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Dependence of Conductance on Percolation Backbone Mass

Gerald Paul·Sergey V. Buldyrev·Nikolay V. Dokholyan·Shlomo Havlin·Peter R. King·Youngki Lee·H. Eugene Stanley
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Abstract

On two-dimensional percolation clusters at the percolation threshold, we study $<σ(M_B,r)>$, the average conductance of the backbone, defined by two points separated by Euclidean distance $r$, of mass $M_B$. We find that with increasing $M_B$ and for fixed r, $<σ(M_B,r)>$ asymptotically {\it decreases} to a constant, in contrast with the behavior of homogeneous sytems and non-random fractals (such as the Sierpinski gasket) in which conductance increases with increasing $M_B$. We explain this behavior by studying the distribution of shortest paths between the two points on clusters with a given $M_B$. We also study the dependence of conductance on $M_B$ slightly above the percolation threshold.

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BibTeXRIS

Gerald Paul, Sergey V. Buldyrev, Nikolay V. Dokholyan, Shlomo Havlin, Peter R. King, Youngki Lee, H. Eugene Stanley. 1999-10-15. Dependence of Conductance on Percolation Backbone Mass. https://doi.org/10.1103/physreve.61.3435

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