Energy Minimization and Flux Domain Structure in the Intermediate State of a Type-I Superconductor |
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Authors: | R Choksi R V Kohn and F Otto |
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Institution: | (1) Department of Mathematics, Simon Fraser University, Burnaby, BC V5A 1S6, Canada;(2) Courant Institute, New York University, New York, NY 10012, USA;(3) Angewandte Mathematik, Universität Bonn, 53115 Bonn, Germany |
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Abstract: | The intermediate state of a type-I
superconductor involves a fine-scale mixture of normal
and superconducting domains. We take the viewpoint, due
to Landau, that the realizable domain patterns
are (local) minima of a nonconvex variational
problem. We examine the scaling law of the minimum
energy and the qualitative properties of domain patterns
achieving that law. Our analysis is restricted to the
simplest possible case: a superconducting plate
in a transverse magnetic field. Our methods
include explicit geometric constructions leading
to upper bounds and ansatz-free inequalities leading
to lower bounds. The problem is unexpectedly rich
when the applied field is near-zero or near-critical.
In these regimes there are two small parameters, and
the ground state patterns depend on the relation between
them. |
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Keywords: | |
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