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archive. org / web / 20070106114002 / http : / / www. wwf. org. uk / filelibrary / pdf / mpas - marinespacialplanning. pdf douvere, fanny ; ehler, charles n. 2006 ( 2006 ). the international perspective : lessons from recent european experience with marine spatial planning ( pdf ). symposium on management for spatial and temporal complexity in ocean ecosystems in the 21st century at the 20th annual meeting of the society for conservation biology. san jose, california. { { cite conference } } : cs1 maint : numeric names : authors list ( link ) gopnik, morgan ; fieseler, clare ; cantral, laura ; mcclellan, kate ; pendleton, linwood ; crowder, larry ( 2012 ). " coming to the table : early stakeholder engagement in marine spatial planning ". marine policy. 36 ( 5 ) : 1139 β 49. doi : 10. 1016 / j. marpol. 2012. 02. 012. stelzenmuller, vanessa ; breen, patricia ; stamford, tammy ; thomsen, frank ; badalamenti, fabio ; borja, angel ; buhl - mortensen, lene ; carlstom, julia ; d'anna, giovanni ; dankers, norbert ; degraer, steven ; dujin, mike ; fiorentino, fabio ; galparsoro, ibon ; giakoumi, sylvaine ; gristina, michele ; johnson, kate ; jones, peter j. s. ; katsanevakis, stelios ; knittweis, leyla ; kyriazi, zacharoula ; pipitone, carlo ; piwowarczyk, joanna ; rabaut, marijn ; sΓΈrensen, thomas k. ; van dalfsen, jan ; vassilopoulou, vassiliki ; vega fernandez, tomas ; vincx, magda ; et al. ( 2013 ). " monitoring and evaluation of spatially managed areas : a generic framework for implementation of ecosystem based marine management and its application ". marine policy. 37 : 149 β 64. doi : 10. 1016 / j. marpol. 2012. 04. 012. erbach, gregor. " spatial planning for the'blue economy': maritime spatial planning and integrated coastal management " ( pdf ). library briefing. library of the european parliament. retrieved 2 may 2013
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marpol. 2012. 04. 012. erbach, gregor. " spatial planning for the'blue economy': maritime spatial planning and integrated coastal management " ( pdf ). library briefing. library of the european parliament. retrieved 2 may 2013. = = external links and references = = unesco international ocean council msp guide noaa's msp information site marine spatial planning from plymouth marine institute white house memorandum creating interagency ocean policy task force mesma toolbox for monitoring and evaluation of marine spatial planning
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the techila distributed computing engine ( earlier known as techila grid ) is a commercial grid computing software product. techila distributed computing engine is developed and licensed by techila technologies ltd, a privately held company headquartered in tampere, finland. the product is also available as an on - demand solution in google cloud launcher, the online marketplace created and operated by google. according to idc, techila enables organizations to create hpc infrastructure without the capital investments and operating expenses required by new hpc hardware. = = product features = = techila distributed computing engine is a distributed computing middleware and management solution, which can be used to access and manage on - premises and cloud it resources for various high - performance computing ( hpc ) uses, including high - throughput computing ( htc ) scenarios. it creates a scalable computing service and execution environment that can also support applications that are deployed within production environments. the technology of techila distributed computing engine is built on an autonomic computing architecture that is patented by techila technologies. this has facilitated the development of features such as automated system management and fault tolerance, which can simplify the deployment, use, and administration of large - scale distributed computing systems. = = architecture = = = = = techila server = = = techila server is a java - based software product, which is designed to optimize the performance of a techila distributed computing engine environment and the jobs in it. the optimization done by techila server supports large jobs, and can also make the system suitable for running small computational jobs. the performance of techila distributed computing engine in different scenarios was evaluated in a thesis at the tampere university of technology. originally, the techila server was delivered as an embedded appliance. the embedded appliance product was discontinued in 2012. currently, techila server is delivered either as a virtual appliance or using cloud - specific deployment tools. = = = techila worker = = = techila worker is the software agent that must be installed on each computer that will participate in a techila distributed computing engine environment. the computers can be physical, or they can be virtualized computers running on a hypervisor or in a cloud virtual machine. techila distributed computing engine supports following public cloud services : microsoft azure, amazon ec2 and google compute engine. once the techila worker software is installed on a computer, it will authenticate the computer to the techila server using a certificate, and the system will use self - management to automatically confi
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microsoft azure, amazon ec2 and google compute engine. once the techila worker software is installed on a computer, it will authenticate the computer to the techila server using a certificate, and the system will use self - management to automatically configure the computer to run jobs received from the techila server. techila worker is a java - based client middleware component that can be run on microsoft windows or linux. because of this, the client computers participating in the techila distributed computing engine system can have different hardware and software platforms. techila worker software runs on the lowest possible priority on the computer. the techila worker is also interoperable with batch - queuing systems, like the slurm, torque, or oracle grid engine ( previously known as sun grid engine, sge ). this interoperability allows existing hpc users to use their existing infrastructures as a part of a techila distributed computing engine system without the techila worker interfering with the other system. = = = techila sdk = = = techila sdk ( earlier known as techila grid management kit or techila gmk ) is a library of software components that connect applications to the techila distributed computing engine environment. the sdk includes plug - ins for many commonly used research and development tools and languages, such as matlab, r, python, perl, java, c # /. net c / c + +, fortran, and command - line interface script. the applications that have been developed using application programming interfaces in the techila sdk can also be deployed within production environments and run as a service in a soa environment. techila sdk supports both windows and linux operating systems. = = = administrator user interface = = = a web - based administrator user interface provides administrators an interface to the techila server. the administrator user interface allows monitoring system activity, view and control job execution, execution policy, monitor and control techila workers and techila worker groups, control security settings, and manage users. = = history = = the motivation for techila distributed computing engine was to simplify grid computing, enabling fast simulations, and analyses without the complexity associated with traditional high - performance computing systems. the security of the techila distributed computing engine was evaluated by nixu ltd in 2008. following this evaluation, the technology gained acceptance in security - sensitive industries, including finance and insurance, engineering, and pharmaceuticals. in 2011, a research team at the university of helsinki demonstrated the techila distributed computing engine β s ability
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##u ltd in 2008. following this evaluation, the technology gained acceptance in security - sensitive industries, including finance and insurance, engineering, and pharmaceuticals. in 2011, a research team at the university of helsinki demonstrated the techila distributed computing engine β s ability to autonomously manage large - scale computing environments, including extensive deployments of windows azure cloud instances. the university also showcased how the engine enhances the usability and efficiency of large - scale cluster resources in projects utilizing matlab, r, python, java, and c / c + + / c #. the techila distributed computing engine system allows computational resources to be organized into device groups, to improve control for organizational, security, compliance, and administrative needs. despite its capacity for managing large - scale systems such as csc β it center for science, the engine is equally effective in smaller environments. for instance, the tutgrid at tampere university of technology uses techila to harness idle capacity from desktop pcs and other computers for scientific computing tasks. = = external links = = google cloud platform blog about techila available in google cloud launcher software systems for distributed scientific computing innofinland prizes of the president of the republic 2009 to techila ansys advantage volume vii - a perfect fit = = references = =
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a light valve ( lv ) is a device for varying the quantity of light, from a source, which reaches a target. examples of targets are computer screen surfaces, or a wall screen in the case of a light projector. there are two basic principles of achieving this. one is by deflecting the light on its way to the target ( a reflective lv ). the other method is to block the light ( a transmissive lv ). the blocking method has found its way into liquid crystal displays ( lcds ), video projectors and rear projection tvs. in this type of screens and projectors, the source light is first polarised by a filter in one direction and then passed on to another filter, filled with liquid crystals. by changing the voltage applied to this crystal filter, it will work as a switching polarising filter, giving different gray scales of the light coming out. the light is changed only once for each image frame. the light valve thus consists of the two polarising filters, where one has a voltage controlled switch function thanks to the properties of the liquid crystals. this type of valve is often referred to as a liquid crystal light valve. the other principle, the reflective lv, works by either reflecting the light towards the target or deflecting it away. the portion of light that is reflected on the target decides the gray scale. this re - and deflection occurs many times a second. should this happen at too low a frequency, the human eye and brain would perceive it as flickering, but due to sufficiently high frequency, a human will be " tricked " into viewing it as a continuum, a smooth shift in brightness. examples of the reflective lv type are the digital micromirror device ( dmd ), eidophor's oil - film based system, and the grating light valve. = = see also = = femtosecond pulse shaping multiphoton intrapulse interference phase scan spatial light modulator = = references = =
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the diffie β hellman problem ( dhp ) is a mathematical problem first proposed by whitfield diffie and martin hellman in the context of cryptography and serves as the theoretical basis of the diffie β hellman key exchange and its derivatives. the motivation for this problem is that many security systems use one - way functions : mathematical operations that are fast to compute, but hard to reverse. for example, they enable encrypting a message, but reversing the encryption is difficult. if solving the dhp were easy, these systems would be easily broken. = = problem description = = the diffie β hellman problem is stated informally as follows : given an element g { \ displaystyle g } and the values of g x { \ displaystyle g ^ { x } } and g y { \ displaystyle g ^ { y } }, what is the value of g x y { \ displaystyle g ^ { xy } }? formally, g { \ displaystyle g } is a generator of some group ( typically the multiplicative group of a finite field or an elliptic curve group ) and x { \ displaystyle x } and y { \ displaystyle y } are randomly chosen integers. for example, in the diffie β hellman key exchange, an eavesdropper observes g x { \ displaystyle g ^ { x } } and g y { \ displaystyle g ^ { y } } exchanged as part of the protocol, and the two parties both compute the shared key g x y { \ displaystyle g ^ { xy } }. a fast means of solving the dhp would allow an eavesdropper to violate the privacy of the diffie β hellman key exchange and many of its variants, including elgamal encryption. = = computational complexity = = in cryptography, for certain groups, it is assumed that the dhp is hard, and this is often called the diffie β hellman assumption. the problem has survived scrutiny for a few decades and no " easy " solution has yet been publicized. as of 2006, the most efficient means known to solve the dhp is to solve the discrete logarithm problem ( dlp ), which is to find x given g and gx. in fact, significant progress ( by den boer, maurer, wolf, boneh and lipton ) has been made towards showing that over many groups the dhp is almost as hard as the dlp. there is no proof to date that either
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in fact, significant progress ( by den boer, maurer, wolf, boneh and lipton ) has been made towards showing that over many groups the dhp is almost as hard as the dlp. there is no proof to date that either the dhp or the dlp is a hard problem, except in generic groups ( by nechaev and shoup ). a proof that either problem is hard implies that p = np. = = other variants = = many variants of the diffie β hellman problem have been considered. the most significant variant is the decisional diffie β hellman problem ( ddhp ), which is to distinguish gxy from a random group element, given g, gx, and gy. sometimes the dhp is called the computational diffie β hellman problem ( cdhp ) to more clearly distinguish it from the ddhp. recently groups with pairings have become popular, and in these groups the ddhp is easy, yet the cdhp is still assumed to be hard. for less significant variants of the dhp see the references. = = see also = = discrete logarithm problem elliptic - curve cryptography elliptic - curve diffie β hellman diffie β hellman key exchange = = references = =
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tides in marginal seas are tides affected by their location in semi - enclosed areas along the margins of continents and differ from tides in the open oceans. tides are water level variations caused by the gravitational interaction between the moon, the sun and the earth. the resulting tidal force is a secondary effect of gravity : it is the difference between the actual gravitational force and the centrifugal force. while the centrifugal force is constant across the earth, the gravitational force is dependent on the distance between the two bodies and is therefore not constant across the earth. the tidal force is thus the difference between these two forces on each location on the earth. in an idealized situation, assuming a planet with no landmasses ( an aqua planet ), the tidal force would result in two tidal bulges on opposite sides of the earth. this is called the equilibrium tide. however, due to global and local ocean responses different tidal patterns are generated. the complicated ocean responses are the result of the continental barriers, resonance due to the shape of the ocean basin, the tidal waves impossibility to keep up with the moons tracking, the coriolis acceleration and the elastic response of the solid earth. in addition, when the tide arrives in the shallow seas it interacts with the sea floor which leads to the deformation of the tidal wave. as a results, tides in shallow waters tend to be larger, of shorter wavelength, and possibly nonlinear relative to tides in the deep ocean. = = tides on the continental shelf = = the transition from the deep ocean to the continental shelf, known as the continental slope, is characterized by a sudden decrease in water depth. in order to apply to the conservation of energy, the tidal wave has to deform as a result of the decrease in water depth. the total energy of a linear progressive wave per wavelength is the sum of the potential energy ( pe ) and the kinetic energy ( ke ). the potential and kinetic energy integrated over a complete wavelength are the same, under the assumption that the water level variations are small compared to the water depth ( Ξ· < < h { \ displaystyle \ eta < < h } ). 0 Ξ» p e = 0 Ξ» k e = 1 2 Ο g 0 Ξ» Ξ· 2 d x { \ displaystyle \ int _ { 0 } ^ { \ lambda } pe = \ int _ { 0 } ^ { \ lambda } ke = { \ frac { 1 } { 2 } } \ rho g \ int _ { 0 } ^ { \ lambda }
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_ { 0 } ^ { \ lambda } pe = \ int _ { 0 } ^ { \ lambda } ke = { \ frac { 1 } { 2 } } \ rho g \ int _ { 0 } ^ { \ lambda } \ eta ^ { 2 } dx } where Ο { \ displaystyle \ rho } is the density, g { \ displaystyle g } the gravitation acceleration and Ξ· { \ displaystyle \ eta } the vertical tidal elevation. the total wave energy becomes : e = Ο g 0 Ξ» Ξ· 2 d x { \ displaystyle e = \ rho g \ int _ { 0 } ^ { \ lambda } \ eta ^ { 2 } dx } if we now solve for a harmonic wave Ξ· ( x ) = a c o s ( k x ) { \ displaystyle \ eta ( x ) = acos ( kx ) }, where k { \ displaystyle k } is the wave number and a { \ displaystyle a } the amplitude, the total energy per unit area of surface becomes : e s = 1 2 Ο g a 2 { \ displaystyle e _ { s } = { \ frac { 1 } { 2 } } \ rho ga ^ { 2 } } a tidal wave has a wavelength that is much larger than the water depth. and thus according to the dispersion of gravity waves, they travel with the phase and group velocity of a shallow water wave : c p = c g = g h { \ displaystyle c _ { p } = c _ { g } = { \ sqrt { gh } } }. the wave energy is transmitted by the group velocity of a wave and thus the energy flux ( f e { \ displaystyle f _ { e } } ) is given by : f e = 1 2 Ο g a 2 g h { \ displaystyle f _ { e } = { \ frac { 1 } { 2 } } \ rho ga ^ { 2 } { \ sqrt { gh } } } the energy flux needs to be conserved and with Ο { \ displaystyle \ rho } and g { \ displaystyle g } constant, this leads to : f e, 1 = f e, 2 a 1 2 g h 1 = a 2 2 g h 2 { \ displaystyle f _ { e, 1 } = f _ { e, 2 } \ longrightarrow { a _ { 1 } } ^ { 2 } { \ sqrt
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2 g h 1 = a 2 2 g h 2 { \ displaystyle f _ { e, 1 } = f _ { e, 2 } \ longrightarrow { a _ { 1 } } ^ { 2 } { \ sqrt { gh _ { 1 } } } = { a _ { 2 } } ^ { 2 } { \ sqrt { gh _ { 2 } } } } where h 2 < h 1 { \ displaystyle h2 < h1 } and thus a 2 > a 1 { \ displaystyle a _ { 2 } > a _ { 1 } }. when the tidal wave propagates onto the continental shelf, the water depth ( h ) { \ displaystyle ( h ) } decreases. in order to conserve the energy flux, the amplitude of the wave needs to increase ( see figure 1 ). = = = transmission coefficient = = = the above explanation is a simplification as not all tidal wave energy is transmitted, but it is partly reflected at the continental slope. the transmission coefficient of the tidal wave is given by : a 2 a 1 = 2 c 1 ( c 1 + c 2 ) { \ displaystyle { \ frac { a _ { 2 } } { a _ { 1 } } } = { \ frac { 2c _ { 1 } } { ( c _ { 1 } + c _ { 2 } ) } } } this equation indicates that when c 1 = c 2 { \ displaystyle c _ { 1 } = c _ { 2 } } the transmitted tidal wave has the same amplitude as the original wave. furthermore, the transmitted wave will be larger than the original wave when c 1 > c 2 { \ displaystyle c _ { 1 } > c _ { 2 } } as is the case for the transition to the continental shelf. the reflected wave amplitude ( a β² { \ displaystyle a ^ {'} } ) is determined by the reflection coefficient of the tidal wave : a β² a 1 = c 1 β c 2 ( c 1 + c 2 ) { \ displaystyle { \ frac { a ^ {'} } { a _ { 1 } } } = { \ frac { c _ { 1 } - c _ { 2 } } { ( c _ { 1 } + c _ { 2 } ) } } } this equation indicates that when c 1 = c 2 { \ displaystyle c _ { 1 } = c _ { 2 } } there is no reflected wave and if c
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( c _ { 1 } + c _ { 2 } ) } } } this equation indicates that when c 1 = c 2 { \ displaystyle c _ { 1 } = c _ { 2 } } there is no reflected wave and if c 1 > c 2 { \ displaystyle c _ { 1 } > c _ { 2 } } the reflected tidal wave will be smaller than the original tidal wave. = = = internal tide and mixing = = = at the continental shelf the reflection and transmission of the tidal wave can lead to the generation of internal tides on the pycnocline. the surface ( i. e. barotropic ) tide generates these internal tides where stratified waters are forced upwards over a sloping bottom topography. the internal tide extracts energy from the surface tide and propagates both in shoreward and seaward direction. the shoreward propagating internal waves shoals when reaching shallower water where the wave energy is dissipated by wave breaking. the shoaling of the internal tide drives mixing across the pycnocline, high levels carbon sequestration and sediment resuspension. furthermore, through nutrient mixing the shoaling of the internal tide has a fundamental control on the functioning of ecosystems on the continental margin. = = tidal propagation along coasts = = after entering the continental shelf, a tidal wave quickly faces a boundary in the form of a landmass. when the tidal wave reaches a continental margin, it continues as a boundary trapped kelvin wave. along the coast, a boundary trapped kelvin is also known as a coastal kelvin wave or edge wave. a kelvin wave is a special type of gravity wave that can exist when there is ( 1 ) gravity and stable stratification, ( 2 ) sufficient coriolis force and ( 3 ) the presence of a vertical boundary. kelvin waves are important in the ocean and shelf seas, they form a balance between inertia, the coriolis force and the pressure gradient force. the simplest equations that describe the dynamics of kelvin waves are the linearized shallow water equations for homogeneous, in - viscid flows. these equations can be linearized for a small rossby number, no frictional forces and under the assumption that the wave height is small compared to the water depth ( Ξ· < < h { \ displaystyle \ eta < < h } ). the linearized depth - averaged shallow water equations become : u momentum equation : β u β t β f v = β g β Ξ· β x { \ displaystyle { \
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< < h { \ displaystyle \ eta < < h } ). the linearized depth - averaged shallow water equations become : u momentum equation : β u β t β f v = β g β Ξ· β x { \ displaystyle { \ frac { \ partial u } { \ partial t } } - fv = - g { \ frac { \ partial \ eta } { \ partial x } } } v momentum equation : β v β t + f u = β g β Ξ· β y { \ displaystyle { \ frac { \ partial v } { \ partial t } } + fu = - g { \ frac { \ partial \ eta } { \ partial y } } } the continuity equation : β Ξ· β t + h ( β u β x + β v β y ) = 0 { \ displaystyle { \ frac { \ partial \ eta } { \ partial t } } + h ( { \ frac { \ partial u } { \ partial x } } + { \ frac { \ partial v } { \ partial y } } ) = 0 } where u { \ displaystyle u } is the zonal velocity ( x { \ displaystyle x } direction ), v { \ displaystyle v } the meridional velocity ( y { \ displaystyle y } direction ), t { \ displaystyle t } is time and f { \ displaystyle f } is the coriolis frequency. kelvin waves are named after lord kelvin, who first described them after finding solutions to the linearized shallow water equations with the boundary condition u ( x, y, t ) = 0 { \ displaystyle u ( x, y, t ) = 0 }. when this assumption is made the linearized depth - averaged shallow water equations that can describe a kelvin wave become : u momentum equation : v = β g f β Ξ· β x { \ displaystyle v = { \ frac { - g } { f } } { \ frac { \ partial \ eta } { \ partial x } } } v momentum equation : β v β t = β g β Ξ· β y { \ displaystyle { \ frac { \ partial v } { \ partial t } } = - g { \ frac { \ partial \ eta } { \ partial y } } } the continuity equation : β Ξ· β t + h β v β y = 0 { \ displaystyle { \ frac { \ partial \ eta } { \ partial t } } + h {
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partial \ eta } { \ partial y } } } the continuity equation : β Ξ· β t + h β v β y = 0 { \ displaystyle { \ frac { \ partial \ eta } { \ partial t } } + h { \ frac { \ partial v } { \ partial y } } = 0 } now it is possible to get an expression for Ξ· { \ displaystyle \ eta }, by taking the time derivative of the continuity equation and substituting the momentum equation : β 2 Ξ· β t 2 β g h β 2 Ξ· β y 2 = 0 { \ displaystyle { \ frac { \ partial ^ { 2 } \ eta } { \ partial t ^ { 2 } } } - gh { \ frac { \ partial ^ { 2 } \ eta } { \ partial y ^ { 2 } } } = 0 } the same can be done for v { \ displaystyle v }, by taking the time derivative of the v momentum equation and substituting the continuity equation β 2 v β t 2 β g h β 2 v β y 2 = 0 { \ displaystyle { \ frac { \ partial ^ { 2 } v } { \ partial t ^ { 2 } } } - gh { \ frac { \ partial ^ { 2 } v } { \ partial y ^ { 2 } } } = 0 } both of these equations take the form of the classical wave equation, where c = g h { \ displaystyle c = { \ sqrt { gh } } }. which is the same velocity as the tidal wave and thus of a shallow water wave. these preceding equations govern the dynamics of a one - dimensional non - dispersive wave, for which the following general solution exist : Ξ· = β h f ( y + c t ) e β x r { \ displaystyle \ eta = - h \ f ( y + ct ) \ e ^ { \ frac { - x } { r } } } v = g h f ( y + c t ) e β x r { \ displaystyle v = { \ sqrt { gh } } \ f ( y + ct ) \ e ^ { \ frac { - x } { r } } } where length r = g h f { \ displaystyle r = { \ frac { \ sqrt { gh } } { f } } } is the rossby radius of deformation and f ( y + c t ) { \ displaystyle f ( y + ct
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h f { \ displaystyle r = { \ frac { \ sqrt { gh } } { f } } } is the rossby radius of deformation and f ( y + c t ) { \ displaystyle f ( y + ct ) } is an arbitrary function describing the wave motion. in the most simple form f { \ displaystyle f } is a cosine or sine function which describes a wave motion in the positive and negative direction. the rossby radius of deformation is a typical length scale in the ocean and atmosphere that indicates when rotational effects become important. the rossby radius of deformation is a measure for the trapping distance of a coastal kelvin wave. the exponential term results in an amplitude that decays away from the coast. the expression of tides as a bounded kelvin wave is well observable in enclosed shelf seas around the world ( e. g. the english channel, the north sea or the yellow sea ). animation 1 shows the behaviour of a simplified case of a kelvin wave in an enclosed shelf sea for the case with ( lower panel ) and without friction ( upper panel ). the shape of an enclosed shelf sea is represented as a simple rectangular domain in the northern hemisphere which is open on the left hand side and closed on the right hand side. the tidal wave, a kelvin wave, enters the domain in the lower left corner and travels to the right with the coast on its right. the sea surface height ( ssh, left panels of animation 1 ), the tidal elevation, is maximum at the coast and decreases towards the centre of the domain. the tidal currents ( right panels of animation 1 ) are in the direction of wave propagation under the crest and in the opposite direction under the through. they are both maximum under the crest and the trough of the waves and decrease towards the centre. this was expected as the equations for Ξ· { \ displaystyle \ eta } and v { \ displaystyle v } are in phase as they both depend on the same arbitrary function describing the wave motion and exponential decay term. therefore this set of equations describes a wave that travels along the coast with a maximum amplitude at the coast which declines towards the ocean. these solutions also indicate that a kelvin wave always travels with the coast on their right hand side in the northern hemisphere and with the coast at their left hand side in the southern hemisphere. in the limit of no rotation where f β 0 { \ displaystyle f \ rightarrow 0 }, the exponential term increase without a bound and the wave will become a simple gravity wave
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the coast at their left hand side in the southern hemisphere. in the limit of no rotation where f β 0 { \ displaystyle f \ rightarrow 0 }, the exponential term increase without a bound and the wave will become a simple gravity wave orientated perpendicular to the coast. in the next section, it will be shown how these kelvin waves behaves when traveling along a coast, in an enclosed shelf seas or in estuaries and basins. = = = tides in enclosed shelf seas = = = the expression of tides as a bounded kelvin wave is well observable in enclosed shelf seas around the world ( e. g. the english channel, the north sea or the yellow sea ). animation 1 shows the behaviour of a simplified case of a kelvin wave in an enclosed shelf sea for the case with ( lower panel ) and without friction ( upper panel ). the shape of an enclosed shelf sea is represented as a simple rectangular domain in the northern hemisphere which is open on the left hand side and closed on the right hand side. the tidal wave, a kelvin wave, enters the domain in the lower left corner and travels to the right with the coast on its right. the sea surface height ( ssh, left panels of animation 1 ), the tidal elevation, is maximum at the coast and decreases towards the centre of the domain. the tidal currents ( right panels of animation 1 ) are in the direction of wave propagation under the crest and in the opposite direction under the through. they are both maximum under the crest and the trough of the waves and decrease towards the centre. this was expected as the equations for Ξ· { \ displaystyle \ eta } and v { \ displaystyle v } are in phase as they both depend on the same arbitrary function describing the wave motion and exponential decay term. on the enclosed right hand side, the kelvin wave is reflected and because it always travels with the coast on its right, it will now travel in the opposite direction. the energy of the incoming kelvin wave is transferred through poincare waves along the enclosed side of the domain to the outgoing kelvin wave. the final pattern of the ssh and the tidal currents is made up of the sum of the two kelvin waves. these two can amplify each other and this amplification is maximum when the length of the shelf sea is a quarter wavelength of the tidal wave. next to that, the sum of the two kelvin waves result in several static minima's in the centre of the domain which hardly experience any tidal motion, these are called amphid
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of the shelf sea is a quarter wavelength of the tidal wave. next to that, the sum of the two kelvin waves result in several static minima's in the centre of the domain which hardly experience any tidal motion, these are called amphidromic points. in the upper panel of figure 2, the absolute time averaged ssh is shown in red shading and the dotted lines show the zero tidal elevation level at roughly hourly intervals, also known as cotidal lines. where these lines intersect the tidal elevation is zero during a full tidal period and thus this is the location of the amphidromic points. in the real world, the reflected kelvin wave has a lower amplitude due to energy loss as a result of friction and through the transfer via poincare waves ( lower left panel of animation 1 ). the tidal currents are proportional to the wave amplitude and therefore also decrease on the side of the reflected wave ( lower right panel of animation 1 ). finally, the static minima's are no longer in the centre of the domain as wave amplitude is no longer symmetric. therefore, the amphidromic points shift towards the side of the reflected wave ( lower panel figure 2 ). the dynamics of a tidal kelvin wave in enclosed shelf sea is well manifested and studied in the north sea. = = = tides in estuaries and basins = = = when tides enter estuaries or basins, the boundary conditions change as the geometry changes drastically. the water depth becomes shallower and the width decreases, next to that the depth and width become significantly variable over the length and width of the estuary or basin. as a result the tidal wave deforms which affects the tidal amplitude, phase speed and the relative phase between tidal velocity and elevation. the deformation of the tide is largely controlled by the competition between bottom friction and channel convergence. channel convergence increases the tidal amplitude and phase speed as the energy of the tidal wave is traveling through a smaller area while bottom friction decrease the amplitude through energy loss. the modification of the tide leads to the creation of overtides ( e. g. m 4 { \ displaystyle m _ { 4 } } tidal constituents ) or higher harmonics. these overtides are multiples, sums or differences of the astronomical tidal constituents and as a result the tidal wave can become asymmetric. a tidal asymmetry is a difference between the duration of the rise and the fall of the tidal water elevation and this can manifest itself as a difference in flood / ebb tidal currents. the tidal asymmetry and
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can become asymmetric. a tidal asymmetry is a difference between the duration of the rise and the fall of the tidal water elevation and this can manifest itself as a difference in flood / ebb tidal currents. the tidal asymmetry and the resulting currents are important for the sediment transport and turbidity in estuaries and tidal basins. each estuary and basin has its own distinct geometry and these can be subdivided in several groups of similar geometries with its own tidal dynamics. = = see also = = = = references = =
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in solid mechanics, in the field of rotordynamics, the critical speed is the theoretical angular velocity that excites the natural frequency of a rotating object, such as a shaft, propeller, leadscrew, or gear. as the speed of rotation approaches the object's natural frequency, the object begins to resonate, which dramatically increases system vibration. the resulting resonance occurs regardless of orientation. when the rotational speed is equal to the natural frequency, then that speed is referred to as a critical speed. = = critical speed of shafts = = all rotating shafts, even in the absence of external load, will deflect during rotation. the unbalanced mass of the rotating object causes deflection that will create resonant vibration at certain speeds, known as the critical speeds. the magnitude of deflection depends upon the following : stiffness of the shaft and its support total mass of shaft and attached parts unbalance of the mass with respect to the axis of rotation the amount of damping in the system in general, it is necessary to calculate the critical speed of a rotating shaft, such as a fan shaft, in order to avoid issues with noise and vibration. = = critical speed equation = = like vibrating strings and other elastic structures, shafts and beams can vibrate in different mode shapes, with corresponding natural frequencies. the first vibrational mode corresponds to the lowest natural frequency. higher modes of vibration correspond to higher natural frequencies. often when considering rotating shafts, only the first natural frequency is needed. there are two main methods used to calculate critical speed β the rayleigh β ritz method and dunkerley's method. both calculate an approximation of the first natural frequency of vibration, which is assumed to be nearly equal to the critical speed of rotation. the rayleigh β ritz method is discussed here. for a shaft that is divided into n segments, the first natural frequency for a given beam, in rad / s, can be approximated as : Ο 1 β g i = 1 n w i y i i = 1 n w i y i 2 { \ displaystyle \ omega _ { 1 } \ approx { \ sqrt { \ frac { g \ sum _ { i = 1 } ^ { n } { w _ { i } y _ { i } } } { \ sum _ { i = 1 } ^ { n } { w _ { i } y _ { i } ^ { 2 } } } } } } where g is the acceleration of gravity, and
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} y _ { i } } } { \ sum _ { i = 1 } ^ { n } { w _ { i } y _ { i } ^ { 2 } } } } } } where g is the acceleration of gravity, and the w i { \ displaystyle w _ { i } } are the weights of each segment, and the y i { \ displaystyle y _ { i } } are the static deflections ( under gravitational loading only ) of the center of each segment. generally speaking, if n is 2 or higher, this method tends to slightly overestimate the first natural frequency, with the estimate becoming better the higher n is. if n is only 1, this method tends to underestimate the first natural frequency, but the equation simplifies to : Ο 1 β g y m a x { \ displaystyle \ omega _ { 1 } \ approx { \ sqrt { \ frac { g } { y _ { max } } } } } where y m a x { \ displaystyle y _ { max } } is the max static deflection of the shaft. these speeds are in rad / s, but can be converted to rpm by multiplying by 60 2 β Ο { \ displaystyle { \ frac { 60 } { 2 * \ pi } } }. if a beam has multiple types of loading, deflections can be found for each, and then summed. if the shaft diameter changes along its length, deflection calculations become much more difficult. the static deflection expresses the relationship between rigidity of the shaft and inertial forces ; it includes all the loads applied to the shaft when placed horizontally. however, the relationship is valid no matter what the orientation of the shaft is. a system's critical speeds depend upon the magnitude, location, and relative phase of shaft unbalance, the shaft's geometry and mechanical properties, and the stiffness and mass properties of the support structure. many practical applications suggest as good practice that the maximum operating speed should not exceed 75 % of the critical speed ; however, some systems operate above the first critical speed, or supercritically. in such cases, it is important to accelerate the shaft through the first natural frequency quickly so that large deflections don't develop. = = see also = = damping ratio oscillate natural frequency resonance campbell diagram vibration = = references = =
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the epidemiology of herpes simplex is of substantial epidemiologic and public health interest. worldwide, the rate of infection with herpes simplex virus β counting both hsv - 1 and hsv - 2 β is around 90 %. although many people infected with hsv develop labial or genital lesions ( herpes simplex ), the majority are either undiagnosed or display no physical symptoms β individuals with no symptoms are described as asymptomatic or as having subclinical herpes. in many infections, the first symptom a person will have of their own infection is the horizontal transmission to a sexual partner or the vertical transmission of neonatal herpes to a newborn at term. since most asymptomatic individuals are unaware of their infection, they are considered at high risk for spreading hsv. many studies have been performed around the world to estimate the numbers of individuals infected with hsv - 1 and hsv - 2 by determining if they have developed antibodies against either viral species. this information provides population prevalence of hsv viral infections in individuals with or without active disease. note that there are population subgroups that are more vulnerable for hsv infections, such as cancer chemotherapy patients. = = europe = = large differences in hsv - 1 seroprevalence are seen in different european countries. hsv - 1 seroprevalence is high in bulgaria ( 83. 9 % ) and the czech republic ( 80. 6 % ), and lower in belgium ( 67. 4 % ), the netherlands ( 56. 7 % ), and finland ( 52. 4 % ). the typical age at which hsv - 1 infection is acquired ranges from 5 to 9 years in central and eastern european countries like bulgaria and the czech republic, to over 25 years of age in northern european countries such as finland, the netherlands, germany, and england and wales. young adults in northern european countries are less likely to be infected with hsv - 1. european women are more likely to be hsv - 1 seropositive than men. hsv - 2 seropositivity is widely distributed in europeans older than 12, although there are large differences in the percentage of the population exposed to hsv - 2. bulgaria has a high ( 23. 9 % ) hsv - 2 seroprevalence relative to other european countries : germany ( 13. 9 % ), finland ( 13. 4 % ), belgium ( 11. 1 % ),
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. bulgaria has a high ( 23. 9 % ) hsv - 2 seroprevalence relative to other european countries : germany ( 13. 9 % ), finland ( 13. 4 % ), belgium ( 11. 1 % ), the netherlands ( 8. 8 % ), the czech republic ( 6. 0 % ), and england and wales ( 4. 2 % ). women are more likely to be seropositive than men, and likely acquire the virus at an earlier age. in each country of europe, hsv - 2 seropositivity becomes more common from adolescence onwards and increases in the population with age, with a decline in the older age groups in some countries. = = north america = = = = = united states = = = the most recent data for hsv - 2 was published in march 2010, based on a national health and nutrition examination survey study performed between 2005 and 2013 by cdc. about 1 in 6 americans ( 16. 2 % ) aged 14 to 49 is infected with hsv - 2. hsv - 2 prevalence was nearly twice as high among women ( 20. 9 % ) than men ( 11. 5 % ), and was more than three times higher among blacks ( 39. 2 % ) than non - hispanic whites ( 12. 3 % ). the most affected group was black women, with a prevalence rate of 48 %. prevalence increased with age and number of partners. only 18. 9 % of those infected had previously been aware of their infection. african americans and immigrants from developing countries typically have an hsv - 1 seroprevalance in their adolescent population that is two or three times higher than that of caucasian americans. many white americans become sexually active while seronegative for hsv - 1. the absence of antibodies from a prior oral hsv - 1 infection leaves these individuals susceptible to herpes whitlow, herpes gladiatorum, and hsv - 1 genital infection. primary genital infection brings with it the risk of vertical transmission to the neonate, and is highest if the mother contracts a primary infection during the third trimester of pregnancy. in the u. s. the number of genital infections caused by hsv - 1 is now thought to be about 50 % of first episodes of genital infection. in healthy adults, hsv - 2 infection occurs more frequently in the united states than in europe. seroprevalence rates in the united states appeared to be increasing, rising from 16. 4 % in
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of first episodes of genital infection. in healthy adults, hsv - 2 infection occurs more frequently in the united states than in europe. seroprevalence rates in the united states appeared to be increasing, rising from 16. 4 % in 1976 to 21. 8 % in 1994. however, this trend seems to have reversed itself in recent years, dropping to 17. 2 % in 2004. the current prevalence of genital herpes caused by hsv - 2 in the u. s. is roughly one in four or five adults, with approximately 50 million people infected with genital herpes and an estimated 0. 5 million new genital herpes infections occurring each year. african americans appear more susceptible to hsv - 2, although the presence of active genital symptoms is more likely in caucasian americans. the largest increase in hsv - 2 acquisition during the past few years is in white adolescents. people with many lifetime sexual partners and those who are sexually active from a young age are also at higher - risk for the transmission of hsv - 2 in the u. s. due to the anatomical nature of the vagina women are at higher risk than men for acquiring hsv - 2 infection, and the chance of being infected increases with age. this is evident despite women on average having a lower number of sexual partners. as of 2022, the cdc reports that 48 % of african american women and 46 % of african american males in the united states are infected with the hsv - 2 virus. = = = canada = = = according to a study in ontario, of people between the ages of 15 and 16, 26. 9 % of men, 32 % of non - pregnant women, and 55 % of pregnant women tested positive for hsv - 1 antibodies. between the ages of 40 and 44, 54. 7 % of men, 88. 7 % of women, and 69. 2 % of pregnant women tested positive for hsv - 1 antibodies. the overall age - gender standardized seroprevelance for hsv - 1 antibodies was 51. 1 %. teenagers are less likely to be seropositive for hsv - 2 β antibodies against this virus are only found in 0 β 3. 8 % of 15 - and 16 - year - olds. however, 21 % of individuals in their early forties have antibodies against hsv - 2, reflecting the sexually transmitted nature of this virus. when standardising for age, hsv - 2 seroprevalence in ontario for individuals between the ages of 15
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21 % of individuals in their early forties have antibodies against hsv - 2, reflecting the sexually transmitted nature of this virus. when standardising for age, hsv - 2 seroprevalence in ontario for individuals between the ages of 15 and 44 was 9. 1 %. rates for canadian people infected with hsv - 2 is much lower than estimated levels of hsv - 2 seroprevalence in people of a similar age range in the united states. hsv - 2 seroprevalence in pregnant women between the ages of 15 and 44 in british columbia is similar, with 57 % having antibodies for hsv - 1 and 13 % having antibodies for hsv - 2. in british columbia in 1999, the seroprevalence of hsv - 2 antibody in leftover serum submitted for antenatal testing revealed a prevalence of 17. 3 %, ranging from 7. 1 % in women 15 β 19 years old to 28. 2 % in those 40 β 44 years. β’ in attendees at an alberta sexually transmitted infection ( sti ) clinic in 1994 and 1995, the seroprevalence of hsv - 1 and - 2 in leftover sera was 56 % and 19 %, respectively. in nova scotia, 58. 1 % of 1, 790 hsv isolates from genital lesion cultures in women were hsv - 1 ; in men, 36. 7 % of 468 isolates were hsv - 1 = = africa = = = = = sub - saharan africa = = = hsv - 2 is more common in sub - saharan africa than in europe or the north america. up to 82 % of women and 53 % of men in sub - saharan africa are seropositive for hsv - 2. these are the highest levels of hsv - 2 infection in the world, although exact levels vary from country to country in this continent. in most african countries, hsv - 2 prevalence increases with age. however, age - associated decreases in hsv - 2 seroprevalence has been observed for women in uganda and zambia, and in men in ethiopia, benin, and uganda. = = = northern africa = = = genital herpes appears less common in northern africa compared to sub - saharan africa. for example, only 26 % of middle - aged women have antibodies for hsv - 2 in morocco. women are more likely to be infected with hsv - 2 once they are over the age of 40. children in egypt with acute lym
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. for example, only 26 % of middle - aged women have antibodies for hsv - 2 in morocco. women are more likely to be infected with hsv - 2 once they are over the age of 40. children in egypt with acute lymphoblastic leukemia are often infected with hsv from a young age β hsv - 1 or hsv - 2 antibodies are present in an estimated 54 % of children under the age of 5, and 77 % in children over 10 years of age. algerian children are also likely to acquire hsv - 1 infection at a young age ( under 6 ) and 81. 25 % of the population has antibodies to hsv - 1 by the age of 15. = = central and south america = = relative to rates in europe and north america, hsv - 2 seroprevalency is high in central and south america. infection levels are estimated at 20 % to 60 %. during the mid - 1980s, hsv - 2 prevalence was 33 % in 25 - to 29 - year - old women and 45 % in those aged 40 and over in costa rica. in the early 1990s hsv - 2 prevalence was approximately 45 % among women over 60 in mexico. the highest hsv - 2 prevalence in central or south america β 60 % β has been found in colombian middle - aged women, although similar hsv - 2 prevalence has been observed in younger women in haiti ( 54 % ). hsv - 2 infects about 30 % of women over 30 years old in colombia, costa rica, mexico, and panama. hsv - 2 antibodies were found in more than 41 % of women of childbearing age in brazil. however, no increase in seroprevalence was associated with age in women over 40 years old in brazil β hsv - 2 prevalence was estimated at 50 % among women aged 40 β 49, 33 % among women 50 β 59, and 42 % among women over 60. women in brazil are more likely to acquire an hsv - 2 infection if their male partners had history of anal sex and had many sexual partners in his lifetime. in peru, hsv - 2 prevalence is also high among women in their 30s but is lower in men. = = asia = = = = = eastern and south east asia = = = hsv - 1 seroprevalence in some asian countries is low, relative to other countries worldwide, with only 51 % women in thailand, and between 50 and 60 % in japan possessing antibodies. hsv - 2 ser
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asia = = = hsv - 1 seroprevalence in some asian countries is low, relative to other countries worldwide, with only 51 % women in thailand, and between 50 and 60 % in japan possessing antibodies. hsv - 2 seroprevalence in developing asian countries is comparable ( 10 β 30 % ) to that observed in north america and northern europe. however, estimates of hsv - 2 infectivity in thailand are higher than observed in other eastern asian countries ; total hsv - 2 seroprevalence is approximately 37 % in this country. hsv - 2 seroprevalence is low in women in the philippines ( 9 % ), although commencing activity while young is associated with an increase risk of acquiring hsv - 2 infection ; woman starting sexual activity by the time they reach 17 are seven times more likely to be hsv - 2 seropositive than those starting sexual activity when over 21. in south korea, incidence of hsv - 2 infection in those under the age of 20 is low, only 2. 7 % in men and 3. 0 % in women. seroprevalence levels increase in older south koreans however, such that the population over 20 that has antibodies against hsv - 2 is 21. 7 % of men and 28 % of women. = = = southern asia = = = in india 63 % of individuals were seropositive in 2005, within this figure, 33. 3 % were positive for hsv - 1 and 16. 6 % are seropositive for hsv - 2. those with both hsv - 1 and hsv - 2 antibodies are estimated at 13. 3 % of the population. indian men are more likely to be infected with hsv - 2 than women, and increasing seroprevalence of this virus is associated with an increasing age. = = = west asia = = = turkey β high levels of hsv - 1 ( 97 % ) and hsv - 2 ( 42 % ) were found amongst pregnant women in the city of erzurum in eastern anatolia region, turkey. in istanbul however, lower hsv - 2 seroprevalence was observed ; hsv - 2 antibodies were found in 4. 8 % of sexually active adults, while hsv - 1 antibodies were found in 85. 3 %. only 5 % of pregnant women were infected with hsv - 2, and 98 % were infected with hsv - 1. prevalence of these viruses was higher in sex workers of istanbul, reaching
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##v - 1 antibodies were found in 85. 3 %. only 5 % of pregnant women were infected with hsv - 2, and 98 % were infected with hsv - 1. prevalence of these viruses was higher in sex workers of istanbul, reaching levels of 99 % and 60 % for hsv - 1 and hsv - 2 prevalence respectively. jordan β the prevalence of hsv - 2 in jordan is 52. 8 % for men and 41. 5 % for women. israel β hsv - 1 seroprevalence is 59. 8 % in the population of israel and increases with age in both genders but the adolescent seroprevalence has been declining as in most industrialized nations. an estimated 9. 2 % of israeli adults are infected with hsv - 2. infection of either hsv - 1 or hsv - 2 is higher in females ; hsv - 2 seroprevalence reaches 20. 5 % in females in their 40s. these values are similar to levels in hsv infection in europe. antibodies for hsv - 1 or hsv - 2 are also more likely to be found individuals born outside of israel, and individuals residing in jerusalem and southern israel ; people of jewish origin living in israel are less likely to possess antibodies against herpes. among pregnant women in israel a small scale cross sectional study found the prevalence of hsv - 2 infection was 13. 3 % and that of hsv - 1 was 94. 9 %. the hsv - 2 infection rate was 3 - fold higher among immigrants from the former soviet union ( 27. 5 % ) than among israeli - born jewish and arab women ( 9 % ). approximately 78 % of hsv - 2 infections in israel are asymptomatic. hsv - 1 causes 66. 3 % of genital herpes in the tel aviv area. syria β genital herpes infection from hsv - 2 is predicted to be low in syria although hsv - 1 levels are high. hsv - 1 infections is common ( 95 % ) among healthy syrians over the age of 30, while hsv - 2 prevalence is low in healthy individuals ( 0. 15 % ), and persons infected with other sexually transmitted diseases ( 9. 5 % ). high risk groups for acquiring hsv - 2 in syria, include prostitutes and bar girls ; they have 34 % and 20 % seroprevalence respectively. = = oceania = = in australia, a study using data from 1999 revealed the seroprevalence of
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acquiring hsv - 2 in syria, include prostitutes and bar girls ; they have 34 % and 20 % seroprevalence respectively. = = oceania = = in australia, a study using data from 1999 revealed the seroprevalence of hsv - 1 was at 76. 5 %, with significant differences associated with age, gender and indigenous status, which were not specified. an estimated 12 % of australian adults were seropositive for hsv - 2, with higher prevalence in women ( 16 % ) than in men ( 8 % ). larger cities had higher hsv - 2 seroprevalence ( 13 % ) than rural populations ( 9 % ). higher prevalence was found in indigenous australians ( 18 % ) than non - indigenous australians ( 12 % ). as in the u. s., hsv - 1 is increasingly identified as the cause of genital herpes in australians ; hsv - 1 was identified in the anogenital area of only 3 % of the population in 1980, but had risen to 41 % in 2001. this was most common in females and persons under 25. the number of genital herpes infections appears to be rising in new zealand with three times more cases in 1993 compared to 1977. in this country, hsv - 2 affects 60 % more women than men of similar age. = = references = =
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in robotics, the wake - up robot problem refers to a situation where an autonomous robot is carried to an arbitrary location and put to operation, and the robot must localize itself without any prior knowledge. the wake - up robot problem is closely related to the kidnapped robot problem. = = see also = = exploration problem simultaneous localization and mapping = = references = =
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the american board of internal medicine ( abim ) is a 501 ( c ) ( 3 ) nonprofit, self - appointed physician - evaluation organization that certifies physicians practicing internal medicine and its subspecialties. the american board of internal medicine is not a membership society, educational institution, or licensing body. = = history = = the american board of internal medicine was established on february 28, 1936, by the american medical association and the american college of physicians to issue certification to physicians. in 1989, abim began requiring maintenance of certification ( moc ) examinations every 10 years for continued board certification. abim is the largest of 24 member certifying boards of the american board of medical specialties. the american board of internal medicine categorizes physicians into one or more of its 20 subspecialties based on training and the passing of a standardized exam, namely : adolescent medicine adult congenital heart disease advanced heart failure & transplant cardiology cardiovascular disease clinical cardiac electrophysiology intensive care medicine endocrinology, diabetes & metabolism gastroenterology geriatric medicine hematology hospice & palliative medicine hospital medicine infectious disease interventional cardiology medical oncology nephrology pulmonary disease rheumatology sleep medicine transplant hepatology the certification exams'" blueprints " for each of these specialties can be found at their website. the current president and chief executive officer of the american board of internal medicine is furman s. mcdonald, md, mph. the american board of internal medicine adopted a governance structure that consists of three entities, namely a board of directors, abim council, specialty boards and advisory committees, and approval committees. = = certification = = american board of internal medicine board certification demonstrates that physicians have completed a residency in a specified medical specialty and have passed a rigorous knowledge assessment exam. additionally, certification encompasses the six general competencies established by the accreditation council on graduate medical education ( acgme ). following regulations established by the american board of medical specialties, in order to be certified, a physician must : complete the requisite predoctoral medical education meet the training requirements meet the licensure requirements and procedural requirements pass a secure board certification examination physicians may become board certified when they have successfully completed residency or fellowship training and by passing a secure examination. unlike licensure, board certification is not a requirement to practice medicine. many hospitals require internists to be board certified in order to have admitting privileges, and many health plans require certification for contracting or eligibility for select networks. the
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a secure examination. unlike licensure, board certification is not a requirement to practice medicine. many hospitals require internists to be board certified in order to have admitting privileges, and many health plans require certification for contracting or eligibility for select networks. the american board of internal medicine asserts that there is a growing body of research that suggests : a physician's ability to independently and accurately self - assess is in dispute, with research showing no consensus and more clinical experience does not necessarily lead to better outcomes of care. fewer than 30 % of physicians examine their own performance data and try to improve. the moc program structure tries to address these concerns with a sound theoretical rationale via the six acgme competencies framework and a respectable body of scientific evidence, and to address its relationship to patient outcomes, physician performance, validity of the assessment or educational methods utilized and learning or improvement potential. the validity of the studies that the american board of internal medicine cites to support these arguments has been questioned, because the authors of these studies are individuals who are employed by, or have previously been employed by, the american board of medical specialties or its related bodies ( see hawkins, richard e. ). in addition, there appears to be a tightly knit, self - credentialed " patient safety / medical quality " industry developing in the united states, from which the authors of many of the studies supporting maintenance of certification have emerged. the american board of internal medicine is an organization that attempts to assess physicians through proprietary testing and completion of required modules. the american board of internal medicine has issued more than 425, 000 initial certificates in internal medicine and its subspecialties in the united states and its territories since its founding. from 2001 to 2013, american board of internal medicine certified 91, 024 physicians in general internal medicine. from 2001 to 2013, the american board of internal medicine certified more than 10, 000 cardiologists and more than 6, 400 medical oncologists. more than 140, 000 physicians β including more than 8, 000 physicians holding certifications that hold certifications which are valid indefinitely β are currently enrolled in the american board of internal medicine's maintenance of certification program. = = = maintenance of certification ( moc ) = = = the american board of internal medicine asserts that research shows that physician knowledge deteriorates and practice habits and patterns fail to change, over time, in response to medical advances. every 10 years, some internists and subspecialists certified in or after 1990 renew their certifications through the american board
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shows that physician knowledge deteriorates and practice habits and patterns fail to change, over time, in response to medical advances. every 10 years, some internists and subspecialists certified in or after 1990 renew their certifications through the american board of internal medicine's maintenance of certification program. the american board of internal medicine's maintenance of certification program changed in january 2014. the program now requires physicians to : possess a valid medical license earn maintenance of certification points ( points count toward all certificates you are maintaining ) some maintenance of certification activity every two years 100 maintenance of certification points every five years pass maintenance of certification exam in one's specialty every 10 years = = = = criticism of maintenance of certification program = = = = the maintenance of certification program has been criticized for taking time away from patient care, not being proven to improve patient care, and costing more in time and expense than it can justify. on february 3, 2015, the american board of internal medicine announced more changes to the maintenance of certification program. in a press release, the american board of internal medicine apologized that it had " clearly got it wrong ", and it admitted that the program changes in january 2014 were instituted prematurely. the american board of internal medicine has suspended the patient survey and patient safety components for at least two years, and it will make changes to the secure exam to make it more reflective of medical practice among others. the final form of maintenance of certification remains to be seen. on march 10, 2015, an article written by kurt eichenwald for newsweek raised skepticism of the abim foundation and its merit. and there is another organization called the abim foundation that does... well, it's not quite clear what it does. its website reads like a lot of mumbo - jumbo. the foundation conducts surveys on how " organizational leaders have advanced professionalism among practicing physicians. " and it is very proud of its " choosing wisely " program, an initiative " to help providers and patients engage in conversations to reduce overuse of tests and procedures, " with pamphlets, videos and other means. doesn't sound like much, until you crack open the 990s. this organization is loaded. in the tax year ended 2013, it brought in $ 20 million β not from contributions, not from selling a product, not for providing a service. no, the foundation earned $ 20 million on the $ 74 million in assets it holds. the foundation racked up $ 5. 2 million in expenses, which β other than $ 245, 000
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from selling a product, not for providing a service. no, the foundation earned $ 20 million on the $ 74 million in assets it holds. the foundation racked up $ 5. 2 million in expenses, which β other than $ 245, 000 it gave to the abim β was divided into two categories : compensation and " other. " who is getting all this compensation? the very same people who are top earners at the abim. deep in the filings, it says the foundation spends $ 1. 9 million in " program and project expenses, " with no explanation what the programs and projects are. there are some expenditures, though, that are easy to understand : the foundation spends $ 153, 439 a year on at least one condominium. and it picks up the tab so the spouse of the top - officer can fly along on business trips for free. in july 2015, the annals of internal medicine published an independent cost - analysis of the american board of internal medicine's maintenance of certification program. using simulation modeling of the entire american board of internal medicine - certified workforce of us physicians, researchers from the university of california san francisco and stanford university estimated that the feb 2015 version of american board of internal medicine maintenance of certification would cost $ 5. 7 billion over ten years, including $ 561 million in american board of internal medicine's fees and $ 5. 1 billion in time costs ( arising from 32. 7 million physician hours spent completing maintenance of certification requirements ). internists will incur an average of $ 23, 607 ( 95 % ci, $ 5, 380 to $ 66, 383 ) in maintenance of certification costs over 10 years, ranging from $ 16, 725 for general internists to $ 40, 495 for hematologists - oncologists. the authors concluded that " a rigorous evaluation of its effect on clinical and economic outcomes is warranted to balance potential gains in health care quality and efficiency against the high costs identified in this study. " for the first time, the american board of internal medicine faces competition in the certification business from another entity, the national board of physicians and surgeons ( nbpas. org ). much of the controversy about the recent behavior of the american board of internal medicine is detailed on their new competitor's website, including a debate between the rival parties. in a survey on sermo, a physician - only website, 97 % of physicians favored the elimination of maintenance of certification. = = see also = = american osteopathic board of internal
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s website, including a debate between the rival parties. in a survey on sermo, a physician - only website, 97 % of physicians favored the elimination of maintenance of certification. = = see also = = american osteopathic board of internal medicine abim foundation = = references = = = = external links = = official website
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cellular senescence is a phenomenon characterized by the cessation of cell division. in their experiments during the early 1960s, leonard hayflick and paul moorhead found that normal human fetal fibroblasts in culture reach a maximum of approximately 50 cell population doublings before becoming senescent. this process called the hayflick limit is also known as " replicative senescence ", since it is brought about through replication. hayflick's discovery of mortal cells paved the path for the discovery and understanding of cellular aging molecular pathways. cellular senescence can be initiated by a wide variety of stress inducing factors. these stress factors include both environmental and internal damaging events, abnormal cellular growth, oxidative stress, autophagy factors, among many other things. the physiological importance for cell senescence has been attributed to prevention of carcinogenesis, and more recently, aging, development, and tissue repair. senescent cells contribute to the aging phenotype, including frailty syndrome, sarcopenia, and aging - associated diseases. senescent astrocytes and microglia contribute to neurodegeneration. = = cellular mechanisms = = = = = stress response and dna damage = = = mechanistically, replicative senescence can be triggered by a dna damage response due to the shortening of telomeres. cells can also be induced to senesce by dna damage in response to elevated reactive oxygen species ( ros ), activation of oncogenes, and cell - cell fusion. normally, cell senescence is reached through a combination of a variety of factors ( i. e., both telomere shortening and oxidative stress ). the dna damage response ( ddr ) arrests cell cycle progression until dna damage, such as double - strand breaks ( dsbs ), are repaired. senescent cells display persistent ddr that appears to be resistant to endogenous dna repair activities. the prolonged ddr activates both atm and atr dna damage kinases. the phosphorylation cascade initiated by these two kinases causes the eventual arrest of the cell cycle. depending on the severity of the dna damage, the cells may no longer be able to undergo repair and either go through apoptosis or cell senescence. such senescent cells in mammalian culture and tissues retain dsbs and ddr markers. it has been proposed that retained dsbs are major drivers of the aging process. mutations in genes relating to genome maintenance has been linked with premature aging diseases, supporting
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such senescent cells in mammalian culture and tissues retain dsbs and ddr markers. it has been proposed that retained dsbs are major drivers of the aging process. mutations in genes relating to genome maintenance has been linked with premature aging diseases, supporting the role of cell senescence in aging. depletion of nad + can lead to dna damage and cellular senescence in vascular smooth muscle cells. although senescent cells can no longer replicate, they remain metabolically active and commonly adopt an immunogenic phenotype that enables them to be eliminated by the immune system. the phenotype consists of a pro - inflammatory secretome, the up - regulation of immune ligands, a pro - survival response, promiscuous gene expression ( pge ), and stain positive for senescence - associated Ξ² - galactosidase activity. two proteins, senescence - associated beta - galactosidase and p16ink4a, are regarded as biomarkers of cellular senescence. however, this results in a false positive for cells that naturally have these two proteins such as maturing tissue macrophages with senescence - associated beta - galactosidase and t - cells with p16ink4a. the nucleus of senescent cells is characterized by senescence - associated heterochromatin foci ( sahf ) and dna segments with chromatin alterations reinforcing senescence ( dna - scars ). senescent cells affect tumour suppression, wound healing and possibly embryonic / placental development and a pathological role in age - related diseases. = = = cell growth and size = = = cell growth plays a crucial role in cell proliferation, regulating cellular homeostasis and cell cycle progression through dynamic changes in cell size. and like dna damage, it can promote senescence by triggering a prolonged cell cycle arrest. while a typical increase in cell size controls for concentrations of cell cycle activators, an excess of growth can drive a permanent halt on cell proliferation as a result of various mechanistic interactions with cell - cycle signaling pathways and thresholds present. as the cell increases in size without sufficient proliferation, cellular homeostasis becomes more and more difficult to achieve ; the cell experiences cytoplasmic dilution and succumbs to a permanent cell cycle arrest. more particularly, the osmotic stress caused by this overgrowth is linked to an accumulation of p21 during g0 / g1 arrest, consequently preventing re - entry into s phase. additionally
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succumbs to a permanent cell cycle arrest. more particularly, the osmotic stress caused by this overgrowth is linked to an accumulation of p21 during g0 / g1 arrest, consequently preventing re - entry into s phase. additionally, the persistent growth of the cell during this arrest, as driven by mtor signaling, causes phenotypes characteristic of senescent cells such as cellular hypertrophy, sasp and lysosomal hyperfunctions. the enlarged cells that are able to re - enter the cell cycle are prone to dna damage and experience abnormalities in signaling for repair ( nhej pathway ), eventually leading to a replication failure and a permanent cell - cycle exit. overall, a consistent correlation between larger cell size and senescence has been established. understanding this mechanistic relationship is useful for addressing different treatment sensitivities in clinical contexts. for tumors presenting growth signal mutations, cell cycle inhibitors ( cdk4 / 6 and cdk7 inhibitors ) hold potential to be a more useful therapeutic, given this cell - size dependency of cellular senescence. = = = role of telomeres = = = telomeres are dna tandem repeats at the end of chromosomes that shorten during each cycle of cell division. recently, the role of telomeres in cellular senescence has aroused general interest, especially with a view to the possible genetically adverse effects of cloning. the successive shortening of the chromosomal telomeres with each cell cycle is also believed to limit the number of divisions of the cell, contributing to aging. after sufficient shortening, proteins responsible for maintaining telomere structure, such as trf2, are displaced, resulting in the telomere being recognized as a site of a double - strand break. this induces replicative senescence. theoretically, it is possible upon the discovery of the exact mechanism of biological immortality to genetically engineer cells with the same capability. the length of the telomere strand has senescent effects ; telomere shortening activates extensive alterations in alternative rna splicing that produce senescent toxins such as progerin, which degrades tissue and makes it more prone to failure. = = = role of oncogenes = = = brafv600e and ras are two oncogenes implicated in cellular senescence. brafv600e induces senescence through synthesis and secretion of igfbp7. ras activates the mapk cascade which results in increased p53
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##e and ras are two oncogenes implicated in cellular senescence. brafv600e induces senescence through synthesis and secretion of igfbp7. ras activates the mapk cascade which results in increased p53 activation and p16ink4a upregulation. the transition to a state of senescence due to oncogene mutations are irreversible and have been termed oncogene - induced senescence ( ois ). interestingly, even after oncogenic activation of a tissue, several researchers have identified a senescent phenotype. researchers have identified a senescent phenotype in benign lesions of the skin carrying oncogenic mutations in neurofibroma patients with a defect that specifically causes an increase in ras. this finding has been highly reproducible in benign prostate lesions, in melanocytic lesions of uv - irradiated hgf / sf - transgenic mice, in lymphocytes and in the mammary gland from n - ras transgenic mice, and in hyperplasias of the pituitary gland of mice with deregulated e2f activity. the key to these findings is that genetic manipulations that abrogated the senescence response led to full - blown malignancy in those carcinomas. as such, the evidence suggests senescent cells can be associated with pre - malignant stages of the tumor. further, it has been speculated that a senescent phenotype might serve as a promising marker for staging. there are two types of senescence in vitro. the irreversible senescence which is mediated by ink4a / rb and p53 pathways and the reversible senescent phenotype which is mediated by p53. this suggests that p53 pathway could be effectively harnessed as a therapeutic intervention to trigger senescence and ultimately mitigate tumorigenesis. p53 has been shown to have promising therapeutic relevance in an oncological context. in the 2007 nature paper by xue et al., rnai was used to regulate endogenous p53 in a liver carcinoma model. xue et al. utilized a chimaeric liver cancer mouse model and transduced this model with the ras oncogene. they took embryonic progenitor cells, transduced those cells with oncogenic ras, along with the tetracycline transactivator ( tta ) protein to control p53 expression using doxycy
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oncogene. they took embryonic progenitor cells, transduced those cells with oncogenic ras, along with the tetracycline transactivator ( tta ) protein to control p53 expression using doxycycline, a tetracycline analog and tetracycline responsive short hairpin rna ( shrna ). in the absence of dox, p53 was actively suppressed as the microrna levels increased, so as dox was administered, p53 microrna was turned off to facilitate the expression of p53. the liver cancers that expressed ras showed signs of senescence following p53 reactivation including an increase in senescence associated b - galactosidase protein. even if the expression of p53 was transiently activated or deactivated, senescence via sa b - gal was observed. xue et al. show that by briefly reactivating p53 in tumors without functional p53 activity, tumor regression is observed. the induction of cellular senescence was associated with an increase in inflammatory cytokines as is expected based on the sasp. the presence of both senescence and an increase in immune activity is able to regress and limit liver carcinoma growth in this mouse model. = = signaling pathways = = there are several reported signaling pathways that lead to cellular senescence including the p53 and p16ink4a pathways. both of these pathways are activated in response to cellular stressors and lead to cell cycle inhibition. p53 activates p21 which deactivates cyclin - dependent kinase 2 ( cdk 2 ). without cdk 2, retinoblastoma protein ( prb ) remains in its active, hypophosphorylated form and binds to the transcription factor e2f1, an important cell cycle regulator. this represses the transcriptional targets of e2f1, leading to cell cycle arrest after the g1 phase. p16ink4a also activates prb, but through inactivation of cyclin - dependent kinase 4 ( cdk 4 ) and cyclin - dependent kinase 6 ( cdk 6 ). p16ink4a is responsible for the induction of premature, stress - induced senescence. this is not irreversible ; silencing of p16ink4a through promotor methylation or deletion of the p16ink4a locus allows the cell to resume the cell cycle if senescence was initiated by p16ink4a
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irreversible ; silencing of p16ink4a through promotor methylation or deletion of the p16ink4a locus allows the cell to resume the cell cycle if senescence was initiated by p16ink4a activation. senescence - associated secretory phenotype ( sasp ) gene expression is induced by a number of transcription factors, including c / ebpΞ², of which the most important is nf - ΞΊb. aberrant oncogenes, dna damage, and oxidative stress induce mitogen - activated protein kinases, which are the upstream regulators of nf - ΞΊb. inhibition of the mechanistic target of rapamycin ( mtor ) suppresses cellular senescence, hence cellular senescence is inhibited by rapamycin. = = characteristics of senescent cells = = senescent cells are highly heterogenous, which has caused most authorities in the field to believe that a universal marker of senescent cells will not be found, and that a multi - marker approach is required for the detection of senescent cells. for this reason, the cellular senescence program network was created to identify and characterize senescent cells in different body tissues. senescent cells are especially common in skin and adipose tissue. senescent cells are usually larger than non - senescent cells. transformation of a dividing cell into a non - dividing senescent cell is a slow process that can take up to six weeks. senescent cells affect tumor suppression, wound healing and possibly embryonic / placental development, and play a pathological role in age - related diseases. there are two primary tumor suppressor pathways known to mediate senescence : p14arf / p53 and ink4a / rb. more specifically p16ink4a - prb tumor suppressor and p53 are known effectors of senescence. most cancer cells have a mutated p53 and p16ink4a - prb, which allows the cancer cells to escape a senescent fate. the p16 protein is a cyclin dependent kinase ( cdk ) inhibitor and it activates rb tumor suppressor. p16 binds to cdk 4 / 6 to inhibit the kinase activity and inhibit rb tumor suppressor via phosphorylation. the rb tumor suppressor has been shown to associate with e2f1 ( a protein necessary for transcription ) in its monophosphorylated form, which inhibit
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the kinase activity and inhibit rb tumor suppressor via phosphorylation. the rb tumor suppressor has been shown to associate with e2f1 ( a protein necessary for transcription ) in its monophosphorylated form, which inhibits transcription of downstream target genes involved in the g1 / s transition. as part of a feedback loop, increased phosphorylation of rb increases p16 expression that inhibits cdk4 / 6. reduced cdk4 / 6 kinase activity results in higher levels of the hypo - phosphorylated ( monophosphorylated ) form of rb, which subsequently leads to reduced levels of p16 expression. the removal of aggregated p16 ink 4a positive senescent cells can delay tissue dysfunction and ultimately extend life. in the 2011 nature paper by baker et al. a novel transgene, ink - attac, was used to inducibly eliminate p16 ink4a - positive senescent cells by action of a small molecule - induced activation of caspase 8, resulting in apoptosis. a bubr1 h / h mouse model known to experience the clinicopathological characteristics of aging - infertility, abnormal curvature to the spine, sarcopenia, cataracts, fat loss, dermal thinning, arrhythmias, etc. was used to test the consequences of p16ink4a removal. in these mice p16 ink4a aggregates in aging tissues including the skeletal and eye muscle, and adipose tissues. baker et al. found that if the senescent cells are removed, it is possible to delay age - associated disorders. not only does p16 play an important role in aging, but also in auto - immune diseases like rheumatoid arthritis that progressively lead to mobility impairment in advanced disease. in the nervous system, senescence has been described in astrocytes and microglia, but is less understood in neurons. because senescence arrests cell division, studies of senescence in the brain were focused mainly on glial cells and less studies were focused on nondividing neurons. analyzing single nucleus rna - seq data from human brains suggested p19 as a marker for senescent neurons, which are strongly associated with neurons containing neurofibrillary tangle. = = = sasp = = = the secretome of senescent cells is very complex. the products are mainly associated with inflammation, proliferation, and changes in the extracellular matrix. a
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associated with neurons containing neurofibrillary tangle. = = = sasp = = = the secretome of senescent cells is very complex. the products are mainly associated with inflammation, proliferation, and changes in the extracellular matrix. a senescence associated secretory phenotype ( sasp ) consisting of inflammatory cytokines, growth factors, and proteases is another characteristic feature of senescent cells. there are many sasp effector mechanisms that utilize autocrine or paracrine signalling. sasp induces an unfolded protein response in the endoplasmic reticulum because of an accumulation of unfolded proteins, resulting in proteotoxic impairment of cell function. autophagy is upregulated to promote survival, while inflammaging is simultaneously induced. considering cytokines, sasp molecules il - 6 and il - 8 are likely to cause senescence without affecting healthy neighbor cells. il - 1beta, unlike il - 6 or il - 8, is able to induce senescence in normal cells with paracrine signaling. il - 1beta is also dependent on cleavage of il - 1 by caspase - 1, causing a pro - inflammatory response. growth factors, gm - csf and vegf also serve as sasp molecules. from the cellular perspective, cooperation of transcriptional factors nf - ΞΊb and c / ebpΞ² increase the level of sasp expression. regulation of the sasp is managed through a transcription level autocrine feedback loop, but most importantly by a continuous ddr. proteins p53, p21, p16ink4a, and bmi - 1 have been termed as major senescence signalling factors, allowing them to serve as markers. other markers register morphology changes, reorganization of chromatin, apoptosis resistance, altered metabolism, enlarged cytoplasm or abnormal shape of the nucleus. sasps have distinct effects depending on the cellular context, including inflammatory or anti - inflammatory and tumor or anti - tumor effects. while considered a pro - tumorogenic effect, they likely support already tumor - primed cells instead of shifting healthy cells into transformation. likewise, they operate as anti - tumor protectors by facilitating the elimination of damaged cells by phagocytes. the sasp is associated with many age - related diseases, including type 2 diabetes and atherosclerosis. this has motivated researchers to develop senolytic drugs to kill and eliminate senescent cells to improve health in the elderly. the nucleus of sen
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##p is associated with many age - related diseases, including type 2 diabetes and atherosclerosis. this has motivated researchers to develop senolytic drugs to kill and eliminate senescent cells to improve health in the elderly. the nucleus of senescent cells is characterized by senescence - associated heterochromatin foci ( sahf ) and dna segments with chromatin alterations reinforcing senescence ( dna - scars ). = = clearance of senescent cells by the immune system = = due to the heterogeneous nature of senescent cells, different immune system cells eliminate different senescent cells. specific components of the senescence - associated secretory phenotype ( sasp ) factors secreted by senescent cells attract and activate different components of both the innate and adaptive immune system. natural killer cells ( nk cells ) and macrophages play a major role in clearance of senescent cells. natural killer cells directly kill senescent cells, and produce cytokines which activate macrophages which remove senescent cells. senescent cells can be phagocytized by neutrophils as well as by macrophages. senolytic drugs which induce apoptosis in senescent cells rely on phagocytic immune system cells to remove the apoptosed cells. natural killer cells can use nkg2d killer activation receptors to detect the mica and ulbp2 ligands which become upregulated on senescent cells. the senescent cells are killed using perforin pore - forming cytolytic protein. cd8 + cytotoxic t - lymphocytes also use nkg2d receptors to detect senescent cells, and promote killing similar to nk cells. aging of the immune system ( immunosenescence ) results in a diminished capacity of the immune system to remove senescent cells, thereby leading to an increase in senescent cells. chronic inflammation due to sasp from senescent cells can also reduce the capacity of the immune system to remove senescent cells. t cells, b cells, and nk cells have all been reported to become senescent themselves. senescent - like aging cd8 + cytotoxic t - lymphocytes become more innate in structure and function, resembling nk cells. immune system cells can be recruited by sasp to senescent cells, after which the sasp from the senescent
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##8 + cytotoxic t - lymphocytes become more innate in structure and function, resembling nk cells. immune system cells can be recruited by sasp to senescent cells, after which the sasp from the senescent cells can induce the immune system cells to become senescent. chimeric antigen receptor t cells have been proposed as an alternative means to senolytic drugs for the elimination of senescent cells. urokinase receptors have been found to be highly expressed on senescent cells, leading researchers to use chimeric antigen receptor t cells to eliminate senescent cells in mice. chimeric antigen receptor natural killer cells have been proposed as an allogeneic means of eliminating senescent cells. = = transient senescence = = it is important to recognize that cellular senescence is not inherently a negative phenomenon. during mammalian embryogenesis, programmed cellular senescence plays a role in tissue remodeling via macrophage infiltration and subsequent clearance of senescent cells. a study on the mesonephros and endolymphatic sac in mice highlighted the importance of cellular senescence for eventual morphogenesis of the embryonic kidney and the inner ear, respectively. they serve to direct tissue repair and regeneration. cellular senescence limits fibrosis during wound closure by inducing cell cycle arrest in myofibroblasts once they have fulfilled their function. when these cells have accomplished these tasks, the immune system clears them away. this phenomenon is termed acute senescence. senescence of hepatic stellate cells could prevent progression of liver fibrosis, although this has not been implemented as a therapy, and would carry the risk of hepatic dysfunction. the negative implications of cellular senescence present themselves in the transition from acute to chronic senescence. when the immune system cannot clear senescent cells at the rate at which senescent cells are being produced, possibly as a result of the decline in immune function with age, accumulation of these cells leads to a disruption in tissue homeostasis. = = cellular senescence in mammalian disease = = transplantation of only a few ( 1 per 10, 000 ) senescent cells into lean middle - aged mice was shown to be sufficient to induce frailty, early onset of aging - associated diseases, and premature death. biomarkers of cellular senescence have been shown to accumulate in tissues of older individuals. the accumulation of senescent cells in tissues of vertebrates with age is thought to contribute to
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early onset of aging - associated diseases, and premature death. biomarkers of cellular senescence have been shown to accumulate in tissues of older individuals. the accumulation of senescent cells in tissues of vertebrates with age is thought to contribute to the development of ageing - related diseases, including alzheimer's disease, amyotrophic lateral sclerosis, endocrine disorders including type 2 diabetes, and various cancers. progeria is another example of a disease that may be related to cell senescence. the disease is thought to be caused by mutations in the dna damage response, telomere shortening, or a combination of the two. progeroid syndromes are all examples of aging diseases where cell senescence appears to be implicated. = = = list of progeroid syndromes = = = hutchinson β gilford progeria syndrome rothmund β thomson syndrome werner syndrome bloom syndrome cockayne syndrome xeroderma pigmentosum trichothiodystrophy xeroderma pigmentosum - cockayne syndrome restrictive dermopathy mandibuloacral dysplasia fanconi anaemia seckel syndrome ataxia telangiectasia dyskeratosis congenita hoyeraal β hreidarsson syndrome nestor - guillermo progeria syndrome = = senolytic drugs = = targeting senescent cells is a promising strategy to overcome age - related disease, simultaneous alleviate multiple comorbidities, and mitigate the effects of frailty. removing the senescent cells by inducing apoptosis is the most straightforward option, and there are several agents that have been shown to accomplish this. some of these senolytic drugs take advantage of the senescent - cell anti - apoptotic pathways ( scaps ) ; knocking out expression of the proteins involved in these pathways can lead to the death of senescent cells, leaving healthy cells. = = organisms lacking senescence = = cellular senescence is not observed in some organisms, including perennial plants, sponges, corals, and lobsters. in other organisms, where cellular senescence is observed, cells eventually become post - mitotic : they can no longer replicate themselves through the process of cellular mitosis ( i. e., cells experience replicative senescence ). how and why cells become post - mitotic in some species has been the subject of much research and speculation, but it has been suggested that cellular senescence evolved as a way to prevent the onset and spread of
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cells experience replicative senescence ). how and why cells become post - mitotic in some species has been the subject of much research and speculation, but it has been suggested that cellular senescence evolved as a way to prevent the onset and spread of cancer. somatic cells that have divided many times will have accumulated dna mutations and would be more susceptible to becoming cancerous if cell division continued. as such, it is becoming apparent that senescent cells undergo conversion to an immunologic phenotype that enables them to be eliminated by the immune system. = = see also = = ageing senolytic apoptosis mitotic catastrophe necrosis senescence dna damage dna repair cell cycle telomeres progeroid syndromes carcinogenesis = = references = = = = further reading = = = = external links = = media related to cellular senescence at wikimedia commons
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in epidemiology, environmental diseases are diseases that can be directly attributed to environmental factors ( as distinct from genetic factors or infection ). apart from the true monogenic genetic disorders, which are rare, environment is a major determinant of the development of disease. diet, exposure to toxins, pathogens, radiation, and chemicals found in almost all personal care products and household cleaners, stress, racism, and physical and mental abuse are causes of a large segment of non - hereditary disease. if a disease process is concluded to be the result of a combination of genetic and environmental factor influences, its etiological origin can be referred to as having a multifactorial pattern. there are many different types of environmental disease including : disease caused by physical factors in the environment, such as skin cancer caused by excessive exposure to ultraviolet radiation in sunlight disease caused by exposure to toxic or irritant chemicals in the environment such as toxic metals disease caused by exposures to toxins from biologic agents in the environment, such as aflatoxicosis from molds that produce aflatoxin disease caused by exposure to toxic social factors in the environment, such as racism lifestyle disease such as cardiovascular disease, diseases caused by substance abuse such as alcoholism, and smoking - related disease = = environmental diseases vs. pollution - related diseases = = environmental diseases are a direct result from the environment. meanwhile, pollution - related diseases are attributed to exposure to toxicants or toxins in the air, water, and soil. therefore, all pollution - related disease are environmental diseases, but not all environmental diseases are pollution - related diseases. = = urban - associated diseases = = urban areas are highly dense regions that currently hold ~ 50 % of the global population, a number expected to grow to 70 % by 2050, and produce over 80 % of the global gdp. these areas are known to have a higher incidence of certain diseases, which is of particular concern given their rapid growth. the urban environment includes many risk factors for a variety of different environmental diseases. some of these risk factors, for instance, air - pollution, are well known, while others such as altered microbial exposure are less familiar to the general public. for instance, asthma can be induced and exacerbated by combustion related pollution, which is more prevalent in urban areas. on the other hand, urban areas, compared to their rural counterparts, lack diverse microbial communities, which can help prevent the development of asthma. both of these effects lead to a higher incidence of asthma in cities.
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is more prevalent in urban areas. on the other hand, urban areas, compared to their rural counterparts, lack diverse microbial communities, which can help prevent the development of asthma. both of these effects lead to a higher incidence of asthma in cities. infectious diseases are also often more common in cities, as transfer between hosts is facilitated by high population densities. however, recent research shows that increased access to healthcare weakens the urban association with these diseases, and the net effect is still unclear. many mental health disorders have also been associated with urban areas, especially in low socioeconomic areas. increased levels of stress, air & light & noise pollution, and reduced " green " space are all urban - associated environmental effects that are adversely linked to mental health. though urban areas are often correlated with dirtiness and disease, they are likely to have more access to higher quality health care which can lead to more positive health outcomes. this benefit will continue to grow as innovation in health technologies steadily rises. taking this into account, while overall trends do exist, urban risk factors are nuanced and often city and context dependent. = = chemicals = = = = = metals = = = poisoning by lead and mercury has been known since antiquity. other toxic metals or metals that are known to evoke adverse immune reactions are arsenic, phosphorus, zinc, beryllium, cadmium, chromium, manganese, nickel, cobalt, osmium, platinum, selenium, tellurium, thallium, uranium, and vanadium. = = = halogens = = = there are many other diseases likely to have been caused by common anions found in natural drinking water. fluoride is one of the most common found in drier climates where the geology favors release of fluoride ions to soil as the rocks decompose. in sri lanka, 90 % of the country is underlain by crystalline metamorphic rocks of which most carry mica as a major mineral. mica carries fluoride in their structure and releases to soil when decomposes. in the dry and arid climates, fluoride concentrates on top soil and slowly dissolves in shallow groundwater. this has been the cause of high fluoride levels in drinking water where the majority of the rural sri lankans obtain their drinking water from backyard wells. high fluoride in drinking water has caused a high incidence of fluorosis among dry zone population in sri lanka. however, in the wet zone, high rainfall effectively removes fluoride from soils where
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##s obtain their drinking water from backyard wells. high fluoride in drinking water has caused a high incidence of fluorosis among dry zone population in sri lanka. however, in the wet zone, high rainfall effectively removes fluoride from soils where no fluorosis is evident. in some parts of sri lanka iodine deficiency has also been noted which has been identified as a result of iodine fixation by hydrated iron oxide found in lateritic soils in wet coastal lowlands. = = = organic compounds = = = additionally, there are environmental diseases caused by the aromatic carbon compounds including : benzene, hexachlorocyclohexane, toluene diisocyanate, phenol, pentachlorophenol, quinone and hydroquinone. also included are the aromatic nitro -, amino -, and pyridilium - deratives : nitrobenzene, dinitrobenzene, trinitrotoluene, paramethylaminophenol sulfate ( metol ), dinitro - ortho - cresol, aniline, trinitrophenylmethylnitramine ( tetryl ), hexanitrodiphenylamine ( aurantia ), phenylenediamines, and paraquat. the aliphatic carbon compounds can also cause environmental disease. included in these are methanol, nitroglycerine, nitrocellulose, dimethylnitrosamine, and the halogenated hydrocarbons : methyl chloride, methyl bromide, trichloroethylene, carbon tetrachloride, and the chlorinated naphthalenes. also included are glycols : ethylene chlorhydrin and diethylene dioxide = = = noxious gases = = = noxious gases can be categorized as : simple asphyxiants, chemical asphyxiants, and irritant gases. the simple asphixiants are nitrogen, methane, and carbon dioxide. the chemical asphyxiants are carbon monoxide, sulfuretted hydrogen and hydrogen cyanide. the irritant gases are sulfur dioxide, ammonia, nitrogen dioxide, chlorine, phosgene, and fluorine and its compounds, which include luroine and hydrofluoric acid, fluorspar, fluorapatite, cryolite, and organic fluorine compounds
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dioxide, chlorine, phosgene, and fluorine and its compounds, which include luroine and hydrofluoric acid, fluorspar, fluorapatite, cryolite, and organic fluorine compounds. = = categorization and surveillance = = the u. s. coast guard has developed a coast guard - wide comprehensive system for surveillance of workplace diseases. the american medical association's fifth edition of the current medical information and terminology ( cmit ) was used as a reference to expand the basic list of 50 sentinel health events ( occupational ) [ she ( o ) ] published by the national institute for occupational health and safety ( niosh ), september, 1983. = = see also = = = = references = = = = notes = = the diseases of occupations, sixth edition, donald hunter, c. b. e., d. sc., m. d., f. r. c. p., hodder and stoughton, london. isbn 0 - 340 - 22084 - 8, 1978. aviat space environ med. 1991 aug ; 62 ( 8 ) : 795 - 7. use of sentinel health events ( occupational ) in computer assisted occupational health surveillance. stockwell jr, adess ml, titlow tb, zaharias gr. u. s. coast guard office of health services, washington, d. c.
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in the mathematical field of topology, a free loop is a variant of the notion of a loop. whereas a loop has a distinguished point on it, called its basepoint, a free loop lacks such a distinguished point. formally, let x { \ displaystyle x } be a topological space. then a free loop in x { \ displaystyle x } is an equivalence class of continuous functions from the circle s 1 { \ displaystyle s ^ { 1 } } to x { \ displaystyle x }. two loops are equivalent if they differ by a reparameterization of the circle. that is, f g { \ displaystyle f \ sim g } if there exists a homeomorphism Ο : s 1 β s 1 { \ displaystyle \ psi : s ^ { 1 } \ rightarrow s ^ { 1 } } such that g = f β Ο. { \ displaystyle g = f \ circ \ psi. } thus, a free loop, as opposed to a based loop used in the definition of the fundamental group, is a map from the circle to the space without the basepoint - preserving restriction. assuming the space is path - connected, free homotopy classes of free loops correspond to conjugacy classes in the fundamental group. recently, interest in the space of all free loops l x { \ displaystyle lx } has grown with the advent of string topology, i. e. the study of new algebraic structures on the homology of the free loop space. = = see also = = loop space loop ( topology ) quasigroup = = further reading = = brylinski, jean - luc : loop spaces, characteristic classes and geometric quantization. reprint of the 1993 edition. modern birkhauser classics. birkhauser boston, inc., boston, ma, 2008. cohen and voronov : notes on string topology
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diatribe de progidiosis crucibus is a 1661 work by the jesuit scholar athanasius kircher. it was printed in rome by blasius deversin and dedicated to archduke leopold wilhelm of austria. a second edition of the work was published in rome in 1666 and a german translation appeared in gaspar schott's joco - seriorum naturae et artis ( wurzburg, 1666 ). diatribe is kircher's most succinct and explicit statement in favour of seeking rational causes for phenomena through an understanding of natural laws, derived from observation, rather than seeking miraculous explanations. : 233 β 4 this continued the theme he had taken up in scrutinium physico - medicum ( 1658 ) and pursued in greater detail in mundus subterraneus ( 1665 ). : 154 = = background = = on 3 july 1660 an eruption of vesuvius began. a plume of ejected material rose up to 4 km into the air and was carried off to the southeast by the wind. as was normal for vesuvius, the late stages of the eruption involved the ejection of white ash. along with this ash, free twinned augite phenocrysts were ejected, causing small cross - shaped objects to fall from the sky. this phenomenon appeared on the day the sun entered leo ( 21 july ). the population of naples believed at first that these crosses were a sign from their patron saint, saint gennaro, that he would protect them from the volcano. however many people in southern italy soon grew fearful that the crosses were a token of god's anger. : 51 kircher wanted to undertake an investigation of the phenomenon that would reassure people and help avoid panic. he had an intense dislike of superstition and its simplistic view of the world, which led people to prefer the idea of the disruptive intervention of a miracle rather than seeking to understand the complex mechanisms by which the world and nature operated. he had a prior research interest in vesusius, having had himself lowered into its crater for research purposes in 1638. : 25 between august and october 1660, kircher travelled to the hamlets of somma and ottaviano to look for primary evidence himself, and also read accounts from other witnesses in southern italy. : 153 these reported various extraordinary discoveries, such as that the crosses had appeared on altar drapes, and on objects inside locked chests and shuttered rooms. : 177 = =
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primary evidence himself, and also read accounts from other witnesses in southern italy. : 153 these reported various extraordinary discoveries, such as that the crosses had appeared on altar drapes, and on objects inside locked chests and shuttered rooms. : 177 = = discussion and conclusions = = the first two thirds of the work consists of a pars historica and a pars physica, setting out both a historic narrative of the phenomenon and a physical description. : 153 three possible explanations for the mysterious crosses were considered. firstly, they may have been miraculous and involved a direct intervention by god in the events of the world ; secondly, angels or demons might have made use of natural forces in extraordinary ways ; and thirdly, the laws of nature could provide a perfectly good explanation. : 233 β 4 in kircher's view the ultimate cause of all things was divine will, but this was expressed, for the most part, through understandable natural laws ; studying these laws therefore revealed the forces that lay beneath natural phenomena. : 233 β 4 the explanation for the cross - shaped marks, he concluded, was that fine ash and moisture had settled on cloth, taking cruciform shape defined by the weave itself. kircher noted that the crosses had been seen on linen cloth but not on garments of wool, and that they had appeared only under certain specific conditions of temperature and moisture, : 233 β 4 causing " guttulae nitrosae " ( nitrous drops ) to form on the surface. : 153 to support his conclusion kircher noted two instances of similar phenomena ; when a tomcat had sprayed linen in the laundry room at the jesuit college in rome, the effect produced was yellow crosses following the weave of the cloth ; the same had also been observed in the bed - linen of an elderly jesuit who had accidentally wet his bed. he maintained however that an explanation through the operation of natural laws did not mean that the phenomenon did not contain an important divine message : " [ portents are ] like hieroglyphic symbols swathed in enigmatic and allegorical meanings which the divine wisdom records in heaven, earth, and the elements as if in a hook and sets it before mortals to read ; when they withdraw from the paths of divine will they are terrified by the threats held out before them, and turn back toward better fruits. = = critical reception = = like all of kircher's work, diatribe had to be submitted to the censors of the jesuit order before it could be published. they
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out before them, and turn back toward better fruits. = = critical reception = = like all of kircher's work, diatribe had to be submitted to the censors of the jesuit order before it could be published. they did not block it, but informed kircher that this was not the quality of work the order was expecting its scholars to produce. : 35, 95 they noted that crosses had been found on meat and fruit as well as linen. furthermore, crosses were still continuing to appear, after the eruption had stopped and after the sun had moved out of leo. if they waited until the autumn rains washed the remaining ash out of the air, they would be able to see whether the conclusions of diatribe still seemed satisfactory or not. they therefore recommended that publication should be delayed. before publication in 1661, kircher added a discussion about the appearance of crosses on fruit and meat, arguing that, like linen, these were fibrous materials capable of producing the same effect on their surfaces. the work was widely disparaged, and in 1677, gioseffo petrucci published prodromo apologetico alli studi chircheriani which sought to defend kircher against those who thought his explanation of the phenomenon was too credulous. : 153 = = references = = = = external links = = digital copy of diatribe
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a hypothetical solar system object is a planet, natural satellite, subsatellite or similar body in the solar system whose existence is not known, but has been inferred from observational scientific evidence. over the years a number of hypothetical planets have been proposed, and many have been disproved. however, even today there is scientific speculation about the possibility of planets yet unknown that may exist beyond the range of our current knowledge. = = planets = = counter - earth, a planet situated on the other side of the sun from that of the earth. fifth planet ( hypothetical ), historical speculation about a planet between the orbits of mars and jupiter. phaeton, a planet situated between the orbits of mars and jupiter whose destruction supposedly led to the formation of the asteroid belt. this hypothesis is now considered unlikely, since the asteroid belt has far too little mass to have resulted from the explosion of a large planet. in 2018, a study from researchers at the university of florida found the asteroid belt was created from the fragments of at least five or six ancient planetary - sized objects instead of a single planet. krypton, named after the destroyed native world of superman, theorized by michael ovenden to have been a gas giant between mars and jupiter nearly as large as saturn and also attributed for the formation of the asteroid belt planet v, a planet thought by john chambers and jack lissauer to have once existed between mars and the asteroid belt, based on computer simulations. various planets beyond neptune : planet nine, a planet proposed to explain apparent alignments in the orbits of a number of distant trans - neptunian objects. planet x, a hypothetical planet beyond neptune. initially employed to account for supposed perturbations ( systematic deviations ) in the orbits of uranus and neptune, belief in its existence ultimately inspired the search for pluto. the concept has since been abandoned following more precise measurements of neptune's mass, which accounted for all observed perturbations. hyperion, a planet hypothesized in 1848 by jacques babinet. " planet ten ", a large distant 10th planet theorized in 2000 to have had an effect on kuiper belt formation. tyche, a hypothetical planet in the oort cloud supposedly responsible for producing the statistical excess in long period comets in a band. results from the wise telescope survey in 2014 have ruled it out. up to three planets at 42 ( named oceanus ), 56, and 72 au ( both unnamed ) from the sun respectively, proposed by thomas jefferson jackson
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period comets in a band. results from the wise telescope survey in 2014 have ruled it out. up to three planets at 42 ( named oceanus ), 56, and 72 au ( both unnamed ) from the sun respectively, proposed by thomas jefferson jackson see in 1909. brahma and vishnu, proposed by venkatesh p. ketakar. hades, proposed by theodor grigull " planet ten " as proposed by volk and malhotra, a mars - sized planetoid believed to be responsible for the inclination of kuiper belt objects beyond the kuiper cliff at 50 au " planet ten " as proposed by sverre aarseth and carlos and raul de la fuente marcos, which they believe stabilizes the orbits of other kuiper belt objects planets o, p, q, r, s, t, and u, proposed by william henry pickering a trans - plutonian planet proposed by tadashi mukai and patryk sofia lykawka, roughly the size of earth or mars with an eccentric orbit between 100 and 200 au another trans - neptunian planet at 1, 500 au away from the sun, proposed by rodney gomes in 2012 theia or orpheus, a mars - sized impactor believed to have collided with the earth roughly 4. 5 billion years ago ; an event which created the moon. evidence from 2019 suggests that it may have originated in the outer solar system. vulcan, a hypothetical planet once believed to exist inside the orbit of mercury. initially proposed as the cause for the perturbations in the orbit of mercury, some astronomers spent many years searching for it, with many instances of people claiming to have found it. the perturbations in mercury's orbit were later accounted for via einstein's general theory of relativity. vulcanoids, asteroids that may exist within a gravitationally stable region inside mercury's orbit. they may have originated as debris resulting from a collision between mercury and another protoplanet, stripping away much of mercury's inner crust and mantle. none have been detected by stereo or soho. the lack of vulcanoids led to a suggestion in 2016 that a super - earth planet that once orbited the sun closer to mercury was able to clear its neighborhood before spiraling down into the sun. the fifth giant is a hypothetical fifth giant planet originally in an orbit between saturn and uranus but was ejected from the solar system into interstellar space after a close encounter with jupiter, resulting in a rapid divergence of jupiter's and saturn '
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. the fifth giant is a hypothetical fifth giant planet originally in an orbit between saturn and uranus but was ejected from the solar system into interstellar space after a close encounter with jupiter, resulting in a rapid divergence of jupiter's and saturn's orbit which may have ensured the orbital stability of the terrestrial planets in the inner solar system. it may have also precipitated the late heavy bombardment of the inner solar system. the fifth giant may be the hypothetical planet nine, remaining captured due to either the gravity of a nearby star or drag from the gaseous remnants of the solar nebula which reduced the eccentricity of its orbit. a and b, two super - earth ( or even supergiant ) planets theorized by michael woolfson as part of his capture theory on solar system formation. originally the solar system's two innermost planets, these two collided, ejecting a ( save its moons mars, the moon, pluto, and the other dwarf planets ) out of the solar system and shattering b to form the earth, venus, mercury, asteroid belt, and comets. a captured planet from another solar system was proposed to exist in the oort cloud much further than the hypothetical planet nine. = = moons = = chiron, a moon of saturn supposedly sighted by hermann goldschmidt in 1861 but never observed by anyone else. chrysalis, a hypothetical moon of saturn, named in 2022 by scientists of the massachusetts institute of technology using data from the cassini β huygens mission, thought to have been torn apart by saturn's tidal forces, somewhere between 200 and 100 million years ago, with up to 99 % of its mass being swallowed by saturn, and the remaining 1 % forming the rings of saturn. other moons of earth, such as petit's moon, lilith, waltemath's moons and bagby's moons. mercury's moon, hypothesised to account for an unusual pattern of radiation detected by mariner 10 in the vicinity of mercury. subsequent data from the mission revealed the actual source to be the star 31 crateris. neith, a purported moon of venus, falsely detected by a number of telescopic observers in the 17th and 18th centuries. now known not to exist, the object has been explained as a series of misidentified stars and internal reflections inside the optics of particular telescope designs. it was also alternatively proposed by jean - charles houzeau to be a heliocentric planet that orbited the sun every 283 days and be in conjunction with
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series of misidentified stars and internal reflections inside the optics of particular telescope designs. it was also alternatively proposed by jean - charles houzeau to be a heliocentric planet that orbited the sun every 283 days and be in conjunction with venus every 1080 days. themis, a moon of saturn which astronomer william pickering claimed to have discovered in 1905, but which was never observed again. = = stars = = nemesis, a brown or red dwarf whose existence was suggested in 1984 by physicist richard a. muller, based on purported periodicities in mass extinctions within earth's fossil record. its regular passage through the solar system's oort cloud would send large numbers of comets towards earth, massively increasing the chances of an impact. also believed to be the cause of minor planet sedna's unusual elongated orbit. the existence of the nemesis in the modern solar system was ruled out in 2014 after the infrared survey performed by wise spacecraft found no brown dwarf up to 10, 000 astronomical units ( 0. 16 ly ) from sun. raymond arthur lyttleton's model on the formation of the solar system had a former binary star system by the sun, which merged and broke into two due to rotational instability forming jupiter and saturn. fred hoyle's model on solar system formation had a former and more massive binary companion to the sun that exploded in a supernova due to nuclear fusion failing within its interior and it collapsing as a result ( which had not yet been verified at the time ). the star's supernova remnant would be captured by the sun and shaped into a protoplanetary disk, from which the planets formed. one assumption suggests that the hypothetical planet nine is actually a primordial black hole. = = see also = = = = references = =
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in physics, the clebsch β gordan ( cg ) coefficients are numbers that arise in angular momentum coupling in quantum mechanics. they appear as the expansion coefficients of total angular momentum eigenstates in an uncoupled tensor product basis. in more mathematical terms, the cg coefficients are used in representation theory, particularly of compact lie groups, to perform the explicit direct sum decomposition of the tensor product of two irreducible representations ( i. e., a reducible representation into irreducible representations, in cases where the numbers and types of irreducible components are already known abstractly ). the name derives from the german mathematicians alfred clebsch and paul gordan, who encountered an equivalent problem in invariant theory. from a vector calculus perspective, the cg coefficients associated with the so ( 3 ) group can be defined simply in terms of integrals of products of spherical harmonics and their complex conjugates. the addition of spins in quantum - mechanical terms can be read directly from this approach as spherical harmonics are eigenfunctions of total angular momentum and projection thereof onto an axis, and the integrals correspond to the hilbert space inner product. from the formal definition of angular momentum, recursion relations for the clebsch β gordan coefficients can be found. there also exist complicated explicit formulas for their direct calculation. the formulas below use dirac's bra β ket notation and the condon β shortley phase convention is adopted. = = review of the angular momentum operators = = angular momentum operators are self - adjoint operators jx, jy, and jz that satisfy the commutation relations [ j k, j l ] β‘ j k j l β j l j k = i Ξ΅ k l m j m k, l, m β { x, y, z }, { \ displaystyle { \ begin { aligned } & [ \ mathrm { j } _ { k }, \ mathrm { j } _ { l } ] \ equiv \ mathrm { j } _ { k } \ mathrm { j } _ { l } - \ mathrm { j } _ { l } \ mathrm { j } _ { k } = i \ hbar \ varepsilon _ { klm } \ mathrm { j } _ { m } & k, l, m & \ in \ { \ mathrm { x, y, z } \ }, \ end { aligned } } }
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varepsilon _ { klm } \ mathrm { j } _ { m } & k, l, m & \ in \ { \ mathrm { x, y, z } \ }, \ end { aligned } } } where Ξ΅klm is the levi - civita symbol. together the three operators define a vector operator, a rank one cartesian tensor operator, j = ( j x, j y, j z ). { \ displaystyle \ mathbf { j } = ( \ mathrm { j _ { x } }, \ mathrm { j _ { y } }, \ mathrm { j _ { z } } ). } it is also known as a spherical vector, since it is also a spherical tensor operator. it is only for rank one that spherical tensor operators coincide with the cartesian tensor operators. by developing this concept further, one can define another operator j2 as the inner product of j with itself : j 2 = j x 2 + j y 2 + j z 2. { \ displaystyle \ mathbf { j } ^ { 2 } = \ mathrm { j _ { x } ^ { 2 } } + \ mathrm { j _ { y } ^ { 2 } } + \ mathrm { j _ { z } ^ { 2 } }. } this is an example of a casimir operator. it is diagonal and its eigenvalue characterizes the particular irreducible representation of the angular momentum algebra s o ( 3, r ) s u ( 2 ) { \ displaystyle { \ mathfrak { so } } ( 3, \ mathbb { r } ) \ cong { \ mathfrak { su } } ( 2 ) }. this is physically interpreted as the square of the total angular momentum of the states on which the representation acts. one can also define raising ( j + ) and lowering ( jβ ) operators, the so - called ladder operators, j Β± = j x Β± i j y. { \ displaystyle \ mathrm { j _ { \ pm } } = \ mathrm { j _ { x } } \ pm i \ mathrm { j _ { y } }. } = = spherical basis for angular momentum eigenstates = = it can be shown from the above definitions that j2 commutes with jx, jy, and jz : [ j 2, j k ] = 0 k β { x, y, z }. { \ displays
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##tes = = it can be shown from the above definitions that j2 commutes with jx, jy, and jz : [ j 2, j k ] = 0 k β { x, y, z }. { \ displaystyle { \ begin { aligned } & [ \ mathbf { j } ^ { 2 }, \ mathrm { j } _ { k } ] = 0 & k & \ in \ { \ mathrm { x }, \ mathrm { y }, \ mathrm { z } \ }. \ end { aligned } } } when two hermitian operators commute, a common set of eigenstates exists. conventionally, j2 and jz are chosen. from the commutation relations, the possible eigenvalues can be found. these eigenstates are denoted | j m β© where j is the angular momentum quantum number and m is the angular momentum projection onto the z - axis. they comprise the spherical basis, are complete, and satisfy the following eigenvalue equations, j 2 | j m β© = 2 j ( j + 1 ) | j m β©, j β { 0, 1 2, 1, 3 2, β¦ } j z | j m β© = m | j m β©, m β { β j, β j + 1, β¦, j }. { \ displaystyle { \ begin { aligned } \ mathbf { j } ^ { 2 } | j \, m \ rangle & = \ hbar ^ { 2 } j ( j + 1 ) | j \, m \ rangle, & j & \ in \ { 0, { \ tfrac { 1 } { 2 } }, 1, { \ tfrac { 3 } { 2 } }, \ ldots \ } \ \ \ mathrm { j _ { z } } | j \, m \ rangle & = \ hbar m | j \, m \ rangle, & m & \ in \ { - j, - j + 1, \ ldots, j \ }. \ end { aligned } } } the raising and lowering operators can be used to alter the value of m, j Β± | j m β© = c Β± ( j, m ) | j ( m Β± 1 ) β©, { \ displaystyle \ mathrm { j } _ { \ pm } | j \, m \ rangle = \ hbar c _ { \ pm
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= c Β± ( j, m ) | j ( m Β± 1 ) β©, { \ displaystyle \ mathrm { j } _ { \ pm } | j \, m \ rangle = \ hbar c _ { \ pm } ( j, m ) | j \, ( m \ pm 1 ) \ rangle, } where the ladder coefficient is given by : in principle, one may also introduce a ( possibly complex ) phase factor in the definition of c Β± ( j, m ) { \ displaystyle c _ { \ pm } ( j, m ) }. the choice made in this article is in agreement with the condon β shortley phase convention. the angular momentum states are orthogonal ( because their eigenvalues with respect to a hermitian operator are distinct ) and are assumed to be normalized, β¨ j m | j β² m β² β© = Ξ΄ j, j β² Ξ΄ m, m β². { \ displaystyle \ langle j \, m | j'\, m'\ rangle = \ delta _ { j, j'} \ delta _ { m, m'}. } here the italicized j and m denote integer or half - integer angular momentum quantum numbers of a particle or of a system. on the other hand, the roman jx, jy, jz, j +, jβ, and j2 denote operators. the Ξ΄ { \ displaystyle \ delta } symbols are kronecker deltas. = = tensor product space = = we now consider systems with two physically different angular momenta j1 and j2. examples include the spin and the orbital angular momentum of a single electron, or the spins of two electrons, or the orbital angular momenta of two electrons. mathematically, this means that the angular momentum operators act on a space v 1 { \ displaystyle v _ { 1 } } of dimension 2 j 1 + 1 { \ displaystyle 2j _ { 1 } + 1 } and also on a space v 2 { \ displaystyle v _ { 2 } } of dimension 2 j 2 + 1 { \ displaystyle 2j _ { 2 } + 1 }. we are then going to define a family of " total angular momentum " operators acting on the tensor product space v 1 β v 2 { \ displaystyle v _ { 1 } \ otimes v _ { 2 } }, which has dimension ( 2 j 1 + 1 ) ( 2 j 2 + 1 ) { \ displaystyle (
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tensor product space v 1 β v 2 { \ displaystyle v _ { 1 } \ otimes v _ { 2 } }, which has dimension ( 2 j 1 + 1 ) ( 2 j 2 + 1 ) { \ displaystyle ( 2j _ { 1 } + 1 ) ( 2j _ { 2 } + 1 ) }. the action of the total angular momentum operator on this space constitutes a representation of the su ( 2 ) lie algebra, but a reducible one. the reduction of this reducible representation into irreducible pieces is the goal of clebsch β gordan theory. let v1 be the ( 2 j1 + 1 ) - dimensional vector space spanned by the states | j 1 m 1 β©, m 1 β { β j 1, β j 1 + 1, β¦, j 1 }, { \ displaystyle { \ begin { aligned } & | j _ { 1 } \, m _ { 1 } \ rangle, & m _ { 1 } & \ in \ { - j _ { 1 }, - j _ { 1 } + 1, \ ldots, j _ { 1 } \ } \ end { aligned } }, } and v2 the ( 2 j2 + 1 ) - dimensional vector space spanned by the states | j 2 m 2 β©, m 2 β { β j 2, β j 2 + 1, β¦, j 2 }. { \ displaystyle { \ begin { aligned } & | j _ { 2 } \, m _ { 2 } \ rangle, & m _ { 2 } & \ in \ { - j _ { 2 }, - j _ { 2 } + 1, \ ldots, j _ { 2 } \ } \ end { aligned } }. } the tensor product of these spaces, v3 β‘ v1 β v2, has a ( 2 j1 + 1 ) ( 2 j2 + 1 ) - dimensional uncoupled basis | j 1 m 1 j 2 m 2 β© β‘ | j 1 m 1 β© β | j 2 m 2 β©, m 1 β { β j 1, β j 1 + 1, β¦, j 1 }, m 2 β { β j 2, β j 2 + 1, β¦, j 2 }. { \ displaystyle | j _ { 1 } \, m _ { 1 } \, j _ { 2 } \, m _ { 2 } \ rangle \ equiv | j _ { 1
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, β¦, j 2 }. { \ displaystyle | j _ { 1 } \, m _ { 1 } \, j _ { 2 } \, m _ { 2 } \ rangle \ equiv | j _ { 1 } \, m _ { 1 } \ rangle \ otimes | j _ { 2 } \, m _ { 2 } \ rangle, \ quad m _ { 1 } \ in \ { - j _ { 1 }, - j _ { 1 } + 1, \ ldots, j _ { 1 } \ }, \ quad m _ { 2 } \ in \ { - j _ { 2 }, - j _ { 2 } + 1, \ ldots, j _ { 2 } \ }. } angular momentum operators are defined to act on states in v3 in the following manner : ( j 1 β 1 ) | j 1 m 1 j 2 m 2 β© β‘ j 1 | j 1 m 1 β© β | j 2 m 2 β© { \ displaystyle ( \ mathbf { j } _ { 1 } \ otimes 1 ) | j _ { 1 } \, m _ { 1 } \, j _ { 2 } \, m _ { 2 } \ rangle \ equiv \ mathbf { j } _ { 1 } | j _ { 1 } \, m _ { 1 } \ rangle \ otimes | j _ { 2 } \, m _ { 2 } \ rangle } and ( 1 β j 2 ) | j 1 m 1 j 2 m 2 β© β‘ | j 1 m 1 β© β j 2 | j 2 m 2 β©, { \ displaystyle ( 1 \ otimes \ mathrm { \ mathbf { j } } _ { 2 } ) | j _ { 1 } \, m _ { 1 } \, j _ { 2 } \, m _ { 2 } \ rangle \ equiv | j _ { 1 } \, m _ { 1 } \ rangle \ otimes \ mathbf { j } _ { 2 } | j _ { 2 } \, m _ { 2 } \ rangle, } where 1 denotes the identity operator. the total angular momentum operators are defined by the coproduct ( or tensor product ) of the two representations acting on v1βv2, the total angular momentum operators can be shown to satisfy the very same commutation relations, [ j k
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total angular momentum operators are defined by the coproduct ( or tensor product ) of the two representations acting on v1βv2, the total angular momentum operators can be shown to satisfy the very same commutation relations, [ j k, j l ] = i Ξ΅ k l m j m, { \ displaystyle [ \ mathrm { j } _ { k }, \ mathrm { j } _ { l } ] = i \ hbar \ varepsilon _ { klm } \ mathrm { j } _ { m } ~, } where k, l, m β { x, y, z }. indeed, the preceding construction is the standard method for constructing an action of a lie algebra on a tensor product representation. hence, a set of coupled eigenstates exist for the total angular momentum operator as well, j 2 | [ j 1 j 2 ] j m β© = 2 j ( j + 1 ) | [ j 1 j 2 ] j m β© j z | [ j 1 j 2 ] j m β© = m | [ j 1 j 2 ] j m β© { \ displaystyle { \ begin { aligned } \ mathbf { j } ^ { 2 } | [ j _ { 1 } \, j _ { 2 } ] \, j \, m \ rangle & = \ hbar ^ { 2 } j ( j + 1 ) | [ j _ { 1 } \, j _ { 2 } ] \, j \, m \ rangle \ \ \ mathrm { j _ { z } } | [ j _ { 1 } \, j _ { 2 } ] \, j \, m \ rangle & = \ hbar m | [ j _ { 1 } \, j _ { 2 } ] \, j \, m \ rangle \ end { aligned } } } for m β { βj, βj + 1,..., j }. note that it is common to omit the [ j1 j2 ] part. the total angular momentum quantum number j must satisfy the triangular condition that | j 1 β j 2 | β€ j β€ j 1 + j 2, { \ displaystyle | j _ { 1 } - j _ { 2 } | \ leq j \ leq j _ { 1 } + j _ { 2 }, } such that the three nonnegative integer or half - integer values could correspond to the three sides of a
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1 } - j _ { 2 } | \ leq j \ leq j _ { 1 } + j _ { 2 }, } such that the three nonnegative integer or half - integer values could correspond to the three sides of a triangle. the total number of total angular momentum eigenstates is necessarily equal to the dimension of v3 : j = | j 1 β j 2 | j 1 + j 2 ( 2 j + 1 ) = ( 2 j 1 + 1 ) ( 2 j 2 + 1 ). { \ displaystyle \ sum _ { j = | j _ { 1 } - j _ { 2 } | } ^ { j _ { 1 } + j _ { 2 } } ( 2j + 1 ) = ( 2j _ { 1 } + 1 ) ( 2j _ { 2 } + 1 ) ~. } as this computation suggests, the tensor product representation decomposes as the direct sum of one copy of each of the irreducible representations of dimension 2 j + 1 { \ displaystyle 2j + 1 }, where j { \ displaystyle j } ranges from | j 1 β j 2 | { \ displaystyle | j _ { 1 } - j _ { 2 } | } to j 1 + j 2 { \ displaystyle j _ { 1 } + j _ { 2 } } in increments of 1. as an example, consider the tensor product of the three - dimensional representation corresponding to j 1 = 1 { \ displaystyle j _ { 1 } = 1 } with the two - dimensional representation with j 2 = 1 / 2 { \ displaystyle j _ { 2 } = 1 / 2 }. the possible values of j { \ displaystyle j } are then j = 1 / 2 { \ displaystyle j = 1 / 2 } and j = 3 / 2 { \ displaystyle j = 3 / 2 }. thus, the six - dimensional tensor product representation decomposes as the direct sum of a two - dimensional representation and a four - dimensional representation. the goal is now to describe the preceding decomposition explicitly, that is, to explicitly describe basis elements in the tensor product space for each of the component representations that arise. the total angular momentum states form an orthonormal basis of v3 : β¨ j m | j β² m β² β© = Ξ΄ j, j β² Ξ΄ m, m β². { \ displaystyle \ left \ langle j \, m | j'\, m'\ right
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##rmal basis of v3 : β¨ j m | j β² m β² β© = Ξ΄ j, j β² Ξ΄ m, m β². { \ displaystyle \ left \ langle j \, m | j'\, m'\ right \ rangle = \ delta _ { j, j'} \ delta _ { m, m'} ~. } these rules may be iterated to, e. g., combine n doublets ( s = 1 / 2 ) to obtain the clebsch - gordan decomposition series, ( catalan's triangle ), 2 β n = k = 0 n / 2 ( n + 1 β 2 k n + 1 ( n + 1 k ) ) ( n + 1 β 2 k ), { \ displaystyle \ mathbf { 2 } ^ { \ otimes n } = \ bigoplus _ { k = 0 } ^ { \ lfloor n / 2 \ rfloor } ~ \ left ( { \ frac { n + 1 - 2k } { n + 1 } } { n + 1 \ choose k } \ right ) ~ ( \ mathbf { n } + \ mathbf { 1 } - \ mathbf { 2 } \ mathbf { k } ) ~, } where n / 2 { \ displaystyle \ lfloor n / 2 \ rfloor } is the integer floor function ; and the number preceding the boldface irreducible representation dimensionality ( 2j + 1 ) label indicates multiplicity of that representation in the representation reduction. for instance, from this formula, addition of three spin 1 / 2s yields a spin 3 / 2 and two spin 1 / 2s, 2 β 2 β 2 = 4 β 2 β 2 { \ displaystyle { \ mathbf { 2 } } \ otimes { \ mathbf { 2 } } \ otimes { \ mathbf { 2 } } = { \ mathbf { 4 } } \ oplus { \ mathbf { 2 } } \ oplus { \ mathbf { 2 } } }. = = formal definition of clebsch β gordan coefficients = = the coupled states can be expanded via the completeness relation ( resolution of identity ) in the uncoupled basis the expansion coefficients β¨ j 1 m 1 j 2 m 2 | j m β© { \ displaystyle \ langle j _ { 1 } \, m _ { 1 } \, j _ { 2 }
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) in the uncoupled basis the expansion coefficients β¨ j 1 m 1 j 2 m 2 | j m β© { \ displaystyle \ langle j _ { 1 } \, m _ { 1 } \, j _ { 2 } \, m _ { 2 } | j \, m \ rangle } are the clebsch β gordan coefficients. note that some authors write them in a different order such as β¨ j1 j2 ; m1 m2 | j m β©. another common notation is β¨ j1 m1 j2 m2 | j m β© = cjmj1m1j2m2. applying the operators j = j β 1 + 1 β j j z = j z β 1 + 1 β j z { \ displaystyle { \ begin { aligned } \ mathrm { j } & = \ mathrm { j } \ otimes 1 + 1 \ otimes \ mathrm { j } \ \ \ mathrm { j } _ { \ mathrm { z } } & = \ mathrm { j } _ { \ mathrm { z } } \ otimes 1 + 1 \ otimes \ mathrm { j } _ { \ mathrm { z } } \ end { aligned } } } to both sides of the defining equation shows that the clebsch β gordan coefficients can only be nonzero when | j 1 β j 2 | β€ j β€ j 1 + j 2 m = m 1 + m 2. { \ displaystyle { \ begin { aligned } | j _ { 1 } - j _ { 2 } | \ leq j & \ leq j _ { 1 } + j _ { 2 } \ \ m & = m _ { 1 } + m _ { 2 }. \ end { aligned } } } = = recursion relations = = the recursion relations were discovered by physicist giulio racah from the hebrew university of jerusalem in 1941. applying the total angular momentum raising and lowering operators j Β± = j Β± β 1 + 1 β j Β± { \ displaystyle \ mathrm { j } _ { \ pm } = \ mathrm { j } _ { \ pm } \ otimes 1 + 1 \ otimes \ mathrm { j } _ { \ pm } } to the left hand side of the defining equation gives j Β± | [ j 1 j 2 ] j m β© = c Β± ( j, m ) | [ j 1 j 2
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##s \ mathrm { j } _ { \ pm } } to the left hand side of the defining equation gives j Β± | [ j 1 j 2 ] j m β© = c Β± ( j, m ) | [ j 1 j 2 ] j ( m Β± 1 ) β© = c Β± ( j, m ) m 1, m 2 | j 1 m 1 j 2 m 2 β© β¨ j 1 m 1 j 2 m 2 | j ( m Β± 1 ) β© { \ displaystyle { \ begin { aligned } \ mathrm { j } _ { \ pm } | [ j _ { 1 } \, j _ { 2 } ] \, j \, m \ rangle & = \ hbar c _ { \ pm } ( j, m ) | [ j _ { 1 } \, j _ { 2 } ] \, j \, ( m \ pm 1 ) \ rangle \ \ & = \ hbar c _ { \ pm } ( j, m ) \ sum _ { m _ { 1 }, m _ { 2 } } | j _ { 1 } \, m _ { 1 } \, j _ { 2 } \, m _ { 2 } \ rangle \ langle j _ { 1 } \, m _ { 1 } \, j _ { 2 } \, m _ { 2 } | j \, ( m \ pm 1 ) \ rangle \ end { aligned } } } applying the same operators to the right hand side gives j Β± m 1, m 2 | j 1 m 1 j 2 m 2 β© β¨ j 1 m 1 j 2 m 2 | j m β© = m 1, m 2 ( c Β± ( j 1, m 1 ) | j 1 ( m 1 Β± 1 ) j 2 m 2 β© + c Β± ( j 2, m 2 ) | j 1 m 1 j 2 ( m 2 Β± 1 ) β© ) β¨ j 1 m 1 j 2 m 2 | j m β© = m 1, m 2 | j 1 m 1 j 2 m 2 β© ( c Β± ( j 1, m 1 1 ) β¨ j 1 ( m 1 1 ) j 2 m 2 | j m β© + c Β± ( j 2, m 2 1 ) β¨ j 1 m 1 j 2 ( m 2 1 ) | j m β© ). { \ displaystyle { \ begin { aligned } \ mathrm { j } _ { \ pm
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c Β± ( j 2, m 2 1 ) β¨ j 1 m 1 j 2 ( m 2 1 ) | j m β© ). { \ displaystyle { \ begin { aligned } \ mathrm { j } _ { \ pm } & \ sum _ { m _ { 1 }, m _ { 2 } } | j _ { 1 } \, m _ { 1 } \, j _ { 2 } \, m _ { 2 } \ rangle \ langle j _ { 1 } \, m _ { 1 } \, j _ { 2 } \, m _ { 2 } | j \, m \ rangle \ \ = \ hbar & \ sum _ { m _ { 1 }, m _ { 2 } } { \ bigl ( } c _ { \ pm } ( j _ { 1 }, m _ { 1 } ) | j _ { 1 } \, ( m _ { 1 } \ pm 1 ) \, j _ { 2 } \, m _ { 2 } \ rangle + c _ { \ pm } ( j _ { 2 }, m _ { 2 } ) | j _ { 1 } \, m _ { 1 } \, j _ { 2 } \, ( m _ { 2 } \ pm 1 ) \ rangle { \ bigr ) } \ langle j _ { 1 } \, m _ { 1 } \, j _ { 2 } \, m _ { 2 } | j \, m \ rangle \ \ = \ hbar & \ sum _ { m _ { 1 }, m _ { 2 } } | j _ { 1 } \, m _ { 1 } \, j _ { 2 } \, m _ { 2 } \ rangle { \ bigl ( } c _ { \ pm } ( j _ { 1 }, m _ { 1 } \ mp 1 ) \ langle j _ { 1 } \, ( m _ { 1 } \ mp 1 ) \, j _ { 2 } \, m _ { 2 } | j \, m \ rangle + c _ { \ pm } ( j _ { 2 }, m _ { 2 } \ mp 1 ) \ langle j _ { 1 } \, m _ { 1 } \, j _ { 2 } \, ( m _ { 2 } \ mp 1 ) | j \, m \ rangle { \ bigr ) }. \
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\ langle j _ { 1 } \, m _ { 1 } \, j _ { 2 } \, ( m _ { 2 } \ mp 1 ) | j \, m \ rangle { \ bigr ) }. \ end { aligned } } } combining these results gives recursion relations for the clebsch β gordan coefficients, where cΒ± was defined in 1 : c Β± ( j, m ) β¨ j 1 m 1 j 2 m 2 | j ( m Β± 1 ) β© = c Β± ( j 1, m 1 1 ) β¨ j 1 ( m 1 1 ) j 2 m 2 | j m β© + c Β± ( j 2, m 2 1 ) β¨ j 1 m 1 j 2 ( m 2 1 ) | j m β©. { \ displaystyle c _ { \ pm } ( j, m ) \ langle j _ { 1 } \, m _ { 1 } \, j _ { 2 } \, m _ { 2 } | j \, ( m \ pm 1 ) \ rangle = c _ { \ pm } ( j _ { 1 }, m _ { 1 } \ mp 1 ) \ langle j _ { 1 } \, ( m _ { 1 } \ mp 1 ) \, j _ { 2 } \, m _ { 2 } | j \, m \ rangle + c _ { \ pm } ( j _ { 2 }, m _ { 2 } \ mp 1 ) \ langle j _ { 1 } \, m _ { 1 } \, j _ { 2 } \, ( m _ { 2 } \ mp 1 ) | j \, m \ rangle. } taking the upper sign with the condition that m = j gives initial recursion relation : 0 = c + ( j 1, m 1 β 1 ) β¨ j 1 ( m 1 β 1 ) j 2 m 2 | j j β© + c + ( j 2, m 2 β 1 ) β¨ j 1 m 1 j 2 ( m 2 β 1 ) | j j β©. { \ displaystyle 0 = c _ { + } ( j _ { 1 }, m _ { 1 } - 1 ) \ langle j _ { 1 } \, ( m _ { 1 } - 1 ) \, j _ { 2 } \, m _ { 2 } | j \, j \ rangle + c _ { + } ( j _ { 2 },
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_ { 1 } \, ( m _ { 1 } - 1 ) \, j _ { 2 } \, m _ { 2 } | j \, j \ rangle + c _ { + } ( j _ { 2 }, m _ { 2 } - 1 ) \ langle j _ { 1 } \, m _ { 1 } \, j _ { 2 } \, ( m _ { 2 } - 1 ) | j \, j \ rangle. } in the condon β shortley phase convention, one adds the constraint that β¨ j 1 j 1 j 2 ( j β j 1 ) | j j β© > 0 { \ displaystyle \ langle j _ { 1 } \, j _ { 1 } \, j _ { 2 } \, ( j - j _ { 1 } ) | j \, j \ rangle > 0 } ( and is therefore also real ). the clebsch β gordan coefficients β¨ j1 m1 j2 m2 | j m β© can then be found from these recursion relations. the normalization is fixed by the requirement that the sum of the squares, which equivalent to the requirement that the norm of the state | [ j1 j2 ] j j β© must be one. the lower sign in the recursion relation can be used to find all the clebsch β gordan coefficients with m = j β 1. repeated use of that equation gives all coefficients. this procedure to find the clebsch β gordan coefficients shows that they are all real in the condon β shortley phase convention. = = explicit expression = = = = orthogonality relations = = these are most clearly written down by introducing the alternative notation β¨ j m | j 1 m 1 j 2 m 2 β© β‘ β¨ j 1 m 1 j 2 m 2 | j m β© { \ displaystyle \ langle j \, m | j _ { 1 } \, m _ { 1 } \, j _ { 2 } \, m _ { 2 } \ rangle \ equiv \ langle j _ { 1 } \, m _ { 1 } \, j _ { 2 } \, m _ { 2 } | j \, m \ rangle } the first orthogonality relation is j = | j 1 β j 2 | j 1 + j 2 m = β j j β¨ j 1 m 1 j 2 m 2 | j m β© β¨ j m | j 1 m 1 β² j
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the first orthogonality relation is j = | j 1 β j 2 | j 1 + j 2 m = β j j β¨ j 1 m 1 j 2 m 2 | j m β© β¨ j m | j 1 m 1 β² j 2 m 2 β² β© = β¨ j 1 m 1 j 2 m 2 | j 1 m 1 β² j 2 m 2 β² β© = Ξ΄ m 1, m 1 β² Ξ΄ m 2, m 2 β² { \ displaystyle \ sum _ { j = | j _ { 1 } - j _ { 2 } | } ^ { j _ { 1 } + j _ { 2 } } \ sum _ { m = - j } ^ { j } \ langle j _ { 1 } \, m _ { 1 } \, j _ { 2 } \, m _ { 2 } | j \, m \ rangle \ langle j \, m | j _ { 1 } \, m _ { 1 }'\, j _ { 2 } \, m _ { 2 }'\ rangle = \ langle j _ { 1 } \, m _ { 1 } \, j _ { 2 } \, m _ { 2 } | j _ { 1 } \, m _ { 1 }'\, j _ { 2 } \, m _ { 2 }'\ rangle = \ delta _ { m _ { 1 }, m _ { 1 }'} \ delta _ { m _ { 2 }, m _ { 2 }'} } ( derived from the fact that 1 = x | x β© β¨ x | { \ textstyle \ mathbf { 1 } = \ sum _ { x } | x \ rangle \ langle x | } ) and the second one is m 1, m 2 β¨ j m | j 1 m 1 j 2 m 2 β© β¨ j 1 m 1 j 2 m 2 | j β² m β² β© = β¨ j m | j β² m β² β© = Ξ΄ j, j β² Ξ΄ m, m β². { \ displaystyle \ sum _ { m _ { 1 }, m _ { 2 } } \ langle j \, m | j _ { 1 } \, m _ { 1 } \, j _ { 2 } \, m _ { 2 } \ rangle \ langle j _ { 1 } \, m _ { 1 } \, j _ { 2 } \, m _ { 2 } | j '
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} \, j _ { 2 } \, m _ { 2 } \ rangle \ langle j _ { 1 } \, m _ { 1 } \, j _ { 2 } \, m _ { 2 } | j'\, m'\ rangle = \ langle j \, m | j'\, m'\ rangle = \ delta _ { j, j'} \ delta _ { m, m'}. } = = special cases = = for j = 0 the clebsch β gordan coefficients are given by β¨ j 1 m 1 j 2 m 2 | 0 0 β© = Ξ΄ j 1, j 2 Ξ΄ m 1, β m 2 ( β 1 ) j 1 β m 1 2 j 1 + 1. { \ displaystyle \ langle j _ { 1 } \, m _ { 1 } \, j _ { 2 } \, m _ { 2 } | 0 \, 0 \ rangle = \ delta _ { j _ { 1 }, j _ { 2 } } \ delta _ { m _ { 1 }, - m _ { 2 } } { \ frac { ( - 1 ) ^ { j _ { 1 } - m _ { 1 } } } { \ sqrt { 2j _ { 1 } + 1 } } }. } for j = j1 + j2 and m = j we have β¨ j 1 j 1 j 2 j 2 | ( j 1 + j 2 ) ( j 1 + j 2 ) β© = 1. { \ displaystyle \ langle j _ { 1 } \, j _ { 1 } \, j _ { 2 } \, j _ { 2 } | ( j _ { 1 } + j _ { 2 } ) \, ( j _ { 1 } + j _ { 2 } ) \ rangle = 1. } for j1 = j2 = j / 2 and m1 = βm2 we have β¨ j 1 m 1 j 1 ( β m 1 ) | ( 2 j 1 ) 0 β© = ( 2 j 1 )! 2 ( j 1 β m 1 )! ( j 1 + m 1 )! ( 4 j 1 )!. { \ displaystyle \ langle j _ { 1 } \, m _ { 1 } \, j _ { 1 } \, ( - m _ { 1 } ) | ( 2j _ { 1 } ) \, 0 \ rangle = { \ frac
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##le j _ { 1 } \, m _ { 1 } \, j _ { 1 } \, ( - m _ { 1 } ) | ( 2j _ { 1 } ) \, 0 \ rangle = { \ frac { ( 2j _ { 1 } )! ^ { 2 } } { ( j _ { 1 } - m _ { 1 } )! ( j _ { 1 } + m _ { 1 } )! { \ sqrt { ( 4j _ { 1 } )! } } } }. } for j1 = j2 = m1 = βm2 we have β¨ j 1 j 1 j 1 ( β j 1 ) | j 0 β© = ( 2 j 1 )! 2 j + 1 ( j + 2 j 1 + 1 )! ( 2 j 1 β j )!. { \ displaystyle \ langle j _ { 1 } \, j _ { 1 } \, j _ { 1 } \, ( - j _ { 1 } ) | j \, 0 \ rangle = ( 2j _ { 1 } )! { \ sqrt { \ frac { 2j + 1 } { ( j + 2j _ { 1 } + 1 )! ( 2j _ { 1 } - j )! } } }. } for j2 = 1, m2 = 0 we have β¨ j 1 m 1 0 | ( j 1 + 1 ) m β© = ( j 1 β m + 1 ) ( j 1 + m + 1 ) ( 2 j 1 + 1 ) ( j 1 + 1 ) β¨ j 1 m 1 0 | j 1 m β© = m j 1 ( j 1 + 1 ) β¨ j 1 m 1 0 | ( j 1 β 1 ) m β© = β ( j 1 β m ) ( j 1 + m ) j 1 ( 2 j 1 + 1 ) { \ displaystyle { \ begin { aligned } \ langle j _ { 1 } \, m \, 1 \, 0 | ( j _ { 1 } + 1 ) \, m \ rangle & = { \ sqrt { \ frac { ( j _ { 1 } - m + 1 ) ( j _ { 1 } + m + 1 ) } { ( 2j _ { 1 } + 1 ) ( j _ { 1 } + 1 ) } } } \ \ \ langle j _ { 1 } \, m \, 1 \, 0 | j _ { 1 }
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) } { ( 2j _ { 1 } + 1 ) ( j _ { 1 } + 1 ) } } } \ \ \ langle j _ { 1 } \, m \, 1 \, 0 | j _ { 1 } \, m \ rangle & = { \ frac { m } { \ sqrt { j _ { 1 } ( j _ { 1 } + 1 ) } } } \ \ \ langle j _ { 1 } \, m \, 1 \, 0 | ( j _ { 1 } - 1 ) \, m \ rangle & = - { \ sqrt { \ frac { ( j _ { 1 } - m ) ( j _ { 1 } + m ) } { j _ { 1 } ( 2j _ { 1 } + 1 ) } } } \ end { aligned } } } for j2 = 1 / 2 we have β¨ j 1 ( m β 1 2 ) 1 2 1 2 | ( j 1 Β± 1 2 ) m β© = Β± 1 2 ( 1 Β± m j 1 + 1 2 ) β¨ j 1 ( m + 1 2 ) 1 2 ( β 1 2 ) | ( j 1 Β± 1 2 ) m β© = 1 2 ( 1 m j 1 + 1 2 ) { \ displaystyle { \ begin { aligned } \ left \ langle j _ { 1 } \, \ left ( m - { \ frac { 1 } { 2 } } \ right ) \, { \ frac { 1 } { 2 } } \, { \ frac { 1 } { 2 } } { \ bigg | } \ left ( j _ { 1 } \ pm { \ frac { 1 } { 2 } } \ right ) \, m \ right \ rangle & = \ pm { \ sqrt { { \ frac { 1 } { 2 } } \ left ( 1 \ pm { \ frac { m } { j _ { 1 } + { \ frac { 1 } { 2 } } } } \ right ) } } \ \ \ left \ langle j _ { 1 } \, \ left ( m + { \ frac { 1 } { 2 } } \ right ) \, { \ frac { 1 } { 2 } } \, \ left ( - { \ frac { 1 } { 2 } } \ right ) { \ bigg | } \ left ( j _ { 1 } \ pm { \ fra
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{ \ frac { 1 } { 2 } } \, \ left ( - { \ frac { 1 } { 2 } } \ right ) { \ bigg | } \ left ( j _ { 1 } \ pm { \ frac { 1 } { 2 } } \ right ) \, m \ right \ rangle & = { \ sqrt { { \ frac { 1 } { 2 } } \ left ( 1 \ mp { \ frac { m } { j _ { 1 } + { \ frac { 1 } { 2 } } } } \ right ) } } \ end { aligned } } } = = symmetry properties = = β¨ j 1 m 1 j 2 m 2 | j m β© = ( β 1 ) j 1 + j 2 β j β¨ j 1 ( β m 1 ) j 2 ( β m 2 ) | j ( β m ) β© = ( β 1 ) j 1 + j 2 β j β¨ j 2 m 2 j 1 m 1 | j m β© = ( β 1 ) j 1 β m 1 2 j + 1 2 j 2 + 1 β¨ j 1 m 1 j ( β m ) | j 2 ( β m 2 ) β© = ( β 1 ) j 2 + m 2 2 j + 1 2 j 1 + 1 β¨ j ( β m ) j 2 m 2 | j 1 ( β m 1 ) β© = ( β 1 ) j 1 β m 1 2 j + 1 2 j 2 + 1 β¨ j m j 1 ( β m 1 ) | j 2 m 2 β© = ( β 1 ) j 2 + m 2 2 j + 1 2 j 1 + 1 β¨ j 2 ( β m 2 ) j m | j 1 m 1 β© { \ displaystyle { \ begin { aligned } \ langle j _ { 1 } \, m _ { 1 } \, j _ { 2 } \, m _ { 2 } | j \, m \ rangle & = ( - 1 ) ^ { j _ { 1 } + j _ { 2 } - j } \ langle j _ { 1 } \, ( - m _ { 1 } ) \, j _ { 2 } \, ( - m _ { 2 } ) | j \, ( - m ) \ rangle \ \ & = ( - 1 ) ^ { j _ { 1 } + j _ { 2 } - j } \ langle j _ { 2 } \, m _ { 2 } \,
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\, ( - m ) \ rangle \ \ & = ( - 1 ) ^ { j _ { 1 } + j _ { 2 } - j } \ langle j _ { 2 } \, m _ { 2 } \, j _ { 1 } \, m _ { 1 } | j \, m \ rangle \ \ & = ( - 1 ) ^ { j _ { 1 } - m _ { 1 } } { \ sqrt { \ frac { 2j + 1 } { 2j _ { 2 } + 1 } } } \ langle j _ { 1 } \, m _ { 1 } \, j \, ( - m ) | j _ { 2 } \, ( - m _ { 2 } ) \ rangle \ \ & = ( - 1 ) ^ { j _ { 2 } + m _ { 2 } } { \ sqrt { \ frac { 2j + 1 } { 2j _ { 1 } + 1 } } } \ langle j \, ( - m ) \, j _ { 2 } \, m _ { 2 } | j _ { 1 } \, ( - m _ { 1 } ) \ rangle \ \ & = ( - 1 ) ^ { j _ { 1 } - m _ { 1 } } { \ sqrt { \ frac { 2j + 1 } { 2j _ { 2 } + 1 } } } \ langle j \, m \, j _ { 1 } \, ( - m _ { 1 } ) | j _ { 2 } \, m _ { 2 } \ rangle \ \ & = ( - 1 ) ^ { j _ { 2 } + m _ { 2 } } { \ sqrt { \ frac { 2j + 1 } { 2j _ { 1 } + 1 } } } \ langle j _ { 2 } \, ( - m _ { 2 } ) \, j \, m | j _ { 1 } \, m _ { 1 } \ rangle \ end { aligned } } } a convenient way to derive these relations is by converting the clebsch β gordan coefficients to wigner 3 - j symbols using 3. the symmetry properties of wigner 3 - j symbols are much simpler. = = = rules for phase factors = = = care is needed when simplifying phase factors : a quantum number may be a half - integer rather than an integer, therefore
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. the symmetry properties of wigner 3 - j symbols are much simpler. = = = rules for phase factors = = = care is needed when simplifying phase factors : a quantum number may be a half - integer rather than an integer, therefore ( β1 ) 2k is not necessarily 1 for a given quantum number k unless it can be proven to be an integer. instead, it is replaced by the following weaker rule : ( β 1 ) 4 k = 1 { \ displaystyle ( - 1 ) ^ { 4k } = 1 } for any angular - momentum - like quantum number k. nonetheless, a combination of ji and mi is always an integer, so the stronger rule applies for these combinations : ( β 1 ) 2 ( j i β m i ) = 1 { \ displaystyle ( - 1 ) ^ { 2 ( j _ { i } - m _ { i } ) } = 1 } this identity also holds if the sign of either ji or mi or both is reversed. it is useful to observe that any phase factor for a given ( ji, mi ) pair can be reduced to the canonical form : ( β 1 ) a j i + b ( j i β m i ) { \ displaystyle ( - 1 ) ^ { aj _ { i } + b ( j _ { i } - m _ { i } ) } } where a β { 0, 1, 2, 3 } and b β { 0, 1 } ( other conventions are possible too ). converting phase factors into this form makes it easy to tell whether two phase factors are equivalent. ( note that this form is only locally canonical : it fails to take into account the rules that govern combinations of ( ji, mi ) pairs such as the one described in the next paragraph. ) an additional rule holds for combinations of j1, j2, and j3 that are related by a clebsch - gordan coefficient or wigner 3 - j symbol : ( β 1 ) 2 ( j 1 + j 2 + j 3 ) = 1 { \ displaystyle ( - 1 ) ^ { 2 ( j _ { 1 } + j _ { 2 } + j _ { 3 } ) } = 1 } this identity also holds if the sign of any ji is reversed, or if any of them are substituted with an mi instead. = = relation to wigner 3 - j symbols = = clebsch β gordan coefficients are related to wigner 3 - j symbols which have more convenient symmetry relations. the factor (
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or if any of them are substituted with an mi instead. = = relation to wigner 3 - j symbols = = clebsch β gordan coefficients are related to wigner 3 - j symbols which have more convenient symmetry relations. the factor ( β1 ) 2 j2 is due to the condon β shortley constraint that β¨ j1 j1 j2 ( j β j1 ) | j j β© > 0, while ( β1 ) j β m is due to the time - reversed nature of | j m β©. this allows to reach the general expression : β¨ j 1 m 1 j 2 m 2 | j m β© β‘ Ξ΄ ( m 1 + m 2, m ) ( 2 j + 1 ) ( j 1 + j 2 β j )! ( j 1 β j 2 + j )! ( β j 1 + j 2 + j )! ( j 1 + j 2 + j + 1 )! Γ Γ ( j 1 β m 1 )! ( j 1 + m 1 )! ( j 2 β m 2 )! ( j 2 + m 2 )! ( j β m )! ( j + m )! Γ Γ k = k n ( β 1 ) k k! ( j 1 + j 2 β j β k )! ( j 1 β m 1 β k )! ( j 2 + m 2 β k )! ( j β j 2 + m 1 + k )! ( j β j 1 β m 2 + k )!,. { \ displaystyle { \ begin { aligned } \ langle j _ { 1 } \, m _ { 1 } \, j _ { 2 } \, m _ { 2 } | j \, m \ rangle & \ equiv \ delta ( m _ { 1 } + m _ { 2 }, m ) { \ sqrt { \ frac { ( 2j + 1 ) ( j _ { 1 } + j _ { 2 } - j )! ( j _ { 1 } - j _ { 2 } + j )! ( - j _ { 1 } + j _ { 2 } + j )! } { ( j _ { 1 } + j _ { 2 } + j + 1 )! } } } \ \ times { } \ \ [ 6pt ] & \ times { \ sqrt { ( j _ { 1 } - m _ { 1 } )! ( j _ { 1 } + m _ { 1 } )! (
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} } \ \ times { } \ \ [ 6pt ] & \ times { \ sqrt { ( j _ { 1 } - m _ { 1 } )! ( j _ { 1 } + m _ { 1 } )! ( j _ { 2 } - m _ { 2 } )! ( j _ { 2 } + m _ { 2 } )! ( j - m )! ( j + m )! } } \ \ times { } \ \ [ 6pt ] & \ times \ sum _ { k = k } ^ { n } { \ frac { ( - 1 ) ^ { k } } { k! ( j _ { 1 } + j _ { 2 } - j - k )! ( j _ { 1 } - m _ { 1 } - k )! ( j _ { 2 } + m _ { 2 } - k )! ( j - j _ { 2 } + m _ { 1 } + k )! ( j - j _ { 1 } - m _ { 2 } + k )! } }, \ end { aligned } }. } the summation is performed over those integer values k for which the argument of each factorial in the denominator is non - negative, i. e. summation limits k and n are taken equal : the lower one k = max ( 0, j 2 β j β m 1, j 1 β j + m 2 ), { \ displaystyle k = \ max ( 0, j _ { 2 } - j - m _ { 1 }, j _ { 1 } - j + m _ { 2 } ), } the upper one n = min ( j 1 + j 2 β j, j 1 β m 1, j 2 + m 2 ). { \ displaystyle n = \ min ( j _ { 1 } + j _ { 2 } - j, j _ { 1 } - m _ { 1 }, j _ { 2 } + m _ { 2 } ). } factorials of negative numbers are conventionally taken equal to zero, so that the values of the 3j symbol at, for example, j 3 > j 1 + j 2 { \ displaystyle j _ { 3 } > j _ { 1 } + j _ { 2 } } or j 1 < m 1 { \ displaystyle j _ { 1 } < m _ { 1 } } are automatically set to zero. = = relation to wigner d - matrices =
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j _ { 1 } + j _ { 2 } } or j 1 < m 1 { \ displaystyle j _ { 1 } < m _ { 1 } } are automatically set to zero. = = relation to wigner d - matrices = = 0 2 Ο d Ξ± 0 Ο sin Ξ² d Ξ² 0 2 Ο d Ξ³ d m, k j ( Ξ±, Ξ², Ξ³ ) β d m 1, k 1 j 1 ( Ξ±, Ξ², Ξ³ ) d m 2, k 2 j 2 ( Ξ±, Ξ², Ξ³ ) = 8 Ο 2 2 j + 1 β¨ j 1 m 1 j 2 m 2 | j m β© β¨ j 1 k 1 j 2 k 2 | j k β© { \ displaystyle { \ begin { aligned } & \ int _ { 0 } ^ { 2 \ pi } d \ alpha \ int _ { 0 } ^ { \ pi } \ sin \ beta \, d \ beta \ int _ { 0 } ^ { 2 \ pi } d \ gamma \, d _ { m, k } ^ { j } ( \ alpha, \ beta, \ gamma ) ^ { * } d _ { m _ { 1 }, k _ { 1 } } ^ { j _ { 1 } } ( \ alpha, \ beta, \ gamma ) d _ { m _ { 2 }, k _ { 2 } } ^ { j _ { 2 } } ( \ alpha, \ beta, \ gamma ) \ \ { } = { } & { \ frac { 8 \ pi ^ { 2 } } { 2j + 1 } } \ langle j _ { 1 } \, m _ { 1 } \, j _ { 2 } \, m _ { 2 } | j \, m \ rangle \ langle j _ { 1 } \, k _ { 1 } \, j _ { 2 } \, k _ { 2 } | j \, k \ rangle \ end { aligned } } } = = relation to spherical harmonics = = in the case where integers are involved, the coefficients can be related to integrals of spherical harmonics : 4 Ο y β 1 m 1 β ( Ο ) y β 2 m 2 β ( Ο ) y l m ( Ο ) d Ο = ( 2 β 1 + 1 ) ( 2 β 2 + 1 ) 4 Ο ( 2 l + 1 ) β¨ β 1 0 β 2 0 | l 0 β© β¨ β 1 m 1 β 2 m 2
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l m ( Ο ) d Ο = ( 2 β 1 + 1 ) ( 2 β 2 + 1 ) 4 Ο ( 2 l + 1 ) β¨ β 1 0 β 2 0 | l 0 β© β¨ β 1 m 1 β 2 m 2 | l m β© { \ displaystyle \ int _ { 4 \ pi } y _ { \ ell _ { 1 } } ^ { m _ { 1 } } { } ^ { * } ( \ omega ) y _ { \ ell _ { 2 } } ^ { m _ { 2 } } { } ^ { * } ( \ omega ) y _ { l } ^ { m } ( \ omega ) \, d \ omega = { \ sqrt { \ frac { ( 2 \ ell _ { 1 } + 1 ) ( 2 \ ell _ { 2 } + 1 ) } { 4 \ pi ( 2l + 1 ) } } } \ langle \ ell _ { 1 } \, 0 \, \ ell _ { 2 } \, 0 | l \, 0 \ rangle \ langle \ ell _ { 1 } \, m _ { 1 } \, \ ell _ { 2 } \, m _ { 2 } | l \, m \ rangle } it follows from this and orthonormality of the spherical harmonics that cg coefficients are in fact the expansion coefficients of a product of two spherical harmonics in terms of a single spherical harmonic : y β 1 m 1 ( Ο ) y β 2 m 2 ( Ο ) = l, m ( 2 β 1 + 1 ) ( 2 β 2 + 1 ) 4 Ο ( 2 l + 1 ) β¨ β 1 0 β 2 0 | l 0 β© β¨ β 1 m 1 β 2 m 2 | l m β© y l m ( Ο ) { \ displaystyle y _ { \ ell _ { 1 } } ^ { m _ { 1 } } ( \ omega ) y _ { \ ell _ { 2 } } ^ { m _ { 2 } } ( \ omega ) = \ sum _ { l, m } { \ sqrt { \ frac { ( 2 \ ell _ { 1 } + 1 ) ( 2 \ ell _ { 2 } + 1 ) } { 4 \ pi ( 2l + 1 ) } } } \ langle \ ell _ { 1 } \, 0 \, \ ell _ { 2 } \, 0 | l
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ell _ { 2 } + 1 ) } { 4 \ pi ( 2l + 1 ) } } } \ langle \ ell _ { 1 } \, 0 \, \ ell _ { 2 } \, 0 | l \, 0 \ rangle \ langle \ ell _ { 1 } \, m _ { 1 } \, \ ell _ { 2 } \, m _ { 2 } | l \, m \ rangle y _ { l } ^ { m } ( \ omega ) } = = other properties = = m ( β 1 ) j β m β¨ j m j ( β m ) | j 0 β© = Ξ΄ j, 0 2 j + 1 { \ displaystyle \ sum _ { m } ( - 1 ) ^ { j - m } \ langle j \, m \, j \, ( - m ) | j \, 0 \ rangle = \ delta _ { j, 0 } { \ sqrt { 2j + 1 } } } = = clebsch β gordan coefficients for specific groups = = for arbitrary groups and their representations, clebsch β gordan coefficients are not known in general. however, algorithms to produce clebsch β gordan coefficients for the special unitary group su ( n ) are known. in particular, su ( 3 ) clebsch - gordan coefficients have been computed and tabulated because of their utility in characterizing hadronic decays, where a flavor - su ( 3 ) symmetry exists that relates the up, down, and strange quarks. a web interface for tabulating su ( n ) clebsch β gordan coefficients is readily available. = = see also = = = = remarks = = = = notes = = = = references = = alex, a. ; kalus, m. ; huckleberry, a. ; von delft, j. ( 2011 ). " a numerical algorithm for the explicit calculation of su ( n ) and sl ( n, c ) clebsch β gordan coefficients ". j. math. phys. 82 ( 2 ) : 023507. arxiv : 1009. 0437. bibcode : 2011jmp.... 52b3507a. doi : 10. 1063 / 1. 3521562. s2cid 55572438. condon, edward u. ; shortley, g. h. ( 1970 ). "
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. 52b3507a. doi : 10. 1063 / 1. 3521562. s2cid 55572438. condon, edward u. ; shortley, g. h. ( 1970 ). " ch. 3 ". the theory of atomic spectra. cambridge : cambridge university press. isbn 978 - 0 - 521 - 09209 - 8. edmonds, a. r. ( 1957 ). angular momentum in quantum mechanics. princeton, new jersey : princeton university press. isbn 978 - 0 - 691 - 07912 - 7. { { cite book } } : isbn / date incompatibility ( help ) greiner, walter ; muller, berndt ( 1994 ). quantum mechanics : symmetries ( 2nd ed. ). springer verlag. isbn 978 - 3540580805. hall, brian c. ( 2015 ), lie groups, lie algebras, and representations : an elementary introduction, graduate texts in mathematics, vol. 222 ( 2nd ed. ), springer, isbn 978 - 3319134666 kaplan, l. m. ; resnikoff, m. ( 1967 ). " matrix products and explicit 3, 6, 9, and 12j coefficients of the regular representation of su ( n ) ". j. math. phys. 8 ( 11 ) : 2194. bibcode : 1967jmp..... 8. 2194k. doi : 10. 1063 / 1. 1705141. kaeding, thomas ( 1995 ). " tables of su ( 3 ) isoscalar factors ". atomic data and nuclear data tables. 61 ( 2 ) : 233 β 288. arxiv : nucl - th / 9502037. bibcode : 1995adndt.. 61.. 233k. doi : 10. 1006 / adnd. 1995. 1011. merzbacher, eugen ( 1998 ). quantum mechanics ( 3rd ed. ). john wiley. pp. 428 β 9. isbn 978 - 0 - 471 - 88702 - 7. albert messiah ( 1966 ). quantum mechanics ( vols. i & ii ), english translation from french by g. m. temmer. north holland, john wiley & sons. de swart, j. j. ( 1963 ). " the octet model and its clebsch - gordan coefficients ". rev. mod. phys. ( submitted manuscript ). 35 (
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north holland, john wiley & sons. de swart, j. j. ( 1963 ). " the octet model and its clebsch - gordan coefficients ". rev. mod. phys. ( submitted manuscript ). 35 ( 4 ) : 916. bibcode : 1963rvmp... 35.. 916d. doi : 10. 1103 / revmodphys. 35. 916. = = external links = = nakamura, kenzo ; et al. ( 2010 ). " review of particle physics : clebsch - gordan coefficients, spherical harmonics, and d functions " ( pdf ). journal of physics g : nuclear and particle physics. 37 ( 75021 ) : 368. bibcode : 2010jphg... 37g5021n. doi : 10. 1088 / 0954 - 3899 / 37 / 7a / 075021. partial update for 2012 edition clebsch β gordan, 3 - j and 6 - j coefficient web calculator downloadable clebsch β gordan coefficient calculator for mac and windows web interface for tabulating su ( n ) clebsch β gordan coefficients = = further reading = =
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geometric mechanics is a branch of mathematics applying particular geometric methods to many areas of mechanics, from mechanics of particles and rigid bodies to fluid mechanics and control theory. geometric mechanics applies principally to systems for which the configuration space is a lie group, or a group of diffeomorphisms, or more generally where some aspect of the configuration space has this group structure. for example, the configuration space of a rigid body such as a satellite is the group of euclidean motions ( translations and rotations in space ), while the configuration space for a liquid crystal is the group of diffeomorphisms coupled with an internal state ( gauge symmetry or order parameter ). = = momentum map and reduction = = one of the principal ideas of geometric mechanics is reduction, which goes back to jacobi's elimination of the node in the 3 - body problem, but in its modern form is due to k. meyer ( 1973 ) and independently j. e. marsden and a. weinstein ( 1974 ), both inspired by the work of smale ( 1970 ). symmetry of a hamiltonian or lagrangian system gives rise to conserved quantities, by noether's theorem, and these conserved quantities are the components of the momentum map j. if p is the phase space and g the symmetry group, the momentum map is a map j : p β g β { \ displaystyle \ mathbf { j } : p \ to { \ mathfrak { g } } ^ { * } }, and the reduced spaces are quotients of the level sets of j by the subgroup of g preserving the level set in question : for ΞΌ β g β { \ displaystyle \ mu \ in { \ mathfrak { g } } ^ { * } } one defines p ΞΌ = j β 1 ( ΞΌ ) / g ΞΌ { \ displaystyle p _ { \ mu } = \ mathbf { j } ^ { - 1 } ( \ mu ) / g _ { \ mu } }, and this reduced space is a symplectic manifold if ΞΌ { \ displaystyle \ mu } is a regular value of j. = = variational principles = = hamilton's principle lagrange d'alembert principle maupertuis'principle of least action euler β poincare vakonomic = = geometric integrators = = one of the important developments arising from the geometric approach to mechanics is the incorporation of the geometry into numerical methods. in particular symplectic and variational integ
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euler β poincare vakonomic = = geometric integrators = = one of the important developments arising from the geometric approach to mechanics is the incorporation of the geometry into numerical methods. in particular symplectic and variational integrators are proving particularly accurate for long - term integration of hamiltonian and lagrangian systems. = = history = = the term " geometric mechanics " occasionally refers to 17th - century mechanics. as a modern subject, geometric mechanics has its roots in four works written in the 1960s. these were by vladimir arnold ( 1966 ), stephen smale ( 1970 ) and jean - marie souriau ( 1970 ), and the first edition of abraham and marsden's foundation of mechanics ( 1967 ). arnold's fundamental work showed that euler's equations for the free rigid body are the equations for geodesic flow on the rotation group so ( 3 ) and carried this geometric insight over to the dynamics of ideal fluids, where the rotation group is replaced by the group of volume - preserving diffeomorphisms. smale's paper on topology and mechanics investigates the conserved quantities arising from noether's theorem when a lie group of symmetries acts on a mechanical system, and defines what is now called the momentum map ( which smale calls angular momentum ), and he raises questions about the topology of the energy - momentum level surfaces and the effect on the dynamics. in his book, souriau also considers the conserved quantities arising from the action of a group of symmetries, but he concentrates more on the geometric structures involved ( for example the equivariance properties of this momentum for a wide class of symmetries ), and less on questions of dynamics. these ideas, and particularly those of smale were central in the second edition of foundations of mechanics ( abraham and marsden, 1978 ). = = applications = = computer graphics control theory β see bloch ( 2003 ) liquid crystals β see gay - balmaz, ratiu, tronci ( 2013 ) magnetohydrodynamics molecular oscillations nonholonomic constraints β see bloch ( 2003 ) nonlinear stability plasmas β see holm, marsden, weinstein ( 1985 ) quantum mechanics quantum chemistry β see foskett, holm, tronci ( 2019 ) superfluids thermodynamics β see gay - balmaz, yoshimra ( 2018 ) trajectory planning for space exploration underwater vehicles variational integrators ; see
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##kett, holm, tronci ( 2019 ) superfluids thermodynamics β see gay - balmaz, yoshimra ( 2018 ) trajectory planning for space exploration underwater vehicles variational integrators ; see marsden and west ( 2001 ) = = references = = abraham, ralph ; marsden, jerrold e. ( 1978 ), foundations of mechanics ( 2nd ed. ), addison - wesley arnold, vladimir ( 1966 ), " sur la geometrie differentielle des groupes de lie de dimension infine et ses applications a l'hydrodynamique des fluides parfaits " ( pdf ), annales de l'institut fourier, 16 : 319 β 361, doi : 10. 5802 / aif. 233 arnold, vladimir ( 1978 ), mathematical methods for classical mechanics, springer - verlag bloch, anthony ( 2003 ). nonholonomic mechanics and control. springer - verlag. foskett, michael s. ; holm, darryl d. ; tronci, cesare ( 2019 ). " geometry of nonadiabatic quantum hydrodynamics ". acta applicandae mathematicae. 162 ( 1 ) : 63 β 103. arxiv : 1807. 01031. doi : 10. 1007 / s10440 - 019 - 00257 - 1. s2cid 85531406. gay - balmaz, francois ; ratiu, tudor ; tronci, cesare ( 2013 ). " equivalent theories of liquid crystal dynamics ". arch. ration. mech. anal. 210 ( 3 ) : 773 β 811. arxiv : 1102. 2918. bibcode : 2013arrma. 210.. 773g. doi : 10. 1007 / s00205 - 013 - 0673 - 1. s2cid 14968950. holm, darryl d. ; marsden, jerrold e. ; ratiu, tudor s. ; weinstein, alan ( 1985 ). " nonlinear stability of fluid and plasma equilibria ". physics reports. 123 ( 1 β 2 ) : 1 β 116. bibcode : 1985phr... 123.... 1h. doi : 10. 1016 / 0370 - 1573 ( 85 ) 90028 - 6. libermann, paulette ; marle, charles - michel ( 1987
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##ode : 1985phr... 123.... 1h. doi : 10. 1016 / 0370 - 1573 ( 85 ) 90028 - 6. libermann, paulette ; marle, charles - michel ( 1987 ). symplectic geometry and analytical mechanics. mathematics and its applications. vol. 35. dordrecht : d. reidel. doi : 10. 1007 / 978 - 94 - 009 - 3807 - 6. isbn 90 - 277 - 2438 - 5. marsden, jerrold ; weinstein, alan ( 1974 ), " reduction of symplectic manifolds with symmetry ", reports on mathematical physics, 5 ( 1 ) : 121 β 130, bibcode : 1974rpmp.... 5.. 121m, doi : 10. 1016 / 0034 - 4877 ( 74 ) 90021 - 4 marsden, jerrold ; ratiu, tudor s. ( 1999 ). introduction to mechanics and symmetry. texts in applied mathematics ( 2 ed. ). new york : springer - verlag. isbn 0 - 387 - 98643 - x. meyer, kenneth ( 1973 ). " symmetries and integrals in mechanics ". dynamical systems ( proc. sympos., univ. bahia, salvador, 1971 ). new york : academic press. pp. 259 β 272. ortega, juan - pablo ; ratiu, tudor s. ( 2004 ). momentum maps and hamiltonian reduction. progress in mathematics. vol. 222. birkhauser boston. isbn 0 - 8176 - 4307 - 9. smale, stephen ( 1970 ), " topology and mechanics i ", inventiones mathematicae, 10 ( 4 ) : 305 β 331, bibcode : 1970inmat.. 10.. 305s, doi : 10. 1007 / bf01418778, s2cid 189831616 souriau, jean - marie ( 1970 ), structure des systemes dynamiques, dunod
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a crystal model is a teaching aid used for understanding concepts in crystallography and the morphology of crystals. models are ideal to learn recognizing symmetry elements in crystals. = = rome de l'isle = = the first real collections of crystal models were produced by rome de l'isle. he actually offered sets of small ( ca 3 cm ) models made of " terra cotta " in order to stimulate the sales of the expensive four - volume set of his book " cristallographie " ( 1783 ). the models were manufactured by his co - workers arnould carangeot, lhermina and swebach - desfontaines, who produced numerous large sets ( up to 448 models in each set ). in order to exactly transfer interplanar angles from natural crystals to the terra cotta models, carangeot invented and designed a prototype of a contact goniometer. this instrument, that proved to be an invaluable tool in geometric crystallography, enabled the measurement of interplanar angles with a precision of about half a degree. teylers museum in haarlem has a complete set of these terracotta models that were bought in paris ( in 1785 ) by martin van marum, the first director of the museum. after over 200 years, this collection is still complete and in perfect condition at teylers museum. = = rene just hauy = = almost two decades later, rene just hauy introduced wooden crystal models to illustrate the two - dimensional drawings in the atlas volume of his " traite de mineralogie " ( 1801 ). for the production of crystal models, wood appeared to be much more convenient than clay. especially pear wood permitted getting smooth faces, sharp edges and accurate dihedral angles required for the production of these three - dimensional objects. in general, the angular accuracy was very high and some models, especially those illustrating crystal twins and hauy's figures of decrement, still appear as masterpieces of fine woodwork and carving. skilful craftsmen such as pleuvin, beloeuf and lambotin ( to name only a few ) became specialists in this field and the models they offered were highly esteemed. between 1802 and 1804, martin van marum bought 597 of these pear wood models, 550 of these are still present in the collection of teylers museum. each model is labeled, mentioning a number and the name of the crystal form. this set is the most complete collection of hauy crystal models that
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of these pear wood models, 550 of these are still present in the collection of teylers museum. each model is labeled, mentioning a number and the name of the crystal form. this set is the most complete collection of hauy crystal models that still survives. that van marum was able to acquire such a unique collection was due to his networking. van marum allowed hauy as a member of the hollandsche maatschappij, a nomination to which hauy attached great value. hauy mentioned this membership in all of his publications. after their introduction by rome de l'isle and hauy, crystal models were increasingly demanded both by scholars for teaching purposes as well as by mineral collectors. the quality of the models improved due to the technical progress in their production. several mineralogists and crystallographers started designing their own series of models. although pear wood kept a prominent place, models were also manufactured using materials like plaster, cast iron, lead, brass, glass, porcelain, cardboard, etc. = = the krantz company = = in 1833, adam august krantz ( who studied pharmacy and later " geognosie " at the bergakademie freiberg ) founded the krantz company in bonn. four years later, krantz moved to berlin and sold minerals, fossils, rocks and basically acquired a monopoly in the production of crystal models made of pear wood or walnut. ever since its foundation, the firm was always in contact with renowned scientists and important collectors. hence in 1880, krantz proposed a series of 743 pear wood models compiled for teaching purposes by the crystallographer paul groth. seven years later, a supplementary collection of 213 models was available. at the onset of the 20th century, friedrich krantz ( a nephew of august krantz, with a degree in mineralogy ) supported by his teacher the crystallographer carl hintze, offered a collection of 928 models including most of the groth models. later, and along with many other productions, a dana collection of 282 models was manufactured. krantz offered a choice of collections of wooden models in different sizes ( 5, 10, 15 β 25 cm ). in addition, he sold a variety of glass models having the crystallographic axes illustrated by colored silk threads or with the holohedral form made of cardboard inside. also available were models in massive cut and polished glass ( colored and uncolored ), cardboard models, wire crystal models, crystal lattice models, models
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##raphic axes illustrated by colored silk threads or with the holohedral form made of cardboard inside. also available were models in massive cut and polished glass ( colored and uncolored ), cardboard models, wire crystal models, crystal lattice models, models with rotating parts, etc. over the years, krantz published numerous detailed catalogues of the collections he offered ; they constitute a precious documentation. = = external links = = teylers universum early crystal models = = references = =
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a radio atmospheric signal or sferic ( sometimes also spelled " spheric " ) is a broadband electromagnetic impulse that occurs as a result of natural atmospheric lightning discharges. sferics may propagate from their lightning source without major attenuation in the earth β ionosphere waveguide, and can be received thousands of kilometres from their source. on a time - domain plot, a sferic may appear as a single high - amplitude spike in the time - domain data. on a spectrogram, a sferic appears as a vertical stripe ( reflecting its broadband and impulsive nature ) that may extend from a few khz to several tens of khz, depending on atmospheric conditions. sferics received from about 2, 000 kilometres'distance or greater have their frequencies slightly offset in time, producing tweeks. when the electromagnetic energy from a sferic escapes the earth - ionosphere waveguide and enters the magnetosphere, it becomes dispersed by the near - earth plasma, forming a whistler signal. because the source of the whistler is an impulse ( i. e., the sferic ), a whistler may be interpreted as the impulse response of the magnetosphere ( for the conditions at that particular instant ). = = introduction = = a lightning channel with all its branches and its electric currents behaves like a huge antenna system from which electromagnetic waves of all frequencies are radiated. beyond a distance where luminosity is visible and thunder can be heard ( typically about 10 km ), these electromagnetic impulses are the only sources of direct information about thunderstorm activity on the ground. transients electric currents during return strokes ( r strokes ) or intracloud strokes ( k strokes ) are the main sources for the generation of impulse - type electromagnetic radiation known as sferics ( sometimes called atmospherics ). while this impulsive radiation dominates at frequencies less than about 100 khz, ( loosely called long waves ), a continuous noise component becomes increasingly important at higher frequencies. the longwave electromagnetic propagation of sferics takes place within the earth - ionosphere waveguide between the earth's surface and the ionospheric d - and e - layers. whistlers generated by lightning strokes can propagate into the magnetosphere along the geomagnetic lines of force. finally, upper - atmospheric lightning or sprites, that occur at mesospheric altitudes, are short - lived electric breakdown phenomena, probably generated by giant lightning events on the ground. = = source properties = = = = = basic stroke parameters = = =
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upper - atmospheric lightning or sprites, that occur at mesospheric altitudes, are short - lived electric breakdown phenomena, probably generated by giant lightning events on the ground. = = source properties = = = = = basic stroke parameters = = = in a typical cloud - to - ground stroke ( r stroke ), negative electric charge ( electrons ) of the order of q β 1 c stored within the lightning channel is lowered to the ground within a typical impulse time interval of Ο = 100 ΞΌs. this corresponds to an average current flowing within the channel of the order of j β qβΟ = 10 ka. maximum spectral energy is generated near frequencies of f β 1βΟ = 10 khz, or at wavelengths of Ξ» = cβf β 30 km ( where c is the speed of light ). in typical intracloud k - strokes, positive electric charge of the order of q β 10 mc in the upper part of the channel and an equivalent amount of negative charge in its lower part neutralize within a typical time interval of Ο β 25 ΞΌs. the corresponding values for average electric current, frequency and wavelength are j β 400 a, f β 40 khz, and Ξ» β 7. 5 km. the energy of k - strokes is in general two orders of magnitude weaker than the energy of r - strokes. the typical length of lightning channels can be estimated to be of the order of β β 1 / 4Ξ» = 8 km for r - strokes and β β 1 / 2Ξ» = 4 km for k - strokes. often, a continuing current component flows between successive r - strokes. its " pulse " time typically varies between about 10 β 150 ms, its electric current is of the order of j β 100 a, corresponding to the numbers of q β 1 β 20 c, f β 7 β 100 hz and Ξ» β 3 β 40 mm. both r - strokes as well as k - strokes produce sferics seen as a coherent impulse waveform within a broadband receiver tuned between 1 β 100 khz. the electric field strength of the impulse increases to a maximum value within a few microseconds and then declines like a damped oscillator. the orientation of the field strength increase depends on whether it is a negative or a positive discharge the visible part of a lightning channel has a typical length of about 5 km. another part of comparable length may be hidden in the cloud and may have a significant horizontal branch. evidently, the dominant wavelength of the electromagnetic waves of r - and k - strokes is much larger than
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lightning channel has a typical length of about 5 km. another part of comparable length may be hidden in the cloud and may have a significant horizontal branch. evidently, the dominant wavelength of the electromagnetic waves of r - and k - strokes is much larger than their channel lengths. the physics of electromagnetic wave propagation within the channel must thus be derived from full wave theory, because the ray concept breaks down. = = = electric channel current = = = the channel of a r stroke can be considered as a thin isolated wire of length l and diameter d in which negative electric charge has been stored. in terms of electric circuit theory, one can adopt a simple transmission line model with a capacitor, where the charge is stored, a resistance of the channel, and an inductance simulating the electric properties of the channel. at the moment of contact with the perfectly conducting earth surface, the charge is lowered to the ground. in order to fulfill the boundary conditions at the top of the wire ( zero electric current ) and at the ground ( zero electric voltage ), only standing resonant waves modes can exit. the fundamental mode which transports electric charge to the ground most effectively, has thus a wavelength Ξ» four times the channel length l. in the case of the k stroke, the lower boundary is the same as the upper boundary. of course, this picture is valid only for wave mode 1 ( Ξ» / 4 antenna ) and perhaps for mode 2 ( Ξ» / 2 antenna ), because these modes do not yet " feel " the contorted configuration of the real lightning channel. the higher order modes contribute to the incoherent noisy signals in the higher frequency range ( > 100 khz ). = = transfer function of earth β ionosphere waveguide = = sferics can be simulated approximately by the electromagnetic radiation field of a vertical hertzian dipole antenna. the maximum spectral amplitude of the sferic typically is near 5 khz. beyond this maximum, the spectral amplitude decreases as 1 / f if the earth's surface were perfectly conducting. the effect of the real ground is to attenuate the higher frequencies more strongly than the lower frequencies ( sommerfeld's ground wave ). r strokes emit most of their energy within the elf / vlf range ( elf = extremely low frequencies, < 3 khz ; vlf = very low frequencies, 3 β 30 khz ). these waves are reflected and attenuated on the ground as well as within the ionospheric d layer, near 70 km altitude during day time conditions,
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, < 3 khz ; vlf = very low frequencies, 3 β 30 khz ). these waves are reflected and attenuated on the ground as well as within the ionospheric d layer, near 70 km altitude during day time conditions, and near 90 km height during the night. reflection and attenuation on the ground depends on frequency, distance, and orography. in the case of the ionospheric d - layer, it depends, in addition, on time of day, season, latitude, and the geomagnetic field in a complicated manner. vlf propagation within the earth β ionosphere waveguide can be described by ray theory and by wave theory. when distances are less than about 500 km ( depending on frequency ), then ray theory is appropriate. the ground wave and the first hop ( or sky ) wave reflected at the ionospheric d layer interfere with each other. at distances greater than about 500 km, sky waves reflected several times at the ionosphere must be added. therefore, mode theory is here more appropriate. the first mode is least attenuated within the earth β ionosphere waveguide, and thus dominates at distances greater than about 1000 km. the earth β ionosphere waveguide is dispersive. its propagation characteristics are described by a transfer function t ( Ο, f ) depending mainly on distance Ο and frequency f. in the vlf range, only mode one is important at distances larger than about 1000 km. least attenuation of this mode occurs at about 15 khz. therefore, the earth β ionosphere waveguide behaves like a bandpass filter, selecting this band out of a broadband signal. the 15 khz signal dominates at distances greater than about 5000 km. for elf waves ( < 3 khz ), ray theory becomes invalid, and only mode theory is appropriate. here, the zeroth mode begins to dominate and is responsible for the second window at greater distances. resonant waves of this zeroth mode can be excited in the earth β ionosphere waveguide cavity, mainly by the continuing current components of lightning flowing between two return strokes. their wavelengths are integral fractions of the earth's circumference, and their resonance frequencies can thus be approximately determined by fm mc / ( 2Οa ) 7. 5 m hz ( with m = 1, 2,... ; a the earth's radius and c the speed of light ). these resonant modes with their fundamental frequency of f1 7. 5 hz are known
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7. 5 m hz ( with m = 1, 2,... ; a the earth's radius and c the speed of light ). these resonant modes with their fundamental frequency of f1 7. 5 hz are known as schumann resonances. = = monitoring thunderstorm activity with sferics = = about 100 lightning strokes per second are generated all over the world excited by thunderstorms located mainly in the continental areas at low and middle latitudes. in order to monitor the thunderstorm activity, sferics are the appropriate means. measurements of schumann resonances at only a few stations around the world can monitor the global lightning activity fairly well. one can apply the dispersive property of the earth β ionosphere waveguide by measuring the group velocity of a sferic signal at different frequencies together with its direction of arrival. the group time delay difference of neighbouring frequencies in the lower vlf band is directly proportional to the distance of the source. since the attenuation of vlf waves is smaller for west to east propagation and during the night, thunderstorm activity up to distances of about 10, 000 km can be observed for signals arriving from the west during night time conditions. otherwise, the transmission range is of the order of 5, 000 km. for the regional range ( < 1, 000 km ), the usual way is magnetic direction finding as well as time of arrival measurements of a sferic signal observed simultaneously at several stations. presumption of such measurements is the concentration on one individual impulse. if one measures simultaneously several pulses, interference takes place with a beat frequency equal to the inversal average sequence time of the pulses. = = atmospheric noise = = the signal - to - noise ratio determines the sensibility and sensitivity of telecommunication systems ( e. g., radio receivers ). an analog signal must clearly exceed the noise amplitude in order to become detectable. atmospheric noise is one of the most important sources for the limitation of the detection of radio signals. the steady electric discharging currents in a lightning channel cause a series of incoherent impulses in the whole frequency range, the amplitudes of which decreases approximately with the inverse frequency. in the elf - range, technical noise from 50 to 60 hz, natural noise from the magnetosphere, etc. dominates. in the vlf - range, there are the coherent impulses from r - and k - strokes, appearing out of the background noise. beyond about 100 khz, the noise amplitude becomes more and more incoherent.
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, etc. dominates. in the vlf - range, there are the coherent impulses from r - and k - strokes, appearing out of the background noise. beyond about 100 khz, the noise amplitude becomes more and more incoherent. in addition, technical noise from electric motors, ignition systems of motor cars, etc., are superimposed. finally, beyond the high frequency band ( 3 β 30 mhz ) extraterrestrial noise ( noise of galactic origin, solar noise ) dominates. the atmospheric noise depends on frequency, location and time of day and year. worldwide measurements of that noise are documented in ccir - reports. = = see also = = 1955 great plains tornado outbreak cluster one, a pink floyd track using sferics and dawn chorus as an overture = = footnotes = = = = references = = = = external links = = http : / / www. srh. noaa. gov / oun / wxevents / 19550525 / stormelectricity. php radio in space and time - whistler, sferics and tweeks, g. wiessala in radiouser 1 / 2013, uk
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in computing, particularly in the context of the unix operating system and its workalikes, fork is an operation whereby a process creates a copy of itself. it is an interface which is required for compliance with the posix and single unix specification standards. it is usually implemented as a c standard library wrapper to the fork, clone, or other system calls of the kernel. fork is the primary method of process creation on unix - like operating systems. = = overview = = in multitasking operating systems, processes ( running programs ) need a way to create new processes, e. g. to run other programs. fork and its variants are typically the only way of doing so in unix - like systems. for a process to start the execution of a different program, it first forks to create a copy of itself. then, the copy, called the " child process ", makes any environment changes the child will need and then calls the exec system call to overlay itself with the new program : it ceases execution of its former program in favor of the new. ( or, in rarer cases, the child forgoes the exec and continues executing, as a separate process, some other functionality of the original program. ) the fork operation creates a separate address space for the child. the child process has an exact copy of all the memory segments of the parent process. in modern unix variants that follow the virtual memory model from sunos - 4. 0, copy - on - write semantics are implemented and the physical memory need not be actually copied. instead, virtual memory pages in both processes may refer to the same pages of physical memory until one of them writes to such a page : then it is copied. this optimization is important in the common case where fork is used in conjunction with exec to execute a new program : typically, the child process performs only a small set of actions before it ceases execution of its program in favour of the program to be started, and it requires very few, if any, of its parent's data structures. when a process calls fork, it is deemed the parent process and the newly created process is its child. after the fork, both processes not only run the same program, but they resume execution as though both had called the system call. they can then inspect the call's return value to determine their status, child or parent, and act accordingly. = = history = = one of the earliest references to a fork concept appeared in a multiprocessor system design by melvin
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