Nonequilibrium steady solutions of the Boltzmann equation

Details Nonequilibrium steady solutions of the Boltzmann equation Nonequilibrium steady solutions of the Boltzmann equation

2011-01-21

arxiv.org/abs/1101.4137v1

Nonlinear Sciences

Chaotic Dynamics

43 pages, 21 figures

Scientific paper

10.1016/j.bbr.2011.03.031

We report a study of the homogeneous isotropic Boltzmann equation for an open system. We seek for nonequilibrium steady solutions in presence of forcing and dissipation. Using the language of weak turbulence theory, we analyze the possibility to observe Kolmogorov-Zakharov steady distributions. We derive a differential approximation model and we find that the expected nonequilibrium steady solutions have always the form of warm cascades. We propose an analytical prediction for relation between the forcing and dissipation and the thermodynamic quantities of the system. Specifically, we find that the temperature of the system is independent of the forcing amplitude and determined only by the forcing and dissipation scales. Finally, we perform direct numerical simulations of the Boltzmann equation finding consistent results with our theoretical predictions.

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