Energy and Vorticity of the Ginzburg-Landau Model with Variable Magnetic\n Field

2014/11/20 by Kamel Attar, Attar, Kamel
Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Spectral Theory in Mathematical Physics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.1411.5479

openalex publication_date 2014/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the Ginzburg-Landau functional with a variable applied magnetic\nfield in a bounded and smooth two dimensional domain. The applied magnetic\nfield varies smoothly and is allowed to vanish non-degenerately along a curve.\nAssuming that the strength of the applied magnetic field varies between two\ncharacteristic scales, and the Ginzburg-Landau parameter tends to +\∞, we\ndetermine an accurate asymptotic formula for the minimizing energy and show\nthat the energy minimizers have vortices. The new aspect in the presence of a\nvariable magnetic field is that the density of vortices in the sample is not\nuniform.\n

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