Minimal fragmentation problem

TL;DR

This paper introduces a minimal fragmentation model where identical bodies are split into two parts, enabling analytical solutions for shape and mass distributions, which are validated by numerical simulations.

Contribution

It provides the first analytical results for shape and mass distributions in a minimal fragmentation model with only binary splits.

Findings

Power-law regimes observed in shape and mass distributions.

Analytical solutions match numerical simulations.

Model simplifies understanding of fragmentation processes.

Abstract

As an alternative to the paradigmatic fragmentation problem of a single object crushed into a great number of pieces, we survey a large collection of identical bodies, each one randomly split into two fragments only. While some key features of usual fragmentation are preserved, this minimal approach allows for closed analytical results on both, shape abundances and mass distributions for the fragments, with robust power-law regimes. All the results are compared to numerical simulations.