Coherence vortices of partially coherent beams in the far field

Based on the propagation law of cross-spectral density function, studied in this paper are the coherence vortices of partially coherent, quasi-monochromatic singular beams with Gaussian envelope and Schell-model correlator in the far field, where our main attention is paid to the evolution of far-field coherence vortices into intensity vortices of fully coherent beams. The results show that, although there are usually no zeros of intensity in partially coherent beams with Gaussian envelope and Schell-model correlator, zeros of spectral degree of coherence exist. The coherence vortices of spectral degree of coherence depend on the relative coherence length, mode index and positions of pairs of points. If a point and mode index are kept fixed, the position of coherence vortices changes with the increase of the relative coherence length. For the low coherent case there is a circular phase dislocation. In the coherent limit coherence vortices become intensity vortices of fully coherent Laguerre--Gaussian beams.     

结构振动诱导流场及附加质量的数值分析

将大型柔性结构低速振动诱导流体流场的问题, 归结为无粘性不可压缩无旋流动平面问题．在偶极子配置法基础上,发展了一种在结构和流体接触面上混合配置源汇和偶极子的奇点配置法,能够计算翼型、柱型等结构在流体中低速振动时诱导的流体流场并推导出流场的动能表达式,最终得到流体附加质量．给出了几个具有解析解的算例验证了此方法的可靠性．     

THEORETICAL RELATIONS OF BOUNDARY DISPLACEMENT DERIVATIVES AND TRACTIONS AT SINGULAR BOUNDARY POINT FOR 2D ISOTROPIC ELASTIC PROBLEMS

Although boundary displacement and traction are independent field variables in boundary conditions of an elasticity problem at a non-singular boundary point, there exist definite relations of singularity intensities between boundary displacement derivatives and tractions at a singular boundary point. The analytical forms of the relations at a singular smooth point for 2D isotropic elastic problems have been established in this work. By using the relations, positions of the singular boundary points and the corresponding singularity intensities of the unknown boundary field variables can be determined a priori. Therefore, more appropriate shape functions of the unknown boundary field variables in singular elements can be constructed. A numerical example shows that the accuracy of the BEM analysis using the developed theory is greatly increased.     

各向异性杆扭转问题的各向同性化域外奇点镜像法

本文通过简单的坐标变换,将各向异性杆的简单扭转问题转化成相应的各向同性杆的扭转问题,并按域外奇点镜像法求解,经逆变换得到所需的应力分量．     

非均匀弹性支承Reissner板分析的域外奇点法

本文基于Ｒｅｉｓｎｅｒ厚板理论,采用域外奇点法分析了非均匀弹性支承的厚板该法能方便地应用于工程计算中,处理诸如筏形基础筏板、桩数较多的桩基承台和高层建筑转换厚板等工程问题     

留数定理在Mellin逆变换中的应用

应用留数定理及其推论,同时结合Mellin变换和Mellin逆变换的定义,给出几类函数Mellin逆变换的求解技巧和方法.     

SINGULARITIES OF SPHERICAL FOUR-BAR MOTION

The |ink curve of a sphericel four-bar mechanism can be separated into two branches.The condition that the double points of the curve must satisfy is given. The double points maybe the double points of either branch, or the intersection points of the two branches.     

微分方程奇点指数的几何计算法

本提供一种简单的计算奇点指数的方法，中的结论和例子说明了新方法在计算微分方程指数方面的简洁性。     

用燕尾突变理论来讨论交通流预测

交通流本身是一个动态过程，运用尖点突变理论来分析交通流的预测时只考虑了流量和密度，而忽视了时间因素，这本身就不是很合理的．基于这个基础之上，采用燕尾突变理论来讨论交通流预测时将时间因素考虑进去，并给出一个算例表明了此方法预测的效果更符合现实。     

一类二阶方程的解的收敛性

本文研究一类二阶常微分方程解的渐近性态，假设方程具有正阻尼及适当保证所有解有界的条件成立，我们证明了每个解收敛于奇点，该结果能够用于系统的奇点集是不可数的情形。