周期运动观测实验仪

当周期运动超出视觉停留范围时,直接观测周期运动(如转动、振动)就较为困难.利用计算机进行图像采集处理,既不直观,价格又不菲.为此,设计了周期运动观测实验仪.该仪器利用锁相成像观测法观测周期运动的物体,设置光源闪烁频率与周期运动频率一致,当光源开启时间足够短时,即可获得锁相状态下物体的准静态图像.     

一类特殊非线性振子周期运动的分析

本文从能量积分出发推导出F＝-cx^n类型的特殊非线性振子运动的周期振幅关系式，并得到一些归纳性结论。     

单摆运动周期的近似解

导出了两个简单、衫、精度高的单摆运动周期近似公式,并指出在数学及研究等工作中应注意近似计算方法的应用。     

一类非线性动力系统的稳定性及周期运动

根据“库仑扭秤”实验的原理提出了一个非线性动力系统模型,分析了其稳定性及其周期运动．     

光学双稳态中从三频准周期运动过渡到混沌

研究了在绝热近似条件下具有两个时间延迟反馈迴路的混合光学双稳态中动力学行为。在此模型中,该系统可由高维映象来描写增加输入光强保持两时延比ω=3/5,观察到了从三频准周期运动到混沌的过渡。此结果对理解湍流有重要意义。 关键词：     

电磁阻尼落体运动实验仪研究

设计了电磁阻尼落体实验仪,可以定量研究受电磁阻尼的落体运动过程,在不同的阻尼条件下验证速度和路程公式,并计算出阻尼系数.     

基于MATLAB中SIMULINK的准周期弹跳运动的仿真模拟

使用MATLAB/SIMULINK仿真软件建立了刚性小球在谐振桌面上做准周期性弹跳运动的动力学模型,对小球在不同倍频下的准周期运动进行了仿真模拟,并得到了小球运动的相图。结果表明：控制参数的选取对小球的动力学行为有着很大的影响。     

单摆周期的相图求法

对单摆相图作了讨论,并由相图求出了单摆的运动周期。     

地球磁层电磁场中粒子引导中心漂移运动模型的周期轨

运用Mawhin重合度理论探讨了一类非线性问题的周期解,然后将其应用于地球磁层电磁场中粒子引导中心漂移运动模型的周期轨的研究,得到了一定条件下该模型存在周期轨的结果.     

基础水平运动的弹簧摆的周期解与稳定性

针对基础水平运动的弹簧摆的非线性动力学响应进行研究,利用拉格朗日方程建立了系统的动力学方程.将离散傅里叶变换、谐波平衡法以及同伦延拓方法相结合,对系统的周期响应进行求解,避免了传统方法计算中使用泰勒展开引起的小振幅的限制,与数值计算结果的对比表明该求解方法具有较高的精确度.利用Floquet理论分析了周期响应的稳定性,给出了基础运动振幅和频率对系统周期响应的影响.研究发现:对应某些基础频率和振幅,系统的周期响应可能发生Hopf分岔;利用数值计算研究了Hopf分岔后系统响应随基础频率和振幅的变化,发现系统出现了倍周期运动、拟周期运动和混沌等复杂的动力学行为.研究表明系统进入混沌的主要路径是拟周期环面破裂和阵发性.     

Periodic Motion of Atoms Near a Charged Wire

We study the classical motion of an atom in the vicinity of an infinite straight wire which carries an oscillating uniform charge. This system has been proposed as a mechanism for trapping cold neutral atoms. The parameters of the problem are the magnitude Q and frequency of oscillation of the charge, the mass M and polarizability of the atom, and the angular momentum L of the atom about the wire. For 0 and 2MQ ² greater than, but close to, L ², we prove that the atom's radial motion is periodic (with period 2/), and that the atom moves in a helical path around the wire. For 2MQ ² L ² we prove that the atom must either collide with the wire or else escape to infinity in the radial direction.     

Twist Property of Periodic Motion of an Atom Near a Charged Wire

We study the Lyapunov stability of periodic motion of an atom in the vicinity of an infinite straight wire with an oscillating uniform charge, which serves as a mechanism for trapping cold neutral atoms. It is proved by King and Leséniewski that the system has classical periodic motion for a certain range of parameters. In this Letter, we will prove, using the Birkhoff Normal Forms and Morse Twist Theorem, that such a periodic state is of twist type. As a result, besides the stability of the periodic state in the sense of Lyapunov, the system has infinitely many interesting bound states such as subharmonics and quasi-periodic states.     

基于图像视觉作动控制的寿命试验台研制

为实现飞机阻力伞锁寿命试验的自动化检测与控制,针对产品的结构特点和寿命试验要求,设计了电液伺服加载装置模拟开伞载荷,利用特殊设计的作动机构实现锁的自动锁闭,采用基于OTSU全局阈值选取算法的图像分割及特征识别技术,进行产品锁闭状态的非接触式检测,以检测结果为驱动信号,实现了“挂载-锁闭-加载-卸载-开锁”的自动循环控制,多批次试验应用表明,系统工作稳定、可靠,显著提升了长周期寿命试验项目的工作效率和质量控制水平。     

Velocity Multistability vs. Ergodicity Breaking in a Biased Periodic Potential

Multistability, i.e., the coexistence of several attractors for a given set of system parameters, is one of the most important phenomena occurring in dynamical systems. We consider it in the velocity dynamics of a Brownian particle, driven by thermal fluctuations and moving in a biased periodic potential. In doing so, we focus on the impact of ergodicity—A concept which lies at the core of statistical mechanics. The latter implies that a single trajectory of the system is representative for the whole ensemble and, as a consequence, the initial conditions of the dynamics are fully forgotten. The ergodicity of the deterministic counterpart is strongly broken, and we discuss how the velocity multistability depends on the starting position and velocity of the particle. While for non-zero temperatures the ergodicity is, in principle, restored, in the low temperature regime the velocity dynamics is still affected by initial conditions due to weak ergodicity breaking. For moderate and high temperatures, the multistability is robust with respect to the choice of the starting position and velocity of the particle.     

Alternative Simulating Technique for Periodic Motion in the Presence of Multiplicative White Noise

An effective approach for simulating the periodic motion of an overdamped particle subjected to a multiplicative white-noise source is described. The accurate calculations for the velocity of the particle and its correlation function can be realized by introducing an inertial term. The results show that fluctuation around a time-averaged quantity increases with decreasing time step in the overdamped white-noise algorithm, however, a massive white-noise technique greatly reduces this spurious drift. In particular, the present algorithm converges on the correct values of the calculated quantities, while the mass of the particle approaches to zero.     

Chaotic Behavior of a Brownian Particle in a Periodic Potential

The classical deterministic dynamics of a Brownian particle with a time-dependent periodic perturbation in a spatially periodic potential is investigated. We have constructed a perturbed chaotic solution near the heteroclinic orbit of the nonlinear dynamics system by using the Constant-Variation method. Theoretical analysis and numerical result show that the motion of the Brownian particle is a kind of chaotic motion. The corresponding chaotic region in parameter space is obtained analytically and numerically.     

Chaotic Behavior of a Brownian Particle in a Periodic Potential

The classical deterministic dynamics of a Brownian particle with a time-dependent periodic perturbation in a spatially periodic potential is investigated. We have constructed a perturbed chaotic solution near the heteroclinic orbit of the nonlinear dynamics system by using the Constant-Variation method. Theoretical analysis and numerical result show that the motion of the Brownian particle is a kind of chaotic motion. The corresponding chaotic region in parameter space is obtained analytically and numerically.     

Testing of Multifractional Brownian Motion

Fractional Brownian motion (FBM) is a generalization of the classical Brownian motion. Most of its statistical properties are characterized by the self-similarity (Hurst) index 0<H<1. In nature one often observes changes in the dynamics of a system over time. For example, this is true in single-particle tracking experiments where a transient behavior is revealed. The stationarity of increments of FBM restricts substantially its applicability to model such phenomena. Several generalizations of FBM have been proposed in the literature. One of these is called multifractional Brownian motion (MFBM) where the Hurst index becomes a function of time. In this paper, we introduce a rigorous statistical test on MFBM based on its covariance function. We consider three examples of the functions of the Hurst parameter: linear, logistic, and periodic. We study the power of the test for alternatives being MFBMs with different linear, logistic, and periodic Hurst exponent functions by utilizing Monte Carlo simulations. We also analyze mean-squared displacement (MSD) for the three cases of MFBM by comparing the ensemble average MSD and ensemble average time average MSD, which is related to the notion of ergodicity breaking. We believe that the presented results will be helpful in the analysis of various anomalous diffusion phenomena.     

不同管口浸没方式下气泡运动特性实验研究

为了对比研究不同管口浸没方式下气泡的运动特性,通过可视化实验揭示了顶部、侧部和底部三种管口浸没方式下的气泡上升运动过程,得到了气泡形状、等效直径、位移、速度以及高宽比的变化规律,通过获得相邻气泡质心间垂直距离定量表征了气泡在上升过程中的紊乱程度.研究结果表明,顶部管口浸没方式下的气泡形态明显区别于侧部和底部管口浸没方式...