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Efficient measurement of the percolation threshold for fully penetrable discs

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, , Citation J Quintanilla et al 2000 J. Phys. A: Math. Gen. 33 L399 DOI 10.1088/0305-4470/33/42/104

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1 Department of Mathematics, University of North Texas, Denton, TX 76203, USA

2 Princeton Materials Institute and Department of Chemistry, Princeton University, Princeton, NJ 08544, USA

3 Department of Chemical Engineering, University of Michigan, Ann Arbor, MI 48109-2136, USA

4 Corresponding author.

Dates

  1. Received 28 February 2000

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0305-4470/33/42/L399

Abstract

We study the percolation threshold for fully penetrable discs by measuring the average location of the frontier for a statistically inhomogeneous distribution of fully penetrable discs. We use two different algorithms to efficiently simulate the frontier, including the continuum analogue of an algorithm previously used for gradient percolation on a square lattice. We find that ϕc = 0.676 339±0.000 004, thus providing an extra significant digit of accuracy to this constant.

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