Vortex Motion in Ginzburg-Landau Equations with Background Potentials and Thermal Fluctuations

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Vortex Motion in Ginzburg-Landau Equations with Background Potentials and Thermal Fluctuations

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2020-10

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In this work, we investigate several models of superconductivity and the motion of vortices within them. We introduce anonisothermal model that incorporates thermal fluctuations away from a critical temperature and prove global well-posedness of weak solutions in the physically relevant setting. We then prove a motion law for systems with time-dependent background potentials in terms of a simple system of ordinary differential equations. Finally, we numerically investigate the convergence of simulated vortices to these motion laws and use the motion law for time-dependent potentials to develop a heuristic for use in nonisothermal systems.

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University of Minnesota Ph.D. dissertation. October 2020. Major: Mathematics. Advisor: Daniel Spirn. 1 computer file (PDF); 131 pages.

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Steil, Trevor. (2020). Vortex Motion in Ginzburg-Landau Equations with Background Potentials and Thermal Fluctuations. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/218059.

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