论文标题
非弹性麦克斯韦混合物的高度碰撞力矩。应用于均匀的冷却和均匀的剪切流量状态
High-degree collisional moments of inelastic Maxwell mixtures. Application to the homogeneous cooling and uniform shear flow states
论文作者
论文摘要
考虑到$ d $ d $二维的非弹性麦克斯韦模型的Boltzmann方程被认为是在粒状二进制混合物中确定第二，第三和第四级的碰撞力矩。当没有扩散时，这些碰撞力矩是根据每个物种分布功能的速度矩（每种物种的质量通量消失）精确评估的。相应相关的特征值以及跨系数作为正常恢复系数和混合物参数（质量，直径和组成）的功能。结果应用于在两种不同的非平衡情况下的力矩（以热速度缩放）的时间演变的分析：均质冷却状态（HCS）和均匀（或简单的）剪切流（USF）状态。对于HCS的情况，与简单的颗粒气体发生的情况相反，这表明第三级和第四级矩可能会及时散开，因为系统的参数的给定值。对混合物的参数空间对这些瞬间的时间行为的影响进行了详尽的研究。然后，在示踪剂极限中研究了USF中二级和三级速度矩的时间演变（即，当其中一个物种的浓度可忽略不计时）。如预期的那样，虽然二级力矩总是会收敛的，但示踪剂物种的三级力矩也可以在长期限制中发散。
The Boltzmann equation for $d$-dimensional inelastic Maxwell models is considered to determine the collisional moments of second, third and fourth degree in a granular binary mixture. These collisional moments are exactly evaluated in terms of the velocity moments of the distribution function of each species when diffusion is absent (mass flux of each species vanishes). The corresponding associated eigenvalues as well as cross coefficients are obtained as functions of the coefficients of normal restitution and the parameters of the mixture (masses, diameters and composition). The results are applied to the analysis of the time evolution of the moments (scaled with a thermal speed) in two different nonequilibrium situations: the homogeneous cooling state (HCS) and the uniform (or simple) shear flow (USF) state. In the case of the HCS, in contrast to what happens for simple granular gases, it is shown that the third and fourth degree moments could diverge in time for given values of the parameters of the system. An exhaustive study on the influence of the parameter space of the mixture on the time behavior of these moments is carried out. Then, the time evolution of the second- and third-degree velocity moments in the USF is studied in the tracer limit (namely, when the concentration of one of the species is negligible). As expected, while the second-degree moments are always convergent, the third-degree moments of the tracer species can be also divergent in the long time limit.
