Computation for conductance distributions of percolation lattice cells

Abstract

For a network, built from links whose conductances are given by some discrete statistical distribution, including a finite zero-conductance probability, and where links are assumed independent, the distribution of conductances for the network as a whole is of interest in the study of percolation on lattices. This quantity is computed by different methods for a set of test networks. It is found that the computation is more efficiently done by manipulating the networks themselves in a suitable representation rather than by computing with symbolic expressions for their conductance. In particular, with ordinary computer algebra systems there were severe limitations due to expression growth in this study.