Interpolation on spherical geodesic grids: A comparative study

Most operational models in atmospheric physics, meteorology and climatology nowadays adopt spherical geodesic grids and require “ad hoc” developed interpolation procedures. The author does a comparison between chosen representatives of linear, distance-based and cubic interpolation schemes outlining their advantages and drawbacks in this specific application field. Numerical experiments on a standard test problem, while confirming a good performance of linear and distance-based schemes in a single interpolation step, also show their minor accuracy with respect to the cubic scheme in the more realistic simulation of advection of a meteorological field.     

Numerical simulation of soft palate movement and airflow in human upper airway by fluid-structure interaction method

In this paper, the authors present airflow field characteristics of human upper airway and soft palate movement attitude during breathing. On the basis of the data taken from the spiral computerized tomography images of a healthy person and a patient with Obstructive Sleep Apnea-Hypopnea Syndrome (OSAHS), three-dimensional models of upper airway cavity and soft palate are reconstructed by the method of surface rendering. Numerical simulation is performed for airflow in the upper airway and displacement of soft palate by fluid-structure interaction analysis. The reconstructed three-dimensional models precisely preserve the original configuration of upper airways and soft palate. The results of the pressure and velocity distributions in the airflow field are quantitatively determined, and the displacement of soft palate is presented. Pressure gradients of airway are lower for the healthy person and the airflow distribution is quite uniform in the case of free breathing. However, the OSAHS patient remarkably escalates both the pressure and velocity in the upper airway, and causes higher displacement of the soft palate. The present study is useful in revealing pathogenesis and quantitative mutual relationship between configuration and function of the upper airway as well as in diagnosing diseases related to anatomical structure and function of the upper airway. The project supported by the National Natural Science Foundation of China (10672036, 10472025 and 10421002), the Natural Science Foundation of Liaoning Province (20032109). English text was polished by Yunming Chen.     

全息模拟再现像的三维重构

提出一种全息模拟再现像的三维重构方法，可以模拟再现得到三维再现像.计算机模拟再现许多幅在不同深度位置的二维光强分布；利用灰度级变化的聚焦度评价方法，通过寻找最大聚焦度值，确定再现三维像各像点的深度信息.实验证明,该方法能实现模拟再现像的三维重构，使数字全息术有希望成为一种全新的三维面形检测技术.再现像三维重构的实现可以更客观地对全息图进行像质评价，并验证计算机制全息术算法的正确性.     

高温超导体磁通跳跃数值模拟

文中基于超导磁通动力学理论,考虑电磁力与热激活对磁通运动的影响,基本物理模型由等效电阻率随超导体温度和磁场变化的磁通扩散方程,以及比热随超导体温度变化的热传导方程组成。在此基础上,用差分法数值求解了这一复杂非线性系统的磁热耦合控制方程,得到了与实验观测结果基本一致的数值模拟结果。结果还表明：外加磁场变化速度、超导体初始温度以及超导尺寸对于磁通跳跃均产生明显的影响。     

On the Numerical Range of Operator Polynomials

An upper bound for the number of components of the numerical range of matrix polynomials is established. We also establish a necessary condition and a sufficient condition for the connectedness of the numerical range of a quadratic selfadjoint matrix polynomial. The boundary of the numerical range of linear matrix polynomials is also considered.     

连续级联喇曼光纤激光器耦合波方程的修正

从最基本的耦合波方程出发，考虑光波正反向传输的情况下，推导出了一个全面的、准确的关于连续级联喇曼光纤激光器的理论模型，描述了各级Stokes光波功率沿光纤长度的变化.指出了相关一些文献中存在的不足，并且给出了多级斯托克斯光波相互作用的有效作用面积的表达式.此模型有助于喇曼光纤激光器的设计.     

子系统为S≥3的非线性大系统在近平衡区内的稳定性

本文采用文[1,2]中提出的平衡结构法研究子系统s≥3的非线性大系统在近平衡区内的稳定性;得到了判别这类大系统稳定性的两个一般性准则.     

Gd3+对Ca0.8Zn0.2TiO3:Pr3+红色发光材料的敏化作用

采用溶胶-凝胶法在较低温度下合成了红色发光材料Ca0.8Zn0.2TiO3:0.002Pr3 ,xGd3 .金属离子预先溶解含有柠檬酸的乙二醇溶液中.XRD表明在800℃灼烧2h形成了钛酸盐的晶体.荧光检测结果表明所合成样品的特征激发峰为330nm、特征发射峰为614nm,分别对应于O(2p)→Ti(3d)带间跃迁和Pr3 的1D2→3H4的特征发射.样品的发光强度随x的不同而不同,发光强度增强了29%-69%.当x＝0.0005时,即nPr3 :nGd3 ＝4∶1时样品的红色发光强度最强,发光强度增强了69%.     

Numerical differentiation from a viewpoint of regularization theory

In this paper, we discuss the classical ill-posed problem of numerical differentiation, assuming that the smoothness of the function to be differentiated is unknown. Using recent results on adaptive regularization of general ill-posed problems, we propose new rules for the choice of the stepsize in the finite-difference methods, and for the regularization parameter choice in numerical differentiation regularized by the iterated Tikhonov method. These methods are shown to be effective for the differentiation of noisy functions, and the order-optimal convergence results for them are proved.

     

大型稀疏无约束最优化问题的行列修正算法

本文提出了一类适用于大型稀疏最优化问题的简单易行的行列修正算法，获得了新算法的局部超一性收敛性，大量的数值试验表明这是一个较为理想的修正算不。新算法同样可以用来求解大型对称性非线性方程组。