1.54μmEr3+,Yb3+共掺玻璃激光器的速率方程及数值分析

LD抽运共掺Er,Yb玻璃激光器中的跃迁过程较复杂,针对双掺离子之间的能量传递和Er3+的多种跃迁过程,给出了详细的准三能级系统的速率方程,在合理简化后进行了数值分析,分析了Er3+掺杂浓度和介质长度、抽运光斑、输出镜透过率、谐振腔长、抽运光的椭圆度等因素对激光阈值及斜率效率的影响. 关键词： 1.54μm激光 Er3+玻璃 速率方程 数值分析     

NUMERICAL ANALYSIS OF QUASICONFORMAL MAPPINGS BY CIRCLE PACKINGS

Thurston proposed that conformal mappings can be approximated by circle packing isomorphisms and the approach can be implemented efficiently. Based on the circle packing methods the rate of convergence of approximating solutions for quasiconformai mappings in the plane is discussed.     

Approximating Clarke’s subgradients of semismooth functions by divided differences

We show that the algorithm presented in an earlier paper by Studniarski (Numer. Math., 55:685–693, 1989) can be applied, after only a small modification, to approximate numerically Clarke’s subgradients of semismooth functions of two variables. Results of computational testing of this modified algorithm are also reported.      

圆外区域求解Helmholtz方程

1引言许多科学和工程计算问题都可以归结为无界区域上的偏微分方程边值问题．而求解椭圆方程边值问题的常用技术是有限元方法,可是对于无界区域,在用有限元方法求解时,往往遇到困难．最简单的办法显然是直接略去区域的无界部分求解,但这样做或者导致过低的计算精度,或者要付出很高的计算代价．边界归化,即将求解偏微分方程边值问题转化为边界积分方程,是求解某些无界区域问题的强有力的手段．自70年代以来,有限元和     

Passively Q-switched Self-frequency Doubling NYAB laser with GaAs Saturable Absorber

By using a passive Q-switch with GaAs saturable absorber, the Q-switched self-frequency doubling NYAB laser at 0.531μm has been successfully realized. The pulse width and the single pulse energy are measured. The numerical solutions of the coupling wave rate equations are in agreement with the experimental results.     

刚性方程组M~.(t)+C~.X(t)+KX(t)=F(t)解的探讨

讨论了刚性常微分方程组(1)的解析解和数值解,给出了解的一般形式和应用该算法的数值例子.     

激光穿透焊的三维数值模拟

本文对激光穿透焊进行了三维数值模拟，除考虑焊接速度影响外，还研究了Ｍａｒａｎｇｏｎｉ对流对熔池流动与传热的影响。将三维数值模拟结果与相应的二维模拟结果进行了比较，结果表明，Ｍａｒａｎｇｏｎｉ对流对熔池的形成有很大的影响，因此不可忽略。本文还给出了估计激光穿透焊中蒸气孔尺寸与焊接热效率的方法。     

Extension of a combined analytical/numerical initial value problem solver for unsteady periodic flow

Here we describe analytical and numerical modifications that extend the Differential Reduced Ejector/ mixer Analysis (DREA), a combined analytical/numerical, multiple species ejector/mixing code developed for preliminary design applications, to apply to periodic unsteady flow. An unsteady periodic flow modelling capability opens a range of pertinent simulation problems including pulse detonation engines (PDE), internal combustion engine ICE applications, mixing enhancement and more fundamental fluid dynamic unsteadiness, e.g. fan instability/vortex shedding problems. Although mapping between steady and periodic forms for a scalar equation is a classical problem in applied mathematics, we will show that extension to systems of equations and, moreover, problems with complex initial conditions are more challenging. Additionally, the inherent large gradient initial condition singularities that are characteristic of mixing flows and that have greatly influenced the DREA code formulation, place considerable limitations on the use of numerical solution methods. Fortunately, using the combined analytical–numerical form of the DREA formulation, a successful formulation is developed and described. Comparison of this method with experimental measurements for jet flows with excitation shows reasonable agreement with the simulation. Other flow fields are presented to demonstrate the capabilities of the model. As such, we demonstrate that unsteady periodic effects can be included within the simple, efficient, coarse grid DREA implementation that has been the original intent of the DREA development effort, namely, to provide a viable tool where more complex and expensive models are inappropriate. Copyright © 2002 John Wiley & Sons, Ltd.     

数值孔径与数字剪切散斑干涉条纹亮度的关系

分析了数字剪切散斑干涉条纹图的形成理论，并获得了条纹亮度与摄象机数值孔径等参数的精确关系式，从理论分析和实验验证均得出在采用小的摄象机数值孔径和３ｍＷ Ｈｅ－Ｎｅ激光器的情况下，仍可获得比较满意的数字剪切散斑干涉条纹图，理论工作及其结论对于进行数字剪切散斑干涉实验的最佳参数选择具有指导作用。     

大规模界约束优化的子空间截断牛顿法

给出了大规模界约束优化的一个子空间截断牛顿法。利用截断牛顿法修正非有效约束所对应的变量，用投影梯度法修正有效约束所对应的变量，文中证明了方法的整体收敛性，并对方法进行了数值试验，且与子空间有限内存拟牛顿法进行了数值比较。