Ginzburg-Landau Vortices
Title | Ginzburg-Landau Vortices PDF eBook |
Author | Fabrice Bethuel |
Publisher | Birkhäuser |
Pages | 188 |
Release | 2017-09-21 |
Genre | Mathematics |
ISBN | 3319666738 |
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.
Vortices in the Magnetic Ginzburg-Landau Model
Title | Vortices in the Magnetic Ginzburg-Landau Model PDF eBook |
Author | Etienne Sandier |
Publisher | Springer Science & Business Media |
Pages | 327 |
Release | 2008-05-14 |
Genre | Mathematics |
ISBN | 0817645500 |
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
Title | Linear and Nonlinear Aspects of Vortices PDF eBook |
Author | Frank Pacard |
Publisher | Springer Science & Business Media |
Pages | 358 |
Release | 2000-06-22 |
Genre | Mathematics |
ISBN | 9780817641337 |
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 Vortices
Title | Ginzburg-Landau Vortices PDF eBook |
Author | |
Publisher | |
Pages | 186 |
Release | 2004 |
Genre | Bifurcation theory |
ISBN | 9787040161410 |
Linear and Nonlinear Aspects of Vortices
Title | Linear and Nonlinear Aspects of Vortices PDF eBook |
Author | Frank Pacard |
Publisher | Springer Science & Business Media |
Pages | 342 |
Release | 2012-12-06 |
Genre | Mathematics |
ISBN | 146121386X |
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 Vortices for Thin Ferromagnetic Films
Title | Ginzburg-Landau Vortices for Thin Ferromagnetic Films PDF eBook |
Author | Roger Moser |
Publisher | |
Pages | 27 |
Release | 2003 |
Genre | |
ISBN |
Ginzburg–Landau Theory of Condensates
Title | Ginzburg–Landau Theory of Condensates PDF eBook |
Author | Baruch Rosenstein |
Publisher | Cambridge University Press |
Pages | 355 |
Release | 2021-11-18 |
Genre | Science |
ISBN | 1108836852 |
A primer on Ginzberg-Landau Theory considering common and topological excitations including their thermodynamics and dynamical phenomena.