A New Method to Determine the Derivatives of the Laplace Coefficients

The determination of the secular variations of the orbital elements of objects in N-body systems is based on the literal development of the perturbing function. The development makes use of the Laplace coefficients and their derivatives. In this paper a new method is described for the analytical computation of the derivatives of the Laplace coefficients. It is an explicit formula in the sense that it only contains the Laplace coefficients and the parameter on which the Laplace coefficients depend. The advantage of this method is that it is unnecessary to calculate all the derivatives up to the desired order. It is enough to calculate the Laplace coefficients. Easy coding is a further benefit of the method and it provides more accurate numerical results. The paper describes in detail the application of the method through an example and gives comparison with former methods.This revised version was published online in October 2005 with corrections to the Cover Date.     

集合预报方法研究及应用进展综述

简要介绍了国内外集合预报研究及业务应用进展。涉及集合预报的4个方面：初始扰动生成、数值模式选择、预报信息提炼和预报系统及结果评价。结果可供改进我国集合预报业务的研究工作参考。     

奇异摄动问题UWMCB法的非古典估计

用ＵＷＭＣＢ法对一维的对流扩散问题进行分析，指出：当以对流为主时，可得到非古典的局部收敛估计及一致收敛估计，证实ＵＷＭＣＢ法是一种精度较高的数值解方法．     

一类非线性奇异边值问题的解的存在性

本文研究了如下的高阶奇异边值问题解的存在性ｙ（ｎ）＋ｆ（ｔ，ｙ，ｙ＇，．．．，ｙ（ｎ－２））＝０，ｎ≥２，０＜ｔ＜１，ｙ（ｉ）（０）＝０，０≤ｉ≤＜ｎ－２，ｙ（ｎ－１）（１）＝０其中，ｆ（ｔ，ｙ１，．．．，ｙｍ－１）在ｙｉ＝０处有奇性，ｉ＝１，．．．，ｎ－１。我们给出了该问题解存在的一个新的充分条件     

Investigation of Motion of Two Hinged Bodies Moored by Mooring Lines in Waves

In this paper, the motions are studied of a multi-body which is composed of two plates hinged together and moored by eight mooring lines in regular waves. The experimental results are compared with computational results. The linear po-tential theory and the perturbation method are combined to study this complicated system. The former is used to calculate the wave forces acting on the plates and the motion responses of them, while the latter is used to describe the dynamic character of the eight mooring lines coupled with the two hinged plates. Some response results of each plate are presented and comparisons between calculated results and experimental data are given. All the calculations are confined to regular beam waves.     

华南一次飑线过程线状对流模态变异机理研究

利用高时空分辨率的地面观测资料、探空资料、NCEP再分析资料和多普勒天气雷达资料,并结合中尺度数值模式WRF分析2013年5月15日发生在广西广东地区的一次强飑线过程,着重分析了中尺度对流系统(Mesoscale Convective System,MCS)由平行型(PS)模态到拖尾型(TS)模态的转变过程及机理。结果表明,此次飑线过程发生于高层弱辐散区,500 hPa有明显短波槽东移发展,850 hPa有切变线和低空暖湿急流,地面有冷锋和低压倒槽。西侧初始对流发展为PS型MCS模态,成熟期无雷暴高压。东侧减弱的初始对流再次加强发展后与西侧PS型MCS合并发展成为TS型MCS模态。数值模拟结果显示,PS型模态具有平行于对流线的气压梯度力和加速度分量,该分量产生了平行于对流线的风分量。TS型模态中,平行于对流线的气压梯度力和加速度很小,而垂直于对流线的气压梯度力和加速度很大,正是由于平行于对流线的加速度分量的消失和垂直于对流线的加速度分量的增强促使对流线内部相对系统流场由平行向转变为垂直向,导致MCS模态由PS型转为TS型。     

Solution of stochastic groundwater flow by infinite series,and convergence of the one-dimensional expansion

This paper investigates analytical solutions of stochastic Darcy flow in randomly heterogeneous porous media. We focus on infinite series solutions of the steady-state equations in the case of continuous porous media whose saturated log-conductivity (lnK) is a gaussian random field. The standard deviation of lnK is denoted . The solution method is based on a Taylor series expansion in terms of parameter , around the value =0, of the hydraulic head (H) and gradient (J). The head solution H is expressed, for any spatial dimension, as an infinite hierarchy of Green's function integrals, and the hydraulic gradient J is given by a linear first-order recursion involving a stochastic integral operator. The convergence of the -expansion solution is not guaranteed a priori. In one dimension, however, we prove convergence by solving explicitly the hierarchical sequence of equations to all orders. An infinite-order stochastic solution is obtained in the form of a -power series that converges for any finite value of . It is pointed out that other expansion methods based on K rather than lnK yield divergent series. The infinite-order solution depends on the integration method and the boundary conditions imposed on individual order equations. The most flexible and general method is that based on Laplacian Green's functions and boundary integrals. Imposing zero head conditions for all orders greater than one yields meaningful far-field gradient conditions. The whole approach can serve as a basis for treatment of higher-dimensional problems.     

旋转地球上不可压缩流体惯性重力波的频率方程

用微扰动方法对旋转地球上不可压缩流体的控制方程组进行线性化,得到了扰动解和流体界面上惯性重力波的频率方程。表面惯性重力波和惯性重力内波的相速公式都是这个更普遍的频率方程的特殊情况。     

Perturbation Analysis of the Attached Water Mass Effect on Offshore Platform Dynamic Response

- Theoretically speaking, it is impossible to make the differential equation of motion uncoupled for the natural modes of a system in consideration of the attached water. The hydro-elastic structure is equal to the, non-proportional damping system. In this paper a perturbation analysis method is put forward. The structure motion equation is strictly solved mathematically, and the non-proportional damping problem is transformed into a series of proportional damping ones in the superposition form. The paper also presents the calculation formula of the dyanamic response of the structure being subjected to harmonic and arbitrary load. The convergence of the proposed method is also studied in this paper, and the corresponding convergence conditions are given. Finally, the proposed method is used to analyze the displacement response of a real offshore platform. The calculation results show that this method has the characteristics of high accuracy and fast convergence.