Pinning phenomena in the Ginzburg-Landau model of superconductivity
From MaRDI portal
Publication:1606234
DOI10.1016/S0021-7824(00)01180-6zbMath1027.35123arXivcond-mat/0004177OpenAlexW2050357837MaRDI QIDQ1606234
Amandine Aftalion, Sylvia Serfaty, Etienne Sandier
Publication date: 24 July 2002
Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/cond-mat/0004177
energy estimatesapproximate solutionssuperconductorsvorticesGinzburg-Landau energyconvergence of measureshomogenized free-boundary problem
Variational methods applied to PDEs (35A15) Existence of solutions for minimax problems (49J35) Statistical mechanics of superconductors (82D55) NLS equations (nonlinear Schrödinger equations) (35Q55) Free boundary problems for PDEs (35R35) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27)
Related Items
Pinning with a variable magnetic field of the two dimensional Ginzburg-Landau model, Dynamic stability and instability of pinned fundamental vortices, ON THE HESSIAN OF THE ENERGY FORM IN THE GINZBURG–LANDAU MODEL OF SUPERCONDUCTIVITY, Inhomogeneous vortex patterns in rotating Bose-Einstein condensates, Pinning phenomena near the lower critical field for superconductor, On approximation of Ginzburg-Landau minimizers by \(\mathbb{S}^1\)-valued maps in domains with vanishingly small holes, The Ginzburg-Landau energy with a pinning term oscillating faster than the coherence length, Vortex pinning with bounded fields for the Ginzburg-Landau equation., Spot Dynamics in a Reaction-Diffusion Model of Plant Root Hair Initiation, Limiting vorticities for the Ginzburg-Landau equations., On a model of rotating superfluids, Radial solutions for the Ginzburg-Landau equation with applied magnetic field., Limiting vorticities for superconducting thin films, Energy estimate for the type-II superconducting film, Analytic and geometric properties of dislocation singularities, Mean-field dynamics for Ginzburg-Landau vortices with pinning and forcing, Lines of vortices for solutions of the Ginzburg-Landau equations, Magnetic Ginzburg-Landau functional with discontinuous constraint, Vorticity measure of type-II superconducting thin films, Magnetic vortices for a Ginzburg-Landau type energy with discontinuous constraint, A rigorous derivation of a free-boundary problem arising in superconductivity, Pinning of magnetic vortices by an external potential, Ginzburg-Landau vortex dynamics with pinning and strong applied currents, Vortex rings in fast rotating Bose-Einstein condensates, Multi-vortex solutions to Ginzburg-Landau equations with external potential, Explicit expression of the microscopic renormalized energy for a pinned Ginzburg-Landau functional, THE GINZBURG–LANDAU FUNCTIONAL WITH A DISCONTINUOUS AND RAPIDLY OSCILLATING PINNING TERM. PART I: THE ZERO DEGREE CASE, A product-estimate for Ginzburg-Landau and corollaries, Magnetic Ginzburg-Landau energy with a periodic rapidly oscillating and diluted pinning term, Existence of the weak solution of coupled time-dependent Ginzburg–Landau equations, Giant vortex and the breakdown of strong pinning in a rotating Bose-Einstein condensate, Remarks on an equation of the Ginzburg-Landau type, Pinning effects and their breakdown for a Ginzburg–Landau model with normal inclusions, Estimates of the energy of type-II superconductor
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- The embedding of the positive cone of $H^{-1}$ in $W^{-1,\,q}$ is compact for all $q<2$ (with a remark of Haim Brezis)
- Lower bounds for the energy of unit vector fields and applications
- Asymptotic behavior of minimizers for the Ginzburg-Landau functional with weight. I
- Vortices for a variational problem related to superconductivity
- Stable configurations in superconductivity: Uniqueness, multiplicity, and vortex-nucleation
- Global minimizers for the Ginzburg-Landau functional below the first critical magnetic field
- A rigorous derivation of a free-boundary problem arising in superconductivity
- A Ginzburg–Landau problem with weight having minima on the boundary
- LOCAL MINIMIZERS FOR THE GINZBURG–LANDAU ENERGY NEAR CRITICAL MAGNETIC FIELD: PART II
- ON THE ENERGY OF TYPE-II SUPERCONDUCTORS IN THE MIXED PHASE
- A Ginzburg–Landau type model of superconducting/normal junctions including Josephson junctions
- A mean-field model of superconducting vortices
- LOCAL MINIMIZERS FOR THE GINZBURG–LANDAU ENERGY NEAR CRITICAL MAGNETIC FIELD: PART I
- Ginzburg-Landau vortices
