The shape of invasion percolation clusters in random and correlated media

Abstract

The shape of two-dimensional invasion percolation clusters are studied numerically for bothnon-trapping (NTIP) and trapping (TIP) invasion percolation processes. Two differentanisotropy quantifiers, the anisotropy parameter and the asphericity, are used for probingthe degree of anisotropy of clusters. We observe that, in spite of the difference in scalingproperties of NTIP and TIP, there is no difference in the values of anisotropyquantifiers of these processes. Furthermore, we find that, in completely randommedia, the invasion percolation clusters are on average slightly less isotropic thanstandard percolation clusters. Introducing isotropic long-range correlations into themedia reduces the isotropy of the invasion percolation clusters. The effect is morepronounced for the case of persisting long-range correlations. The implicationof boundary conditions on the shape of clusters is another subject of interest.Compared to the case of free boundary conditions, IP clusters of conventionalrectangular geometry turn out to be more isotropic. Moreover, we see that inconventional rectangular geometry the NTIP clusters are more isotropic than the TIPclusters.