Energy minimization and flux domain structure in the intermediate state of a type-I superconductor

R. Choksi, Robert Kohn, F. Otto

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)119-171
Number of pages53
JournalJournal of Nonlinear Science
Volume14
Issue number2
DOIs
StatePublished - Mar 2004

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Energy Minimization
Scaling laws
Superconductor
Ground state
Superconducting materials
Magnetic fields
Fluxes
Nonconvex Variational Problems
Scale Mixture
Qualitative Properties
Explicit Methods
Scaling Laws
Local Minima
Small Parameter
Ground State
Two Parameters
Transverse
Magnetic Field
Lower bound
Upper bound

ASJC Scopus subject areas

  • Applied Mathematics
  • Modeling and Simulation
  • Engineering(all)

Cite this

Energy minimization and flux domain structure in the intermediate state of a type-I superconductor. / Choksi, R.; Kohn, Robert; Otto, F.

In: Journal of Nonlinear Science, Vol. 14, No. 2, 03.2004, p. 119-171.

Research output: Contribution to journalArticle

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