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

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dc.contributor.advisorBritton, David Ten_ZA
dc.contributor.advisorHärting, Margiten_ZA
dc.contributor.authorCorker, Lloyd Aen_ZA
dc.date.accessioned2014-08-13T20:05:25Z
dc.date.available2014-08-13T20:05:25Z
dc.date.issued2006en_ZA
dc.descriptionIncludes bibliographical references (leaves 63-65).en_ZA
dc.description.abstractThis 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.en_ZA
dc.identifier.apacitationCorker, L. A. (2006). <i>Drift-diffusion of a vacancy in inhomogeneous media and its material constants : a Fokker-Planck equation approach with an application to foreign exchange data</i>. (Thesis). University of Cape Town ,Faculty of Science ,Department of Physics. Retrieved from http://hdl.handle.net/11427/6527en_ZA
dc.identifier.chicagocitationCorker, Lloyd A. <i>"Drift-diffusion of a vacancy in inhomogeneous media and its material constants : a Fokker-Planck equation approach with an application to foreign exchange data."</i> Thesis., University of Cape Town ,Faculty of Science ,Department of Physics, 2006. http://hdl.handle.net/11427/6527en_ZA
dc.identifier.citationCorker, L. 2006. Drift-diffusion of a vacancy in inhomogeneous media and its material constants : a Fokker-Planck equation approach with an application to foreign exchange data. University of Cape Town.en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Corker, Lloyd A AB - 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. DA - 2006 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 2006 T1 - Drift-diffusion of a vacancy in inhomogeneous media and its material constants : a Fokker-Planck equation approach with an application to foreign exchange data TI - Drift-diffusion of a vacancy in inhomogeneous media and its material constants : a Fokker-Planck equation approach with an application to foreign exchange data UR - http://hdl.handle.net/11427/6527 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/6527
dc.identifier.vancouvercitationCorker LA. Drift-diffusion of a vacancy in inhomogeneous media and its material constants : a Fokker-Planck equation approach with an application to foreign exchange data. [Thesis]. University of Cape Town ,Faculty of Science ,Department of Physics, 2006 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/6527en_ZA
dc.language.isoengen_ZA
dc.publisher.departmentDepartment of Physicsen_ZA
dc.publisher.facultyFaculty of Scienceen_ZA
dc.publisher.institutionUniversity of Cape Town
dc.subject.otherPhysicsen_ZA
dc.titleDrift-diffusion of a vacancy in inhomogeneous media and its material constants : a Fokker-Planck equation approach with an application to foreign exchange dataen_ZA
dc.typeMaster Thesis
dc.type.qualificationlevelMasters
dc.type.qualificationnameMScen_ZA
uct.type.filetypeText
uct.type.filetypeImage
uct.type.publicationResearchen_ZA
uct.type.resourceThesisen_ZA
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