No-Enclave Percolation Corresponds to Holes in the Cluster Backbone

Hao Hu, Robert M. Ziff, and Youjin Deng
Phys. Rev. Lett. 117, 185701 – Published 27 October 2016

Abstract

The no-enclave percolation (NEP) model introduced recently by Sheinman et al. can be mapped to a problem of holes within a standard percolation backbone, and numerical measurements of such holes give the same size-distribution exponent τ=1.82(1) as found for the NEP model. An argument is given that τ=1+dB/21.822 for backbone holes, where dB is the backbone dimension. On the other hand, a model of simple holes within a percolation cluster yields τ=1+df/2=187/961.948, where df is the fractal dimension of the cluster, and this value is consistent with the experimental results of gel collapse of Sheinman et al., which give τ=1.91(6). This suggests that the gel clusters are of the universality class of percolation cluster holes. Both models give a discontinuous maximum hole size at pc, signifying explosive percolation behavior.

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  • Received 12 May 2016

DOI:https://doi.org/10.1103/PhysRevLett.117.185701

© 2016 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & Thermodynamics

Authors & Affiliations

Hao Hu1,*, Robert M. Ziff2, and Youjin Deng1,†

  • 1Hefei National Laboratory for Physical Sciences at Microscale, Department of Modern Physics, University of Science and Technology of China, Hefei 230027, China
  • 2Center for the Study of Complex Systems and Department of Chemical Engineering, University of Michigan, Ann Arbor, Michigan 48109-2136, USA

  • *Present address: School of Chemical and Biomedical Engineering, 62 Nanyang Drive, Singapore 637459.
  • yjdeng@ustc.edu.cn

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Issue

Vol. 117, Iss. 18 — 28 October 2016

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