Nonlinear propagation and ponderomotive force of electromagnetic plane waves of arbitrary polarisation in a magnetoplasma

Ponderomotive self-effects of plane uniform electromagnetic modes of a magnetoplasma introduce stop- and pass-band structures in the dispersion characteristics of the waves resulting in Bragg reflection, etc.     

周期性外力驱动的混沌摆

为了简单直观地呈现混沌现象,研制了受周期驱动力驱动的混沌摆实验系统. 实验系统由力学机构、采集机构和数据处理分析仪组成. 力学机构是受周期外力驱动的复摆;采集机构采用无触点角度传感器,通过串口通信实时将数据传输给计算机;数据处理分析仪用虚拟仪器平台LabVIEW软件编程实现. 该系统可实时显示反映混沌基本特征的角度时序图、角速度时序图和相图.     

Nonlinear ponderomotive force effects on plasma resonance cones

The nonlinear equation is derived governing the field on two-dimensional resonance cones in a plasma for all frequencies for which the resonance cones exist. This equation reduces to the modified Korteweg-de Vries equation only if the electric field is real.     

外周期力驱动的倒摆混沌运动演示仪

设计并制作了受周期外力驱动的倒摆演示实验装置．利用自主开发的软件可自动演示和记录摆球运动状态的时间序列并存储实验数据．通过改变摆长、驱动电压，观察到该系统存在通过倍周期分岔通向混沌的过程．     

Generation of magnetic fields by the non-stationary ponderomotive force of electromagnetic waves in plasmas with streaming electrons

It is shown that the non-stationary ponderomotive force of large amplitude electromagnetic waves in plasmas with streaming electrons can spontaneously create magnetic fields. The present result may account for the magnetic fields in laser-produces plasmas, in cosmic plasmas, as well as in galactic and inter-galactic spaces.     

Nonlinear localized waves in a periodic medium

We analyze the existence and stability of nonlinear localized waves in a periodic medium described by the Kronig-Penney model with a nonlinear defect. We demonstrate the existence of a novel type of stable nonlinear band-gap localized state, and also reveal a generic physical mechanism of the oscillatory wave instabilities associated with the band-gap resonances.     

Nonlinear self-trapping of matter waves in periodic potentials

We report the first experimental observation of nonlinear self-trapping of Bose-condensed 87Rb atoms in a one-dimensional waveguide with a superimposed deep periodic potential . The trapping effect is confirmed directly by imaging the atomic spatial distribution. Increasing the nonlinearity we move the system from the diffusive regime, characterized by an expansion of the condensate, to the nonlinearity dominated self-trapping regime, where the initial expansion stops and the width remains finite. The data are in quantitative agreement with the solutions of the corresponding discrete nonlinear equation. Our results reveal that the effect of nonlinear self-trapping is of local nature, and is closely related to the macroscopic self-trapping phenomenon already predicted for double-well systems.     

Propagation of travelling waves in sub-excitable systems driven by noise and periodic forcing

It has been reported that traveling waves propagate periodically and stably in sub-excitable systems driven by noise [Phys. Rev. Lett. 88, 138301 (2002)]. As a further investigation, here we observe different types of traveling waves under different noises and periodic forces, using a simplified Oregonator model. Depending on different noises and periodic forces, we have observed different types of wave propagation (or their disappearance). Moreover, reversal phenomena are observed in this system based on the numerical experiments in the one-dimensional space. We explain this as an effect of periodic forces. Thus, we give qualitative explanations for how stable reversal phenomena appear, which seem to arise from the mixing function of the periodic force and the noise. The output period and three velocities (normal, positive and negative) of the travelling waves are defined and their relationship with the periodic forces, along with the types of waves, are also studied in sub-excitable system under a fixed noise intensity. Electronic supplementary material Supplementary Online Material     

Stochastic resonance of a damped oscillator with frequency fluctuation driven by a periodic external force

<正>Considering a damped linear oscillator model subjected to a white noise with an inherent angular frequency and a periodic external driving force,we derive the analytic expression of the first moment of output response,and study the stochastic resonance phenomenon in a system.The results show that the output response of this system behaves as a simple harmonic vibration,of which the frequency is the same as the external driving frequency,and the variations of amplitude with the driving frequency and the inherent frequency present a bona fide stochastic resonance.     

Distribution functions for the Brownian motion of particles in a periodic potential driven by an external force

The stationary distribution functions for the Brownian motion of particles driven by an external force are calculated by expanding the velocity part into Hermite functions and the space part into a Fourier series. Insertion into the Fokker-Planck equation leads to a matrix continued fraction for the lowest two coefficients of the Hermite functions. Higher order terms are found by reverse iteration. Results are shown for a cosine potential. The good convergence allows the calculation in the full range of damping constants. For small friction the distribution function is in good agreement with previous results and the maxima are given by the solutions without noise.     

Nonlinear periodic waves on the charged surfactant-covered surface of a viscous fluid

The profile of a periodic capillary-gravitational wave propagating over the surfactant-covered surface of a fluid is found in the second-order approximation in initial deformation amplitude. It is shown that the surfactant film appreciably affects the intensity of nonlinear interaction between harmonics constituting the nonlinear wave.     

Nonlinear periodic waves on the charged surface of a viscous finite-conductivity fluid

The profile of a periodic capillary-gravitational wave propagating over the surface of a viscous finite-conductivity fluid is found in a second-order approximation in initial deformation amplitude. When the finiteness of the rate with which the potential of the fluid smoothes out as capillary-gravitational waves travel over its free surface is taken into account, the intensity of nonlinear interaction between the waves changes. This intensity is found to depend on the electric charge surface density, conductivity of the fluid, and wavenumbers. The finiteness of the potential smoothing rate influences the nonlinear interaction between the waves nonmonotonically.     

Nonlinear periodic waves on the charged free surface of a perfect fluid

Analytical expressions for the profile of a nonlinear wave and for a nonlinear correction to its frequency are derived in the fourth-order approximation in amplitude of a periodic traveling wave on a uniformly charged free surface of an infinitely deep perfect incompressible fluid. It is found that corrections to the amplitude and frequency of the nonlinear wave are absent if the problem is solved under the initial condition that provides the constancy of the first-order amplitude and wavelength in time. Nonlinear analysis of conditions for instability of the fluid free surface against the surface charge shows that the critical charge density and wave-number of the least stable wave are not constant (as in the linear theory) and decrease with growing amplitude of the wave.     

Nonlinear ion acoustic solitary waves in electron-positron-ion inhomogeneous plasma

A theoretical investigation has been made for studying the propagation of ion-acoustic waves (IAWs) in a weakly inhomogeneous, collisionless, unmagnetized, three-component plasmas, whose constituents are inertial ions, nonthermal electrons, and Boltzmannian positrons. Employing reductive perturbation method (RPM), the variable coefficients Korteweg-de Varies equation (KdV) is derived. At the critical ion density, the KdV equation is not suitable for describing the system. Thus, a new set of stretched coordinates is considered to derive the modified variable coefficients KdV equation. Above (below) this critical point the system supports compressive (rarefactive) solitons. The effect of plasma parameters on the soliton profile has been considered. It has been shown that the width and the amplitude of the soliton affected by wave propagation speed, ratio of positron-to-electron density, and nonthermal parameter.     

Quantum system driven by periodic external field

A quantum Floquet Theory for a periodically driven system is studied. For this purpose the periodic external fields are changed to have an increasing amplitude with exp(t), where is an infinitestimal positive number to be taken to be zero at the end. By using the expansions in terms of inverse powers of the driving frequency, periodic factors of the time evolution operator are factorized successively. Each step corresponds to a periodically driven system with different strength of external field. This approach produces a time-independent effective Hamiltonian. The effectiveness of the method is examined by applying it to simple models; 1) a forced harmonic oscillator, 2) a particle in the double-well potential, and 3) a hydrogen atom in an electric potential.     

Nonlinear capillary-gravitational periodic waves on the charged surface of a finite-thickness viscous liquid

An analytical expression for the time evolution of the profile of a nonlinear periodic capillary-gravitational wave traveling over the charged surface of a viscous incompressible finite-thickness liquid is found. The calculation is carried out in the second order of smallness in wave amplitude. It is shown that the dependence of a nonlinear correction to a linear solution on the liquid viscosity and liquid layer thickness changes qualitatively in going from thick to thin liquid layers.