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Full-Text Articles in Physics
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 …
Rate Equation And Scaling For Fragmentation With Mass Loss, Boyd F. Edwards, M. Cai, H. Han
Rate Equation And Scaling For Fragmentation With Mass Loss, Boyd F. Edwards, M. Cai, H. Han
All Physics Faculty Publications
A linear rate equation describes fragmentation with continuous and discrete mass loss typified by consumption of porous reactive solids and two-phase heterogeneous solids. For a mass-dependent fragmentation rate xα and a continuous-mass-loss rate εxγ,σ=γ-α-1<0 yields a>‘‘recession regime’’ where small particles lose mass continuously without breaking, σ>0 yields a ‘‘fragmentation regime’’ where all particles break, and σ=0 yields scaling for α>0. Shattering for α<0 and>σ≥0 is runaway fragmentation producing an infinte number of particles in a finite time, Exact and asymptotic solutions, exponent relations, and connections with static percolation are found.