Ginzburg-Landau Phase Transition Theory and Superconductivity (International Series of Numerical Mathematics)
Edition: 1 edition
Publisher: Birkhauser
Published: January 25, 2001
Language: eng
Format: Hardcover
Number of pages: 383
ISBN-13: 9783764364861
Subjects: Electricity, magnetism & electromagnetism; Electronics & Communications Engineering; Numerical analysis; Vortex-motion; Science; Mathematics; Solid State Physics; Numerical Solutions Of Differential Equations; Statistical Physics; Phase transformations (Statistical physics); Science/Mathematics; Phase transformations (Statist; General; Ingenieurwissenschaften; Mathematics / General; Numerische Analysis; theoretische Physik; Differential equations, Nonlin; Differential Equations; Mathematical Physics; Superconductivity; Differential equations, Nonlinear; Numerical solutions
First sentence: Before starting formally our introduction, we define some mathematical symbols that will be used throughout this book.
Description: The theory of complex Ginzburg-Landau type phase transition and its applications to superconductivity and superfluidity has been a topic of great interest to theoretical physicists and has been continously and persistently studied since the 1950s. In this monograph, we collect, rearrange and refine recent research results in the complex G-L theory with or without immediate applications to the theory of superconductivity. The purpose is to present as many mathematically sound results as possible on various aspects of the PDE system, including rigorous mathematical analysis, formal asymptotics as well as numerical analysis. The book starts with some physical background material and discussions on the modelling and theoretical studies of physicists that invite further mathematical research. We then treat the mathematical scaling in a systematic way and analyze the implications on various limit problems. After addressing the mathematical foundation and formal asymptotic analysis of vortex motion we move on to rigorous results on existence, regularity and long-time behavior of solutions, as well as the vortex location and law of motion. Furthermore, we look at various ways of deriving lower-dimensional models from higher-dimensional ones and study rigorous results for the pinning of vortices. The book is meant to provide an authoritative reference for applied mathematicians, theoretical physicists and engineers interested in the quantitative description of superconductivity using Ginzburg-Landau theory.