Exact enumeration and scaling for fragmentation of percolation clusters
- Department of Physics, West Virginia University, Morgantown, West Virginia 26506 (United States)
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 {ital 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}.
- DOE Contract Number:
- FG22-89PC89791
- OSTI ID:
- 7198423
- Journal Information:
- Physical Review A. General Physics; (United States), Vol. 46:10; ISSN 1050-2947
- Country of Publication:
- United States
- Language:
- English
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