Serfaty, SylviaOverview
Publication Timeline
Most widely held works by
Sylvia Serfaty
Vortices in the magnetic GinzburgLandau model
by Etienne Sandier
(
)
14 editions published in 2007 in English and held by 464 WorldCat member libraries worldwide With the discovery of typeII 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 BoseEinstein condensation. This book presents the mathematics of superconducting vortices in the framework of the acclaimed twodimensional GinzburgLandau model, with or without magnetic field, and in the limit of a large GinzburgLandau 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 socalled 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 nonminimizing solutions. Thus, this book retraces in an almost entirely selfcontained way many results that are scattered in series of articles, while containing a number of previously unpublished results as well.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 GinzburgLandau 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 GINZBURGLANDAU 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 GINZBURGLANDAU DES SUPRACONDUCTEURS SOUMIS A UN CHAMP MAGNETIQUE EXTERIEUR H E X ; DANS LA LIMITE DE LONDON OU , LE PARAMETRE DE GINZBURGLANDAU 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 BETHUELBREZISHELEIN ET ALMEIDABETHUEL. 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, SEMBLETIL, 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 GrossPitaevskii pour un condensat de BoseEinstein 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 GinzburgLandau
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 GinzburgLandau 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 gaugeinvariant Jacobians (vorticity measures) in the dual of a function space defined in terms of Lorentz and LorentzZygmund spaces
Analysis of several sharpinterface 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 twodimensional GinzburgLandau system that concentrate on a smooth closed curve
Energy driven pattern formation in a nonlocal CahnHilliard 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 OhtaKawasaki 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 Gammalimit 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 Gammalimit energy determines which the geoemtric arrangement of the droplets. Without appealing at all to the EulerLagrange 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 nonminimizing critical points of the energy is also uniform and that droplets are spherical in some averaged sense. Next we study a nonlocal 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 MuratovKnupfer 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 nonlocality when minimizing, but also that the change in perimeter slaves to the change of the nonlocal term in this scaling regime Audience Level
Related Identities

Languages
Covers
