Collision statistics, thermodynamics, and transport coefficients of hard hyperspheres in three, four, and five dimensions

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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.
Original languageEnglish
Pages (from-to)044513
Number of pages7
JournalJournal of Chemical Physics
Volume122
DOIs
Publication statusPublished - 22 Jan 2005

Keywords

  • collision statistics
  • thermodynamics
  • hard hyperspheres

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