No-Enclave Percolation Corresponds to Holes in the Cluster Backbone

Hao Hu, Robert M. Ziff, Youjin Deng
2016 Physical Review Letters  
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 these holes gives the size-distribution exponent τ = 1.82(1) of the NEP model. An argument is given that τ=1 + d_B/2 ≈ 1.822 where d_B is the backbone dimension. On the other hand, a model of simple holes within a percolation cluster implies τ = 1 + d_f/2 = 187/96 ≈ 1.948, where d_f is the fractal dimension of the
more » ... cluster, and this value is consistent with Sheinman et al.'s experimental results of gel collapse which gives τ = 1.91(6). Both models yield a discontinuous maximum hole size at p_c, signifying explosive percolation behavior. At p_c, the largest hole fills exactly half the system, due to symmetry. Extensive numerical simulations confirm our results.
doi:10.1103/physrevlett.117.185701 pmid:27835010 fatcat:sk43qfwpobgnvi3bepeka7ucaa