Nonlinearity and Chaos in Molecular Vibrations
Nonlinearity and Chaos in Molecular Vibrations

Author: Guozhen Wu

Publisher: Elsevier

Published: 2005-07-01

Total Pages: 321

ISBN-13: 0080459072

DOWNLOAD EBOOK

Nonlinearity and Chaos in Molecular Vibrations deals systematically with a Lie algebraic approach to the study of nonlinear properties of molecular highly excited vibrations. The fundamental concepts of nonlinear dynamics such as chaos, fractals, quasiperiodicity, resonance, and the Lyapunov exponent, and their roles in the study of molecular vibrations are presented.The 20 chapters cover the basic ideas, the concept of dynamical groups, the integrable two-mode SU(2) system, the unintegrable three-mode SU(3) system, the noncompact su(1,1) algebraic application, su(3) symmetry breaking and its application and the quantal effect of asymmetric molecular rotation. Emphasis is given to: resonance and chaos, the fractal structure of eigencoefficients, the C-H bend motion of acetylene, regular and chaotic motion of DCN, the existence of approximately conserved quantum numbers, one-electronic motion in multi-sites, the Lyapunov exponent, actions of periodic trajectories and quantization, the H function and its application in vibrational relaxation as well as the Dixon dip and its destruction and chaos in the transitional states. This approach bridges the gap between molecular vibrational spectroscopy and nonlinear dynamics.The book presents a framework of information that readers can use to build their knowledge, and is therefore highly recommended for all those working in or studying molecular physics, molecular spectroscopy, chemical physics and theoretical physics. * Discusses nonlinearity and chaotic phenomena in molecular vibrations* Approaches the complicated highly excited molecular vibration* Provides clear information for students and researchers looking to expand knowledge in this field

Molecular Vibrations: An Algebraic And Nonlinear Approach
Molecular Vibrations: An Algebraic And Nonlinear Approach

Author: Guozhen Wu

Publisher: World Scientific

Published: 2018-08-07

Total Pages: 248

ISBN-13: 9813270713

DOWNLOAD EBOOK

This book focuses on the main idea that highly-excited molecular vibration is a nonlinear, many-body and semiclassical system. Therefore, many ideas and techniques in nonlinear fields such as chaos, resonance, Lyapunov exponent, etc. can be incorporated into this study. Together with the Lie algebraic coset algorithm, readers are able to approach the topics in a simple arithmetic and realistic way in contrast to the traditional solving of Schrödinger equation.Covering the author's research in over two decades, these works bridge the gaps between molecular vibration and nonlinear sciences, many new characters are introduced for molecular highly-excited vibration from a fresh viewpoint of nonlinearity, especially, the chaos. Related works of the elementary ideas in this field can be found in the first three chapters for the readers to be familiar with, while the rest of the chapters offer concrete examples with flourishing ideas and results on system dynamics which are not known or neglected by the traditional wave function algorithm.

Applications of Chaos and Nonlinear Dynamics in Science and Engineering - Vol. 4
Applications of Chaos and Nonlinear Dynamics in Science and Engineering - Vol. 4

Author: Santo Banerjee

Publisher: Springer

Published: 2015-05-04

Total Pages: 308

ISBN-13: 3319170376

DOWNLOAD EBOOK

Chaos and nonlinear dynamics initially developed as a new emergent field with its foundation in physics and applied mathematics. The highly generic, interdisciplinary quality of the insights gained in the last few decades has spawned myriad applications in almost all branches of science and technology—and even well beyond. Wherever quantitative modeling and analysis of complex, nonlinear phenomena is required, chaos theory and its methods can play a key role. his fourth volume concentrates on reviewing further relevant contemporary applications of chaotic and nonlinear dynamics as they apply to the various cuttingedge branches of science and engineering. This encompasses, but is not limited to, topics such as synchronization in complex networks and chaotic circuits, time series analysis, ecological and biological patterns, stochastic control theory and vibrations in mechanical systems. Featuring contributions from active and leading research groups, this collection is ideal both as a reference and as a ‘recipe book’ full of tried and tested, successful engineering applications.

An Introduction to Nonlinear Chemical Dynamics
An Introduction to Nonlinear Chemical Dynamics

Author: Irving R. Epstein

Publisher: Oxford University Press

Published: 1998-10-22

Total Pages: 407

ISBN-13: 0198025661

DOWNLOAD EBOOK

Just a few decades ago, chemical oscillations were thought to be exotic reactions of only theoretical interest. Now known to govern an array of physical and biological processes, including the regulation of the heart, these oscillations are being studied by a diverse group across the sciences. This book is the first introduction to nonlinear chemical dynamics written specifically for chemists. It covers oscillating reactions, chaos, and chemical pattern formation, and includes numerous practical suggestions on reactor design, data analysis, and computer simulations. Assuming only an undergraduate knowledge of chemistry, the book is an ideal starting point for research in the field. The book begins with a brief history of nonlinear chemical dynamics and a review of the basic mathematics and chemistry. The authors then provide an extensive overview of nonlinear dynamics, starting with the flow reactor and moving on to a detailed discussion of chemical oscillators. Throughout the authors emphasize the chemical mechanistic basis for self-organization. The overview is followed by a series of chapters on more advanced topics, including complex oscillations, biological systems, polymers, interactions between fields and waves, and Turing patterns. Underscoring the hands-on nature of the material, the book concludes with a series of classroom-tested demonstrations and experiments appropriate for an undergraduate laboratory.

Introduction to Experimental Nonlinear Dynamics
Introduction to Experimental Nonlinear Dynamics

Author: Lawrence N. Virgin

Publisher: Cambridge University Press

Published: 2000-03-28

Total Pages: 274

ISBN-13: 9780521662864

DOWNLOAD EBOOK

Nonlinear behavior can be found in such highly disparate areas as population biology and aircraft wing flutter. For this reason, nonlinear dynamics and chaos have become very active fields of research. This work uses an extended case study--an experiment in mechanical vibration--to introduce and explore the subject of nonlinear behavior and chaos from an engineering perspective. After a review of basic principles, the text then describes a cart-on-a-track oscillator and shows what happens when it is gradually subjected to greater excitation, thereby encountering the full spectrum of nonlinear behavior, from simple free decay to chaos. Advanced undergraduate and graduate students, as well as practicing engineers, will find this book a lively, accessible introduction to the subject.

Chaos In Laser-matter Interactions
Chaos In Laser-matter Interactions

Author: Peter W Milonni

Publisher: World Scientific Publishing Company

Published: 1987-06-01

Total Pages: 383

ISBN-13: 9813103892

DOWNLOAD EBOOK

Contents: Dissipative Systems: Introduction Nonlinearity Period Doubling to Chaos Lyapunov Exponent Power Spectra Correlations Remarks Feigenbaum Universality Feigenbaum Universality: Outline of Exact Renormalization Theory Experimental Observations Duffing Oscillator Period Doubling to Chaos in a CO2 Laser Experiment Bifurcations Intermittency (Pomeau-Manneville) Route to Chaos Quasiperiodicity to Chaos: Ruelle-Takens-Newhouse Scenario Strange Attractors, Dimensions, and Fractals Measuring Lyapunov Exponents Measuring Dimensions Kolmogorov Entropy Noise Maxwell-Bloch Equations Lorentz Model and Single-Mode Laser Single-Mode Instabilities: Homogeneous Broadening Mode Splitting Inhomogeneous Broadening: Chaos Associated with Casperson Instability Inhomogeneous Broadening: Experiments Multimode Instabilities Physical Explanations of Self-Pulsing Instabilities Transverse Mode Effects More Laser Instabilities Optical Bistability Chaos in Optically Bistability Hamiltonian Systems: Classical Hamiltonian Systems Integrability and Action-Angle Variables Integrability, Invariant Tori, and Quasiperiodicity Ergodicity, Mixing, and Chaos Fermi-Pasta-Ulam Model KAM Theorem Overlapping Resonances Henon-Heiles Model Characterization of Chaotic Behavior Is Classical Physics Really Deterministic? Kicked Pendulum and Standard Mapping Chaos in a Classical Model of Multiple-Photon Excitation of Molecular Vibrations Chaos in a Classical Model of a Rotating Molecule in a Laser Field Stochastic Excitation Quantum Chaos Regular and Irregular Spectra Kicked Two-State System Chaos in the Jaynes-Cummings Model Quantum Theory of the Kicked Pendulum Localization Classical and Quantum Calculations for a Hydrogen Atom in a Microwave Field Epilogue Readership: Laser scientists and engineers, physicists, applied mathematicians and researchers in nonlinear dynamics. Related Books Free and Guided Optical Beams Laser Cleaning II A Bouquet of Numbers and Other Scientific Offerings Universal Fluctuations Geometric Perturbation Theory in Physics

Recent Trends In Chaotic, Nonlinear And Complex Dynamics
Recent Trends In Chaotic, Nonlinear And Complex Dynamics

Author: Jan Awrejcewicz

Publisher: World Scientific

Published: 2021-07-26

Total Pages: 561

ISBN-13: 981122191X

DOWNLOAD EBOOK

In recent years, enormous progress has been made on nonlinear dynamics particularly on chaos and complex phenomena. This unique volume presents the advances made in theory, analysis, numerical simulation and experimental realization, promising novel practical applications on various topics of current interest on chaos and related fields of nonlinear dynamics.Particularly, the focus is on the following topics: synchronization vs. chaotic phenomena, chaos and its control in engineering dynamical systems, fractal-based dynamics, uncertainty and unpredictability measures vs. chaos, Hamiltonian systems and systems with time delay, local/global stability, bifurcations and their control, applications of machine learning to chaos, nonlinear vibrations of lumped mass mechanical/mechatronic systems (rigid body and coupled oscillator dynamics) governed by ODEs and continuous structural members (beams, plates, shells) vibrations governed by PDEs, patterns formation, chaos in micro- and nano-mechanical systems, chaotic reduced-order models, energy absorption/harvesting from chaotic, chaos vs. resonance phenomena, chaos exhibited by discontinuous systems, chaos in lab experiments.The present volume forms an invaluable source on recent trends in chaotic and complex dynamics for any researcher and newcomers to the field of nonlinear dynamics.

Nonlinear Dynamics and Chaotic Phenomena
Nonlinear Dynamics and Chaotic Phenomena

Author: B.K Shivamoggi

Publisher: Springer Science & Business Media

Published: 2013-03-09

Total Pages: 415

ISBN-13: 9401724423

DOWNLOAD EBOOK

FolJowing the formulation of the laws of mechanics by Newton, Lagrange sought to clarify and emphasize their geometrical character. Poincare and Liapunov successfuIJy developed analytical mechanics further along these lines. In this approach, one represents the evolution of all possible states (positions and momenta) by the flow in phase space, or more efficiently, by mappings on manifolds with a symplectic geometry, and tries to understand qualitative features of this problem, rather than solving it explicitly. One important outcome of this line of inquiry is the discovery that vastly different physical systems can actually be abstracted to a few universal forms, like Mandelbrot's fractal and Smale's horse-shoe map, even though the underlying processes are not completely understood. This, of course, implies that much of the observed diversity is only apparent and arises from different ways of looking at the same system. Thus, modern nonlinear dynamics 1 is very much akin to classical thermodynamics in that the ideas and results appear to be applicable to vastly different physical systems. Chaos theory, which occupies a central place in modem nonlinear dynamics, refers to a deterministic development with chaotic outcome. Computers have contributed considerably to progress in chaos theory via impressive complex graphics. However, this approach lacks organization and therefore does not afford complete insight into the underlying complex dynamical behavior. This dynamical behavior mandates concepts and methods from such areas of mathematics and physics as nonlinear differential equations, bifurcation theory, Hamiltonian dynamics, number theory, topology, fractals, and others.

Nonlinear Dynamics and Chaos: Advances and Perspectives
Nonlinear Dynamics and Chaos: Advances and Perspectives

Author: Marco Thiel

Publisher: Springer

Published: 2010-05-17

Total Pages: 300

ISBN-13: 3642046290

DOWNLOAD EBOOK

This book is a collection of papers contributed by some of the greatest names in the areas of chaos and nonlinear dynamics. Each paper examines a research topic at the frontier of the area of dynamical systems. As well as reviewing recent results, each paper also discusses the future perspectives of each topic. The result is an invaluable snapshot of the state of the ?eld by some of the most important researchers in the area. The ?rst contribution in this book (the section entitled “How did you get into Chaos?”) is actually not a paper, but a collection of personal accounts by a number of participants of the conference held in Aberdeen in September 2007 to honour Celso Grebogi’s 60th birthday. At the instigation of James Yorke, many of the most well-known scientists in the area agreed to share their tales on how they got involved in chaos during a celebratory dinner in Celso’s honour during the conference. This was recorded in video, we felt that these accounts were a valuable historic document for the ?eld. So we decided to transcribe it and include it here as the ?rst section of the book.