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

Pramana

Ajit C Balram1¹  Deepak Dhar2² 

[1] Department of Physics, Indian Institute of Science Education and Research, Sai Trinity Building, Garware Circle, Sutarwadi, Pashan, Pune 411 021, India$$;Department of Theoretical Physics, Tata Institute of Fundamental Research, 1 Homi Bhabha Road, Mumbai 400 005, India$$

关键词: Continuum percolation;    overlapping discs;    critical percolation threshold.;   

DOI  :  

学科分类：物理（综合）

来源: Indian Academy of Sciences

【 摘 要 】

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.

【 授权许可】

Unknown