The Resource GinzburgLandau vortices, by Fabrice Bethuel, Haim Brezis, Frederic Helein, (electronic resource)
GinzburgLandau vortices, by Fabrice Bethuel, Haim Brezis, Frederic Helein, (electronic resource)
Resource Information
The item GinzburgLandau vortices, by Fabrice Bethuel, Haim Brezis, Frederic Helein, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.This item is available to borrow from 1 library branch.
Resource Information
The item GinzburgLandau vortices, by Fabrice Bethuel, Haim Brezis, Frederic Helein, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.
This item is available to borrow from 1 library branch.
 Summary
 This book is concerned with the study in two dimensions of stationary solutions of uɛ of a complex valued GinzburgLandau 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 ustar of minimizers uɛ exists. Moreover, ustar 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 ustar 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 ustar has infinite energy, one can think of ustar 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 onesemester 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).
 Language
 eng
 Extent
 1 online resource (XXIX, 159 pages)
 Contents

 Introduction
 Energy Estimates for S1Valued Maps
 A Lower Bound for the Energy of S1Valued 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: ustar is Born!  ustar Coincides with THE Canonical Harmonic Map having Singularities (aj)
 The Configuration (aj) Minimizes the Renormalization Energy W
 Some Additional Properties of uɛ
 NonMinimizing Solutions of the GinzburgLandau Equation
 Open Problems
 Isbn
 9783319666730
 Label
 GinzburgLandau vortices
 Title
 GinzburgLandau vortices
 Statement of responsibility
 by Fabrice Bethuel, Haim Brezis, Frederic Helein
 Language
 eng
 Summary
 This book is concerned with the study in two dimensions of stationary solutions of uɛ of a complex valued GinzburgLandau 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 ustar of minimizers uɛ exists. Moreover, ustar 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 ustar 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 ustar has infinite energy, one can think of ustar 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 onesemester 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).
 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
 GinzburgLandau vortices, by Fabrice Bethuel, Haim Brezis, Frederic Helein, (electronic resource)
 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 S1Valued Maps  A Lower Bound for the Energy of S1Valued 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: ustar is Born!  ustar Coincides with THE Canonical Harmonic Map having Singularities (aj)  The Configuration (aj) Minimizes the Renormalization Energy W  Some Additional Properties of uɛ  NonMinimizing Solutions of the GinzburgLandau Equation  Open Problems
 Control code
 9783319666730
 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, noncommercial 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
 10.1007/9783319666730
 Other physical details
 1 illustration
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (OCoLC)1029692913
 Label
 GinzburgLandau vortices, by Fabrice Bethuel, Haim Brezis, Frederic Helein, (electronic resource)
 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 S1Valued Maps  A Lower Bound for the Energy of S1Valued 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: ustar is Born!  ustar Coincides with THE Canonical Harmonic Map having Singularities (aj)  The Configuration (aj) Minimizes the Renormalization Energy W  Some Additional Properties of uɛ  NonMinimizing Solutions of the GinzburgLandau Equation  Open Problems
 Control code
 9783319666730
 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, noncommercial 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
 10.1007/9783319666730
 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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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.library.eui.eu/portal/GinzburgLandauvorticesbyFabriceBethuel/OI6BWSCx6y0/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.eui.eu/portal/GinzburgLandauvorticesbyFabriceBethuel/OI6BWSCx6y0/">GinzburgLandau vortices, by Fabrice Bethuel, Haim Brezis, Frederic Helein, (electronic resource)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.eui.eu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.eui.eu/">European University Institute</a></span></span></span></span></div>