Vlasov's Equation on a Great Circle and the Landau Damping Phenomenon

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dc.contributor.authorShen, Shengyi
dc.contributor.supervisorDiacu, Florin
dc.contributor.supervisorIbrahim, Slim
dc.date.accessioned2014-12-16T16:32:14Z
dc.date.available2014-12-16T16:32:14Z
dc.date.copyright2014en_US
dc.date.issued2014-12-16
dc.degree.departmentDepartment of Mathematics and Statistics
dc.degree.levelMaster of Science M.Sc.en_US
dc.description.abstractVlasov's equation describes the time evolution of the distribution function for a collisionless physical system of identical particles, such as plasma or galaxies. Together with Poisson's equation, which yields the potential, it forms the Vlasov-Poisson system. In Euclidean space this system has been extensively studied in the past century. It has been recently shown that the Valsov-Poisson system exhibits an interesting, counter-intuitive phenomenon called Landau damping. Our universe, however, may not be at on a large scale, so it is important to introduce and study a natural extension of the Vlasov-Poisson systems to spaces of constant curvature. Our starting point is the unit sphere S2, but we further restrict our study to one of its great circles. We show that, even for this reduced model, the potential function has more singularities than in the classical case. Our main result is to derive a Penrose stability criterion for the linear Landau damping phenomenon.en_US
dc.description.proquestcode0405en_US
dc.description.proquestemailshengyis@uvic.caen_US
dc.description.scholarlevelGraduateen_US
dc.identifier.urihttp://hdl.handle.net/1828/5768
dc.languageEnglisheng
dc.language.isoenen_US
dc.rights.tempAvailable to the World Wide Weben_US
dc.subjectVlasov's equationen_US
dc.subjectVlasov-Poissonen_US
dc.subjectLandau dampingen_US
dc.subjectPrinciple valueen_US
dc.titleVlasov's Equation on a Great Circle and the Landau Damping Phenomenonen_US
dc.typeThesisen_US

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