Stochastic modeling on fragmentation process over lifetime and its dynamical scaling law of fragment distribution

Abstract

We propose a stochastic model of a fragmentation process, developed by taking into account fragment lifetime as a function of their size based on the Gibrat process. If lifetime is determined by a power function of fragment size, numerical results indicate that size distributions at different times can be collapsed into a single time-invariant curve by scaling size by average fragment size (i.e., the distribution obeys the dynamical scaling law). If lifetime is determined by a logarithmic function of fragment size, the distribution does not obey the scaling law. The necessary and sufficient condition that the scaling law is obeyed is obtained by a scaling analysis of the master equation.

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Cited by in corpus (6)

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• Morphology-dependent random binary fragmentation of in silico fractal-like agglomerates
• Fragment size density estimator for shrinkage-induced fracture based on a physics-informed neural network
• Scaling laws of shrinkage induced fragmentation phenomena
• Memory of rotation in residual stress of paste