Shock-Like Dynamics of Inelastic Gases

TL;DR

This paper demonstrates that the long-term behavior of one-dimensional inelastic gases mirrors that of sticky gases, with universal statistical properties and dynamics described by the inviscid Burgers equation, regardless of inelasticity degree.

Contribution

It reveals the asymptotic independence of inelastic gas dynamics from inelasticity and connects microscopic behavior to continuum Burgers equation predictions.

Findings

Velocity fluctuations match those of sticky gases.

Temperature decays as t^{-2/3}.

Discontinuities form in velocity profiles.

Abstract

We provide a simple physical picture which suggests that the asymptotic dynamics of inelastic gases in one dimension is independent of the degree of inelasticity. Statistical characteristics, including velocity fluctuations and the velocity distribution are identical to those of a perfectly inelastic sticky gas, which in turn is described by the inviscid Burgers equation. Asymptotic predictions of this continuum theory, including the t^{-2/3} temperature decay and the development of discontinuities in the velocity profile, are verified numerically for inelastic gases.