2016/05/12 by Hao Hu, Robert M. Ziff, Youjin Deng · 15 citations
Mathematics · Physics and Astronomy · #Approx #Cluster (spacecraft) #Combinatorics #Complex Network Analysis Techniques #Dimension (graph theory) #Exponent #Fractal #Fractal dimension #Mathematical analysis #Mathematics #Percolation (cognitive psychology) #Percolation critical exponents #Percolation theory #Percolation threshold #Physics #Quantum mechanics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.dis-nn
paper · pdf · doi:10.1103/physrevlett.117.185701
published in Physical Review Letters 117(18), 185701 (American Physical Society) · 5 pages, 6 figures
arxiv created 2016/05/12 · openalex publication_date 2016/10/27 · arxiv updated 2016/11/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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/2≈1.822 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=187/96≈1.948, 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.