Boussinesq方程的发展形式与Airy波理论差异性研究

应用势流理论，采用递推函数方法推导出一个新形式的Ｂｏｕｓｉｎｅｓｑ方程。通过对新方程的参数设置，可以讨论出Ｂｏｕｓｓｉｎｅｓｑ方程发展趋势和不同的发展形式。对浅水波动的描述方程，Ｂｏｕｓｓｉｎｅｓｑ方程的发展趋势为适用水深范围的拓展。拓展应用范围的大小则由其方程频散特征向Ａｉｒｙ波频散解逼近程度来决定。而Ｂｏｕｓｉｎｅｑ方程又不同于Ａｉｒｙ波，主要原因是Ｂｏｕｓｓｉｎｅｓｑ方程中含有线性频散项，Ａｉｒｙ波则只是长波首项近似，无线性频散项。其频散特征为精确的线性频散解。对实际水波传播而言，Ａｉｒｙ波理论的局限性是不言而喻的。     

Flow past an axisymmetric body embedded in a saturated porous mediumÉcoulement derrière un corps à symétrie axiale plongé dans un milieu poreux saturé

The problem of viscous fluid past an axisymmetric body embedded in a fluid saturated porous medium is studied using the Brinkman's extension. A general formula for the drag on the body is derived in the form of a limit of an expression involving the stream function characterizing the flow. The flow past an axisymmetric approximate sphere is also considered. The stream function in this case is obtained in terms of Bessel functions and Gegenbauer's functions. The drag acting on the body is evaluated by using the formula derived. Its variation is studied with respect to geometric and permeability parameters. The special cases of flow past a sphere and a spheroid are obtained from the present analysis. To cite this article: D. Srinivasa Charya, J.V. Ramana Murthy, C. R. Mecanique 330 (2002) 417–423.     

Computer algebra-perturbation solution to a nonlinear wave equation

In this paper, the higher-order asymptotic solution to the Cauchy problem of a nonlinear wave equation is found by using a computer algebra-perturbation method. The secular terms in the solution from straightforward expansions are eliminated with the straining of characteristic, coordinates and the use of the renormalization technique, and the four-term uniformly valid solution is obtained with the symbolic computation by using a computer algebra system. The comparison of the derived asymptotic solution and the numerical solution shows that they coincide with each other for smaller ε and agree quite well for larger ε (e. g., ε=0.25) Project supported by the National Natural Science Foundation of China and Shanghai Municiple Natural Science Foundation     

Approximate inertial manifolds for reaction-diffusion equations in high space dimension

The concept of approximate inertial manifolds was introduced by Foiaset al. (1987) in the case of the two-dimensional Navier-Stokes equations. These manifolds are finite dimensional smooth manifolds such that the orbits enter a very thin neighborhood of the manifold after a transient time; this concept replaces the one of inertial manifold when either an inertial manifold does not exist or its existence is not known. Our aim in this paper is to prove that approximate inertial manifolds exist for reaction-diffusion equations in high space dimension by opposition with exact inertial manifolds whose existence has only been proved in low dimension and for which nonexistence results have been obtained in space dimensionn=4.     

A defect correction approach to turbulence modeling

A method for resolving turbulent flow problems is presented, aiming at competing with the existing mathematical tractable Approximate Deconvolution Models in terms of accuracy, and outperforming these models in terms of the computational time needed. Full numerical analysis is performed, and the method is shown to be stable, easy to implement and parallelize, and computationally fast. The proposed method employs the defect correction approach to solve spatially filtered Navier–Stokes equations. A simple numerical test is provided that compares the method against the approximate deconvolution turbulence model (ADM). When resolving a fluid flow at high Reynolds number, the numerical example verifies the key feature of the method: while having the accuracy comparable to that of the ADM, the method computes in less than 80% of the time needed for the turbulence model—even before the parallelization.© 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 268–288, 2015     

A modification of the successive projections algorithm for spectral variable selection in the presence of unknown interferents

This work proposes a modification to the successive projections algorithm (SPA) aimed at selecting spectral variables for multiple linear regression (MLR) in the presence of unknown interferents not included in the calibration data set. The modified algorithm favours the selection of variables in which the effect of the interferent is less pronounced. The proposed procedure can be regarded as an adaptive modelling technique, because the spectral features of the samples to be analyzed are considered in the variable selection process. The advantages of this new approach are demonstrated in two analytical problems, namely (1) ultraviolet–visible spectrometric determination of tartrazine, allure red and sunset yellow in aqueous solutions under the interference of erythrosine, and (2) near-infrared spectrometric determination of ethanol in gasoline under the interference of toluene. In these case studies, the performance of conventional MLR-SPA models is substantially degraded by the presence of the interferent. This problem is circumvented by applying the proposed Adaptive MLR-SPA approach, which results in prediction errors smaller than those obtained by three other multivariate calibration techniques, namely stepwise regression, full-spectrum partial-least-squares (PLS) and PLS with variables selected by a genetic algorithm. An inspection of the variable selection results reveals that the Adaptive approach successfully avoids spectral regions in which the interference is more intense.     

On the quest for positivity in operator algebras

We show that in every nonzero operator algebra with a contractive approximate identity (or c.a.i.), there is a nonzero operator T such that ‖I−T‖?1. In fact, there is a c.a.i. consisting of operators T with ‖I−2T‖?1. So, the numerical range of the elements of our contractive approximate identity is contained in the closed disk center and radius . This is the necessarily weakened form of the result for C^?-algebras, where there is always a contractive approximate identity consisting of operators with 0?T?1 - the numerical range is contained in the real interval [0,1]. So, if an operator algebra has a c.a.i., it must have operators with a “certain amount” of positivity.     

非线性不等式组的光滑近似方法及其收敛性

将非线性不等式组的求解转化成非线性最小二乘问题,利用引入的光滑辅助函数,构造新的极小化问题来逐次逼近最小二乘问题.在一定的条件下,文中所提出的光滑高斯-牛顿算法的全局收敛性得到保证.适当条件下,算法的局部二阶收敛性得到了证明.文后的数值试验表明本文算法有效.     

Reproducing Kernel method for the solution of nonlinear hyperbolic telegraph equation with an integral condition

In this article, an iterative method is proposed for solving nonlinear hyperbolic telegraph equation with an integral condition. Its exact solution is represented in the form of series in the reproducing kernel space. In the mean time, the n‐term approximation u_n(x, t) of the exact solution u(x, t) is obtained and is proved to converge to the exact solution. Moreover, the partial derivatives of u_n(x, t) are also convergent to the partial derivatives of u(x, t). Some numerical examples have been studied to demonstrate the accuracy of the present method. Results obtained by the method have been compared with the exact solution of each example and are found to be in good agreement with each other. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27: 867–886, 2011     

Design of experiments on 135 cloned poplar trees to map environmental influence in greenhouse

To find and ascertain phenotypic differences, minimal variation between biological replicates is always desired. Variation between the replicates can originate from genetic transformation but also from environmental effects in the greenhouse. Design of experiments (DoE) has been used in field trials for many years and proven its value but is underused within functional genomics including greenhouse experiments. We propose a strategy to estimate the effect of environmental factors with the ultimate goal of minimizing variation between biological replicates, based on DoE. DoE can be analyzed in many ways. We present a graphical solution together with solutions based on classical statistics as well as the newly developed OPLS methodology.In this study, we used DoE to evaluate the influence of plant specific factors (plant size, shoot type, plant quality, and amount of fertilizer) and rotation of plant positions on height and section area of 135 cloned wild type poplar trees grown in the greenhouse. Statistical analysis revealed that plant position was the main contributor to variability among biological replicates and applying a plant rotation scheme could reduce this variation.