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Precise percolation thresholds of two-dimensional random systems comprising overlapping ellipses

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  • Li, Jiantong
  • Östling, Mikael

Abstract

This work explores the percolation thresholds of continuum systems consisting of randomly-oriented overlapping ellipses. High-precision percolation thresholds for various homogeneous ellipse systems with different aspect ratios are obtained from extensive Monte Carlo simulations based on the incorporation of Vieillard-Baron’s contact function of two identical ellipses with our efficient algorithm for continuum percolation. In addition, we generalize Vieillard-Baron’s contact function from identical ellipses to unequal ellipses, and extend the Monte Carlo algorithm to heterogeneous ellipse systems where the ellipses have different dimensions and/or aspect ratios. Based on the concept of modified excluded area, a general law is verified for precise prediction of percolation threshold for many heterogeneous ellipse systems. In particular, the study of heterogeneous ellipse systems gains insight into the apparent percolation threshold symmetry observed earlier in systems comprising unequal circles (Consiglio et al., 2004).

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:462:y:2016:i:c:p:940-950
    DOI: 10.1016/j.physa.2016.06.020
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    References listed on IDEAS

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    1. Hovi, J.-P. & Aharony, Amnon, 1995. "Renormalization group, scaling and universality in spanning probability for percolation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 221(1), pages 68-79.
    2. 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.
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    Cited by:

    1. Lin, Jianjun & Chen, Huisu & Zhao, Qingxin & Li, Mingqi, 2021. "Statistical analysis of the critical percolation of ITZ around polygonal aggregates in three-phase concrete materials," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 572(C).

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