Wave Packets And Their Bifurcations In Geophysical Fluid Dynamics PDF Download
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| Author | : Huijun Yang |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 253 |
| Release | : 2013-06-29 |
| Genre | : Science |
| ISBN | : 1475743815 |
Download Wave Packets and Their Bifurcations in Geophysical Fluid Dynamics Book in PDF, ePub and Kindle
The material in this book is based predominantly on my recent work. It is the first monograph on the subject, though some support material may overlap other monographs. The investigation of wave packets and their bi furcations is very interesting, and useful theoretically and in practice, not only in geophysical fluid dynamics, which is the field to which the theory is being applied here, but also in other fields in mathematics and the natural sciences. I hope that the applied mathematician will find reading this book worthwhile, especially the material on the behavior of highly nonlinear dy namic systems. However, it is my belief that applying the concepts and methods developed here to other fields will be both interesting and con structive, since there are numerous phenomena in other areas of physics that share the characteristics of those in geophysical fluid dynamics. The theory developed here provides an effective tool to investigate the structure and the structural changes of dynamic systems in physics. Applications of the theory in geophysical fluid dynamics are an example of its usefulness and effectiveness. Some of the results presented here give us more insight into the nature of geophysical fluids. Moreover, the material is presented systematically and developmentally. Necessary basic knowledge is provided to make the book more readable for graduate students and researchers in such fields as applied mathematics, geophysical fluid dynamics, atmospheric sciences, and physical oceanogra phy.
| Author | : Carlo Marchioro |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 295 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461242843 |
Download Mathematical Theory of Incompressible Nonviscous Fluids Book in PDF, ePub and Kindle
Fluid dynamics is an ancient science incredibly alive today. Modern technol ogy and new needs require a deeper knowledge of the behavior of real fluids, and new discoveries or steps forward pose, quite often, challenging and diffi cult new mathematical {::oblems. In this framework, a special role is played by incompressible nonviscous (sometimes called perfect) flows. This is a mathematical model consisting essentially of an evolution equation (the Euler equation) for the velocity field of fluids. Such an equation, which is nothing other than the Newton laws plus some additional structural hypo theses, was discovered by Euler in 1755, and although it is more than two centuries old, many fundamental questions concerning its solutions are still open. In particular, it is not known whether the solutions, for reasonably general initial conditions, develop singularities in a finite time, and very little is known about the long-term behavior of smooth solutions. These and other basic problems are still open, and this is one of the reasons why the mathe matical theory of perfect flows is far from being completed. Incompressible flows have been attached, by many distinguished mathe maticians, with a large variety of mathematical techniques so that, today, this field constitutes a very rich and stimulating part of applied mathematics.
| Author | : Augusto Visintin |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 420 |
| Release | : 2013-06-29 |
| Genre | : Mathematics |
| ISBN | : 3662115573 |
Download Differential Models of Hysteresis Book in PDF, ePub and Kindle
Hysteresis effects occur in science and engineering: plasticity, ferromagnetism, ferroelectricity are well-known examples. This volume provides a self-contained and comprehensive introduction to the analysis of hysteresis models, and illustrates several new results in this field.
| Author | : Jack K. Hale |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 286 |
| Release | : 2006-04-18 |
| Genre | : Mathematics |
| ISBN | : 0387228969 |
Download Dynamics in Infinite Dimensions Book in PDF, ePub and Kindle
State-of-the-art in qualitative theory of functional differential equations; Most of the new material has never appeared in book form and some not even in papers; Second edition updated with new topics and results; Methods discussed will apply to other equations and applications
| Author | : George R. Sell |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 692 |
| Release | : 2002-01-02 |
| Genre | : Mathematics |
| ISBN | : 9780387983479 |
Download Dynamics of Evolutionary Equations Book in PDF, ePub and Kindle
The theory and applications of infinite dimensional dynamical systems have attracted the attention of scientists for quite some time. Dynamical issues arise in equations that attempt to model phenomena that change with time. The infi nite dimensional aspects occur when forces that describe the motion depend on spatial variables, or on the history of the motion. In the case of spatially depen dent problems, the model equations are generally partial differential equations, and problems that depend on the past give rise to differential-delay equations. Because the nonlinearities occurring in thse equations need not be small, one needs good dynamical theories to understand the longtime behavior of solutions. Our basic objective in writing this book is to prepare an entree for scholars who are beginning their journey into the world of dynamical systems, especially in infinite dimensional spaces. In order to accomplish this, we start with the key concepts of a semiflow and a flow. As is well known, the basic elements of dynamical systems, such as the theory of attractors and other invariant sets, have their origins here.
| Author | : Helena E. Nusse |
| Publisher | : Springer |
| Total Pages | : 502 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1468402315 |
Download Dynamics: Numerical Explorations Book in PDF, ePub and Kindle
Co-author J.A. Yorke developed an array of tools to help visualize the properties of dynamical systems, while Yorke found it useful to combine these various basic tools into one single package: Dynamics. The program together with this manual provides an introduction to and an overview of fundamental, sophisticated tools and numerical methods together with many simple examples. All numerical methods described in this handbook are implemented in the program, which is capable of, among others: iterating maps and solving differential equations; plotting trajectories; featuring an array of simple commands; printing a created picture in resolution higher than that of the screen. Requires a UNIX workstation running X11 graphics or a PC.
| Author | : Robert Vein |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 392 |
| Release | : 2006-05-07 |
| Genre | : Mathematics |
| ISBN | : 0387227741 |
Download Determinants and Their Applications in Mathematical Physics Book in PDF, ePub and Kindle
A unique and detailed account of all important relations in the analytic theory of determinants, from the classical work of Laplace, Cauchy and Jacobi to the latest 20th century developments. The first five chapters are purely mathematical in nature and make extensive use of the column vector notation and scaled cofactors. They contain a number of important relations involving derivatives which prove beyond a doubt that the theory of determinants has emerged from the confines of classical algebra into the brighter world of analysis. Chapter 6 is devoted to the verifications of the known determinantal solutions of several nonlinear equations which arise in three branches of mathematical physics, namely lattice, soliton and relativity theory. The solutions are verified by applying theorems established in earlier chapters, and the book ends with an extensive bibliography and index. Several contributions have never been published before. Indispensable for mathematicians, physicists and engineers wishing to become acquainted with this topic.
| Author | : David Colton |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 316 |
| Release | : 2013-04-17 |
| Genre | : Mathematics |
| ISBN | : 3662028352 |
Download Inverse Acoustic and Electromagnetic Scattering Theory Book in PDF, ePub and Kindle
It has now been almost ten years since our first book on scattering theory ap peared [32]. At that time we claimed that "in recent years the development of integral equation methods for the direct scattering problem seems to be nearing completion, whereas the use of such an approach to study the inverse scattering problem has progressed to an extent that a 'state of the art' survey appears highly desirable". Since we wrote these words, the inverse scattering problem for acoustic and electromagnetic waves has grown from being a few theoreti cal considerations with limited numerical implementations to a weH developed mathematical theory with tested numerical algorithms. This maturing of the field of inverse scattering theory has been based on the realization that such problems are in general not only nonlinear but also improperly posed in the sense that the solution does not depend continuously on the measured data. This was emphasized in [32] and treated with the ideas and tools available at that time. Now, almost ten years later, these initial ideas have developed to the extent that a monograph summarizing the mathematical basis of the field seems appropriate. This book is oUf attempt to write such a monograph. The inverse scattering problem for acoustic and electromagnetic waves can broadly be divided into two classes, the inverse obstacle problem and the inverse medium problem.
| Author | : A.J. Lichtenberg |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 708 |
| Release | : 2013-03-14 |
| Genre | : Mathematics |
| ISBN | : 1475721846 |
Download Regular and Chaotic Dynamics Book in PDF, ePub and Kindle
This book treats nonlinear dynamics in both Hamiltonian and dissipative systems. The emphasis is on the mechanics for generating chaotic motion, methods of calculating the transitions from regular to chaotic motion, and the dynamical and statistical properties of the dynamics when it is chaotic. The new edition brings the subject matter in a rapidly expanding field up to date, and has greatly expanded the treatment of dissipative dynamics to include most important subjects.
| Author | : Jan A. Sanders |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 447 |
| Release | : 2007-08-18 |
| Genre | : Mathematics |
| ISBN | : 0387489185 |
Download Averaging Methods in Nonlinear Dynamical Systems Book in PDF, ePub and Kindle
Perturbation theory and in particular normal form theory has shown strong growth in recent decades. This book is a drastic revision of the first edition of the averaging book. The updated chapters represent new insights in averaging, in particular its relation with dynamical systems and the theory of normal forms. Also new are survey appendices on invariant manifolds. One of the most striking features of the book is the collection of examples, which range from the very simple to some that are elaborate, realistic, and of considerable practical importance. Most of them are presented in careful detail and are illustrated with illuminating diagrams.
