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

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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

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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.

Vibrational Dynamics Of Molecules
Vibrational Dynamics Of Molecules

Author: Joel M Bowman

Publisher: World Scientific

Published: 2022-06-14

Total Pages: 603

ISBN-13: 9811237921

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Vibrational Dynamics of Molecules represents the definitive concise text on the cutting-edge field of vibrational molecular chemistry. The chapter contributors are a Who's Who of world leaders in the field. The editor, Joel Bowman, is widely considered as one of the founding fathers of theoretical reaction dynamics. The included topics span the field, from fundamental theory such as collocation methods and vibrational CI methods, to interesting applications such as astrochemistry, supramolecular systems and virtual computational spectroscopy. This is a useful reference for theoretical chemists, spectroscopists, physicists, undergraduate and graduate students, lecturers and software developers.

Non-Linear Dynamics and Fundamental Interactions
Non-Linear Dynamics and Fundamental Interactions

Author: Faqir Khanna

Publisher: Springer Science & Business Media

Published: 2006-06-26

Total Pages: 345

ISBN-13: 1402039492

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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.

Encyclopedia of Nonlinear Science
Encyclopedia of Nonlinear Science

Author: Alwyn Scott

Publisher: Routledge

Published: 2006-05-17

Total Pages: 1107

ISBN-13: 1135455589

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In 438 alphabetically-arranged essays, this work provides a useful overview of the core mathematical background for nonlinear science, as well as its applications to key problems in ecology and biological systems, chemical reaction-diffusion problems, geophysics, economics, electrical and mechanical oscillations in engineering systems, lasers and nonlinear optics, fluid mechanics and turbulence, and condensed matter physics, among others.

Let's Face Chaos Through Nonlinear Dynamics
Let's Face Chaos Through Nonlinear Dynamics

Author: Marko Robnik

Publisher: American Institute of Physics

Published: 2008-12-04

Total Pages: 390

ISBN-13: 9780735406070

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This volume contains papers written by the invited lecturers and the contributors (short reports and posters). The papers do not necessarily cover exactly one-to-one what has been presented at the conference - for that we would need at least one thousand pages - but contains the material related to the presentations, either in the sense of a review (20%) or in the sense of a new original contribution (80%). The volume is a valuable source of scientific information in the general field of nonlinear science in its broadest sense, namely in the fundamental and applied physics, and in the interdisciplinary physics.

Vibrational Spectroscopy
Vibrational Spectroscopy

Author: Guozhen Wu

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2019-04-15

Total Pages: 206

ISBN-13: 3110625091

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The book presents principles of molecular vibrational spectroscopy from the viewpoint of Raman, Raman optical activity and high excitation. The quantum mechanical basis, vibrational analysis, representation of point groups and its applications are discussed as well. With exercises, it is an essential text for graduates, lecturers, and also researchers.

Visions Of Nonlinear Science In The 21st Century
Visions Of Nonlinear Science In The 21st Century

Author: Wai-kai Chen

Publisher: World Scientific

Published: 1999-07-03

Total Pages: 871

ISBN-13: 9814496626

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Authoritative and visionary, this festschrift features 12 highly readable expositions of virtually all currently active aspects of nonlinear science. It has been painstakingly researched and written by leading scientists and eminent expositors, including L Shilnikov, R Seydel, I Prigogine, W Porod, C Mira, M Lakshmanan, W Lauterborn, A Holden, H Haken, C Grebogi, E Doedel and L Chua; each chapter addresses a current and intensively researched area of nonlinear science and chaos, including nonlinear dynamics, mathematics, numerics and technology. Handsomely produced with high resolution color graphics for enhanced readability, this book has been carefully written at a high level of exposition and is somewhat self-contained.Each chapter includes a tutorial and background information, as well as a survey of each area's main results and state of the art. Of special interest to both beginners and seasoned researchers is the identification of future trends and challenging yet tractable problems that are likely to be solved before the end of the 21st century. The visionary and provocative nature of this book makes it a valuable and lasting reference.

Applied Mathematics, Modeling and Computer Simulation
Applied Mathematics, Modeling and Computer Simulation

Author: C.-H. Chen

Publisher: IOS Press

Published: 2024-01-19

Total Pages: 1266

ISBN-13: 1643684590

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Applied mathematics, modelling, and computer simulation are central to many aspects of engineering and computer science, and continue to be of intrinsic importance to the development of modern technologies. This book presents the proceedings of AMMCS 2023, the 3rd International Conference on Applied Mathematics, Modeling and Computer Simulation, held on 12 and 13 August 2023 in Wuhan, China. The conference provided an ideal opportunity for scholars and researchers to communicate important recent developments in their areas of specialization to their colleagues, and to scientists in related disciplines. More than 250 submissions were received for the conference, of which 133 were selected for presentation at the conference and inclusion here after a thorough peer-review process. These range from the theoretical and conceptual to strongly pragmatic papers addressing industrial best practice, and cover topics such as mathematical modeling and application; engineering applications and scientific computations; and the simulation of intelligent systems. The book explores practical experiences and enlightening ideas, and will be of interest to researchers, practitioners, and to all those working in the fields of applied mathematics, modeling and computer simulation.

The Nonlinear Universe
The Nonlinear Universe

Author: Alwyn C. Scott

Publisher: Springer Science & Business Media

Published: 2007-10-02

Total Pages: 371

ISBN-13: 3540341536

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Written in Alwyn Scott’s inimitable style, one that readers will find both lucid and accessible, this masterwork elucidates the explosion of activity in nonlinear science in recent decades. The book explains the wide-ranging implications of nonlinear phenomena for future developments in many areas of modern science, including mathematics, physics, engineering, chemistry, biology, and neuroscience. Arguably as important as quantum theory, modern nonlinear science is essential for understanding the scientific developments of the twenty-first century.