A Γ-convergence result for 2D type-I superconductors

2025/04/28 by Cosenza, Alessandro, Goldman, Michael, Zilio, Alessandro
#35Q56 #49J10 #49J45 #82D55 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2504.19587

Abstract

We consider a 2D non-standard Modica-Mortola type functional. This functional arises from the Ginzburg-Landau theory of type-I superconductors in the case of an infinitely long sample and in the regime of comparable penetration and coherence lengthes. We prove that the functional Γ-converges to the perimeter functional. This result is a first step in understanding how to extend the results of Conti, Goldman, Otto, Serfaty (2018) to the regime of non vanishing Ginzburg-Landau parameter κ.

Citations

• New dimensional bounds for a branched transport problem
• From energy bounds to dimensional estimates in a branched transport model for type-I superconductors
• Two-well linearization for solid-solid phase transitions
• Two-well linearization for solid-solid phase transitions
• Two-well rigidity and multidimensional sharp-interface limits for solid-solid phase transitions
• Self-similar minimizers of a branched transport functional
• A branched transport limit of the Ginzburg-Landau functional
• Branched Microstructures in the Ginzburg-Landau Model of Type-I Superconductors
• Phase segregation for binary mixtures of Bose-Einstein Condensates
• Dynamic Formation of Metastable Intermediate State Patterns in Type-I Superconductors
• Equilibrium topology of the intermediate state in type-I superconductors of different shapes
• Topological Hysteresis in the Intermediate State of Type-I Superconductors

Related

• Gamma-convergence of 2D Ginzburg-Landau functionals with vortex concentration along curves
• A branched transport limit of the Ginzburg-Landau functional
• On the Ginzburg -Landau energy with a magnetic field vanishing along a curve
• From constant to non-degenerately vanishing magnetic fields in superconductivity
• Γ-Convergence of the Ginzburg-Landau Functional with tangential boundary conditions