Universality and cluster structures in continuum models of percolation with two different radius distributions

Abstract

The percolation thresholds and the fractal cluster structures for continuum models of percolation with uniform (CM1) and variable radius (CM2) distributions of discs and spheres are investigated and compared with the results of ordinary lattice percolation. Configurations of up to 250000 discs (2 dimensions) and 100000 spheres (3 dimensions) are numerically simulated. In two dimensions the authors find distinctly different percolation concentrationss for models CM1 and CM2. In the three-dimensional systems the percolation concentration for both models cannot be distinguished within their limits of accuracy. The fractal dimensions of the cluster hull, surface and volume are the same as in the corresponding lattice models. The Harris criterion for the continuum percolation problem is confirmed by their simulation.