Effect of dissipation on density profile of one-dimensional gas

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 zzc with z the vertical coordinate. The numerically determined value for zc is mgzc/kBT≈1.1613, where g is the gravitational constant and m is the particle mass