The shape of invasion perclation clusters in random and correlated media

TL;DR

This study numerically investigates the shape and anisotropy of two-dimensional invasion percolation clusters in various media, revealing effects of correlations, boundary conditions, and process types on cluster isotropy.

Contribution

It provides a comparative analysis of NTIP and TIP clusters' anisotropy in random and correlated media, highlighting the influence of boundary conditions and long-range correlations.

Findings

In spite of different scaling, NTIP and TIP have similar anisotropy values.

Random media produce slightly less isotropic clusters than standard percolation.

Long-range correlations decrease cluster isotropy, especially persistent correlations.

Abstract

The shape of two-dimensional invasion percolation clusters are studied numerically for both non-trapping (NTIP) and trapping (TIP) invasion percolation processes. Two different anisotropy quantifiers, the anisotropy parameter and the asphericity are used for probing the degree of anisotropy of clusters. We observe that in spite of the difference in scaling properties of NTIP and TIP, there is no difference in the values of anisotropy quantifiers of these processes. Furthermore, we find that in completely random media, the invasion percolation clusters are on average slightly less isotropic than standard percolation clusters. Introducing isotropic long-range correlations into the media reduces the isotropy of the invasion percolation clusters. The effect is more pronounced for the case of persisting long-range correlations. The implication of boundary conditions on the shape of clusters is another subject of interest. Compared to the case of free boundary conditions, IP clusters of conventional rectangular geometry turn out to be more isotropic. Moreover, we see that in conventional rectangular geometry the NTIP clusters are more isotropic than TIP clusters.