A branched transport limit of the Ginzburg-Landau functional

2017/04/10 by Conti, Sergio, Goldman, Michael, Otto, Felix +1
#Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1704.02764

Abstract

We study the Ginzburg-Landau model of type-I superconductors in the regime of small external magnetic fields. We show that, in an appropriate asymptotic regime, flux patterns are described by a simplified branched transportation functional. We derive the simplified functional from the full Ginzburg-Landau model rigorously via Γ-convergence. The detailed analysis of the limiting procedure and the study of the limiting functional lead to a precise understanding of the multiple scales contained in the model.

Related

• Branched Microstructures in the Ginzburg-Landau Model of Type-I Superconductors
• From energy bounds to dimensional estimates in a branched transport model for type-I superconductors
• On the Ginzburg -Landau energy with a magnetic field vanishing along a curve
• A Γ-convergence result for 2D type-I superconductors
• Pinning phenomena in the Ginzburg-Landau Model of Superconductivity