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Quasi-elastic solutions to the nonlinear Boltzmann equation for dissipative gases | | Alain Barrat
; E. Trizac
; M. H. Ernst
; | | Date: |
22 Jan 2007 | | Subject: | Statistical Mechanics | | 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. | | Source: | arXiv, cond-mat/0701494 | | Services: | Forum | Review | PDF | Favorites | |
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