Multiphase Averaging For Classical Systems

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Multiphase Averaging for Classical Systems

P. Lochak,C. Meunier
Multiphase Averaging for Classical Systems Book PDF

Author : P. Lochak,C. Meunier
Publisher : Springer Science & Business Media
Page : 360 pages
File Size : 40,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461210443

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Multiphase Averaging for Classical Systems by P. Lochak,C. Meunier Pdf

In the past several decades many significant results in averaging for systems of ODE's have been obtained. These results have not attracted a tention in proportion to their importance, partly because they have been overshadowed by KAM theory, and partly because they remain widely scattered - and often untranslated - throughout the Russian literature. The present book seeks to remedy that situation by providing a summary, including proofs, of averaging and related techniques for single and multiphase systems of ODE's. The first part of the book surveys most of what is known in the general case and examines the role of ergodicity in averaging. Stronger stability results are then obtained for the special case of Hamiltonian systems, and the relation of these results to KAM Theory is discussed. Finally, in view of their close relation to averaging methods, both classical and quantum adiabatic theorems are considered at some length. With the inclusion of nine concise appendices, the book is very nearly self-contained, and should serve the needs of both physicists desiring an accessible summary of known results, and of mathematicians seeing an introduction to current areas of research in averaging.

The Method of Volume Averaging

S. Whitaker
The Method of Volume Averaging Book PDF

Author : S. Whitaker
Publisher : Springer Science & Business Media
Page : 236 pages
File Size : 44,8 Mb
Release : 2013-03-09
Category : Science
ISBN : 9789401733892

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The Method of Volume Averaging by S. Whitaker Pdf

Multiphase systems dominate nearly every area of science and technology, and the method of volume averaging provides a rigorous foundation for the analysis of these systems. The development is based on classical continuum physics, and it provides both the spatially smoothed equations and a method of predicting the effective transport coefficients that appear in those equations. The text is based on a ten-week graduate course that has been taught for more than 20 years at the University of California at Davis and at other universities around the world. Problems dealing with both the theoretical foundations and the applications are included with each chapter, and detailed solutions for all problems are available from the author. The course has attracted participants from chemical engineering, mechanical engineering, civil engineering, hydrologic science, mathematics, chemistry and physics.

Hamiltonian Dynamical Systems

H.S. Dumas,K.R. Meyer,D.S. Schmidt
Hamiltonian Dynamical Systems Book PDF

Author : H.S. Dumas,K.R. Meyer,D.S. Schmidt
Publisher : Springer Science & Business Media
Page : 392 pages
File Size : 53,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461384489

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Hamiltonian Dynamical Systems by H.S. Dumas,K.R. Meyer,D.S. Schmidt Pdf

From its origins nearly two centuries ago, Hamiltonian dynamics has grown to embrace the physics of nearly all systems that evolve without dissipation, as well as a number of branches of mathematics, some of which were literally created along the way. This volume contains the proceedings of the International Conference on Hamiltonian Dynamical Systems; its contents reflect the wide scope and increasing influence of Hamiltonian methods, with contributions from a whole spectrum of researchers in mathematics and physics from more than half a dozen countries, as well as several researchers in the history of science. With the inclusion of several historical articles, this volume is not only a slice of state-of-the-art methodology in Hamiltonian dynamics, but also a slice of the bigger picture in which that methodology is imbedded.

Hamiltonian Systems with Three or More Degrees of Freedom

Carles Simó
Hamiltonian Systems with Three or More Degrees of Freedom Book PDF

Author : Carles Simó
Publisher : Springer Science & Business Media
Page : 681 pages
File Size : 45,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401146739

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Hamiltonian Systems with Three or More Degrees of Freedom by Carles Simó Pdf

A survey of current knowledge about Hamiltonian systems with three or more degrees of freedom and related topics. The Hamiltonian systems appearing in most of the applications are non-integrable. Hence methods to prove non-integrability results are presented and the different meaning attributed to non-integrability are discussed. For systems near an integrable one, it can be shown that, under suitable conditions, some parts of the integrable structure, most of the invariant tori, survive. Many of the papers discuss near-integrable systems. From a topological point of view, some singularities must appear in different problems, either caustics, geodesics, moving wavefronts, etc. This is also related to singularities in the projections of invariant objects, and can be used as a signature of these objects. Hyperbolic dynamics appear as a source on unpredictable behaviour and several mechanisms of hyperbolicity are presented. The destruction of tori leads to Aubrey-Mather objects, and this is touched on for a related class of systems. Examples without periodic orbits are constructed, against a classical conjecture. Other topics concern higher dimensional systems, either finite (networks and localised vibrations on them) or infinite, like the quasiperiodic Schrödinger operator or nonlinear hyperbolic PDE displaying quasiperiodic solutions. Most of the applications presented concern celestial mechanics problems, like the asteroid problem, the design of spacecraft orbits, and methods to compute periodic solutions.

Perturbations

James A. Murdock
Perturbations Book PDF

Author : James A. Murdock
Publisher : SIAM
Page : 358 pages
File Size : 46,8 Mb
Release : 1999-01-01
Category : Mathematics
ISBN : 1611971098

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Perturbations by James A. Murdock Pdf

Perturbations: Theory and Methods gives a thorough introduction to both regular and singular perturbation methods for algebraic and differential equations. Unlike most introductory books on the subject, this one distinguishes between formal and rigorous asymptotic validity, which are commonly confused in books that treat perturbation theory as a bag of heuristic tricks with no foundation. The meaning of "uniformity" is carefully explained in a variety of contexts. All standard methods, such as rescaling, multiple scales, averaging, matching, and the WKB method are covered, and the asymptotic validity (in the rigorous sense) of each method is carefully proved. First published in 1991, this book is still useful today because it is an introduction. It combines perturbation results with those known through other methods. Sometimes a geometrical result (such as the existence of a periodic solution) is rigorously deduced from a perturbation result, and at other times a knowledge of the geometry of the solutions is used to aid in the selection of an effective perturbation method. Dr. Murdock's approach differs from other introductory texts because he attempts to present perturbation theory as a natural part of a larger whole, the mathematical theory of differential equations. He explores the meaning of the results and their connections to other ways of studying the same problems.

Random Perturbations of Dynamical Systems

Mark I. Freidlin,Alexander D. Wentzell
Random Perturbations of Dynamical Systems Book PDF

Author : Mark I. Freidlin,Alexander D. Wentzell
Publisher : Springer Science & Business Media
Page : 483 pages
File Size : 52,7 Mb
Release : 2012-05-31
Category : Mathematics
ISBN : 9783642258473

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Random Perturbations of Dynamical Systems by Mark I. Freidlin,Alexander D. Wentzell Pdf

Many notions and results presented in the previous editions of this volume have since become quite popular in applications, and many of them have been “rediscovered” in applied papers. In the present 3rd edition small changes were made to the chapters in which long-time behavior of the perturbed system is determined by large deviations. Most of these changes concern terminology. In particular, it is explained that the notion of sub-limiting distribution for a given initial point and a time scale is identical to the idea of metastability, that the stochastic resonance is a manifestation of metastability, and that the theory of this effect is a part of the large deviation theory. The reader will also find new comments on the notion of quasi-potential that the authors introduced more than forty years ago, and new references to recent papers in which the proofs of some conjectures included in previous editions have been obtained. Apart from the above mentioned changes the main innovations in the 3rd edition concern the averaging principle. A new Section on deterministic perturbations of one-degree-of-freedom systems was added in Chapter 8. It is shown there that pure deterministic perturbations of an oscillator may lead to a stochastic, in a certain sense, long-time behavior of the system, if the corresponding Hamiltonian has saddle points. The usefulness of a joint consideration of classical theory of deterministic perturbations together with stochastic perturbations is illustrated in this section. Also a new Chapter 9 has been inserted in which deterministic and stochastic perturbations of systems with many degrees of freedom are considered. Because of the resonances, stochastic regularization in this case is even more important.

The Earth-Moon System as a Dynamical Laboratory

Elisa Maria Alessi,Josep Masdemont,Alessandro Rossi
The Earth Moon System as a Dynamical Laboratory Book PDF

Author : Elisa Maria Alessi,Josep Masdemont,Alessandro Rossi
Publisher : Frontiers Media SA
Page : 156 pages
File Size : 52,6 Mb
Release : 2019-09-25
Category : Electronic
ISBN : 9782889630448

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The Earth-Moon System as a Dynamical Laboratory by Elisa Maria Alessi,Josep Masdemont,Alessandro Rossi Pdf

The Earth-Moon neighborhood is the scene of a large variety of applications that concern asteroids, lunar exploration and space debris in Earth orbit. In particular, recent efforts by the scientific community have focused on the possibility of extending the human operations beyond the radiation belts; of exploiting in-situ resources, either on the lunar surface or on asteroids retrieved to the vicinity of the Earth; and of mitigating the space debris concern by taking advantage of the lunar perturbation. The characteristic dynamics in the cislunar space represents an opportunity for the mission designer, but also a challenge in terms of theoretical understanding and operational control. This Research Topic covers the Earth-Moon dynamics in its complexity and allure, considering the most relevant aspects for both natural and artificial objects, in order to get a new comprehension of the dynamics at stake along with the operational procedures that can handle it.

Hamiltonian Partial Differential Equations and Applications

Philippe Guyenne,David Nicholls,Catherine Sulem
Hamiltonian Partial Differential Equations and Applications Book PDF

Author : Philippe Guyenne,David Nicholls,Catherine Sulem
Publisher : Springer
Page : 449 pages
File Size : 53,9 Mb
Release : 2015-09-11
Category : Mathematics
ISBN : 9781493929504

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Hamiltonian Partial Differential Equations and Applications by Philippe Guyenne,David Nicholls,Catherine Sulem Pdf

This book is a unique selection of work by world-class experts exploring the latest developments in Hamiltonian partial differential equations and their applications. Topics covered within are representative of the field’s wide scope, including KAM and normal form theories, perturbation and variational methods, integrable systems, stability of nonlinear solutions as well as applications to cosmology, fluid mechanics and water waves. The volume contains both surveys and original research papers and gives a concise overview of the above topics, with results ranging from mathematical modeling to rigorous analysis and numerical simulation. It will be of particular interest to graduate students as well as researchers in mathematics and physics, who wish to learn more about the powerful and elegant analytical techniques for Hamiltonian partial differential equations.

Mathematical Aspects of Classical and Celestial Mechanics

Vladimir I. Arnold,Valery V. Kozlov,Anatoly I. Neishtadt
Mathematical Aspects of Classical and Celestial Mechanics Book PDF

Author : Vladimir I. Arnold,Valery V. Kozlov,Anatoly I. Neishtadt
Publisher : Springer Science & Business Media
Page : 505 pages
File Size : 46,6 Mb
Release : 2007-07-05
Category : Mathematics
ISBN : 9783540489269

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Mathematical Aspects of Classical and Celestial Mechanics by Vladimir I. Arnold,Valery V. Kozlov,Anatoly I. Neishtadt Pdf

The main purpose of the book is to acquaint mathematicians, physicists and engineers with classical mechanics as a whole, in both its traditional and its contemporary aspects. As such, it describes the fundamental principles, problems, and methods of classical mechanics, with the emphasis firmly laid on the working apparatus, rather than the physical foundations or applications. Chapters cover the n-body problem, symmetry groups of mechanical systems and the corresponding conservation laws, the problem of the integrability of the equations of motion, the theory of oscillations and perturbation theory.

Normally Hyperbolic Invariant Manifolds in Dynamical Systems

Stephen Wiggins
Normally Hyperbolic Invariant Manifolds in Dynamical Systems Book PDF

Author : Stephen Wiggins
Publisher : Springer Science & Business Media
Page : 198 pages
File Size : 43,6 Mb
Release : 2013-11-22
Category : Mathematics
ISBN : 9781461243120

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Normally Hyperbolic Invariant Manifolds in Dynamical Systems by Stephen Wiggins Pdf

In the past ten years, there has been much progress in understanding the global dynamics of systems with several degrees-of-freedom. An important tool in these studies has been the theory of normally hyperbolic invariant manifolds and foliations of normally hyperbolic invariant manifolds. In recent years these techniques have been used for the development of global perturbation methods, the study of resonance phenomena in coupled oscillators, geometric singular perturbation theory, and the study of bursting phenomena in biological oscillators. "Invariant manifold theorems" have become standard tools for applied mathematicians, physicists, engineers, and virtually anyone working on nonlinear problems from a geometric viewpoint. In this book, the author gives a self-contained development of these ideas as well as proofs of the main theorems along the lines of the seminal works of Fenichel. In general, the Fenichel theory is very valuable for many applications, but it is not easy for people to get into from existing literature. This book provides an excellent avenue to that. Wiggins also describes a variety of settings where these techniques can be used in applications.

Iterative Solution of Large Sparse Systems of Equations

Wolfgang Hackbusch
Iterative Solution of Large Sparse Systems of Equations Book PDF

Author : Wolfgang Hackbusch
Publisher : Springer Science & Business Media
Page : 450 pages
File Size : 48,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461242888

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Iterative Solution of Large Sparse Systems of Equations by Wolfgang Hackbusch Pdf

This book presents the description of the state of modern iterative techniques together with systematic analysis. The first chapters discuss the classical methods. Comprehensive chapters are devoted to semi-iterative techniques (Chebyshev methods), transformations, incomplete decompositions, gradient and conjugate gradient methods, multi-grid methods and domain decomposition techniques (including e.g. the additive and multiplicative Schwartz method). In contrast to other books all techniques are described algebraically. For instance, for the domain decomposition method this is a new but helpful approach. Every technique described is illustrated by a Pascal program applicable to a class of model problem.

Analysis and Simulation of Chaotic Systems

Frank C. Hoppensteadt
Analysis and Simulation of Chaotic Systems Book PDF

Author : Frank C. Hoppensteadt
Publisher : Springer Science & Business Media
Page : 321 pages
File Size : 50,6 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475722758

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Analysis and Simulation of Chaotic Systems by Frank C. Hoppensteadt Pdf

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.

Critical Point Theory and Hamiltonian Systems

Jean Mawhin
Critical Point Theory and Hamiltonian Systems Book PDF

Author : Jean Mawhin
Publisher : Springer Science & Business Media
Page : 292 pages
File Size : 48,8 Mb
Release : 2013-04-17
Category : Science
ISBN : 9781475720617

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Critical Point Theory and Hamiltonian Systems by Jean Mawhin Pdf

FACHGEB The last decade has seen a tremendous development in critical point theory in infinite dimensional spaces and its application to nonlinear boundary value problems. In particular, striking results were obtained in the classical problem of periodic solutions of Hamiltonian systems. This book provides a systematic presentation of the most basic tools of critical point theory: minimization, convex functions and Fenchel transform, dual least action principle, Ekeland variational principle, minimax methods, Lusternik- Schirelmann theory for Z2 and S1 symmetries, Morse theory for possibly degenerate critical points and non-degenerate critical manifolds. Each technique is illustrated by applications to the discussion of the existence, multiplicity, and bifurcation of the periodic solutions of Hamiltonian systems. Among the treated questions are the periodic solutions with fixed period or fixed energy of autonomous systems, the existence of subharmonics in the non-autonomous case, the asymptotically linear Hamiltonian systems, free and forced superlinear problems. Application of those results to the equations of mechanical pendulum, to Josephson systems of solid state physics and to questions from celestial mechanics are given. The aim of the book is to introduce a reader familiar to more classical techniques of ordinary differential equations to the powerful approach of modern critical point theory. The style of the exposition has been adapted to this goal. The new topological tools are introduced in a progressive but detailed way and immediately applied to differential equation problems. The abstract tools can also be applied to partial differential equations and the reader will also find the basic references in this direction in the bibliography of more than 500 items which concludes the book. ERSCHEIN

Infinite-Dimensional Dynamical Systems in Mechanics and Physics

Roger Temam
Infinite Dimensional Dynamical Systems in Mechanics and Physics Book PDF

Author : Roger Temam
Publisher : Springer Science & Business Media
Page : 517 pages
File Size : 43,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468403138

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Infinite-Dimensional Dynamical Systems in Mechanics and Physics by Roger Temam Pdf

This is the first attempt at a systematic study of infinite dimensional dynamical systems generated by dissipative evolution partial differential equations arising in mechanics and physics. Other areas of science and technology are included where appropriate. The relation between infinite and finite dimensional systems is presented from a synthetic viewpoint and equations considered include reaction-diffusion, Navier-Stokes and other fluid mechanics equations, magnetohydrodynamics, thermohydraulics, pattern formation, Ginzburg-Landau, damped wave and an introduction to inertial manifolds.

Theory of Orbits

Dino Boccaletti,Giuseppe Pucacco
Theory of Orbits Book PDF

Author : Dino Boccaletti,Giuseppe Pucacco
Publisher : Springer Science & Business Media
Page : 430 pages
File Size : 49,8 Mb
Release : 2013-03-09
Category : Science
ISBN : 9783662092408

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Theory of Orbits by Dino Boccaletti,Giuseppe Pucacco Pdf

Half a century ago, S. Chandrasekhar wrote these words in the preface to his 1 celebrated and successful book: In this monograph an attempt has been made to present the theory of stellar dy namics as a branch of classical dynamics - a discipline in the same general category as celestial mechanics. [ ... ] Indeed, several of the problems of modern stellar dy namical theory are so severely classical that it is difficult to believe that they are not already discussed, for example, in Jacobi's Vorlesungen. Since then, stellar dynamics has developed in several directions and at var ious levels, basically three viewpoints remaining from which to look at the problems encountered in the interpretation of the phenomenology. Roughly speaking, we can say that a stellar system (cluster, galaxy, etc.) can be con sidered from the point of view of celestial mechanics (the N-body problem with N» 1), fluid mechanics (the system is represented by a material con tinuum), or statistical mechanics (one defines a distribution function for the positions and the states of motion of the components of the system).