Symmetry of the continuum percolation threshold in systems of two different size objects

R. Consiglio, R.N.A. Zouain, D.R. Baker, G. Paul and H.E. Stanley

Physica A: Statistical Mechanics and its Applications, 2004, vol. 343, issue C, 343-347

Abstract: We study the continuum percolation in systems composed of overlapping objects of two different sizes. We show that when treated as a function of the volumetric fraction f as opposed to the concentration x, the percolation threshold exhibits the symmetry ηc(f,r)=ηc(1−f,r) where r is the ratio of the volumes of the objects. Knowledge of this symmetry has the following benefits: (i) the position of the maximum of the percolation threshold is then known to be at exactly f=1/2 for any r and (ii) full knowledge of the percolation threshold is obtained by performing simulations only for f∈[0,12] or f∈[12,1], whichever is computationally easier.

Keywords: Continuum percolation; Symmetry (search for similar items in EconPapers)
Date: 2004
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:343:y:2004:i:c:p:343-347

DOI: 10.1016/j.physa.2004.05.051

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