No-Enclave Percolation Corresponds to Holes in the Cluster Backbone.
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+d_{B}/2≈1.822 for backbone holes, where d_{B} is the backbone dimension. On the other hand, a model of simple holes within a percolation cluster yields τ=1+d_{f}/2=187/96≈1.948, where d_{f} 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 p_{c}, signifying explosive percolation behavior.
Hefei National Laboratory for Physical Sciences at Microscale, Department of Modern Physics, University of Science and Technology of China, Hefei 230027, China.
Hao
H
Hu
Center for the Study of Complex Systems and Department of Chemical Engineering, University of Michigan, Ann Arbor, Michigan 48109-2136, USA.
Robert M
RM
Ziff
Hefei National Laboratory for Physical Sciences at Microscale, Department of Modern Physics, University of Science and Technology of China, Hefei 230027, China.
Youjin
Y
Deng