Dynamics of the breakdown of granular clusters

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.

5 pages, 6 eps figures included

References in corpus (4)

• Hysteretic clustering in granular gas
• Sudden Collapse of a Granular Cluster
• Bifurcation Diagram for Compartmentalized Granular Gases
• Urn model of separation of sand

Cited by in corpus (12)

• Nonequilibrium Statistical Mechanics of the Zero-Range Process and Related Models
• Spontaneous Ratchet Effect in a Granular Gas
• Analytic study of clustering in shaken granular material using zero-range processes
• Discontinuous condensation transition and nonequivalence of ensembles in a zero-range process
• Instability of condensation in the zero-range process with random interaction
• Bistable Clustering in Driven Granular Mixtures
• Inelastic hard-rods in a periodic potential
• Analytic study of the three-urn model for separation of sand
• Ehrenfest urn model with interaction
• Non-equilibrium thermodynamics and Phase transition of Ehrenfest urns with interactions
• Drifting diffusion on a circle as continuous limit of a multiurn Ehrenfest model
• A heterogeneous zero-range process related to a two-dimensional walk model