### 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 language | English (US) |
---|---|

Pages (from-to) | 119-171 |

Number of pages | 53 |

Journal | Journal of Nonlinear Science |

Volume | 14 |

Issue number | 2 |

DOIs | |

State | Published - Mar 2004 |

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### ASJC Scopus subject areas

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

### Cite this

*Journal of Nonlinear Science*,

*14*(2), 119-171. https://doi.org/10.1007/s00332-004-0568-2

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

Research output: Contribution to journal › Article

*Journal of Nonlinear Science*, vol. 14, no. 2, pp. 119-171. https://doi.org/10.1007/s00332-004-0568-2

}

TY - JOUR

T1 - Energy minimization and flux domain structure in the intermediate state of a type-I superconductor

AU - Choksi, R.

AU - Kohn, Robert

AU - Otto, F.

PY - 2004/3

Y1 - 2004/3

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84867955074&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84867955074&partnerID=8YFLogxK

U2 - 10.1007/s00332-004-0568-2

DO - 10.1007/s00332-004-0568-2

M3 - Article

AN - SCOPUS:84867955074

VL - 14

SP - 119

EP - 171

JO - Journal of Nonlinear Science

JF - Journal of Nonlinear Science

SN - 0938-8974

IS - 2

ER -