Binomial multiplicative model of critical fragmentation

TL;DR

This paper introduces a binomial multiplicative model to describe low impact energy fragmentation, revealing multi-scaling properties and partial agreement with experimental data.

Contribution

The study proposes a simple biased cascade model that captures the multi-scaling behavior observed in low impact energy fragmentation experiments.

Findings

Weighted mean mass scales with a pseudo control parameter multiplicity

Multi-scaling exponents match experimental results

Model does not fully explain power-law distribution in complete fragmentation

Abstract

We report the binomial multiplicative model for low impact energy fragmentation. Impact fragmentation experiments were performed for low impact energy region, and it was found that the weighted mean mass is scaled by the pseudo control parameter multiplicity. We revealed that the power of this scaling is a non-integer (fractal) value and has a multi-scaling property. This multi-scaling can be interpreted by a binomial multiplicative (simple biased cascade) model. Although the model cannot explain the power-law of fragment-mass cumulative distribution in fully fragmented states, it can produce the multi-scaling exponents that agree with experimental results well.