Wave Packets And Their Bifurcations In Geophysical Fluid Dynamics

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Wave Packets And Their Bifurcations In Geophysical Fluid Dynamics

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Author : Huijun Yang
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29

Wave Packets And Their Bifurcations In Geophysical Fluid Dynamics written by Huijun Yang and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Science categories.

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.

Introduction To Functional Differential Equations

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Author : Jack K. Hale
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-21

Introduction To Functional Differential Equations written by Jack K. Hale and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-21 with Mathematics categories.

The present book builds upon an earlier work of J. Hale, "Theory of Func tional Differential Equations" published in 1977. We have tried to maintain the spirit of that book and have retained approximately one-third of the material intact. One major change was a complete new presentation of lin ear systems (Chapters 6~9) for retarded and neutral functional differential equations. The theory of dissipative systems (Chapter 4) and global at tractors was completely revamped as well as the invariant manifold theory (Chapter 10) near equilibrium points and periodic orbits. A more complete theory of neutral equations is presented (see Chapters 1, 2, 3, 9, and 10). Chapter 12 is completely new and contains a guide to active topics of re search. In the sections on supplementary remarks, we have included many references to recent literature, but, of course, not nearly all, because the subject is so extensive. Jack K. Hale Sjoerd M. Verduyn Lunel Contents Preface............................................................ v Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . . . . . . . . . . . . . 1. Linear differential difference equations . . . . . . . . . . . . . . 11 . . . . . . 1.1 Differential and difference equations. . . . . . . . . . . . . . . . . . . . 11 . . . . . . . . 1.2 Retarded differential difference equations. . . . . . . . . . . . . . . . 13 . . . . . . . 1.3 Exponential estimates of x( ¢,f) . . . . . . . . . . . . . . . . . . . . . 15 . . . . . . . . . . 1.4 The characteristic equation . . . . . . . . . . . . . . . . . . . . . . . . 17 . . . . . . . . . . . . 1.5 The fundamental solution. . . . . . . . . . . . . . . . . . . . . . . . . . 18 . . . . . . . . . . . . 1.6 The variation-of-constantsformula............................. 23 1. 7 Neutral differential difference equations . . . . . . . . . . . . . . . . . 25 . . . . . . . 1.8 Supplementary remarks. . . . . . . . . . . . . . . . . . . . . . . . . . . 34 . . . . . . . . . . . . . 2. Functional differential equations: Basic theory . . . . . . . . 38 . . 2.1 Definition of a retarded equation. . . . . . . . . . . . . . . . . . . . . . 38 . . . . . . . . . 2.2 Existence, uniqueness, and continuous dependence . . . . . . . . . . 39 . . . 2.3 Continuation of solutions . . . . . . . . . . . . . . . . . . . . . . . . . . 44 . . . . . . . . . . . .

Nonlinear Problems Of Elasticity

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Author : Stuart Antman
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14

Nonlinear Problems Of Elasticity written by Stuart Antman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.

The scientists of the seventeenth and eighteenth centuries, led by Jas. Bernoulli and Euler, created a coherent theory of the mechanics of strings and rods undergoing planar deformations. They introduced the basic con cepts of strain, both extensional and flexural, of contact force with its com ponents of tension and shear force, and of contact couple. They extended Newton's Law of Motion for a mass point to a law valid for any deformable body. Euler formulated its independent and much subtler complement, the Angular Momentum Principle. (Euler also gave effective variational characterizations of the governing equations. ) These scientists breathed life into the theory by proposing, formulating, and solving the problems of the suspension bridge, the catenary, the velaria, the elastica, and the small transverse vibrations of an elastic string. (The level of difficulty of some of these problems is such that even today their descriptions are sel dom vouchsafed to undergraduates. The realization that such profound and beautiful results could be deduced by mathematical reasoning from fundamental physical principles furnished a significant contribution to the intellectual climate of the Age of Reason. ) At first, those who solved these problems did not distinguish between linear and nonlinear equations, and so were not intimidated by the latter. By the middle of the nineteenth century, Cauchy had constructed the basic framework of three-dimensional continuum mechanics on the founda tions built by his eighteenth-century predecessors.

Dynamics Numerical Explorations

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Author : Helena E. Nusse
language : en
Publisher: Springer
Release Date : 2012-12-06

Dynamics Numerical Explorations written by Helena E. Nusse and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

Plotting trajectories is a useful capability in exploring a dynamical system, but it is just the beginning. The Maryland Chaos Group developed an array of tools to help visualize the properties of dynamical systems induding automatic method for plotting all "basins and attractors " , and for automatically searching for all computing "straddle trajectories", periodic orbits of a specified period. In the investigations of the Maryland Chaos Group, I. A. Yorke found it useful to be able to combine these various basic tools with each other into so that each new study could benefit a single package that grew with time from the previous programming efforts. He has been writing this software and distributing versions for the last nine years. The resulting program Dynamics requires either a Unix workstation running XII graphics or an IBM PC compatible computer. Eric I. Kostelich has put in a great deal of effort to port the program to Unix workstations. Some basic tools in Dynamics, such as the computation of Lyapunov exponents and the use of Newton's method are standard. The method of computation of stable and unstable manifolds is superior to standard procedures. Dynamics is currently being used extensively in our research and it is being used in undergraduate courses. Dynamics: Numerical Explora#ons provides an introduction to and overview of fundamental tools and numerical methods together with many simple examples. All the numerical methods described in this book are implemented in Dynamics.

The Mathematical Theory Of Dilute Gases

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Author : Carlo Cercignani
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01

The Mathematical Theory Of Dilute Gases written by Carlo Cercignani and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Science categories.

The idea for this book was conceived by the authors some time in 1988, and a first outline of the manuscript was drawn up during a summer school on mathematical physics held in Ravello in September 1988, where all three of us were present as lecturers or organizers. The project was in some sense inherited from our friend Marvin Shinbrot, who had planned a book about recent progress for the Boltzmann equation, but, due to his untimely death in 1987, never got to do it. When we drew up the first outline, we could not anticipate how long the actual writing would stretch out. Our ambitions were high: We wanted to cover the modern mathematical theory of the Boltzmann equation, with rigorous proofs, in a complete and readable volume. As the years progressed, we withdrew to some degree from this first ambition- there was just too much material, too scattered, sometimes incomplete, sometimes not rigor ous enough. However, in the writing process itself, the need for the book became ever more apparent. The last twenty years have seen an amazing number of significant results in the field, many of them published in incom plete form, sometimes in obscure places, and sometimes without technical details. We made it our objective to collect these results, classify them, and present them as best we could. The choice of topics remains, of course, subjective.

Analysis And Simulation Of Chaotic Systems

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Author : Frank C. Hoppensteadt
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

Analysis And Simulation Of Chaotic Systems written by Frank C. Hoppensteadt and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.

Analysis and Simulation of Chaotic Systems is a text designed to be used at the graduate level in applied mathematics for students from mathematics, engineering, physics, chemistry and biology. The book can be used as a stand-alone text for a full year course or it can be heavily supplemented with material of more mathematical, more engineering or more scientific nature. Computations and computer simulations are used throughout this text to illustrate phenomena discussed and to supply readers with probes to use on new problems.

Infinite Dimensional Dynamical Systems In Mechanics And Physics

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Author : Roger Temam
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-11

Infinite Dimensional Dynamical Systems In Mechanics And Physics written by Roger Temam and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-11 with Mathematics categories.

In this book the author presents the dynamical systems in infinite dimension, especially those generated by dissipative partial differential equations. This book attempts a systematic study of infinite dimensional dynamical systems generated by dissipative evolution partial differential equations arising in mechanics and physics and in other areas of sciences and technology. This second edition has been updated and extended.

Chaos And Socio Spatial Dynamics

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Author : Dimitrios S. Dendrinos
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Chaos And Socio Spatial Dynamics written by Dimitrios S. Dendrinos and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

Presents a discrete in time-space universal map of relative dynamics that is used to unfold an extensive catalogue of dynamic events not previously discussed in mathematical or social science literature. With emphasis on the chaotic dynamics that may ensue, the book describes the evolution on the basis of temporal and locational advantages. It explains nonlinear discrete time dynamic maps primarily through numerical simulations. These very rich qualitative dynamics are linked to evolution processes in socio-spatial systems. Important features include: The analytical properties of the one-stock, two- and three-location map; the numerical results from the one- and two-stock, two- and three-location dynamics; and the demonstration of the map's potential applicability in the social sciences through simulating population dynamics of the U.S. Regions over a two-century period. In addition, this book includes new findings: the Hopf equivalent discrete time dynamics bifurcation; the Feigenbaum slope-sequences; the presence of strange local attractors and containers; switching of extreme states; the presence of different types of turbulence; local and global turbulence. Intended for researchers and advanced graduate students in applied mathematics and an interest in dynamics and chaos. Mathematical social scientists in many other fields will also find this book useful.

Imperfect Bifurcation In Structures And Materials

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Author : Kiyohiro Ikeda
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

Imperfect Bifurcation In Structures And Materials written by Kiyohiro Ikeda and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Science categories.

Many physical systems lose or gain stability and pattern through bifurca tion behavior. Extensive research of this behavior is carried out in many fields of science and engineering. The study of dynamic bifurcation be havior, for example, has made clear the mechanism of dynamic instability and chaos. The group-theoretic bifurcation theory is an established means to deal with the formation and selection of patterns in association with symmetry-breaking bifurcation. Since all physical systems are "imperfect," in that they inevitably involve some initial imperfections, the study of im perfect bifurcation (bifurcation of imperfect systems) has drawn a keen mathematical interest to yield a series of important results, such as the universal unfolding. In structural mechanics, bifurcation behavior has been studied to model the buckling and failure of structural systems. The sharp reduction of the strength of structural systems by initial imperfections is formulated as im perfection sensitivity laws. A series of statistical studies has been conducted to make clear the dependence of the strength of structures on the statis tical variation of initial imperfections. A difficulty in these studies arises from the presence of a large number of initial imperfections. At this state, most of these studies are carried out based on the Monte Carlo simulation for a number of initial imperfections, or, on an imperfection sensitivity law against a single initial imperfection.

Applied Functional Analysis

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Author : Eberhard Zeidler
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Applied Functional Analysis written by Eberhard Zeidler and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

A theory is the more impressive, the simpler are its premises, the more distinct are the things it connects, and the broader is its range of applicability. Albert Einstein There are two different ways of teaching mathematics, namely, (i) the systematic way, and (ii) the application-oriented way. More precisely, by (i), I mean a systematic presentation of the material governed by the desire for mathematical perfection and completeness of the results. In contrast to (i), approach (ii) starts out from the question "What are the most important applications?" and then tries to answer this question as quickly as possible. Here, one walks directly on the main road and does not wander into all the nice and interesting side roads. The present book is based on the second approach. It is addressed to undergraduate and beginning graduate students of mathematics, physics, and engineering who want to learn how functional analysis elegantly solves mathematical problems that are related to our real world and that have played an important role in the history of mathematics. The reader should sense that the theory is being developed, not simply for its own sake, but for the effective solution of concrete problems. viii Preface Our introduction to applied functional analysis is divided into two parts: Part I: Applications to Mathematical Physics (AMS Vol. 108); Part II: Main Principles and Their Applications (AMS Vol. 109). A detailed discussion of the contents can be found in the preface to AMS Vol. 108.