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Percolation Theory

Percolation Theory represents one of the simplest models of a disordered system. Consider a square lattice, where each site is occupied randomly with probability p or empty with probability 1-p. Occupied and empty sites may stand for very different physical properties. For simplicity, let us assume that the occupied sites are electrical conductors, the empty sites represent insulators, and that electrical current can flow between nearest neighbor conductor sites. At low concentration p, the conductor sites are either isolated or form small clusters of nearest neighbor sites. Two conductor sites belong to the same cluster if they are connected by a path of nearest neighbor conductor sites, and a current can flow between them. At low p values, the mixture is an insulator, since a conducting path connecting opposite edges of the lattice does not exist. At large p values, on the other hand, many conduction paths between opposite edges exist, where electrical current can flow, and the mixture is a conductor. At some concentration in between, therefore, a threshold concentration pc must exist where for the first time electrical current can percolate from one edge to the other. Below pc, we have an insulator; above pc we have a conductor. The threshold concentration is called the percolation threshold, or, since it separates two different phases, the critical concentration.

Web Resources On Percolation Theory

http://www.cna.org/isaac/Glossb.htm

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