An Introduction To The Theory Of Wave Maps And Related Geometric Problems

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Publisher : World Scientific Publishing Company
ISBN 13 : 9814713929
Total Pages : 496 pages
Book Rating : 4.8/5 (147 download)

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Book Synopsis An Introduction To The Theory Of Wave Maps And Related Geometric Problems by : Dan-andrei Geba

Download or read book An Introduction To The Theory Of Wave Maps And Related Geometric Problems written by Dan-andrei Geba and published by World Scientific Publishing Company. This book was released on 2016-08-18 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: The wave maps system is one of the most beautiful and challenging nonlinear hyperbolic systems, which has captured the attention of mathematicians for more than thirty years now. In the study of its various issues, such as the well-posedness theory, the formation of singularities, and the stability of the solitons, in order to obtain optimal results, one has to use intricate tools coming not only from analysis, but also from geometry and topology. Moreover, the wave maps system is nothing other than the Euler-Lagrange system for the nonlinear sigma model, which is one of the fundamental problems in classical field theory. One of the goals of our book is to give an up-to-date and almost self-contained overview of the main regularity results proved for wave maps. Another one is to introduce, to a wide mathematical audience, physically motivated generalizations of the wave maps system (e.g., the Skyrme model), which are extremely interesting and difficult in their own right.

Geometric Wave Equations

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Publisher : American Mathematical Soc.
ISBN 13 : 0821827499
Total Pages : 154 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Geometric Wave Equations by : Jalal M. Ihsan Shatah

Download or read book Geometric Wave Equations written by Jalal M. Ihsan Shatah and published by American Mathematical Soc.. This book was released on 2000 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains notes of the lectures given at the Courant Institute and a DMV-Seminar at Oberwolfach. The focus is on the recent work of the authors on semilinear wave equations with critical Sobolev exponents and on wave maps in two space dimensions. Background material and references have been added to make the notes self-contained. The book is suitable for use in a graduate-level course on the topic. Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University.

An Introduction to the Mathematical Theory of Waves

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Publisher : American Mathematical Soc.
ISBN 13 : 0821820397
Total Pages : 212 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis An Introduction to the Mathematical Theory of Waves by : Roger Knobel

Download or read book An Introduction to the Mathematical Theory of Waves written by Roger Knobel and published by American Mathematical Soc.. This book was released on 2000 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on an undergraduate course taught at the IAS/Park City Mathematics Institute (Utah) on linear and nonlinear waves. The first part of the text overviews the concept of a wave, describes one-dimensional waves using functions of two variables, provides an introduction to partial differential equations, and discusses computer-aided visualization techniques. The second part of the book discusses traveling waves, leading to a description of solitary waves and soliton solutions of the Klein-Gordon and Korteweg-deVries equations. The wave equation is derived to model the small vibrations of a taut string, and solutions are constructed via d'Alembert's formula and Fourier series.The last part of the book discusses waves arising from conservation laws. After deriving and discussing the scalar conservation law, its solution is described using the method of characteristics, leading to the formation of shock and rarefaction waves. Applications of these concepts are then given for models of traffic flow. The intent of this book is to create a text suitable for independent study by undergraduate students in mathematics, engineering, and science. The content of the book is meant to be self-contained, requiring no special reference material. Access to computer software such as MathematicaR, MATLABR, or MapleR is recommended, but not necessary. Scripts for MATLAB applications will be available via the Web. Exercises are given within the text to allow further practice with selected topics.

Nonlinear Partial Differential Equations in Geometry and Physics

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Publisher : Birkhäuser
ISBN 13 : 3034888953
Total Pages : 166 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Nonlinear Partial Differential Equations in Geometry and Physics by : Garth Baker

Download or read book Nonlinear Partial Differential Equations in Geometry and Physics written by Garth Baker and published by Birkhäuser. This book was released on 2012-12-06 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the proceedings of a series of lectures hosted by the Math ematics Department of The University of Tennessee, Knoxville, March 22-24, 1995, under the title "Nonlinear Partial Differential Equations in Geometry and Physics" . While the relevance of partial differential equations to problems in differen tial geometry has been recognized since the early days of the latter subject, the idea that differential equations of differential-geometric origin can be useful in the formulation of physical theories is a much more recent one. Perhaps the earliest emergence of systems of nonlinear partial differential equations having deep geo metric and physical importance were the Einstein equations of general relativity (1915). Several basic aspects of the initial value problem for the Einstein equa tions, such as existence, regularity and stability of solutions remain prime research areas today. eighty years after Einstein's work. An even more recent development is the realization that structures originally the context of models in theoretical physics may turn out to have introduced in important geometric or topological applications. Perhaps its emergence can be traced back to 1954, with the introduction of a non-abelian version of Maxwell's equations as a model in elementary-particle physics, by the physicists C.N. Yang and R. Mills. The rich geometric structure ofthe Yang-Mills equations was brought to the attention of mathematicians through work of M.F. Atiyah, :"J. Hitchin, I.

Developments of Harmonic Maps, Wave Maps and Yang-Mills Fields into Biharmonic Maps, Biwave Maps and Bi-Yang-Mills Fields

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Publisher : Springer Science & Business Media
ISBN 13 : 3034805349
Total Pages : 418 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Developments of Harmonic Maps, Wave Maps and Yang-Mills Fields into Biharmonic Maps, Biwave Maps and Bi-Yang-Mills Fields by : Yuan-Jen Chiang

Download or read book Developments of Harmonic Maps, Wave Maps and Yang-Mills Fields into Biharmonic Maps, Biwave Maps and Bi-Yang-Mills Fields written by Yuan-Jen Chiang and published by Springer Science & Business Media. This book was released on 2013-06-18 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: Harmonic maps between Riemannian manifolds were first established by James Eells and Joseph H. Sampson in 1964. Wave maps are harmonic maps on Minkowski spaces and have been studied since the 1990s. Yang-Mills fields, the critical points of Yang-Mills functionals of connections whose curvature tensors are harmonic, were explored by a few physicists in the 1950s, and biharmonic maps (generalizing harmonic maps) were introduced by Guoying Jiang in 1986. The book presents an overview of the important developments made in these fields since they first came up. Furthermore, it introduces biwave maps (generalizing wave maps) which were first studied by the author in 2009, and bi-Yang-Mills fields (generalizing Yang-Mills fields) first investigated by Toshiyuki Ichiyama, Jun-Ichi Inoguchi and Hajime Urakawa in 2008. Other topics discussed are exponential harmonic maps, exponential wave maps and exponential Yang-Mills fields.

Geometric Theory of Functions of a Complex Variable

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Publisher : American Mathematical Soc.
ISBN 13 : 9780821886557
Total Pages : 690 pages
Book Rating : 4.8/5 (865 download)

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Book Synopsis Geometric Theory of Functions of a Complex Variable by : Gennadiĭ Mikhaĭlovich Goluzin

Download or read book Geometric Theory of Functions of a Complex Variable written by Gennadiĭ Mikhaĭlovich Goluzin and published by American Mathematical Soc.. This book was released on 1969 with total page 690 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Mathematics Unlimited - 2001 and Beyond

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Publisher : Springer
ISBN 13 : 364256478X
Total Pages : 1219 pages
Book Rating : 4.6/5 (425 download)

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Book Synopsis Mathematics Unlimited - 2001 and Beyond by : Björn Engquist

Download or read book Mathematics Unlimited - 2001 and Beyond written by Björn Engquist and published by Springer. This book was released on 2017-04-05 with total page 1219 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a book guaranteed to delight the reader. It not only depicts the state of mathematics at the end of the century, but is also full of remarkable insights into its future de- velopment as we enter a new millennium. True to its title, the book extends beyond the spectrum of mathematics to in- clude contributions from other related sciences. You will enjoy reading the many stimulating contributions and gain insights into the astounding progress of mathematics and the perspectives for its future. One of the editors, Björn Eng- quist, is a world-renowned researcher in computational sci- ence and engineering. The second editor, Wilfried Schmid, is a distinguished mathematician at Harvard University. Likewi- se the authors are all foremost mathematicians and scien- tists, and their biographies and photographs appear at the end of the book. Unique in both form and content, this is a "must-read" for every mathematician and scientist and, in particular, for graduates still choosing their specialty. Limited collector's edition - an exclusive and timeless work. This special, numbered edition will be available until June 1, 2000. Firm orders only.

New Trends in Stochastic Analysis and Related Topics

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Publisher : World Scientific
ISBN 13 : 9814360910
Total Pages : 458 pages
Book Rating : 4.8/5 (143 download)

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Book Synopsis New Trends in Stochastic Analysis and Related Topics by : Huaizhong Zhao

Download or read book New Trends in Stochastic Analysis and Related Topics written by Huaizhong Zhao and published by World Scientific. This book was released on 2012 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: The volume is dedicated to Professor David Elworthy to celebrate his fundamental contribution and exceptional influence on stochastic analysis and related fields. Stochastic analysis has been profoundly developed as a vital fundamental research area in mathematics in recent decades. It has been discovered to have intrinsic connections with many other areas of mathematics such as partial differential equations, functional analysis, topology, differential geometry, dynamical systems, etc. Mathematicians developed many mathematical tools in stochastic analysis to understand and model random phenomena in physics, biology, finance, fluid, environment science, etc. This volume contains 12 comprehensive review/new articles written by world leading researchers (by invitation) and their collaborators. It covers stochastic analysis on manifolds, rough paths, Dirichlet forms, stochastic partial differential equations, stochastic dynamical systems, infinite dimensional analysis, stochastic flows, quantum stochastic analysis and stochastic Hamilton Jacobi theory. Articles contain cutting edge research methodology, results and ideas in relevant fields. They are of interest to research mathematicians and postgraduate students in stochastic analysis, probability, partial differential equations, dynamical systems, mathematical physics, as well as to physicists, financial mathematicians, engineers, etc.

The Mathematical Theory of Permanent Progressive Water-waves

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Publisher : World Scientific
ISBN 13 : 9789810244507
Total Pages : 248 pages
Book Rating : 4.2/5 (445 download)

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Book Synopsis The Mathematical Theory of Permanent Progressive Water-waves by : Hisashi Okamoto

Download or read book The Mathematical Theory of Permanent Progressive Water-waves written by Hisashi Okamoto and published by World Scientific. This book was released on 2001 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a self-contained introduction to the theory of periodic, progressive, permanent waves on the surface of incompressible inviscid fluid. The problem of permanent water-waves has attracted a large number of physicists and mathematicians since Stokes' pioneering papers appeared in 1847 and 1880. Among many aspects of the problem, the authors focus on periodic progressive waves, which mean waves traveling at a constant speed with no change of shape. As a consequence, everything about standing waves are excluded and solitary waves are studied only partly. However, even for this restricted problem, quite a number of papers and books, in physics and mathematics, have appeared and more will continue to appear, showing the richness of the subject. In fact, there remain many open questions to be answered.The present book consists of two parts: numerical experiments and normal form analysis of the bifurcation equations. Prerequisite for reading it is an elementary knowledge of the Euler equations for incompressible inviscid fluid and of bifurcation theory. Readers are also expected to know functional analysis at an elementary level. Numerical experiments are reported so that any reader can re-examine the results with minimal labor: the methods used in this book are well-known and are described as clearly as possible. Thus, the reader with an elementary knowledge of numerical computation will have little difficulty in the re-examination.

A Modern Introduction to the Mathematical Theory of Water Waves

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Publisher : Cambridge University Press
ISBN 13 : 9780521591720
Total Pages : 464 pages
Book Rating : 4.5/5 (917 download)

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Book Synopsis A Modern Introduction to the Mathematical Theory of Water Waves by : R. S. Johnson

Download or read book A Modern Introduction to the Mathematical Theory of Water Waves written by R. S. Johnson and published by Cambridge University Press. This book was released on 1997-10-28 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: For over a hundred years, the theory of water waves has been a source of intriguing and often difficult mathematical problems. Virtually every classical mathematical technique appears somewhere within its confines. Beginning with the introduction of the appropriate equations of fluid mechanics, the opening chapters of this text consider the classical problems in linear and nonlinear water-wave theory. This sets the stage for a study of more modern aspects, problems that give rise to soliton-type equations. The book closes with an introduction to the effects of viscosity. All the mathematical developments are presented in the most straightforward manner, with worked examples and simple cases carefully explained. Exercises, further reading, and historical notes on some of the important characters in the field round off the book and make this an ideal text for a beginning graduate course on water waves.

Geometric Phases In Physics

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Publisher : World Scientific
ISBN 13 : 981450758X
Total Pages : 527 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Geometric Phases In Physics by : Alfred Shapere

Download or read book Geometric Phases In Physics written by Alfred Shapere and published by World Scientific. This book was released on 1989-07-01 with total page 527 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the last few years, considerable interest has been focused on the phase that waves accumulate when the equations governing the waves vary slowly. The recent flurry of activity was set off by a paper by Michael Berry, where it was found that the adiabatic evolution of energy eigenfunctions in quantum mechanics contains a phase of geometric origin (now known as ‘Berry's phase’) in addition to the usual dynamical phase derived from Schrödinger's equation. This observation, though basically elementary, seems to be quite profound. Phases with similar mathematical origins have been identified and found to be important in a startling variety of physical contexts, ranging from nuclear magnetic resonance and low-Reynolds number hydrodynamics to quantum field theory. This volume is a collection of original papers and reprints, with commentary, on the subject.

Mathematical Reviews

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Publisher :
ISBN 13 :
Total Pages : 884 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Mathematical Reviews by :

Download or read book Mathematical Reviews written by and published by . This book was released on 2007 with total page 884 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Optimal Mass Transport on Euclidean Spaces

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Publisher : Cambridge University Press
ISBN 13 : 1009189263
Total Pages : 318 pages
Book Rating : 4.0/5 (91 download)

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Book Synopsis Optimal Mass Transport on Euclidean Spaces by : Francesco Maggi

Download or read book Optimal Mass Transport on Euclidean Spaces written by Francesco Maggi and published by Cambridge University Press. This book was released on 2023-10-31 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a graduate-level introduction to the key ideas and theoretical foundation of the vibrant field of optimal mass transport in the Euclidean setting. Taking a pedagogical approach, it introduces concepts gradually and in an accessible way, while also remaining technically and conceptually complete.

Introduction to Operator Theory

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Publisher : CRC Press
ISBN 13 : 9780582237438
Total Pages : 168 pages
Book Rating : 4.2/5 (374 download)

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Book Synopsis Introduction to Operator Theory by : Takashi Yoshino

Download or read book Introduction to Operator Theory written by Takashi Yoshino and published by CRC Press. This book was released on 1993-12-05 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introductory exposition of the study of operator theory, presenting an interesting and rapid approach to some results which are not normally treated in an introductory source. The volume includes recent results and coverage of the current state of the field.

Miscellaneous Publication - National Bureau of Standards

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Publisher :
ISBN 13 :
Total Pages : 1180 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Miscellaneous Publication - National Bureau of Standards by : United States. National Bureau of Standards

Download or read book Miscellaneous Publication - National Bureau of Standards written by United States. National Bureau of Standards and published by . This book was released on 1934 with total page 1180 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Publications of the National Bureau of Standards

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Publisher :
ISBN 13 :
Total Pages : 764 pages
Book Rating : 4.:/5 (4 download)

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Book Synopsis Publications of the National Bureau of Standards by : United States. National Bureau of Standards

Download or read book Publications of the National Bureau of Standards written by United States. National Bureau of Standards and published by . This book was released on 1960 with total page 764 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Supplementary List of Publications of the National Bureau of Standards

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Publisher :
ISBN 13 :
Total Pages : 776 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Supplementary List of Publications of the National Bureau of Standards by :

Download or read book Supplementary List of Publications of the National Bureau of Standards written by and published by . This book was released on 1960 with total page 776 pages. Available in PDF, EPUB and Kindle. Book excerpt: