Lagrangian singularities of steady two-dimensional flow     

Walter Pauls  Takeshi Matsumoto 《地球物理与天体物理流体动力学》2013,107(1):61-75

The Lagrangian complex-space singularities of the steady Eulerian flow with stream function sin x ₁ cos x ₂ are studied by numerical and analytical methods. The Lagrangian singular manifold is analytic. Its minimum distance from the real domain decreases logarithmically at short times and exponentially at large times.  相似文献   

一种利用流形学习进行多影像匹配的方法     

李爱霞  关泽群  冯甜甜 《武汉大学学报(信息科学版)》2012,37(11)

提出了一种利用流形学习方法进行多影像匹配的算法。通过两组宽基线序列影像的匹配实验,并与LE-SIFT方法、SVD-SIFT方法和基于局部线性映射的LLE-SVD方法进行了对比分析。结果表明,本文方法在获得多幅影像的共同匹配结果和利用多幅影像之间的约束实现两幅影像匹配的结果上都优于现有方法。  相似文献   

Dynamics in the Center Manifold Around L2 in the Quasi-Bicircular Problem     

M. A. Andreu 《Celestial Mechanics and Dynamical Astronomy》2002,84(2):105-133

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Motion Around The Triangular Equilibrium Points Of The Restricted Three-Body Problem Under Angular Velocity Variation     

K.?E.?PapadakisEmail author 《Astrophysics and Space Science》2005,299(2):129-148

We study numerically the asymmetric periodic orbits which emanate from the triangular equilibrium points of the restricted three-body problem under the assumption that the angular velocity ω varies and for the Sun–Jupiter mass distribution. The symmetric periodic orbits emanating from the collinear Lagrangian point L ₃, which are related to them, are also examined. The analytic determination of the initial conditions of the long- and short-period Trojan families around the equilibrium points, is given. The corresponding families were examined, for a combination of the mass ratio and the angular velocity (case of equal eigenfrequencies), and also for the critical value ω = 2, at which the triangular equilibria disappear by coalescing with the inner collinear equilibrium point L ₁. We also compute the horizontal and the vertical stability of these families for the angular velocity parameter ω under consideration. Series of horizontal–critical periodic orbits of the short-Trojan families with the angular velocity ω and the mass ratio μ as parameters, are given.  相似文献   

层状岩石边坡倾倒破坏过程的数值流形方法模拟   总被引：3，自引：0，他引：3  

刘红岩  秦四清 《水文地质工程地质》2006,33(5):22-25

层状岩石边坡的倾倒破坏是岩石边坡失稳破坏的主要形式之一。本文利用数值流形方法对一层状岩石边坡的倾倒破坏过程进行了模拟。模拟结果表明：在不考虑块体间粘结力的情况下，块体间的摩擦角决定着岩石边坡的稳定性。随着摩擦角的增加，块体间的摩擦系数增大，岩石边坡的稳定性增强，并出现相应的滑动区、倾倒区和稳定区。模拟结果与相应的理论预测结果相吻合。  相似文献   

Evaluation of Reinforced Concrete Design for an Underground Outlet Manifold in Shanxi Yellow River Diversion Project   总被引：1，自引：0，他引：1  

W. Z. Chen  W. S. Zhu  S. C. Li  X. B. Qiu 《Rock Mechanics and Rock Engineering》2004,37(3):213-228

Summary In order to verify the design feasibility of the reinforced concrete lining of the outlet manifold in Shanxi Yellow River Diversion Project (YRDP), field investigations on rock mass deformability, in situ stress and hydraulic jacking measurements have been carried out. Based on the results obtained, 3-D FEM numerical analyses have been performed to calculate the stress distribution in a reinforced concrete lining under internal and external water pressure. Furthermore, the initial designed shape and steel ratio of concrete have been modified to satisfy the requirements for the limit crack width design criteria in China and decrease the tensile stress level in concrete. The new steel ratio of reinforced concrete has been calculated on the basis of the numerical results considering the modified shape of the outlet manifold. Both the owner and designer of YRDP have adopted the steel ratio of concrete in the working design and construction of the outlet manifold.  相似文献   

The Evolution of the Stable and Unstable Manifold of an Equilibrium Point     

Kenneth R. Meyer 《Celestial Mechanics and Dynamical Astronomy》1998,70(3):159-165

We consider the evolution of the stable and unstable manifolds of an equilibrium point of a Hamiltonian system of two degrees of freedom which depends on a parameter,ν. The eigenvalues of the linearized system are complex for ν < 0 and purely imaginary for ν > 0. Thus for ν < 0 the equilibrium has a two‐dimensional stable manifold and a two‐dimensional unstable manifold, but for ν > 0 these stable and unstable manifolds are gone. We study the system defined by the truncated generic normal form in this situation. One of two things happens depending on the sign of a certain quantity in the normal form expansion. In one case the two families detach as a single invariant manifold and recedes from the equilibrium as ν tends away from 0 through positive values. In the other case the stable and unstable manifold are globally connected for ν < 0 and the whole structure of these manifolds shrinks to the equilibrium as ν → 0 and disappears. These considerations have interesting implications about Strömgren's conjecture in celestial mechanics and the blue sky catastrophe of Devaney.  相似文献   

Tangential‐projection algorithm for manifold representation in unidentifiable model updating problems     

Lambros S. Katafygiotis  Heung‐Fai Lam 《地震工程与结构动力学》2002,31(4):791-812

The problem of updating a structural model and its associated uncertainties by utilizing structural response data is addressed. In an identifiable case, the posterior probability density function (PDF) of the uncertain model parameters for given measured data can be approximated by a weighted sum of Gaussian distributions centered at a number of discrete optimal values of the parameters at which some positive measure‐of‐fit function is minimized. The present paper focuses on the problem of model updating in the general unidentifiable case for which certain simplifying assumptions available for identifiable cases are not valid. In this case, the PDF is distributed in the neighbourhood of an extended and usually highly complex manifold of the parameter space that cannot be calculated explicitly. The computational difficulties associated with calculating the highly complex posterior PDF are discussed and a new adaptive algorithm, referred to as the tangential‐projection (TP) algorithm, allowing for an efficient approximate representation of the above manifold and the posterior PDF is presented. Using this approximation, expressions for calculating the uncertain predictive response are established. A numerical example involving noisy data is presented to demonstrate the proposed method. Copyright © 2002 John Wiley & Sons, Ltd.  相似文献   

基于数值流形法的反倾层状岩质边坡倾倒破坏分析     

王欢欢  郭明珠 《震灾防御技术》2021,16(2):346-351

边坡破坏是累积性过程，从变形到破坏的过程中会产生永久位移，如果永久位移过大，极有可能产生滑坡。因此根据不同工况下采集到的位移数据，分析地震作用下反倾层状岩质边坡在不同内摩擦角下的破坏特征。利用二维数值流形法（NMM），以青藏高原金沙江流域西藏昌都地区芒康县索多西乡贡扎倾倒滑坡为研究对象，依据实地考察数据及室内力学试验得到的物理力学参数，建立数值计算模型，模拟地震作用下反倾层状岩质边坡倾倒破坏过程，并在边坡上布置3组监测点获取位移数据。模拟结果表明:随着内摩擦角的增大，边坡坡体从开始破坏到新的平衡状态和达到最大位移所需的时间越短，同时，滑动块体最大水平位移逐渐减小；内摩擦角＜40°时，坡体在前15 s呈整体移动趋势，大部分岩块产生整体滑移，靠近坡顶处的岩块发生轻微转动，推动前面的岩块加速滑动，呈倾倒-滑移模式；内摩擦角＞40°时，靠近坡顶的岩块首先产生滑动，并转动驱使前面的岩块，推动坡脚处岩块产生滑动，最终上部岩块达到新的平衡，呈渐进式倾倒破坏，产生整体性破坏的可能性较小。  相似文献   

3D multivalued travel time and amplitude maps   总被引：2，自引：0，他引：2  

P. S. Lucio  G. Lambaré  A. Hanyga 《Pure and Applied Geophysics》1996,148(3-4):449-479

An algorithm for computing multivalued maps for travel time, amplitude and any other ray related variable in 3D smooth velocity models is presented. It is based on the construction of successive isochrons by tracing a uniformly dense discrete set of rays by fixed travel-time steps. Ray tracing is based on Hamiltonian formulation and includes computation of paraxial matrices. A ray density criterion ensures uniform ray density along isochrons over the entire ray field including caustics. Applications to complex models are shown.  相似文献