Lue L
School of Chemical Engineering and Analytical Science, The University of Manchester, P.O. Box 88, Sackville Street, Manchester M60 1QD, United Kingdom.
J Chem Phys. 2005 Jan 22;122(4):44513. doi: 10.1063/1.1834498.
The collision statistics of hard hyperspheres are investigated. An exact, analytical formula is developed for the distribution of speeds of a sphere on collision, which is shown to be related to the average time between collisions for a sphere with a particular velocity. In addition, the relationship between the collision rate and the compressibility factor is generalized to arbitrary dimensions. Molecular dynamics simulations are performed for d=3, 4, and 5 dimensional hard-hypersphere fluids. From these simulations, the equation of state of these systems, the self-diffusion coefficient, the shear viscosity, and the thermal conductivity are determined as a function of density. Various aspects of the collision statistics and their dependence on the density and dimensionality of the system are also studied.
研究了硬超球的碰撞统计。推导出了一个精确的解析公式，用于描述球体碰撞时的速度分布，该公式表明与具有特定速度的球体的平均碰撞时间有关。此外，碰撞率与压缩因子之间的关系被推广到任意维度。对三维、四维和五维的硬超球流体进行了分子动力学模拟。通过这些模拟，确定了这些系统的状态方程、自扩散系数、剪切粘度和热导率作为密度的函数。还研究了碰撞统计的各个方面及其对系统密度和维度的依赖性。
