论文标题
非弹性和粗糙的麦克斯韦颗粒的颗粒气
Granular gas of inelastic and rough Maxwell particles
论文作者
论文摘要
最广泛使用的颗粒气体模型可能是非弹性硬球模型（IHSM），其中谷物被认为是完全光滑的球体，与正常恢复的恒定系数相撞。一个更容易处理的模型是非弹性麦克斯韦模型（IMM），其中速度依赖性碰撞速率被有效的平均场常数取代。许多研究人员利用了这种简化，以在IMM中找到许多确切的结果。另一方面，IHSM和IMM都忽略了粗糙度的影响 - 通常存在于真实晶粒中 - 对颗粒气的动态特性。这是由无弹性粗糙的硬球模型（IRHSM）修复的，除了正常恢复的系数外，还引入了恒定的切向恢复系数。与从IHSM到IMM进行的简化时，我们在本文中提出了一个无弹性粗糙的Maxwell模型（IRMM），以简化IRHSM。提出的模型的障碍性通过对一级和二级碰撞力矩以及第三和第四级最相关的碰撞力矩的确切评估来说明。结果应用于旋转与翻译温度比和均匀冷却状态下速度累积剂的评估。
The most widely used model for granular gases is perhaps the inelastic hard-sphere model (IHSM), where the grains are assumed to be perfectly smooth spheres colliding with a constant coefficient of normal restitution. A much more tractable model is the inelastic Maxwell model (IMM), in which the velocity-dependent collision rate is replaced by an effective mean-field constant. This simplification has been taken advantage of by many researchers to find a number of exact results within the IMM. On the other hand, both the IHSM and IMM neglect the impact of roughness -- generally present in real grains -- on the dynamic properties of a granular gas. This is remedied by the inelastic rough hard-sphere model (IRHSM), where, apart from the coefficient of normal restitution, a constant coefficient of tangential restitution is introduced. In parallel to the simplification carried out when going from the IHSM to the IMM, we propose in this paper an inelastic rough Maxwell model (IRMM) as a simplification of the IRHSM. The tractability of the proposed model is illustrated by the exact evaluation of the collisional moments of first and second degree, and the most relevant ones of third and fourth degree. The results are applied to the evaluation of the rotational-to-translational temperature ratio and the velocity cumulants in the homogeneous cooling state.
