Solitons And Chaos In Nonlinear Periodic Structures
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| Author | : Ardeshir Guran |
| Publisher | : World Scientific |
| Total Pages | : 248 |
| Release | : 1997-12-16 |
| Genre | : Science |
| ISBN | : 981450078X |
This book is a collection of papers on the subject of nonlinear dynamics and its applications written by experts in this field. It offers the reader a sampling of exciting research areas in this fast-growing field. The topics covered include chaos, tools to analyze motions, fractal boundaries, dynamics of the Fitzhugh-Nagumo equation, structural control, separation of contaminations from signal of interest, parametric excitation, stochastic bifurcation, mode localization in repetitive structures, Toda lattice, transition from soliton to chaotic motion, nonlinear normal modes, noise perturbations of nonlinear dynamical systems, and phase locking of coupled limit cycle oscillators. Mathematical methods include Lie transforms, Monte Carlo simulations, stochastic calculus, perturbation methods and proper orthogonal decomposition. Applications include gyrodynamics, tether connected satellites, shell buckling, nonlinear circuits, volume oscillations of a large lake, systems with stick-slip friction, imperfect or disordered structures, overturning of rigid blocks, central pattern generators, flow induced oscillations, shape control and vibration suppression of elastic structures.All of these diverse contributions have a common thread: the world of nonlinear behavior. Although linear dynamics is an invaluable tool, there are many problems where nonlinear effects are essential. Some examples include bifurcation of solutions, stability of motion, the effects of large displacements, and subharmonic resonance. This book shows how nonlinear dynamics is currently being utilized and investigated. It will be of interest to engineers, applied mathematicians and physicists.
| Author | : Eryk Infeld |
| Publisher | : Cambridge University Press |
| Total Pages | : 416 |
| Release | : 2000-07-13 |
| Genre | : Mathematics |
| ISBN | : 9780521635578 |
The second edition of a highly successful book on nonlinear waves, solitons and chaos.
| Author | : Anatoli? Mikha?lovich Kamchatnov |
| Publisher | : World Scientific |
| Total Pages | : 399 |
| Release | : 2000 |
| Genre | : Science |
| ISBN | : 981024407X |
Although the mathematical theory of nonlinear waves and solitons has made great progress, its applications to concrete physical problems are rather poor, especially when compared with the classical theory of linear dispersive waves and nonlinear fluid motion. The Whitham method, which describes the combining action of the dispersive and nonlinear effects as modulations of periodic waves, is not widely used by applied mathematicians and physicists, though it provides a direct and natural way to treat various problems in nonlinear wave theory. Therefore it is topical to describe recent developments of the Whitham theory in a clear and simple form suitable for applications in various branches of physics.This book develops the techniques of the theory of nonlinear periodic waves at elementary level and in great pedagogical detail. It provides an introduction to a Whitham's theory of modulation in a form suitable for applications. The exposition is based on a thorough analysis of representative examples taken from fluid mechanics, nonlinear optics and plasma physics rather than on the formulation and study of a mathematical theory. Much attention is paid to physical motivations of the mathematical methods developed in the book. The main applications considered include the theory of collisionless shock waves in dispersive systems and the nonlinear theory of soliton formation in modulationally unstable systems. Exercises are provided to amplify the discussion of important topics such as singular perturbation theory, Riemann invariants, the finite gap integration method, and Whitham equations and their solutions.
| Author | : Terence William Barrett |
| Publisher | : World Scientific |
| Total Pages | : 807 |
| Release | : 1995-11-16 |
| Genre | : Science |
| ISBN | : 9814501085 |
Advanced Electromagnetism: Foundations, Theory and Applications treats what is conventionally called electromagnetism or Maxwell's theory within the context of gauge theory or Yang-Mills theory. A major theme of this book is that fields are not stand-alone entities but are defined by their boundary conditions. The book has practical relevance to efficient antenna design, the understanding of forces and stresses in high energy pulses, ring laser gyros, high speed computer logic elements, efficient transfer of power, parametric conversion, and many other devices and systems. Conventional electromagnetism is shown to be an underdeveloped, rather than a completely developed, field of endeavor, with major challenges in development still to be met.
| Author | : Ardshir Guran |
| Publisher | : World Scientific |
| Total Pages | : 254 |
| Release | : 1997 |
| Genre | : Science |
| ISBN | : 9789810229825 |
This book is a collection of papers on the subject of nonlinear dynamics and its applications written by experts in this field. It offers the reader a sampling of exciting research areas in this fast-growing field. The topics covered include chaos, tools to analyze motions, fractal boundaries, dynamics of the Fitzhugh-Nagumo equation, structural control, separation of contaminations from signal of interest, parametric excitation, stochastic bifurcation, mode localization in repetitive structures, Toda lattice, transition from soliton to chaotic motion, nonlinear normal modes, noise perturbations of nonlinear dynamical systems, and phase locking of coupled limit cycle oscillators. Mathematical methods include Lie transforms, Monte Carlo simulations, stochastic calculus, perturbation methods and proper orthogonal decomposition. Applications include gyrodynamics, tether connected satellites, shell buckling, nonlinear circuits, volume oscillations of a large lake, systems with stick-slip friction, imperfect or disordered structures, overturning of rigid blocks, central pattern generators, flow induced oscillations, shape control and vibration suppression of elastic structures.All of these diverse contributions have a common thread: the world of nonlinear behavior. Although linear dynamics is an invaluable tool, there are many problems where nonlinear effects are essential. Some examples include bifurcation of solutions, stability of motion, the effects of large displacements, and subharmonic resonance. This book shows how nonlinear dynamics is currently being utilized and investigated. It will be of interest to engineers, applied mathematicians and physicists.
| Author | : Steven H. Strogatz |
| Publisher | : CRC Press |
| Total Pages | : 532 |
| Release | : 2018-05-04 |
| Genre | : Mathematics |
| ISBN | : 0429961111 |
This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.
| Author | : D.L. Mills |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 191 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 3662002132 |
One intriguing aspect of physics is its dynamic and rapidly evolving nature; exciting new fields can become moribund within relatively few years, only to revive and grow again in a dramatic and expolisve manner in response to new developments. This has been the case for the fields of optics and atomic physics. In the 1950s, and perhaps into the early 1960s, both fields appeared mature, fully developed, and perhaps even a bit dull as a consequence. The appearance of the laser has tumed both of these fields into dynamic areas of research, within which fundamental and profound questions are being explored. The research of the past two or three decades has led also to very important applications and to new devices. The dye laser, which enables a very narrow line to be tuned over an appreciable spectral range, has led to a virtual revolution in the spec troscopy of atoms, molecules, and the condensed phases of matter. A parallel development, readily detectable in the recent literature of theoretical physics, has been the substantial advance in OUf understand ing of highly nonlinear phenomena. Numerous texts are devoted to exposition of the theoretical methods which may be used to extract useful information from the important equations encountered in the various fields of physics. A survey of the contemporary literature of nonlinear optics shows that in this area one encounters a large fraction of the basic equations and principles of nonlinear physics.
| Author | : Friedrich Pfeiffer |
| Publisher | : World Scientific |
| Total Pages | : 329 |
| Release | : 2001 |
| Genre | : Technology & Engineering |
| ISBN | : 9812811273 |
Dynamics with friction: Modeling, analysis and experiments, part II. ch. 1. Interaction of vibration and friction at dry sliding contacts / Daniel P. Hess -- ch. 2. Vibrations and friction-induced instability in discs / John E. Mottershead -- ch. 3. Dynamics of flexible links in kinematic chains / Dan B. Marghitu and Ardeshir Guran -- ch. 4. Solitons, chaos and modal interactions in periodic structures / M.A. Davies and F.C. Moon -- ch. 5. Analysis and modeling of an experimental frictionally excited beam / R.V. Kappagantu and B.F. Feeny -- ch. 6. Transient waves in linear viscoelastic media / Francesco Mainardi -- ch. 7. Dynamic stability and nonlinear parametric vibrations of rectangular plates / G.L. Ostiguy -- ch. 8. Friction modelling and dynamic computation / J.P. Meijaard -- ch. 9. Damping through use of passive and semi-active dry friction forces / Aldo A. Ferri
| Author | : A. Driessen |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 179 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 9401512671 |
Nonlinear optical phenomena can be exploited in advanced devices for transport, processing, and storage of information. These are needed as the present-day approach - mainly using on electron-based technology - faces the challenges of increasing demand on bandwidth and processing speed. A key role in the development of nonlinear devices is the availability of novel materials with the required nonlinear optical properties. With such materials, scientific creativity and careful design, promising concepts have been developed resulting in the demonstration of devices. This book contains the proceedings of NOIS 2000 (Nonlinear Optics for the Information Society) Annual Meeting of the COST Action P2, held at the University of Twente, in Enschede, The Netherlands, on 26-27 October, 2000. It comprises a selection of the presentations at the meeting, reporting state-of-the-art research and developments in the field of applications of nonlinear phenomena in information technology.
| Author | : Francesco Romeo |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 332 |
| Release | : 2013-07-30 |
| Genre | : Technology & Engineering |
| ISBN | : 3709113091 |
Waves and defect modes in structures media.- Piezoelectric superlattices and shunted periodic arrays as tunable periodic structures and metamaterials.- Topology optimization.- Map-based approaches for periodic structures.- Methodologies for nonlinear periodic media. The contributions in this volume present both the theoretical background and an overview of the state-of-the art in wave propagation in linear and nonlinear periodic media in a consistent format. They combine the material issued from a variety of engineering applications, spanning a wide range of length scale, characterized by structures and materials, both man-made and naturally occurring, featuring geometry, micro-structural and/or materials properties that vary periodically in space, including periodically stiffened plates, shells and beam-like as well as bladed disc assemblies, phononic metamaterials, photonic crystals and ordered granular media. Along with linear models and applications, analytical methodologies for analyzing and exploiting complex dynamical phenomena arising in nonlinear periodic systems are also presented.
