Superconvergence of discontinuous Galerkin finite element method for the stationary Navier‐Stokes equations

This article focuses on discontinuous Galerkin method for the two‐ or three‐dimensional stationary incompressible Navier‐Stokes equations. The velocity field is approximated by discontinuous locally solenoidal finite element, and the pressure is approximated by the standard conforming finite element. Then, superconvergence of nonconforming finite element approximations is applied by using least‐squares surface fitting for the stationary Navier‐Stokes equations. The method ameliorates the two noticeable disadvantages about the given finite element pair. Finally, the superconvergence result is provided under some regular assumptions. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 23: 421–436, 2007     

Numerical analysis for the periodic response of nonsmooth dynamic systems of high-dimension

This paper deals with the numerical solution of high dimensional dynamic systems with nonsmooth characteristics, such as structural elastoplasticity, mechanical clearance and dry friction. As a stable periodic response of the system attracts its transient response, it may be extracted from the transient response somehow. The paper suggests a novel iteration scheme to extrapolate the periodic response from a short time history of its transient response by curve fitting. Compared with the current schemes such as shooting and incremental harmonic balancing, the present scheme makes full use of the information within the transient response and the system characters, then its computation efficiency has increased by an order and the numerical convergence depending on the initial iteration has greatly improved.The subject supported by the Chinese Foundation of Aeronautical Science     

灰色Verhulst模型的样条插值函数的残差修正

本用样条函数对灰色Verhulst模型的残差序列进行插值拟合，然后作用于二阶线性微分方程，并以此修正原模型，得到一种新的预测模型的数值解，提高了拟合的精确度。     

Likelihood estimation of soft-core interaction potentials for Gibbsian point patterns

The likelihood method is developed for the analysis of socalled regular point patterns. Approximating the normalizing factor of Gibbs canonical distribution, we simultaneously estimate two parameters, one for the scale and the other which measures the softness (or hardness), of repulsive interactions between points. The approximations are useful up to a considerably high density. Some real data are analyzed to illustrate the utility of the parameters for characterizing the regular point pattern.     

人工神经网络及其在分析化学中的应用

人工神经网络是一种新兴的计算方法，有着广阔的发展前途，目前在分析化学领域已经有了多方面的应用。本文简要介绍了人工神经网络的原理及其在分析化学中的应用。     

Sixth algebraic order trigonometrically fitted predictor–corrector methods for the numerical solution of the radial Schrödinger equation

Our new trigonometrically fitted predictor–corrector (P–C) schemes presented here are based on the well known Adams–Bashforth–Moulton methods: the predictor is based on the fifth order Adams–Bashforth scheme and the corrector on the sixth order Adams–Moulton scheme. We tested the efficiency of our newly developed schemes against well known methods, with excellent results. The numerical experiments showed that at least one of our schemes is noticeably more efficient compared to other methods, some of which are specially designed for this type of problem. It is also worth mentioning that this is the first time that sixth algebraic order trigonometrically fitted Adams–Bashforth–Moulton P–C schemes are used to efficiently solve the radial Schrödinger equation.Active Member of the European Academy of Sciences and Arts     

桥联双β-环糊精对N-[4-(1-芘基)]丁酰-D/L-苯丙氨酸的手性识别及机理研究

利用紫外-可见吸收和荧光发射光谱, 结合非线性最小二乘法拟合曲线以及分子力学(MM2)模拟系统地研究了手性分子N-[4-(1-芘基)]丁酰-D/L-苯丙氨酸(PDP和PLP, 总称PPs)与β-环糊精(β-CD)、 2-位硒桥联双β-CD(2-SeCD)和2-位碲桥联双β-CD(2-TeCD)的包结能力大小及这3个环糊精对PPs手性识别能力的差异和识别机理. 研究结果表明, PPs不能与单疏水空腔的β-CD形成很好的包结复合物, 与具有较长桥联链的2-TeCD结合能力最强. 2-TeCD与PDP和PLP的结合常数分别为2.33×104和6.07×103 L/mol, 对PPs的手性识别比达到KD/KL=3.84, 高于2-SeCD(KD/KL=2.61). 用MM2模拟得出了PPs与这两个双环糊精形成复合物的三维结构: PPs的绝大部分位于双环糊精两个空腔之间, 但是在这两个复合物中, 苯环与芘环所成的二面角不同. 此外, PPs与这两个双环糊精作用时均存在明显的氢键相互作用, 且2-TeCD强于2-SeCD.     

Fitting complex potential energy surfaces to simple model potentials: application of the simplex-annealing method

A stochastic method of optimization, which combines simulated annealing with simplex, is implemented to fit the parameters of a simple model potential. The main characteristic of the method is that it explores the whole space of the parameters of the model potential, and therefore it is very efficient in locating the global minimum of the cost function, in addition to being independent of the initial guess of the parameters. The method is employed to fit the complex intermolecular potential energy surface of the dimer of water, using as a reference the spectroscopic quality anisotropic site-site potential of Feller et al. The simple model potential chosen for its reparameterization is the MCY model potential of Clementi et al. The quality of the fit is assessed by comparing the geometry of the minimum, the harmonic frequencies, and the second virial coefficients of the parameterized potential with the reference one. Finally, to prove more rigorously the robustness of this method, it is compared with standard nonstochastic methods of optimization.     

溶剂蒸气对聚对苯二甲酸乙二酯作用的差示扫描量热研究

用差示扫描量热(DSC)研究了几种有机溶剂蒸气对聚对苯二甲酸乙二酯(PET)的作用,表明可分为反应性的和非反应性的两种。同时,对于非反应性的作用,依冷结晶峰面积的变化,又可分为三种类型:冷结晶峰面积不变,经诱导期后下降,无诱导期而迅速下降。双冷结晶峰现象在一些非反应性溶剂处理过的PET试样的DSC曲线也观察到。     

Analyzing electrochemical noise with Chebyshev’s discrete polynomials

The principles underlying a novel method intended for analyzing experimental data obtained when studying fluctuation processes are considered. The method in question is Chebyshev’s spectroscopy. The application of this method allows one to determine statistic characteristics of steady-state electrochemical noise against the background of severe deterministic interference without invoking the procedure of the fitting of the initial data. The potentialities of this novel method, which is intended for treating noise experiment, are demonstrated by examining model examples and analyzing the electrochemical noise generated by a lithium electrode placed in an aprotic organic electrolyte.