IJPAM: Volume 38, No. 4 (2007)

ON THE SELF-DIFFUSION COEFFICIENT
FOR HARD SPHERES

Eugen Grycko
Faculty of Mathematics and Computer Science
University of Hagen
Lützowstr. 125
Hagen, D-58094, GERMANY
e-mail: eugen.grycko@fernuni-hagen.de


Abstract.$N$ hard spheres are injected into a 3-dimensional container. The initial positions of the spheres are generated according to the uniform distribution and the initial velocities according to a centered normal distribution. The Newtonian dynamics is imposed on the system (fluid). In the computer experiment imitating the (thermal) motion of the spheres the phenomenon of self-diffusion is observed and can be evaluated statistically entailing an estimate of the self-diffusion coefficient. A general formula for the dependence of the self-diffusion coefficient on the (thermodynamic) state of the model fluid is established involving a mathematical constant that can be estimated from computer experimental data.

As an application, the quantitative prediction of laboratory measurements of the self-diffusion coefficient as function of temperature is discussed for noble gases.

Received: July 7, 2007

AMS Subject Classification: 82B05, 76R50

Key Words and Phrases: wiener process, molecular dynamics, regression analysis, computer experiment

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 38
Issue: 4