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

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dc.creatorBarrat, Alain
dc.creatorTrizac, E.
dc.creatorErnst, M. H.
dc.date2007-01-22
dc.date2007-07-03
dc.date.accessioned2026-07-07T08:13:36Z
dc.date.available2026-07-07T08:13:36Z
dc.descriptionThe 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.
dc.identifierhttps://arxiv.org/abs/cond-mat/0701494
dc.identifierhttp://arxiv.org/abs/cond-mat/0701494
dc.identifierJournal of Physics A Mathematical and Theoretical 40 (23/03/2007) 4057-4073
dc.identifierdoi:10.1088/1751-8113/40/15/001
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/132827
dc.subjectStatistical Mechanics
dc.titleQuasi-elastic solutions to the nonlinear Boltzmann equation for dissipative gases
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