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Transport coefficients ofd-dimensional inelastic Maxwell models

Authors
Journal
Physica A Statistical Mechanics and its Applications
0378-4371
Publisher
Elsevier
Publication Date
Volume
321
Identifiers
DOI: 10.1016/s0378-4371(02)01005-1
Keywords
  • Transport Coefficients
  • Granular Gases
  • Inelastic Maxwell Models
  • Boltzmann Equation
Disciplines
  • Mathematics

Abstract

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.

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