Dynamics of the breakdown of granular clusters

TL;DR

This paper investigates the breakdown dynamics of granular clusters using an urn model, revealing how fluctuations and finite-size effects influence stability and diffusion behaviors.

Contribution

It introduces an urn model that accounts for fluctuations and finite-size effects, providing new insights into the stability and diffusion of granular clusters.

Findings

Cluster lifetime diverges as N^{1/3} at stability limits

Absence of continuous transition for more than two urns

Post-breakdown diffusion can be normal or anomalous

Abstract

Recently van der Meer et al. studied the breakdown of a granular cluster (Phys. Rev. Lett. {\bf 88}, 174302 (2002)). We reexamine this problem using an urn model, which takes into account fluctuations and finite-size effects. General arguments are given for the absence of a continuous transition when the number of urns (compartments) is greater than two. Monte Carlo simulations show that the lifetime of a cluster $\tau$ diverges at the limits of stability as $\tau\sim N^{1/3}$, where $N$ is the number of balls. After the breakdown, depending on the dynamical rules of our urn model, either normal or anomalous diffusion of the cluster takes place.