Reduced Functions, Gradients and Hessians from Fixed-Point Iterations for State Equations

In design optimization and parameter identification, the objective, or response function(s) are typically linked to the actually independent variables through equality constraints, which we will refer to as state equations. Our key assumption is that it is impossible to form and factor the corresponding constraint Jacobian, but one has instead some fixed-point algorithm for computing a feasible state, given any reasonable value of the independent variables. Assuming that this iteration is eventually contractive, we will show how reduced gradients (Jacobians) and Hessians (in other words, the total derivatives) of the response(s) with respect to the independent variables can be obtained via algorithmic, or automatic, differentiation (AD). In our approach the actual application of the so-called reverse, or adjoint differentiation mode is kept local to each iteration step. Consequently, the memory requirement is typically not unduly enlarged. The resulting approximating Lagrange multipliers are used to compute estimates of the reduced function values that can be shown to converge twice as fast as the underlying state space iteration. By a combination with the forward mode of AD, one can also obtain extra-accurate directional derivatives of the reduced functions as well as feasible state space directions and the corresponding reduced or projected Hessians of the Lagrangian. Our approach is verified by test calculations on an aircraft wing with two responses, namely, the lift and drag coefficient, and two variables, namely, the angle of attack and the Mach number. The state is a 2-dimensional flow field defined as solution of the discretized Euler equation under transonic conditions.     

用数码相机实现未琅禾费衍射测量细丝直径

介绍利用激光获得丝夫琅禾费衍射图样，并采用数码相机实现计算机辅助非接触自动测量细丝直径的方法，以及将其用于设计性实验的尝试。     

A reference solution for phase change with convection

A reference solutions for phase change involving convection in the melt is currently missing. In the present study, we focus on the problem of melting of pure tin in a square cavity heated from the side, which is used as a benchmark test problem. The mathematical model used for the simulations is based on the enthalpy formulation. Extensive numerical computations are performed with grids as fine as 800 × 800. The convergence of the numerical solution is demonstrated and its level assessed. Data values and plots are provided for use as a reference solution. Copyright © 2005 John Wiley & Sons, Ltd.     

化学测量仪器检定/校准有关问题的探讨

介绍了化学测量仪器的分类、特点、检定/校准的必要性及化学计量检定/校准的现状,分析了化学计量标准的特点,探讨了化学计量最高标准的划定和考核的有关问题。     

Automatic Deformation Analysis in Electronic Speckle Pattern Interferometry Using One Speckle Interferogram of Deformed Object

We propose a new fringe analysis method that uses only one speckle interferogram of a deformed object to obtain phase change distribution by deformation. This method uses cos^-1 operations to extract absolute, not signed, values of new phase after deformation. Considering the phase changes in a small local area, true phase changes retain almost the same value by assuming a continuous deformation in the area. This retention determines the sign of the new phase. From the new phase and the initial phase, the phase change distribution by the deformation can be obtained. Experimental results show the usefulness of this method.     

DQAINF: an algorithm for automatic integration of infinite oscillating tails

We describe an automatic quadrature routine which is specifically designed for real functions having a certain type of infinite oscillating tails. The algorithm is designed to integrate a vector function over an infinite interval. A FORTRAN implementation of the algorithm is included.The algorithm combines an adaptive subdivision strategy with extrapolation and requires that the decay of all the functions in the vector is the same. The algorithm is based on the assumption that the oscillating behavior is due to a periodic function with the property that it changes sign when evaluated at points of distance half a period. We assume that this period is known. The algorithm offers a choice of three different quasi-linear extrapolation procedures, namely the Euler transformation and two modifications of this transformation.This work was supported by The Norwegian Research Council for Science and the Humanities.     

以LCD为目标的自动定焦判据选择

在光学综合自动测量中 ,使用液晶显示屏作为分划板可以大大简化结构 ,提高效率 ,真正地实现自动测量。由于液晶显示具有对比度低、噪声大等特点 ,所以根据液晶的这些特点以及图像处理和CCD信号接收的特点选择两种适用的判据进行了分析和试验比较 ,并给出了结果。结果表明 ,这两种判别函数都适用于以液晶显示屏为目标和用图像处理方法进行光学参数测量的系统 ,其中锐度判别函数更优于信息熵判别函数 ,前者具有更好的抗干扰性和稳定性 ,而且其判定结果更接近目视清晰度判别     

类型γ射线能谱指纹的识别机理

放射源的辐射指纹能起到标识和鉴别放射性物体的作用.在涉及核弹头不可逆销毁过程的深度核裁军核查中,核弹头的辐射指纹对标识和鉴别裁减下来的核弹头将起到关键作用.预先研究辐射指纹的有关技术,如识别机理的研究,将有助于深度核裁军的核弹头核查技术发展.以实验室放射源为研究对象,探索了类型γ射线能谱指纹的同一性识别机理.类型γ射线指纹识别机理的研究,就是要找出一种合适的方法,以较高的置信度,描述两个正在进行比较的γ射线指纹是否为同一放射源的指纹.采用了谱形比较法,并用谱相似度概念来描述两个指纹的相似程度.在谱形比较思想的指导下,编制了放射源类型指纹识别软件,并通过放射源同一性的识别实验验证了软件的有效性,同时研究了谱相似度随统计涨落和测量条件,如时间、源强和本底等因素的变化情况.研究结果表明:1)用相似度概念来描述两个指纹的相似程度,回答两个待比较的γ射线能谱是否代表同一类型放射源,是切实可行的;2)该识别机理只具备识别放射源类型的能力,而对同一类型、差异甚微的放射源个体还不能识别 关键词： γ射线能谱指纹 辐射指纹 识别机理 核查技术     

Impact of Partial Separability on Large-Scale Optimization

ELSO is an environment for the solution oflarge-scale optimization problems. With ELSO the user is required to provide only code for the evaluation of a partially separable function. ELSO exploits the partialseparability structure of the function to computethe gradient efficiently using automatic differentiation.We demonstrate ELSO's efficiency by comparing thevarious options available in ELSO.Our conclusion is that the hybrid option in ELSOprovides performance comparable to the hand-coded option, while having the significantadvantage of not requiring a hand-coded gradient orthe sparsity pattern of the partially separable function.In our test problems, which have carefully coded gradients,the computing time for the hybrid AD option is within a factor of two of thehand-coded option.     

Solid phase synthesis of azapeptides using an automatic synthesizer

Peptides containing azaglycine located terminally or within the backbone have been prepared in the solid phase by means of an automatic synthesizer.