Numerical multilinear algebra and its applications

Numerical multilinear algebra (or called tensor computation), in which instead of matrices and vectors the higher-order tensors are considered in numerical viewpoint, is a new branch of computational mathematics. Although it is an extension of numerical linear algebra, it has many essential differences from numerical linear algebra and more difficulties than it. In this paper, we present a survey on the state of the art knowledge on this topic, which is incomplete, and indicate some new trends for further research. Our survey also contains a detailed bibliography as its important part. We hope that this new area will be receiving more attention of more scholars.      

Fragment-Based Ab Initio Molecular Dynamics Simulation for Combustion

We develop a fragment-based ab initio molecular dynamics (FB-AIMD) method for efficient dynamics simulation of the combustion process. In this method, the intermolecular interactions are treated by a fragment-based many-body expansion in which three- or higher body interactions are neglected, while two-body interactions are computed if the distance between the two fragments is smaller than a cutoff value. The accuracy of the method was verified by comparing FB-AIMD calculated energies and atomic forces of several different systems with those obtained by standard full system quantum calculations. The computational cost of the FB-AIMD method scales linearly with the size of the system, and the calculation is easily parallelizable. The method is applied to methane combustion as a benchmark. Detailed reaction network of methane reaction is analyzed, and important reaction species are tracked in real time. The current result of methane simulation is in excellent agreement with known experimental findings and with prior theoretical studies.     

一类质量—黏弹性弹簧系统的简谐受迫振动

研究一类质量－弹簧系统的简谐受迫振动。弹簧为黏弹性材料，其特性由分数导数型本构关系描述。求出了系统的稳态响应，并讨论了材料黏性系数对幅频特性的影响。     

三维复合介质波动方程多尺度辛几何算法

本文针对三维复合介质波动方程,提出了一类多尺度辛几何算法.其主要内容有:1.快速振荡系数三维波动方程的多尺度渐近分析与收敛性估计;2.均匀化波动方程的辛几何算法;3.多尺度辛几何算法与数值实验结果.     

Second-order nonlinear least squares estimation

The ordinary least squares estimation is based on minimization of the squared distance of the response variable to its conditional mean given the predictor variable. We extend this method by including in the criterion function the distance of the squared response variable to its second conditional moment. It is shown that this “second-order” least squares estimator is asymptotically more efficient than the ordinary least squares estimator if the third moment of the random error is nonzero, and both estimators have the same asymptotic covariance matrix if the error distribution is symmetric. Simulation studies show that the variance reduction of the new estimator can be as high as 50% for sample sizes lower than 100. As a by-product, the joint asymptotic covariance matrix of the ordinary least squares estimators for the regression parameter and for the random error variance is also derived, which is only available in the literature for very special cases, e.g. that random error has a normal distribution. The results apply to both linear and nonlinear regression models, where the random error distributions are not necessarily known.     

Impact of organic contamination on the laser-induced damage in vacuum

The impact of two organic contaminations on the damage characteristics of anti-reflector (AR) at 1064 nm is investigated. Contamination experiments were made with toluene and acetone in liquid phase on the surface of AR coatings. Chemical and morphological characterization methods were used to identify and understand the damage process. The possible damage process is analyzed and discussed. It is found that toluene decreases laser-induced damage threshold and acetone seems to be benign and has little influence on laser-induced damage threshold due to its quickly spreading into the coating. Adsorption and droplet micro-lensing effect mechanism are the main cause of enhanced laser-induced damage of toluene.     

高功率微波对双层屏蔽腔体的孔缝耦合特性

 用多模传输线模型对高功率微波与双层屏蔽腔体的孔缝耦合特性进行了研究,此方法可以考虑高功率微波孔缝耦合进入腔内时的较宽的频率范围。用这种模拟方法获得了双层屏蔽腔体微波耦合的一些规律性结果：双层屏蔽可以使得腔体内的耦合电场比单层屏蔽时有显著的减弱,这与FDTD方法的结论是一致的;双层屏蔽外腔体中的一些谐振会影响到内腔体的耦合系数,外腔体中的场模式经由内孔缝会影响内腔体中的场模式;不论是单层屏蔽还是双层屏蔽,保持每层孔缝总面积不变时,随着孔阵中孔缝数量的增加,进入腔体内的耦合电场也逐步地减弱,这与单层屏蔽时的结论一致;通风总面积不变的情况下,孔缝数量越多,屏蔽效能越好。     

Z箍缩靶用聚合物丝的弛豫特性

 聚苯乙烯（PS）,聚乙烯（PE）及其的氘代物是Z箍缩驱动惯性约束聚变（ICF）实验中的重要固体燃料容器材料,针对物理实验对其形状的特殊要求,利用高压毛细管流变仪及HAUL-OFF熔体拉伸测试单元进行熔融纺丝,制备出直径为30～100 μm的聚合物丝样品。通过对PS,PE以及氘代聚苯乙烯（DPS）丝的力学弛豫性质研究发现：在相同的恒定应力下,实验用PS丝的蠕变量明显小于PE丝,PS丝表现出更好的尺寸稳定性;当定伸长为1％时,PS丝的松弛率明显小于PE丝;DPS丝的蠕变及应力松弛行为与PS丝具有相同的变化趋势。     

卵磷脂涂敷生物膜色谱固定相的制备及其稳定性的考察

 将卵磷脂涂敷的硅胶作为生物膜固定相 ,并以此研究了药物与生物膜的相互作用。实验发现 ,卵磷脂涂敷的硅胶固定相的适宜使用温度为 2 0℃～ 30℃ ,而且卵磷脂中合适的胆固醇含量会使制备的生物膜固定相的稳定性有所增加。对药物在这种生物膜色谱固定相上的保留行为的研究表明 ,胆固醇含量、缓冲试剂组成、流动相中盐浓度及pH值等都会影响色谱柱对药物的选择性。卵磷脂涂敷生物膜色谱固定相的制备方法简便 ,通过固定相及流动相的改变可以很方便地模拟人体的生理环境 ,因而可以用于研究药物在体内的吸收和分布状况以及药物的初步筛选。     

Convergence of Newton's method for convex best interpolation

Summary. In this paper, we consider the problem of finding a convex function which interpolates given points and has a minimal norm of the second derivative. This problem reduces to a system of equations involving semismooth functions. We study a Newton-type method utilizing Clarke's generalized Jacobian and prove that its local convergence is superlinear. For a special choice of a matrix in the generalized Jacobian, we obtain the Newton method proposed by Irvine et al. [17] and settle the question of its convergence. By using a line search strategy, we present a global extension of the Newton method considered. The efficiency of the proposed global strategy is confirmed with numerical experiments. Received October 26, 1998 / Revised version received October 20, 1999 / Published online August 2, 2000