Temporal development of invasion percolation

Abstract

The authors consider the dynamics of invasion percolation for different models. This process exhibits scaling behaviours which, in the simplest case, can be related to some critical static properties of usual percolation. In particular, the concept of bursts is shown to be of fundamental importance. The critical exponents they derive are checked numerically on a case of invasion percolation where growth is restricted to the hull of the existing cluster.