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Quasi-elastic solutions to the nonlinear Boltzmann equation for dissipative gases

Alain Barrat·E. Trizac·M. H. Ernst
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Abstract

The solutions of the one-dimensional homogeneous nonlinear Boltzmann equation are studied in the QE-limit (Quasi-Elastic; infinitesimal dissipation) by a combination of analytical and numerical techniques. Their behavior at large velocities differs qualitatively from that for higher dimensional systems. In our generic model, a dissipative fluid is maintained in a non-equilibrium steady state by a stochastic or deterministic driving force. The velocity distribution for stochastic driving is regular and for infinitesimal dissipation, has a stretched exponential tail, with an unusual stretching exponent $b_{QE} = 2b$, twice as large as the standard one for the corresponding $d$-dimensional system at finite dissipation. For deterministic driving the behavior is more subtle and displays singularities, such as multi-peaked velocity distribution functions. We classify the corresponding velocity distributions according to the nature and scaling behavior of such singularities.

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Alain Barrat, E. Trizac, M. H. Ernst. 2007-07-03. Quasi-elastic solutions to the nonlinear Boltzmann equation for dissipative gases. https://doi.org/10.1088/1751-8113%2F40%2F15%2F001

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