Nonlinear Resonances
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Nonlinear Resonances
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Author : Shanmuganathan Rajasekar
language : en
Publisher: Springer
Release Date : 2015-11-30
Nonlinear Resonances written by Shanmuganathan Rajasekar and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-30 with Science categories.
This introductory text presents the basic aspects and most important features of various types of resonances and anti-resonances in dynamical systems. In particular, for each resonance, it covers the theoretical concepts, illustrates them with case studies, and reviews the available information on mechanisms, characterization, numerical simulations, experimental realizations, possible quantum analogues, applications and significant advances made over the years. Resonances are one of the most fundamental phenomena exhibited by nonlinear systems and refer to specific realizations of maximum response of a system due to the ability of that system to store and transfer energy received from an external forcing source. Resonances are of particular importance in physical, engineering and biological systems - they can prove to be advantageous in many applications, while leading to instability and even disasters in others. The book is self-contained, providing the details of mathematical derivations and techniques involved in numerical simulations. Though primarily intended for graduate students, it can also be considered a reference book for any researcher interested in the dynamics of resonant phenomena.
Nonlinear Resonance Analysis
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Author : Elena Kartashova
language : en
Publisher: Cambridge University Press
Release Date : 2010-10-21
Nonlinear Resonance Analysis written by Elena Kartashova and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-10-21 with Science categories.
Nonlinear resonance analysis is a unique mathematical tool that can be used to study resonances in relation to, but independently of, any single area of application. This is the first book to present the theory of nonlinear resonances as a new scientific field, with its own theory, computational methods, applications and open questions. The book includes several worked examples, mostly taken from fluid dynamics, to explain the concepts discussed. Each chapter demonstrates how nonlinear resonance analysis can be applied to real systems, including large-scale phenomena in the Earth's atmosphere and novel wave turbulent regimes, and explains a range of laboratory experiments. The book also contains a detailed description of the latest computer software in the field. It is suitable for graduate students and researchers in nonlinear science and wave turbulence, along with fluid mechanics and number theory. Colour versions of a selection of the figures are available at www.cambridge.org/9780521763608.
Nonlinear Resonances In The Motion Of Rolling Reentry Bodies
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Author : Ali Hasan Nayfeh
language : en
Publisher:
Release Date : 1971
Nonlinear Resonances In The Motion Of Rolling Reentry Bodies written by Ali Hasan Nayfeh and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with Body of revolution categories.
The method of multiple scales has been used to analyze the motion of rolling reentry bodies under the influence of nonlinear pitch, damping, and Magnus moments. Each of these moments is assumed to be a cubic function of angle of attack.
Nonlinear Resonances And Some Of Their Applications To Information Processing
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Author : Ibrahim Usama Bello
language : en
Publisher:
Release Date : 2021
Nonlinear Resonances And Some Of Their Applications To Information Processing written by Ibrahim Usama Bello and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with categories.
The study of resonance phenomena in nonlinear dynamical systems has drawn considerable attention for years. The most studied nonlinear resonance is undoubtedly the famous stochastic resonance, which consists of perturbing a nonlinear system with an appropriate amount of noise to enhance the detection of a subthreshold input signal. Since the introduction of stochastic resonance in the context of climate dynamics, it was later observed that a deterministic high frequency perturbation can replace noise leading to vibrational resonance. Even if this latter resonance was investigated in many areas of science for more than two decades now, it is still receiving attentions. It is the subject of this thesis, which numerically analyzes the occurrence of this phenomenon in two different nonlinear systems, and which suggests applications in the context of subthreshold images perception. First, we analyze the motion of a particle with a given mass which is submitted to a nonlinear force deriving from a double-well potential. For both considered cases of linear and nonlinear space-dependent damping, we establish that there exists a critical mass beyond which vibrational resonance ceases to exist. Next, we analyze how the nonlinearity affects vibrational resonance in the Chua's circuit model. Especially, we show that better resonances can be achieved when Chua's system experiences a truncated sinusoidal nonlinearity instead of the conventional sawtooth nonlinearity. Moreover, when the system driving consists of two close low frequencies, we observe that the high frequency perturbation can induce resonances at the two input low frequencies but also at a lower frequency via the mechanisms of vibrational resonance and ghost-vibrational resonance. Lastly, we consider the perception of subthreshold images through perturbed threshold detectors. In terms of image perception, we show that detectors which are based on vibrational resonance clearly outperform detectors based on stochastic resonance.
The Mechanics Of Nonlinear Systems With Internal Resonances
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Author : Arkadiy I. Manevich
language : en
Publisher: World Scientific
Release Date : 2005
The Mechanics Of Nonlinear Systems With Internal Resonances written by Arkadiy I. Manevich and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Science categories.
One of the most important features of nonlinear systems with several degrees of freedom is the presence of internal resonances at certain relations between natural frequencies of different modes. This monograph is the first book devoted predominantly to internal resonances in different mechanical systems including those of practical importance.The main purpose is to consider the internal resonances from the general point of view and to elucidate their role in applied nonlinear dynamics by using an efficient approach based on introducing the complex representation of equations of motion (together with the multiple scale method). Considered here are autonomous and nonautonomous discrete two-degree-of-freedom systems, infinite chains of particles, and continuous systems, including circular rings and cylindrical shells. Specific attention is paid to the case of one-to-one internal resonance in systems with cubic nonlinearities. Steady-state and nonstationary regimes of motion, interaction of the internal and external resonances at forced oscillations, and bifurcations of steady-state modes and their stability are systematically studied.
Nonlinear Waves In Bounded Media The Mathematics Of Resonance
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Author : Seymour Brian R
language : en
Publisher: World Scientific
Release Date : 2017-01-18
Nonlinear Waves In Bounded Media The Mathematics Of Resonance written by Seymour Brian R and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-18 with Technology & Engineering categories.
This unique book aims to treat a class of nonlinear waves that are reflected from the boundaries of media of finite extent. It involves both standing (unforced) waves and resonant oscillations due to external periodic forcing. The waves are both hyperbolic and dispersive. To achieve this aim, the book develops the necessary understanding of linear waves and the mathematical techniques of nonlinear waves before dealing with nonlinear waves in bounded media. The examples used come mainly from gas dynamics, water waves and viscoelastic waves.
Electromagnetic Resonances In Nonlinear Optics
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Author : Michel Neviere
language : en
Publisher: CRC Press
Release Date : 2000-09-20
Electromagnetic Resonances In Nonlinear Optics written by Michel Neviere and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-09-20 with Science categories.
This book is devoted to the numerous phenomena arising from the interplay between electromagnetic resonances and nonlinear optical interactions. These resonances are associated with surface plasmas or guided waves, excited in nonlinear optical resonators such as prisms or grating couplers. Topics include rigorous theories of diffraction by gratings
The Mechanics Of Nonlinear Systems With Internal Resonances
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Author : Arkadiy I. Manevich
language : en
Publisher: World Scientific
Release Date : 2005
The Mechanics Of Nonlinear Systems With Internal Resonances written by Arkadiy I. Manevich and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Science categories.
One of the most important features of nonlinear systems with several degrees of freedom is the presence of internal resonances at certain relations between natural frequencies of different modes. This monograph is the first book devoted predominantly to internal resonances in different mechanical systems including those of practical importance.The main purpose is to consider the internal resonances from the general point of view and to elucidate their role in applied nonlinear dynamics by using an efficient approach based on introducing the complex representation of equations of motion (together with the multiple scale method). Considered here are autonomous and nonautonomous discrete two-degree-of-freedom systems, infinite chains of particles, and continuous systems, including circular rings and cylindrical shells. Specific attention is paid to the case of one-to-one internal resonance in systems with cubic nonlinearities. Steady-state and nonstationary regimes of motion, interaction of the internal and external resonances at forced oscillations, and bifurcations of steady-state modes and their stability are systematically studied.
Waves And Structures In Nonlinear Nondispersive Media
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Author : Sergey Nikolaevich Gurbatov
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-03-23
Waves And Structures In Nonlinear Nondispersive Media written by Sergey Nikolaevich Gurbatov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-03-23 with Science categories.
"Waves and Structures in Nonlinear Nondispersive Media: General Theory and Applications to Nonlinear Acoustics” is devoted completely to nonlinear structures. The general theory is given here in parallel with mathematical models. Many concrete examples illustrate the general analysis of Part I. Part II is devoted to applications to nonlinear acoustics, including specific nonlinear models and exact solutions, physical mechanisms of nonlinearity, sawtooth-shaped wave propagation, self-action phenomena, nonlinear resonances and engineering application (medicine, nondestructive testing, geophysics, etc.). This book is designed for graduate and postgraduate students studying the theory of nonlinear waves of various physical nature. It may also be useful as a handbook for engineers and researchers who encounter the necessity of taking nonlinear wave effects into account of their work. Dr. Gurbatov S.N. is the head of Department, and Vice Rector for Research of Nizhny Novgorod State University. Dr. Rudenko O.V. is the Full member of Russian Academy of Sciences, the head of Department at Moscow University and Professor at BTH (Sweden). Dr. Saichev A.I. is the Professor at the Faculty of Radiophysics of Nizhny Novgorod State University, Professor of ETH Zürich.
Resonant Nonlinear Interactions Of Light With Matter
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Author : Valerii S. Butylkin
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Resonant Nonlinear Interactions Of Light With Matter written by Valerii S. Butylkin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
This book is devoted primarily to the various kinds of resonant nonlinear in teractions of light with two-level (or, in many cases, multilevel) systems. The interactions can involve one-photon as well as multiphoton processes in which some combinations of frequencies of participating photons are close to tran sitions of atoms or molecules (e.g., we consider stimulated Raman scattering (SRS) as a resonant interaction). This approach involves a broad spectrum of problems. Discussion of some of the basic phenomena as well as the pertinent theory could be found, for instance, in such well-known books as the ones due to N. Bloembergen; S.A. Akhmanov and R.V. Khokhlov; L. Allen and J.H. Eberly, and to V.M. Fain and Ya.1. Khanin. The book "Quantum Electronics" by A. Yariv could serve as an introductory guide to the subject. Thus, some of the basic material in the present book will already be well known to the reader who is an expert in the field. There are, for instance, general density matrix equations; two-level model and basic effects associated with this model, such as saturation of one-photon absorption and Raby oscillations; some basic multiphoton processes such as two-photon absorption, SRS, etc.