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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 Fluctuating Nonlinear Oscillators by : Mark Dykman
Download or read book Fluctuating Nonlinear Oscillators written by Mark Dykman and published by OUP Oxford. This book was released on 2012-07-26 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides a unifying insight into fluctuation phenomena in a broad variety of vibrational systems of current interest. It consists of individual chapters written by leading experts in the field. The chapters are self-contained and complement each other. The ongoing rapid development of well-characterized mesoscopic vibrational systems has made it possible to address fundamental physics problems and to explore new approaches to quantum and classical measurements, with applications to quantum information, condensed matter physics, and engineering. The book gives an account of major results in this direction. The topics include dynamics and quantum control of microcavity modes coupled to qubits, measurements with bifurcation-based amplifiers and new types of such amplifiers; switching rate scaling and new quantum mechanisms of metastable decay; wave mixing and parametric excitation in the quantum regime; collective phenomena and the interaction-induced discrete time symmetry breaking; and back-action and shot noise in electron-vibrational systems.
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 239 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 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 317 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 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 123 pages. Available in PDF, EPUB and Kindle. Book excerpt: Coupled Nonlinear Oscillators
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 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 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 Quantum Machines by : Michel Devoret
Download or read book Quantum Machines written by Michel Devoret and published by Oxford University Press, USA. This book was released on 2014 with total page 601 pages. Available in PDF, EPUB and Kindle. Book excerpt: What is a quantum machine? Can we say that lasers and transistors are quantum machines? After all, physicists advertise these devices as the two main spin-offs of the understanding of quantum physics. In a true quantum machine, the signal collective variables must themselves be treated as quantum operators. Other engineered quantum systems based on natural, rather than artificial, degrees of freedom can also qualify as quantum machines. This book provides the basic knowledge needed to understand and investigate the physics of these novel systems.
Book Synopsis Langevin Equation, The: With Applications To Stochastic Problems In Physics, Chemistry And Electrical Engineering (Fourth Edition) by : Kalmykov Yuri P
Download or read book Langevin Equation, The: With Applications To Stochastic Problems In Physics, Chemistry And Electrical Engineering (Fourth Edition) written by Kalmykov Yuri P and published by World Scientific. This book was released on 2017-03-22 with total page 928 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our original objective in writing this book was to demonstrate how the concept of the equation of motion of a Brownian particle — the Langevin equation or Newtonian-like evolution equation of the random phase space variables describing the motion — first formulated by Langevin in 1908 — so making him inter alia the founder of the subject of stochastic differential equations, may be extended to solve the nonlinear problems arising from the Brownian motion in a potential. Such problems appear under various guises in many diverse applications in physics, chemistry, biology, electrical engineering, etc. However, they have been invariably treated (following the original approach of Einstein and Smoluchowski) via the Fokker–Planck equation for the evolution of the probability density function in phase space. Thus the more simple direct dynamical approach of Langevin which we use and extend here, has been virtually ignored as far as the Brownian motion in a potential is concerned. In addition two other considerations have driven us to write this new edition of The Langevin Equation. First, more than five years have elapsed since the publication of the third edition and following many suggestions and comments of our colleagues and other interested readers, it became increasingly evident to us that the book should be revised in order to give a better presentation of the contents. In particular, several chapters appearing in the third edition have been rewritten so as to provide a more direct appeal to the particular community involved and at the same time to emphasize via a synergetic approach how seemingly unrelated physical problems all involving random noise may be described using virtually identical mathematical methods. Secondly, in that period many new and exciting developments have occurred in the application of the Langevin equation to Brownian motion. Consequently, in order to accommodate all these, a very large amount of new material has been added so as to present a comprehensive overview of the subject.
Book Synopsis Computational Neuroscience by : James M. Bower
Download or read book Computational Neuroscience written by James M. Bower and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 633 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume includes papers presented at the Sixth Annual Computational Neurosci ence meeting (CNS*97) held in Big Sky, Montana, July 6-10, 1997. This collection includes 103 of the 196 papers presented at the meeting. Acceptance for meeting presentation was based on the peer review of preliminary papers originally submitted in January of 1997. The papers in this volume represent final versions of this work submitted in January of 1998. Taken together they provide a cross section of computational neuroscience and represent well the continued vitality and growth of this field. The meeting in Montana was unusual in several respects. First, to our knowledge it was the first international scientific meeting with opening ceremonies on horseback. Second, after five days of rigorous scientific discussion and debate, meeting participants were able to resolve all remaining conflicts in barrel race competitions. Otherwise the magnificence of Montana and the Big Sky Ski Resort assured that the meeting will not soon be forgotten. Scientifically, this volume once again represents the remarkable breadth of subjects that can be approached with computational tools. This volume and the continuing CNS meet ings make it clear that there is almost no subject or area of modem neuroscience research that is not appropriate for computational studies.
Book Synopsis Nonlinear Oscillations of a Triatomic Molecule by : Sean O. Wilson
Download or read book Nonlinear Oscillations of a Triatomic Molecule written by Sean O. Wilson and published by . This book was released on 2002-06-01 with total page 73 pages. Available in PDF, EPUB and Kindle. Book excerpt: Due to nonlinearity in the coupling, one of the vibrational modes of a straight symmetric triatomic molecule can be unstable for amplitudes greater than a threshold value, The instability is due to the mode parametrically exciting another mode. The threshold amplitude decreases if the difference of the frequency of the two modes is reduced. We consider the simplest case of a symmetric rectilinear molecule where the coupling has a cubic nonlinearity in addition to a linear restoring force. Approximate analytical results are in good agreement with numerical simulations of the exact equations of motion, although in some cases the actual behavior fundamentally deviates from the perturbative theory. Two physical demonstrations of the instability are described, where the apparatus are a system of gliders coupled by springs and magnets on an air track. Possible quantum mechanical implications are discussed. This work is a fundamental generalization of the parametric instability of two linearly coupled nonlinear oscillators that was reported in a previous investigation.
Book Synopsis Chaotic Oscillators by : Tomasz Kapitaniak
Download or read book Chaotic Oscillators written by Tomasz Kapitaniak and published by World Scientific. This book was released on 1992 with total page 672 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume brings together a comprehensive selection of over fifty reprints on the theory and applications of chaotic oscillators. Included are fundamental mathematical papers describing methods for the investigation of chaotic behavior in oscillatory systems as well as the most important applications in physics and engineering. There is currently no book similar to this collection.
Book Synopsis Truly Nonlinear Oscillations by : Ronald E. Mickens
Download or read book Truly Nonlinear Oscillations written by Ronald E. Mickens and published by World Scientific. This book was released on 2010 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique book provides a concise presentation of many of the fundamental strategies for calculating approximations to the oscillatory solutions of "truly nonlinear" (TNL) oscillator equations. The volume gives a general overview of the author's work on harmonic balance, iteration and combined linearization-averaging methods. However, full discussions are also presented on parameter expansion procedures and a first-order averaging technique for TNL oscillators. The calculational basis of each method is clarified by applying them to a set of standard TNL oscillator equations. This allows a direct comparison to be made among the various methods. The book is self-contained and therefore suitable for both classroom use and self-study by students and professionals who desire to learn, understand, and apply this technique to the field of nonlinear oscillations.
Book Synopsis Collective Dynamics of the Winfree Model of Coupled Nonlinear Oscillators by : Joel Thevatharman Ariaratnam
Download or read book Collective Dynamics of the Winfree Model of Coupled Nonlinear Oscillators written by Joel Thevatharman Ariaratnam and published by . This book was released on 2002 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Analytical Methods for Nonlinear Oscillators and Solitary Waves by : Chu-Hui He
Download or read book Analytical Methods for Nonlinear Oscillators and Solitary Waves written by Chu-Hui He and published by Frontiers Media SA. This book was released on 2023-11-24 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: The most well-known analytical method is the perturbation method, which has led to the great discovery of Neptune in 1846, and since then mathematical prediction and empirical observation became two sides of a coin in physics. However, the perturbation method is based on the small parameter assumption, and the obtained solutions are valid only for weakly nonlinear equations, which have greatly limited their applications to modern physical problems. To overcome the shortcomings, many mathematicians and physicists have been extensively developing various technologies for several centuries, however, there is no universal method for all nonlinear problems, and mathematical prediction with remarkably high accuracy is still much needed for modern physics, for example, the solitary waves traveling along an unsmooth boundary, the low-frequency property of a harvesting energy device, the pull-in voltage in a micro-electromechanical system. Now various effective analytical methods have appeared in the open literature, e.g., the homotopy perturbation method and the variational iteration method. An analytical solution provides a fast insight into its physical properties of a practical problem, e.g., frequency-amplitude relation of a nonlinear oscillator, solitary wave in an optical fiber, pull-in instability of a microelectromechanical system, making mathematical prediction even more attractive in modern physics. Nonlinear physics has been developing into a new stage, where the fractal-fractional differential equations have to be adopted to describe more accurately discontinuous problems, and it becomes ever more difficult to find an analytical solution for such nonlinear problems, and the analytical methods for fractal-fractional differential equations have laid the foundations for nonlinear physics.
