Phase Transitions in Systems with Aggregation and Shattering

TL;DR

This paper investigates a model of cluster dynamics involving aggregation and shattering, revealing a phase transition influenced heavily by initial conditions and the probability of shattering events.

Contribution

It introduces a new model of cluster evolution with a phase transition driven by shattering probability and initial conditions, expanding understanding of aggregation-shattering systems.

Findings

A phase transition occurs when shattering probability exceeds a threshold.

The phase transition's nature depends strongly on initial conditions.

The model highlights the impact of initial cluster configurations on system behavior.

Abstract

We consider a system of clusters made of elementary building blocks, monomers, and evolving via collisions between diffusing monomers and immobile composite clusters. In our model, the cluster-monomer collision can lead to the attachment of the monomer to the cluster (addition process) or to the total break-up of the cluster (shattering process). A phase transition, separating qualitatively different behaviors, occurs when the probability of shattering events exceeds a certain threshold. The novel feature of the phase transition is the dramatic dependence on the initial conditions.