Ginzburg-Landau Vortices 2017 Edition Contributor(s): Bethuel, Fabrice (Author), Brezis, Haïm (Author), Hélein, Frédéric (Author) |
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ISBN: 331966672X ISBN-13: 9783319666723 Publisher: Birkhauser OUR PRICE: $75.99 Product Type: Paperback - Other Formats Published: October 2017 |
Additional Information |
BISAC Categories: - Mathematics | Differential Equations - General - Mathematics | Applied - Science | Physics - Mathematical & Computational |
Dewey: 515.353 |
Series: Modern Birkhäuser Classics |
Physical Information: 0.44" H x 6.54" W x 9.32" (0.74 lbs) 159 pages |
Descriptions, Reviews, Etc. |
Publisher 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. |