The parameter uniform numerical method for singularly perturbed parabolic reaction–diffusion problems on equidistributed grids

This article presents the study of singularly perturbed parabolic reaction–diffusion problems with boundary layers. To solve these problems, we use a modified backward Euler finite difference scheme on layer adapted nonuniform meshes at each time level. The nonuniform meshes are obtained by equidistribution of a positive monitor function, which involves the second-order spatial derivative of the singular component of the solution. The equidistributing monitor function at each time level allows us to use this technique to non-linear parabolic problems. The truncation error and the stability analysis are obtained. Parameter–uniform error estimates are derived for the numerical solution. To support the theoretical results, numerical experiments are carried out.     

共孔径偏振耦合分光的旋转四分之一波片相位补偿技术

 在地平式折轴望远镜中开展自适应光学激光导星实验，研究了共孔径发射接收信标激光束偏振耦合分光效率随望远镜方位角和天顶角变化的补偿技术。提出了一种由四分之一波片和法拉第旋光器构成的相位补偿器，通过旋转四分之一波片以实时补偿由于望远镜旋转导致的光路相位延迟量的变化。数值计算表明，望远镜处于任意方位角和天顶角位置时，通过1°步长旋转四分之一波片，可使补偿后的偏振分光效率理论上达到99.90％以上。实验从原理上定性地验证了该方法的有效性。只要测量出镜面的相位延迟，便可计算得到望远镜处于不同方位角和天顶角情况下有效补偿所需的四分之一波片旋转角度，据此可建立实用的旋转波片偏振补偿装置。     

共孔径偏振耦合分光系统中反射镜造成的相位延迟差的测量

 激光信标共孔径发射接收偏振分光系统的动态相位补偿需要测量望远镜各反射镜对s光和p光的相位延迟差。利用Stokes矢量和Mueller矩阵建立了物理模型，并推导出用测得的回光功率计算相位延迟差的解析式。提出一种通过实验测量回光功率计算反射镜相位延迟差的方法，解决了在0～2p范围内唯一确定反射镜相位延迟差的问题。实际测量了两块反射镜的相位延迟差，并将测量结果用于动态相位补偿偏振分光实验，验证了该方法的正确性。分析了偏振分光棱镜、法拉第旋光器以及近似计算这3个主要的测量误差源，并估计总测量误差约为1°。     

Adaptive anisotropic noise filtering for magnitude MR data

Conventional noise filtering schemes applied to magnitude magnetic resonance (MR) images tacitly assume Gauss distributed noise. Magnitude MR data, however, are Rice distributed. Not incorporating this knowledge leads inevitably to biased results, in particular when applying such filters in regions with low signal-to-noise ratio. In this work, we show how the Rice data probability distribution can be incorporated so as to construct a noise filter that is far less biased.     

Computation of complex fluid flows using an adaptive grid method

Recently the concept of adaptive grid computation has received much attention in the computational fluid dynamics research community. This paper continues the previous efforts of multiple one-dimensional procedures in developing and asessing the ideas of adaptive grid computation. The focus points here are the issue of numerical stability induced by the grid distribution and the accuracy comparison with previously reported work. Two two-dimensional problems with complicated characteristics—namely, flow in a channel with a sudden expansion and natural convection in an enclosed square cavity—are used to demonstrate some salient features of the adaptive grid method. For the channel flow, by appropriate distribution of the grid points the numerical algorithm can more effectively dampen out the instabilities, especially those related to artificial boundary treatments, and hence can converge to a steady-state solution more rapidly. For a more accurate finite difference operator, which contains less undesirable numerical diffusion, the present adaptive grid method can yield a steady-state and convergent solution, while uniform grids produce non-convergent and numerically oscillating solutions. Furthermore, the grid distribution resulting from the adaptive procedure is very responsive to the different characteristics of laminar and turbulent flows. For the problem of natural convection, a combination of a multiple one-dimensional adaptive procedure and a variational formulation is found very useful. Comparisons of the solutions on uniform and adaptive grids with the reported benchmark calculations demonstrate the important role that the adaptive grid computation can play in resolving complicated flow characteristics.     

A multiplier method with automatic limitation of penalty growth

This paper presents a multiplier method for solving optimization problems with equality and inequality constraints. The method realizes all the good features that were foreseen by R. Fletcher for this type of algorithm in the past, but which suffers from none of the drawbacks of the earlier attempts.Research sponsored by the National Science Foundation (RANN) Grant ENV76-04264 the National Science Foundation Grant ENG73-08214-A01 and the Sweden-American Foundation.     

单双层共轭系统的共轭高度对等晕角的影响

 简要介绍了传统自适应光学系统的局限性和多层共轭自适应光学基本原理。模拟了单双层共轭校正系统的共轭高度，并结合平程与垂程(HV模型)两种传输状态对系统等晕角增益作了进一步的分析。对单层共轭系统，在20 km的传输距离内，在平程中整个区域都属于等晕角放大区，共轭高度的最佳位置在传输距离的中间（约10 km处），等晕角取极大值，增益效果较好；但垂程中增益效果变差，且等晕角放大区也仅在3.6 km之内。对双层共轭系统来说，第1层共轭高度的变形镜主要对近距离畸变波前进行校正，并对整个传输距离的等晕角影响很大，是双层共轭系统的关键因素；第2层共轭高度对远距离等晕角影响较大。     

变形镜波前补偿能力的空间频域分析

 利用滤波器原理从空间频域分析了连续镜面分立驱动变形镜对波前的补偿能力。将变形镜等效为一高通滤波器，通过数值计算分析了滤波器函数与驱动器密度、高斯指数、交连值等变形镜主要参数的关系，解释了参数变化对波前拟合能力的影响。结果表明：驱动器密度是波前补偿能力的决定因素，增大高斯指数和交连值一定程度上有利于低空间频率波前的补偿。应用中应该根据待补偿波前的特征正确地选择和调整变形镜参数。     

光束旋转90°多程放大系统的波前误差校正

光束通过神光-Ⅲ原型装置四程放大系统发生了90°旋转和扩束。在四程放大系统腔镜处放置变形镜校正系统像差是一种新的自适应光学方案，推导出被校正像差与变形镜面形之间的数学关系。理论推导表明，在扩束比大于1的前提下，腔镜处变形镜可以校正系统输出的任意类型的像差，且变形镜对应的面形唯一。理论分析和计算仿真说明该方案的校正能力与像差类型和扩束比有关，扩束比增大将增强变形镜校正像散的能力，但系统旋光消像散的能力也将减弱。