Browsing by Author "Steil, Trevor"

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    Vortex Motion in Ginzburg-Landau Equations with Background Potentials and Thermal Fluctuations
    (2020-10) Steil, Trevor
    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.