Transport coefficients of d-dimensional inelastic Maxwell models
Abstract
Due to the mathematical complexity of the Boltzmann equation for inelastic hard spheres, a kinetic model has recently been proposed whereby the collision rate (which is proportional to the relative velocity for hard spheres) is replaced by an average velocity-independent value. The resulting inelastic Maxwell model has received a large amount of recent interest, especially in connection with the high energy tail of homogeneous states. In this paper the transport coefficients of inelastic Maxwell models in d dimensions are derived by means of the Chapman-Enskog method for unforced systems as well as for systems driven by a Gaussian thermostat and by a white noise thermostat. Comparison with known transport coefficients of inelastic hard spheres shows that their dependence on inelasticity is captured by the inelastic Maxwell models only in a mild qualitative way. Paradoxically, a much simpler BGK-like model kinetic equation is closer to the results for inelastic hard spheres than the inelastic Maxwell model
Keywords
Cite
@article{arxiv.cond-mat/0204071,
title = {Transport coefficients of d-dimensional inelastic Maxwell models},
author = {Andres Santos},
journal= {arXiv preprint arXiv:cond-mat/0204071},
year = {2007}
}
Comments
29 pages, 7 figures; Elsevier style; Some equations and figures corrected; Accepted for publication in Physica A