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Transport coefficients of d-dimensional inelastic Maxwell models

Author

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  • Santos, Andrés

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.

Suggested Citation

  • Santos, Andrés, 2003. "Transport coefficients of d-dimensional inelastic Maxwell models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 321(3), pages 442-466.
    • Handle: RePEc:eee:phsmap:v:321:y:2003:i:3:p:442-466
    DOI: 10.1016/S0378-4371(02)01005-1
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