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At a critical threshold p c, large clusters and long-range connectivity first appear, and this is called the percolation threshold. Depending on the method for obtaining the random network, one distinguishes between the site percolation threshold and the bond percolation threshold.
Percolation typically exhibits universality. Statistical physics concepts such as scaling theory, renormalization, phase transition, critical phenomena and fractals are used to characterize percolation properties. Combinatorics is commonly employed to study percolation thresholds.
For site percolation on the square lattice, the value of p c is not known from analytic derivation but only via simulations of large lattices which provide the estimate p c = 0.59274621 ± 0.00000013. [7] A limit case for lattices in high dimensions is given by the Bethe lattice, whose threshold is at p c = 1 / z − 1 for a ...
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Percolation is the study of connectivity in random systems, such as electrical conductivity in random conductor/insulator systems, fluid flow in porous media, gelation in polymer systems, etc. [1] At a critical fraction of connectivity or porosity, long-range connectivity can take place, leading to long-range flow.
For different models including the random subgraphs of grid graphs, the connected components are described by percolation theory. A key question in this theory is the existence of a percolation threshold, a critical probability above which a giant component (or infinite component) exists and below which it does not. [33]
Conductivity near the percolation threshold in physics, occurs in a mixture between a dielectric and a metallic component. The conductivity σ {\displaystyle \sigma } and the dielectric constant ϵ {\displaystyle \epsilon } of this mixture show a critical behavior if the fraction of the metallic component reaches the percolation threshold .
Percolation threshold; R. Random cluster model; W. Water retention on random surfaces This page was last edited on 20 May 2018, at 05:31 (UTC). Text is available ...