• Scaling relation for determining the critical threshold for continuum percolation of overlapping discs of two sizes

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      https://www.ias.ac.in/article/fulltext/pram/074/01/0109-0114

    • Keywords

       

      Continuum percolation; overlapping discs; critical percolation threshold.

    • Abstract

       

      We study continuum percolation of overlapping circular discs of two sizes. We propose a phenomenological scaling equation for the increase in the effective size of the larger discs due to the presence of the smaller discs. The critical percolation threshold as a function of the ratio of sizes of discs, for different values of the relative areal densities of two discs, can be described in terms of a scaling function of only one variable. The recent accurate Monte Carlo estimates of critical threshold by Quintanilla and Ziff [Phys. Rev. E76, 051115 (2007)] are in very good agreement with the proposed scaling relation.

    • Author Affiliations

       

      Ajit C Balram1 Deepak Dhar2

      1. Department of Physics, Indian Institute of Science Education and Research, Sai Trinity Building, Garware Circle, Sutarwadi, Pashan, Pune 411 021, India
      2. Department of Theoretical Physics, Tata Institute of Fundamental Research, 1 Homi Bhabha Road, Mumbai 400 005, India
    • Dates

       
  • Pramana – Journal of Physics | News

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