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The Resource Ginzburg-Landau vortices, by Fabrice Bethuel, Haim Brezis, Frederic Helein, (electronic resource)

Ginzburg-Landau vortices, by Fabrice Bethuel, Haim Brezis, Frederic Helein, (electronic resource)

Label
Ginzburg-Landau vortices
Title
Ginzburg-Landau vortices
Statement of responsibility
by Fabrice Bethuel, Haim Brezis, Frederic Helein
Creator
Contributor
Author
Subject
Language
eng
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 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 singularities have infinite energy, but after removing the core energy we are lead to a concept of finite renormalized energy. The location of the singularities is completely determined by minimizing the renormalized energy among all possible configurations of defects. The limit u-star can also be viewed as a geometrical object. It is a minimizing harmonic map into S1 with prescribed boundary condition g. Topological obstructions imply that every map u into S1 with u = g on the boundary must have infinite energy. Even though u-star has infinite energy, one can think of u-star as having “less” infinite energy than any other map u with u = g on the boundary. 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. "...the book gives a very stimulating account of an interesting minimization problem. It can be a fruitful source of ideas for those who work through the material carefully." - Alexander Mielke, Zeitschrift für angewandte Mathematik und Physik 46(5).--
Member of
Assigning source
Provided by publisher
http://library.link/vocab/creatorName
Bethuel, Fabrice
Image bit depth
0
Literary form
non fiction
Nature of contents
dictionaries
http://library.link/vocab/relatedWorkOrContributorName
  • Brezis, Haim.
  • Helein, Frederic.
Series statement
  • Springer eBooks
  • Modern Birkhäuser Classics
http://library.link/vocab/subjectName
  • Mathematics
  • Mathematical physics
Label
Ginzburg-Landau vortices, by Fabrice Bethuel, Haim Brezis, Frederic Helein, (electronic resource)
Link
https://eui.idm.oclc.org/login?url=http://link.springer.com/openurl?genre=book&isbn=978-3-319-66672-3
Instantiates
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
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 uɛ -- Toward Locating the Singularities: Bad Discs and Good Discs -- An Upper Bound for the Energy of uɛ away from the Singularities -- uɛ_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 uɛ -- Non-Minimizing Solutions of the Ginzburg-Landau Equation -- Open Problems
Control code
978-3-319-66673-0
Dimensions
unknown
Extent
1 online resource (XXIX, 159 pages)
File format
multiple file formats
Form of item
  • online
  • electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9783319666730
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-3-319-66673-0
Other physical details
1 illustration
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)1029692913
Label
Ginzburg-Landau vortices, by Fabrice Bethuel, Haim Brezis, Frederic Helein, (electronic resource)
Link
https://eui.idm.oclc.org/login?url=http://link.springer.com/openurl?genre=book&isbn=978-3-319-66672-3
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
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 uɛ -- Toward Locating the Singularities: Bad Discs and Good Discs -- An Upper Bound for the Energy of uɛ away from the Singularities -- uɛ_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 uɛ -- Non-Minimizing Solutions of the Ginzburg-Landau Equation -- Open Problems
Control code
978-3-319-66673-0
Dimensions
unknown
Extent
1 online resource (XXIX, 159 pages)
File format
multiple file formats
Form of item
  • online
  • electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9783319666730
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-3-319-66673-0
Other physical details
1 illustration
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)1029692913

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