Ginzburg Landau Vortices
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Ginzburg Landau Vortices
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Author : Fabrice Bethuel
language : en
Publisher: Birkhäuser
Release Date : 2017-09-21
Ginzburg Landau Vortices written by Fabrice Bethuel and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-21 with Mathematics categories.
This book is concerned with the study in two dimensions of stationary solutions of uɛ of a complex valued Ginzburg-Landau equation involving a small parameter ɛ. Such problems are related to questions occurring in physics, e.g., phase transition phenomena in superconductors and superfluids. The parameter ɛ has a dimension of a length which is usually small. Thus, it is of great interest to study the asymptotics as ɛ tends to zero. One of the main results asserts that the limit u-star of minimizers uɛ exists. Moreover, u-star is smooth except at a finite number of points called defects or vortices in physics. The number of these defects is exactly the Brouwer degree – or winding number – of the boundary condition. Each singularity has degree one – or as physicists would say, vortices are quantized. The material presented in this book covers mostly original results by the authors. It assumes a moderate knowledge of nonlinear functional analysis, partial differential equations, and complex functions. This book is designed for researchers and graduate students alike, and can be used as a one-semester text. The present softcover reprint is designed to make this classic text available to a wider audience.
Ginzburg Landau Vortices
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Author :
language : en
Publisher:
Release Date : 2004
Ginzburg Landau Vortices written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Bifurcation theory categories.
Coulomb Gases And Ginzburg Landau Vortices
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Author : Sylvia Serfaty
language : en
Publisher: Erich Schmidt Verlag GmbH & Co. KG
Release Date : 2015
Coulomb Gases And Ginzburg Landau Vortices written by Sylvia Serfaty and has been published by Erich Schmidt Verlag GmbH & Co. KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with Continuum mechanics categories.
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.
Vortices In The Magnetic Ginzburg Landau Model
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Author : Etienne Sandier
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-05-14
Vortices In The Magnetic Ginzburg Landau Model written by Etienne Sandier and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-05-14 with Mathematics categories.
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.
Linear And Nonlinear Aspects Of Vortices
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Author : Frank Pacard
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Linear And Nonlinear Aspects Of Vortices written by Frank Pacard and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Aimed at mathematicians, physicists, engineers, and grad students, this monograph will be useful for the nonlinear analysis of problems arising in geometry or mathematical physics. The material presented covers recent and original results by the authors, and serves as an excellent classroom text or a valuable self-study resource.
Ginzburg Landau Theory Of Condensates
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Author : Baruch Rosenstein
language : en
Publisher: Cambridge University Press
Release Date : 2021-11-18
Ginzburg Landau Theory Of Condensates written by Baruch Rosenstein and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-18 with Science categories.
A primer on Ginzberg-Landau Theory considering common and topological excitations including their thermodynamics and dynamical phenomena.
Ginzburg Landau Theory Of Condensates
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Author : Baruch Rosenstein
language : en
Publisher: Cambridge University Press
Release Date : 2021-11-18
Ginzburg Landau Theory Of Condensates written by Baruch Rosenstein and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-18 with Science categories.
A primer on Ginzberg-Landau Theory considering common and topological excitations including their thermodynamics and dynamical phenomena.
Ginzburg Landau Phase Transition Theory And Superconductivity
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Author : K.-H. Hoffmann
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Ginzburg Landau Phase Transition Theory And Superconductivity written by K.-H. Hoffmann and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This monograph compiles, rearranges, and refines recent research results in the complex G-L theory with or without immediate applications to the theory of superconductivity. An authoritative reference for applied mathematicians, theoretical physicists and engineers interested in the quantitative description of superconductivity using Ginzburg-Landau theory.
Ginzburg Landau Phase Transition Theory And Superconductivity
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Author : Karl-Heinz Hoffmann
language : en
Publisher:
Release Date : 2001
Ginzburg Landau Phase Transition Theory And Superconductivity written by Karl-Heinz Hoffmann and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Differential equations, Nonlinear categories.
This monograph compiles, rearranges, and refines recent research results in the complex G-L theory with or without immediate applications to the theory of superconductivity. An authoritative reference for applied mathematicians, theoretical physicists and engineers interested in the quantitative description of superconductivity using Ginzburg-Landau theory.
The Vortex State
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Author : N. Bontemps
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
The Vortex State written by N. Bontemps and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
One of the most spectacular consequences of the description of the superfluid condensate in superfluid He or in superconductors as a single macroscopic quantum state is the quantization of circulation, resulting in quantized vortex lines. This book draws no distinction between superfluid He3 and He4 and superconductors. The reader will find the essential introductory chapters and the most recent theoretical and experimental progress in our understanding of the vortex state in both superconductors and superfluids, from lectures given by leading experts in the field, both experimentalists and theoreticians, who gathered in Cargèse for a NATO ASI. The peculiar features related to short coherence lengths, 2D geometry, high temperatures, disorder, and pinning are thoroughly discussed.