Download or read book Ginzburg Landau Vortices written by Fabrice Bethuel and published by Birkhäuser. This book was released on 2017-09-21 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Vortices in the Magnetic Ginzburg Landau Model written by Etienne Sandier and published by Springer Science & Business Media. This book was released on 2008-05-14 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Linear and Nonlinear Aspects of Vortices written by Frank Pacard and published by Springer Science & Business Media. This book was released on 2000-06-22 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aimed at mathematicians, physicists, engineers, and grad students, this monograph will be useful for the nonlinear analysis of problems arising in geometry or mathematical physics. The material presented covers recent and original results by the authors, and serves as an excellent classroom text or a valuable self-study resource.
Download or read book Ginzburg Landau Vortices written by and published by . This book was released on 2004 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Linear and Nonlinear Aspects of Vortices written by Frank Pacard and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aimed at mathematicians, physicists, engineers, and grad students, this monograph will be useful for the nonlinear analysis of problems arising in geometry or mathematical physics. The material presented covers recent and original results by the authors, and serves as an excellent classroom text or a valuable self-study resource.
Download or read book Ginzburg Landau Theory of Condensates written by Baruch Rosenstein and published by Cambridge University Press. This book was released on 2021-11-18 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: A primer on Ginzberg-Landau Theory considering common and topological excitations including their thermodynamics and dynamical phenomena.
Download or read book Ginzburg Landau Vortices for Thin Ferromagnetic Films written by Roger Moser and published by . This book was released on 2003 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Ginzburg Landau Phase Transition Theory and Superconductivity written by K.-H. Hoffmann and published by Nelson Thornes. This book was released on 2001 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph compiles, rearranges, and refines recent research results in the complex G-L theory with or without immediate applications to the theory of superconductivity. An authoritative reference for applied mathematicians, theoretical physicists and engineers interested in the quantitative description of superconductivity using Ginzburg-Landau theory.
Download or read book Coulomb Gases and Ginzburg Landau Vortices written by Sylvia Serfaty and published by Erich Schmidt Verlag GmbH & Co. KG. This book was released on 2015 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: The topic of this book is systems of points in Coulomb interaction, in particular, the classical Coulomb gas, and vortices in the Ginzburg-Landau model of superconductivity. The classical Coulomb and Log gases are classical statistical mechanics models, which have seen important developments in the mathematical literature due to their connection with random matrices and approximation theory. At low temperature these systems are expected to ``crystallize'' to so-called Fekete sets, which exhibit microscopically a lattice structure. The Ginzburg-Landau model, on the other hand, describes superconductors. In superconducting materials subjected to an external magnetic field, densely packed point vortices emerge, forming perfect triangular lattice patterns, so-called Abrikosov lattices. This book describes these two systems and explores the similarity between them. It presents the mathematical tools developed to analyze the interaction between the Coulomb particles or the vortices, at the microscopic scale, and describes a ``renormalized energy'' governing the point patterns. This is believed to measure the disorder of a point configuration and to be minimized by the Abrikosov lattice in dimension 2. This book gives a self-contained presentation of results on the mean field limit of the Coulomb gas system, with or without temperature, and of the derivation of the renormalized energy. It also provides a streamlined presentation of the similar analysis that can be performed for the Ginzburg-Landau model, including a review of the vortex-specific tools and the derivation of the critical fields, the mean-field limit, and the renormalized energy.
Download or read book Ginzburg Landau Vortices Driven by the Landau Lifshitz Gilbert Equation written by and published by . This book was released on 2009 with total page 39 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Introduction To Nonlinear Dynamics For Physicists written by Henry D I Abarbanel and published by World Scientific. This book was released on 1993-06-23 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: This series of lectures aims to address three main questions that anyone interested in the study of nonlinear dynamics should ask and ponder over. What is nonlinear dynamics and how does it differ from linear dynamics which permeates all familiar textbooks? Why should the physicist study nonlinear systems and leave the comfortable territory of linearity? How can one progress in the study of nonlinear systems both in the analysis of these systems and in learning about new systems from observing their experimental behavior? While it is impossible to answer these questions in the finest detail, this series of lectures nonetheless successfully points the way for the interested reader. Other useful problems have also been incorporated as a study guide. By presenting both substantial qualitative information about phenomena in nonlinear systems and at the same time sufficient quantitative material, the author hopes that readers would learn how to progress on their own in the study of such similar material hereon.
Download or read book Dynamics for Ginzburg Landau Vortices Under a Mixed Flow written by and published by . This book was released on 2008 with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Superconductivity written by R.D. Parks and published by Routledge. This book was released on 2018-03-29 with total page 780 pages. Available in PDF, EPUB and Kindle. Book excerpt: First published in 1969. CRC Press is an imprint of Taylor & Francis.
Download or read book Singular Ginzburg Landau Vortices written by Mats Aigner and published by . This book was released on 1998 with total page 75 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Dynamics of Ginzburg Landau Vortices written by Robert L. Jerrard and published by . This book was released on 1995 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book 30 Years of the Landau Institute written by Isaak Markovich Khalatnikov and published by World Scientific. This book was released on 1996 with total page 802 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Landau Institute for Theoretical Physics was created in 1965 by a group of LD Landau's pupils. Very soon, it was widely recognized as one of the world's leading centers in theoretical physics. According to Science Magazine, the Institute in the eighties had the highest citation index among all the scientific organizations in the former Soviet Union. This collection of the best papers of the Institute reflects the development of the many directions in the exact sciences during the last 30 years. The reader can find the original formulations of well-known notions in condensed matter theory, quantum field theory, mathematical physics and astrophysics, which were introduced by members of the Landau Institute.The following are some of the achievements described in this book: monopoles (A Polyakov), instantons (A Belavin et al.), weak crystallization (S Brazovskii), spin superfluidity (I Fomin), finite band potentials (S Novikov) and paraconductivity (A Larkin, L Aslamasov).
Download or read book Topics on Mathematics for Smart Systems written by Bernadette Miara and published by World Scientific. This book was released on 2007 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume gathers articles presented at a prominent European conference on smart systems and summarizes the activities carried out by a research and training network supported by the European community. The contributions aim to exhibit new research topics in the areas of materials science, advanced mathematical tools, and elements of control and numerical algorithms relevant to the design and optimization of smart systems.
