Microscopic renormalized energy for a pinned Ginzburg-Landau functional. The circular and degree one caseReportar como inadecuado




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1 LAMA - Laboratoire d-Analyse et de Mathématiques Appliquées

Abstract : We study the vortex location for minimizers of a Ginzburg-Landau energy with a discontinuous constraint. The discontinuous constraint appears in the potential a2 − |u|22. The function a is piecewise constant: it takes the value 0 < b < 1 in small disjoint domains called inclusions and 1 otherwise. It is proved, under some assumptions on the smallness of the inclusions and on their interdistances, that the vortices of minimizers are trapped inside the inclusions. Moreover the asymptotic location of the vortices inside an inclusion depends only on three parameters: the value b, the geometry of the inclusion and the number of vortices inside the inclusion. It is expected that, if an inclusion containing a unique vortex is a disk, then the asymptotic location of the vortex is the center of the inclusion. This article is dedicated to the proof of this expectation.

keyword : Ginzburg-Landau type energy pinning renormalized energy





Autor: Mickaël Dos Santos -

Fuente: https://hal.archives-ouvertes.fr/



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