Energy and stability in the Full Two Body Problem

The conditions for relative equilibria and their stability in the Full Two Body Problem are derived for an ellipsoid–sphere system. Under constant angular momentum it is found that at most two solutions exist for the long-axis solutions with the closer solution being unstable while the other one is stable. As the non-equilibrium problem is more common in nature, we look at periodic orbits in the F2BP close to the relative equilibrium conditions. Families of periodic orbits can be computed where the minimum energy state of one family is the relative equilibrium state. We give results on the relative equilibria, periodic orbits and dynamics that may allow transition from the unstable configuration to a stable one via energy dissipation.      

突变理论在边坡工程应用的研究进展

突变理论是非线性科学领域中的一个重要分支,作为一种数学工具已经在众多领域得到广泛应用,在边坡工程中的应用尤为活跃。首先简述了突变理论的发展概况和基本原理,然后分别从3个方面详细论述了突变理论在边坡工程应用中的研究进展,即基于尖点突变法的边(斜)坡稳定性分析、基于突变级数法的边(斜)坡稳定性评价和基于灰色理论、模糊数学的尖点突变预测模型对滑坡时间预报,重点讨论了相应的理论模型、应用方法和实际效果,最后结合目前存在的问题探讨突变理论在边坡工程的发展趋势。     

细砂堆积稳定性试验研究

土体发生坍塌破坏不是偶然的现象,受控于多种因素,而这些因素均为变量,不能精确地知道它们的数值.土体颗粒的大小和形状、表面特征、排列形式及它们之间的连接特征,是影响土体坍塌破坏的因素.通过干燥细砂在3种密实度下的物理模型试验,对试验破坏过程及破坏形态进行分析,找出影响细砂堆积稳定性的因素及内部破坏机理.     

On the nonlinear evolution of columnar vortices in a rotating environment

We examine the three-dimensional, nonlinear evolution of columnar vortices in a rotating environment. As the initial vorticity distribution, a wavetrain of finite amplitude Kelvin-Helmholtz vortices in shear is employed. Through direct numerical simulation of the Navier-Stokes equations we seek to better understand the process of maturation of the various three-dimensional modes of instability to which such vortical flows are subject, especially those which exist as a consequence of the action of the Coriolis force. In the absence of rotational influence, we thereby demonstrate that the nonlinear evolution of columnar vortices is most strongly controlled by one or the other of two mechanisms. One mechanism of instability is identifiable as a so-called elliptical instability, which promotes the initial bending of vortex tubes in a sinusoidal fashion, while the other is a hyperbolic mode, which is responsible for the development of streamwise vortex streaks in the "braids" between adjacent vortex cores. In the rotating case, anticyclonic vortices are strongly destabilized by weak background rotation, while rapid rotation stabilizes both the cyclones and anticyclones. The strong anticyclones are subject to two distinct forms of instability, namely a Coriolis force modified elliptical instability and an inertial (centrifugal) instability. The former instability is very similar to the nonrotating form of the elliptical instability as it promotes bending of vortex tubes, while the latter instability grows on the edge of the vortex core and generates streaks of vorticity, which surround the vortex core itself. These results of direct numerical simulation fully verify the results of previous linear stability analyses. Taken together, they provide a simple explanation for the broken symmetry that is often observed to be characteristic of the von Karman vortex streets that develop in the atmospheric lee of oceanic islands.     

西安市黑河水库左坝肩渗漏三维数值模拟及坝肩坡体稳定性分析

直接针对西安市黑河水库左坝肩渗漏这一重大工程实际问题展开研究与计算。应用三维有限差分方法对左坝肩单薄山梁的初始渗流场、蓄水后的渗流场进行了数值模拟 ,分析渗漏方式、计算相应的渗漏量 ,并通过计算说明了断层是集中渗漏通道。而后利用三维数值计算提供的水位值 ,应用极限平衡分析法 ,对左坝肩岩质斜坡稳定性进行计算与分析 ,计算结果对实际工程的决策与治理提供重要的依据。     

孕震系统中的1/f噪声行为

根据自组织临界现象理论,研究7海城、唐山等7个大地震前、后中小地震的活动特征,计算了不同孕震时期地震活动的功率谱特征.初步结果表明描述地震活动的谱幂律指数p值在大震发生前有明显的增高倾向.主震前一年及主震当年,p值一般落在闪变噪声的谱域,其他时间一般很小.最后讨论了地震孕育的物理过程及孕震系统的稳定性.     

Numerical simulation of a stratigraphic model

A multi-lithology diffusive stratigraphic model is considered, which simulates at large scales in space and time the infill of sedimentary basins governed by the interaction between tectonics displacements, eustatic variations, sediment supply, and sediment transport laws. The model accounts for the mass conservation of each sediment lithology resulting in a mixed parabolic, hyperbolic system of partial differential equations (PDEs) for the lithology concentrations and the sediment thickness. It also takes into account a limit on the rock alteration velocity modeled as a unilaterality constraint. To obtain a robust, fast, and accurate simulation, fully and semi-implicit finite volume discre tization schemes are derived for which the existence of stable solutions is proved. Then, the set of nonlinear equations is solved using a Newton algorithm adapted to the unilaterality constraint, and preconditioning strategies are defined for the solution of the linear system at each Newton iteration. They are based on an algebraic approximate decoupling of the sediment thickness and the concentration variables as well as on a proper preconditioning of each variable. These algorithms are studied and compared in terms of robustness, scalability, and efficiency on two real basin test cases.     

论热动平衡判据有关的几个问题

对平衡态和线性准平衡态的稳定性及其与力学中相关概念的相似问题作了论述，并就蒸气中液滴的不稳定性进行了讨论。     

结合某滑坡浅谈人类活动对地质环境的影响

文章通过某滑坡的现场调查、勘探取样及综合分析计算,着重说明了人类活动对滑坡体的稳定性影响,以及工程建设中保护生态与地质环境的重要性。     

“坎儿井”式排(截)水盲沟在滑坡治理中的应用

地下水影响滑坡稳定性。采用竖井分段开挖的"坎儿井"式排(截)水工程治理,取得较好效果,值得推广。