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020 _a9780817645502
_99780817645502
024 7 _a10.1007/9780817645502
_2doi
035 _avtls000333549
039 9 _a201509030802
_bVLOAD
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040 _aMX-SnUAN
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_cMX-SnUAN
_erda
050 4 _aQA370-380
100 1 _aSandier, Etienne.
_eautor
_9306189
245 1 0 _aVortices in the Magnetic Ginzburg-Landau Model /
_cby Etienne Sandier, Sylvia Serfaty.
264 1 _aBoston, MA :
_bBirkhäuser Boston,
_c2007.
300 _axii, 322 páginas 13 ilustraciones
_brecurso en línea.
336 _atexto
_btxt
_2rdacontent
337 _acomputadora
_bc
_2rdamedia
338 _arecurso en línea
_bcr
_2rdacarrier
347 _aarchivo de texto
_bPDF
_2rda
490 0 _aProgress in Nonlinear Differential Equations and Their Applications ;
_v70
500 _aSpringer eBooks
505 0 _aPhysical 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 _aWith 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.
590 _aPara consulta fuera de la UANL se requiere clave de acceso remoto.
700 1 _aSerfaty, Sylvia.
_eautor
_9306190
710 2 _aSpringerLink (Servicio en línea)
_9299170
776 0 8 _iEdición impresa:
_z9780817643164
856 4 0 _uhttp://remoto.dgb.uanl.mx/login?url=http://dx.doi.org/10.1007/978-0-8176-4550-2
_zConectar a Springer E-Books (Para consulta externa se requiere previa autentificación en Biblioteca Digital UANL)
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999 _c280919
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