Scaling relation for determining the critical threshold for continuum percolation of overlapping discs of two sizes |
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Authors: | Ajit C Balram and Deepak Dhar |
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Institution: | 1.Department of Physics,Indian Institute of Science Education and Research,Pune,India;2.Department of Theoretical Physics,Tata Institute of Fundamental Research,Mumbai,India |
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Abstract: | We study continuum percolation of overlapping circular discs of two sizes. We propose a phenomenological scaling equation
for the increase in the effective size of the larger discs due to the presence of the smaller discs. The critical percolation
threshold as a function of the ratio of sizes of discs, for different values of the relative areal densities of two discs,
can be described in terms of a scaling function of only one variable. The recent accurate Monte Carlo estimates of critical
threshold by Quintanilla and Ziff Phys. Rev.
E76, 051115 (2007)] are in very good agreement with the proposed scaling relation. |
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