论文标题
非线性阻力下均质非弹性颗粒气的动力学理论和记忆效应
Kinetic Theory and Memory Effects of Homogeneous Inelastic Granular Gases under Nonlinear Drag
论文作者
论文摘要
我们研究了浸入由较小颗粒的热浴中浸入的稀颗粒气体，其质量在这项工作中比颗粒小的颗粒小得多。假定颗粒颗粒具有非弹性和硬相互作用，在正常恢复的恒定系数所致的碰撞中失去了能量。与热浴的相互作用是通过非线性阻力力以及白色噪声随机力建模的。该系统的动力学理论由endkog- fokker-planck方程描述，用于单粒子速度分布函数。为了获得温度衰老和稳态的明确结果，开发了麦克斯韦和第一层近似值。后者考虑了多余的峰度与温度的耦合。将理论预测与直接模拟蒙特卡洛和事件驱动的分子动力学模拟进行了比较。虽然颗粒温度的良好结果是从麦克斯韦近似值中获得的，但在使用第一个超声量近似时，发现了更好的一致性，尤其是随着非弹性和阻力非线性的增加。另外，后者近似对于计算记忆效应（例如MPEMBA和类似Kovacs）至关重要。
We study a dilute granular gas immersed in a thermal bath made of smaller particles with masses not much smaller than the granular ones in this work. Granular particles are assumed to have inelastic and hard interactions, losing energy in collisions as accounted by a constant coefficient of normal restitution. The interaction with the thermal bath is modeled by a nonlinear drag force plus a white-noise stochastic force. The kinetic theory for this system is described by an Enskog--Fokker--Planck equation for the one-particle velocity distribution function. To get explicit results of the temperature aging and steady states, Maxwellian and first Sonine approximations are developed. The latter takes into account the coupling of the excess kurtosis with the temperature. Theoretical predictions are compared with direct simulation Monte Carlo and event-driven molecular dynamics simulations. While good results for the granular temperature are obtained from the Maxwellian approximation, a much better agreement, especially as inelasticity and drag nonlinearity increase, is found when using the first Sonine approximation. The latter approximation is, additionally, crucial to account for memory effects such as Mpemba and Kovacs-like ones.
