Publication

A complete graph effective medium approximation for lattice and continuum percolation

Claudio Grimaldi
2011
Journal Articles

Abstract

In this paper we introduce an effective medium theory that is capable of describing site percolation in both lattice and continuum three-dimensional systems. By exploiting self-consistency with a complete graph or network of identical conductors, the resulting effective medium equation allows for a straightforward estimate of the percolation threshold, which compares well with the available numerical results. The present formalism is easily generalized to describe transport in conductor-insulator composites with different microstructure properties. Copyright (C) EPLA, 2011

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https://infoscience.epfl.ch/entities/publication/ca820337-990b-4c22-8c39-a26ae5d4f41e

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Claudio Grimaldi
2011
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/ca820337-990b-4c22-8c39-a26ae5d4f41e

About this result

Related concepts (22)

Percolation threshold

The percolation threshold is a mathematical concept in percolation theory that describes the formation of long-range connectivity in random systems. Below the threshold a giant connected component does not exist; while above it, there exists a giant component of the order of system size. In engineering and coffee making, percolation represents the flow of fluids through porous media, but in the mathematics and physics worlds it generally refers to simplified lattice models of random systems or networks (graphs), and the nature of the connectivity in them.

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 (cognitive psychology).

Percolation

In physics, chemistry, and materials science, percolation () refers to the movement and filtering of fluids through porous materials. It is described by Darcy's law. Broader applications have since been developed that cover connectivity of many systems modeled as lattices or graphs, analogous to connectivity of lattice components in the filtration problem that modulates capacity for percolation.

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