Vibrational-Rotational Excitations in Nonlinear Molecular Systems PDF Download
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Author: Alexander A. Ovchinnikov
Publisher: Springer Science & Business Media
ISBN: 1461513170
Category : Science
Languages : en
Pages : 361
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Book Description
"If there would be no God ~ then what a staff-captain am I?" ~ said one of the characters in a novel by Dostoevskii. In a similar way we can exclaim: "If there would be no nonlinearity ~ than what physics would that be'?". Really, the most interesting and exciting effects are described by non linear equations, and vanish in the linear approximation. For example, the general theory of relativity by A.Einstein comes to mind first - one of the most beautiful physical theories, which is in fact essentially nonlinear. Next, the phase transitions crystal ~ liquid and liquid ~ gas are due to the anhar monicity of inter-particle interactions, to dissociation and infinite motion. Similarly, transitions into the superconducting state or the superftuid would be impossible with purely harmonic interaction potentials. Another bril liant achievement in nonlinear physics was the construction of a laser and the subsequent development of nonlinear optics. The latter describes the in teraction of the matter with light of super-high intensity, when multi-quanta intra-molecular transitions become essential. Last, we should note here the very beautiful mathematical theory ~ the theory of catastrophes. Its subject is the study of invariant general properties of multi-dimensional surfaces in the vicinity of bifurcation points with respect to continuous transformations.
Author: Alexander A. Ovchinnikov
Publisher: Springer Science & Business Media
ISBN: 1461513170
Category : Science
Languages : en
Pages : 361
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Book Description
"If there would be no God ~ then what a staff-captain am I?" ~ said one of the characters in a novel by Dostoevskii. In a similar way we can exclaim: "If there would be no nonlinearity ~ than what physics would that be'?". Really, the most interesting and exciting effects are described by non linear equations, and vanish in the linear approximation. For example, the general theory of relativity by A.Einstein comes to mind first - one of the most beautiful physical theories, which is in fact essentially nonlinear. Next, the phase transitions crystal ~ liquid and liquid ~ gas are due to the anhar monicity of inter-particle interactions, to dissociation and infinite motion. Similarly, transitions into the superconducting state or the superftuid would be impossible with purely harmonic interaction potentials. Another bril liant achievement in nonlinear physics was the construction of a laser and the subsequent development of nonlinear optics. The latter describes the in teraction of the matter with light of super-high intensity, when multi-quanta intra-molecular transitions become essential. Last, we should note here the very beautiful mathematical theory ~ the theory of catastrophes. Its subject is the study of invariant general properties of multi-dimensional surfaces in the vicinity of bifurcation points with respect to continuous transformations.
Author: Wu Guozhen
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: Leonid I. Manevitch
Publisher: Springer
ISBN: 9811046662
Category : Technology & Engineering
Languages : en
Pages : 448
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Book Description
This book suggests a new common approach to the study of resonance energy transport based on the recently developed concept of Limiting Phase Trajectories (LPTs), presenting applications of the approach to significant nonlinear problems from different fields of physics and mechanics. In order to highlight the novelty and perspectives of the developed approach, it places the LPT concept in the context of dynamical phenomena related to the energy transfer problems and applies the theory to numerous problems of practical importance. This approach leads to the conclusion that strongly nonstationary resonance processes in nonlinear oscillator arrays and nanostructures are characterized either by maximum possible energy exchange between the clusters of oscillators (coherence domains) or by maximum energy transfer from an external source of energy to the chain. The trajectories corresponding to these processes are referred to as LPTs. The development and the use of the LPTs concept a re motivated by the fact that non-stationary processes in a broad variety of finite-dimensional physical models are beyond the well-known paradigm of nonlinear normal modes (NNMs), which is fully justified either for stationary processes or for nonstationary non-resonance processes described exactly or approximately by the combinations of the non-resonant normal modes. Thus, the role of LPTs in understanding and analyzing of intense resonance energy transfer is similar to the role of NNMs for the stationary processes. The book is a valuable resource for engineers needing to deal effectively with the problems arising in the fields of mechanical and physical applications, when the natural physical model is quite complicated. At the same time, the mathematical analysis means that it is of interest to researchers working on the theory and numerical investigation of nonlinear oscillations.
Author: Srihari Keshavamurthy
Publisher: CRC Press
ISBN: 1439816662
Category : Science
Languages : en
Pages : 424
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Book Description
A prominent aspect of quantum theory, tunneling arises in a variety of contexts across several fields of study, including nuclear, atomic, molecular, and optical physics and has led to technologically relevant applications in mesoscopic science. Exploring mechanisms and consequences, Dynamical Tunneling: Theory and Experiment presents the work of i
Author: Janez Bonca
Publisher: Springer Science & Business Media
ISBN: 9400700431
Category : Technology & Engineering
Languages : en
Pages : 335
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Book Description
Recent advances in nanoscience have demonstrated that fundamentally new physical phenomena are found when systems are reduced to sizes comparable to the fundamental microscopic length scales of the material investigated. There has been great interest in this research due, in particular, to its role in the development of spintronics, molecular electronics and quantum information processing. The contributions to this volume describe new advances in many of these fundamental and fascinating areas of nanophysics, including carbon nanotubes, graphene, magnetic nanostructures, transport through coupled quantum dots, spintronics, molecular electronics, and quantum information processing.
Author: Dusan Papousek
Publisher: World Scientific
ISBN: 9814502456
Category : Science
Languages : en
Pages : 576
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Book Description
The book reviews the results of vibration-rotational spectroscopy of molecules obtained recently by combining modern computational methods of quantum chemistry with the new techniques of high-resolution rotational and vibration-rotational spectroscopy. It shows for example that the tunneling vibration-rotational spectroscopy of the van der Waals complexes provides a new look at intermolecular forces while the high precision and sensitivity of the submillimeter-wave and Fourier transform microwave spectroscopy make it possible to study complex rotational spectra of molecules in excited vibrational states. New results of high level ab initio quantum chemical computations of vibrational and rotational energy levels and dipole moment functions of unusual molecules will be discussed together with the recent discovery of clustering of energy levels in asymmetric tops. Group theoretical analysis of floppy molecules, especially the tunneling effects in nonrigid molecules, will also be discussed.
Author: M.S. Feld
Publisher: Springer Science & Business Media
ISBN: 3642814956
Category : Science
Languages : en
Pages : 390
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Book Description
Author: Iliya I Blekhman
Publisher: World Scientific
ISBN: 9814494747
Category : Mathematics
Languages : en
Pages : 535
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Book Description
This important book deals with vibrational mechanics — the new, intensively developing section of nonlinear dynamics and the theory of nonlinear oscillations. It offers a general approach to the study of the effect of vibration on nonlinear mechanical systems.The book presents the mathematical apparatus of vibrational mechanics which is used to describe such nonlinear effects as the disappearance and appearance under vibration of stable positions of equilibrium and motions (i.e. attractors), the change of the rheological properties of the media, self-synchronization, self-balancing, the vibrational maintenance or deceleration (retardation) of the rotation of unbalanced rotors, resonances in the motions of celestial bodies, vibrational displacement and shift, vibrational excitation of streams and the transportation of bodies in the fluid. The book considers the use of these effects in creating new vibrational machines, technologies, and also principally new materials (”dynamical materials”).Vibrational Mechanics contains many results published only in Russian and therefore unknown to the specialists in the West, and also a review of the new results obtained by researchers after the book was first published in Russia.
Author: N. Bloembergen
Publisher: World Scientific
ISBN: 9810225911
Category : Science
Languages : en
Pages : 640
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Book Description
This selection of papers in the field of nonlinear optics contains reprints of original research, and general reviews written since 1960 up to the present. Brief comments by the author place each paper in a historical context of the evolution of nonlinear optics. Papers are selected from a more comprehensive bibliography either on the basis of their influence on subsequent developments or because they were originally published in journals or conference proceedings which are less easily accessible.
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
