The gravitational Vlasov-Poisson system on the unit 2-sphere with initial data along a great circle

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dc.contributor.authorLind, Crystal
dc.contributor.supervisorDiacu, Florin
dc.contributor.supervisorIbrahim, Slim
dc.date.accessioned2014-08-27T18:03:22Z
dc.date.available2014-08-27T18:03:22Z
dc.date.copyright2014en_US
dc.date.issued2014-08-27
dc.degree.departmentDepartment of Mathematics and Statistics
dc.degree.levelMaster of Science M.Sc.en_US
dc.description.abstractThe Vlasov-Poisson system is most commonly used to model the movement of charged particles in a plasma or of stars in a galaxy. It consists of a kinetic equation known as the Vlasov equation coupled with a force determined by the Poisson equation. The system in Euclidean space is well-known and has been extensively studied under various assumptions. In this paper, we derive the Vlasov-Poisson equations assuming the particles exist only on the 2-sphere, then take an in-depth look at particles which initially lie along a great circle of the sphere. We show that any great circle is an invariant set of the equations of motion and prove that the total energy, number of particles, and entropy of the system are conserved for circular initial distributions.en_US
dc.description.scholarlevelGraduateen_US
dc.identifier.urihttp://hdl.handle.net/1828/5613
dc.languageEnglisheng
dc.language.isoenen_US
dc.rights.tempAvailable to the World Wide Weben_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/2.5/ca/*
dc.subjectVlasoven_US
dc.subjectPoissonen_US
dc.subjectCurved spacesen_US
dc.subject2-sphereen_US
dc.subjectKinetic equationsen_US
dc.subjectCollisionless Boltzmann equationen_US
dc.subjectGauss's Lawen_US
dc.subjectConservation lawsen_US
dc.subjectNon-Euclideanen_US
dc.subjectPotentialen_US
dc.subjectGravitational Forceen_US
dc.subjectGravitational potentialen_US
dc.subjectGravityen_US
dc.subjectEquation of motionen_US
dc.titleThe gravitational Vlasov-Poisson system on the unit 2-sphere with initial data along a great circleen_US
dc.typeThesisen_US

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