Drift-diffusion of a vacancy in inhomogeneous media and its material constants : a Fokker-Planck equation approach with an application to foreign exchange data

This study derived the mobility and diffusion coefficients of a Fokker-Planck equation describing a vacancy hopping in inhomogeneous media in one dimension under a directed stress. The study used the general master equation as a basis for a physical model because of the mesoscopic view that the change in average concentration is inadequate to describe small fluctuations in a system and that a probabilistic approach is needed. By van Kampen's system-size expansion a master equation was expanded to obtain a nonlinear Fokker-Planck equation of the diffusive type. The Einstein relation was obtained and satisfied. As an application to a physical system we considered the simple one dimension case of a point defect diffusing by a hopping mechanism under an applied stress using data obtained from the implantation of krypton ions on a pre-existing stress state in polycrystalline titanium. From this data we estimated the stress gradient and from literature used the vacancy migration enthalpy to find the diffusion coefficients, and by the Einstein relation, the mobility, the coefficients of a Fokker-Planck equation. As an application to a non physical system the study set up a Fokker-Planck equation which described incremental changes in foreign exchange (FX) prices. The Fokker-Planck equation was completely determined by the drift and diffusion coefficients extracted directly from the actual FX prices. The purpose here was to show the importance of a 'physical model' or the existence of the Markov property for the establishment of a Fokker-Planck equation and by starting from a master equation for non physical systems which would make for better understanding of the underlying statistical equations of motion of the fluctuating system.

Grantor dc:publisher.institution

Department of Physics

Year dc:date.issued

2006

Author dc:creator

• Corker, Lloyd A

Advisors dc:contributor.advisor

• Britton, David T
• Härting, Margit

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/11427/6527

OAI identifier oai:identifier

oai:open.uct.ac.za:11427/6527