Minima de L'intégrale D'action du Problème Newtoniende 4 Corps de Masses Égales Dans R3: Orbites 'Hip-Hop'

We consider the problem of 4 bodies of equal masses in R ³ for the Newtonian r⁻¹ potential. We address the question of the absolute minima of the action integral among (anti)symmetric loops of class H ¹ whose period is fixed. It is the simplest case for which the results of [4] (corrected in [5]) do not apply: the minima cannot be the relative equilibria whose configuration is an absolute minimum of the potential among the configurations having a given moment of inertia with respect to their center of mass. This is because the regular tetrahedron cannot have a relative equilibrium motion in R ³ (see [2]). We show that the absolute minima of the action are not homographic motions. We also show that if we force the configuration to admit a certain type of symmetry of order 4, the absolute minimum is a collisionless orbit whose configuration ‘hesitates’ between the central configuration of the square and the one of the tetrahedron. We call these orbits ‘hip-hop’. A similar result holds in case of a symmetry of order 3 where the central configuration of the equilateral triangle with a body at the center of mass replaces the square. This revised version was published online in July 2006 with corrections to the Cover Date.     

On the Dynamics and Topology of the Elliptic Rectilinear Restricted 3-Body Problem

We study a symmetric collinear restricted 3-body problem, where the equal mass primaries perform elliptic collisions, while a third massless body moves in the line between the primaries, during the time between two consecutive elliptic collisions. After desingularizing binary and triple collisions, we prove the existence of a transversal heteroclinic orbit beginning and ending in triple collision. This orbit is the unique homothetic orbit that the problem possess. Finally, we describe the topology of the compact extended phase space. This revised version was published online in July 2006 with corrections to the Cover Date.     

Perturbations of the Kepler Problem in Global Coordinates

The usual action-angle variables for the Kepler Problem (the Delaunay variables) are not globally defined, leaving out some orbits (circular orbits or those lying on the xy-plane). Moreover they are trascendental functions of the physical variables, making it quite difficult to write the perturbed Hamiltonian. The way-out proposed here is to pass to a 8-dimensional rank-6 Poisson manifold, that is, to parametrize the state of the Kepler Problem with two 4-dimensional vectors mutually orthogonal and of equal norm. This revised version was published online in July 2006 with corrections to the Cover Date.     

Sequential integrated inversion of refraction and wide-angle reflection traveltimes and gravity data for two-dimensional velocity structures

A new algorithm is presented for the integrated 2-D inversion of seismic traveltime and gravity data. The algorithm adopts the 'maximum likelihood' regularization scheme. We construct a 'probability density function' which includes three kinds of information: information derived from gravity measurements; information derived from the seismic traveltime inversion procedure applied to the model; and information on the physical correlation among the density and the velocity parameters. We assume a linear relation between density and velocity, which can be node-dependent; that is, we can choose different relationships for different parts of the velocity–density grid. In addition, our procedure allows us to consider a covariance matrix related to the error propagation in linking density to velocity. We use seismic data to estimate starting velocity values and the position of boundary nodes. Subsequently, the sequential integrated inversion (SII) optimizes the layer velocities and densities for our models. The procedure is applicable, as an additional step, to any type of seismic tomographic inversion.
We illustrate the method by comparing the velocity models recovered from a standard seismic traveltime inversion with those retrieved using our algorithm. The inversion of synthetic data calculated for a 2-D isotropic, laterally inhomogeneous model shows the stability and accuracy of this procedure, demonstrates the improvements to the recovery of true velocity anomalies, and proves that this technique can efficiently overcome some of the limitations of both gravity and seismic traveltime inversions, when they are used independently.
An interpretation of field data from the 1994 Vesuvius test experiment is also presented. At depths down to 4.5 km, the model retrieved after a SII shows a more detailed structure than the model obtained from an interpretation of seismic traveltime only, and yields additional information for a further study of the area.     

陆地中低放核废物地质处置的发展与现状

介绍全球陆地中的中低放核废物处置的发展与现状,重点介绍近地表埋藏处置法,废矿井处置法和深岩硐地质处置法,并简要概述一些国家在陆地核废物处置领域内出现的问题及对策。     

长沙电力学院3号教学楼人工挖孔灌注桩工程地质问题及其处理措施

长沙电力学院 3号教学楼人工挖孔桩基的施工条件极差。经灵活采用多种经济实用的措施处理 ,成功地解决了流砂、流泥、管涌、坍塌、护壁吊烂与整体失稳等技术难题。     

Problem regions and regional problems of socioeconomic development in China: A perspective from the coordinated development of industrialization,informatization, urbanization and agricultural modernization

Identifying the problem regions and regional problems, and thus improving regional policies, are crucial for the sustainable development of various economic entities. The coordinated development of industrialization, informatization, urbanization and agricultural modernization（hereinafter referred to as ＂Sihua＂） is not only a practical need but an important strategic direction of integrating urban-rural development and regional development in recent China, and it also provides a significant perspective for identifying problem regions and regional problems so as to improve the regional policies. This study mainly aims to： firstly, establish a comprehensive evaluation index system so as to explore the spatial pattern of coordinated development of Sihua in China at prefecture level; secondly, to develop an evaluation criteria system to identify the problem regions and regional problems from the perspective of coordinated development of Sihua. This paper comes first in the scientific community to evaluate the coordinated development state of Sihua in China at prefecture level and identify the problem regions and regional problems from the perspective of Sihua development by quantitative analysis. This study may benefit the improvement of regional policies and thus contribute to the sustainable socio-economic development of China.     

A new modelling method for evaluating external disturbing potential based on theory of unified representation of gravitational field

1　ＩｎｔｒｏｄｕｃｔｉｏｎＣｏｎｖｅｎｔｉｏｎａｌｅｖａｌｕａｔｉｎｇｍｏｄｅｌｓｏｆｅｘｔｅｒｎａｌｇｒａｖｉ ｔａｔｉｏｎａｌｆｉｅｌｄｏｆｔｈｅｅａｒｔｈａｒｅｎｏｔｈｉｎｇｅｌｓｅｔｈａｎａｋｉｎｄｏｆｒｅａｌｉｚａｔｉｏｎｓｏｆｎｕｍｅｒｉｃａｌｓｏｌｕｔｉｏｎｓｔｏｇｅｏｄｅ ｔｉｃｂｏｕｎｄａｒｙｖａｌｕｅ ｐｒｏｂｌｅｍ .Ｉｎｔｈｅｓｅｎｓｅｏｆｌｉｎ ｅａｒｉｚａｔｉｏｎ ,ｇｅｏｄｅｔｉｃｂｏｕｎｄａｒｙｖａｌｕｅｐｒｏｂｌｅｍｓａｒｅｒｅ ｄｕｃｅｄｔｏｅｘｔｅｒｎａｌｂｏｕｎｄ…     

浅析宜昌磷矿开发中存在的问题及对策

宜昌磷矿资源量大、品位高。经过 30余年的发展 ,已成为该地区经济收入的重要来源之一。但在开发中仍存在矿山规模过小过滥 ,设备利用率低 ,建设资金浪费 ,采富弃贫 ,资源严重浪费 ;产品附加值低 ,可持续发展后劲泛力 ;矿业秩序混乱 ,安全陷患多 ;生态环境严重被破坏等问题。针对存在问题应采取的对策为缩小开采规模 ,提高产品附加值 ;减少矿山生活服务设施投入 ,增加矿山企业的生产规模 ;减少村办、个体小矿山 ,坚持国有矿山的主导地位以及加强区域间合作 ,走矿肥集合与矿化集合的道路等。     

A least-squares penalty method algorithm for inverse problems of steady-state aquifer models

Based on the generalized Gauss–Newton method, a new algorithm to minimize the objective function of the penalty method in (Bentley LR. Adv Wat Res 1993;14:137–48) for inverse problems of steady-state aquifer models is proposed. Through detailed analysis of the “built-in” but irregular weighting effects of the coefficient matrix on the residuals on the discrete governing equations, a so-called scaling matrix is introduced to improve the great irregular weighting effects of these residuals adaptively in every Gauss–Newton iteration. Numerical results demonstrate that if the scaling matrix equals the identity matrix (i.e., the irregular weighting effects of the coefficient matrix are not balanced), our algorithm does not perform well, e.g., the computation cost is higher than that of the traditional method, and what is worse is the calculations fail to converge for some initial values of the unknown parameters. This poor situation takes a favourable turn dramatically if the scaling matrix is slightly improved and a simple preconditioning technique is adopted: For naturally chosen simple diagonal forms of the scaling matrix and the preconditioner, the method performs well and gives accurate results with low computational cost just like the traditional methods, and improvements are obtained on: (1) widening the range of the initial values of the unknown parameters within which the minimizing iterations can converge, (2) reducing the computational cost in every Gauss–Newton iteration, (3) improving the irregular weighting effects of the coefficient matrix of the discrete governing equations. Consequently, the example inverse problem in Bentley (loc. cit.) is solved with the same accuracy, less computational effort and without the regularization term containing prior information on the unknown parameters. Moreover, numerical example shows that this method can solve the inverse problem of the quasilinear Boussinesq equation almost as fast as the linear one.In every Gauss–Newton iteration of our algorithm, one needs to solve a linear least-squares system about the corrections of both the parameters and the groundwater heads on all the discrete nodes only once. In comparison, every Gauss–Newton iteration of the traditional method has to solve the discrete governing equations as many times as one plus the number of unknown parameters or head observation wells (Yeh WW-G. Wat Resour Res 1986;22:95–108).All these facts demonstrate the potential of the algorithm to solve inverse problems of more complicated non-linear aquifer models naturally and quickly on the basis of finding suitable forms of the scaling matrix and the preconditioner.