Inclusion of α-phenyl-N-p-methylphenyl Nitrone in β- Cyclodextrin: Formation of 1G : 1H and 1G : 2H Complexes and the Remarkably Fast 1,3-Dipolar Cycloaddition of the 1G : 2H Complex with Olefins in the Solid State

The nitrone is found to be included in the -cyclodextrin cavity in two different stoichiometries viz., 1G : 1H and 1G : 2H – the existence of which is proved by physical methods. The 1G : 2H complex of the nitrone serves as a good potent dipolarophile in the 1,3-dipolar cycloaddition reactions with olefins resulting in rate acceleration and regioselection.     

Accelerated quasicontinuum: a practical perspective on hyper-QC with application to nanoindentation

Abstract

Hyper-QC is a multiscale method based on the quasicontinuum (QC) method in which time is accelerated using hyperdynamics through the addition of a suitable bias potential. This paper describes the practical details of implementing and carrying out hyper-QC simulations and introduces a novel mechanism-based bias potential for deformation processes in face-centred cubic (fcc) systems. The factors limiting the maximum achievable acceleration are discussed. The method is demonstrated for nanoindentation into a thin film of single crystal fcc nickel at near experimental loading rates. Speed up factors as high as 10,000 are achieved. The simulations reveal a thermally activated dislocation nucleation mechanism with a logarithmic dependence on temperature and indenter velocity in agreement with a theoretical model.     

A Finite Volume Implicit Euler Scheme for the Linearized Shallow Water Equations: Stability and Convergence

The linearized shallow water equations are discretized in space by a finite volume method and in time by an implicit Euler scheme. Stability and convergence of the scheme are proved.     

An Inverse Problem in Periodic Diffractive Optics: Reconstruction of Lipschitz Grating Profiles

We consider the problem of recovering a two-dimensional periodic structure from scattered waves measured above the structure. Following an approach by Kirsch and Kress, this inverse problem is reformulated as a nonlinear optimization problem. We develop a theoretical basis for the reconstruction method in the case of an arbitrary Lipschitz grating profile. The convergence analysis is based on new perturbation and stability results for the forward problem.     

On the complexity of extending the convergence ball of Wang’s method for finding a zero of a derivative

Ball convergence results are very important, since they demonstrate the complexity in choosing initial points for iterative methods. One of the most important problems in the study of iterative methods is to determine the convergence ball. This ball is small in general restricting the choice of initial points. We address this problem in the case of Wang’s method utilized to determine a zero of a derivative. Finding such a zero has many applications in computational fields, especially in function optimization. In particular, we find the convergence ball of Wang’s method using hypotheses up to the second derivative in contrast to earlier studies using hypotheses up to the fourth derivative. This way, we also extend the applicability of Wang’s method. Numerical experiments used to test the convergence criteria complete this study.     

求解矩阵方程AXB+CXD=F参数迭代法的最优参数分析

本文针对求矩阵方程AXB+CXD=F唯一解的参数迭代法，分析当矩阵A，B，C，D均是Hermite正（负）定矩阵时，迭代矩阵的特征值表达式，给出了最优参数的确定方法，并提出了相应的加速算法.     

Quintic hyperbolic nonpolynomial spline and finite difference method for nonlinear second order differential equations and its application

An efficient numerical method based on quintic nonpolynomial spline basis and high order finite difference approximations has been presented. The scheme deals with the space containing hyperbolic and polynomial functions as spline basis. With the help of spline functions we derive consistency conditions and high order discretizations of the differential equation with the significant first order derivative. The error analysis of the new method is discussed briefly. The new method is analyzed for its efficiency using the physical problems. The order and accuracy of the proposed method have been analyzed in terms of maximum errors and root mean square errors.     

宽离子能量检测范围垂直引入反射式飞行时间质谱仪的研制

本实验室研制了国内首台宽离子能量检测范围飞行时间质谱仪。仪器采用紧凑式电子轰击源设计,配合离子透镜系统有效的调制离子流,飞行时间质量分析器采用了离子垂直引入式,双场加速和双场反射以及大尺寸MCP检测装置设计。仪器单离子信号半峰宽约2 ns,仪器分辨率优于1600FWHM,检测实际样品质量范围为1~127 amu(仪器理论质量检测上限优于800 amu),可检测离子能量范围优于2个数量级(3~140 eV)。若该TOF质量分析器与短瞬高压脉冲放电离子源耦合联用,可广泛应用于高能离子束的快速检测,如真空阴极放电对制备薄膜、离子注入材料的表征,导电材料的离子电荷态分布以及离子扩散速度的测定等。