Vortex filament equation and its solutions and energies

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dc.contributor.advisorCalini, Annalisa
dc.contributor.committeeMemberCox, Ben
dc.contributor.committeeMemberIvey, Thomas
dc.contributor.committeeMemberLafortune, Stephane
dc.contributor.committeeMemberLeMesurier, Brenton
dc.creatorEpperson, Kelly Scott
dc.date.accessioned2016-10-18T16:14:13Z
dc.date.available2016-10-18T16:14:13Z
dc.date.issued2014-08-18
dc.description.abstractFirst, we will give the derivation of the Vortex Filament Equation (VFE) and discuss the concept of conserved quantities. Then we will discuss Fourier knots and their relationship to the VFE. We will also give some results pertaining to Fourier knots evolving under the VFE, and make some conjectures on future avenues of research. Finally, we will discuss knot energies, focusing on the Mobius or O’Hara energy and the Brylinski Beta function of a knot, again presenting results and offering conjectures. We will show the results of numerical experiments at appropriate times in the text.en_US
dc.description.sponsorshipCollege of Charleston. Graduate School; College of Charleston. Department of Mathematics.en_US
dc.identifier.urihttp://hdl.handle.net/123456789/3136
dc.language.isoen_USen_US
dc.subjectVortex -- motion; Mathematicsen_US
dc.titleVortex filament equation and its solutions and energiesen_US
dc.typeThesisen_US
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