A semi-analytic boundary element method for parabolic problems

A new semi-analytic solution method is proposed for solving linear parabolic problems using the boundary element method. This method constructs a solution as an eigenfunction expansion using separation of variables. The eigenfunctions are determined using the dual reciprocity boundary element method. This separation of variables-dual reciprocity method (SOV-DRM) allows a solution to be determined without requiring either time-stepping or domain discretisation. The accuracy and computational efficiency of the SOV-DRM is found to improve as time increases. These properties make the SOV-DRM an attractive technique for solving parabolic problems.     

波浪对圆柱外接圆弧型防波堤绕射的解析计算

在微幅波绕射理论的基础上,使用特征函数展开法,推导了圆柱外接圆弧型防波堤复合结构的水波绕射的解析解,并据此计算了该结构所受到的波浪载荷以及绕射波面分布。计算结果表明:与单一圆柱相比,外接圆弧型防波堤的存在可明显降低作用于圆柱的波浪载荷和圆柱表面的波浪爬高;采用外接堤表面密实或透空而内圆柱表面透空的结构形式可以取得圆柱防浪的较佳效果;结构透空系数、波浪入射角度、外接堤张角、外堤半径与水深比、水深与波长比等因素的变化对绕射波浪作用均存在一定影响。     

Prüfer method for periodic and semi-periodic sturm-liouville eigenvalue problems ∗

In reference [19], the authors developed a shooting algorithm for Sturm-Liouville eigenvalue problems associated with periodic and semi-periodic boundary conditions. The technique is based on the application of the Floquet theory, and it has proven to be efficient for computing eigenvalues. However, the performance of this technique depends upon the choice of the starting eigenvalues. In the present paper, we continue our study and employ the Prüfer method. An attractive property of this method is that eigenvalues can usually be accurately computed even when no information on the eigenvalue distribution is provided. Sufficient conditions for convergence, error bounds and a procedure to improve the stability are discussed. Some numerical examples are given to illustrate the effectiveness of the proposed method.     

MATLAB计算分子振动本征值和本征函数

分子动力学和分子光谱等的研究中,常常需要计算分子的振动本征值和振动本征函数。采用传统计算语言编程实现,往往繁琐而困难。MATLAB语言以矩阵为基本元素,自带的库函数可以高效便捷地解决计算其中涉及的许多数学问题。本文采用MATLAB语言计算了Morse势和双井(double well)势的振动本征值和振动本征函数。结果表明,MATLAB语言用于分子振动本征值和本征函数的计算,是一种简洁、高效的运算工具。所编制的程序具有普适性,只需对势能函数进行简单修改即可用于真实双原子分子的振动计算。     

本征函数法的推广及其应用

将本征函数法进行了推广,并结合传统方法的优点和经典的振动问题提出推广的本征函数法.放宽了对边界条件的要求,改善了传统方法的繁冗过程,得到求解非齐次振动问题的普遍方法.推广的本征函数法可应用于热传导问题.     

气体静压轴颈轴承振动频率特性研究

针对气体静压主轴的运动特性和气体静压润滑轴承的参数结构，提出了采用质量一弹簧结构方法来等效气体静压轴颈轴承系统，并建立了系统二自由度运动方程，最终确定了系统的主坐标系和固有频率。仿真实验证明，当气源干扰力频率与系统的固有频率相等时，会发生共振现象，导致主轴中心运动轨迹发散。     

无序体系薛定谔算子格林函数及谱分布

无序体系通常有着独特的光电性质,随着材料应用的深入,无序体系渐渐引起关注.研究无序体系的物理性质,最重要的便是它的电子性质,这与薛定谔算子谱的性质有关.而研究薛定谔算子谱的性质,关键是要研究格林函数的衰减性.它从数理角度描述了微观粒子的运动状态,对相应物理现象的解释和预测很有意义.通过两类典型无序体系薛定谔算子格林函数的衰减性质及谱分布的相关推论,可以看出,两种算子具有一定相似性,但目前对这两种算子格林函数衰减性的研究采用的是不同的方法.后续可以寻求更统一的对准周期体系和随机体系或其他无序体系特征函数局域化的研究方法,并推广到更一般的无序体系中.     

Characteristics of heating process in microwave applicators with elements in periodic motion

Moving elements have been widely used in microwave applicators to improve heating uniformity. However, elements in periodic motion can lead to temperature oscillations in the process of heating. In this case, the processed samples are difficult to reach target temperature and the control system may also become unstable. Aiming at overcoming these problems, we investigate the temperature response of the heating process in microwave applicators with elements in periodical motion in this article. By modeling periodical motion as a periodical heat source, the temperature characteristics can be obtained by solving the heat transfer equation with eigenfunction expansions. The results show that the amplitude of temperature oscillations decreases with angular velocity of the element's motion, which is verified by experiments. It means that temperature oscillations can be reduced by increasing the element's velocity, which is helpful to improve the heating performance in microwave applicators.     

等离子体压强和粘度效应的线性化数值分析

从线性化理想磁流体方程组出发, 应用半解析方法, 数值求解了圆柱位型等离子体压强和粘度对轴向本征函数的影响, 主要结论包括:无论等离子体粘度如何变化, 轴向本征函数均随着等离子体压强的增大而减小。等离子体半径较小 (约小于0.3) 时的轴向本征函数均为负值, 等离子体半径较大 (约大于0.3) 时的轴向本征函数均为正值。压强较低时, 靠近圆柱中心和等离子体壁处的轴向本征函数受粘度影响较大。     

基于设计空间的基本开关电容电路滤波器设计

提出了一种运用符号和数值计算与离散非线性优化相结合的滤波器设计方法——设计空间法,把滤波器的技术指标,即滤波器设计中要用到的一组参数映射到设计空间,并根据给定的准则寻找这一设计空间的最佳解决方案。然后介绍了一种新型的具有独立零点设置的基本二阶开关电容电路,最后通过实例阐述了用设计空间法设计一开关电容（SC）低通滤波器,实验证明了该方法的可行性,并且得到了预期的效果。