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Exact Enumeration And Scaling For Fragmentation Of Percolation Clusters, Boyd F. Edwards, M. F. Gyure, M. V. Ferer
Exact Enumeration And Scaling For Fragmentation Of Percolation Clusters, Boyd F. Edwards, M. F. Gyure, M. V. Ferer
All Physics Faculty Publications
The fragmentation properties of percolation clusters yield information about their structure. Monte Carlo simulations and exact cluster enumeration for a square bond lattice and exact calculations for the Bethe lattice are used to study the fragmentation probability as(p) of clusters of mass s at an occupation probability p and the likelihood bs′s(p) that fragmentation of an s cluster will result in a daughter cluster of mass s′. Evidence is presented to support the scaling laws as(pc)∼s and bs′s(pc)=s-φg(s′/s), with φ=2-σ given by the standard cluster-number scaling …
Fragmentation Of Percolation Clusters At The Percolation Threshold, M. F. Gyure, Boyd F. Edwards
Fragmentation Of Percolation Clusters At The Percolation Threshold, M. F. Gyure, Boyd F. Edwards
All Physics Faculty Publications
A scaling theory and simulation results are presented for fragmentation of percolation clusters by random bond dilution. At the percolation threshold, scaling forms describe the average number of fragmenting bonds and the distribution of cluster masses produced by fragmentation. A relationship between the scaling exponents and standard percolation exponents is verified in one dimension, on the Bethe lattice, and for Monte Carlo simulations on a square lattice. These results further describe the structure of percolation clusters and provide kernels relevant to rate equations for fragmentation.