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Fluctuating Nonlinear Oscillators
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Book Synopsis Fluctuating Nonlinear Oscillators by : Mark Dykman
Download or read book Fluctuating Nonlinear Oscillators written by Mark Dykman and published by Oxford University Press. This book was released on 2012-07-26 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides a unifying insight into a broad range of phenomena displayed by vibrational systems of current interest. The chapters complement each other to give an account of the major fundamental results and applications in quantum information, condensed matter physics, and engineering.
Book Synopsis Strong Nonlinear Oscillators by : Livija Cveticanin
Download or read book Strong Nonlinear Oscillators written by Livija Cveticanin and published by Springer. This book was released on 2017-05-29 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook presents the motion of pure nonlinear oscillatory systems and various solution procedures which give the approximate solutions of the strong nonlinear oscillator equations. It presents the author’s original method for the analytical solution procedure of the pure nonlinear oscillator system. After an introduction, the physical explanation of the pure nonlinearity and of the pure nonlinear oscillator is given. The analytical solution for free and forced vibrations of the one-degree-of-freedom strong nonlinear system with constant and time variable parameters is considered. In this second edition of the book, the number of approximate solving procedures for strong nonlinear oscillators is enlarged and a variety of procedures for solving free strong nonlinear oscillators is suggested. A method for error estimation is also given which is suitable to compare the exact and approximate solutions. Besides the oscillators with one degree-of-freedom, the one and two mass oscillatory systems with two-degrees-of-freedom and continuous oscillators are considered. The chaos and chaos suppression in ideal and non-ideal mechanical systems is explained. In this second edition more attention is given to the application of the suggested methodologies and obtained results to some practical problems in physics, mechanics, electronics and biomechanics. Thus, for the oscillator with two degrees-of-freedom, a generalization of the solving procedure is performed. Based on the obtained results, vibrations of the vocal cord are analyzed. In the book the vibration of the axially purely nonlinear rod as a continuous system is investigated. The developed solving procedure and the solutions are applied to discuss the muscle vibration. Vibrations of an optomechanical system are analyzed using the oscillations of an oscillator with odd or even quadratic nonlinearities. The extension of the forced vibrations of the system is realized by introducing the Ateb periodic excitation force which is the series of a trigonometric function. The book is self-consistent and suitable for researchers and as a textbook for students and also professionals and engineers who apply these techniques to the field of nonlinear oscillations.
Book Synopsis Strongly Nonlinear Oscillators by : Livija Cveticanin
Download or read book Strongly Nonlinear Oscillators written by Livija Cveticanin and published by Springer. This book was released on 2014-05-22 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides the presentation of the motion of pure nonlinear oscillatory systems and various solution procedures which give the approximate solutions of the strong nonlinear oscillator equations. The book presents the original author’s method for the analytical solution procedure of the pure nonlinear oscillator system. After an introduction, the physical explanation of the pure nonlinearity and of the pure nonlinear oscillator is given. The analytical solution for free and forced vibrations of the one-degree-of-freedom strong nonlinear system with constant and time variable parameter is considered. Special attention is given to the one and two mass oscillatory systems with two-degrees-of-freedom. The criteria for the deterministic chaos in ideal and non-ideal pure nonlinear oscillators are derived analytically. The method for suppressing chaos is developed. Important problems are discussed in didactic exercises. The book is self-consistent and suitable as a textbook for students and also for professionals and engineers who apply these techniques to the field of nonlinear oscillations.
Book Synopsis Chaos in Nonlinear Oscillators by : Muthusamy Lakshmanan
Download or read book Chaos in Nonlinear Oscillators written by Muthusamy Lakshmanan and published by World Scientific. This book was released on 1996 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with the bifurcation and chaotic aspects of damped and driven nonlinear oscillators. The analytical and numerical aspects of the chaotic dynamics of these oscillators are covered, together with appropriate experimental studies using nonlinear electronic circuits. Recent exciting developments in chaos research are also discussed, such as the control and synchronization of chaos and possible technological applications.
Book Synopsis Coupled Nonlinear Oscillators by : J. Chandra
Download or read book Coupled Nonlinear Oscillators written by J. Chandra and published by Elsevier. This book was released on 1983-01-01 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt: Coupled Nonlinear Oscillators
Book Synopsis Coarse-grained Models of Nonlinear Oscillators by : Navendu Patil
Download or read book Coarse-grained Models of Nonlinear Oscillators written by Navendu Patil and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In many practical situations, time series data are gathered and used to gain an understanding of the dynamics of a complex physical system. Whether the result of experimental measurements or numerical simulations, it is of particular importance to use such data to provide a model-based and objective quantification of the dynamical complexity of a system, which, together with a measure of its stochasticity, determine fundamental limits to the system's predictability. However, a number of approaches for estimating complexity are based on information theory and require sequences of coarse-grained, or more specifically, discrete observables, which are not usually directly available, and typically have to be generated from continuous-valued discrete-time series.In this work, we obtain discrete observables for systems, whose underlying generating mechanism is deterministic chaos, solely from their time series data. We devise a selection procedure to pick good observables from a candidate set, which have a simple structure in the space of continuous observations, and also remain particularly faithful to the original time series measurements without much loss of the relevant information. Using coarse-grained observables, we build computational models, which while being minimal in a specific sense, are in turn capable of statistically reproducing input sequence of these observables with high likelihood on average, at par with its true probability. From these coarse-grained, computational models, we then calculate information-theoretic quantities that distinguish apparent randomness from the deterministic structure of the system dynamics, as hidden in the time series data and captured by its discrete observables. Using these measures, we quantify the interaction effect of the external stochastic fluctuations with the underlying deterministic chaotic behavior of the driven nonlinear oscillators. We confirm the transition in the measure of randomness as a function of the noise level, from almost constant to a significantly high power-law growth regime. Finally, we study the noise-induced transitions of stable periodic orbits as part of the major problem of distinguishing chaos from noise, using noisy experimental measurements alone. We find that the possibility of such distinction is dependent on the amplitude of external stochastic fluctuations and also, to an extent, on the choice of coarse-grained observables.
Book Synopsis Nonlinear Oscillations by : Ivana Kovacic
Download or read book Nonlinear Oscillations written by Ivana Kovacic and published by Springer Nature. This book was released on 2020-08-14 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents exact, closed-form solutions for the response of a variety of nonlinear oscillators (free, damped, forced). The solutions presented are expressed in terms of special functions. To help the reader understand these `non-standard' functions, detailed explanations and rich illustrations of their meanings and contents are provided. In addition, it is shown that these exact solutions in certain cases comprise the well-known approximate solutions for some nonlinear oscillations.
Book Synopsis Interactions of Nonlinear Oscillators Under Time Varying Parameters by : Shalom Yariv
Download or read book Interactions of Nonlinear Oscillators Under Time Varying Parameters written by Shalom Yariv and published by . This book was released on 1994 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Fluctuation Phenomenon in a Nonlinear Microelectromechanical Oscillator by : Corey Alan Stambaugh
Download or read book Fluctuation Phenomenon in a Nonlinear Microelectromechanical Oscillator written by Corey Alan Stambaugh and published by . This book was released on 2009 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: ABSTRACT: This dissertation details my research on the effects of fluctuations on vibrational systems driven out of equilibrium. Under the right conditions such systems will exhibit multiple stable states. When the fluctuations are large enough, the systems may overcome an activation barrier and switch from one stable state to another. The transitions lead to large changes in the system's vibrational amplitude. These changes can have a large impact on the performance and behavior of the system. The activation barrier plays a major role in determining how the system reacts to noise. We study its dependence on the system parameters, driving amplitude and driving frequency. Previous theoretical work has predicted that the barrier should display specific dependences, on these parameters, that are independent of the system. In this dissertation we test these predictions in our system, along with examining other features that systems possessing multiple stable states and driven out of equilibrium are expected to show. The system used in this study is a micro-electromechanical torsional oscillator. The device is fabricated using a standard commercial process that is reliable and customizable. The device provides a robust system that can be operated at different temperatures, pressures and in different resonant modes. When the damping of the system is small enough and the drive is large enough, the system displays multistable states. The micro-electromechanical torsional oscillators used in these studies are ideal apparatus for studying the transitions that occur between states of a multistable system when fluctuations are present.
Book Synopsis Nonlinear Oscillators with Constant Time Delay by : W. J. CUNNINGHAM
Download or read book Nonlinear Oscillators with Constant Time Delay written by W. J. CUNNINGHAM and published by . This book was released on 1955 with total page 1 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Psychology of Time by : Simon Grondin
Download or read book Psychology of Time written by Simon Grondin and published by Emerald Group Publishing. This book was released on 2008-11-03 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: Developments in the field of timing and time perception have multiplied the number of relevant questions regarding psychological time, and helped to provide answers and open many avenues of thought. This book brings together presentations of many of the main ideas, findings, hypotheses and theories that experimental psychology offers to the field.
Book Synopsis A Multiple Scales Approach to Nonlinear Oscillators by : Randy A. Sierra
Download or read book A Multiple Scales Approach to Nonlinear Oscillators written by Randy A. Sierra and published by . This book was released on 2012 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Stochastic and Collective Properties of Nonlinear Oscillators by : Oleg Boris Kogan
Download or read book Stochastic and Collective Properties of Nonlinear Oscillators written by Oleg Boris Kogan and published by . This book was released on 2009 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Chaotic Response of Nonlinear Oscillators by : Kazuhisa Tomita
Download or read book Chaotic Response of Nonlinear Oscillators written by Kazuhisa Tomita and published by . This book was released on 1982 with total page 53 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Thermal Fluctuations And Relaxation Processes In Nanomagnets by : William T Coffey
Download or read book Thermal Fluctuations And Relaxation Processes In Nanomagnets written by William T Coffey and published by World Scientific. This book was released on 2020-05-21 with total page 709 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting in a coherent and accessible fashion current results in nanomagnetism, this book constitutes a comprehensive, rigorous and readable account, from first principles of the classical and quantum theories underlying the dynamics of magnetic nanoparticles subject to thermal fluctuations.Starting with the Larmor-like equation for a giant spin, both the stochastic (Langevin) equation of motion of the magnetization and the associated evolution (Fokker-Planck) equation for the distribution function of the magnetization orientations of ferromagnetic nanoparticles (classical spins) in a heat bath are developed along with their solution (using angular momentum theory) for arbitrary magnetocrystalline-Zeeman energy. Thus, observables such as the magnetization reversal time, relaxation functions, dynamic susceptibilities, etc. are calculated and compared with the predictions of classical escape rate theory including in the most general case spin-torque-transfer. Regarding quantum effects, which are based on the reduced spin density matrix evolution equation in Hilbert space as is described at length, they are comprehensively treated via the Wigner-Stratonovich formulation of the quantum mechanics of spins via their orientational quasi-probability distributions on a classically meaningful representation space. Here, as suggested by the relevant Weyl symbols, the latter is the configuration space of the polar angles. Hence, one is led, by mapping the reduced density matrix equation onto that space, to a master equation for the quasi-probability evolution akin to the Fokker-Planck equation which may be solved in a similar way. Thus, one may study in a classical-like manner the evolution of observables with spin number ranging from an elementary spin to molecular clusters to the classical limit, viz. a nanoparticle. The entire discussion hinges on the one-to-one correspondence between polarization operators in Hilbert space and the spherical harmonics allied to concepts of spin coherent states long familiar in quantum optics.Catering for the reader with only a passing knowledge of statistical and quantum mechanics, the book serves as an introductory text on a complicated subject where the literature is remarkably sparse.
Book Synopsis Introduction to Nonlinear Oscillations by : Vladimir I. Nekorkin
Download or read book Introduction to Nonlinear Oscillations written by Vladimir I. Nekorkin and published by John Wiley & Sons. This book was released on 2016-05-02 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: A systematic outline of the basic theory of oscillations, combining several tools in a single textbook. The author explains fundamental ideas and methods, while equally aiming to teach students the techniques of solving specific (practical) or more complex problems. Following an introduction to fundamental notions and concepts of modern nonlinear dynamics, the text goes on to set out the basics of stability theory, as well as bifurcation theory in one and two-dimensional cases. Foundations of asymptotic methods and the theory of relaxation oscillations are presented, with much attention paid to a method of mappings and its applications. With each chapter including exercises and solutions, including computer problems, this book can be used in courses on oscillation theory for physics and engineering students. It also serves as a good reference for students and scientists in computational neuroscience.
Book Synopsis The Influence of Connectivity on the Global Dynamics of Nonlinear Oscillator Ensembles by : Jeffery L. Rogers
Download or read book The Influence of Connectivity on the Global Dynamics of Nonlinear Oscillator Ensembles written by Jeffery L. Rogers and published by . This book was released on 1994 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt:
