Coarse grained dynamics of the freely cooling granular gas in one dimension

TL;DR

This paper investigates the clustering dynamics of a one-dimensional freely cooling granular gas, revealing a velocity-dependent fragmentation process and a power-law cluster size distribution linked to velocity fluctuations.

Contribution

It introduces a velocity-dependent restitution model and uncovers a crossover in cluster behavior, connecting velocity fluctuations to cluster size distribution scaling.

Findings

Cluster fragmentation rate sharply increases beyond a velocity-dependent time scale.

Cluster size distribution develops a nontrivial power law after the crossover.

Velocity fluctuations within clusters become comparable to a velocity scale $\delta$ at the crossover.

Abstract

We study the dynamics and structure of clusters in the inhomogeneous clustered regime of a freely cooling granular gas of point particles in one dimension. The coefficient of restitution is modeled as $r_0<1$ or 1 depending on whether the relative speed is greater or smaller than a velocity scale $\delta$. The effective fragmentation rate of a cluster is shown to rise sharply beyond a $\delta$ dependent time scale. This crossover is coincident with the velocity fluctuations within a cluster becoming order $\delta$. Beyond this crossover time, the cluster size distribution develops a nontrivial power law distribution, whose scaling properties are related to those of the velocity fluctuations. We argue that these underlying features are responsible behind the recently observed nontrivial coarsening behaviour in the one dimensional freely cooling granular gas.