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arXiv · 1407.8461

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

Shin-ichi Ito·Satoshi Yukawa
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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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Shin-ichi Ito, Satoshi Yukawa. 2014-07-31. Stochastic modeling on fragmentation process over lifetime and its dynamical scaling law of fragment distribution. https://doi.org/10.7566/jpsj.83.124005

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