Effect of Dissipation on Density Profile of One Dimensional Gas

TL;DR

This paper investigates how dissipation affects the density distribution of a one-dimensional gas under gravity, revealing a change in the density correction sign at a specific height, with implications for understanding dissipative systems.

Contribution

The study provides a perturbative analysis of the Boltzmann equation showing how inelastic collisions influence the density profile in a gravitational field.

Findings

Positive density correction below z_c

Negative density correction above z_c

Critical height z_c approximately satisfies mgz_c/k_BT ≈ 1.1613

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 $mgz_c/k_BT\approx 1.1613$, where g is the gravitational constant and m is the particle mass.