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.© 2005 American Institute of Physics.
- Compressibility; Equation of state; Fluids; Hard-sphere model; Spheres; Thermal conductivity; Transport properties; Virial coefficient; Viscosity (collision statistics, thermodn., and transport coeffs. of hard hyperspheres in three, four, and five dimensions); Diffusion (self-; collision statistics, thermodn., and transport coeffs. of hard hyperspheres in three, four, and five dimensions)