Stochastic Resonance In Harmonic And Fractional Oscillators
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Stochastic Resonance In Harmonic And Fractional Oscillators
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Author : Katrin Laas
language : en
Publisher:
Release Date : 2012
Stochastic Resonance In Harmonic And Fractional Oscillators written by Katrin Laas and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Harmonic oscillators categories.
The Noisy Oscillator
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Author : M. Gitterman
language : en
Publisher: World Scientific
Release Date : 2005
The Noisy Oscillator written by M. Gitterman 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.
Stochastic Processes; Fluctuation Phenomena; Classical Statistical Mechanics; Oscillator; Brownian Motion; Stochastic Resonance; Multiplicative Noise.
Oscillator And Pendulum With A Random Mass
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Author : Moshe Gitterman
language : en
Publisher: World Scientific
Release Date : 2015-01-05
Oscillator And Pendulum With A Random Mass written by Moshe Gitterman and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-01-05 with Science categories.
Stochastic descriptions of a harmonic oscillator can be obtained by adding additive noise, or/and three types of multiplicative noise: random frequency, random damping and random mass. The first three types of noise were intensively studied in many published articles. In this book the fourth case, that of random mass, is considered in the context of the harmonic oscillator and its immediate nonlinear generalization — the pendulum. To our knowledge it is the first book fully dedicated to this problem.Two interrelated methods, the Langevin equation and the Fokker-Planck equations, as well as the Lyapunov stability method are used for the mathematical analysis. After a short introduction, the two main parts of the book describe the different properties of the random harmonic oscillator and the random pendulum with random masses. As an example, the stochastic resonance is studied, where the noise plays an unusual role, increasing the applied weak periodic signal, and also the vibration resonance in dynamic systems, where the role of noise is played by the second high-frequency periodic signal.First and second averaged moments have been calculated for a system with different types of additive and multiplicative noises, which define the stability of a system. The calculations have been extended to two multiplicative noises and to quadratic noise. This book is useful for students and scientists working in different fields of statistical physics.
Noisy Oscillator The Random Mass Frequency Damping 2nd Edition
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Author : Moshe Gitterman
language : en
Publisher: World Scientific Publishing Company
Release Date : 2012-12-18
Noisy Oscillator The Random Mass Frequency Damping 2nd Edition written by Moshe Gitterman and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-18 with Science categories.
The properties of the harmonic oscillator with random frequency or/and random damping formed the content of the first edition. The second edition includes hundreds of publications on this subject since 2005. The noisy oscillator continues to be the subject of intensive studies in physics, chemistry, biology, and social sciences.The new and the latest type of a stochastic oscillator has also been considered, namely, an oscillator with random mass. Such model describes, among other phenomena, Brownian motion with adhesion, where the molecules of the surrounding medium not only randomly collide, but also stick to the Brownian particle for some (random) time, thereby changing its mass. This edition contains two new chapters, eight new sections and an expanded bibliography. A wide group of researchers, students and teachers will benefit from this book.
Fractional Vibrations With Applications To Euler Bernoulli Beams
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Author : Ming Li
language : en
Publisher: CRC Press
Release Date : 2024-01-15
Fractional Vibrations With Applications To Euler Bernoulli Beams written by Ming Li and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-01-15 with Technology & Engineering categories.
The book examines vibration phenomena with an emphasis on fractional vibrations using the functional form of linear vibrations with frequency-dependent mass, damping, or stiffness, covering the theoretical analysis potentially applicable to structures and, in particular, ship hulls. Covering the six classes of fractional vibrators and seven classes of fractionally damped Euler-Bernoulli beams that play a major role in hull vibrations, this book presents analytical formulas of all results with concise expressions and elementary functions that set it apart from other recondite studies. The results show that equivalent mass or damping can be negative and depends on fractional orders. Other key highlights of the book include a concise mathematical explanation of the Rayleigh damping assumption, a novel description of the nonlinearity of fractional vibrations, and a new concept of fractional motion, offering exciting additions to the field of fractional vibrations. This title will be a must-read for students, mathematicians, physicists, and engineers interested in vibration phenomena and novel vibration performances, especially fractional vibrations.
Noisy Oscillator The The First Hundred Years From Einstein Until Now
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Author : Moshe Gitterman
language : en
Publisher: World Scientific
Release Date : 2005-11-09
Noisy Oscillator The The First Hundred Years From Einstein Until Now written by Moshe Gitterman and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-11-09 with Science categories.
This book contains comprehensive descriptions of stochastic processes described by underdamped and overdamped oscillator equations with additive and multiplicative random forcing. The latter is associated with random frequency or random damping. The coverage includes descriptions of various new phenomena discovered in the last hundred years since the explanation of Brownian motion by Einstein, Smoluchovski and Langevin, such as the shift of stable points, noise-enhanced stability, stochastic resonance, resonant activation, and stabilization of metastable states. In addition to many applications in physics, chemistry, biology, medicine, economics and sociology, these discoveries have clarified the deep relationship between determinism and stochasticity, which turns out to be complimentary rather than contradictory, with noise playing both constructive and destructive roles.
Stochastic Resonance And Measurement Back Action In Nonlinear Oscillators
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Author : Lance A. Labun
language : en
Publisher:
Release Date : 2007
Stochastic Resonance And Measurement Back Action In Nonlinear Oscillators written by Lance A. Labun and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with categories.
Analytical Methods For Nonlinear Oscillators And Solitary Waves
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Author : Chu-Hui He
language : en
Publisher: Frontiers Media SA
Release Date : 2023-11-24
Analytical Methods For Nonlinear Oscillators And Solitary Waves written by Chu-Hui He and has been published by Frontiers Media SA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-24 with Science categories.
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.
Simulation Of Dynamic Systems With Matlab And Simulink
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Author : Harold Klee
language : en
Publisher: CRC Press
Release Date : 2018-02-02
Simulation Of Dynamic Systems With Matlab And Simulink written by Harold Klee and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-02 with Mathematics categories.
Continuous-system simulation is an increasingly important tool for optimizing the performance of real-world systems. The book presents an integrated treatment of continuous simulation with all the background and essential prerequisites in one setting. It features updated chapters and two new sections on Black Swan and the Stochastic Information Packet (SIP) and Stochastic Library Units with Relationships Preserved (SLURP) Standard. The new edition includes basic concepts, mathematical tools, and the common principles of various simulation models for different phenomena, as well as an abundance of case studies, real-world examples, homework problems, and equations to develop a practical understanding of concepts.
Stochastic Response Of Van Der Pol Oscillator With Two Kinds Of Fractional Derivatives Under Gaussian White Noise Excitation Project Supported By The National Natural Science Foundation Of China Grant Nos 11472212 11532011 And 11502201
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Author :
language : en
Publisher:
Release Date : 2015
Stochastic Response Of Van Der Pol Oscillator With Two Kinds Of Fractional Derivatives Under Gaussian White Noise Excitation Project Supported By The National Natural Science Foundation Of China Grant Nos 11472212 11532011 And 11502201 written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with categories.
Abstract: This paper aims to investigate the stochastic response of the van der Pol (VDP) oscillator with two kinds of fractional derivatives under Gaussian white noise excitation. First, the fractional VDP oscillator is replaced by an equivalent VDP oscillator without fractional derivative terms by using the generalized harmonic balance technique. Then, the stochastic averaging method is applied to the equivalent VDP oscillator to obtain the analytical solution. Finally, the analytical solutions are validated by numerical results from the Monte Carlo simulation of the original fractional VDP oscillator. The numerical results not only demonstrate the accuracy of the proposed approach but also show that the fractional order, the fractional coefficient and the intensity of Gaussian white noise play important roles in the responses of the fractional VDP oscillator. An interesting phenomenon we found is that the effects of the fractional order of two kinds of fractional derivative items on the fractional stochastic systems are totally contrary.