Title

Exact solution of a one-dimensional Boltzmann equation for a granular tracer particle

DOI

10.1016/j.physa.2006.04.059

Document Type

Journal Article

Publication Date

1-1-2007

Publication Title

Physica A: Statistical Mechanics and its Applications

Volume

373

First Page

313

Last Page

323

ISSN

3784371

Keywords

Boltzmann equation, Granular gas, Green-Kubo relation

Abstract

We consider a one-dimensional system consisting of a granular tracer particle of mass M in a bath of thermalized particles each of mass m. When the mass ratio, M / m, is equal to the coefficient of restitution, α, the system maps to a one-dimensional elastic gas. In this case the Boltzmann equation can be solved exactly. We also obtain expressions for the velocity autocorrelation function and the diffusion coefficient. Numerical simulations of the Boltzmann equation are performed for M / m ≠ α where no analytical solution is available. It appears that the dynamical features remain qualitatively similar to those found in the exactly solvable case. © 2006 Elsevier B.V. All rights reserved.

Open Access

Green Accepted

Share

COinS