Topological estimation of percolation thresholds
Neher RA, Mecke K, Wagner H (2008)
Publication Status: Published
Publication Type: Journal article
Publication year: 2008
Journal
Publisher: IOP PUBLISHING LTD
DOI: 10.1088/1742-5468/2008/01/P01011
Abstract
Global physical properties of random media change qualitatively at a percolation threshold, where isolated clusters merge to form one infinite connected component. The precise knowledge of percolation thresholds is thus of paramount importance. For two-dimensional lattice graphs, we use the universal scaling form of the cluster size distributions to derive a relation between the mean Euler characteristic of the critical percolation patterns and the threshold density pc. From this relation, we deduce a simple rule to estimate pc, which is remarkably accurate. We present some evidence that similar relations might hold for continuum percolation and percolation in higher dimensions.
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Germany (DE)How to cite
APA:
Neher, R.A., Mecke, K., & Wagner, H. (2008). Topological estimation of percolation thresholds. Journal of Statistical Mechanics-Theory and Experiment. https://dx.doi.org/10.1088/1742-5468/2008/01/P01011
MLA:
Neher, Richard A., Klaus Mecke, and Herbert Wagner. "Topological estimation of percolation thresholds." Journal of Statistical Mechanics-Theory and Experiment (2008).
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