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Combinatorics And Physics
Combinatorial physics or physical combinatorics is the area of interaction between physics and combinatorics. Overview :"Combinatorial Physics is an emerging area which unites combinatorial and discrete mathematical techniques applied to theoretical physics, especially Quantum Theory." :"Physical combinatorics might be defined naively as combinatorics guided by ideas or insights from physics" Combinatorics has always played an important role in quantum field theory and statistical physics. However, combinatorial physics only emerged as a specific field after a seminal work by Alain Connes and Dirk Kreimer, showing that the renormalization of Feynman diagrams can be described by a Hopf algebra. Combinatorial physics can be characterized by the use of algebraic concepts to interpret and solve physical problems involving combinatorics. It gives rise to a particularly harmonious collaboration between mathematicians and physicists. Among the significant physical results of combinatori ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Physics
Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of events." Physics is one of the most fundamental scientific disciplines, with its main goal being to understand how the universe behaves. "Physics is one of the most fundamental of the sciences. Scientists of all disciplines use the ideas of physics, including chemists who study the structure of molecules, paleontologists who try to reconstruct how dinosaurs walked, and climatologists who study how human activities affect the atmosphere and oceans. Physics is also the foundation of all engineering and technology. No engineer could design a flat-screen TV, an interplanetary spacecraft, or even a better mousetrap without first understanding the basic laws of physic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ice-type Model
In statistical mechanics, the ice-type models or six-vertex models are a family of vertex models for crystal lattices with hydrogen bonds. The first such model was introduced by Linus Pauling in 1935 to account for the residual entropy of water ice. Variants have been proposed as models of certain ferroelectric and antiferroelectric crystals. In 1967, Elliott H. Lieb found the exact solution to a two-dimensional ice model known as "square ice". The exact solution in three dimensions is only known for a special "frozen" state. Description An ice-type model is a lattice model defined on a lattice of coordination number 4. That is, each vertex of the lattice is connected by an edge to four "nearest neighbours". A state of the model consists of an arrow on each edge of the lattice, such that the number of arrows pointing inwards at each vertex is 2. This restriction on the arrow configurations is known as the ice rule. In graph theoretic terms, the states are Eulerian orientatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jaroslav Nešetřil
Jaroslav (Jarik) Nešetřil (; born March 13, 1946 in Brno) is a Czech mathematician, working at Charles University in Prague. His research areas include combinatorics (structural combinatorics, Ramsey theory), graph theory (coloring problems, sparse structures), algebra (representation of structures, categories, homomorphisms), posets (diagram and dimension problems), computer science (complexity, NP-completeness). Education and career Nešetřil received his Ph.D. from Charles University in 1973 under the supervision of Aleš Pultr and Gert Sabidussi. He is responsible for more than 300 publications. Since 2006, he is chairman of the Committee of Mathematics of Czech Republic (the Czech partner of IMU). Jaroslav Nešetřil is Editor in Chief of ''Computer Science Review'' and ''INTEGERS: the Electronic Journal of Combinatorial Number Theory''. He is also honorary editor of ''Electronic Journal of Graph Theory and Applications''. Since 2008, Jaroslav Nešetřil belongs to th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graham Brightwell
Graham Brightwell is a British mathematician working in the field of discrete mathematics. Currently a professor at the London School of Economics, he has published nearly 100 papers in pure mathematics, including over a dozen with Béla Bollobás. His research interests include random combinatorial structures; partially ordered sets; algorithms; random graphs; discrete mathematics and graph theory. (Bollobás supervised his PhD on "Linear Extensions of Partially Ordered Sets" at Cambridge, awarded 1988.) Othello Brightwell started playing Othello in 1985, after finding himself sharing an apartment with fellow mathematician and Othello player Imre Leader Imre Bennett Leader is a British Othello player, employed as a professor of pure mathematics at Cambridge University. As a child, he was a pupil at the private St Paul's School and won a silver medal on the British team at the 1981 Internatio .... He has finished three times as runner-up in the World Othello Champion ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maxim Kontsevich
Maxim Lvovich Kontsevich (russian: Макси́м Льво́вич Конце́вич, ; born 25 August 1964) is a Russian and French mathematician and mathematical physicist. He is a professor at the Institut des Hautes Études Scientifiques and a distinguished professor at the University of Miami. He received the Henri Poincaré Prize in 1997, the Fields Medal in 1998, the Crafoord Prize in 2008, the Shaw Prize and Fundamental Physics Prize in 2012, and the Breakthrough Prize in Mathematics in 2014. Academic career and research He was born into the family of Lev Kontsevich, Soviet orientalist and author of the Kontsevich system. After ranking second in the All-Union Mathematics Olympiads, he attended Moscow State University but left without a degree in 1985 to become a researcher at the Institute for Information Transmission Problems in Moscow. While at the institute he published papers that caught the interest of the Max Planck Institute in Bonn and was invited for three ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Clive W
Clive is a name. People and fictional characters with the name include: People Given name * Clive Allen (born 1961), English football player * Clive Anderson (born 1952), British television, radio presenter, comedy writer and former barrister * Clive Barker (born 1952), English writer, film director and visual artist * Clive Barker (artist, born 1940), British pop artist * Clive Barker (soccer) (born 1944), South African coach * Clive Barnes (1927–2008), English writer and critic, dance and theater critic for ''The New York Times'' * Clive Bell (1881–1964), English art critic * Clive Brook (1887–1974), British film actor * Clive Burr (1957–2013), British musician, former drummer with Iron Maiden * Clive Campbell (footballer), New Zealand footballer in the 1970s and early '80s * Clive Campbell (born 1955), Jamaican-born DJ with the stage name DJ Kool Herc * Clive Clark (golfer) (born 1945), English golfer * Clive Clark (footballer) (1940–2014), English former footballer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ted Bastin
Edward William "Ted" Bastin (8 January 1926 – 15 October 2011) was a physicist and mathematician who held doctorate degrees in mathematics from Queen Mary College, London University and physics from King's College, Cambridge, to which he won an Isaac Newton studentship. For a time, he was visiting fellow at Stanford University, California and a research fellow, King's College, Cambridge, England. The boats stored at the River Cam boathouse, King's College, Cambridge, include "Ted", the lightweight wooden scull named after Ted Bastin, who won races in it for King's from 1950 to 1953. Work Bastin’s research specialties included the foundations of physics, especially the discrete and finite aspects of quantum mechanics and relativity. He believed that a view of physical space in which space is defined not as a continuum but as a finite set of points was capable of resolving the clash between the continuum aspect of the classic theory of relativity and the discrete aspect of quan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Mechanics
Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, quantum field theory, quantum technology, and quantum information science. Classical physics, the collection of theories that existed before the advent of quantum mechanics, describes many aspects of nature at an ordinary (macroscopic) scale, but is not sufficient for describing them at small (atomic and subatomic) scales. Most theories in classical physics can be derived from quantum mechanics as an approximation valid at large (macroscopic) scale. Quantum mechanics differs from classical physics in that energy, momentum, angular momentum, and other quantities of a bound system are restricted to discrete values ( quantization); objects have characteristics of both particles and waves (wave–particle duality); and there are limits to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Combinatorics And Dynamical Systems
The mathematical disciplines of combinatorics and dynamical systems interact in a number of ways. The ergodic theory of dynamical systems has recently been used to prove combinatorial theorems about number theory which has given rise to the field of arithmetic combinatorics. Also dynamical systems theory is heavily involved in the relatively recent field of combinatorics on words. Also combinatorial aspects of dynamical systems are studied. Dynamical systems can be defined on combinatorial objects; see for example graph dynamical system. See also *Symbolic dynamics *Analytic combinatorics *Combinatorics and physics *Arithmetic dynamics Arithmetic dynamics is a field that amalgamates two areas of mathematics, dynamical systems and number theory. Classically, discrete dynamics refers to the study of the iteration of self-maps of the complex plane or real line. Arithmetic dynamics is ... References * *. *. *. *. *. *. *. *. *. *. *. *. External linksCombinatorics of Iterated Functions ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Partition Function (mathematics)
The partition function or configuration integral, as used in probability theory, information theory and dynamical systems, is a generalization of the definition of a partition function in statistical mechanics. It is a special case of a normalizing constant in probability theory, for the Boltzmann distribution. The partition function occurs in many problems of probability theory because, in situations where there is a natural symmetry, its associated probability measure, the Gibbs measure, has the Markov property. This means that the partition function occurs not only in physical systems with translation symmetry, but also in such varied settings as neural networks (the Hopfield network), and applications such as genomics, corpus linguistics and artificial intelligence, which employ Markov networks, and Markov logic networks. The Gibbs measure is also the unique measure that has the property of maximizing the entropy for a fixed expectation value of the energy; this underlies the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tutte Polynomial
The Tutte polynomial, also called the dichromate or the Tutte–Whitney polynomial, is a graph polynomial. It is a polynomial in two variables which plays an important role in graph theory. It is defined for every undirected graph G and contains information about how the graph is connected. It is denoted by T_G. The importance of this polynomial stems from the information it contains about G. Though originally studied in algebraic graph theory as a generalization of counting problems related to graph coloring and nowhere-zero flow, it contains several famous other specializations from other sciences such as the Jones polynomial from knot theory and the partition functions of the Potts model from statistical physics. It is also the source of several central computational problems in theoretical computer science. The Tutte polynomial has several equivalent definitions. It is equivalent to Whitney’s rank polynomial, Tutte’s own dichromatic polynomial and Fortuin–Kasteleyn ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Percolation Theory
In statistical physics and mathematics, percolation theory describes the behavior of a network when nodes or links are added. This is a geometric type of phase transition, since at a critical fraction of addition the network of small, disconnected clusters merge into significantly larger connected, so-called spanning clusters. The applications of percolation theory to materials science and in many other disciplines are discussed here and in the articles network theory and percolation. Introduction A representative question (and the source of the name) is as follows. Assume that some liquid is poured on top of some porous material. Will the liquid be able to make its way from hole to hole and reach the bottom? This physical question is modelled mathematically as a three-dimensional network of vertices, usually called "sites", in which the edge or "bonds" between each two neighbors may be open (allowing the liquid through) with probability , or closed with probability , and th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
