Density functional theory for molecular and periodic systems using density fitting and continuous fast multipole method: Stress tensor

A full implementation of the analytical stress tensor for periodic systems is reported in the TURBOMOLE program package within the framework of Kohn–Sham density functional theory using Gaussian-type orbitals as basis functions. It is the extension of the implementation of analytical energy gradients (Lazarski et al., Journal of Computational Chemistry 2016, 37, 2518–2526) to the stress tensor for the purpose of optimization of lattice vectors. Its key component is the efficient calculation of the Coulomb contribution by combining density fitting approximation and continuous fast multipole method. For the exchange-correlation (XC) part the hierarchical numerical integration scheme (Burow and Sierka, Journal of Chemical Theory and Computation 2011, 7, 3097–3104) is extended to XC weight derivatives and stress tensor. The computational efficiency and favorable scaling behavior of the stress tensor implementation are demonstrated for various model systems. The overall computational effort for energy gradient and stress tensor for the largest systems investigated is shown to be at most two and a half times the computational effort for the Kohn–Sham matrix formation. © 2019 Wiley Periodicals, Inc.     

圆平板挤压膜实验及其参数识别

完成了简谐激励下水中平行圆板的挤压膜振动实验．用最小二乘法识别出非线性粘性挤压膜力模型中的４个系数．不同挤压膜厚、不同频率和不同振幅情况的数值模拟结果与实验值吻合较好．研究结果表明，所用模型可较好地描述粘性挤压膜运动，识别出的系数在一定范围内给出良好精度的数值模拟．     

On the Validity of Darcy's Law for Stable High-Concentration Displacements in Granular Porous Media

Recently, it has been suggested that Darcy's Law might not be applicable for modelling miscible, density-dependent flow in porous media. To investigate this, three sets of careful laboratory column experiments were performed on coarse and medium sands, consisting of upward displacement of water by sodium chloride solutions with concentrations ranging from 5 to 200g/l. Data on salt concentrations and water pressures were collected in horizontal transects along the flow direction. Salt concentration data were also collected in the influent and exit lines. The experimental data were analysed using a simplified approach based on Darcy's Law alone, applied with the assumption of a sharp interface. Darcy's Law was used to estimate porous medium permeability by fitting predictions to experimental data. Consistent estimates of permeability were obtained for each set of experiments. The results indicate that Darcy's Law adequately describes high concentration displacements through saturated coarse- and medium-grained porous media.     

The Chebyshev Hyperplane Optimization Problem

We consider the following problem. Given a finite set of pointsy ^j in we want to determine a hyperplane H such that the maximum Euclidean distance betweenH and the pointsy ^j is minimized. This problem(CHOP) is a non-convex optimization problem with a special structure. Forexample, all local minima can be shown to be strongly unique. We present agenericity analysis of the problem. Two different global optimizationapproaches are considered for solving (CHOP). The first is a Lipschitzoptimization method; the other a cutting plane method for concaveoptimization. The local structure of the problem is elucidated by analysingthe relation between (CHOP) and certain associated linear optimizationproblems. We report on numerical experiments.     

基于MATLAB的最小二乘法处理杨氏模量测量数据的研究

分析了支撑共振法测量固体材料杨氏模量的实验原理,用最小二乘法代替外延法处理测量数据,给出MATLAB数学软件具体处理程序,运行得到试样基振频率并直接求出其杨氏模量以及相对误差,大大的简化了实验的计算处理过程并且减小了实验误差。     

基于多维状态参量和时间序列对电机的异常检测

针对传统对电机的异常检测常常出现误判或滞后的情况,采用基于时间序列对电机单一状态参量用AR拟合,同时利用SOM神经网络无监督的方式量化电机数据。然后,利用得到的量化序列结合AR曲线得到序列的转移概率,及早发现某种状态参量的异常变化;之后,DBSCAN算法挖掘多维参数之间特征关系来确定电机是否出现异常。最后结合实例说明该方法的检测过程,并对比验证了该方法的优越性。     

Water mist attenuates guided laser based on Monte Carlo method

The round-trip attenuating process of lasers used for guiding in artificial water mists is studied with the Monte-Carlo method. A new way for confirming the scattering directions of photons is established based on calculating Mie cumulative probability distribution function of the polydisperse mist and user defined function fitting by Matlab. Two Monte-Carlo methods for photons tracking are mentioned and their efficiencies are discussed and balanced in this paper. A conclusion is come to that the Wight method is evidently more efficiency than the Event method, and the former is adopted in this paper. The radiuses of frequently-used water mists are usually in the range of 10¹–10² μm which are found to be suited to attenuate the 10.6 μm laser and can be used for laser stealth. But the effect is worse for 1.06 μm laser.     

基于粗对准与精对准信号分开探测的对准系统

提出了一种用于光刻装置的对准系统。该对准系统所用的标记包含多个相位子光栅。其中,标记±1级衍射光的光强信息用于产生粗对准信号。在粗对准信号上,通过峰值检测和信号拟合获得最大峰值点,该峰值点即为粗对准位置。同时,在另一光路中,精细子光栅的±1级衍射光的光强信息用于产生精对准信号。利用余弦或正弦曲线对该精对准信号进行拟合,得到一系列的波峰点。距离粗对准位置最近的波峰点即为精对准位置。当精细子光栅的周期足够小时,该对准系统可获得5nm级的重复精度。     

Origin在费米-狄拉克实验中的应用

Origin软件是一个多文档界面的应用程序,功能强大,普遍用于数据分析和科研绘图．运用该软件对费米-狄拉克实验的数据进行处理,数据处理误差小,图形美观、方便、快捷,也更科学、合理．