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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...
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , |
| Autor Corporativo: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Boston, MA :
Birkhäuser Boston : Imprint: Birkhäuser,
2007.
|
| Edición: | 1st ed. 2007. |
| Colección: | Progress in Nonlinear Differential Equations and Their Applications,
70 |
| Temas: | |
| Acceso en línea: | Texto Completo |
MARC
| LEADER | 00000nam a22000005i 4500 | ||
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| 001 | 978-0-8176-4550-2 | ||
| 003 | DE-He213 | ||
| 005 | 20220114105043.0 | ||
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| 008 | 100301s2007 xxu| s |||| 0|eng d | ||
| 020 | |a 9780817645502 |9 978-0-8176-4550-2 | ||
| 024 | 7 | |a 10.1007/978-0-8176-4550-2 |2 doi | |
| 050 | 4 | |a QA370-380 | |
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| 100 | 1 | |a Sandier, Etienne. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a Vortices in the Magnetic Ginzburg-Landau Model |h [electronic resource] / |c by Etienne Sandier, Sylvia Serfaty. |
| 250 | |a 1st ed. 2007. | ||
| 264 | 1 | |a Boston, MA : |b Birkhäuser Boston : |b Imprint: Birkhäuser, |c 2007. | |
| 300 | |a XII, 322 p. 13 illus. |b online resource. | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a text file |b PDF |2 rda | ||
| 490 | 1 | |a Progress in Nonlinear Differential Equations and Their Applications, |x 2374-0280 ; |v 70 | |
| 505 | 0 | |a Physical Presentation of the Model-Critical Fields -- First Properties of Solutions to the Ginzburg-Landau Equations -- The Vortex-Balls Construction -- Coupling the Ball Construction to the Pohozaev Identity and Applications -- Jacobian Estimate -- The Obstacle Problem -- Higher Values of the Applied Field -- The Intermediate Regime -- The Case of a Bounded Number of Vortices -- Branches of Solutions -- Back to Global Minimization -- Asymptotics for Solutions -- A Guide to the Literature -- Open Problems. | |
| 520 | |a 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. | ||
| 650 | 0 | |a Differential equations. | |
| 650 | 0 | |a Mathematical physics. | |
| 650 | 0 | |a Functions of complex variables. | |
| 650 | 1 | 4 | |a Differential Equations. |
| 650 | 2 | 4 | |a Theoretical, Mathematical and Computational Physics. |
| 650 | 2 | 4 | |a Functions of a Complex Variable. |
| 700 | 1 | |a Serfaty, Sylvia. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 710 | 2 | |a SpringerLink (Online service) | |
| 773 | 0 | |t Springer Nature eBook | |
| 776 | 0 | 8 | |i Printed edition: |z 9780817671518 |
| 776 | 0 | 8 | |i Printed edition: |z 9780817643164 |
| 830 | 0 | |a Progress in Nonlinear Differential Equations and Their Applications, |x 2374-0280 ; |v 70 | |
| 856 | 4 | 0 | |u https://doi.uam.elogim.com/10.1007/978-0-8176-4550-2 |z Texto Completo |
| 912 | |a ZDB-2-SMA | ||
| 912 | |a ZDB-2-SXMS | ||
| 950 | |a Mathematics and Statistics (SpringerNature-11649) | ||
| 950 | |a Mathematics and Statistics (R0) (SpringerNature-43713) | ||