Journal ArticleDOI
Bifurcations with local gauge symmetries in the Ginzburg-Landau equations
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TLDR
In this paper, the formation of the Abrikosov vortex lattice in the Ginzburg-Landau model of Type-II superconductors is analyzed rigorously in the context of steady-state equivariant bifurcation theory by the proper implementation of a gauge fixing procedure.About:
This article is published in Physica D: Nonlinear Phenomena.The article was published on 1992-04-01. It has received 20 citations till now. The article focuses on the topics: Gauge symmetry & Supersymmetric gauge theory.read more
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Finite element methods for the time-dependent Ginzburg-Landau model of superconductivity
TL;DR: In this article, the initial-boundary value problem for the time-dependent Ginzburg-Landau equations that model the macroscopic behavior of superconductors is considered and the convergence of finite-dimensional, semidiscrete Galerkin approximations is studied as is a fully-discrete scheme.
Journal ArticleDOI
Lowest Landau level approach in superconductivity for the Abrikosov lattice close to H_{{c}_{2}}
Amandine Aftalion,Sylvia Serfaty +1 more
TL;DR: In this paper, the authors studied the Ginzburg-landau energy of a superconductor submitted to a magnetic field and showed that the mean energy per unit volume can be approximated by a reduced energy on a torus.
Journal ArticleDOI
Statics and dynamics of magnetic vortices and of Nielsen–Olesen (Nambu) strings
TL;DR: In this article, the authors review recent works on statics and dynamics of magnetic vortices in the Ginzburg-Landau model of superconductivity and of Nielsen-Olesen (Nambu) strings in the Abelian-Higgs model of particle physics.
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Magnetic Vortices, Abrikosov Lattices and Automorphic Functions
TL;DR: The Ginzburg-Landau theory of superconductivity as discussed by the authors is a macroscopic theory based on the Ginzberg - Landau equations, which has a profound influence on physics well beyond their original designation area.
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Abrikosov Lattice Solutions of the Ginzburg-Landau Equations
TL;DR: In this paper, the authors gave a proof of existence of Abrikosov vortex lattices in the Ginzburg-Landau model of superconductivity and showed that these lattices are the same lattices as the ones in this paper.
References
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Book
A Course of Modern Analysis
TL;DR: The volume now gives a somewhat exhaustive account of the various ramifications of the subject, which are set out in an attractive manner and should become indispensable, not only as a textbook for advanced students, but as a work of reference to those whose aim is to extend the knowledge of analysis.
Book
An introduction to variational inequalities and their applications
TL;DR: In this paper, the SIAM edition Preface Glossary of notations Introduction Part I. Variational Inequalities in Rn Part II. Free Boundary Problems Governed by Elliptic Equations and Systems Part VII. A One Phase Stefan Problem Bibliography Index.
BookDOI
Singularities and groups in bifurcation theory
TL;DR: Singularities and groups in bifurcation theory as mentioned in this paper have been used to solve the problem of finding a group of singularities in a set of problems with multiple solutions.