03922nam a22004815i 4500 978-0-8176-4550-2 DE-He213 20260521092027.0 cr nn 008mamaa 100301s2007 xxu| s |||| 0|eng d 9780817645502 99780817645502 10.1007/978-0-8176-4550-2 doi 515.353 23 Sandier, Etienne. author. Vortices in the Magnetic Ginzburg-Landau Model [electronic resource] / by Etienne Sandier, Sylvia Serfaty. Boston, MA : Birkhäuser Boston, 2007. XII, 322 p. 13 illus. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Progress in Nonlinear Differential Equations and Their Applications ; 70 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. 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self-contained way many results that are scattered in series of articles, while containing a number of previously unpublished results as well.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. MATHEMATICS. FUNCTIONS OF COMPLEX VARIABLES. DIFFERENTIAL EQUATIONS, PARTIAL. MATHEMATICAL PHYSICS. MATHEMATICS. PARTIAL DIFFERENTIAL EQUATIONS. MATHEMATICAL AND COMPUTATIONAL PHYSICS. FUNCTIONS OF A COMPLEX VARIABLE. Serfaty, Sylvia. author. SpringerLink (Online service) Springer eBooks Printed edition: 9780817643164 Progress in Nonlinear Differential Equations and Their Applications ; 70 http://dx.doi.org/10.1007/978-0-8176-4550-2 Ver el texto completo en las instalaciones del CICY ZDB-2-SMA ddc ER 35629 35629 0 0 ddc 0 0 LE CICY CICY EL 2025-10-06 0 515.353 2025-10-06 08:44:36 2025-10-06 ER