Statistics of the critical percolation backbone with spatial long-range correlations

Abstract

We study the statistics of the backbone cluster between two sites separated by distance $r$ in two-dimensional percolation networks subjected to spatial long-range correlations. We find that the distribution of backbone mass follows the scaling {\it ansatz}, $P(M_B)\sim M_B^{-(\alpha +1)}f(M_B/M_0)$, where $f(x)=(\alpha +\eta x^{\eta })\exp (-x^{\eta })$ is a cutoff function, and $M_0$ and $\eta$ are cutoff parameters. Our results from extensive computational simulations indicate that this scaling form is applicable to both correlated and uncorrelated cases. We show that the exponent $\alpha$ can be directly related to the fractal dimension of the backbone $d_B$, and should therefore depend on the imposed degree of long-range correlations.

5 pages, 5 figures

References in corpus (1)

• Traveling length and minimal traveling time for flow through percolation networks with long-range spatial correlations

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