方柱和双方柱绕流的数值模拟

通过采用时间分裂步势函数有限元法,求解非定常二维不可压Navier-Stokes方程。对绕单个方柱和串列双方柱的绕流问题进行了数值模拟。给出了随时间变化柱体周围的流速分布,柱体的受力情况。本文计算结果与文献[1]的计算结果及[2]的部分实验结果趋势相符。     

NUMERICAL INVESTIGATION OF FLOW PATTERNS IN DIFFERENT PUMP INTAKE SYSTEMS

A 3-D numerical model for pump intake is established based on the Navier-Stokes equations with the RNG turbulence model and the VOF method to simulate the free surface.The applicability of the proposed model is validated by a test case of non-symmetric pump-intake bay.The predicted locations,structures and shapes of all vortices are in good agreement with those observed in experiments,though with some differences in vorticity strengths.The flow pattern and the efficiency of five types of pump intake systems are studied.The discharge and the velocity uniformity of the intake system are used as indices to evaluate its performance.     

用谱方法求解N—S方程

湍流研究具有重要的理论和工程意义，谱方法能达到快速收敛、高效和边界层中高分辨率、高精度，用谱方法边界条件处理也方便，谱方法随着数值方法的改善和计算机系统的发展，它在湍流数值模拟中的作用愈加重要，这里介绍了一平直醴道及两个同一圆柱间的三维N-S方程数值求解的谱主京城 平直槽道中在平行壁面的x及z方向上用富氏展开，在法向（y）用契比雪夫多项式展开，与平直槽道相似，在θ和z方向用富氏展开，在法向r用契比雪夫多项式展开，为解N-S方程，在时间方向用Crank-Nicholson格式，非线性项用Adam-Bashforth格式，边界和连续条件精确满足。由平直槽道和二同心圆柱间流动的数值模拟结果表明谱方法是N-S方程数值模拟的有效方法，数值结果与理论结果相符甚好。     

数值求解不可压Navier-Stokes方程的隐式算法

本文提出了一个求解二维不可压Navier-Stokes方程的隐式算法。这种方法隐式联立地处理了控制方程,和一般的迭代算法相比它具有更好的稳定性和收敛性。二维Poissuill流动的数值解和分析解是非常一致的,S形流道内分离流的计算结果和实验结果相比也是令人满意的。     

线性代数教学实践中的体会

结合线性代数课程本身的特点和学生实际情况,通过对线性代数课程的教学实践,提出了线性代数抽象概念讲解要与具体实例相结合,激发学生的学习兴趣,提高学生分析、归纳、总结和演绎的基本素质,改进教学方法和手段等措施来提高课程的教学质量。     

A new higher-order weak approximation scheme for stochastic differential equations and the Runge–Kutta method

The authors report on the construction of a new algorithm for the weak approximation of stochastic differential equations. In this algorithm, an ODE-valued random variable whose average approximates the solution of the given stochastic differential equation is constructed by using the notion of free Lie algebras. It is proved that the classical Runge–Kutta method for ODEs is directly applicable to the ODE drawn from the random variable. In a numerical experiment, this is applied to the problem of pricing Asian options under the Heston stochastic volatility model. Compared with some other methods, this algorithm is significantly faster. This research was partly supported by the Ministry of Education, Science, Sports and Culture, Grant-in-Aid for Scientific Research (C), 15540110, 2003 and 18540113, 2006, the 21st century COE program at Graduate School of Mathematical Sciences, the University of Tokyo, and JSPS Core-to-Core Program 18005.     

Bartlett adjustments for systems of linear equations with linear restrictions

Simple matrix formulae are derived for calculating a Bartlett adjustment to the likelihood ratio test statistic for testing linear parameter restrictions in a system of linear equations. For the special case of column and/or row restrictions on the matrix of coefficients the adjustment is a simple function of matrix dimensions being invariant to sample observations and the error covariance matrix. An example of testing for homogeneity and symmetry in a demand system is given.     

The geography of trade in goods and asset holdings

Gravity models have been widely used to describe bilateral trade in goods. Portes and Rey [Portes, R., Rey, H., 2005. The Determinants of Cross-Border Equity Flows. Journal of International Economics, 65(2), 269-296.] applied this framework to cross-border equity flows and found that distance, which proxies information asymmetries, is a surprisingly very large barrier to cross-border asset trade. We adopt a different point of view and explore the complementarity between bilateral trade in goods and bilateral asset holdings in a simultaneous gravity equations framework. Providing different instruments for both endogenous variables, we show that a 10% increase in bilateral trade raises bilateral asset holdings by 6% to 7%. The reverse causality is also significant, albeit smaller. Controlling for trade, the impact of distance on asset holdings is drastically reduced.     

Poisson Regression for Clustered Data

We compare five methods for parameter estimation of a Poisson regression model for clustered data: (1) ordinary (naive) Poisson regression (OP), which ignores intracluster correlation, (2) Poisson regression with fixed cluster‐specific intercepts (FI), (3) a generalized estimating equations (GEE) approach with an equi‐correlation matrix, (4) an exact generalized estimating equations (EGEE) approach with an exact covariance matrix, and (5) maximum likelihood (ML). Special attention is given to the simplest case of the Poisson regression with a cluster‐specific intercept random when the asymptotic covariance matrix is obtained in closed form. We prove that methods 1–5, except GEE, produce the same estimates of slope coefficients for balanced data (an equal number of observations in each cluster and the same vectors of covariates). All five methods lead to consistent estimates of slopes but have different efficiency for unbalanced data design. It is shown that the FI approach can be derived as a limiting case of maximum likelihood when the cluster variance increases to infinity. Exact asymptotic covariance matrices are derived for each method. In terms of asymptotic efficiency, the methods split into two groups: OP & GEE and EGEE & FI & ML. Thus, contrary to the existing practice, there is no advantage in using GEE because it is substantially outperformed by EGEE and FI. In particular, EGEE does not require integration and is easy to compute with the asymptotic variances of the slope estimates close to those of the ML.     

非线性延迟系统Runge-Kutta方法的稳定性探讨

针对时间依赖型的非线性多变延迟系统,采用变步长的Runge-Kutta方法求解,证明了匹配一定插值方法的代数稳定的Runge-Kutta方法是VR稳定的。