Exact solution of a one-dimensional Boltzmann equation for a granular tracer particle
Physica A: Statistical Mechanics and its Applications
Boltzmann equation, Granular gas, Green-Kubo relation
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.
Piasecki, J., Talbot, J., & Viot, P. (2007). Exact solution of a one-dimensional Boltzmann equation for a granular tracer particle. Physica A: Statistical Mechanics and its Applications, 373, 313-323. https://doi.org/10.1016/j.physa.2006.04.059