弹簧摆运动的研究

由初值用差分递推方法模拟弹簧摆的运动,把小球的运动分为横向和径向两个方向,经过研究得出:初始摆角的增大会影响径向的周期运动规律,而劲度系数的变化会影响横向的周期运动规律,大的劲度系数也会对径向周期振动的幅度造成起伏,选择小的摆角和合适的劲度系数可以近似地使小球在横向和径向两个方向上都作周期性运动,且两个方向上运动的耦合影响都很小.     

Duffing方程的变分迭代解法

应用变分迭代算法分析了Dufing方程的强迫振动,得到了整个区域内(0 < ε < ∞)一致有效的近似解,其近似周期的最大相对误差小于5.66%,并得到了在整个区域内一致有效的主共振和次共振频率。     

H桥正弦逆变器的快变和慢变稳定性及混沌行为研究

正弦逆变器是一个时变非线性系统,存在快变和慢变两种尺度的稳定性.以比例控制一阶H桥正弦逆变器为例,引入了快变和慢变两种尺度,建立了H桥正弦逆变器的快变和慢变离散模型.针对快变稳定性,提出了折叠图和功率谱分析方法;针对慢变稳定性,提出周期时变非线性离散系统慢变平衡点定义和慢变稳定性定理,指出了慢变不稳定是周期时变系统混沌行为的有效判据.研究表明,所提出的方法能够很好地分析正弦逆变器出现的快变和慢变不稳定现象及混沌行为. 关键词： 周期时变离散系统 H桥正弦逆变器 快变不稳定 慢变不稳定     

互补变分原理及其在微扰理论近似中的应用

以正则变分和线性变分函数为基础，对互补变分原理作了论证，推导出二阶能量修正的上界和不受任何条件限制的下界，对具体计算方法作了详细的研究，得出互补变分原理在微扰理论近似中的应用，所求氢原子和极化率结果比一般的发法的微扰法所得结果更接近于实验值，并指出这理论可以推广应用到激发态或处理高阶修正问题。     

跃变参数混沌同步及其应用

建立了跃变参数混沌同步的数学模型，提出并证明了其同步的充分条件，在理论上分析了充分条件的可实现性.提出了跃变参数混沌同步和跃变周期同步的有效算法，借助Chua混沌系统仿真实现了参数跃变混沌同步保密通信.最后，分析了跃变参数混沌保密通信对抗现有混沌窃听方法的性能.仿真结果表明跃变参数混沌同步及其保密通信具有易实现和强保密性等优点.     

用EXCEL模拟变加速运动的尝试

利用"微元"思想借助Excel软件的计算功能推演出在变力作用下的运动规律,并可以描绘出各物理量之间的关系图像.列举了三个实例,简谐运动、洛伦兹力作用下的圆周运动、带电小球在复合场中的运动.     

参数不定的旋转圆盘在有界扰动下混沌振动的滑模变结构控制

为了消除具有不确定参数的旋转圆盘横向混沌振动,克服其对整个系统及工作状况的不利影响,假设作用在旋转圆盘上的集中力不确定且有界,并鉴于干扰的普遍存在性,对有界扰动下的旋转圆盘横向振动的四维非线性方程进行了复杂动力学特征分析,包括相轨迹图、Lyapunov指数和庞加莱映射图,这些特征加深了对其的认识,同时也证明该四维动力系统含有混沌吸引子.为了保证系统控制的鲁棒性,利用滑模变结构法,将旋转圆盘从混沌轨道先后控制到任意固定点和周期轨道,并用MATLAB模拟验证其有效性.结果证明,用滑膜变结构法能够使系统严格地跟 关键词： 旋转圆盘 混沌 滑模变结构控制 有界扰动     

椭圆曲面摆参数振动的数值计算及仿真

为研究变摆长参数振动的规律,以椭圆曲面摆装置为对象,根据刚体定轴转动定律及椭圆曲线方程,构建了椭圆曲面摆的二阶变系数齐次微分动力学方程.运用四阶龙格-库达法对方程进行数值求解,并结合MATLAB软件绘制了椭圆曲面摆振动不同的图像,给出椭圆曲面摆在无阻尼状态时的方程通解形式,在此基础上,讨论了不同参数对椭圆曲面摆振动特性的影响情况.研究表明,椭圆曲面摆与单摆振动类似,在无阻尼状态时小球摆动符合正弦函数变化规律,小球摆动周期受到阻尼系数、椭圆曲面几何尺寸、振幅等参数影响.研究结论丰富了关于变摆长单摆参数振动教学内容.     

变周期慢波系统内同步问题的研究

由于行波管的工作依赖于其慢波系统中的电子注与沿轴传输交变电磁场之间的相互作用而完成,而这样的相互作用要求沿轴传输的交变电磁场必须与电子注有着近乎同步的速度,所以慢波系统内的同步问题就成了研究行波管的一个很重要的问题.而变周期慢波系统是将一般慢波系统的周期进行变化而形成的,它可以比原周期慢波系统有着更宽的带宽,更高的互作用效率,还可以选择空间谐波.本文分析了变周期慢波系统内的空间谐波,提出了使慢波系统内的一次空间谐波一直与电子注同步所需要满足的原则,最后以变周期折叠波导为例,证明了这个原则. 关键词： 变周期 慢波系统 空间谐波 同步     

非晶态石英的变电荷分子动力学模拟

基于迭代变电荷方法,用分子动力学模拟了非晶态石英的结构与振动特征.首先利用熔化-猝火方法得到了非晶石英的平衡结构.在此基础上获得了体系不同原子对之间的对关联函数、键角分布函数和振动频谱等,结果与实验数据均符合较好.变电荷方法的计算结果表明,非晶石英体系内粒子的电荷与石英晶体内粒子电荷显著不同,并且出现了较大的涨落. 关键词： 分子动力学 变电荷 非晶石英     

Surface modification of polypropylene and compatibilization of interfaces in incompatible blends of polypropylene with polystyrene by plasma of CO2

The effect of surface modification of polypropylene (PP) film is induced by CO₂ plasma in this study. The change in chemical structures on the surface of PP film is characterized by X-ray photoelectron spectroscopy (XPS) and Fourier transform infrared (FT-IR). The polarity of modified surface of PP film is investigated by contact angle method. The compatibilization of interfaces between polypropylene and polystyrene phases in incompatible blends is studied by the treatment of plasma of CO₂. Transition layer thickness is measured by small angle light scattering (SALS).     

Threshold of femtosecond laser-induced damage in transparent materials

The rate at which conduction-band electrons (CBE) absorb laser energy is calculated by both the quantum mechanical and the classical methods. Here fused silica irradiated with a 780-nm femtosecond-pulse laser is used as an example. It is found that the rate obtained by the quantum mechanical method is about one-third of that by the classical method, and it is much less than the direct-current limit. In the flux-doubling model, the avalanche rate in fused silica is 4 I  ps^-1 obtained by the quantum mechanical method, while it is about 13.7 I  ps^-1 by the classical method, where the laser intensity I is in units of TW cm^-2. The differential equation of the evolution of CBE density is solved numerically, and it is found that the combination of CBE–hole recombination, CBE diffusion and initial CBE density (<10¹³ cm^-3) is not important. The dependence of avalanche breakdown threshold on laser-pulse duration is presented. The threshold calculated by the quantum mechanical method agrees well with experimental results, while the threshold obtained by the classical method differs greatly from the experiments. Received: 18 December 2000 / Accepted: 27 April 2001 / Published online: 27 June 2001     

Theoretical study of mesoscopic stochastic mechanism and effects of finite size on cell cycle of fission yeast

Based on a deterministic cell cycle model, the mesoscopic stochastic differential equations are theoretically derived from the biochemical reactions. The effects of the finite cell size on the cell cycle regulation in the wild type and wee1^-cdc25Δ double mutant type are numerically studied by virtue of the chemical Langevin equations. (i) When the system is driven only by the internal noise, our numerical results are in qualitative agreement well with some experimental observations and data. (ii) A parameter, which is sensitive to two resettings of M-phase promoting factor to G₂, is treated as a stochastic variable, and the system driven only by the external noise for double mutant type is investigated. (iii) When the system is driven by both the internal and external noise, a simple discussion about the combined effect for double mutant type is given. Our results imply some experimental results would be explained by introducing the appropriate internal or external noise into the cell cycle system.     

Thermonuclear fusion in the irradiation of large clusters of deuterium iodide with a field of a superatomic femtosecond laser pulse

A theory of thermonuclear fusion caused by the irradiation of deuterium-iodide clusters with the field of a superatomic femtosecond laser pulse is developed. It is based on considering the process in which the sequential above-barrier multiple internal ionization of atomic ions within a cluster is accompanied by external field ionization. The theory is illustrated by taking the example of a cluster that is formed by 10⁶ molecules of deuterium iodide and which is irradiated with a laser pulse of duration 50 fs and intensity 2×10¹⁸ W/cm² at the peak. This case is dominated by I²⁶⁺ atomic ions. The yield of neutrons from thermonuclear fusion in a deuteron-deuteron collision upon the passage of a laser pulse is calculated. The result is 10⁵ neutrons per laser pulse. The mean kinetic energy of deuterons is estimated at 50 keV. Owing to induced inverse bremsstrahlung in scattering on multiply charged atomic ions, the electron temperature increases up to 28 keV. The role of the Mie resonance in the heating of the electron component is discussed.     

Master Equation and Fokker–Planck Equation: Comparison of Entropy and of Rate Constants

A usual approximation of the master equation is provided by the Fokker–Planck equation. For chemical systems with one species, we prove generally that the prediction of the rate constant of the metastable state given by the Master equation and the Fokker–Planck approximation differ exponentially with respect to the size of the system. We show that this is related to the fact that the entropy of the metastable state is not described correctly by the Fokker–Planck equation. We prove that the rate given by the Fokker–Planck equation overestimates that rate given by the Master equation.     

超冷铯Rydberg原子寿命的测量

本文从实验上采用两步激发超冷基态原子获得超冷Rydberg原子,通过选择场电离的方法获得超冷Rydberg原子的离子信号.改变延迟时间测得Rydberg原子布居数随时间的变化关系,用两种方法拟合实验数据得到36D和34S态原子的有效寿命,与现有理论结果一致. 关键词： Rydberg原子 寿命 黑体辐射 场电离     

掺杂Fe对VH2解氢性能影响的第一性原理研究

采用密度泛函理论(DFT)的第一性原理的平面波超软赝势方法,研究了Fe掺杂对VH₂的电子结构和解氢性能的影响.通过计算Fe掺杂VH₂前后体系的合金形成热、V-H之间的重叠布居数、电子态密度、电子密度,发现Fe掺杂VH₂后,随着Fe含量增加,合金体系的晶胞参数和晶胞体积逐渐减少;体系的负合金形成热逐渐减少,且掺杂后体系的负合金形成热都比VH₂的负合金形成热小,体系的稳定性降低;电子态密度计算也显示Fe掺杂后费米能级处的电子浓度增加,体系稳定性降低;重叠布居数和电子密度计算表明掺杂后V-H之间的重叠布居数由0.1减小为0.08或0.09,V-H之间的电子密度减少,说明V和H原子之间的相互作用减弱,提高了VH₂的解氢性能.计算结果解释了实验现象. 关键词： Fe掺杂 电子结构 解氢性能 第一性原理计算     

Intensity dependence of multiphoton dissociation in formaldehyde

A new intensity-dependent measurement of multiple-photon dissociation (MPD) in H₂CO, HDCO, and D₂CO gases by the use of an intense pulsed CO₂TEA laser is reported. In this measurement the energy and duration of the laser pulses are kept constant, and the intensity is varied by irradiating the sample using concave mirrors of different focal lengths. A model calculation is used to analyze and fit the present and previous experimental MPD data of HDCO and D₂CO. In this model it is assumed that dissociation is obtained by a repeated mechanism in which coherent multiphoton excitation (CME) of the molecule to high vibration-rotation states |v, J〉 is followed by intramolecular transfer of the excitation energy (ITEE) to the other modes of the molecule. In the calculations the CME is described in the framework of the density matrix formalism with relaxations, and is used to calculate absorption from the ground state as well as absorption from excited states reached by the energy redistribution in the molecule. The ITEE process is assumed to be intensity independent and to cause a random energy distribution in each transferring process. It is found that the experimental results are consistent with the absorption of 14±4 and 17±5 photons per molecule for HDCO and D₂CO, respectively, and this is sufficient to cause their dissociation.     

Formation of the nanodots and change of the characteristics of thin magnetic films under laser irradiation

Results of experimental investigations of laser radiation interaction with the Ti, Co, NiFe, TbFe and LaSrMnO₃ films are presented. It is shown, that it is possible to improve magnetic characteristics and to obtain magnetic films with regular distribution of nanodots by the laser radiation. It is observed an increasing of magnetic permeability and the reduction of the coercive force after irradiation of the NiFe films by the nanosecond laser pulses that are induced by the substantial growth of the size of the nanodots in the process of recrystallization. Magnetic nanodots of 100–200 nm size are produced by the method of the laser cutting of the continuous magnetic films, or are formed in a nonmagnetic matrix by the diffusion in the multilayered films and oxidization of TbFe and LaSrMnO_3−x films at the irradiation of the nanosecond laser pulses.     

Scattering of light by a periodic structure in the presence of randomness IV. Limit of detection by curve fitting

In the context of scattering of light, we determine the extent of randomness within which a hidden periodic part can still be detected. The detection is carried out using a technique called the extended matched filtering, first introduced by us in this context. The earlier prediction, before our technique was introduced, had placed the limit of detection, by intensity measurements alone, at (r ₀/Λ) ∼ 0.33, where r₀ is the coherence length of light for scattering by the rough part of the surface and Λ is the wavelength of the periodic part of the surface. In our earlier works we have shown that by intensity measurements alone, the limit of detection can be taken to a much lower value of (r ₀/Λ), when the extended matched filtering method is employed. In this paper we follow the extended matched filtering method, and try to reach the lowest possible value of detection in (r ₀/Λ) by fitting the data to a polynomial. It is concluded by our numerical work that the lowest possible limit for detection from intensity measurements alone is (r ₀/Λ) = 0.11.