Vortices in the Magnetic Ginzburg-Landau Model
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 su...
Shranjeno v:
| Auteurs principaux: | , |
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| Format: | Livre numérique |
| Jezik: | Anglais |
| Izdano: |
Boston, MA :
Birkhäuser Boston
[20..].
Cham : Springer Nature |
| Izdaja: | 1st ed. 2007. |
| Serija: | Progress in Nonlinear Differential Equations and Their Applications
70 |
| Teme: | |
| Online dostop: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Sporočilo: |
L'impression du document génère 326 p. Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Vortices in the magnetic Ginzburg-Landau model, Etienne Sandier, Sylvia Serfaty, 2007, Boston, Birkhäuser, 1 vol. (XII-322 p.), Progress in nonlinear differential equations and their applications, 978-0-8176-4316-4 • Vortices in the Magnetic Ginzburg-Landau Model, Texte imprimé, 9780817671518 • Vortices in the magnetic Ginzburg-Landau model, Etienne Sandier, Sylvia Serfaty, 2007, Boston, Birkhäuser, 1 vol. (XII-322 p.), Progress in nonlinear differential equations and their applications, 978-0-8176-4316-4 |
| Izvleček: | 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. |
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| Opis knjige/članka: | L'impression du document génère 326 p. Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Bibliografija: | Bibliogr. Index |
| ISBN: | 9780817645502 |
| ISSN: | 2374-0280 |
| Dostop: | Accès en ligne pour les établissements français bénéficiaires des licences nationales Accès soumis à abonnement pour tout autre établissement Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 |