Recent Progress in the Simulation of Chiral Systems with Real Time Propagation Methods

In this brief review, an overview about recent efforts to simulate the spectroscopic signatures of chiral molecules is given with focus on real time propagation approaches to solve the time-dependent Schrödinger equation. In particular the simulation of electric circular dichroism spectra and vibrational Raman optical activity is discussed. In comparison to linear absorption spectra, where only the response of the electric dipole moment is necessary, the response of the magnetic dipole moment and electric quadrupole moment is more intricate. Issues such as gauge origin dependence, basis set dependence, non-local potentials and the dipole approximation are addressed.     

相干梯度敏感干涉测量技术及在静态断裂力学实验中的应用

介绍了相干梯度敏感(CGS)干涉测量技术的基本原理及其在静态Ⅰ型断裂实验中的应用,验证了该方法对裂纹尖端局部变形场和断裂特性进行定量研究的可行性。给出了代表静态Ⅰ型裂纹尖端奇异场光力学信息的CGS控制方程,模拟并分析了Ⅰ型裂纹尖端的CGS条纹模式,对静态Ⅰ型裂纹尖端变形场和断裂特性进行了三点弯曲的CGS试验,并提取了应力强度因子KⅠ。结果表明,试验结果与理论分析结果相吻合。     

宽频带激光自由空间传输的调制特性研究

基于惠更斯-菲涅耳衍射积分公式,研究了宽带光束在菲涅耳衍射区的自由空间传输特性,得到宽带光束传输的调制深度与光束带宽Δλ及菲涅耳数F的变化关系。结果表明:一定的带宽对光束的均匀性有适当的改善;当光束的带宽Δλ<2λ0/F时,带宽越大,光束越均匀;当带宽满足条件Δλ=2λ0/F时,菲涅耳衍射完全消失;在一定的菲涅耳数范围内,宽带光束的调制深度随菲涅耳数振荡变化,振荡曲线的主极大值和次极大值分别出现在菲涅耳数为奇数和偶数处,而极小值则出现在菲涅耳数F=2k±1/3(k=1,2,3,…)处,在极小值处光束的均匀性最好。     

Acoustoelastic effect simulation by time–space finite element formulation based on quadratic interpolation of the acceleration

Acoustoelastic effect describes the change of ultrasound velocity due to the initial stress. Its simulation involves a numerical analysis of nonlinear elastodynamics and requires high accuracy in the time domain. A time–space finite element formulation, derived from the quadratic interpolation of the acceleration within a time segment, is proposed for an accurate simulation of the acoustoelastic effect in the present study. Ten different integration schemes are generated based on this formulation and nine of them are found to be conditionally stable. Among the nine stable schemes, one is found to obtain a spectral radius of one when the normalized step ratio is less than 5.477, indicating no numerical dissipation or numerical divergence. Compared with integration schemes from previous studies, this integration scheme demonstrates better performance in calculation accuracy and energy conservation. A two-stage approach, namely the static stage and the dynamic stage, has been employed in the simulation of the acoustoelastic effect. The former stage is adopted to obtain the initial stress and the latter stage, where the proposed integration scheme is implemented, is adopted to simulate the ultrasound propagation in an initial stress state. The simulation results of the dynamic stage show that the ultrasound velocity increases in a compression stress state and decreases in a tension stress state for aluminum alloy, which is in good agreement with previous experimental studies. Together with the simulation result of the static stage, it is conjectured that the acoustoelastic effect results from the stress-dependent elastic modulus.     

A New Strategy in Boosting Information Spread

Finding a seed set to propagate more information within a specific budget is defined as the influence maximization (IM) problem. The traditional IM model contains two cardinal aspects: (i) the influence propagation model and (ii) effective/efficient seed-seeking algorithms. However, most of models only consider one kind of node (i.e., influential nodes), ignoring the role of other nodes (e.g., boosting nodes) in the spreading process, which are irrational. Specifically, in the real-world propagation scenario, the boosting nodes always improve the spread of influence from the initial activated seeds, which is an efficient and cost-economic measure. In this paper, we consider the realistic budgeted influence maximization (RBIM) problem, which contains two kind of nodes to improve the diffusion of influence. Facing the newly modified objective function, we propose a novel B-degree discount algorithm to solve it. The novel B-degree discount algorithm which adopts the cost-economic boosting nodes to retweet the influence from the predecessor nodes can greatly reduce the cost, and performs better than other state-of-the-art algorithms in both effect and efficiency on RBIM problem solving.     

骨断裂力学概述

本文涉及近年来骨断裂力学的发展成果.对建立在张开型和剪切型断裂能基础上的方法作了回顾,并讨论了密度、试件厚度和裂纹速度对骨断裂的影响.最后简述了人股骨的试验研究.      

带形域内裂纹对SH波散射问题的边界元解

采用边界元法研究含裂纹的带形域各向同性弹性体，裂纹对SH波的散射问题，推导出带形域情况下不同边界条件的各种Green函数，导出了以裂纹张开位移为未知数的边界积分方程，计算出表面散射场和总位移．算例表明，利用所提供的格林函数和边界元格式解答带形域的散射问题比较方便．     

复杂载荷三维裂纹分析双重边界元法

提出可用于高温、高转速状态下的热动力机械三维含裂构件热弹性分析方法——双重边界元法.首先建立了考虑温度及离心载荷的双重边界积分方程组,并对边界积分方程组的选取及适用范围进行了讨论。然后提出角非快调元模型离散技术。接着提出超奇异积分方程分析去除奇异性方法及数值积分技术.数值算例表明计算结果与有关权函数解十分吻合,说明了用双重边界元法计算复杂载荷条件下三维应力强度因子的有效性.还讨论了有关热应力强度因子权函数解的适用范围.     

压电材料平面裂纹尖端场的杂交应力有限元分析

基于复势理论和杂交变分原理建立了一种适用于力电耦合分析的杂交应力有限元模 型. 给出了建立刚度矩阵的主要公式和推导过程，单元内的位移场和应力场采用满足平 衡方程的复变函数级数解，假设的复变函数级数解事先精确满足裂纹的无应力和电位移法向 分量为零的条件，单元外边界的位移场假设按抛物线变化, 单元的刚度矩阵采用Gauss积分的方法得出. 通过对力电耦合裂尖场的数值计算验证了程序 的正确性和单元的有效性，同时也用所得结果校验了理论解.     

On the influence of singular-type finite elements on the critical force in studying the buckling of a circular plate with a crack

The axisymmetric buckling (delamination) of a circular disk (plate) with a penny-shaped crack is analyzed using a continuum model, piecewise-homogeneous model, and the three-dimensional linearized theory of stability. The FEM is used. The analysis is carried out using various singular and ordinary finite elements. The numerical results obtained indicate that it is not necessary to use singular finite elements to solve the problem Published in Prikladnaya Mekhanika, Vol. 43, No. 9, pp. 120–129, September 2007.