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

Author

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

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.

Suggested Citation

  • Consiglio, R. & Zouain, R.N.A. & Baker, D.R. & Paul, G. & Stanley, H.E., 2004. "Symmetry of the continuum percolation threshold in systems of two different size objects," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 343(C), pages 343-347.
    • Handle: RePEc:eee:phsmap:v:343:y:2004:i:c:p:343-347
    DOI: 10.1016/j.physa.2004.05.051
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    Cited by:

    1. Li, Jiantong & Östling, Mikael, 2016. "Precise percolation thresholds of two-dimensional random systems comprising overlapping ellipses," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 940-950.
    2. Lin, Jianjun & Chen, Huisu & Liu, Lin & Zhang, Rongling, 2020. "Impact of particle size ratio on the percolation thresholds of 2D bidisperse granular systems composed of overlapping superellipses," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 544(C).

    More about this item

    Keywords

    Continuum percolation; Symmetry;

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