Effect of Dissipation on Density Profile of One Dimensional Gas

Abstract

We study the effect of dissipation on the density profile of a one dimensional gas that is subject to gravity. The gas is in thermal equilibrium at temperature T with a heat reservoir at the bottom wall. Perturbative analysis of the Boltzmann equation reveals that the correction due to dissipation resulting from inelastic collisions is positive for $0<z<z_c$ and negative for $z>z_c$ with z the vertical coordinate. The numerically determined value for $z_c$ is $mg{z}_c/k_{B}T\approx 1.1613$, where g is the gravitational constant and m is the particle mass.

9 Pages, 1 Figure. To Appear in Physica A