# Scaling and Multiscaling in Models of Fragmentation

Source: [Scaling and Multiscaling in Models of Fragmentation](<https://www.sota2.com/research/paper/68fa24122c2a37601939ee21>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T07:55:39.697Z

Authors: P. L. Krapivsky, E. Ben-Naim

Published: 1994-07-20T19:08:04.000Z

## 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.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/cond-mat/9407084>)

[PDF](<https://arxiv.org/pdf/cond-mat/9407084.pdf>)