FULL DISCRETE NONLINEAR GALERKIN METHOD FOR THE NAVIER-STOKES EQUATIONS

This paper deals with the inertial manifold and the approximate inertial manifold concepts of the Navier-Stokes equations with nonhomogeneous boundary conditions and inertial algorithm. Furtheremore, we provide the error estimates of the approximate solutions of the Navier-Stokes Equations.     

The preparation of thick-film glass capillary columns

A detailed method for the routine preparation of glass capillary columns is presented. The method consists of coating a glass tube with quartz powder prior to pulling the tube into a capillary. The inner surface of the capillary consists of an even distribution of quartz particles fused to the walls. This surface has been found readily deactivated by standard procedures and ideal for the preparation of thick-film glass capillary columns. The method has been thoroughly tested in two independent laboratories to ensure that the procedures described are reproducible.     

迈克尔逊风场干涉仪基准光程差及步长误差容限分析

迈克尔逊干涉仪风场探测是在一定的基准光程差的基础上,通过动镜步进或四分区镀膜的方法,获得一个波长范围内步进间隔为λ/4的四步干涉强度.在此过程中存在的基准光程差误差及步长误差将对结果产生影响.对在一定的结果不确定度允许范围内的误差变量的容限值进行了讨论.在可以预知的误差存在情况下的精确结果的得出给出了计算方法.     

基于分步式压印光刻的激光干涉仪纳米级测量及误差研究

针对在未做隔离保护处理的环境中,基于Michelson干涉原理的激光干涉仪测量系统存在严重的干扰误差,不适合分步式压印光刻纳米级对准测量的要求.采用Edlen公式的分析及计算,不仅在理论上揭示出环境温度、湿度、气压等变化对激光干涉仪测量准确度的影响,而且证明影响测量准确度的最大干扰源是空气流动的结果.通过气流隔离措施和系统测量反馈校正控制器,能够实时补偿激光干涉仪两路信号的相差.最终,测量漂移误差在10 min内由13 nm降低到5 nm以内,满足压印光刻在100 mm行程中达到20 nm定位准确度要求.     

步进扫描差示扫描量热法研究不同链结构的聚乙烯类聚烯烃热力学特性

采用步进扫描差示扫描量热法研究了几种具有不同链结构的聚乙烯类聚烯烃的热力学性质.结果表明,不同链结构的聚烯烃在热力学平衡熔融态下,其绝对比热容的温度依赖性在实验误差范围内几乎相同;而无论链结构的变化如何,在极低温度下稳定结晶态的热容也非常接近.但在熔融温度范围内,比热容对不同聚烯烃的链结构非常敏感,这是由于在远低于聚烯烃主熔化峰温度范围内,聚乙烯晶体结构中的不同支链的影响.在时间-热流的步进扫描曲线中,具有长支链结构的聚烯烃表现出独特的熔融-再结晶行为,这可能是由于交联点之间较长的受约束链段的运动在熔融过程中得到释放并重排所致.     

Effective wave propagation along a rough thin-elastic beam

Two methods for computing the complex-valued effective wavenumber of a rough beam in the context of linear time-harmonic theory are presented. The roughness of the beam is modelled as a continuous random process of known characteristic length and root-mean-square amplitude for either the beam mass or the beam rigidity. The first method is based on a random sampling method, with the effective wave field calculated as the mean of a large ensemble of wave fields for individual realisations of the roughness. The individual wave fields are calculated using a step approximation, which is validated for a deterministic problem via comparison to results produced by an integral equation approach. The second method assumes a splitting of the length scale of the fluctuations and an observation scale, employing a multiple-scale approximation to derive analytical expressions for the effective attenuation rate and phase change. Numerical comparisons show agreement of the results of the random sampling method and the multiple-scale approximation for a wide range of parameters. It is shown that the effective wavenumbers only differ by a real constant between the cases of varying beam mass and rigidity.     

A computer program for automated step edge motion analysis from scanning probe microscopy images

A computer algorithm was developed to automatically track the displacement of straight step edges between sequential scanning probe microscopy images of single-crystal surfaces. The program utilizes the Canny edge detection algorithm followed by the Hough Transform of the edge map to identify step edges according to their direction, relative to the image axes, and according to their displacement, relative to the image origin. The tracking of individual steps is facilitated by the fact that straight edges in general maintain their direction and therefore, steps of similar displacement but different direction can be sorted. The algorithm is based on the assumption that the rate of image acquisition is much greater than the rate of (mono)layer growth/dissolution, requiring that changes in step displacement are small in successive images. The change in step displacement in sequential images leads directly to the calculation of the step speed. By tabulating all changes in step displacement through a sequence of images, a statistical representation of the step edge data is produced. The program was evaluated using a sequence of 20 atomic force microscopy images from a calcite (104) surface growing from a supersaturated aqueous solution. The program required, in total, 5 CPU-minutes running on a Pentium 4 processor to compute the mean step speed with 60% precision whereas the equivalent number of measurements performed “by hand” required 6 person-hours at 70% precision. For comparable output, the computer program therefore represents a factor of about 100 decrease in required effort.     

Step bunching to step-meandering transition induced by electromigration on Si(1 1 1) vicinal surface

The step configuration of a vicinal Si surface is studied under electromigration and a gradient of temperature. An abrupt transition (ΔT = 4 °C) from step-meandering to step bunching is found at 1225 °C for a step-down direct-current direction. This transition starts by random fluctuations which then extend on the whole surface. The transition is studied in the framework of a linear stability analysis of the usual Burton-Cabrera-Frank model by comparing the amplification factors of step-meandering and step bunching instabilities. Both compete at a given temperature, but since the amplification factors behave differently with temperature, bunching abruptly supersedes meandering above a critical temperature.     

RHEED study on continuously repeated step flow and layer-by-layer growth modes in SrRuO3/SrMnO3 superlattice

Nanolayered superlattices composed of ferromagnetic SrRuO₃ and antiferromagnetic SrMnO₃ layers were grown on SrTiO₃ (100) substrates by pulsed laser deposition. Multilayers were grown under predetermined synthesis conditions resulting in growth of SrRuO₃ and SrMnO₃ by step flow and layer-by-layer modes, respectively. The growth of SrMnO₃ was observed to occur through the layer-by-layer during the entire deposition process despite the expected increase in surface roughness because of the incorporation of SrRuO₃ upper layers. Monitoring by reflection high-energy electron diffraction (RHEED) revealed that the growth of every SrMnO₃ layer consisted of a pre-stage during which the gaps on the relatively rough SrRuO₃ surface were filled before the actual growth of the SrMnO₃ layer, which resulted in incomplete half oscillation and change from spot patterns to streaky patterns. The in-plane lattice constant did not show any considerable change in the case of SrRuO₃ and SrMnO₃ layers, despite the considerable lattice mismatch between the two materials (SrRuO₃, SrMnO₃) and SrTiO₃. On the other hand, the RHEED patterns showed the existence of lattice mismatch effects in the out-of-plane lattice constant, which showed significant strains of opposite signs in the different layers, indicating a strong dependence on the composition of the layers and superlattice periodicity. In this paper, the growth characteristics of a SrRuO₃/SrMnO₃ multilayer along with its magnetic properties will be discussed.     

指数分布场合下步进应力加速寿命试验的Bayes分析

当寿命分布为指数分布时，本文给出了步进应力加速寿命试验的一种新的Ｂａｙｅｓ估计，为计算上的方便，本文还给出一种近似方法，数值例子表明，此方法简便可行。