Chapman, S. J. and Heron, D. R. (2003) *A hierarchy of models for superconducting thin films.* SIAM Journal of Applied Mathematics, 63 (6). pp. 2087-2127. ISSN 0036-1399

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## Abstract

A hierarchy of models for type-II superconducting thin films is presented. Through appropriate asymptotic limits this hierarchy passes from the mesoscopic Ginzburg--Landau model to the London model with isolated vortices as -function singularities to vortex-density models and finally to macroscopic critical-state models. At each stage it is found that a key nondimensional parameter is , where is the penetration depth of the magnetic field, a material parameter, and d and L are a typical thickness and lateral dimension of the film,respectively. The models simplify greatly if this parameter is large or small.

Item Type: | Article |
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Subjects: | O - Z > Partial differential equations O - Z > Optics, electromagnetic theory |

Research Groups: | Oxford Centre for Industrial and Applied Mathematics |

ID Code: | 298 |

Deposited By: | Jon Chapman |

Deposited On: | 04 Oct 2006 |

Last Modified: | 20 Jul 2009 14:20 |

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