Entrainment of randomly coupled oscillator networks by a pacemaker

Entrainment by a pacemaker, representing an element with a higher frequency, is numerically investigated for several classes of random networks which consist of identical phase oscillators. We find that the entrainment frequency window of a network decreases exponentially with its depth, defined as the mean forward distance of the elements from the pacemaker. Effectively, only shallow networks can thus exhibit frequency locking to the pacemaker. The exponential dependence is also derived analytically as an approximation for large random asymmetric networks.     

Evolution of a velocity-dependent quantum forced anharmonic oscillator

The exact solution to a velocity-dependent quantum forced anharmonic oscillator is derived by using integral operators and an iteration method. The study is carried out in operational form by use of the creation and annihilation operators of the oscillator. The time development of the displacement and momentum operators of the anharmonic oscillator is given. These operators are presented as a Laplace transform and a subsequent inverse Laplace transform of suitable functionals.     

A periodically forced piecewise linear oscillator

A single-degree of freedom non-linear oscillator is considered. The non-linearity is in the restoring force and is piecewise linear with a single change in slope. Such oscillators provide models for mechanical systems in which components make intermittent contact. A limiting case in which one slope approaches infinity, an impact oscillator, is also considered. Harmonic, subharmonic, and chaotic motions are found to exist and the bifurcations leading to them are analyzed.     

受迫振子的对称性与守恒量

讨论受迫振子体系的对称性和守恒量,导出了其含时位势的具体形式,给出了相应的对称变换算符,并讨论了线谐振子体系的含时守恒量.     

Invariants and coherent states for a nonstationary fermionic forced oscillator

Invariant creation and annihilation operators and related Fock states and coherent states are built up for the system of nonstationary fermionic forced oscillator.     

Consolidated expansions for estimating the response of a randomly driven nonlinear oscillator

We consider a nonlinear oscillator driven by random, Gaussian noise. The oscillator, which is damped and has linear and cubic terms in the restoring force, is often called the Duffing Equation. The Fourier transform of the response is expanded in a series in the coefficient of the nonlinear term. This series is then squared and averaged, and each term in the resulting response spectrum series is expressed in terms of the response spectrum of the linearized harmonic oscillator (i.e., without the cubic term). Since the forcing function is Gaussian, the linear solution is Gaussian. The terms in the series for the response spectrum are then regrouped so that common quantities can be factored out. This process leads to consolidated equations for the response spectrum and the common factors. These consolidated equations are truncated in various ways, and the corresponding solutions are compared with an analog computer experiment. This technique was proposed for turbulent flow by Kraichnan and followed up by Wyld, and has yielded some good results. The numerical results indicate that the truncated consolidated equations can provide a substantial improvement over some other methods used to solve this type of problem. The methods compared with it are (1) the traditional truncated parametric expansion, (2) statistical linearization, and (3) use of the joint-normal hypothesis to express the fourth and sixth moments in terms of the second.Adapted from the Ph.D. dissertation of J. B. Morton, October 1967. Work supported by Fluid Dynamics Branch, Office of Naval Research, while J. B. M. held a N.A.S.A. traineeship.     

On the quantum motion of a generalized time-dependent forced harmonic oscillator

In this work, we use linear invariants and the dynamical invariant method to obtain exact solutions of the Schrödinger equation for the generalized time-dependent forced harmonic oscillator in terms of solutions of a second order ordinary differential equation that describes the amplitude of the classical unforced damped oscillator. In addition, we construct Gaussian wave packet solutions and calculate the fluctuations in coordinate and momentum as well as the quantum correlations between coordinate and momentum. It is shown that the width of the Gaussian packet, fluctuations and correlations do not depend on the external force. As a particular case, we consider the forced Caldirola-Kanai oscillator.     

Extended feynman formula for forced harmonic oscillator

Horváthy's modification of Feynman's original method is generalized to the path integral formula of a forced harmonic oscillator. With this new formula the propagator of a harmonic oscillator with memory is evaluated exactly beyond and at caustics.Work supported in part by the Conselho Nacional de Desenvolvimento Cientifico e Tecnólogico (CNPq), Brazil.     

Large-scale magnetic field generation by randomly forced shearing waves

A rigorous theory for the generation of a large-scale magnetic field by random nonhelically forced motions of a conducting fluid combined with a linear shear is presented in the analytically tractable limit of low magnetic Reynolds number (Rm) and weak shear. The dynamo is kinematic and due to fluctuations in the net (volume-averaged) electromotive force. This is a minimal proof-of-concept quasilinear calculation aiming to put the shear dynamo, a new effect recently found in numerical experiments, on a firm theoretical footing. Numerically observed scalings of the wave number and growth rate of the fastest-growing mode, previously not understood, are derived analytically. The simplicity of the model suggests that shear dynamo action may be a generic property of sheared magnetohydrodynamic turbulence.     

Turbulence in the randomly forced,one-dimensional Burgers flow

The randomly forced, one-dimensional Burgers flow is dealt with by the method of the characteristic functional equation. The time development of the stochastic secondary flow is studied numerically by the Monte Carlo quadrature of the integral representation of solution for two types (white and “red”) of random force fields. A turbulence-like behavior of the flow appears for a supercritical Reynolds number, and its structure is studied in detail.     

Experimental observations of periodic and chaotic regimes in a forced chemical oscillator

Experiments showing periodic and chaotic behavior in a Belousov-Zhabotinski (BZ) reaction mixture in a stirred flow reactor with periodic addition of bromide ions are presented. An alternating sequence of periodic and aperiodic regimes as a function of the period of Br^- pulses is observed in experiments. This behavior is well described by a simple model based on the results of single-pulse experiments.     

On the forced vibrations of an oscillator with a periodically time-varying mass

In this paper the forced vibrations of a linear, single degree of freedom oscillator (sdofo) with a time-varying mass will be studied. The forced vibrations are due to small masses which are periodically hitting and leaving the oscillator with different velocities. Since these small masses stay for some time on the oscillator surface the effective mass of the oscillator will periodically vary in time. Additionally, an external harmonic force will be applied to the oscillator with a time-varying mass. Not only solutions of the oscillator equation will be constructed, but also stability properties for the forced vibrations will be presented for various parameter values.     

Extended Feynman formula for time-dependent forced harmonic oscillator

Horváthy's modification of Feynman's path integral formula is generalized to the time-dependent forced harmonic oscillator. The propagator at caustics is then obtained by using its modified semi-group property. Finally, with our new formula, the propagator for a charged particle in a time-dependent electromagnetic field is evaluated exactly beyond and at caustics.     

分数阶电子振荡器的混沌及其控制

本文研究了分数阶混沌电子振荡器的混沌行为。研究表明：混沌存在于阶数低于3阶的分数阶电子振荡器中，为了说明混沌行为的连续性，本文对分数阶电子振荡器进行了降阶、升阶 （2.8—3.2阶）的仿真分析。最后，本文基于自适应Backstepping法研究了分数阶电子振荡器的混沌控制，仿真结果表明了该方法的有效性和可行性。     

Bistability, period doubling bifurcations and chaos in a periodically forced oscillator

A two parameter mathematical model for a periodically forced nonlinear oscillator is analyzed using analytical and numerical techniques. The model displays phase locking, quasiperiodic dynamics, bistability, period-doubling bifurcations and chaotic dynamics. The regions in which the different dynamical behaviors occur as a function of the two parameters is considered.     

Balancing energy to estimate damping in a forced oscillator with compliant contact

This work identifies damping parameters from compliant-contact vibration systems using an energy balance. To develop the identification algorithms, the energy loss as registered in the force-displacement relationship of the real system is expressed in terms of a theoretical model incorporating an ideal compliant contact. Two approaches, one based on the harmonic response assumption and the other directly integrating the system responses, are developed. Numerical and experimental investigations are performed to illustrate the reliability of the identification algorithms. The method is applied to an experimental industrial linear-bearing system.     

多维耦合受迫量子谐振子的普遍解

运用广义线性量子变换的普遍理论求解多维耦合受迫量子谐振子，给出了系统演化算符的矩阵元、波函数、力学量期望值和配分函数的严格表达式. 关键词： 多维耦合受迫量子谐振子 演化算符矩阵元 配分函数