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Author: Guozhen Wu
Publisher: Elsevier
ISBN: 0080459072
Category : Science
Languages : en
Pages : 321
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Book Description
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
Author: Guozhen Wu
Publisher: Elsevier
ISBN: 0080459072
Category : Science
Languages : en
Pages : 321
Get Book Here
Book Description
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
Author: Guozhen Wu
Publisher: World Scientific
ISBN: 9813270713
Category : Science
Languages : en
Pages : 248
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Book Description
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.
Author: Santo Banerjee
Publisher: Springer
ISBN: 3319170376
Category : Science
Languages : en
Pages : 308
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Book Description
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.
Author: Craig Colwell Martens
Publisher:
ISBN:
Category : Excited state chemistry
Languages : en
Pages : 846
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Book Description
Author: Irving R. Epstein
Publisher: Oxford University Press
ISBN: 0198025661
Category : Science
Languages : en
Pages : 407
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Book Description
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.
Author: Lawrence N. Virgin
Publisher: Cambridge University Press
ISBN: 9780521662864
Category : Science
Languages : en
Pages : 274
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Book Description
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.
Author: Peter W Milonni
Publisher: World Scientific Publishing Company
ISBN: 9813103892
Category : Science
Languages : en
Pages : 383
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Book Description
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
Author: Jan Awrejcewicz
Publisher: World Scientific
ISBN: 981122191X
Category : Science
Languages : en
Pages : 561
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Book Description
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.
Author: Marco Thiel
Publisher: Springer
ISBN: 3642046290
Category : Science
Languages : en
Pages : 300
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Book Description
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.
Author: Faqir Khanna
Publisher: Springer Science & Business Media
ISBN: 1402039492
Category : Science
Languages : en
Pages : 345
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Book Description
This volume contains the papers presented at the NATO Advanced Research Institute on "Non-Linear Dynamics and Fundamental Interactions" held in Tashkent, Uzbekistan, from Oct.10-16,2004. The main objective of the Workshop was to bring together people working in areas of Fundamental physics relating to Quantum Field Theory, Finite Temperature Field theory and their applications to problems in particle physics, phase transitions and overlap regions with the areas of Quantum Chaos. The other important area is related to aspects of Non-Linear Dynamics which has been considered with the topic of chaology. The applications of such techniques are to mesoscopic systems, nanostructures, quantum information, particle physics and cosmology. All this forms a very rich area to review critically and then find aspects that still need careful consideration with possible new developments to find appropriate solutions. There were 29 one-hour talks and a total of seven half-hour talks, mostly by the students. In addition two round table discussions were organised to bring the important topics that still need careful consideration. One was devoted to questions and unsolved problems in Chaos, in particular Quantum Chaos. The other round table discussion considered the outstanding problems in Fundamental Interactions. There were extensive discussions during the two hours devoted to each area. Applications and development of new and diverse techniques was the real focus of these discussions. The conference was ably organised by the local committee consisting of D.U.
