On the global solution of the N-body problem     

L. K. Babadzanjanz 《Celestial Mechanics and Dynamical Astronomy》1993,56(3):427-449

In connection with the publication (Wang Qiu-Dong, 1991) the Poincaré type methods of obtaining the maximal solution of differential equations are discussed. In particular, it is shown that the Wang Qiu-Dong'sglobal solution of the N-body problem has been obtained in Babadzanjanz (1979). First the more general results on differential equations have been published in Babadzanjanz (1978).  相似文献   

Conditioning mean steady state flow on hydraulic head and conductivity through geostatistical inversion   总被引：5，自引：2，他引：3  

A. F.?Hernandez  S. P.?NeumanEmail author  A.?Guadagnini  J.?Carrera 《Stochastic Environmental Research and Risk Assessment (SERRA)》2003,17(5):329-338

Nonlocal moment equations allow one to render deterministically optimum predictions of flow in randomly heterogeneous media and to assess predictive uncertainty conditional on measured values of medium properties. We present a geostatistical inverse algorithm for steady-state flow that makes it possible to further condition such predictions and assessments on measured values of hydraulic head (and/or flux). Our algorithm is based on recursive finite-element approximations of exact first and second conditional moment equations. Hydraulic conductivity is parameterized via universal kriging based on unknown values at pilot points and (optionally) measured values at other discrete locations. Optimum unbiased inverse estimates of natural log hydraulic conductivity, head and flux are obtained by minimizing a residual criterion using the Levenberg-Marquardt algorithm. We illustrate the method for superimposed mean uniform and convergent flows in a bounded two-dimensional domain. Our examples illustrate how conductivity and head data act separately or jointly to reduce parameter estimation errors and model predictive uncertainty.This work is supported in part by NSF/ITR Grant EAR-0110289. The first author was additionally supported by scholarships from CONACYT and Instituto de Investigaciones Electricas of Mexico. Additional support was provided by the European Commission under Contract EVK1-CT-1999-00041 (W-SAHaRA-Stochastic Analysis of Well Head Protection and Risk Assessment).  相似文献   

A BME solution of the inverse problem for saturated groundwater flow   总被引：3，自引：3，他引：0  

M. L.?SerreEmail author  G.?Christakos  H.?Li  C. T.?Miller 《Stochastic Environmental Research and Risk Assessment (SERRA)》2003,17(6):354-369

In most real-world hydrogeologic situations, natural heterogeneity and measurement errors introduce major sources of uncertainty in the solution of the inverse problem. The Bayesian Maximum Entropy (BME) method of modern geostatistics offers an efficient solution to the inverse problem by first assimilating various physical knowledge bases (hydrologic laws, water table elevation data, uncertain hydraulic resistivity measurements, etc.) and then producing robust estimates of the subsurface variables across space. We present specific methods for implementing the BME conceptual framework to solve an inverse problem involving Darcys law for subsurface flow. We illustrate one of these methods in the case of a synthetic one-dimensional case study concerned with the estimation of hydraulic resistivity conditioned on soft data and hydraulic head measurements. The BME framework processes the physical knowledge contained in Darcys law and generates accurate estimates of hydraulic resistivity across space. The optimal distribution of hard and soft data needed to minimize the associated estimation error at a specified sampling cost is determined. This work was supported by grants from the National Institute of Environmental Health Sciences (Grant no. 5 P42 ES05948 and P30ES10126), the National Aeronautics and Space Administration (Grant no. 60-00RFQ041), the Army Research Office (Grant no. DAAG55-98-1-0289), and the National Science Foundation under Agreement No. DMS-0112069.  相似文献   

Special Solutions in a Simplified Restricted Three-Body Problem with Gravitational Radiation Taken into Account     

V. A. Brumberg 《Celestial Mechanics and Dynamical Astronomy》2003,85(3):269-291

The distinctive feature of the relativistic restricted three-body problem within the c ^–5 order of accuracy (2 post-Newtonian approximation) is the presence of the gravitational radiation. To simplify the problem the motion of the massive binary components is assumed to be quasi-circular. In terms of time these orbits have linearly changing radii and quadratically changing phase angles. By substituting this motion into the Newtonian-like equations of motion one gets the quasi-Newtonian restricted quasi-circular three-body problem sufficient to take into account the main indirect perturbations caused by the binary radiation terms. Such problem admits the Lagrange-like quasi-libration solutions and rather simple quasi-circular orbits lying at large distance from the binary.  相似文献   

The Non-Linear Stability of L4 in the Restricted Three-Body Problem when the Bigger Primary is a Triaxial Rigid Body     

P. P. Hallan  Sanjay Jain  K. B. Bhatnagar 《Celestial Mechanics and Dynamical Astronomy》2000,77(3):157-184

The non-linear stability of L ₄ in the restricted three-body problem has been studied when the bigger primary is a triaxial rigid body with its equatorial plane coincident with the plane of motion. It is found that L ₄ is stable in the range of linear stability except for three mass ratios:where A₁, A₂ depend upon the lengths of the semi axes of the triaxial rigid body. This revised version was published online in July 2006 with corrections to the Cover Date.  相似文献   

Invariant Tori in the Secular Motions of the Three-body Planetary Systems     

Ugo Locatelli  Antonio Giorgilli 《Celestial Mechanics and Dynamical Astronomy》2000,78(1-4):47-74

We consider the problem of the applicability of KAM theorem to a realistic problem of three bodies. In the framework of the averaged dynamics over the fast angles for the Sun–Jupiter–Saturn system we can prove the perpetual stability of the orbit. The proof is based on semi-numerical algorithms requiring both explicit algebraic manipulations of series and analytical estimates. The proof is made rigorous by using interval arithmetics in order to control the numerical errors.  相似文献   

Steady- and transient-state inversion in hydrogeology by successive flux estimation     

Philippe Pasquier  Denis Marcotte 《Advances in water resources》2006,29(12):1934-1952

A calibration method to solve the groundwater inverse problem under steady- and transient-state conditions is presented. The method compares kriged and numerical head field gradients to modify hydraulic conductivity without the use of non-linear optimization techniques. The process is repeated iteratively until a close match with piezometric data is reached. The approach includes a damping factor to avoid divergence and oscillation of the solution in areas of low hydraulic gradient and a weighting factor to account for temporal head variation in transient simulations. The efficiency of the method in terms of computing time and calibration results is demonstrated with a synthetic field. It is shown that the proposed method provides parameter fields that reproduce both hydraulic conductivity and piezometric data in few forward model solutions. Stochastic numerical experiments are conducted to evaluate the sensitivity of the method to the damping function and to the head field estimation errors.  相似文献   

武汉城市地下空间工程地质研究   总被引：2，自引：1，他引：2  

宁国民  陈国金  徐绍宇  肖音 《水文地质工程地质》2006,33(6):29-35

利用武汉市现有勘察资料,初步分析研究城市地下空间的物质载体及其空间组合关系,从空间岩土体工程地质性质和赋水条件入手,研究得出武汉城市地下空间的利用存在岩溶地面塌陷、地下水作用、软土变形三大工程地质问题。在此基础上进行地下空间利用区划,指出各区在地下工程建设中需要重点防范的工程地质问题和合理利用地下空间的方法。最后以武汉地铁首期工程为例,分析工程地质优势与问题,提出防范问题的措施建议。  相似文献   

中国西北地区干旱气侯学的新进展及其主要科学问题     

董安祥  白虎志  雷小斌 《干旱气象》2006,24(4):57-62

回顾了“十五”期间中国西北地区干旱气侯学的进展。就遥感监测、西北干旱形成机制、西北地区年代际的气候变化、西北干旱新的强讯号、高原干旱气候生态作物适应性和西北干旱监测预测业务服务综合系统等方面所取得重要研究进展和学术成就,作了系统的回顾;并对21世纪初干旱气侯学的主要科学问题作了展望。  相似文献   

一类退缩反应扩散方程组初边值问题解的存在性和唯一性     

邹赢  李刚  徐金花 《南京气象学院学报》2006,29(2):242-248

利用紧性理论，证明了扩散现象中出现的一类退缩抛物型方程组初边值问题解的存在性和唯一性。  相似文献