Invasion percolation between two sites in two, three, and four dimensions

The mass distribution of invaded clusters in non-trapping invasion percolation between an injection site and air extraction site has been studied, in two, three, and four dimensions. This Study is all extension of the recent study focused Oil two dimensions by Araujo et al. [A.D. Araujo, T.F. Vasconcelos, A.A. Moreira, L.S. Lucena, J.S. Andrade Jr., Phys. Rev. E 72 (2005) 0414041 with respect to higher dimensions. The mass distribution exhibits a power-law behavior, P(m) proportional to m(-alpha). It has been found that the index alpha for p(e) < p(c),p(c) being the percolation threshold of a regular percolation, appears to be independent of the Value of p(e) and is also independent of the lattice dimensionality. When p(e) = p(c), alpha appears to depend marginally on the lattice dimensionality, and the relation alpha = tau - 1. tau being the exponent associated With Cluster size distribution of a regular percolation via n(S) proportional to S(-tau), appears to be valid. (c) 2009 Elsevier B.V. All rights reserved.