Current and vortices in the three-dimensional thin-film Ginzburg -Landau model of superconductivity
Abstract
We study the variable thickness Ginzburg-Landau equations describing type-II superconducting thin films. While the convergence of the order parameter is discussed in a paper by Chapman, Du, and Gunzburger, we turn our attention to the equation for the magnetic potential and obtain results on convergence of various quantities involved in the latter equation. The limiting two-dimensional problem, among other properties, has an advantage, from a computational point of view, of being restricted to a bounded domain. The regularity of the solutions to the three-dimensional problem presents another interest for us. It has been demonstrated earlier that the vortices in the two-dimensional problem are in fact isolated singularities located in the regions of the films with minimal thickness. Using regularity, we describe the geometry of the defects of the solutions (vortices) for the three-dimensional problem.
Degree
Ph.D.
Advisors
Bauman, Purdue University.
Subject Area
Mathematics
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