Response of line focus acoustic microscope to specimen containing a subsurface crack

A numerical model is presented to calculate V(z) and V(x, z) curves for a line focus acoustic microscope and a specimen containing a subsurface crack. In this model, a Gaussian beam which is tracked through the lens into the coupling fluid and into the specimen, interacts with the crack. The numerical approach is based on the solution of singular integral equations by the boundary element method. The system of singular integral equations follows from the conditions at the interface of the coupling fluid and the specimen and on the faces of the crack. An electromechanical reciprocity relation is used to express the voltage at the terminals of the microscope's transducer in terms of the calculated incident and back-scattered fields. V(z) and V(x, z) curves are presented for various locations and orientations of the crack. The characteristic features of the V(z) and particularly the V(x, z) curves, as they relate to crack configuration, are discussed in some detail.     

Higher-order implicit strong numerical schemes for stochastic differential equations

Higher-order implicit numerical methods which are suitable for stiff stochastic differential equations are proposed. These are based on a stochastic Taylor expansion and converge strongly to the corresponding solution of the stochastic differential equation as the time step size converges to zero. The regions of absolute stability of these implicit and related explicit methods are also examined.     

Indirect boundary element method for unsteady linearized flow over prolate and oblate spheroids and hemispheroidal protuberances

The indirect boundary element method was used to study the hydrodynamics of oscillatory viscous flow over prolate and oblate spheroids, and over hemispheroidal bodies hinged to a plate. Analytic techniques, such as spheroidal coordinates, method of images, and series representations, were used to make the numerical methods more efficient. A novel method for computing the hydrodynamic torque was used, since for oscillatory flow the torque cannot be computed directly from the weightings. Instead, a Green's function for torque was derived to compute the torque indirectly from the weightings. For full spheroids, the method was checked by comparing the results to exact solutions at low and high frequencies, and to results computed using the singularity method. For hemispheroids hinged to a plate, the method for low frequencies was checked by comparing the results to previous results, and to exact solutions at high frequencies. Copyright © 2004 John Wiley & Sons, Ltd.     

一类非线性弹簧振子的周期性振动

本文用数值计算的方法讨论了一类非线性弹簧振子的周期性振动及其特点．     

Kinetics and equilibrium of small metallic clusters: Ab initio confinement molecular dynamics study of 4

The ab initio molecular dynamics (AIMD) [1] is combined with the heuristic, successive confinement method of surveying a potential energy surface (PES) [2], thereby offering a framework for the simulation study of kinetics and equilibrium properties of metallic clusters. This approach is applied to the study of Au₄, a cluster possessing a simple but specific PES, which consists of very shallow and deep basins and due to this presents a challenge to the conventional AIMD methods. Among other things, the probabilities of the transitions between isomers have been found, and on this basis, both the time-dependent and equilibrium populations of the isomers have been calculated for the conditions typical of the NeNePo experiments [3] in the femtosecond pump-probe spectroscopy.     

延迟微分方程单支方法的非线性稳定性

本文讨论延迟微分方程单支方法的非线性稳定性 .对于 Kα,β,γ类非线性延迟微分方程 ,我们证明带有线性插值的 G( c,p,q) -代数稳定的单支方法当 c≤ 1时是 GR( p/2 ,q/2 ) -稳定及弱 GAR( p/2 ,q/2 ) -稳定的 ,当 c<1时是 GAR( p/2 ,q/2 ) -稳定的 .最后的数值试验表明了上述结论的正确性 .     

直流电弧等离子体炬的特性研究

介绍了局部热力学平衡下描述直流电弧等离子体炬的磁流体力学模型，采用数值模拟方法研 究了等离子体炬内等离子体的传热和流动特性、湍流对等离子体炬内等离子体特性的影响， 以及等离子体炬运行参数对等离子体特性的影响.将数值模拟结果与已有的实验结果进行了 比较. 关键词： 等离子体炬 磁流体力学 数值模拟     

硅色敏器件对复色光色差辨识能力的数值分析

对复色光的光谱功率分布和色敏器件光谱响应的实验曲线进行了函数拟合，采用Mathematica 4．2计算了具有不同峰值波长和半高宽的高斯分布的复色光在色敏器件中产生的电流比．计算结果表明，待测复色光的峰值波长和半高宽变化对两种典型的色敏器件的输出信号影响的权重比分别为100：1和10：1。权重比说明色敏器件的输出电流比随峰值波长和半高宽的变化非常灵敏，但两者权重不同，其中峰值波长的变化影响更为显著，是影响复色光颜色变化的主要因素．数值分析的结果表明，硅双结色敏器件对复色光色差有良好的辨识能力．两种器件权重比的差异说明了器件制作工艺与其辨识能力的关系，为器件合理设计提供了理论依据．     

微扰影响下组合孤波的传输稳定性研究

针对最近发现的高阶非线性薛定锷方程的组合孤波解，我们数值研究了它在受到包括幅度偏离、参数条件偏离以及随机噪声等不同初始扰动后的传输特性。结果表明一定的精确脉冲在不同的扰动下有类似的稳定趋势。     

用于高数值孔径物镜的可调光瞳滤波器

根据矢量衍射理论，提出了一种用于提高高数值孔径显微物镜纵向分辨率的可调二元环形光瞳滤波器，通过改变滤波器的环半径获得不同的纵向分辨率，并利用共焦显微术点扩散函数的乘积性大大地降低了旁瓣相对主瓣的比值。模拟结果表明，这种新型滤波器不仅可以提高高数值孔径物镜的纵向分辨率，同时基本上不影响横向分辨率。