Wakou Jun'ichi, Isobe Masaharu
Miyakonojo National College of Technology, Miyakonojo-shi, Miyazaki, 885-8567, Japan.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Jun;85(6 Pt 1):061311. doi: 10.1103/PhysRevE.85.061311. Epub 2012 Jun 29.
We investigated the validity of fluctuation-dissipation relations in the nonequilibrium stationary state of fluidized granular media under gravity by two independent approaches, based on theory and numerical simulations. A phenomenological Langevin-type theory describing the fluctuation of center of mass height, which was originally constructed for a one-dimensional granular gas on a vibrating bottom plate, was generalized to any dimensionality, even for the case in which the vibrating bottom plate is replaced by a thermal wall. The theory predicts a fluctuation-dissipation relation known to be satisfied at equilibrium, with a modification that replaces the equilibrium temperature by an effective temperature defined by the center of mass kinetic energy. To test the validity of the fluctuation-dissipation relation, we performed extensive and accurate event-driven molecular dynamics simulations for the model system with a thermal wall at the bottom. The power spectrum and response function of the center of mass height were measured and closely compared with theoretical predictions. It is shown that the fluctuation-dissipation relation for the granular system is satisfied, especially in the high-frequency (short time) region, for a wide range of system parameters. Finally, we describe the relationship between systematic deviations in the low-frequency (long time) region and the time scales of the driven granular system.
我们基于理论和数值模拟，通过两种独立的方法研究了重力作用下流化颗粒介质非平衡稳态中的涨落耗散关系。一种描述质心高度涨落的唯象朗之万型理论，最初是为振动底板上的一维颗粒气体构建的，现被推广到任意维度，甚至在振动底板被热壁取代的情况下也是如此。该理论预测了一种在平衡态已知满足的涨落耗散关系，并做了修正，即用由质心动能定义的有效温度取代平衡温度。为了检验涨落耗散关系的有效性，我们对底部有热壁的模型系统进行了广泛且精确的事件驱动分子动力学模拟。测量了质心高度的功率谱和响应函数，并与理论预测进行了仔细比较。结果表明，对于广泛的系统参数范围，颗粒系统的涨落耗散关系是满足的，特别是在高频（短时间）区域。最后，我们描述了低频（长时间）区域的系统偏差与驱动颗粒系统时间尺度之间的关系。
