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.     

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     

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     

MATLAB曲面绘制中的挖补方法

在MATLAB绘图中,将函数数据的某一部分换成内置变量NaN(或Inf),或者将函数数据中的NaN换成适当的实数,可分别实现绘图中的挖、补方法.并且给出一些具体的应用实例.     

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.     

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)。     

Ag纳米颗粒的光吸收和透射电镜研究

用硼氢化钠作还原剂,制备出两种相对稳定的含银纳米颗粒的水溶胶,用透射电镜（TEM）和光学吸收谱对这些颗粒进行了表征.当被还原的银离子较少时,所形成的银纳米颗粒较小,吸收峰呈现二极等离子体共振吸收峰.当被还原的银离子较多时,银纳米颗粒尺寸变大,并出现二极和四极共振吸收峰.在Ag纳米颗粒形成后,对其溶液稀释,发现其峰形保持不变,而峰位会出现红移,最大红移量可达到10 nm.透射电镜研究表明,低浓度溶胶中的Ag纳米颗粒尺寸较为均匀,平均直径12 nm.高浓度溶胶中的纳米颗粒尺寸呈双尺寸分布特点,少量颗粒直径小于14 nm,大部分颗粒直径大于20 nm.     

用力敏传感器测量乙醇水溶液的表面张力系数与浓度的关系

用硅压阻式力敏传感器测量了纯水、乙醇的表面张力系数，并测量了不同浓度的乙醇水溶液的表面张力系数，得到了乙醇水溶液的表面张力系数随浓度的变化曲线．     

Vassiliev invariants for braids on surfaces

We show that Vassiliev invariants separate braids on a closed oriented surface, and we exhibit a universal Vassiliev invariant for these braids in terms of chord diagrams labeled by elements of the fundamental group of the surface.