Pair connectedness and mean cluster size for continuum-percolation models: Computer-simulation results

We devise a new algorithm to obtain the pair-connectedness function P(r) for continuum-percolation models from computer simulations. It is shown to converge rapidly to the infinite-system limit, even near the percolation threshold, thus providing accurate estimates of P(r) for a wide range of densities. We specifically consider an interpenetrable-particle model (referred to as the penetrable-concentric-shell model) in which D-dimensional spheres (D = 2 or 3) of diameter σ are distributed with an arbitrary degree of impenetrability parameter λ, 0≤λ≤1. Pairs of particles are taken to be "connected" when the interparticle separation is less than σ. The theoretical results of Xu and Stell for P(r) in the case of fully penetrable spheres (λ = 0) are shown to be in excellent agreement with our simulations. We also compute the mean cluster size as a function of density and λ for the case of 2D, and, from these data, estimate the respective percolation thresholds.