Energy Transport in a One-Dimensional Granular Gas

TL;DR

This paper investigates heat conduction in a one-dimensional granular gas, analyzing how different viscous dissipation mechanisms affect thermal transport and momentum conservation, and finds normal conduction in both cases.

Contribution

It introduces a comparative study of two viscous dissipation models in 1D granular gases, highlighting the role of momentum conservation in heat conduction.

Findings

Normal thermal conduction observed in both dissipation mechanisms

Momentum conservation does not significantly alter heat conduction behavior

Provides insights into energy transport in nonlinear granular systems

Abstract

We study heat conduction in one-dimensional granular gases. In particular, we consider two mechanisms of viscous dissipation during inter-grain collisions. In one, the dissipative force is proportional to the grain's velocity and dissipates not only energy but also momentum. In the other, the dissipative force is proportional to the relative velocity of the grains and therefore conserves momentum even while dissipating energy. This allows us to explore the role of momentum conservation in the heat conduction properties of this one-dimensional nonlinear system. We find normal thermal conduction whether or not momentum is conserved.