Stable distribution in fragmentation processes

TL;DR

This paper introduces three exactly solvable models of fragmentation processes where the largest fragment can break with a fixed probability, revealing stable scaling solutions that depend on process details and differ from conventional models.

Contribution

The paper presents three new fragmentation models with exact solutions, highlighting stable scaling behaviors influenced by the probability of breaking the largest fragment.

Findings

Stable scaling solutions depend on the probability p and process specifics.

Models differ from conventional fragmentation models in their features.

Exact long-term solutions are derived for the introduced models.

Abstract

We introduce three models of fragmentation in which the largest fragment in the system can be broken at each time step with a fixed probability, p. We solve these models exactly in the long time limit to reveal stable time invariant (scaling) solutions which depend on p and the precise details of the fragmentation process. Various features of these models are compared with those of conventional fragmentation models.