Vortices in the Magnetic Ginzburg-Landau Model PDF Download

Author: Etienne Sandier
Publisher: Springer Science & Business Media
ISBN: 0817645500
Category : Mathematics
Languages : en
Pages : 327

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Book Description
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.

Author: Fabrice Bethuel
Publisher: Birkhäuser
ISBN: 3319666738
Category : Mathematics
Languages : en
Pages : 188

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Book Description
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.

Author: Baruch Rosenstein
Publisher: Cambridge University Press
ISBN: 1108836852
Category : Science
Languages : en
Pages : 355

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Book Description
A primer on Ginzberg-Landau Theory considering common and topological excitations including their thermodynamics and dynamical phenomena.

Author: Haim Br‚zis
Publisher: World Scientific
ISBN: 9812562036
Category : Mathematics
Languages : en
Pages : 196

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Book Description
The Ginzburg-Landau equation us a mathematical model of superconductors has become an extremely useful tool in many areas of physics where vortices carrying a topological charge appear. The remarkable progress in the mathematical understanding of this equation involves a combined use of mathematical tools from many branches of mathematics. The Ginzburg-Landau model has been an amazing source of new problems and new ideas in analysis, geometry and topology. This collection will meet the urgent needs of the specialists, scholars and graduate students working in this area or related areas.

Author: Denis L. Blackmore
Publisher: World Scientific
ISBN: 9812563202
Category : Science
Languages : en
Pages : 299

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Book Description
Honoring the contributions of one of the field's leading experts, Lu Ting, this indispensable volume contains important new results at the cutting edge of research. A wide variety of significant new analytical and numerical results in critical areas are presented, including point vortex dynamics, superconductor vortices, cavity flows, vortex breakdown, shock/vortex interaction, wake flows, magneto-hydrodynamics, rotary wake flows, and hypersonic vortex phenomena.The book will be invaluable for those interested in the state of the art of vortex dominated flows, both from a theoretical and applied perspective.Professor Lu Ting and Joe Keller have worked together for over 40 years. In their first joint work entitled ?Periodic vibrations of systems governed by nonlinear partial differential equations?, perturbation analysis and bifurcation theory were used to determine the frequencies and modes of vibration of various physical systems. The novelty was the application to partial differential equations of methods which, previously, had been used almost exclusively on ordinary differential equations. Professsor Lu Ting is an expert in both fluid dynamics and the use of matched asymptotic expansions. His physical insight into fluid flows has led the way to finding the appropriate mathematical simplications used in the solutions to many difficult flow problems.

Author: Charles P. Poole
Publisher: Elsevier
ISBN: 0080550487
Category : Science
Languages : en
Pages : 671

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Book Description
Superconductivity, 2E is an encyclopedic treatment of all aspects of the subject, from classic materials to fullerenes. Emphasis is on balanced coverage, with a comprehensive reference list and significant graphicsfrom all areas of the published literature. Widely used theoretical approaches are explained in detail. Topics of special interest include high temperature superconductors, spectroscopy, critical states, transport properties, and tunneling.This book covers the whole field of superconductivity from both the theoretical and the experimental point of view. - Comprehensive coverage of the field of superconductivity - Very up-to date on magnetic properties, fluxons, anisotropies, etc. - Over 2500 references to the literature - Long lists of data on the various types of superconductors

Author: K.-H. Hoffmann
Publisher: Nelson Thornes
ISBN: 9783764364861
Category : Gardening
Languages : en
Pages : 442

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Book Description
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.

Author: N. Bontemps
Publisher: Springer Science & Business Media
ISBN: 9401109745
Category : Science
Languages : en
Pages : 330

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Book Description
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.

Author: R.D. Parks
Publisher: Routledge
ISBN: 1351412876
Category : Technology & Engineering
Languages : en
Pages : 780

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Book Description
First published in 1969. CRC Press is an imprint of Taylor & Francis.

Author: Roderick Melnik
Publisher: John Wiley & Sons
ISBN: 1118853989
Category : Mathematics
Languages : en
Pages : 340

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Book Description
Mathematical and Computational Modeling Illustrates the application of mathematical and computational modeling in a variety of disciplines With an emphasis on the interdisciplinary nature of mathematical and computational modeling, Mathematical and Computational Modeling: With Applications in the Natural and Social Sciences, Engineering, and the Arts features chapters written by well-known, international experts in these fields and presents readers with a host of state-of-theart achievements in the development of mathematical modeling and computational experiment methodology. The book is a valuable guide to the methods, ideas, and tools of applied and computational mathematics as they apply to other disciplines such as the natural and social sciences, engineering, and technology. The book also features: Rigorous mathematical procedures and applications as the driving force behind mathematical innovation and discovery Numerous examples from a wide range of disciplines to emphasize the multidisciplinary application and universality of applied mathematics and mathematical modeling Original results on both fundamental theoretical and applied developments in diverse areas of human knowledge Discussions that promote interdisciplinary interactions between mathematicians, scientists, and engineers Mathematical and Computational Modeling: With Applications in the Natural and Social Sciences, Engineering, and the Arts is an ideal resource for professionals in various areas of mathematical and statistical sciences, modeling and simulation, physics, computer science, engineering, biology and chemistry, and industrial and computational engineering. The book also serves as an excellent textbook for graduate courses in mathematical modeling, applied mathematics, numerical methods, operations research, and optimization.