Vortices in Nonlinear Fields PDF Download
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Author: Len M. Pismen
Publisher: Oxford University Press
ISBN: 9780198501671
Category : Mathematics
Languages : en
Pages : 308
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Book Description
Symmetry breaking is partially responsible for the astounding variety of natural phenomena derived from a few simple and symmetric basic laws. Unique in its multidisciplinary scope, this book considers from a unified point of view the structure and dynamics of vortices in a variety of nonlinear field models with spontaneously broken symmetry. The theory has wide applications, including superfluids, superconductors, rotating spiral waves, and relativistic string theories. This volume is an integrated survey of this rapidly developing field.
Author: Len M. Pismen
Publisher: Oxford University Press
ISBN: 9780198501671
Category : Mathematics
Languages : en
Pages : 308
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Book Description
Symmetry breaking is partially responsible for the astounding variety of natural phenomena derived from a few simple and symmetric basic laws. Unique in its multidisciplinary scope, this book considers from a unified point of view the structure and dynamics of vortices in a variety of nonlinear field models with spontaneously broken symmetry. The theory has wide applications, including superfluids, superconductors, rotating spiral waves, and relativistic string theories. This volume is an integrated survey of this rapidly developing field.
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: Frank Pacard
Publisher: Springer Science & Business Media
ISBN: 9780817641337
Category : Mathematics
Languages : en
Pages : 358
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Book Description
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.
Author: Vieri Benci
Publisher: Springer
ISBN: 3319069144
Category : Mathematics
Languages : en
Pages : 271
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Book Description
The book analyzes the existence of solitons, namely of finite energy solutions of field equations which exhibit stability properties. The book is divided in two parts. In the first part, the authors give an abstract definition of solitary wave and soliton and we develop an abstract existence theory for hylomorphic solitons, namely for those solitons which minimize the energy for a given charge. In the second part, the authors apply this theory to prove the existence of hylomorphic solitons for some classes of field equations (nonlinear Klein-Gordon-Maxwell equations, nonlinear Schrödinger-Maxwell equations, nonlinear beam equation,..). The abstract theory is sufficiently flexible to be applied to other situations, like the existence of vortices. The books is addressed to Mathematicians and Physicists.
Author: Gabriella Tarantello
Publisher: Springer Science & Business Media
ISBN: 0817646086
Category : Science
Languages : en
Pages : 335
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Book Description
This monograph discusses specific examples of selfdual gauge field structures, including the Chern–Simons model, the abelian–Higgs model, and Yang–Mills gauge field theory. The author builds a foundation for gauge theory and selfdual vortices by introducing the basic mathematical language of gauge theory and formulating examples of Chern–Simons–Higgs theories (in both abelian and non-abelian settings). Thereafter, the Electroweak theory and self-gravitating Electroweak strings are examined. The final chapters treat elliptic problems involving Chern–Simmons models, concentration-compactness principles, and Maxwell–Chern–Simons vortices.
Author: S. V. Alekseenko
Publisher: Springer Science & Business Media
ISBN: 3540733760
Category : Technology & Engineering
Languages : en
Pages : 505
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Book Description
This book presents comprehensive and authoritative coverage of the wide field of concentrated vortices observed in nature and technique. The methods for research of their kinematics and dynamics are considered. Special attention is paid to the flows with helical symmetry. The authors have described models of vortex structures used for interpretation of experimental data which serve as a ground for development of theoretical and numerical approaches to vortex investigation.
Author: Yisong Yang
Publisher: Springer Science & Business Media
ISBN: 1475765487
Category : Mathematics
Languages : en
Pages : 571
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Book Description
There are two approaches in the study of differential equations of field theory. The first, finding closed-form solutions, works only for a narrow category of problems. Written by a well-known active researcher, this book focuses on the second, which is to investigate solutions using tools from modern nonlinear analysis.
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: Panayotis G. Kevrekidis
Publisher: Springer Science & Business Media
ISBN: 3540735917
Category : Science
Languages : en
Pages : 398
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Book Description
This book, written by experts in the fields of atomic physics and nonlinear science, covers the important developments in a special aspect of Bose-Einstein condensation, namely nonlinear phenomena in condensates. Topics covered include bright, dark, gap and multidimensional solitons; vortices; vortex lattices; optical lattices; multicomponent condensates; mathematical methods/rigorous results; and the beyond-the-mean-field approach.
Author: Fatkhulla Abdullaev
Publisher: Springer Science & Business Media
ISBN: 9781402021886
Category : Science
Languages : en
Pages : 588
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Book Description
Leading scientists discuss the most recent physical and experimental results in the physics of Bose-Einstein condensate theory, the theory of nonlinear lattices (including quantum and nonlinear lattices), and nonlinear optics and photonics. Classical and quantum aspects of the dynamics of nonlinear waves are considered. The contributions focus on the Gross-Pitaevskii equation and on the quantum nonlinear Schrödinger equation. Recent experimental results on atomic condensates and hydrogen bonded systems are reviewed. Particular attention is given to nonlinear matter waves in periodic potential.
