Analysis of superconductivity models in magnetic fields
Abstract
We analyze minimizers of the Lawrence-Doniach energy for layered superconductors occupying a bounded generalized cylinder. For an applied magnetic field in the intermediate regime that is perpendicular to the layers, we prove an asymptotic formula for the minimum Lawrence-Doniach energy as the reciprocal of the Ginzburg-Landau parameter and the interlayer distance tend to zero. Under an appropriate assumption on these two parameters, we establish comparison results between the minimum Lawrence-Doniach energy and the minimum three-dimensional anisotropic Ginzburg-Landau energy. As a consequence, our asymptotic formula also describes the minimum three-dimensional anisotropic energy as the reciprocal of the Ginzburg-Landau parameter tends to zero.
Degree
Ph.D.
Advisors
Bauman, Purdue University.
Subject Area
Mathematics
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