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Correlation Function (statistical Mechanics)
In statistical mechanics, the correlation function is a measure of the order in a system, as characterized by a mathematical correlation function. Correlation functions describe how microscopic variables, such as spin and density, at different positions are related. More specifically, correlation functions quantify how microscopic variables co-vary with one another on average across space and time. A classic example of such spatial correlations is in ferro- and antiferromagnetic materials, where the spins prefer to align parallel and antiparallel with their nearest neighbors, respectively. The spatial correlation between spins in such materials is shown in the figure to the right. Definitions The most common definition of a correlation function is the canonical ensemble (thermal) average of the scalar product of two random variables, s_1 and s_2, at positions R and R+r and times t and t+\tau: C (r,\tau) = \langle \mathbf(R,t) \cdot \mathbf(R+r,t+\tau)\rangle\ - \langle \mathbf( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ferro Antiferro Spatial Corrs Png
Ferro may refer to: *Iron as in a Ferromagnetic material *Ferro (architecture), a wrought-iron architectural element *Ferro Carril Oeste, an Argentinian football team *Ferro (Covilhã), a civil parish in the municipality of Covilhã, Portugal * Ferro Meridian, an alternative prime meridian through El Hierro *Ferro Lad, comic book superhero *Ferro (footballer) *Ferro (surname) Ferro is an Italian and Portuguese surname related to the word ''ferro'' ("iron"). People with this surname include: *Andrea Ferro, singer of Italian metal band Lacuna Coil * Carlos Ferro (other) *Fiona Ferro, French tennis player *Lorenzo ... * Ferro Watch, a watch company from Turkey {{disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Power Law
In statistics, a power law is a functional relationship between two quantities, where a relative change in one quantity results in a proportional relative change in the other quantity, independent of the initial size of those quantities: one quantity varies as a power of another. For instance, considering the area of a square in terms of the length of its side, if the length is doubled, the area is multiplied by a factor of four. Empirical examples The distributions of a wide variety of physical, biological, and man-made phenomena approximately follow a power law over a wide range of magnitudes: these include the sizes of craters on the moon and of solar flares, the foraging pattern of various species, the sizes of activity patterns of neuronal populations, the frequencies of words in most languages, frequencies of family names, the species richness in clades of organisms, the sizes of power outages, volcanic eruptions, human judgments of stimulus intensity and many other ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Covariance And Correlation
In probability theory and statistics, the mathematical concepts of covariance and correlation are very similar. Both describe the degree to which two random variables or sets of random variables tend to deviate from their expected values in similar ways. If ''X'' and ''Y'' are two random variables, with means (expected values) ''μX'' and ''μY'' and standard deviations ''σX'' and ''σY'', respectively, then their covariance and correlation are as follows: : so that :\rho_ = \sigma_ / (\sigma_X \sigma_Y) where ''E'' is the expected value operator. Notably, correlation is dimensionless while covariance is in units obtained by multiplying the units of the two variables. If ''Y'' always takes on the same values as ''X'', we have the covariance of a variable with itself (i.e. \sigma_), which is called the variance and is more commonly denoted as \sigma_X^2, the square of the standard deviation. The ''correlation'' of a variable with itself is always 1 (except in the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Phase Transitions And Critical Phenomena
''Phase Transitions and Critical Phenomena'' is a 20-volume series of books, comprising review articles on phase transitions and critical phenomena, published during 1972-2001. It is "considered the most authoritative series on the topic". Volumes 1-6 were edited by Cyril Domb and Melville S. Green, and after Green's death, volumes 7-20 were edited by Domb and Joel Lebowitz. Volume 4 was never published. Volume 5 was published in two volumes, as 5A and 5B. Contents * Volume 1: ''Exact Results'' (1972) ** 'Introductory Note on Phase Transitions and Critical Phenomena', by C.N. Yang. ** 'Rigorous Results and Theorems', by R.B. Griffiths. ** 'Dilute Quantum Systems', by J. Ginibre. ** 'The C*-Algebraic Approach to Phase Transitions', by G.G. Emch. ** 'One-dimensional Models — Short Range Forces', by C.J. Thompson ** 'Two-dimensional Ising Models', by H.N.V. Temperley. ** 'Transformation of Ising Models', by I. Syozi. ** 'Two-dimensional Ferroelectric Models', by E.H. Li ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Joel Lebowitz
Joel Louis Lebowitz (born May 10, 1930) is a mathematical physicist widely acknowledged for his outstanding contributions to statistical physics, statistical mechanics and many other fields of Mathematics and Physics. Lebowitz has published more than five hundred papers concerning statistical physics and science in general, and he is one of the founders and editors of the '' Journal of Statistical Physics'', one of the most important peer-reviewed journals concerning scientific research in this area. He has been president of the New York Academy of Sciences. Lebowitz is the George William Hill Professor of Mathematics and Physics at Rutgers University. He is also an active member of the human rights community and a long-term co-chair of the Committee of Concerned Scientists. Biography Lebowitz was born in Taceva, then in Czechoslovakia, now Ukraine, in 1930 into a Jewish family. During World War II he was deported with his family to Auschwitz, where his father, his mother ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Melville S
Melville may refer to: Places Antarctica *Cape Melville (South Shetland Islands) *Melville Peak, King George Island * Melville Glacier, Graham Land * Melville Highlands, Laurie Island * Melville Point, Marie Byrd Land Australia *Cape Melville, Queensland * City of Melville, Western Australia, the local government authority * Electoral district of Melville, Western Australia * Melville Bay, Northern Territory *Melville Island, Northern Territory *Melville, Western Australia, a suburb of Perth Canada *Melville, Saskatchewan, a city *Melville (electoral district), Saskatchewan, a federal electoral district *Melville (provincial electoral district), Saskatchewan *Melville, a community within the town of Caledon, Ontario *Melville Peninsula, Nunavut *Melville Sound, Nunavut *Melville Island (Northwest Territories and Nunavut) *Melville Island (Nova Scotia), in Halifax Harbour *Melville Cove, Halifax, in Halifax Harbour *Melville Island, a small island in the Discovery Islands, Briti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cyril Domb
Cyril Domb FRS (9 December 1920 – 15 February 2012) was a British-Israeli theoretical physicist, best known for his lecturing and writing on the theory of phase transitions and critical phenomena of fluids. He was also known in the Orthodox Jewish world for his writings on science and Judaism. Early life Domb was born on 9 December 1920, the fourth day of Hanukkah, in North London to a Hasidic Jewish family. His father, Yoel, who had shortened his name from Dombrowski to Domb, was a native of Warsaw, while his mother, Sarah, was from Oświęcim, Poland. He was given the Hebrew name of Yechiel. His father and grandfather paid for tutors to educate him in classical Jewish studies, and he also attended '' shiurim'' (Torah classes) given by Rabbi Eliyahu Eliezer Dessler to young men in a nearby synagogue."An Appreciation of Professor Yechiel (Cyril) Domb, z"l, in honor of his shloshim". ''Hamodia'', 29 March 2012, pp. C14–C15. Retrieved 7 April 2012. Domb possessed both an e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arxiv
arXiv (pronounced "archive"—the X represents the Greek letter chi ⟨χ⟩) is an open-access repository of electronic preprints and postprints (known as e-prints) approved for posting after moderation, but not peer review. It consists of scientific papers in the fields of mathematics, physics, astronomy, electrical engineering, computer science, quantitative biology, statistics, mathematical finance and economics, which can be accessed online. In many fields of mathematics and physics, almost all scientific papers are self-archived on the arXiv repository before publication in a peer-reviewed journal. Some publishers also grant permission for authors to archive the peer-reviewed postprint. Begun on August 14, 1991, arXiv.org passed the half-million-article milestone on October 3, 2008, and had hit a million by the end of 2014. As of April 2021, the submission rate is about 16,000 articles per month. History arXiv was made possible by the compact TeX file forma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Inverse Scattering Method
In quantum physics, the quantum inverse scattering method is a method for solving integrable models in 1+1 dimensions, introduced by L. D. Faddeev in 1979. The quantum inverse scattering method relates two different approaches: #the Bethe ansatz, a method of solving integrable quantum models in one space and one time dimension; #the Inverse scattering transform, a method of solving classical integrable differential equations of the evolutionary type. This method led to the formulation of quantum groups. Especially interesting is the Yangian, and the center of the Yangian is given by the quantum determinant. An important concept in the Inverse scattering transform is the Lax representation; the quantum inverse scattering method starts by the quantization of the Lax representation and reproduces the results of the Bethe ansatz. In fact, it allows the Bethe ansatz to be written in a new form: the ''algebraic Bethe ansatz''.cf. e.g. the lectures by N.A. Slavnov, This led ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fluid Mechanics
Fluid mechanics is the branch of physics concerned with the mechanics of fluids ( liquids, gases, and plasmas) and the forces on them. It has applications in a wide range of disciplines, including mechanical, aerospace, civil, chemical and biomedical engineering, geophysics, oceanography, meteorology, astrophysics, and biology. It can be divided into fluid statics, the study of fluids at rest; and fluid dynamics, the study of the effect of forces on fluid motion. It is a branch of continuum mechanics, a subject which models matter without using the information that it is made out of atoms; that is, it models matter from a ''macroscopic'' viewpoint rather than from ''microscopic''. Fluid mechanics, especially fluid dynamics, is an active field of research, typically mathematically complex. Many problems are partly or wholly unsolved and are best addressed by numerical methods, typically using computers. A modern discipline, called computational fluid dynamics (CFD), is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Radial Distribution Function
In statistical mechanics, the radial distribution function, (or pair correlation function) g(r) in a system of particles (atoms, molecules, colloids, etc.), describes how density varies as a function of distance from a reference particle. If a given particle is taken to be at the origin O, and if \rho =N/V is the average number density of particles, then the local time-averaged density at a distance r from O is \rho g(r). This simplified definition holds for a homogeneous and isotropic system. A more general case will be considered below. In simplest terms it is a measure of the probability of finding a particle at a distance of r away from a given reference particle, relative to that for an ideal gas. The general algorithm involves determining how many particles are within a distance of r and r+dr away from a particle. This general theme is depicted to the right, where the red particle is our reference particle, and blue particles are those whose centers are within the circu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
