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Percolation theory information


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 (cognitive psychology).

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Percolation theory

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applications of percolation theory to materials science and in many other disciplines are discussed here and in the articles Network theory and Percolation (cognitive...

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Percolation

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that modulates capacity for percolation. During the last decades, percolation theory, the mathematical study of percolation, has brought new understanding...

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Percolation threshold

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The percolation threshold is a mathematical concept in percolation theory that describes the formation of long-range connectivity in random systems. Below...

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Continuum percolation theory

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underlying points of discrete percolation form types of lattices whereas the underlying points of continuum percolation are often randomly positioned...

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Percolation critical exponents

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In the context of the physical and mathematical theory of percolation, a percolation transition is characterized by a set of universal critical exponents...

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List of mathematical theories

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Order theory Percolation theory Perturbation theory Probability theory Proof theory Quantum theory Queue theory Ramsey theory Random matrix theory Recursion...

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Critical exponent

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bootstrap Ising critical exponents Percolation critical exponents Network science Percolation theory Graph theory Hagen Kleinert and Verena Schulte-Frohlinde...

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Graph theory

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theory Null graph Pebble motion problems Percolation theory Perfect graph Quantum graph Random regular graphs Semantic networks Spectral graph theory...

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Random graph

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Graph theory Interdependent networks Network science Percolation Percolation theory Random graph theory of gelation Regular graph Scale free network Semilinear...

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Universality class

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an analog of mean-field theory (this dimension is 4d for Ising or for directed percolation, and 6d for undirected percolation). Critical exponents are...

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First passage percolation

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percolation is a mathematical method used to describe the paths reachable in a random medium within a given amount of time. First passage percolation...

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Swiss cheese model

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Frosch described Reason's model in mathematical terms as a model in percolation theory, which he analyses as a Bethe lattice. The model includes active and...

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Bootstrap percolation

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In statistical mechanics, bootstrap percolation is a percolation process in which a random initial configuration of active cells is selected from a lattice...

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Directed percolation

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directed percolation is illustrated to the right. In isotropic percolation a spreading agent (e.g. water) introduced at a particular site percolates along...

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Poisson point process

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processes, stochastic geometry, spatial statistics and continuum percolation theory. The Poisson point process can be defined on more abstract spaces...

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Conductivity near the percolation threshold

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the metallic component reaches the percolation threshold. The behavior of the conductivity near this percolation threshold will show a smooth change...

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Complex system

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in many diverse disciplines, including statistical physics, information theory, nonlinear dynamics, anthropology, computer science, meteorology, sociology...

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Fermi paradox

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model based on percolation theory. Colonization efforts may not occur as an unstoppable rush, but rather as an uneven tendency to "percolate" outwards, within...

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Clustering coefficient

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clustered networks a percolation approach is developed. Directed graph Graph theory Network theory Network science Percolation theory Scale free network...

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