Recent developments in continuum percolation

Abstract

While most natural systems to which percolation theory has been applied are continuum systems, most of the developments in percolation theory have been made through the study of lattice models. Recently, two major developments have shown, however, that continuum percolation warrants investigation in its own right, having features with no counterpart on lattices. The first development was in understanding the dependence of the threshold on the particle structure; the second was in finding a relation between critical exponents of physical properties and the local geometrical properties of the system. These developments explained observations in the four major groups of continuum systems: porous media, doped semiconductors, microemulsions and composite materials.