, Volume 146, Issue 1, pp 244-248

A Remark Concerning Percolation Thresholds in Polydisperse Systems of Finite-Diameter Rods

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Abstract

A lattice-based analysis of the percolation threshold for randomly distributed cylindrical particles is generalized to consider arbitrary joint distributions over the radii and lengths of the rods. Effects due to the finite hard core diameter of the particles are accounted for. An analogy to site percolation on a modified Bethe lattice is exploited to yield a result for the percolation threshold that is equivalent to one that has been obtained from integral equation methods in the limit of large aspect ratios for the rods.