Universal scaling dynamics in a perturbed granular gas

TL;DR

This paper investigates the universal scaling behavior of a granular gas's response to localized energy input, revealing dimension-dependent growth and energy decay laws independent of particle restitution.

Contribution

It introduces a universal scaling framework for granular gases' response to localized perturbations, supported by analytical and simulation results across multiple dimensions.

Findings

Disturbance radius scales as t^{1/(d+1)} in d dimensions.

Energy decreases as t^{-d/(d+1)} regardless of restitution coefficient.

Analytical and simulation results agree across 1D, 2D, and 3D.

Abstract

We study the response of a granular system at rest to an instantaneous input of energy in a localised region. We present scaling arguments that show that, in $d$ dimensions, the radius of the resulting disturbance increases with time $t$ as $t^{\alpha}$, and the energy decreases as $t^{-\alpha d}$, where the exponent $\alpha=1/(d+1)$ is independent of the coefficient of restitution. We support our arguments with an exact calculation in one dimension and event driven molecular dynamic simulations of hard sphere particles in two and three dimensions.