Optimal bounded control of harmonically and stochastically excited strongly nonlinear oscillators

A procedure for designing optimal bounded control to minimize the response of harmonically and stochastically excited strongly nonlinear oscillators is proposed. First, the stochastic averaging method for controlled strongly nonlinear oscillators under combined harmonic and white noise excitations using generalized harmonic functions is introduced. Then, the dynamical programming equation for the control problem of minimizing response of the systems is formulated from the partially completed averaged Itô equations by using the dynamical programming principle. The optimal control law is derived from the dynamical programming equation and control constraint without solving the dynamical programming equation. Finally, the stationary probability density of the amplitude and mean amplitude of the optimally controlled systems are obtained from solving the reduced Fokker–Planck–Kolmogorov equation associated with fully completed averaged Itô equations. An example is given to illustrate the proposed procedure and the results obtained are verified by using those from digital simulation.     

The design of autonomous DNA nano-mechanical devices: Walking and rolling DNA

We provide designs for the first autonomousDNA nanomechanical devices that execute cycles of motion without external environmental changes. These DNA devices translate along a circular strand of ssDNA and rotate simultaneously. The designs use various energy sources to fuel the movements, include (i) ATP consumption by DNA ligase in conjunction with restriction enzyme operations, (ii) DNA hybridization energy in trapped states, and (iii) kinetic (heat) energy. We show that each of these energy sources can be used to fuel random bidirectional movements that acquire after n steps an expected translational deviation of O(√n). For the devices using the first two fuel sources, the rate of stepping is accelerated over the rate of random drift due to kinetic (heat) energy. Our first DNA device, which we call walking DNA, achieves random bidirectional motion around a circular ssDNA strand by use of DNA ligase and two restriction enzymes. Our other DNA device, which we call rolling DNA, achieves random bidirectional motion without use of DNA ligase or any restriction enzyme, and instead using hybridization energy. We also describe how to modify the design for the rolling DNA device to include a ``latching mechanism' that fixes the wheels position at specified location along the road, so as to provide for overall unidirectional translational movement. This revised version was published online in June 2006 with corrections to the Cover Date.     

晶振信号同步GPS信号产生高精度时钟的方法及实现

GPS接收机输出的秒脉冲信号存在较大的随机误差，但不存在累计误差。晶振时钟信号的随机误差较小，但存在较大的累计误差。文中根据GPS时钟信号与晶振时钟信号精度互补的特点，建立了晶振信号同步GPS信号的一元二次回归数学模型，估计出GPS时钟随机误差的统计方差和晶振的累计误差；对晶振时钟进行实时修正，产生高精度时钟，并预测了修正后的时钟精度。高精度时钟发生装置已成功地应用于电力系统暂态变化过程的异地同步记录。     

激光外差探测中的全息技术

利用全息技术对本振光束进行调制以实现与信号光束的匹配，进而提高外差效率的原理及实施方法，介绍了作为调制器用的全息位相光栅的研制技术，为在外差探测系统中应用全息技术提供了依据。     

一类非线性振子中有界噪声诱发的混沌运动

研究谐和外力与有界噪声激励联合作用下的一类非线性振子的混沌运动。利用Melnikov方法，通过计算扰动系统的Melnikov积分，分析了系统在参数发生变化时的同宿分岔，得出系统产生混沌运动的参数阈值，并讨论了有界噪声激励对系统的混沌运动的影响。最后利用数值方法模拟了系统的安全盆的侵蚀状况，并进一步通过计算系统运动的Lyapunov指数，给出了由噪声诱发的混沌运动与噪声激励下非混沌运动之间的差别。     

达芬-谐波振子的改进解析逼近解

研究达芬-谐波振子的解析逼近解。所谓达芬-谐波振子是指当位移远小于1时，系统可化为三次非线性振子，而当位移远大于1时，该系统则化为线性谐波振子。通过将变形后的控制方程的线性化与谐波平衡法组合起来，我们建立了达芬-谐波振子频率及周期解的改进解板逼近。改进的解析逼近在振幅的全部取值范围内，包括振幅趋于零及无穷的情况，都有令人非常满意的精度。     

利用辛算法求解谐振子薛定谔方程误差分析

通过谐振子实例揭示了利用辛算法求解薛定谔方程所得波函数的相对误差变化的规律性 .通过计算发现任一时刻波函数在各个x格点处的相对误差完全相同 .波函数实数部分和虚数部分的相对误差随着时间的推演均周期性地在正数和负数之间来回变动 ,其周期为 62 8步或说是πs .波函数的实数部分和虚数部分的相对误差之间有类似于不确定关系的特点 .一个相对误差趋向于无穷小时另一个相对误差趋向于无穷大 .两者的乘积为一稳定的小数 .随着时间的推进这一小数的绝对值缓慢增大     

用复合振子模型计算纳米尺度滑动摩擦力的研究

以光滑界面摩擦为研究对象,探讨用复合振子模型计算纳米尺度滑动摩擦力的原理和方法,推导出滑动摩擦力和摩擦因数的计算公式,并用原子力显微镜探针在硅试样和云母试样上做扫描实验进行验证。实验值与理论计算值的对比结果表明,两者所反映的规律基本一致,表明所提出的理论和方法可行。研究表明,滑动摩擦力与接触面积成线性增长关系,并随宏观振子横向刚度的增大而减小,由于可通过改变摩擦表面的几何形貌来改变宏观振子的横向刚度,因此这一结论将为摩擦控制提供一种新途径。     

On a driven nonlinear circuit and chaotic behaviour

Abstract

The chaotic behaviour of the sinusoidally driven nonlinear circuit proposed by Hunt is investigated. The results are compared with those from other driven nonlinear circuits.     

3.705 μm紧凑型光参量振荡器

报道了一种基于工程应用的3.705 μm紧凑型高稳定性光参量振荡器。采用半导体制冷、强制气体对流冷却和热管导热技术相结合的方式,对主振荡功率放大结构的掺Yb光纤泵浦模块泵浦过程中产生的废热进行有效管理,再将经过耦合后的泵浦光注入到使用温控炉精确控温的PPMgLN晶体,在重复频率为55.56 kHz时,获得了功率不稳定度优于1.5%的1.78 W,脉冲宽度120 ns,峰值波长3.705 μm的线偏中红外激光输出,光光转换效率为12.6%。