Scaling and Multiscaling in Models of Fragmentation

TL;DR

This paper presents a geometric model for fragmentation kinetics across dimensions, revealing simple scaling in 1D and multiscaling in higher dimensions, with implications for understanding complex fragmentation processes.

Contribution

The paper introduces a novel geometric model that captures both simple and multiscaling behaviors in fragmentation across different dimensions.

Findings

1D model aligns with the random scission model and shows simple scaling.

Higher dimensions exhibit multiscaling with multiple length scales.

Fragment volume scales as 1/t over time.

Abstract

We introduce a simple geometric model which describes the kinetics of fragmentation of d-dimensional objects. In one dimension our model coincides with the random scission model and show a simple scaling behavior in the long-time limit. For d>1, the volume of the fragments is characterized by a single scale 1/t, while other geometric properties such as the length are characterized by an infinite number of length scales and thus exhibit multiscaling.