Ginzburg-Landau Vortices (Progress in Nonlinear Differential Equations and Their Applications)
This text presents complete and mathematically rigorous versions of both results either already known by physicists or applied mathematicians, or entirely new. It begins by introducing mathematical tools such as the vortex balls construction and Jacobian estimates. Among the applications presented are: the determination of the vortex densities and vortex locations for energy minimizers in a wide range of regimes of applied fields, the precise expansion of the so-called first critical field in a bounded domain, the existence of branches of solutions with given numbers of vortices, and the derivation of a criticality condition for vortex densities of non-minimizing solutions.
Thus, this book retraces in an almost entirely self-contained way many results that are scattered in series of articles, while containing a number of previously unpublished results as well. The book also provides a list of open problems and a guide to the increasingly diverse mathematical literature on Ginzburg--Landau related topics.
It will benefit both pure and applied mathematicians, physicists, and graduate students having either an introductory or an advanced knowledge of the subject. This important model was introduced by Ginzburg and Landau in the s as a phenomenological model to describe superconductivity consisting in the complete loss of resistivity of certain metals and alloys at very low temperatures All parts of this interesting book are clearly and rigorously written.
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A consistent bibliography is given and several open problems are detailed. This work has to be recommended.
It also represents a tour de force of mathematical analysis, revealing a fascinating and intricate picture of a physical model which may have been unexpected based on heuristic considerations. I strongly recommend this book to researchers who are interested in vortices and other quantized singularities as these methods will continue to be instrumental in forthcoming research in the field. One could also find interesting material to supplement a graduate coursc in variational methods or PDEs. Help Centre. Track My Order.
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Ginzburg-Landau Vortices - Fabrice Bethuel, Haim Brezis, Frederic Helein - Google книги
Ships in 7 to 10 business days. Link Either by signing into your account or linking your membership details before your order is placed. Description Table of Contents Product Details Click on the cover image above to read some pages of this book! We convert the problem into the study of corresponding renormalized energy.
All books of the series Progress in Nonlinear Differential Equations and Their Applications
Then the result is obtained by analyzing the one dimensional model. The author is very grateful to his Ph.
The author would like to thank the referee for a helpful and thorough report, especially for suggestions to simplify the proof of Theorem 2. Article Metrics Views.
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