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Periodic minimizers of the anisotropic Ginzburg-Landau model

Abstract : We consider the anisotropic Ginzburg-Landau model in a three-dimensional periodic setting, in the London limit as the Ginzburg-Landau parameter kappa = 1/epsilon -> infinity. By means of matching upper and lower bounds on the energy of minimizers, we derive an expression for a limiting energy in the spirit of Gamma-convergence. We show that, to highest order as epsilon -> 0, the normalized induced magnetic field approaches a constant vector. We obtain a formula for the lower critical field H(c1) as a function of the orientation of the external field h(ex)(epsilon) with respect to the principal axes of the anisotropy, and determine the direction of the limiting induced field as a minimizer of a convex geometrical problem.
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Submitted on : Tuesday, May 1, 2012 - 7:42:37 PM
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Stan Alama, Lia Bronsard, Etienne Sandier. Periodic minimizers of the anisotropic Ginzburg-Landau model. Calculus of Variations and Partial Differential Equations, Springer Verlag, 2009, 36 (3), pp.399--417. ⟨10.1007/s00526-009-0234-5⟩. ⟨hal-00693039⟩



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