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A Statistical Model of Aggregates Fragmentation (1106.2721v1)

Published 14 Jun 2011 in cond-mat.stat-mech and physics.geo-ph

Abstract: A statistical model of fragmentation of aggregates is proposed, based on the stochastic propagation of cracks through the body. The propagation rules are formulated on a lattice and mimic two important features of the process -- a crack moves against the stress gradient and its energy depletes as it grows. We perform numerical simulations of the model for two-dimensional lattice and reveal that the mass distribution for small and intermediate-size fragments obeys a power-law, F(m)\propto m-3/2, in agreement with experimental observations. We develop an analytical theory which explains the detected power-law and demonstrate that the overall fragment mass distribution in our model agrees qualitatively with that, observed in experiments.

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