Continuum percolation of permeable objects

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Abstract
We study the extent to which excluded volume determines the percolation threshold for permeable elements in the continuum. An expansion due to Coniglio, De Angelis, Forlani, and Lauro exploits a similarity between the statistical mechanics of hard particles and statistics of percolation of permeable objects. This expansion shows that the expectation value of the excluded volume completely determines the threshold at lowest order in element density. Permeable rods in the continuum may be analyzed with the help of Onsager’s treatment of virial coefficients for hard rods. Systems of rods provide cases in which higher-order terms will alter the proportionality of threshold to the inverse of the expected excluded volume and cases in which this proportionality remains exact.

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