Buch, Englisch, Band 70, 322 Seiten, Format (B × H): 163 mm x 237 mm, Gewicht: 1430 g
Reihe: Progress in Nonlinear Differential Equations and Their Applications
Buch, Englisch, Band 70, 322 Seiten, Format (B × H): 163 mm x 237 mm, Gewicht: 1430 g
Reihe: Progress in Nonlinear Differential Equations and Their Applications
ISBN: 978-0-8176-4316-4
Verlag: Birkhauser Boston
This book presents the mathematical study of vortices of the two-dimensional Ginzburg-Landau model, an important phenomenological model used to describe superconductivity. The Ginzburg-Landau functionals considered include both the model cases with and without a magnetic field. The text introduces the reader to essential mathematical techniques and tools for analyzing the Ginzburg-Landau functional, such as the Ball-Method and the Jacobian estimate. These methods are used to determine vortex locations and densities, asymptotic expansions of energy in terms of the vortices, and rigorously derived values of the critical fields. The book concludes with a discussion of convergence and the results obtained through both minimizing and nonminimizing solutions. The book acts a guide to the various branches of Ginzburg-Landau studies, provides context for the study of vortices, and presents a list of open problems in the field. It provides an introduction to the Ginzburg-Landau model, and discusses current research and results.
Zielgruppe
Research
Autoren/Hrsg.
Fachgebiete
- Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik
- Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
- Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure
- Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
- Naturwissenschaften Biowissenschaften Angewandte Biologie Biomathematik
- Mathematik | Informatik Mathematik Mathematische Analysis Funktionentheorie, Komplexe Analysis
- Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
Weitere Infos & Material
Physical Presentation of the Model—Critical Fields.- First Properties of Solutions to the Ginzburg-Landau Equations.- The Vortex-Balls Construction.- Coupling the Ball Construction to the Pohozaev Identity and Applications.- Jacobian Estimate.- The Obstacle Problem.- Higher Values of the Applied Field.- The Intermediate Regime.- The Case of a Bounded Number of Vortices.- Branches of Solutions.- Back to Global Minimization.- Asymptotics for Solutions.- A Guide to the Literature.- Open Problems.
