Rongali Ramakrishna, Alam Meheboob
Engineering Mechanics Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur PO, Bangalore 560064, India.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Jun;89(6):062201. doi: 10.1103/PhysRevE.89.062201. Epub 2014 Jun 9.
The orientational or angular correlation between the directions of the translational and rotational motions is analyzed theoretically for the homogeneous cooling state of a rough granular gas. The dynamical equations are derived using an approximate form of the single-particle distribution function that incorporates angular correlations. The goal is to assess the effects of higher-order angular corrections for which both quadratic- and quartic-order terms (in translational and rotational velocities of particles) are retained in the perturbation expansion of the distribution function. We show that higher-order corrections can markedly affect the steady-state orientational correlation when the normal restitution coefficient is moderate or small, and this effect is more prominent for nearly smooth particles. The transient evolution of orientational correlation is found to be significantly affected by higher-order terms. In particular the higher-order orientational correlations can dominate over the leading-order contribution during short times even in the quasi-elastic limit, although the steady correlation remains unaffected by such corrections in the same limit. The buildup of correlations during the transient stage seems to be closely tied to the evolution of the ratio between the rotational and translational temperatures. It is demonstrated that the transient dynamics of the temperature ratio and its steady state remain insensitive to higher-order angular correlation.
针对粗糙颗粒气体的均匀冷却状态，从理论上分析了平动和转动运动方向之间的取向或角关联。利用包含角关联的单粒子分布函数的近似形式推导了动力学方程。目的是评估高阶角修正的影响，在分布函数的微扰展开中保留了二次项和四次项（关于粒子的平动和转动速度）。我们表明，当法向恢复系数适中或较小时，高阶修正会显著影响稳态取向关联，并且这种效应对于近乎光滑的粒子更为显著。发现取向关联的瞬态演化受到高阶项的显著影响。特别是，即使在准弹性极限下，高阶取向关联在短时间内也可能超过主导阶贡献，尽管在相同极限下稳态关联不受此类修正的影响。瞬态阶段关联的建立似乎与转动和平动温度之比的演化密切相关。结果表明，温度比的瞬态动力学及其稳态对高阶角关联不敏感。
