The Expansion of the Distance Between Two Arbitrary Gravitating Points as Applied to Specific Models of Celestial Bodies

For the complete system of biharmonic functions a suitable representation in spheroidal coordinates is found. It is used for expanding the distance between two arbitrary gravitating points and its inverse quantity in appropriate series. Such expansions can be of interest and useful in a number of problems of celestial mechanics and stellar dynamics.     

用遗传算法解算病态方程

对应用遗传算法解决病态方程问题进行了探讨。利用拟合法而不是通过法方程求解参数，从而避免了法方程系数求逆，使病态方程的解答有了较好的结果。通过模拟计算并和其他方法进行比较，证明该方法是可行的和有效的。     

Fast iterative solution of large undrained soil‐structure interaction problems

In view of rapid developments in iterative solvers, it is timely to re‐examine the merits of using mixed formulation for incompressible problems. This paper presents extensive numerical studies to compare the accuracy of undrained solutions resulting from the standard displacement formulation with a penalty term and the two‐field mixed formulation. The standard displacement and two‐field mixed formulations are solved using both direct and iterative approaches to assess if it is cost‐effective to achieve more accurate solutions. Numerical studies of a simple footing problem show that the mixed formulation is able to solve the incompressible problem ‘exactly’, does not create pressure and stress instabilities, and obviate the need for an ad hoc penalty number. In addition, for large‐scale problems where it is not possible to perform direct solutions entirely within available random access memory, it turns out that the larger system of equations from mixed formulation also can be solved much more efficiently than the smaller system of equations arising from standard formulation by using the symmetric quasi‐minimal residual (SQMR) method with the generalized Jacobi (GJ) preconditioner. Iterative solution by SQMR with GJ preconditioning also is more elegant, faster, and more accurate than the popular Uzawa method. Copyright © 2003 John Wiley & Sons, Ltd.     

Transformation of Lambert Conic Conformal Coordinates from a Global Datum to a Local Datum

This paper treats the problem of how to transform from global datum, for example, from the International Terrestrial Reference System (ITRS), to a local datum, for example, regional or national, for the practical case of the Lambert projection of the sphere or the ellipsoid-of-revolution to the cone. We design the two projection constants n(ϕ₁, ϕ₂) and m(ϕ₁) for the Universal Lambert Conic projection of the ellipsoid-of-revolution. The task to transform from a global datum with respect to the ellipsoid-of-revolution E_A,B² to local datum with respect to the alternative ellipsoid-of-revolution E_a,b², without local ellipsoidal height, is solved by an extended numerical example. Ideas in this paper could be of interest to those working with maps and coordinates transformation from global geodetic datum to local geodetic datum and vice versa, under the Universal Lambert Conic projection, and applicable to precise positioning and navigation, boundary demarcation and determination in the marine environment.     

Parabolic Wave Propagation Modelling in Orthogonal Coordinate Systems

This paper presents a numerical model study of the propagation of water waves using the parabolic approximation of the mild-slope equation in the orthogonal coordinate system. Two types of coordinate systems are studied: (a) a general form of orthogonal coordinate system and (b) the conformal system, a special form of orthogonal coordinate system. Two typical examples, namely, expanded breakwaters and a circular channel, are studied to validate the model. First, the examples are studied by use of the general orthogonal coordinates. Then the same examples are computed by use of the confonnal system. The computational results show that the confonnal coordinate system generally gives better predictions than the general orthogonal system. A numerical technique for generating the conformal grid is combined with the numerical model to improve the practicability of the model. The comparison between the result from the numerical grid system and that from the analytical grid system shows that reliable computational results can be obtained by use of the numerical confonnal grid system.     

二次特征值问题的最佳向后扰动分析

二次特征值问题 (QEP)的主要的求解方法之一是转化为广义特征值问题 (GEP) ,然后用求解广义特征值的方法 (比如 QZ方法 )求解。本文研究由此获得的计算解的范数意义下的最佳向后扰动分析 ,所得结果是 Tisseur最近所得结果的加强。     

Baroclinic Buoyancy-Inertia Joint Stability Parameter

At present, the barotropic buoyant stability parameter has been derived from a vertical virtual displacement of a water parcel. The barotropic inertial stability parameter in the eccentrically cyclogeostrophic, basic current field was derived in 2003 from a horizontal cross-stream virtual displacement of a parcel. By expressing acceleration of a parcel due to a virtual displacement, which is arbitrarily sloping within a vertical section across the basic current, in terms of natural coordinates, we derived the vertical component of baroclinic buoyant stability parameter B ₂ ², the horizontal component of baroclinic inertial stability parameter I ₂ ², the baroclinic joint stability parameter J ², its buoyant component B ² and its inertial component I ². B ² is far greater than I ₂ ², and when neglecting relative vorticity except for vertical shear, a downward convex curve of J ² plotted against the slope of a virtual displacement follows a trend of B ² curve. If a parcel displaces along a horizontal surface or an isopycnal surface, however, B ² vanishes, and J ² becomes equal to I ². Actual parcel is apt to displace not only along the bottom slope, but also along the sea surface and an isopycnal interfacial surface, which is approximately equivalent to an isentropic surface, preferred by lateral mixing and exchange of momentum. Such actual displacement makes B ² vanishing, and grants I ² an important role. The present analysis of I ² examining effects due to curvature and horizontal and vertical shear vorticities are useful in deepening our understanding of baroclinic instability in actual oceanic streams.     

关于GAOR、GSSOR的特征值关系式

对两种广义迭代方法ＧＡＯＲ和ＧＳＳＯＲ分别导出了其迭代矩阵和Ｊａｃｏｂｉ迭代矩阵的特征值之间的关系式，这些结果推广了已有的结果