On Motions Near the Lagrange Equilibrium Point L 4 in the Case of Routh's Critical Mass Ratio

We deal with the planar restricted circular problem of three bodies. We study trajectories in a small neighborhood of the Lagrange equilibrium point L ₄ when mass ratio is close to Routh's value. In particular, we show that the case of proper degeneracy takes place and for most initial conditions trajectories are conditionally-periodic. We obtain an approximate representation of families of periodic solution emanating from the equilibrium point L ₄. We also show that in the case of instability of L ₄ the trajectories starting in a vicinity of L ₄ remain in a finite domain forever. We give an upper bound of this domain. To carry out our investigation, we analyze the dynamics of a general Hamiltonian system with two degrees of freedom in the case of 1 : 1 resonance in detail.This revised version was published online in October 2005 with corrections to the Cover Date.     

Plasma instability at the inner edge of the accretion disk— II

A two-dimensional instability analysis for a magneto-keplerian disk flow around a compact object is presented here. Using the eigenvalue technique, linearly coupled perturbed equations have been numerically solved within the local approximation. It is concluded that Kelvin-Helmholtz, magnetosonic (fast and slow) and resistive electromagnetic modes exist. However, only the magnetosonic mode can destabilise the disk structure. Further, we discuss the properties of different modes as a function of disk parameters and plot the eigenmode structures for different physical quantities.     

Plasma instability at the inner edge of the accretion disk—I

In this paper, the analytical and numerical results of the stability analysis of the accretion disk at the inner boundary is presented. Including the effect of finite conductivity in the disk dynamics, a simple calculation considering only the radial perturbation has been carried out. Within local approximation, it is concluded that the disk is stable to Kelvin-Helmholtz and resistive electromagnetic modes whereas the magnetosonic mode can destabilise the disk structure.     

A numerical study on the role of wind forcing,bottom topography,and nonhydrostacy in coastal upwelling

The responses of coastal upwelling to different magnitudes of wind stress over a narrow and a wide shelf are studied using a 3-D primitive equation numerical model. The results show that the position of the upwelling front depends on both the strength and the duration of the wind forcing. The comparison between different shelf widths shows that wide shelf will limit the cold water intrusion, so that the corresponding decrease in sea surface temperature is less compared to narrow shelves. Besides, the difference between hydrostatic and nonhydrostatic model results shows that nonhydrostatic effects will enhance the growth of surface meandering, and can be more pronounced near steep fronts. Although difference does exist, our results show that the nonhydrostatic effects are very small at least in this idealized study case.     

地球弓激波前的低频磁流体波

一、引言 在地球弓激波前存在着低频磁流体波。这种低频磁流体波是太阳风在地球弓激波上的反射粒子和太阳风粒子之间相互作用产生的。根据人造卫星的观测资料可以得到,在地球弓激波前,Pc3-4脉动频率范围内的低频磁流体波的主频率和行星际磁场强度     

A comprehensive study on the parameters setting in smoothed particle hydrodynamics (SPH) method applied to hydrodynamics problems

Smoothed particle hydrodynamics (SPH) is a meshfree, Lagrangian particle method which has advantages in handling solids with extremely large deformation. Like any other numerical methods, cares must be taken to ensure its desirable accuracy and stability through considering several correction techniques in calculation. The selection of values for parameters in those correction approaches is a key step in SPH simulation, which is always difficult for new beginners to deal well with effectively. This paper examines the common inconsistency and instability problems in SPH method and studies its computational efficiency when applied to hydrodynamics problems with material strength like soil column collapse. We analyzed in detail how the correction techniques mitigate these inconsistency and instability problems. Also, the numerical testing results associate with different values for the parameters used in the correction techniques are provided for better understanding the influence of these parameters and for finding out the desirable values. It is found that (1) the SPH method is easily subjected to an inconsistency problem in the boundary area due to the boundary deficiency, and it can be treated well by adopting “virtual particles” contributing to the particle summations. (2) The numerical oscillation in SPH simulation can be mitigated effectively by artificial viscosity with the suggested parameter values. (3) The tension cracking treatment, artificial viscosity and artificial stress work well in removing the tensile instability problem in SPH method. In addition, the nearest neighboring particle searching (NNPS) algorithm, spacing ratio, smoothing length and time step influence the efficiency and accuracy of SPH method significantly. It is shown that SPH method with suggested parameters values can produce a very good result compared with the experimental result.     

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饱和岩石剪切失稳后效分析

剪切载荷下的饱和岩石,在初始阶段出现几条细的剪切带,最后均形成一条剪切带。为了分析这个现象,将饱和岩石中剪切带的发展分为多阶段的过程进行分析,针对几个有限幅值扰动下剪切带的演化进行研究,获得了剪切带从几个小的非均匀扰动演化为最后充分发展的剪切带的详细过程。结果表明,剪切带的发展由两个阶段组成：非均匀剪切过程和实际剪切带发展过程。     

静力平衡近似下大气中非线性对称运动的稳定性、分岔和突变

本文在考虑基本气流具有非线性切变情况下,导出了对称运动所满足的非线性常微分方程,并用非线性系统的稳定、分岔、突变理论,严格地讨论了非线性对称运动的稳定性、分岔和突变问题,获得了一个推广的对称不稳定判据,找到了突变产生的条件。     

黑洞吸积盘的演化及温度分布的热不稳定性

本文在Ｔｈｏｒｎｅ工作的基础上讨论了吸积盘中黑洞的有关参量的演化，以及由Ｓｃｈｗａｒｚｓｃｈｉｌｄ黑洞吸积盘向Ｋｅｒｒ黑洞吸积盘演化过程中对吸积盘辐射通量的影响，最后针对几个典型的辐射过程，分别讨论了黑洞吸积盘在牛顿框架中的温度分布方程与广义相对论的温度分布方程的热不稳定性，并给出此类问题的热不稳定性的判据。