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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 {ital a}{sub {ital s}}({ital p}) of clusters of mass {ital s} at an occupation probability {ital p} and the likelihood {ital b}{sub {ital s}{prime}{ital s}}({ital p}) that fragmentation of an {ital s} cluster will result in a daughter cluster of mass {ital s}{prime}. Evidence is presented to support the scaling laws {ital a}{sub {ital s}}({ital p}{sub {ital c}}){similar to}{ital s} and {ital b}{sub {ital s}{prime}{ital s}}({ital p}{sub {ital c}})={ital s}{sup {minus}{phi}}{ital g}({ital s}{prime}/{ital s}), with {phi}=2{minus}{sigma} given by the standard cluster-number scaling exponent {sigma}. Simulations for {ital d}=2 verify the finite-size-scaling form {ital c}{sub {ital s}{prime}{ital s}{ital L}}({ital p}{sub {ital c}}) ={ital s}{sup 1{minus}{phi}}{ital {tilde g}}({ital s}{prime}/{ital s},{ital s}/{ital L}{sup {ital d}}{sub {ital f}}) of the product {ital c}{sub {ital s}{prime}{ital s}}({ital p}{sub {ital c}})={ital a}{sub {ital s}}({ital p}{sub {ital c}}){ital b}{sub {ital s}{prime}{ital s}}({ital p}{sub {ital c}}), where {ital L} is the lattice size and {ital d}{sub {ital f}} is the fractal dimension. Exact calculations of the fragmentation probability {ital f}{sub {italmore » s}{ital t}} of a cluster of mass {ital s} and perimeter {ital t} indicate that branches are important even on the maximum perimeter clusters. These calculations also show that the minimum of {ital b}{sub {ital s}{prime}{ital s}}({ital p}) near {ital s}{prime}={ital s}/2, where the two daughter masses are comparable, deepens with increasing {ital p}.« less

Source Citation

Edwards, Boyd F.., Gyure, Mark F.., & Ferer, M.. (1992). Exact Enumeration And Scaling For Fragmentation Of Percolation Clusters. Physical Review A - Atomic, Molecular, and Optical Physics, 46(10), 6252-6264.



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