Vortices in Bose Einstein Condensates

Author: Amandine Aftalion
Publisher: Springer Science & Business Media
ISBN: 9780817644925
Release Date: 2007-10-14
Genre: Mathematics

This book provides an up-to-date approach to the diagnosis and management of endocarditis based on a critical analysis of the recent studies. It is the only up-to-date clinically oriented textbook available on this subject. The book is structured in a format that is easy to follow, clinically relevant and evidence based. The author has a special interest in the application of ultrasound in the study of cardiac structure and function.

Recent Trends in Partial Differential Equations

Author: Xavier Cabré
Publisher: American Mathematical Soc.
ISBN: 9780821838914
Release Date: 2006
Genre: Mathematics

"The research and expository articles for courses and talks given at the 'UIMP-RSME Lluis A. Santaló Summer School' with title 'Recent Trends in Partial Differential Equations'."--Pref.

The Defocusing Nonlinear Schr dinger Equation

Author: Panayotis G. Kevrekidis
Publisher: SIAM
ISBN: 9781611973945
Release Date: 2015-08-04
Genre: Mathematics

Bose?Einstein condensation is a phase transition in which a fraction of particles of a boson gas condenses into the same quantum state known as the Bose?Einstein condensate (BEC). The aim of this book is to present a wide array of findings in the realm of BECs and on the nonlinear SchrÓdinger-type models that arise therein.÷The Defocusing Nonlinear SchrÓdinger Equation÷is a broad study of nonlinear÷excitations in self-defocusing nonlinear media. It summarizes state-of-the-art knowledge on the defocusing nonlinear SchrÓdinger-type models in a single volume and contains a wealth of resources, including over 800 references to relevant articles and monographs and a meticulous index for ease of navigation.

Perspectives in Nonlinear Partial Differential Equations

Author: Henri Berestycki
Publisher: American Mathematical Soc.
ISBN: 9780821841907
Release Date: 2007
Genre: Mathematics

In celebration of Haim Brezis's 60th birthday, a conference was held at the Ecole Polytechnique in Paris, with a program testifying to Brezis's wide-ranging influence on nonlinear analysis and partial differential equations. The articles in this volume are primarily from that conference. They present a rare view of the state of the art of many aspects of nonlinear PDEs, as well as describe new directions that are being opened up in this field. The articles, written by mathematicians at the center of current developments, provide somewhat more personal views of the important developments and challenges.

Spectral Methods in Surface Superconductivity

Author: Søren Fournais
Publisher: Springer Science & Business Media
ISBN: 9780817647971
Release Date: 2010-05-19
Genre: Mathematics

This book examines in detail the nonlinear Ginzburg–Landau functional, the model most commonly used in the study of superconductivity. Specifically covered are cases in the presence of a strong magnetic field and with a sufficiently large Ginzburg–Landau parameter kappa. Spectral Methods in Surface Superconductivity is intended for students and researchers with a graduate-level understanding of functional analysis, spectral theory, and the analysis of partial differential equations. The book also includes an overview of all nonstandard material as well as important semi-classical techniques in spectral theory that are involved in the nonlinear study of superconductivity.

Vortices in the Magnetic Ginzburg Landau Model

Author: Etienne Sandier
Publisher: Springer Science & Business Media
ISBN: 0817645500
Release Date: 2008-05-14
Genre: Mathematics

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.

The Monge Amp re Equation

Author: Cristian E. Gutierrez
Publisher: Springer Science & Business Media
ISBN: 0817641777
Release Date: 2001-05-11
Genre: Mathematics

The Monge-Ampère equation has attracted considerable interest in recent years because of its important role in several areas of applied mathematics. Monge-Ampère type equations have applications in the areas of differential geometry, the calculus of variations, and several optimization problems, such as the Monge-Kantorovitch mass transfer problem. This book stresses the geometric aspects of this beautiful theory, using techniques from harmonic analysis – covering lemmas and set decompositions.

Ginzburg Landau Vortices

Author: Haim Br‚zis
Publisher: World Scientific
ISBN: 9789812562036
Release Date: 2005
Genre: Mathematics

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.

An Introduction to Nonlinear Functional Analysis and Elliptic Problems

Author: Antonio Ambrosetti
Publisher: Springer Science & Business Media
ISBN: 9780817681142
Release Date: 2011-07-19
Genre: Mathematics

This self-contained textbook provides the basic, abstract tools used in nonlinear analysis and their applications to semilinear elliptic boundary value problems and displays how various approaches can easily be applied to a range of model cases. Complete with a preliminary chapter, an appendix that includes further results on weak derivatives, and chapter-by-chapter exercises, this book is a practical text for an introductory course or seminar on nonlinear functional analysis.

A Superfluid Universe

Author: Kerson Huang
Publisher: World Scientific
ISBN: 9789813148482
Release Date: 2016-08-08
Genre: Science

This interesting book provides the physical and mathematical background for a theory describing the universe as a quantum superfluid, and how dark energy and dark matter arise. Presenting a novel theory spanning many different fields in physics, the key concepts in each field are introduced. The reader is only expected to know the rudiments of condensed matter physics, quantum field theory and general relativity to explore this fascinating new model of dark matter and dark energy as facets of a cosmic superfluid.

Elliptic and Parabolic Problems

Author: Catherine Bandle
Publisher: Springer Science & Business Media
ISBN: 9783764373849
Release Date: 2006-01-17
Genre: Mathematics

Haim Brezis has made significant contributions in the fields of partial differential equations and functional analysis, and this volume collects contributions by his former students and collaborators in honor of his 60th anniversary at a conference in Gaeta. It presents new developments in the theory of partial differential equations with emphasis on elliptic and parabolic problems.

A Primer on Quantum Fluids

Author: Carlo F. Barenghi
Publisher: Springer
ISBN: 9783319424767
Release Date: 2016-09-07
Genre: Science

The aim of this primer is to cover the essential theoretical information, quickly and concisely, in order to enable senior undergraduate and beginning graduate students to tackle projects in topical research areas of quantum fluids, for example, solitons, vortices and collective modes. The selection of the material, both regarding the content and level of presentation, draws on the authors analysis of the success of relevant research projects with newcomers to the field, as well as of the students feedback from many taught and self-study courses on the subject matter. Starting with a brief historical overview, this text covers particle statistics, weakly interacting condensates and their dynamics and finally superfluid helium and quantum turbulence. At the end of each chapter (apart from the first) there will be some exercises. Detailed solutions can be made available to instructors upon request to the authors.