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Ginzburg-Landau vortices

Author: Fabrice Bethuel; H Brézis; Frédéric Hélein
Publisher: Cham : Birkhäuser, [2017]
Series: Modern Birkhäuser classics.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Bethuel, Fabrice.
Ginzburg-Landau Vortices.
Cham : Springer International Publishing, ©2017
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Fabrice Bethuel; H Brézis; Frédéric Hélein
ISBN: 9783319666730 3319666738
OCLC Number: 1005011927
Notes: Reprint of the 1994 edition.
Description: 1 online resource
Contents: Introduction --
Energy estimates for S1-valued maps --
A lower bound for the energy of S1-valued maps on perforated domains --
Some basic estimates for ue --
Towards locating the singularities: bad discs and good discs --
An upper bound for the energy of ue away from the singularities --
ue converges: u* is born! --
u* coincides with THE canonical harmonic map having singularities (aj) --
The configuration (aj) minimized the renormalized energy W --
Some additional properties of ue --
Non minimizing solutions of the Ginzburg-Landau equation --
Open problems.
Series Title: Modern Birkhäuser classics.
Responsibility: Fabrice Bethuel, Haïm Brezis, Fréderic Hélein.

Abstract:

This book is concerned with the study in two dimensions of stationary solutions of ue of a complex valued Ginzburg-Landau equation involving a small parameter e. The number of these defects is  Read more...

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    schema:description "Introduction -- Energy estimates for S1-valued maps -- A lower bound for the energy of S1-valued maps on perforated domains -- Some basic estimates for ue -- Towards locating the singularities: bad discs and good discs -- An upper bound for the energy of ue away from the singularities -- ue converges: u* is born! -- u* coincides with THE canonical harmonic map having singularities (aj) -- The configuration (aj) minimized the renormalized energy W -- Some additional properties of ue -- Non minimizing solutions of the Ginzburg-Landau equation -- Open problems."@en ;
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