The Mathematical Institute, University of Oxford, Eprints Archive

A hierarchy of models for superconducting thin films

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



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 $\delta$-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 $\Lambda = \lambda^2/d L$, where $\lambda$ 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
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:29 May 2015 18:19

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