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- W4367594811 abstract "We consider minimizers of a Ginzburg-Landau energy with a discontinuous and rapidly oscillating pinning term, subject to a Dirichlet boundary condition of degree $d > 0$. The pinning term models an unbounded number of small impurities in the domain. We prove that for strongly type II superconductor with impurities, minimizers have exactly d isolated zeros (vortices). These vortices are of degree 1 and pinned by the impurities. As in the standard case studied by Bethuel, Brezis and H'elein, the macroscopic location of vortices is governed by vortex/vortex and vortex/ boundary repelling effects. In some special cases we prove that their macroscopic location tends to minimize the renormalized energy of Bethuel-Brezis-H'elein. In addition, impurities affect the microscopic location of vortices. Our technics allows us to work with impurities having different size. In this situation we prove that vortices are pinned by the largest impurities." @default.
- W4367594811 created "2023-05-02" @default.
- W4367594811 creator A5075287256 @default.
- W4367594811 date "2011-04-21" @default.
- W4367594811 modified "2023-10-14" @default.
- W4367594811 title "The Ginzburg-Landau functional with a discontinuous and rapidly oscillating pinning term. Part II: the non-zero degree case" @default.
- W4367594811 doi "https://doi.org/10.48550/arxiv.1104.4255" @default.
- W4367594811 hasPublicationYear "2011" @default.
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