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

J. Piasecki, J. Talbot and P. Viot

Physica A: Statistical Mechanics and its Applications, 2007, vol. 373, issue C, 313-323

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.

Keywords: Boltzmann equation; Granular gas; Green–Kubo relation (search for similar items in EconPapers)
Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:373:y:2007:i:c:p:313-323

DOI: 10.1016/j.physa.2006.04.059

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