Probabilistic Fragmentation and Effective Power Law

TL;DR

This paper introduces a simple fragmentation model demonstrating that effective power laws with realistic exponents naturally emerge, influenced by the breaking mechanism and initial conditions, aligning well with experimental observations.

Contribution

The study presents a universal fragmentation model that explains the emergence of power law distributions with realistic exponents, accounting for initial conditions and mechanisms.

Findings

Effective power law for mass distribution arises under general conditions.

The exponent has a universal limit but varies with mechanisms and initial conditions.

Model aligns well with experimental fragmentation data.

Abstract

A simple fragmentation model is introduced and analysed. We show that, under very general conditions, an effective power law for the mass distribution arises with realistic exponent. This exponent has a universal limit, but in practice the effective exponent depends on the detailed breaking mechanism and the initial conditions. This dependence is in good agreement with experimental results of fragmentation.