Invasion Percolation: New Algorithms and Universality Classes

Abstract

Employing highly efficient algorithms for simulating invasion percolation (IP), whose execution time scales as O[M log(M)] or better for a cluster of M sites, and for determining the backbone of the cluster, we obtain precise estimates for the fractal dimensions of the sample-spanning cluster, the backbone, and the minimal path in order to identify the universality classes of four different IP processes (site and bond IP, with and without trapping). In two dimensions IP is characterized by two universality classes, one each for IP without trapping, and site and bond IP with trapping. In a three-dimensional site IP with and without trapping is in the universality class of random percolation, while bond IP with trapping is in a distinct universality class, which may be the same as that of optimal paths in strongly disordered media. Show more