Incollection,
Structure of hard-hypersphere fluids in odd dimensions
Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)
Abstract
The structure of single-component fluids of hard hyperspheres in odd space
dimensionalities $d$ is studied with an analytical approximation method.
This is a generalization to an arbitrary odd-number of dimensions of the
Rational-Function Approximation earlier introduced in the study of hard-sphere
fluids S. B. Yuste and A. Santos, Phys. Rev. A 43, 5418 (1991).
The theory makes use of the exact form of the radial distribution function
to first order in density and a simple and accurate generalization
to moderate densities based on simple physical requeriments.
Fourier transform in terms of reverse Bessel polynomials constitute the
mathematical framework of these evaluations from which an analytical
expression of the static structure factor is obtained.
Analytical expressions for thermodynamic quantities such as the
compressibility factor and the isothermal susceptibility are also found.
Structural functions and thermodynamic quantities are explicity evaluated
for fluids at $d=1$, 3, 5, 7, 9, and 11, and compared with those of the
Percus-Yevick approximation and available simulation data.
A simple extension of this generalized RFA method allows us to find
solutions with thermodynamic consistence between the virial and
compressibility routes to the EOS. Excellent agreement with available
Monte Carlo data at $d=5$ and $d=7$ is found.
As a byproduct of the theory, an exact and explicit polynomial
expression for the intersection volume of two hyperspheres in arbitrary
odd dimensions is found.
Tags
- bessel
- distribution
- factor
- fluids
- function
- hard-hypersphere
- polynomials
- radial
- reverse
- statphys23
- structure
- topic-1
