Close-packed granular clusters: hydrostatics and persistent Gaussian fluctuations

TL;DR

This study investigates dense granular clusters in a circular container, revealing Gaussian fluctuations of the cluster's center of mass and validating a hydrostatic model with specific constitutive relations.

Contribution

It demonstrates that granular clusters behave like macro-particles with Gaussian fluctuations, supported by molecular dynamics simulations and hydrostatic equations with Grossman et al.'s constitutive relations.

Findings

Density profile matches hydrostatic equations with Grossman et al.'s relations

Center of mass fluctuations are Gaussian

Fluctuations persist with increasing particle number

Abstract

Dense granular clusters often behave like macro-particles. We address this interesting phenomenon in a model system of inelastically colliding hard disks inside a circular box, driven by a thermal wall at zero gravity. Molecular dynamics simulations show a close-packed cluster of an almost circular shape, weakly fluctuating in space and isolated from the driving wall by a low-density gas. The density profile of the system agrees very well with the azimuthally symmetric solution of granular hydrostatic equations employing constitutive relations by Grossman et al., whereas the widely used Enskog-type constitutive relations show poor accuracy. We find that fluctuations of the center of mass of the system are Gaussian. This suggests an effective Langevin description in terms of a macro-particle, confined by a harmonic potential and driven by a delta-correlated noise. Surprisingly, the fluctuations persist when increasing the number of particles in the system.