Capture in the Circular and Elliptic Restricted Three-Body Problem

In this paper the authors provide a study of the phenomenon of the gravitational capture by using the models of the circular and elliptic restricted three-body problem. In the first part the inadequacy of the circular restricted three-body problem in the study of the phenomenon of the capture in the case of NEAs is shown. In the model of the spatial elliptic restricted three-body problem criteria of the capture are deduced by using the pulsating Hill-regions. This revised version was published online in July 2006 with corrections to the Cover Date.     

用双椭圆方法确定反射点位置

在反射波地震勘探中使用动校正确定反射点位置用到很多假设,如勘探深度要远远大于炮检距;假定倾斜反射界面的反射点与水平反射界面反射点都位于炮检距的中点;近似认为倾斜反射界面的动校正量等于水平反射界面的动校正量;假定反射面倾角固定且较小等,上述假设一定会造成勘探误差。由于反射点位置和反射面倾角未知,所以理论上无法唯一地确定反射点位置。如果反射波传播的介质的波速一定,从炮点发出的地震波,经反射点后,在接收点被接收,其可能的反射点是椭圆的一部分,但还不能唯一确定反射点;再取炮点和另外一个接收点,其可能的反射点是另外一个椭圆的一部分。如果假定反射面是平面,可以是水平面,也可以是有固定倾角的倾斜平面,该平面在地震波射线平面内是一条直线,该直线一定是两椭圆的公切线。把两椭圆方程和切线方程联立,就可以求解出公切点位置,公切点位置就是反射点位置,这就是用双椭圆确定反射点位置的方法。通过建立模型对勘探方法进行了检验,证实了用双椭圆方法确定反射点位置的有效性。双椭圆方法有一个重要的副产品,就是在确定反射面位置的同时计算出反射面的视倾角。     

四叉树网格下的椭圆型缓坡方程数值模型研究

波浪是近岸海域关键的水动力因素之一。考虑到近岸地形复杂、波浪演化显著的特点,建立了四叉树网格体系下的椭圆型缓坡方程数值模型,采用有限体积法对模型进行数值离散,应用GPBiCG(m, n)算法求解离散后的控制方程。模型中根据波浪波长布局计算网格,生成多层次四叉树网格,对复杂计算域有较好的适应性,并且在离散和方程求解中无需引入形函数、不产生复杂的交叉项,节约了存储空间和计算时间。将模型成功应用于物理模型实验及Acapulco海湾的波浪场数值模拟,结果表明该模型能够准确、高效地模拟近岸波浪场,可为近岸波浪场的模拟提供一定的理论和技术支持。     

P/GE-Wang joins P/Slaughter-Burnham and P/Boethin in the club of comets in 1/1 resonance with jupiter

Three comets are now known to be at or near the 1/1 resonance with Jupiter P/Slaughter-Burnham, P/Boethin and the newly discovered P/Ge-Wang. Their orbital evolutions are compared, using the elliptic three-dimensional restricted three-body model Sun-Jupiter-comet. Although details of the individual orbits differ, the three comets have very similar general dynamical behaviours, and stay during a long time at or near the 1/1 resonance, at least for several thousand years.     

Estimation of seismic hazard with allowance for noncircular isoseismals of arbitrary orientation

A new mathematical model describing the field of macroseismic intensity has been elaborated. It is based on elliptic isoseismals. The orientation of the main axes of elliptic isoseismals depends on the direction of stretching of the main geological structures on the investigated territory.The new model of a macroseismic field was applied to the territory of Eastern Uzbekistan. Some results of macroseismic investigations of the effect of large regional earthquakes were used as initial data.A noncircular model of a macroseismic field was introduced into the integral of the seismic shakability of Riznichenko and, according to the model, a macroseismic shakability map for the territory of Eastern Uzbekistan was computed in isolines of the long-term mean return period of vibrations for the intensity I 8.Paper presented at the 21st General Assembly of the European Seismological Commission, Sofia, 1988.     

FAST天线用于VLBI观测系统性能分析

讨论了射电天线用于天文观测和VLBI大地测量时的几项性能参数；列出了我国现有射电天线组成系统时的工作性能和观测精度；计算了利用我国现有射电天线与FAST天线组成基线进行观测时的系统性能以及所要求射电源的最低流量密度。由此可以看出FAST天线用于VLBI观测具有巨大潜力。     

An upscaling method for one‐phase flow in heterogeneous reservoirs. A weighted output least squares (WOLS) approach

In this paper we study the problem of determining the effective permeability on a coarse scale level of problems with strongly varying and discontinuous coefficients defined on a fine scale. The upscaled permeability is defined as the solution of an optimization problem, where the difference between the fine scale and the coarse scale velocity field is minimized. We show that it is not necessary to solve the fine scale pressure equation in order to minimize the associated cost‐functional. Furthermore, we derive a simple technique for computing the derivatives of the cost‐functional needed in the fix‐point iteration used to compute the optimal permeability on the coarse mesh. Finally, the method is illustrated by several analytical examples and numerical experiments. This revised version was published online in July 2006 with corrections to the Cover Date.     

An elliptic problem with integral constraints with application to large-scale geophysical flows

We present a weak formulation of a non-standard elliptic equation whose boundary values are determined in part by integral relations. Existence and uniqueness of its solution are proved, and a finite element discretization is described, analyzed, and implemented on a test problem. The equation is a generalization of one that is solved during integration of the three-dimensional Quasigeostrophic equations, which model large-scale rotating stratified flows, where the integral constraints represent conservation of physical properties.     

Control-Volume Discretization Method for Quadrilateral Grids with Faults and Local Refinements

This paper extends the multipoint flux-approximation (MPFA) control-volume method to quadrilateral grids for which the adjacent cells do not necessarily share corners. Examples are grids with faults and locally refined grids. This paper gives a derivation of the method for such grids. The difference between two-point flux-approximation (TPFA) results and MPFA results for faults and local grid refinements is demonstrated for synthetic problems. Further, the results are compared with results from uniform fine-grid simulations. The effect of repeated fault patterns as well as anisotropy is investigated. Large errors may be found for the TPFA method for flow through a series of faults in an anisotropic medium. Finally, a comparison is done for a reservoir field application.     

塑料排水板处理地基非线性固结计算研究

针对目前国内外竖井地基非线性固结计算大多均采用近似等效法求解的不足,根据软土固结理论及数学理论推导,基于塑料排水板椭圆柱假定,推导了考虑地基土水平渗透系数、压缩模量随固结过程非线性变化影响下的排水板处理地基非线性固结控制方程,并利用数学中非线性微分方程理论,给出了非线性固结解析解。通过与Indraratna等非线性固结近似解对比分析,认为理想井下预压荷载越大（Nu越大）,则Indraratna等近似法成果误差越大;且在Cc/Ck = 1.8、Nu = 5时Indraratna等近似解与该理想井非线性固结精确解析解误差高达16%,而解析解与精确数值解基本一致。最后通过Indraratna等典型工程案例验证分析,认为所得理论更符合工程实际,具有较好的工程应用价值。