Model for the formation of nonequilibrium clusters
Muhammad Sahimi · Physical Review A · 1986
We propose a new and simple model for the formation of kinetic clusters. The model appears to have two critical points. The first one corresponds to a site percolation threshold, at which point a fractal structure appears for the first time, and below which the clusters stop growing after a finite time. The second critical point appears to be exactly the same as the site percolation threshold of the lattice in the directed percolation process, and at which point a qualitative change in the structure of the cluster appears. Various critical properties of the model are computed in two dimensions and they appear to be slightly but consistently different from those of random percolation. The clusters reduce to the Eden model in a special limit, and they appear also to have close connection with ballistic aggregation and cellular automata.