title: Collision statistics, thermodynamics, and transport coefficients of hard hyperspheres in three, four, and five dimensions.
abstract: 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.
authors.affiliation: School of Chemical Engineering and Analytical Science, The University of Manchester, P.O. Box 88, Sackville Street, Manchester M60 1QD, United Kingdom. leo.lue@manchester.ac.uk
authors.forename: L
authors.initials: L
authors.lastname: Lue