Ginzburg-Landau Vortices
Springer International Publishing (Verlag)
978-3-319-66672-3 (ISBN)
This book is concerned with the study in two dimensions of stationary solutions of u of a complex valued Ginzburg-Landau equation involving a small parameter . Such problems are related to questions occurring in physics, e.g., phase transition phenomena in superconductors and superfluids. The parameter has a dimension of a length which is usually small. Thus, it is of great interest to study the asymptotics as tends to zero.
One of the main results asserts that the limit u-star of minimizers u 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.
Introduction.- Energy Estimates for S1-Valued Maps.- A Lower Bound for the Energy of S1-Valued Maps on Perforated Domains.- Some Basic Estimates for u .- Toward Locating the Singularities: Bad Discs and Good Discs.- An Upper Bound for the Energy of u away from the Singularities.- u _n: u-star is Born! - u-star Coincides with THE Canonical Harmonic Map having Singularities (aj).- The Configuration (aj) Minimizes the Renormalization Energy W.- Some Additional Properties of u .- Non-Minimizing Solutions of the Ginzburg-Landau Equation.- Open Problems.
| Erscheinungsdatum | 21.09.2017 |
|---|---|
| Reihe/Serie | Modern Birkhäuser Classics |
| Zusatzinfo | XXIX, 159 p. 5 illus., 1 illus. in color. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Gewicht | 299 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Mathematik / Informatik ► Mathematik ► Angewandte Mathematik | |
| Naturwissenschaften ► Physik / Astronomie | |
| Schlagworte | Differential calculus & equations • Differential calculus & equations • Ginzburg-Landau Vortices • Mathematical Applications in the Physical Sciences • Mathematical Modelling • Mathematics • mathematics and statistics • nonlinear functional analysis • Partial differential equations • Phase Transition Phenomena • superconductors • Superfluids |
| ISBN-10 | 3-319-66672-X / 331966672X |
| ISBN-13 | 978-3-319-66672-3 / 9783319666723 |
| Zustand | Neuware |
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