WorldCat Identities

Serfaty, Sylvia

Overview
Works: 7 works in 23 publications in 2 languages and 476 library holdings
Genres: Conference proceedings 
Classifications: QC611.92, 537.623
Publication Timeline
Key
Publications about  Sylvia Serfaty Publications about Sylvia Serfaty
Publications by  Sylvia Serfaty Publications by Sylvia Serfaty
Most widely held works by Sylvia Serfaty
Vortices in the magnetic Ginzburg-Landau model by Etienne Sandier ( )
14 editions published in 2007 in English and held by 464 WorldCat member libraries worldwide
With the discovery of type-II superconductivity by Abrikosov, the prediction of vortex lattices, and their experimental observation, quantized vortices have become a central object of study in superconductivity, superfluidity, and Bose--Einstein condensation. This book presents the mathematics of superconducting vortices in the framework of the acclaimed two-dimensional Ginzburg-Landau model, with or without magnetic field, and in the limit of a large Ginzburg-Landau parameter, kappa. This text presents complete and mathematically rigorous versions of both results either already known by physicists or applied mathematicians, or entirely new. It begins by introducing mathematical tools such as the vortex balls construction and Jacobian estimates. Among the applications presented are: the determination of the vortex densities and vortex locations for energy minimizers in a wide range of regimes of applied fields, the precise expansion of the so-called first critical field in a bounded domain, the existence of branches of solutions with given numbers of vortices, and the derivation of a criticality condition for vortex densities of non-minimizing solutions. Thus, this book retraces in an almost entirely self-contained way many results that are scattered in series of articles, while containing a number of previously unpublished results as well. The book also provides a list of open problems and a guide to the increasingly diverse mathematical literature on Ginzburg--Landau related topics. It will benefit both pure and applied mathematicians, physicists, and graduate students having either an introductory or an advanced knowledge of the subject
200 ans après Lagrange : journée annuelle : [28 juin 2013] by Société mathématique de France ( Book )
2 editions published in 2013 in French and held by 5 WorldCat member libraries worldwide
ETUDE MATHEMATIQUE DE L'EQUATION DE GINZBURG-LANDAU DE LA SUPRACONDUCTIVITE by Sylvia Serfaty ( Book )
2 editions published in 1999 in French and held by 3 WorldCat member libraries worldwide
CETTE THESE EST CONSACREE A L'ETUDE MATHEMATIQUE DE L'ENERGIE BIDIMENSIONNELLE DE GINZBURG-LANDAU DES SUPRACONDUCTEURS SOUMIS A UN CHAMP MAGNETIQUE EXTERIEUR H E X ; DANS LA LIMITE DE LONDON OU , LE PARAMETRE DE GINZBURG-LANDAU DU MATERIAU, EST GRAND. LE COMPORTEMENT DE CES SUPRACONDUCTEURS EST CARACTERISE PAR LA PRESENCE, POUR LES VALEURS DU CHAMP APPLIQUE COMPRISES ENTRE DEUX CHAMPS CRITIQUES H C 1 ET H C 2, DE TOURBILLONS DE VORTICITE (OU VORTEX), DANS LE MATERIAU. DANS UN PREMIER TEMPS, ON EFFECTUE UNE ETUDE DETAILLEE DE L'ENERGIE EN FONCTION DES VORTEX, A L'AIDE DE METHODES DUES A BETHUEL-BREZIS-HELEIN ET ALMEIDA-BETHUEL. ON OBTIENT AINSI L'EXISTENCE DU PREMIER CHAMP CRITIQUE H C 1 ET SON DEVELOPPEMENT ASYMPTOTIQUE EXPLICITE EN FONCTION DE . ON MONTRE QUE LES MINIMISEURS DE L'ENERGIE N'ONT PAS DE VORTEX POUR H E X < H C 1, ET EN ONT POUR H C 1 H E X H C 2. ON PROUVE EGALEMENT L'EXISTENCE ET L'UNICITE DE LA SOLUTION SANS VORTEX DE L'EQUATION D'EULER ASSOCIEE, AINSI QUE LA COEXISTENCE DE BRANCHES DE SOLUTIONS STABLES A N VORTEX, POUR N ENTIER ARBITRAIRE, ET H E X VARIANT DANS UN LARGE INTERVALLE AUTOUR DE H C 1. L'EXPRESSION DE L'ENERGIE DE CES SOLUTIONS EST DONNEE, ET LEURS VORTEX SONT DECRITS (NOMBRE, DEGRES, POSITIONS), RETROUVANT AINSI LES OBSERVATIONS PHYSIQUES. POUR H C 1 <<<> H E X <<<> H C 2, GRACE A DES TECHNIQUES DE DESCRIPTION DE VORTEX ET DE MINORATIONS D'ENERGIES DUES A ETIENNE SANDIER ; ON OBTIENT, DANS UN TRAVAIL EN COLLABORATION AVEC E. SANDIER, UNE EXPRESSION ASYMPTOTIQUE EXPLICITE ET, SEMBLE-T-IL, NOUVELLE, DE L'ENERGIE DES MINIMISEURS. DE PLUS, ON MONTRE QUE LA DENSITE DE LEURS VORTEX TEND A ETRE UNIFORME ET EGALE A H E X. UN MODELE DE SUPERFLUIDES EN ROTATION EST EGALEMENT ETUDIE, DES RESULTATS TRES SIMILAIRES SONT OBTENUS MALGRE UNE CONDITION DE BORD DIFFERENTE
La théorie de Gross-Pitaevskii pour un condensat de Bose-Einstein en rotation vortex et transitions de phase by Nicolas Rougerie ( Book )
1 edition published in 2010 in French and held by 1 WorldCat member library worldwide
Lorentz space estimates and applied boundary current dynamics for Ginzburg-Landau by Ian Tice ( Book )
1 edition published in 2008 in English and held by 1 WorldCat member library worldwide
The second component extends the ideas and techniques of the first to the case of the Ginzburg-Landau energy with external magnetic field hex in certain interesting regimes of hex . This allows us to show that for configurations close to minimizers or local minimizers of the energy, the vorticity mass of the configuration (u, A) is comparable to the L2,infinity Lorentz space norm of & dtri;Au, the covariant derivative. We also establish convergence of the gauge-invariant Jacobians (vorticity measures) in the dual of a function space defined in terms of Lorentz and Lorentz-Zygmund spaces
Analysis of several sharp-interface limits in variational problems by Nam Quang Le ( Book )
2 editions published in 2008 in English and held by 1 WorldCat member library worldwide
Our final result provides novel qualitative information on the vortices of a two-dimensional Ginzburg-Landau system that concentrate on a smooth closed curve
Energy driven pattern formation in a non-local Cahn-Hilliard energy by Dorian Goldman ( Book )
1 edition published in 2013 in English and held by 1 WorldCat member library worldwide
We study the asymptotic behavior of the Ohta-Kawasaki energy in dimension 2. In that model, two phases appear, and they interact via a nonlocal Coulomb type energy. We focus on the regime where one of the phases has very small volume fraction, thus creating "droplets" of that phase in a sea of the other phase. We compute the Gamma-limit of the leading order energy and yield averaged information for almost minimizers, namely that the density of droplets should be uniform and almost spherical. We then derive a next order Gamma-limit energy determines which the geoemtric arrangement of the droplets. Without appealing at all to the Euler-Lagrange equation, we establish here for all configurations which have "almost minimal energy," the asymptotic roundness and radius of the droplets, and the fact that they asymptotically shrink to points whose arrangement should minimize this energy, in some averaged sense. This leads to expecting to see hexagonal lattices of droplets. In addition, we prove that the density of droplets of non-minimizing critical points of the energy is also uniform and that droplets are spherical in some averaged sense. Next we study a non-local isoperimetric problem in $mathbb{R}2$ and $mathbb{T}2$. We are able to show that the connectedcritical points are determined by perimeter alone, under mild assumptions on the boundary, in the small energy/mass regime. These results differ from the recent results of Julin and Muratov-Knupfer in that they concern general critical points rather than global minimizers to the energy. Our method demonstrates that not only does the perimeter dominate the non-locality when minimizing, but also that the change in perimeter slaves to the change of the non-local term in this scaling regime
 
Audience Level
0
Audience Level
1
  Kids General Special  
Audience level: 0.79 (from 0.00 for ETUDE MATH ... to 1.00 for 200 ans ap ...)
Languages
English (18)
French (5)
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