The Ginzburg-Landau equation us a mathematical model of superconductors has become an extremely useful tool in many areas of physics where vortices carrying a topological charge appear. The remarkable progress in the mathematical understanding of this equation involves a combined use of mathematical tools from many branches of mathematics. The Ginzburg-Landau model has been an amazing source of new problems and new ideas in analysis, geometry and topology. This collection will meet the urgent needs of the specialists, scholars and graduate students working in this area or related areas.
This book reports recent mathematical developments in the Programme "Analysis, Modeling and Simulation of Multiscale Problems", which started as a German research initiative in 2006. Multiscale problems occur in many fields of science, such as microstructures in materials, sharp-interface models, many-particle systems and motions on different spatial and temporal scales in quantum mechanics or in molecular dynamics. The book presents current mathematical foundations of modeling, and proposes efficient numerical treatment.
This book presents the mathematical study of vortices of the two-dimensional Ginzburg-Landau model, an important phenomenological model used to describe superconductivity. The vortices, identified as quantized amounts of vorticity of the superconducting current localized near points, are the objects of many observational and experimental studies, both past and present. The Ginzburg-Landau functionals considered include both the model cases with and without a magnetic field. 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.
This is a comprehensive introduction to Landau-Lifshitz equations and Landau-Lifshitz-Maxwell equations, beginning with the work by Yulin Zhou and Boling Guo in the early 1980s and including most of the work done by this Chinese group led by Zhou and Guo since. The book focuses on aspects such as the existence of weak solutions in multi dimensions, existence and uniqueness of smooth solutions in one dimension, relations with harmonic map heat flows, partial regularity and long time behaviors. The book is a valuable reference book for those who are interested in partial differential equations, geometric analysis and mathematical physics. It may also be used as an advanced textbook by graduate students in these fields. Sample Chapter(s). Chapter 1: Spin Waves and Equations of Ferromagnetic Spin Chain (590 KB). Contents: Spin Waves and Equations of Ferromagnetic Spin Chain; Integrability of Heisenberg Chain; One-Dimensional Landau-Lifshitz Equations; LandauOCoLifshitz Equations and Harmonic Maps; LandauOCoLifshitzOCoMaxwell Equations; Long Time Behavior of Solutions to the System of Ferromagnetic Spin Chain. Readership: Mathematical physicists and researchers interested in Landau-Lifshitz equations."
This second edition has been brought up to date by the inclusion of an extensive new chapter on aspects relevant to high-temperature superconductors. The new edition provides researchers, engineers and other scientists with an introduction to the field and makes useful supplementary reading for graduate students in low-temperature physics.
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 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 idea for this book originated from an International Conference on Mag netic Structures in Superconductors organized by John R. Clem and the author at Argonne National Laboratory (ANL) in September of 1973. Large parts of the book evolved from lectures given to graduate students at the University of TUbingen during the past three years. It is the purpose of this book to provide an introduction to the many features of magnetic flux structures in superconductors and to discuss the this field. Here, in addition to the static proper recent developments in ties of magnetic flux structures, the time-dependent phenomena represent an important subject including flux flow and the transport effects in supercon ductors. Throughout the book the emphasis is placed on the physical phenom ena and the experimental results. We do not attempt a general introduction to superconductivity. Except for a brief discussion of the Ginzburg-Landau theory, with respect to the theoretical developments we only give an outline and refer to the original papers or other reviews for the detail of the calculations. The book is intended for researchers and graduate students interested in the subject of magnetic flux structures in superconductors. It may serve as supplementary material for a graduate course on low-temperature solid state physics. During recent years technological applications of supercon ducting materials are becoming increasingly important. Here the static and dynamic behavior of magnetic flux structures playa distinguished role. The book may be helpful for people envolved in these engineering aspects of superconductivity.
This five-volume handbook focuses on processing techniques, characterization methods, and physical properties of thin films (thin layers of insulating, conducting, or semiconductor material). The editor has composed five separate, thematic volumes on thin films of metals, semimetals, glasses, ceramics, alloys, organics, diamonds, graphites, porous materials, noncrystalline solids, supramolecules, polymers, copolymers, biopolymers, composites, blends, activated carbons, intermetallics, chalcogenides, dyes, pigments, nanostructured materials, biomaterials, inorganic/polymer composites, organoceramics, metallocenes, disordered systems, liquid crystals, quasicrystals, and layered structures.Thin films is a field of the utmost importance in today's materials science, electrical engineering and applied solid state physics; with both research and industrial applications in microelectronics, computer manufacturing, and physical devices.Advanced, high-performance computers, high-definition TV, digital camcorders, sensitive broadband imaging systems, flat-panel displays, robotic systems, and medical electronics and diagnostics are but a few examples of miniaturized device technologies that depend the utilization of thin film materials. The Handbook of Thin Films Materials is a comprehensive reference focusing on processing techniques, characterization methods, and physical properties of these thin film materials.
This five-volume handbook focuses on processing techniques, characterization methods, and physical properties of thin films (thin layers of insulating, conducting, or semiconductor material). The editor has composed five separate, thematic volumes on thin films of metals, semimetals, glasses, ceramics, alloys, organics, diamonds, graphites, porous materials, noncrystalline solids, supramolecules, polymers, copolymers, biopolymers, composites, blends, activated carbons, intermetallics, chalcogenides, dyes, pigments, nanostructured materials, biomaterials, inorganic/polymer composites, organoceramics, metallocenes, disordered systems, liquid crystals, quasicrystals, and layered structures. Thin films is a field of the utmost importance in today's materials science, electrical engineering and applied solid state physics; with both research and industrial applications in microelectronics, computer manufacturing, and physical devices. Advanced, high-performance computers, high-definition TV, digital camcorders, sensitive broadband imaging systems, flat-panel displays, robotic systems, and medical electronics and diagnostics are but a few examples of miniaturized device technologies that depend the utilization of thin film materials. The Handbook of Thin Films Materials is a comprehensive reference focusing on processing techniques, characterization methods, and physical properties of these thin film materials.
