摘要翻译：
在均匀非线性Boltzmann方程的框架内，我们结合解析和数值方法，研究了包括颗粒气体在内的耗散流体动力学的一类广泛的模型。我们使用了前文[J.Stat.Phys.124，549(2006)]中提出的新方法，并将我们的结果推广到不同的加热机制，即确定性非线性摩擦力。我们解析地导出了速度分布的高能尾，并将理论预测与高精度数值模拟进行了比较。得到了非平衡稳态稳定时的拉伸指数形式。我们推导出次主导修正，并强调它们的相关性。在边缘稳定的情况下，幂律行为出现，指数作为超越方程的根。我们还考虑了一些简单的BGK（Bhatnagar,Gross,Krook）模型，由类似的加热装置驱动，以检验我们预测的稳健性。
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英文标题：
《Boltzmann equation for dissipative gases in homogeneous states with
  nonlinear friction》
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作者：
E. Trizac, A. Barrat, M.H. Ernst
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最新提交年份：
2007
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分类信息：

一级分类：Physics        物理学
二级分类：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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英文摘要：
  Combining analytical and numerical methods, we study within the framework of the homogeneous non-linear Boltzmann equation, a broad class of models relevant for the dynamics of dissipative fluids, including granular gases. We use the new method presented in a previous paper [J. Stat. Phys. 124, 549 (2006)] and extend our results to a different heating mechanism, namely a deterministic non-linear 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 non-equilibrium steady state is stable. We derive sub-leading 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 BGK (Bhatnagar, Gross, Krook) models, driven by similar heating devices, to test the robustness of our predictions.
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PDF链接：
https://arxiv.org/pdf/706.4275