riemann tensor are
The vanishing of the second invariant means that some observers measure no gravitomagnetism, which is consistent with what was just said. The fact that the first invariant (the Kretschmann invariant ) is constant reflects the homogeneity of the Gödel spacetime.
The frame fields given above are both inertial, ∇ e → 0 e → 0 = 0 {\displaystyle \nabla _{{\vec {e}}_{0}}{\vec {e}}_{0}=0} , but the vorticity vector of the timelike geodesic congruence defined by the timelike unit vectors is
This means that the world lines of nearby dust particles are twisting about one another. Furthermore, the shear tensor of the congruence e → 0 {\displaystyle {\vec {e}}_{0}} vanishes, so the dust particles exhibit rigid rotation.
If the past light cone of a given observer is studied, it can be found that null geodesics moving orthogonally to ∂ y {\displaystyle \partial _{y}} spiral inwards toward the observer, so that if one looks radially, one sees the other dust grains in progressively time-lagged positions. However, the solution is stationary, so it might seem that an observer riding on a dust grain will not see the other grains rotating about oneself. However, recall that while the first frame given above (the e → j {\displaystyle {\vec {e}}_{j}} ) appears static in the chart, the Fermi–Walker derivatives show that it is spinning with respect to gyroscopes. The second frame (the f → j {\displaystyle {\vec {f}}_{j}} ) appears to be spinning in the chart, but it is gyrostabilized, and a non-spinning inertial observer riding on a dust grain will indeed see the other dust grains rotating clockwise with angular velocity ω {\displaystyle \omega } about his axis of symmetry. It turns out that in addition, optical images are expanded and sheared in the direction of rotation.
If a non-spinning inertial observer looks along his axis of symmetry, one sees one's coaxial non-spinning inertial peers apparently non-spinning with respect to oneself, as would be expected.
According to Hawking and Ellis, another remarkable feature of this spacetime is the fact that, if the inessential y coordinate is suppressed, light emitted from an event on the world line of a given dust particle spirals outwards, forms a circular cusp, then spirals inward and reconverges at a subsequent event on the world line of the original dust particle. This means that observers looking orthogonally to the e → 2 {\displaystyle {\vec {e}}_{2}} direction can see only finitely far out, and also see themselves at an earlier time.
The cusp is a non-geodesic closed null curve. (See the more detailed discussion below using an alternative coordinate chart.)
Because of the homogeneity of the spacetime and the mutual twisting of our family of timelike geodesics, it is more or less inevitable that the Gödel spacetime should have closed timelike curves (CTCs). Indeed, there are CTCs through every event in the Gödel spacetime. This causal anomaly seems to have been regarded as the whole point of the model by Gödel himself, who was apparently striving to prove that Einstein's equations of spacetime are not consistent with what we intuitively understand time to be (i. e. that it passes and the past no longer exists, the position philosophers call presentism , whereas Gödel seems to have been arguing for something more like the philosophy of eternalism ). [ 2 ]
Einstein was aware of Gödel's solution and commented in Albert Einstein: Philosopher-Scientist [ 3 ] that if there are a series of causally-connected events in which "the series is closed in itself" (in other words, a closed timelike curve), then this suggests that there is no good physical way to define whether a given event in the series happened "earlier" or "later" than another event in the series:
In that case the distinction "earlier-later" is abandoned for world-points which lie far apart in a cosmological sense, and those paradoxes, regarding the direction of the causal connection, arise, of which Mr. Gödel has spoken.
Such cosmological solutions of the gravitation-equations (with not vanishing A-constant) have been found by Mr. Gödel. It will be interesting to weigh whether these are not to be excluded on physical grounds.
If the Gödel spacetime admitted any boundary-less temporal hyperslices (e.g. a Cauchy surface ), any such CTC would have to intersect it an odd number of times, contradicting the fact that the spacetime is simply connected. Therefore, this spacetime is not globally hyperbolic .
In this section, we introduce another coordinate chart for the Gödel solution, in which some of the features mentioned above are easier to see.
Gödel did not explain how he found his solution, but there are in fact many possible derivations. We will sketch one here, and at the same time verify some of the claims made above.
Start with a simple frame in a cylindrical type chart, featuring two undetermined functions of the radial coordinate:
Here, we think of the timelike unit vector field e → 0 {\displaystyle {\vec {e}}_{0}} as tangent to the world lines of the dust particles, and their world lines will in general exhibit nonzero vorticity but vanishing expansion and shear. Let us demand that the Einstein tensor match a dust term plus a vacuum energy term. This is equivalent to requiring that it match a perfect fluid; i.e., we require that the components of the Einstein tensor, computed with respect to our frame, take the form
This gives the conditions
Plugging these into the Einstein tensor, we see that in fact we now have μ = p {\displaystyle \mu =p} . The simplest nontrivial spacetime we can construct in this way evidently would have this coefficient be some nonzero but constant function of the radial coordinate. Specifically, with a bit of foresight, let us choose μ = ω 2 {\displaystyle \mu =\omega ^{2}} . This gives
Finally, let us demand that this frame satisfy
This gives c = − 1 / ω {\displaystyle c=-1/\omega } , and our frame becomes
From the metric tensor we find that the vector field ∂ φ {\displaystyle \partial _{\varphi }} , which is spacelike for small radii, becomes null at r = r c {\displaystyle r=r_{c}} where
This is because at that radius we find that e → 3 = ω 2 ∂ φ − ∂ t , {\displaystyle {\vec {e}}_{3}={\tfrac {\omega }{2}}\,\partial _{\varphi }-\partial _{t},} so ω 2 ∂ φ = e → 3 + e → 0 {\displaystyle {\tfrac {\omega }{2}}\,\partial _{\varphi }={\vec {e}}_{3}+{\vec {e}}_{0}} and is therefore null. The circle r = r c {\displaystyle r=r_{c}} at a given t is a closed null curve, but not a null geodesic.
Examining the frame above, we can see that the coordinate z {\displaystyle z} is inessential; our spacetime is the direct product of a factor R with a signature −++ three-manifold. Suppressing z {\displaystyle z} in order to focus our attention on this three-manifold, let us examine how the appearance of the light cones changes as we travel out from the axis of symmetry r = 0 {\displaystyle r=0} :
When we get to the critical radius, the cones become tangent to the closed null curve.
At the critical radius r = r c {\displaystyle r=r_{c}} , the vector field ∂ φ {\displaystyle \partial _{\varphi }} becomes null. For larger radii, it is timelike . Thus, corresponding to our symmetry axis we have a timelike congruence made up of circles and corresponding to certain observers. This congruence is however only defined outside the cylinder r = r c {\displaystyle r=r_{c}} .
This is not a geodesic congruence; rather, each observer in this family must maintain a constant acceleration in order to hold his course. Observers with smaller radii must accelerate harder; as r → r c {\displaystyle r\rightarrow r_{c}} the magnitude of acceleration diverges, which is just what is expected, given that r = r c {\displaystyle r=r_{c}} is a null curve.
If we examine the past light cone of an event on the axis of symmetry, we find the following picture:
Recall that vertical coordinate lines in our chart represent the world lines of the dust particles, but despite their straight appearance in our chart , the congruence formed by these curves has nonzero vorticity, so the world lines are actually twisting about each other . The fact that the null geodesics spiral inwards in the manner shown above means that when our observer, when looking radially outwards , sees nearby dust particles not at their current locations, but at their earlier locations. This is what we would expect if the dust particles are in fact rotating about one another.
The null geodesics are geometrically straight ; in the figure, they appear to be spirals only because the coordinates are "rotating" in order to permit the dust particles to appear stationary.
According to Hawking and Ellis (see monograph cited below), all light rays emitted from an event on the symmetry axis reconverge at a later event on the axis, with the null geodesics forming a circular cusp (which is a null curve, but not a null geodesic):
This implies that in the Gödel lambda dust solution, the absolute future of each event has a character very different from what we might naively expect.
Following Gödel, we can interpret the dust particles as galaxies, so that the Gödel solution becomes a cosmological model of a rotating universe . Besides rotating, this model exhibits no Hubble expansion , so it is not a realistic model of the universe in which we live, but can be taken as illustrating an alternative universe, which would in principle be allowed by general relativity (if one admits the legitimacy of a negative cosmological constant). Less well known solutions of Gödel's exhibit both rotation and Hubble expansion and have other qualities of his first model, but traveling into the past is not possible. According to Stephen Hawking , these models could well be a reasonable description of the universe that we observe , however observational data are compatible only with a very low rate of rotation. [ 4 ] The quality of these observations improved continually up until Gödel's death, and he would always ask "Is the universe rotating yet?" and be told "No, it isn't". [ 5 ]
We have seen that observers lying on the y axis (in the original chart) see the rest of the universe rotating clockwise about that axis. However, the homogeneity of the spacetime shows that the direction but not the position of this "axis" is distinguished.
Some have interpreted the Gödel universe as a counterexample to Einstein's hopes that general relativity should exhibit some kind of Mach's principle , [ 4 ] citing the fact that the matter is rotating (world lines twisting about each other) in a manner sufficient to pick out a preferred direction, although with no distinguished axis of rotation.
Others [ citation needed ] take Mach principle to mean some physical law tying the definition of non-spinning inertial frames at each event to the global distribution and motion of matter everywhere in the universe, and say that because the non-spinning inertial frames are precisely tied to the rotation of the dust in just the way such a Mach principle would suggest, this model does accord with Mach's ideas.
Many other exact solutions that can be interpreted as cosmological models of rotating universes are known. [ 6 ] | https://en.wikipedia.org/wiki/Gödel_metric |
In mathematical logic , a Gödel numbering is a function that assigns to each symbol and well-formed formula of some formal language a unique natural number , called its Gödel number . Kurt Gödel developed the concept for the proof of his incompleteness theorems . [ 1 ] : 173–198
A Gödel numbering can be interpreted as an encoding in which a number is assigned to each symbol of a mathematical notation , after which a sequence of natural numbers can then represent a sequence of symbols. These sequences of natural numbers can again be represented by single natural numbers, facilitating their manipulation in formal theories of arithmetic.
Since the publishing of Gödel's paper in 1931, the term "Gödel numbering" or "Gödel code" has been used to refer to more general assignments of natural numbers to mathematical objects.
Gödel noted that each statement within a system can be represented by a natural number (its Gödel number ). The significance of this was that properties of a statement—such as its truth or falsehood—would be equivalent to determining whether its Gödel number had certain properties. The numbers involved might be very large indeed, but this is not a barrier; all that matters is that such numbers can be constructed.
In simple terms, Gödel devised a method by which every formula or statement that can be formulated in the system gets a unique number, in such a way that formulas and Gödel numbers can be mechanically converted back and forth. There are many ways to do this. A simple example is the way in which English is stored as a sequence of numbers in computers using ASCII . Since ASCII codes are in the range 0 to 127, it is sufficient to pad them to 3 decimal digits and then to concatenate them:
Gödel used a system based on prime factorization . He first assigned a unique natural number to each basic symbol in the formal language of arithmetic with which he was dealing.
To encode an entire formula, which is a sequence of symbols, Gödel used the following system. Given a sequence ( x 1 , x 2 , x 3 , . . . , x n ) {\displaystyle (x_{1},x_{2},x_{3},...,x_{n})} of positive integers, the Gödel encoding of the sequence is the product of the first n primes raised to their corresponding values in the sequence:
According to the fundamental theorem of arithmetic , any number (and, in particular, a number obtained in this way) can be uniquely factored into prime factors , so it is possible to recover the original sequence from its Gödel number (for any given number n of symbols to be encoded).
Gödel specifically used this scheme at two levels: first, to encode sequences of symbols representing formulas, and second, to encode sequences of formulas representing proofs. This allowed him to show a correspondence between statements about natural numbers and statements about the provability of theorems about natural numbers, the proof's key observation ( Gödel 1931 ).
There are more sophisticated (and more concise) ways to construct a Gödel numbering for sequences .
In the specific Gödel numbering used by Nagel and Newman, the Gödel number for the symbol "0" is 6 and the Gödel number for the symbol "=" is 5. Thus, in their system, the Gödel number of the formula "0 = 0" is 2 6 × 3 5 × 5 6 = 243,000,000.
Infinitely many different Gödel numberings are possible. For example, supposing there are K basic symbols, an alternative Gödel numbering could be constructed by invertibly mapping this set of symbols (through, say, an invertible function h ) to the set of digits of a bijective base- K numeral system . A formula consisting of a string of n symbols s 1 s 2 s 3 … s n {\displaystyle s_{1}s_{2}s_{3}\dots s_{n}} would then be mapped to the number
In other words, by placing the set of K basic symbols in some fixed order, such that the i {\displaystyle i} -th symbol corresponds uniquely to the i {\displaystyle i} -th digit of a bijective base- K numeral system, each formula may serve just as the very numeral of its own Gödel number.
For example, the numbering described here has K=1000. [ ii ]
One may use Gödel numbering to show how functions defined by course-of-values recursion are in fact primitive recursive functions .
Once a Gödel numbering for a formal theory is established, each inference rule of the theory can be expressed as a function on the natural numbers. If f is the Gödel mapping and r is an inference rule, then there should be some arithmetical function g r of natural numbers such that if formula C is derived from formulas A and B through an inference rule r , i.e.
then
This is true for the numbering Gödel used, and for any other numbering where the encoded formula can be arithmetically recovered from its Gödel number.
Thus, in a formal theory such as Peano arithmetic in which one can make statements about numbers and their arithmetical relationships to each other, one can use a Gödel numbering to indirectly make statements about the theory itself. This technique allowed Gödel to prove results about the consistency and completeness properties of formal systems .
In computability theory , the term "Gödel numbering" is used in settings more general than the one described above. It can refer to:
Also, the term Gödel numbering is sometimes used when the assigned "numbers" are actually strings, which is necessary when considering models of computation such as Turing machines that manipulate strings rather than numbers. [ citation needed ]
Gödel sets are sometimes used in set theory to encode formulas, and are similar to Gödel numbers, except that one uses sets rather than numbers to do the encoding. In simple cases when one uses a hereditarily finite set to encode formulas this is essentially equivalent to the use of Gödel numbers, but somewhat easier to define because the tree structure of formulas can be modeled by the tree structure of sets. Gödel sets can also be used to encode formulas in infinitary languages .
( 1 × 10 ( 3 − 1 ) + 2 × 10 ( 3 − 2 ) + 3 × 10 ( 3 − 3 ) ) = ( 1 × 10 2 + 2 × 10 1 + 3 × 10 0 ) = ( 100 + 20 + 3 ) {\displaystyle (1\times 10^{(3-1)}+2\times 10^{(3-2)}+3\times 10^{(3-3)})=(1\times 10^{2}+2\times 10^{1}+3\times 10^{0})=(100+20+3)} [ iii ]
...we arrive at 123 {\displaystyle 123} as our numbering—a neat feature. | https://en.wikipedia.org/wiki/Gödel_numbering |
In mathematics , a Gödel numbering for sequences provides an effective way to represent each finite sequence of natural numbers as a single natural number. While a set theoretical embedding is surely possible, the emphasis is on the effectiveness of the functions manipulating such representations of sequences: the operations on sequences (accessing individual members, concatenation) can be "implemented" using total recursive functions , and in fact by primitive recursive functions .
It is usually used to build sequential “ data types ” in arithmetic-based formalizations of some fundamental notions of mathematics. It is a specific case of the more general idea of Gödel numbering . For example, recursive function theory can be regarded as a formalization of the notion of an algorithm , and can be regarded as a programming language to mimic lists by encoding a sequence of natural numbers in a single natural number. [ 1 ] [ 2 ]
Besides using Gödel numbering to encode unique sequences of symbols into unique natural numbers (i.e. place numbers into mutually exclusive or one-to-one correspondence with the sequences), we can use it to encode whole “architectures” of sophisticated “machines”. For example, we can encode Markov algorithms , [ 3 ] or Turing machines [ 4 ] into natural numbers and thereby prove that the expressive power of recursive function theory is no less than that of the former machine-like formalizations of algorithms.
Any such representation of sequences should contain all the information as in the original sequence—most importantly, each individual member must be retrievable. However, the length does not have to match directly; even if we want to handle sequences of different length, we can store length data as a surplus member, [ 5 ] or as the other member of an ordered pair by using a pairing function .
We expect that there is an effective way for this information retrieval process in form of an appropriate total recursive function. We want to find a totally recursive function f with the property that
for all n and for any n -length sequence of natural numbers ⟨ a 0 , … a n − 1 ⟩ {\displaystyle \langle a_{0},\dots a_{n-1}\rangle } , there exists an appropriate natural number a , called the Gödel number of the sequence, such that for all i where 0 ≤ i ≤ n − 1 {\displaystyle 0\leq i\leq n-1} , f ( a , i ) = a i {\displaystyle f(a,i)=a_{i}} .
There are effective functions which can retrieve each member of the original sequence from a Gödel number of the sequence. Moreover, we can define some of them in a constructive way, so we can go well beyond mere proofs of existence .
By an ingenious use of the Chinese remainder theorem , we can constructively define such a recursive function β {\displaystyle \beta } (using simple number-theoretical functions, all of which can be defined in a total recursive way) fulfilling the specifications given above. Gödel defined the β {\displaystyle \beta } function using the Chinese remainder theorem in his article written in 1931. This is a primitive recursive function . [ 6 ]
Thus, for all n and for any n -length sequence of natural numbers ⟨ a 0 , … a n − 1 ⟩ {\displaystyle \langle a_{0},\dots a_{n-1}\rangle } , there exists an appropriate natural number a , called the Gödel number of the sequence such that β ( a , i ) = a i {\displaystyle \beta (a,i)=a_{i}} . [ 7 ]
Our specific solution will depend on a pairing function—there are several ways to implement the pairing function, so one method must be selected. Now, we can abstract from the details of the implementation of the pairing function. We need only to know its “ interface ”: let π {\displaystyle \pi } , K , and L denote the pairing function and its two projection functions, respectively, satisfying specification :
We shall use another auxiliary function that will compute the remainder for natural numbers . Examples:
It can be proven that this function can be implemented as a recursive function.
Using the Chinese remainder theorem , we can prove that implementing β {\displaystyle \beta } as
will work, according to the specification we expect β {\displaystyle \beta } to satisfy. We can use a more concise form by an abuse of notation (constituting a sort of pattern matching ):
Let us achieve even more readability by more modularity and reuse (as these notions are used in computer science [ 8 ] ): by defining ∀ i < n {\displaystyle \forall i<n} the sequence m i = ( i + 1 ) ⋅ m + 1 {\displaystyle m_{i}=(i+1)\cdot m+1} , we can write
We shall use this m i {\displaystyle m_{i}} notation in the proof.
For proving the correctness of the above definition of the β {\displaystyle \beta } function, we shall use several lemmas. These have their own assumptions. Now we try to find out these assumptions, calibrating and tuning their strength carefully: they should not be said in an either superfluously sharp, or unsatisfactorily weak form.
Let a 0 , … a n − 1 {\displaystyle a_{0},\dots a_{n-1}} be a sequence of natural numbers.
Let m be chosen to satisfy
The first assumption is meant as
It is needed to meet an assumption of the Chinese remainder theorem (that of being pairwise coprime ). In the literature, sometimes this requirement is replaced with a stronger one, e.g. constructively built with the factorial function, [ 1 ] but the stronger premise is not required for this proof. [ 2 ]
The second assumption does not concern the Chinese remainder theorem in any way. It will have importance in proving that the specification for β {\displaystyle \beta } is met eventually. It ensures that an x ~ {\displaystyle {\tilde {x}}} solution of the simultaneous congruence system
also satisfies
A stronger assumption for m requiring ∀ i < n ( a i < m ) {\displaystyle \forall i<n\;(a_{i}<m)} automatically satisfies the second assumption (if we define the notation m i {\displaystyle m_{i}} as above).
In the section Hand-tuned assumptions , we required that
In detail:
remembering that ∀ i < n {\displaystyle \forall i<n} we defined m i = ( i + 1 ) ⋅ m + 1 {\displaystyle m_{i}=(i+1)\cdot m+1} .
The proof is by contradiction; assume the negation of the original statement:
We know what “coprime” relation means (in a lucky way, its negation can be formulated in a concise form); thus, let us substitute in the appropriate way:
Using a “more” prenex normal form (but note allowing a constraint-like notation in quantifiers):
Because of a theorem on divisibility , p ∣ m i ∧ p ∣ m j {\displaystyle p\mid m_{i}\land p\mid m_{j}} allows us to also say
Substituting the definitions of m k {\displaystyle m_{k}} -sequence notation, we get m i − m j = ( i − j ) ⋅ m {\displaystyle m_{i}-m_{j}=(i-j)\cdot m} , thus (as equality axioms postulate identity to be a congruence relation [ 10 ] ) we get
Since p is a prime element (note that the irreducible element property is used), we get
Now we must resort to our assumption
The assumption was chosen carefully to be as weak as possible, but strong enough to enable us to use it now.
The assumed negation of the original statement contains an appropriate existential statement using indices i < n ∧ j < n ∧ i ≠ j {\displaystyle i<n\land j<n\land i\neq j} ; this entails i − j ∈ n ¯ ∖ { 0 } {\displaystyle i-j\in {\overline {n}}\setminus \left\{0\right\}} , thus the mentioned assumption can be applied, so i − j ∣ m {\displaystyle i-j\mid m} holds.
We can prove by several means [ 11 ] known in propositional calculus that
holds.
Since i − j ∣ m {\displaystyle i-j\mid m} , by the transitivity property of the divisibility relation, p ∣ i − j → p ∣ m {\displaystyle p\mid i-j\rightarrow p\mid m} . Thus (as equality axioms postulate identity to be a congruence relation [ 10 ] )
can be proven.
The negation of original statement contained
and we have just proved
Thus,
should also hold.
But after substituting the definition of m i {\displaystyle m_{i}} ,
Thus, summarizing the above three statements, by transitivity of the equality ,
should also hold.
However, in the negation of the original statement p is existentially quantified and restricted to primes ∃ p ∈ P r i m e {\displaystyle \exists p\in \mathrm {Prime} } . This establishes the contradiction we wanted to reach.
By reaching contradiction with its negation, we have just proven the original statement:
We build a system of simultaneous congruences
We can write it in a more concise way:
Many statements will be said below, all beginning with " ∀ i < n ( … ) {\displaystyle \forall i<n\;\left(\dots \right)} ". To achieve a more ergonomic treatment, from now on all statements should be read as being in the scope of an ∀ i < n ( … ) {\displaystyle \forall i<n\;\left(\dots \right)} quantification. Thus, ∀ i < n ( {\displaystyle \forall i<n(} begins here.
Let us chose a solution x 0 {\displaystyle x_{0}} for the system of simultaneous congruences. At least one solution must exist, because m 0 , … m n − 1 {\displaystyle m_{0},\dots m_{n-1}} are pairwise comprime as proven in the previous sections, so we can refer to the solution ensured by the Chinese remainder theorem. Thus, from now on we can regard x 0 {\displaystyle x_{0}} as satisfying
which means (by definition of modular arithmetic ) that
Recall the second assumption, “ ∀ i < n ( a i < m i ) {\displaystyle \forall i<n\;\left(a_{i}<m_{i}\right)} ”, and remember that we are now in the scope of an implicit quantification for i , so we don't repeat its quantification for each statement.
The second assumption a i < m i {\displaystyle a_{i}<m_{i}} implies that
Now by transitivity of equality we get
Our original goal was to prove that the definition
is good for achieving what we declared in the specification of β {\displaystyle \beta } : we want β ( π ( x 0 , m ) , i ) = a i {\displaystyle \beta \left(\pi \left(x_{0},m\right),i\right)=a_{i}} to hold.
This can be seen now by transitivity of equality , looking at the above three equations.
(The large scope of i ends here.)
We have just proven the correctness of the definition of β {\displaystyle \beta } : its specification requiring
is met. Although proving this was most important for establishing an encoding scheme for sequences, we have to fill in some gaps yet. These are related notions similar to existence and uniqueness (although on uniqueness, “at most one” should be meant here, and the conjunction of both is delayed as a final result).
Our ultimate question is: what number should stand for the encoding of sequence ⟨ a 0 , … , a n − 1 ⟩ {\displaystyle \left\langle a_{0},\dots ,a_{n-1}\right\rangle } ? The specification declares only an existential quantification, not yet a functional connection. We want a constructive and algorithmic connection: a (total) recursive function that performs the encoding.
This gap can be filled in a straightforward way: we shall use minimalization , and the totality of the resulting function is ensured by everything we have proven till now (i.e. the correctness of the definition of β {\displaystyle \beta } by meeting its specification). In fact, the specification
plays a role here of a more general notion (“special function” [ 12 ] ). The importance of this notion is that it enables us to split off the (sub)class of (total) recursive functions from the (super)class of partial recursive functions. In brief, the specification says that a function f [ 13 ] satisfying the specification
is a special function; that is, for each fixed combination of all-but-last arguments, the function f has root in its last argument:
Thus, let us choose the minimal possible number that fits well in the specification of the β {\displaystyle \beta } function: [ 5 ]
It can be proven (using the notions of the previous section ) that g is (total) recursive.
If we use the above scheme for encoding sequences only in contexts where the length of the sequences is fixed, then no problem arises. In other words, we can use them in an analogous way as arrays are used in programming.
But sometimes we need dynamically stretching sequences, or we need to deal with sequences whose length cannot be typed in a static way. In other words, we may encode sequences in an analogous way to lists in programming.
To illustrate both cases: if we form the Gödel numbering of a Turing machine, then the each row in the matrix of the “program” can be represented with tuples, sequences of fixed length (thus, without storing the length), because the number of the columns is fixed. [ 14 ] But if we want to reason about configuration-like things (of Turing-machines), and specifically if we want to encode the significant part of the tape of a running Turing machine, then we have to represent sequences together with their length. We can mimic dynamically stretching sequences by representing sequence concatenation (or at least, augmenting a sequence with one more element) with a totally recursive function. [ 15 ]
Length can be stored simply as a surplus member: [ 5 ]
The corresponding modification of the proof is straightforward, by adding a surplus
to the system of simultaneous congruences (provided that the surplus member index is chosen to be 0). Also, the assumptions have to be modified accordingly. | https://en.wikipedia.org/wiki/Gödel_numbering_for_sequences |
Görling–Levy perturbation theory ( GLPT ) in Kohn–Sham (KS) density functional theory (DFT) [ 1 ] [ 2 ] is the analogue to what Møller–Plesset perturbation theory (MPPT) [ 3 ] is in Hartree–Fock (HF) theory . [ 4 ] [ 5 ] [ 6 ] [ 7 ] [ 8 ] Its basis is Rayleigh–Schrödinger perturbation theory (RSPT) and the adiabatic connection (AC). It describes electronic correlation effects. It is mostly used to second (GL2), rarely to third (GL3) or fourth (GL4) order, but becomes fast really increasingly computational expensive. It was published in 1993 [ 9 ] and 1994 [ 10 ] by Andreas Görling and Mel Levy .
The basis of GL perturbation theory is the adiabatic connection (AC) with the coupling constant 0 ≤ α ≤ 1 {\textstyle 0\leq \alpha \leq 1} connecting the artificial Kohn–Sham (KS) system of noninteracting electrons α = 0 {\textstyle \alpha =0} to the real system of interacting electrons α = 1 {\textstyle \alpha =1} with the AC Hamiltonian
where N {\textstyle N} is the number of electrons , T ^ = − 1 2 ∑ i ∇ i 2 {\textstyle {\hat {T}}=-{\frac {1}{2}}\sum _{i}\nabla _{i}^{2}} the kinetic energy of the electrons, V ^ ee = ∑ i ∑ j > i | r i − r j | − 1 {\textstyle {\hat {V}}_{\text{ee}}=\sum _{i}\sum _{j>i}|r_{i}-r_{j}|^{-1}} the electron-electron interaction. Görling and Levy expressed the coupling-strength dependent local multiplicative potential under the constraint, that the density n ( r ) {\textstyle n(r)} stays fixed along the AC as
where v S {\textstyle v_{S}} is the KS potential, v H x {\textstyle v_{Hx}} the Hartree - exchange potential in first order, and the correlation potential for second order or higher v c α ( r ) = α 2 v c ( 2 ) + α 3 v c ( 3 ) + α 4 v c ( 4 ) + . . . {\textstyle v_{c}^{\alpha }(r)=\alpha ^{2}v_{c}^{(2)}+\alpha ^{3}v_{c}^{(3)}+\alpha ^{4}v_{c}^{(4)}+...} . As usual in perturbation theory we can express the correlation energy in a power series E c ( 0 ) + α E c ( 1 ) + α 2 E c ( 2 ) + . . . {\textstyle E_{c}^{(0)}+\alpha E_{c}^{(1)}+\alpha ^{2}E_{c}^{(2)}+...} , where in GLPT the zeroth and first contribution vanish i.e. E c ( 0 ) = E c ( 1 ) = 0 {\textstyle E_{c}^{(0)}=E_{c}^{(1)}=0} . The second term is the Görling–Levy second order (GL2) correlation energy [ 9 ] and can be evaluated with using the Slater–Condon rules and Brillouin's theorem in terms of occupied i , j {\textstyle i,j} and unoccupied a , b {\textstyle a,b} KS orbitals and eigenvalues [ 11 ]
where Φ S , Φ k {\textstyle \Phi _{S},\Phi _{k}} are ground state and excited KS determinants with their respective E 0 , E k {\textstyle E_{0},E_{k}} energies and E c MP2 {\textstyle E_{c}^{\text{MP2}}} is exactly the second order Møller–Plesset (MP2) correlation energy but evaluated with KS orbitals, E c S {\textstyle E_{c}^{S}} the so called single excitation contribution to correlation which is missing in regular MPPT, but present in GLPT and v ^ x NL {\textstyle {\hat {v}}_{x}^{\text{NL}}} is the nonlocal exchange operator from Hartree–Fock (HF) theory , v ^ x {\textstyle {\hat {v}}_{x}} is the local Kohn–Sham (KS) exchange operator both evaluated with KS orbitals and lastly the notation ⟨ i j | | a b ⟩ = ⟨ i j | a b ⟩ − ⟨ i j | b a ⟩ {\textstyle \langle ij||ab\rangle =\langle ij|ab\rangle -\langle ij|ba\rangle } .
With GLPT up to infinite order [ 10 ] one could in principle obtain the Hohenberg-Kohn (HK) functional exactly F HK [ n ] ≡ E [ n ] − ∫ d r v ( r ) n ( r ) {\textstyle F_{\text{HK}}[n]\equiv E[n]-\int drv(r)n(r)} in terms of unoccupied and occupied KS orbitals { φ i } {\textstyle \{\varphi _{i}\}} and their eigenvalues { ε i } {\textstyle \{\varepsilon _{i}\}} , where E [ n ] {\textstyle E[n]} is the electronic ground state energy and v ( r ) {\textstyle v(r)} the external potential. This is obviously only conceptually interesting since it is computational impossible. With the coupling constant expression
By setting α = 1 {\textstyle \alpha =1} hence
where in zeroth order E 0 = T S = ⟨ Φ S | T ^ | Φ S ⟩ = ∑ i ∫ d r ϕ i ∗ ( r ) ( − 1 / 2 ∇ 2 ) ϕ i ( r ) {\textstyle E_{0}=T_{S}=\langle \Phi _{S}|{\hat {T}}|\Phi _{S}\rangle =\sum _{i}\int dr\phi _{i}^{*}(r)(-1/2\nabla ^{2})\phi _{i}(r)} is the KS kinetic energy with the KS potential v 0 ( r ) = v S ( r ) {\textstyle v_{0}(r)=v_{S}(r)} and in first order E 1 = ⟨ Φ S | V ^ ee | Φ S ⟩ = E H x [ n ] {\textstyle E_{1}=\langle \Phi _{S}|{\hat {V}}_{\text{ee}}|\Phi _{S}\rangle =E_{Hx}[n]} the Hartree - exchange (Hx) energy and its respective Hx potential v 1 ( r ) = v H x ( r ) {\textstyle v_{1}(r)=v_{Hx}(r)} and from second order the infinite GL n {\textstyle n} correlation (c) energy with n → ∞ {\textstyle n\rightarrow \infty } , which is the exact Kohn–Sham (KS) correlation energy lim n → ∞ E c GLn [ n ] = ∑ j = 2 ∞ E j = E c [ n ] {\textstyle \lim _{n\rightarrow \infty }E_{c}^{\text{GLn}}[n]=\sum _{j=2}^{\infty }E_{j}=E_{c}[n]} and the corresponding correlation potential v c ( r ) = ∑ j = 2 ∞ v j ( r ) {\textstyle v_{c}(r)=\sum _{j=2}^{\infty }v_{j}(r)} . Similarly, if one would do Møller–Plesset perturbation theory up to infinite order one would obtain the exact Hartree–Fock (HF) correlation energy lim n → ∞ E c MPn = E c HF [ { Φ HF , Φ i a , Φ i j a b , Φ i j k a b c , . . . } ] {\textstyle \lim _{n\rightarrow \infty }E_{c}^{\text{MPn}}=E_{c}^{\text{HF}}[\{\Phi ^{\text{HF}},\Phi _{i}^{a},\Phi _{ij}^{ab},\Phi _{ijk}^{abc},...\}]} where i , j , k {\textstyle i,j,k} denote occupied and a , b , c {\textstyle a,b,c} unoccupied HF orbitals and their respective singly, doubly, triply and so on excited Slater determinants . In this notation Φ HF {\textstyle \Phi ^{\text{HF}}} is the HF determinant and Φ S {\textstyle \Phi _{S}} the KS determinant.
In the later half of their article [ 10 ] Görling and Levy connect their perturbation theory to the optimized effective potential method . | https://en.wikipedia.org/wiki/Görling–Levy_pertubation_theory |
In fluid dynamics , Görtler vortices are secondary flows that appear in a boundary layer flow along a concave wall. If the boundary layer is thin compared to the radius of curvature of the wall, the pressure remains constant across the boundary layer. On the other hand, if the boundary layer thickness is comparable to the radius of curvature, the centrifugal action creates a pressure variation across the boundary layer. This leads to the centrifugal instability (Görtler instability) of the boundary layer and consequent formation of Görtler vortices. These phenomena are named after mathematician Henry Görtler [ de ] .
The onset of Görtler vortices can be predicted using the dimensionless number called Görtler number ( G ). It is the ratio of centrifugal effects to the viscous effects in the boundary layer and is defined as
where
Görtler instability occurs when G exceeds about 0.3.
A similar phenomenon arising from the same centrifugal action is sometimes observed in rotational flows which do not follow a curved wall, such as the rib vortices seen in the wakes of cylinders [ 1 ] and generated behind moving structures. [ 2 ] | https://en.wikipedia.org/wiki/Görtler_vortices |
Günter Harder (born 14 March 1938 in Ratzeburg ) is a German mathematician, specializing in arithmetic geometry and number theory .
Harder studied mathematics and physics in Hamburg and Göttingen . Simultaneously with the Staatsexamen in 1964 in Hamburg, he received his doctoral degree (Dr. rer. nat.) under Ernst Witt with a thesis Über die Galoiskohomologie der Tori . [ 1 ] Two years later he completed his habilitation .
After a one-year postdoc position at Princeton University and a position as an assistant professor at the University of Heidelberg , he became a professor ordinarius at the University of Bonn . With the exception of a six-year stay at the former Universität-Gesamthochschule Wuppertal , Harder remained at the University of Bonn until his retirement in 2003. From 1995 to 2006 he was one of the directors of the Max-Planck-Institut für Mathematik in Bonn.
He was a visiting professor at Harvard University , Yale University , at Princeton's Institute for Advanced Study (IAS) (for the academic years 1966–1967, 1972–1973, 1986–1987, autumn of 1983, autumn of 2006), [ 2 ] at the Institut des Hautes Études Scientifiques (I.H.É.S.) in Paris, at the Tata Institute of Fundamental Research in Mumbai, and at the Mathematical Sciences Research Institute (MSRI) at the University of California, Berkeley .
For decades, Harder was known to German mathematicians as the Spiritus Rector for a mathematical workshop held for one week in spring and one week in autumn; the workshop, sponsored by the Mathematical Research Institute of Oberwolfach , introduced young mathematicians and scientists to important new developments in pure mathematics and mathematical sciences. [ citation needed ]
Harder's doctoral students include Kai Behrend , Jörg Bewersdorff , Joachim Schwermer , and Maria Heep-Altiner . [ 1 ]
His research deals with arithmetic geometry, automorphic forms , Shimura varieties , motives , and algebraic number theory . He made foundational contributions to the Waldspurger formula .
With Ina Kersten , he is a co-editor of the collected works of Ernst Witt .
Harder was an invited speaker at the International Congress of Mathematicians in 1970 and gave a talk titled Semisimple group schemes over curves and automorphic functions [ 3 ] and in 1990 with a talk titled Eisenstein cohomology of arithmetic groups and its applications to number theory . [ 4 ] In 1988 he was awarded the Leibniz Prize by the Deutsche Forschungsgemeinschaft .
In 2004 Harder received, with Friedhelm Waldhausen , the von Staudt Prize . [ 5 ] | https://en.wikipedia.org/wiki/Günter_Harder |
Günter Ropohl (14 June 1939 in Cologne , Germany – 28 January 2017) was a German philosopher of technology.
Günter Ropohl studied mechanical engineering and philosophy at Stuttgart University, where he was a scholar of the philosopher Max Bense . After his PhD ( Dr.-Ing. ) in 1970, he wrote his Habilitation thesis in Philosophy und Sociology at Karlsruhe University 1978 under the supervision of Hans Lenk . His work dealt with the systems theory of " Technik " (engl. technique ), leading to the concept of general technology . [ 1 ] In 1979, Ropohl became professor at the Universität Karlsruhe (TH) . Soon after, in 1981, he became professor for Allgemeine Technologie (general technology) and philosophy of technology at the Johann Wolfgang Goethe-Universität in Frankfurt am Main , Germany (until 2004). In the 1980s, he visited his colleague and friend Carl Mitcham in the United States. From 1983 to 1991, i.e. during the period of the Cold War , he was course director and visiting lecturer at the Inter-University Centre Dubrovnik ( Croatia ). In 1988, he was invited as visiting professor at the Rochester Institute of Technology , Rochester NY.
Ropohl was an honorary member of the German Engineering Association ( VDI ), due to his interdisciplinary engagement for the philosophy of technology. He was co-editor of an anthology of the classics in the philosophy of technology in a Continental-European tradition. [ 2 ] Ropohl published 15 monographs, (co-)edited another 15 books and published more than 180 articles. He died on 28 January 2017 at the age of 77. [ 3 ]
A central concept in his work was sociotechnical systems , i.e. he regarded techniques as societal structures. Ropohl was a critic of the systems theory of Niklas Luhmann and voted for the recognition of material culture . His definition of ( German ) "Technik" included a) the utility , b) artificiality and c) functionality . In the focus of his work is the combination of technique as artefact and action , whereas knowledge insinuates the meta-concept of technology . Therefore, he differentiated between engineering sciences and technical sciences . [ 4 ]
Ropohl was well known in the German-speaking academia for his writings on the concepts of Technik and Technologie , the ethics of technology , technology assessment , professional ethics for engineers and on the societal need for educating towards technology literacy.
He received a Festschrift with contributions from academic scholars, focusing on his work and related discourses, both on his 65th and 75th birthday (edited by Nicole C. Karafyllis , see literature), including a complete list of his publications from the late 1960s to 2014. | https://en.wikipedia.org/wiki/Günter_Ropohl |
Günther Friedländer (April 8, 1902 – May 25, 1975) was a German pharmacist, botanist, pharmacognosist , food chemist, an industrialist of medical products, and the founder of Teva Pharmaceutical Industries .
Günther Friedländer was born on April 8, 1902, in Königshütte ( Chorzów ), Upper Silesia , in Germany – a developing coal industry area. His parents were Paula Kober and Adolf Aron Friedlander, a merchant in the footwear industry. In 1912, the Friedländer family moved from Kőnigshütte, an area polluted with coal dust, west to Ratibor , where a small Jewish community lived. At age 11, Friedländer joined the Jewish movement " Blau-Weiss " (Blue-White) in Ratibor. In parallel to his life-science studies, Friedländer wrote stories and plays relevant to events occurring around him, to the meaning of life, and about his longing for the land of Israel and Jerusalem such as: "In our fathers land," "Poem to Jerusalem," " Persephone , the Goddess of Spring," and "Jacob the dreamer."
In 1920, Friedländer was accepted to Wilhelm Friedrich University , School of Pharmacy in Breslau , and became a member of the Zionist student movement: KJV (Kartell Jüdischer Verbindungen). Upon completing his exams and receiving the first science degree, Friedländer went to the University of Bern in Switzerland to do his doctorate studies with Alexander Tschirch . In July 1927, Friedländer completed his doctorate studies summa cum laude and received his doctorate of philosophy for his thesis on "Research in development processes within the field of Pharmacological, botanical and chemical pharmacology." After receiving his Ph.D., Friedländer returned to Breslau and worked as an assistant of Dr. A. Rop in the university faculty for Pharmacy and acted as the laboratory manager, where he taught the Pharmacy faculty students during their two last semesters in the university. At that time, Friedländer was working on analytical chemistry research under the supervision of Dr. A Rop. In November 1929, Friedlander received his pharmacist diploma signed by Dr. Shozol, the Prussian Minister for National Welfare.
In April 1930, Friedländer moved to Görlitz in order to manage the pharmacy and laboratory of his aunt Else Kober, named the "Crown Pharmacy in Görlitz – (1883), "Kronen-Apotheke – Görlitz". Else Kober was a First World War widow, and a bereaved mother to her only child. Her husband Max Kober, Friedländer's uncle and the brother of his mother Paula, was a pharmacist and the owner of the pharmacy in Görlitz. He was drafted to the army during the First World War and mortally wounded. On May 31, 1933, four months after the rise of the Nazis to power, and two months following the "humiliating trip" that was forced by the Nazis on the " white collar " professional Jews in Görliz, Friedländer sailed to Palestine to explore and search for the location to establish his pharmaceutical industry to be named Teva. During his journey in Palestine, he decided to build the company in Jerusalem, and he then returned to Germany . The " Blau-Weiss " movement of which Friedländer was a member in Ratibor, advocated going to nature , to know and to love nature's gift and its flora . Since Balfour declaration in 1917, the "Blue-White" movement adopted Zionism values and taught in its spirit. This was a "life changing" event in Friedländer's life at age of 15. He wrote stories, poems, and a play related to Erez Israel , and directed his life towards Erez Israel to produce there medicine from locally grown plants.
As a student in Wilhelm Friedrich University , Friedländer belonged to and was active in the Zionist student movement. This movement directed its members to immigrate to Erez Israel in the future. As a pharmacist in Görlitz, he was an active member in the Zionist circle and gave lectures from time to time. Immediately after the Nazis came to power – and after the "humiliating trip" that he experienced in Görlitz – he decided that it was time to immigrate to Erez Israel. Once there he planned to establish a pharmaceutical industry specializing in the manufacture of medical products from local plants. On April 2, 1934, Friedländer immigrated to Israel with his first wife Charlotte, followed a month later by his aunt Else Kober on May 8, 1934.
"We aspire to assist human nature by means produced from Nature"; this sentence Friedländer wrote in the year 1923, at age of 21, while he "shaped his vision" during the annual conference of the "Blue-white" organization held in Hohenberg. At this meeting, movement committee delegates, including Friedländer, met with Dr. Chaim Weizmann that told them: "Industry is the basis and foundation for the development of a place. In Palestine there is no industry. You all should prepare for Palestine's needs, which requires specialists like you in applied industry. Go and establish industry there." The two cousins and committee delegates, Kurt Grunwald [ 1 ] and Friedländer, decided at that time to fulfill Weizmann's order and reacted: "When time comes, we will immigrate to Palestine and build there an industry for medicines in the spirit of "Blue White" and we will name it Teva ("Teva" in Hebrew means "Nature"). Teva medical products will be manufactured from local natural materials/minerals and from the plants growing in Erez Israel".
At that time, the people who worked as pharmacists in "Erez Israel" had not completed their academic studies and had not received the diploma. In order to assist these workers to achieve the diploma, Friedländer prepared on May 5, 1934, a memorandum indicating cardinal points that are required for establishing a clinic and a university institute in Jerusalem that will create the basis for the school of pharmacy, a place where professional courses will be taught to pharmacy students that did not complete their formal studies. Their pharmacy will create the basis of the Hebrew Pharmacopeia.
On April 19, 1935, Friedländer wrote a memorandum to Professor Otto Warburg , one of the research pioneers of nature in Erez Israel and the manager of the Botanical Department in the Hebrew University . Friedländer indicated in his memorandum the need for establishing a school of pharmacy in Erez Israel in order to qualify pharmacists to become competent professional workers and provided a plan for Pharmacy school establishment that included various requirements such as: necessities, facilities, facility equipment, teachers and more. Warburg replied that the advocated plan is too expensive and there is no sufficient budget for such a plan and therefore the plan is not applicable.
The Teva company was founded by Friedländer and his aunt Else Kober on May 1, 1935. The company's registered name was "Teva Middle East Pharmaceutical & Chemical Works Co. Ltd. Jerusalem, Palestine." The company was built with an investment of 4,900 pound sterling, part came from private capital and partly from loans intended for German immigrants to establish industries. Credit shortage led to the joining of the banker Dr. Alfred Feuchtwanger [ 2 ] as a partner in Teva with 33% of shares in the company. In 1951, Feuchtwanger initiated the entrance of Teva to the Tel-Aviv stock market as a registered public company. Friedländer used to say during difficult economic times, that a pharmaceutical industry has a strong basis in that: "A Jewish mother will always buy medicine for her children." In the Second World War , the company provided medicine to the allied forces and in particular to the British army present in the Middle East . Within the framework of contacts with the British Mandate regime, Sir Alan Gordon Cunningham , the British high commissioner of Palestine, on behalf of the colonial minister and responsible for the British Mandate, visited Teva. His visit glorified Teva's reputation among the "medicine market" and created a momentum for Teva development.
In 1959, the pharmaceutical section of the Israeli Manufacturer's Association performed a survey grading the pharmaceutical companies in Israel according to several measures. Teva Company from Jerusalem was graded in the first place. Survey results proved that the market likes Teva products, many of them were developed by Friedländer and his staff. Teva workers pride was raised, and they felt there is a reward for their initiative, ideas and strict performance and appreciation for company excellent man-power. During the Second World War and until the termination of the British mandate regime, Teva exported its medical products to Arabic countries. In 1941, Friedländer presented the Teva company products in an exhibition held in Cairo , Egypt . The exhibition was sponsored by the "General Agent and Sole Distribution of medicine in Egypt and Sudan , Syria , and Lebanon . Later on, the Teva company exported its products to the United States , Soviet Union ( USSR ), health institutes in Denmark , Czechoslovakia , Persia , and Burma . In 1954, Teva company received from the Israeli President Mr. Yitzhak Ben Zvi the certificate of "Company Excellence." Friedländer emphasized the importance of education and training of Teva personnel for the various operations as demanded by the pharmaceutical industry as well as on achieving broader knowledge and participation in various courses held outside the company. In 1964, contacts between the Teva company and other companies were developed. These included contacts with Laboratorios Syntex from Mexico, Schering-Plough Corporation , and others.
In 1966, research collaboration of different projects was started between Friedländer and Teva company staff and the Hebrew University and two hospitals. These involved the development of Phenyl-Ethylacetyl-salicylate and Erythromycin Embonate
In the mid-sixties, Else Kober sold her company "controlling holder shares" that represented 1/3 of Teva value to the "Bank of Industry Development." From now on, the partners in Teva were Friedländer, Feuchtwanger, and the "Bank of Industry Development." In the year 1967, Teva company, located in Bayit VeGan neighborhood of Jerusalem, manufactured 250 different products. Scope of manufacturing was 9 million Israeli pounds, scope of export was 1.75 million Israeli pounds, and the annual dividend payment to shareholders was 8%. Friedländer and Kober decided at that time to move the company to another suitable industrial area. The authorities gave Teva 4.25 acres at convenient payment terms in the area of Tamir mountain in Jerusalem in order to build the new company. In the Tel-Aviv stock market, representatives of Assia-Zori company constantly bought Teva shares and as a consequence, a change in the holder share controllers occurred. Dr. Feuchtwanger decided to exit from its partnership and sold his shares of control to Assia-Zori company. The Bank of Industrial Development decided to exit from its partnership and to sell their controlled shares in a bid. Friedländer's power at Teva became weaker. He wished to keep Teva, "the apple of his eye," under his ownership and approached the bid together with Dr. Reuben Hecht , but they lost. Assia-Zori company offered a higher price and won the bid. From then on, Assia-Zori company owned 66% of Teva shares.
When Friedländer heard the bid results, he had a stroke. In November 1968, he sold his shares to Assia-Zori company and retired. On May 25, 1975, Friedländer died and was buried in Jerusalem.
Between 1930 and 1934, Friedländer was active in Zionist Circles in Görlitz. Since 1935, he was active in the organization of the German and Central Europe immigrants. Between 1950 and 1953, he was a member in the team establishing the School of Pharmacy [ 3 ] in Jerusalem and for creating the school image. During the 1950s and 1960s, Friedländer acted as the representative of the pharmaceutical industry in the Israeli Manufacturer's Association.
In 1931, Friedländer married Charlotte Mühsam and had two children. After 24 years, Friedländer and Charlotte divorced. In May 1945, Friedländer married Johanna (Hansi) Singer from the Cohen family, a mother to her son from her first marriage. Together they had one daughter.
Teva Pharmaceutical Industries concern LTD. grants every second year the "Teva founder's prize" to scientist for Excellency. Among them, an award in the name of Friedländer is given.
On September 14, 2016, a circle located at the intersection between the streets Haklai and Shachrai in Bayit VeGan was inaugurated in the name of Friedländer: "The founder of Teva, the pioneer of the pharmaceutical industry in Israel." | https://en.wikipedia.org/wiki/Günther_Friedländer |
The Günther Laukien Prize is a prize presented at the Experimental Nuclear Magnetic Resonance Conference "to recognize recent cutting-edge experimental NMR research with a high probability of enabling beneficial new applications". [ 1 ] The prize was established in 1999 in memoriam to Günther Laukien , who was a pioneer in NMR research. The prize money of $20,000 is financed by Bruker , [ 2 ] the company founded by Laukien. [ 1 ] The recipients of the Günther Laukien Prize have been: [ 3 ]
This science awards article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Günther_Laukien_Prize |
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