Clustering and Non-Gaussian Behavior in Granular Matter

TL;DR

This paper studies a model of granular matter with Brownian particles, revealing how inelastic collisions lead to different spatial and velocity distributions depending on the relative timescales, including clustering and non-Gaussian behavior.

Contribution

It introduces a model showing the transition from homogeneous to clustered states with non-Gaussian velocity distributions based on relaxation and collision timescales.

Findings

Homogeneous density and Gaussian velocities when relaxation time is small.

Strong clustering and non-Gaussian velocities when relaxation time is large.

Existence of a thermodynamic limit for energy and dissipation.

Abstract

We investigate the properties of a model of granular matter consisting of $N$ Brownian particles on a line subject to inelastic mutual collisions. This model displays a genuine thermodynamic limit for the mean values of the energy and the energy dissipation. When the typical relaxation time $\tau$ associated with the Brownian process is small compared with the mean collision time $\tau_c$ the spatial density is nearly homogeneous and the velocity probability distribution is gaussian. In the opposite limit $\tau \gg \tau_c$ one has strong spatial clustering, with a fractal distribution of particles, and the velocity probability distribution strongly deviates from the gaussian one.