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Type of Document Dissertation Author Lin, Haomin URN etd-08212008-195759 Title An Optimal Control Problem for A Time-Dependent Ginzburg-Landau Model of Superconductivity Degree Doctor of Philosophy Department Mathematics, Department of Advisory Committee
Advisor Name Title Janet Peterson Committee Co-Chair Max Gunzburger Committee Co-Chair Xiaomin Wang Committee Member Catalin Trenchea Outside Committee Member Justin Schwartz Outside Committee Member Rudy Horne Outside Committee Member Keywords
- Normal Inclusion
- Superconductivity
- Ginzburg-Landau
- Optimal Control
- Critical Current
Date of Defense 2008-07-31 Availability unrestricted Abstract The motion of vortices in a Type II superconductor destroys the material's superconductivity because it dissipates energy and causes resistance. When a transport current is applied to a clean Type-II superconductor in the mixed state, the vortices will go into motion due to the induced Lorentz force and thus the superconductivity of the material is lost. However, various pinning mechanisms, such as normal inclusions, can inhibit vortex motion and pin the vortices to specific sites. We demonstrate that the placement of the normal inclusion sites has an important effect on the largest electrical current that can be applied to the superconducting material while all vortices remain stationary. Here, an optimal control problem using a time dependent Ginzburg-Landau model is proposed to seek numerically the optimal locations of the normal inclusion sites. An analysis of this optimal control problem is performed, the existence of an optimal control solution is proved and a sensitivity system is given. We then derive a gradient method to solve this optimal control problem. Numerical simulations are performed and the results are presented and discussed.Files
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