Nonuniform FDM for Poisson-Type Equations on a Disk with Singular Solutions

We are concerned with the Dirichlet boundary value problem of Poisson-type equations on a disk. Matsunaga and Yamamoto [8 N. Matsunaga and T. Yamamoto ( 1999 ). Convergence of Swartztrauber–Sweet's approximation for the Poisson-type equation on a disk . Numer. Funct. Anal. Optimz. 20 : 917 – 928 .[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]] proved that if the exact solution u is very smooth over the closure of the disk, then the approximate solution by the Swartztrauber–Sweet scheme with uniform partition is second order accurate. In this article, it is assumed that the exact solution performs singular properties such that its derivatives go to infinity at the boundary of the disk. We use a stretching polynomial-like function with a parameter to construct a local grid refinement and consider the Swartztrauber–Sweet scheme over the non-uniform partition. The effects of the parameter are analyzed completely by carrying out convergence analysis and numerical results show that there exists an optimal value for the parameter to have a best approximated solution.     

Convergence of Extrapolated BDF2 Finite Element Schemes for Unsteady Penetrative Convection Model

Extrapolated two-step backward difference (BDF2) in time and finite element in space discretization for the unsteady penetrative convection model is analyzed. Penetrative convection model employs a nonlinear equation of state making the problem more nonlinear. Optimal order error estimates are derived for the semi-discrete finite element spatial discretization. Two time discretization schemes based on linear extrapolation are proposed and analyzed, namely a coupled and a decoupled scheme. In particular, we show that although both schemes are unconditionally nonlinearly stable, the decoupled scheme converges unconditionally whereas coupled scheme requires that the time step be sufficiently small for convergence. These time discretization schemes can be implemented efficiently in practice, saving computational memory. Numerical computations and numerical convergence checks are presented to demonstrate the efficiency and the accuracy of the schemes.     

On the Associated Primes of Matlis Duals of Top Local Cohomology Modules

After motivating the question, we prove various results about the set of associated primes of Matlis duals of top local cohomology modules. In some cases, we can calculate this set. An easy application of this theory is the well-known fact that Krull dimension can be expressed by the vanishing of local cohomology modules.     

A novel all-optical label processing based on multiple optical orthogonal codes sequences for optical packet switching networks

This paper proposes an all-optical label processing scheme that uses the multiple optical orthogonal codes sequences (MOOCS)-based optical label for optical packet switching (OPS) (MOOCS-OPS) networks. In this scheme, each MOOCS is a permutation or combination of the multiple optical orthogonal codes (MOOC) selected from the multiple-groups optical orthogonal codes (MGOOC). Following a comparison of different optical label processing (OLP) schemes, the principles of MOOCS-OPS network are given and analyzed. Firstly, theoretical analyses are used to prove that MOOCS is able to greatly enlarge the number of available optical labels when compared to the previous single optical orthogonal code (SOOC) for OPS (SOOC-OPS) network. Then, the key units of the MOOCS-based optical label packets, including optical packet generation, optical label erasing, optical label extraction and optical label rewriting etc., are given and studied. These results are used to verify that the proposed MOOCS-OPS scheme is feasible.     

光纤型宽带可调连续波差频产生中红外激光器转换效率的研究

以掺镱光纤激光器为抽运源、掺铒光纤激光器后接掺铒光纤放大器为信号源,利用周期极化掺镁铌酸锂晶体,研究了全光纤化差频产生中红外激光器的转换效率特性。结果表明,抽运光和信号光偏振态影响差频产生过程的转换效率,利用偏振控制器,可将抽运光和信号光偏振方向调节到与晶体光轴方向平行,以获得高的转换效率。抽运光和信号光的光束质量既影响差频产生过程的转换效率,又决定晶体纵向位置的容限,当聚焦系统由自聚焦透镜和焦距100mm平凸透镜组成时,相对转换效率达0.717mW-2,晶体纵向位置容限为44mm。此外,差频光在3126.36~3529.6nm范围内调谐时,转换效率基本保持不变。     

An asymmetric full velocity difference car-following model

This paper presents a car-following model that considers the asymmetric characteristic of the velocity differences of the vehicles in a traffic stream. The problems of the prevalent general force (GF) model and the full velocity difference (FVD) model were solved. Furthermore, the optimal velocity (OV) model, the GF model, and the FVD model are proved to be the special cases of the proposed asymmetric full velocity difference (AFVD) model. The mathematical model is presented, followed by simulation analysis which demonstrates the properties of the AFVD model.     

一种确定光纤传感器中3×3耦合器输出信号相位差的新算法

本文提出了一种基于Bessel函数展开,在频域内精确确定光纤传感器3×3耦合器输出信号相位差的算法。在Mach-Zehnder干涉仪原理的基础上,通过建立3~3耦合器输出信号的数学模型和利用耦合器输出光功率的Bessel展开,完成了算法的理论推导,并且在实验室中进行了声学实验。数据处理结果表明,该算法能够较精确地确定3×3耦合器输出信号的相位差,且相位差与调制频率无关,与理论相符。     

二维随机介质中的能量分布和频谱特性

研究了二维随机介质中能量的空间分布和一些特定区域的频谱特性.结果显示介质中能量呈局域化分布,其分布与介质中颗粒的随机分布有关,还与激发光的波长有密切的关系,介质中能量聚集的区域和介质的准封闭区域有一定关系但并非一一对应.所考察的各准封闭区域的频谱均随时间变化,在同一激发光的激励下各准封闭区域的频谱均不相同,而同一区域在不同的激发光的激励下频谱也不相同.当激发波长与准封闭区域的结构参数偏差较大时,频谱中谱峰会出现此消彼涨的模式竞争现象,而且能量衰减得较快;而当激发波长与该结构参数较接近时,相应的频谱中存在一 关键词： 激光物理 有限时域差分法 局域化 频谱特性     

扫描白光干涉测量技术的算法比较

干涉条纹零光程差位置的确定是扫描白光干涉测量的关键技术之一。介绍了扫描白光干涉法测量物体轮廓的原理,讨论了确定白光干涉条纹零级条纹位置的几种方法,并对随机生成的表面进行了大量的数字模拟测量和分析比较,得出了各种算法对测量准确度的影响。研究结果对白光干涉的应用研究提供了可靠的理论根据。