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Boltzmann equation for dissipative gases in homogeneous states with nonlinear friction

E. Trizac1,2, A. Barrat1,3, and M. H. Ernst4

  • 1Université Paris-Sud, 91405 Orsay, France
  • 2LPTMS (UMR CNRS 8626), 91405 Orsay, France
  • 3LPT (CNRS, UMR 8627), 91405 Orsay, France
  • 4Instituut voor Theoretische Fysica, Universiteit Utrecht, Postbus 80.195, 3508 TD Utrecht, The Netherlands

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Phys. Rev. E 76, 031305 – Published 21 September, 2007

DOI: https://doi.org/10.1103/PhysRevE.76.031305

Abstract

Combining analytical and numerical methods, we study within the framework of the homogeneous nonlinear Boltzmann equation a broad class of models relevant for the dynamics of dissipative fluids, including granular gases. We use the method presented in a previous paper [J. Stat. Phys. 124, 549 (2006)] and extend our results to a different heating mechanism: namely, a deterministic nonlinear friction force. We derive analytically the high-energy tail of the velocity distribution and compare the theoretical predictions with high-precision numerical simulations. Stretched exponential forms are obtained when the nonequilibrium steady state is stable. We derive subleading corrections and emphasize their relevance. In marginal stability cases, power-law behaviors arise, with exponents obtained as the roots of transcendental equations. We also consider some simple Bhatnagar-Gross-Krook models, driven by similar heating devices, to test the robustness of our predictions.

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Outline

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Phys. Rev. E 76, 031305– Published 21 September, 2007
  • Received 12 April 2007

© 2007 American Physical Society

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