Restricted Three-Body Problem: An Approximation of its General Solution – Part One – the Manifold of Symmetric Periodic Solutions     

Kostantinos Papadakis  Constantine Goudas 《Astrophysics and Space Science》2006,305(2):99-124

This paper gives the results of a programme attempting to exploit ‘la seule bréche’ (Poincaré, 1892, p. 82) of non-integrable systems, namely to develop an approximate general solution for the three out of its four component-solutions of the planar restricted three-body problem. This is accomplished by computing a large number of families of ‘solutions précieuses’ (periodic solutions) covering densely the space of initial conditions of this problem. More specifically, we calculated numerically and only for μ = 0.4, all families of symmetric periodic solutions (1st component of the general solution) existing in the domain D:(x ₀ ∊ [−2,2],C ∊ [−2,5]) of the (x ₀, C) space and consisting of symmetric solutions re-entering after 1 up to 50 revolutions (see graph in Fig. 4). Then we tested the parts of the domain D that is void of such families and established that they belong to the category of escape motions (2nd component of the general solution). The approximation of the 3rd component (asymmetric solutions) we shall present in a future publication. The 4th component of the general solution of the problem, namely the one consisting of the bounded non-periodic solutions, is considered as approximated by those of the 1st or the 2nd component on account of the `Last Geometric Theorem of Poincaré' (Birkhoff, 1913). The results obtained provoked interest to repeat the same work inside the larger closed domain D:(x ₀ ∊ [−6,2], C ∊ [−5,5]) and the results are presented in Fig. 15. A test run of the programme developed led to reproduction of the results presented by Hénon (1965) with better accuracy and many additional families not included in the sited paper. Pointer directions construed from the main body of results led to the definition of useful concepts of the basic family of order n, n = 1, 2,… and the completeness criterion of the solution inside a compact sub-domain of the (x ₀, C) space. The same results inspired the ‘partition theorem’, which conjectures the possibility of partitioning an initial conditions domain D into a finite set of sub-domains D i that fulfill the completeness criterion and allow complete approximation of the general solution of this problem by computing a relatively small number of family curves. The numerical results of this project include a large number of families that were computed in detail covering their natural termination, the morphology, and stability of their member solutions. Zooming into sub-domains of D permitted clear presentation of the families of symmetric solutions contained in them. Such zooming was made for various values of the parameter N, which defines the re-entrance revolutions number, which was selected to be from 50 to 500. The areas generating escape solutions have being investigated. In Appendix A we present families of symmetric solutions terminating at asymptotic solutions, and in Appendix B the morphology of large period symmetric solutions though examples of orbits that re-enter after from 8 to 500 revolutions. The paper concludes that approximations of the general solution of the planar restricted problem is possible and presents such approximations, only for some sub-domains that fulfill the completeness criterion, on the basis of sufficiently large number of families.  相似文献   

Hysteresis‐based analysis of overland metal transport     

Surendra Kumar Mishra  J. J. Sansalone  Vijay P. Singh 《水文研究》2003,17(8):1579-1606

Introducing a concept of equivalent mass depth of flow, this study describes the phenomenon of non‐point source pollutant (metal) transport for pavement (or overland) flow in analogy with wave propagation in wide open channels. Hysteretic and normal mass rating curves are developed for runoff rate and mass of 12 dissolved and particulate‐bound metal elements (pollutants) using the rainfall‐runoff and water quality data of the 15 × 20 m² instrumented pavement in Cincinnati, USA. Normal mass rating curves developed for easy computation of pollutant load are found to be of a form similar to Manning's, which is valid for open channel flows. Based on the hysteresis analysis, wave types for dissolution and mixing of particulate‐bound metals are identified. The analysis finds that the second‐order partial‐differential equation normally used for metal transport does not have the efficacy to describe fully the strong non‐linear phenomena such as is described for various metal elements by dynamic waves. In addition, the proportionality concept of the popular SCS‐CN concept is extended for determining the potential maximum metal mass M_p of all the 12 elements transported by a rain storm and related to the antecedent dry period (ADP). For the primary metal zinc element, M_p is found to increase with the ADP and vice versa. Copyright © 2003 John Wiley & Sons, Ltd.  相似文献   

Reliability assessment of serviceability performance of braced retaining walls using a neural network approach     

A. T. C. Goh  F. H. Kulhawy 《国际地质力学数值与分析法杂志》2005,29(6):627-642

In urban environments, one major concern with deep excavations in soft clay is the potentially large ground deformations in and around the excavation. Excessive movements can damage adjacent buildings and utilities. There are many uncertainties associated with the calculation of the ultimate or serviceability performance of a braced excavation system. These include the variabilities of the loadings, geotechnical soil properties, and engineering and geometrical properties of the wall. A risk‐based approach to serviceability performance failure is necessary to incorporate systematically the uncertainties associated with the various design parameters. This paper demonstrates the use of an integrated neural network–reliability method to assess the risk of serviceability failure through the calculation of the reliability index. By first performing a series of parametric studies using the finite element method and then approximating the non‐linear limit state surface (the boundary separating the safe and ‘failure’ domains) through a neural network model, the reliability index can be determined with the aid of a spreadsheet. Two illustrative examples are presented to show how the serviceability performance for braced excavation problems can be assessed using the reliability index. Copyright © 2005 John Wiley & Sons, Ltd.  相似文献   

Predicting ground-motion variations at the Turkey-flat test site,California     

J. Zahradník  J. Jech  V. Barták 《Pure and Applied Geophysics》1991,137(1-2):63-84

Results of a single group participating in an international experiment are analyzed. The experiment served to verify computational predictions of the ground-motion variations due to near-surface geological effects at a site established for that purpose by the California Department of Conservation. Based on an acceleration record at a rock location, and geotechnical model of medium, records at the other locations of a nearby sedimentary deposit were predicted. A 2-D finite-difference sensitivity analysis suggested that the lateral wave-propagation effects are negligibly small, and locally 1-D computations are sufficient for the present site. Those computations are compared with observations not available to the authors during the blind prediction. Peak accelerations, peak velocities and RMS accelerations were predicted with errors less than 159%, 114% and 62%, respectively. Maxima of the response spectra were fitted within a factor of 2. The predicted and observed Husid's plots (i.e., the normalized cumulative plots of the acceleration squared) have the correlation coefficients 0.98. The detected misfits do not show any simple relation to the instrument location, component, frequency, or time.  相似文献   

An operational multiscale system for hazards prediction, mapping, and response     

David P. Bacon  Nash’at N. Ahmad  Thomas J. Dunn  Michael C. Monteith  Ananthakrishna Sarma 《Natural Hazards》2008,44(3):317-327

By definition, a crisis is a situation that requires assistance to be managed. Hence, response to a crisis involves the merging of local and non-local emergency response personnel. In this situation, it is critical that each participant: (1) know the roles and responsibilities of each of the other participants; (2) know the capabilities of each of the participants; and (3) have a common basis for action. For many types of natural disasters, this entails having a common operational picture of the unfolding events, including detailed information on the weather, both current and forecasted, that may impact on either the emergency itself or on response activities. The Consequences Assessment Tool Set (CATS) is a comprehensive package of hazard prediction models and casualty and damage assessment tools that provides a linkage between a modeled or observed effect and the attendant consequences for populations, infrastructure, and resources, and, hence, provides the common operational picture for emergency response. The Operational Multiscale Environment model with Grid Adaptivity (OMEGA) is an atmospheric simulation system that links the latest methods in computational fluid dynamics and high-resolution gridding technologies with numerical weather prediction to provide specific weather analysis and forecast capability that can be merged into the geographic information system framework of CATS. This paper documents the problem of emergency response as an end-to-end system and presents the integrated CATS–OMEGA system as a prototype of such a system that has been used successfully in a number of different situations.  相似文献   

干旱生态环境及水资源对全球气候变暖响应的研究进展   总被引：7，自引：5，他引：2  

邓振镛  张强  辛吉武  赵鸿  王全福  王鹤龄 《冰川冻土》2008,30(1):57-63

西北地区现代气候变化基本特征是冬暖夏干,采用脆弱度和影响指数方法定量评价了生态环境对全球气候变暖响应,重点阐述了西北现代气候变化对干旱生态环境和水资源这两个领域的影响.结果表明: 由于现代气候变干变暖的自然和人为因素的共同作用,导致我国西北地区的黄土高原、黑河流域、石羊河流域、甘南高原和黄河首曲的地域生态环境有不断退化的趋势.气候变干使渭河上游、黄河上游(洮河和大夏河)以及黄土高原中部7条主要河流的径流量呈明显下降趋势,引起水资源短缺.  相似文献   

Nonlinear Analysis of Local Site Effects on Seismic Ground Response in the Bam Earthquake   总被引：1，自引：0，他引：1  

M. H. T. Rayhani  M. H. El Naggar  S. H. Tabatabaei 《Geotechnical and Geological Engineering》2008,26(1):91-100

The influence of local geologic and soil conditions on the intensity of ground shaking is addressed in this study. The amplification of the ground motion due to local site effects resulted in severe damage to dwellings in the Bam area during the 2003 Bam Earthquake. A unique set of strong motion acceleration recordings was obtained at the Bam accelerograph station. Although the highest peak ground acceleration recorded was the vertical component (nearly 1 g), the longitudinal component (fault-parallel motion) clearly had the largest maximum velocity as well as maximum ground displacement. Subsurface geotechnical and geophysical (down-hole) data in two different sites have been obtained and used to estimate the local site condition on earthquake ground motion in the area. The ground response analyses have been conducted considering the nonlinear behavior of the soil deposits using both equivalent linear and nonlinear approaches. The fully nonlinear method embodied in FLAC was used to evaluate the nonlinear soil properties on earthquake wave propagation through the soil layer, and compare with the response from the equivalent linear approach. It is shown that thick alluvium deposits amplified the ground motion and resulted in significant damage in residential buildings in the earthquake stricken region. The comparison of results indicated similar response spectra of the motions for both equivalent and nonlinear analyses, showing peaks in the period range of 0.3–1.5 s. However, the amplification levels of nonlinear analysis were less than the equivalent linear method especially in long periods. The observed response spectra are shown to be above the NEHRP building code design requirements, especially at high frequencies.  相似文献   

海拉尔盆地贝西斜坡北部地区储层特征及影响因素分析   总被引：2，自引：0，他引：2  

李占东  周件林  文华  孙娜 《岩石矿物学杂志》2008,27(1):45-51

通过测井曲线的标准化处理及信息提取、岩心及录井岩屑观察、铸体薄片、物性分析、扫描电镜、压汞分析等技术手段,研究了海拉尔盆地贝西斜坡北部地区南屯组储层的主要岩性特征、物性特征、储集空间类型和影响因素.研究结果表明.海拉尔盆地南屯组以内陆湖相碎屑岩为主,主要包括角砾岩、砾岩、砂砾岩、粗砂岩、细砂岩、粉砂岩、泥质砂岩及泥岩等.南一段储层孔隙度平均值为6.15%,渗透率平均值为0.31 × 10-3μm2,为低孔特低渗型孔隙特征;南二段储层孔隙度平均值为12.18%,渗透率平均值为2.79× 10-3μm2,属于中孔低渗型孔隙特征.储集空间类型以粒间孔隙为主,发育一定的次生孔隙.喉道分为4种类型(Ⅰ类、Ⅱ类、Ⅲ类、Ⅳ类).扇三角洲前缘分支水道砂体、扇三角洲平原辫状河道砂体和滨浅湖砂坝微相砂体为该区有利的储层砂体类型.储层性质主要受沉积相和成岩作用影响.  相似文献   

Numerical and experimental study on hydrodynamic interaction of side-by-side moored multiple vessels   总被引：2，自引：0，他引：2  

S.Y. Hong  J.H. Kim  S.K. Cho  Y.R. Choi  Y.S. Kim 《Ocean Engineering》2005,32(7):783-801

This paper aims to investigate the basic interaction characteristics of side-by-side moored vessels both numerically and experimentally. A higher-order boundary element method (HOBEM) combined with generalized mode approach is applied to analysis of motion and drift force of side-by-side moored multiple vessels (LNG FPSO, LNGC and shuttle tankers). Model tests were carried out for the same floating bodies investigated in the numerical study in regular and irregular waves. Global and local motion responses and drift forces of three vessels are compared with those of calculations. Discussions is highlighted on applicability of numerical method to prediction of sophisticated multi-body interaction problem of which motion behavior is very important to analysis of mooring dynamics of deep sea floating bodies.  相似文献   

Synthetic echograms generated from the relative frequency response   总被引：1，自引：3，他引：1  

Korneliussen  Rolf J; Ona  Egil 《ICES Journal of Marine Science》2003,60(3):636-640

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