Sylvia Serfaty's Books

Vortices in the Magnetic Ginzburg-Landau Model

By: Etienne Sandier,Sylvia Serfaty

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Vortices in the Magnetic Ginzburg-Landau Model

By: Etienne Sandier,Sylvia Serfaty

This book presents the mathematical study of vortices of the two-dimensional Ginzburg-Landau model, an important phenomenological model used to describe superconductivity. The vortices, identified as quantized amounts of vorticity of the superconducting current localized near points, are the objects of many observational and experimental studies, both past and present. The Ginzburg-Landau functionals considered include both the model cases with and without a magnetic field. The book acts a guide to the various branches of Ginzburg-Landau studies, provides context for the study of vortices, and presents a list of open problems in the field.

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Page Count

327

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0817645500

ISBN 13

9780817645502

Vortices in the Magnetic Ginzburg-Landau Model

By: Etienne Sandier,Sylvia Serfaty

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Vortices in the Magnetic Ginzburg-Landau Model

By: Etienne Sandier,Sylvia Serfaty

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N/A

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Solve jigsaw puzzle

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Page Count

327

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0817645500

ISBN 13

9780817645502

Coulomb Gases and Ginzburg-Landau Vortices

By: Sylvia Serfaty

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Coulomb Gases and Ginzburg-Landau Vortices

By: Sylvia Serfaty

The topic of this book is systems of points in Coulomb interaction, in particular, the classical Coulomb gas, and vortices in the Ginzburg-Landau model of superconductivity. The classical Coulomb and Log gases are classical statistical mechanics models, which have seen important developments in the mathematical literature due to their connection with random matrices and approximation theory. At low temperature these systems are expected to ``crystallize'' to so-called Fekete sets, which exhibit microscopically a lattice structure. The Ginzburg-Landau model, on the other hand, describes superconductors. In superconducting materials subjected to an external magnetic field, densely packed point vortices emerge, forming perfect triangular lattice patterns, so-called Abrikosov lattices. This book describes these two systems and explores the similarity between them. It presents the mathematical tools developed to analyze the interaction between the Coulomb particles or the vortices, at the microscopic scale, and describes a ``renormalized energy'' governing the point patterns. This is believed to measure the disorder of a point configuration and to be minimized by the Abrikosov lattice in dimension 2. This book gives a self-contained presentation of results on the mean field limit of the Coulomb gas system, with or without temperature, and of the derivation of the renormalized energy. It also provides a streamlined presentation of the similar analysis that can be performed for the Ginzburg-Landau model, including a review of the vortex-specific tools and the derivation of the critical fields, the mean-field limit, and the renormalized energy.

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Page Count

170

Publisher

Erich Schmidt Verlag GmbH & Co. KG

Published Date

ISBN 10

303719152X

ISBN 13

9783037191521

Book's by Sylvia Serfaty

Vortices in the Magnetic Ginzburg-Landau Model

Vortices in the Magnetic Ginzburg-Landau Model

Vortices in the Magnetic Ginzburg-Landau Model

Vortices in the Magnetic Ginzburg-Landau Model

Coulomb Gases and Ginzburg-Landau Vortices

Coulomb Gases and Ginzburg-Landau Vortices

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