Artificial time integration

Many recent algorithmic approaches involve the construction of a differential equation model for computational purposes, typically by introducing an artificial time variable. The actual computational model involves a discretization of the now time-dependent differential system, usually employing forward Euler. The resulting dynamics of such an algorithm is then a discrete dynamics, and it is expected to be “close enough” to the dynamics of the continuous system (which is typically easier to analyze) provided that small – hence many – time steps, or iterations, are taken. Indeed, recent papers in inverse problems and image processing routinely report results requiring thousands of iterations to converge. This makes one wonder if and how the computational modeling process can be improved to better reflect the actual properties sought. In this article we elaborate on several problem instances that illustrate the above observations. Algorithms may often lend themselves to a dual interpretation, in terms of a simply discretized differential equation with artificial time and in terms of a simple optimization algorithm; such a dual interpretation can be advantageous. We show how a broader computational modeling approach may possibly lead to algorithms with improved efficiency. AMS subject classification (2000)  65L05, 65M32, 65N21, 65N22, 65D18     

On the excitation of a closely spaced array by a line source

An infinite row of periodically spaced, identical rigid circularcylinders is excited by an acoustic line source which is parallelto the generators of the cylinders. A method for calculatingthe scattered field accurately and efficiently is presented.When the cylinders are sufficiently close together, Rayleigh–Blochsurface waves that propagate energy to infinity along the arrayare excited. An expression is derived which enables the amplitudesof these surface waves to be computed without requiring thesolution to the full scattering problem.     

Effect of Cu concentration on the reactions between Sn-Ag-Cu solders and Ni

The reaction between the Sn-Ag-Cu solders and Ni at 250°C for 10 min and 25 h was studied. Nine different Sn-Ag-Cu solders, with the Ag concentration fixed at 3.9 wt.% and Cu concentrations varied between 0.0–3.0 wt.%, were used. When the reaction time was 10 min, the reactions strongly depended on the Cu concentration. At low-Cu concentrations (≦0.2 wt.%), only a continuous (Ni_1−xCu_x)₃Sn₄ layer formed at the interface. When the Cu concentration increased to 0.4 wt.%, a continuous (Ni_1−xCu_x)₃Sn₄ layer and a small amount of discontinuous (Cu_1−yNi_y)₆Sn₅ particles formed at the interface. When the Cu concentration increased to 0.5 wt.%, the amount of (Cu_1−yNi_y)₆Sn₅ increased and (Cu_1−yNi₆)₆Sn₅ became a continuous layer. Beneath this (Cu_1−yNi_y)₆Sn₅ layer was a very thin but continuous layer of (Ni_1−xCu_x)₃Sn₄. At higher Cu concentrations (0.6–3.0 wt.%), (Ni_1−xCu_x)₃Sn₄ disappeared, and only (Cu_1−yNi_y)₆Sn₅ was present. The reactions at 25 h also depended strongly on the Cu concentration, proving that the strong concentration dependence was not a transient phenomenon limited to a short reaction time. The findings of this study were rationalized using the Cu-Ni-Sn isotherm. This study shows that precise control over the Cu concentration in solders is needed to produce consistent results.     

CCD摄像机大视场光学镜头的设计

为提高CCD摄像机的成像质量，同时使镜头结构紧凑、小型化，在大视场光学镜头的设计中，引入标准二次曲面和偶次非球面。根据初级像差理论，分析了非球面的位置、初始结构参数的求解规律。通过理论计算和ZEMAX光学设计软件的优化，给出工作波长为0.4～0.7μm、全视场角为80°，相对孔径为1∶1.5的镜头设计实例。该镜头由7块镜片组成，包括一个标准二次曲面和两个8次方非球面；在40lp/mm空间频率处的MTF值超过0.85，全视场畸变小于3％，像质优良     

Discontinuous travelling wave solutions for certain hyperbolic systems

In an earlier paper on a malignant cell invasion model (Marchantet al., SIAM J. Appl. Math, 60, 2000) we introduced a novelform of discontinuous travelling wave solution. These solutionscould be studied easily by combining behaviour within a phaseplane with the Rankine–Hugoniot shock conditions, whichdescribe properties (such as the ratio of the jump discontinuitiesto the speed of propagation) that solutions may possess. Theseresults were new for several reasons. The shock conditions relateto hyperbolic equations (which the model is) but were appliedin a travelling wave ordinary differential equation phase planeusing techniques that usually apply to parabolic reaction–diffusionsystems. In addition the solutions possess singular behaviournear several points in the phase plane but in spite of thisthere exists a robust and stable family of physically interestingsolutions. In this paper we discuss two previously studied models, oneof detonation theory and one of angiogenesis. We show that eachof these models also possesses a family of discontinuous travellingwave solutions which was not previously discovered. Of particularinterest is the solution which has a blunt interface at thefront of the invading profile. In all three models it is thissolution that is seen to stably evolve from physically relevantinitial data, and for physically relevant parameter values. This work confirms the robustness of these novel travellingwave solutions and their applicability to a wider range of mathematicalmodelling situations.     

Performance and simulation of an on-board guided-wave optical processor for airborne SAR applications

This paper describes the performance and simulation of a compact integrated optical processor for the real-time reconstruction of two-dimensional images in airborne stripmap synthetic aperture radar applications. The functional behavior of the processor is explained in some detail. The design criteria are briefly given. The simulation step allowed the main processor characteristics and properties to be identified. A number of comparisons were obtained in airborne SAR mission scenarios between the predictions of the optical device and those achieved by the modern electronic digital approach, based on the wavefront reconstruction method by matched filtering.     

双面电弧焊接的传热模型

将等离子焊接(PAW)电弧和钨极氩弧焊(TIG)电弧串接,相对作用于工件的正反面形成双面电弧焊接(DSAW)系统,可以引导焊接电流沿工件厚度方向流过小孔,补偿等离子电弧穿透工件时消耗的能量,以有效地提高等离子弧的穿透能力.综合考虑影响双面电弧焊接正反面熔池几何形状的力学因素,建立了熔池表面变形的控制方程,以此为基础并采用帖体曲线坐标系建立了DSAW焊接传热的数学模型,分析了DSAW,PAW焊接传热的差异,从传热的角度解释了DSAW焊接熔深增加的原因.焊接工艺实验表明,计算结果与实测结果吻合良好. 关键词： 双面电弧焊接(DSAW) 传热模型 熔池表面变形模型     

Contact angle hysteresis of liquid drops as means to measure adhesive energy of zein on solid substrates

Adhesion of zein to solid substrates has been studied using surface energy profiles as indices and by adhesion mapping using atomic force microscopy (AFM). Different plasticizers like glycerol and sorbitol have been used to form mixed films with zein and properties of these films are studied using surface energy profiles. Comparison of the results from the different mixed samples with those from the pure zein films showed that force mapping could identify areas rich in protein. The adhesion maps produced were deconvoluted from sample topography and contrasted with the data obtained from contact angle measurements. A comparison of the two methods shows that the extent of contact angle hysteresis is indicative of both hydrophobicity of the surface as well as the force of adhesion. Mechanical properties and microstructure of zein films prepared by casting from solutions and using Langmuir-Blodgett film technique have been investigated. Pure zein seemed brittle and exhibited an essentially linear relationship between stress and strain. Films with plasticizer were tougher than these films. In general, mixed films showed better mechanical properties than pure films and had higher ultimate tensile strength and increased per cent elongation. Further, the mixed films of zein showed a higher force of adhesion compared to the pure films.     

微极各向同性弹性板中的Rayleigh-Lamb波

研究了无应力作用条件下，均匀、各向同性、圆柱形微极结构弹性板中波的传播．导出了对称和斜对称模式下波传播的特征方程．对短波这一极端情况，无应力圆板中对称和斜对称模态波的特征方程退化为Pmyle曲表面波频率方程．并得到薄板的计算结果．给出了位移和微转动分量，并绘制了相应图形．给出了若干特殊情况的研究结果及对称和斜对称模态特征方程的图示．     

纳米颗粒悬浮液池内泡状沸腾的实验研究

本文对纳米颗粒悬浮液在平壁面上池内沸腾进行了实验研究。实验用的纳米粒子为26 nm的铁粉和13 nm的三氧化二铝纳米粉末,基液为去离子水。分别配成体积浓度为0．1％, 1％和2％的悬浮液。实验结果表明,纳米悬浮颗粒对液体沸腾换热过程的影响会随着纳米颗粒性质,颗粒浓度及热流密度大小的不同而出现不同的效果;加入纳米颗粒后, 对基液沸腾换热的影响存在着两个相反的作用机制,它们分别为:纳米颗粒增强了液体内部的热量迁移能力(热物性的影响)和改变了加热面的表面结构特性(加热面特性的影响)。