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

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.     

Chromium speciation in oxide-type compounds: application to minerals,gems, aqueous solutions and silicate glasses

Cr K-edge XANES spectra were obtained for a variety of Cr-bearing model compounds containing Cr(II), Cr(III), Cr(IV), Cr(V) and Cr(VI), in which the Cr-site symmetry is D4h, Oh and Td. The centroid position of the pre-edge feature is a better indicator of the Cr valence than the edge position. In Cr-rich oxides, higher-energy transitions must be excluded in order to refine a robust valence for Cr. The pre-edge for chromates is not unique and varies as a function of the CrO₄ ^2? moiety distortion, which is often related to Cr-polymerization (monochromate vs. dichromate). Both the analogy with the Mn K-pre-edge information and ab initio FEFF calculations of the pre-edge feature for Cr(III) and Cr(VI) confirm the experimental trends. This methodology is applied to the Cr K-edge pre-edge feature collected in gems (emerald, spinel and ruby), the layered minerals fuchsite and kämmererite, two Cr-bearing aqueous solutions and a set of sodo-calcic silicate glasses used for bottling sparkling white wine. In emerald and fuchsite, the Cr-site is differently distorted than its ruby or spinel counterpart. In a Cr(III)-bearing aqueous solution and sodo-calcic glass, no evidence for Cr(III) with Td and C3v symmetry is detected. However, minor amounts of chromate moieties (most likely monomeric) are detected in a glass synthesized in air. Preliminary spectra for the wine bottle glass suggest that only trace amounts of chromates might possibly be present in these glasses.     

柴达木盆地中深层混积岩储层形成机制

通过岩心观测、普通薄片、铸体薄片、扫描电镜、电子探针和岩石物性等分析,系统阐述了柴达木盆地典型中深层(西北区南翼山构造E₃²-N₁)混积岩的岩石学、储集空间/物性和成岩作用等特征,在此基础上讨论了储层形成机制。结果表明,混积岩以(泥质)泥晶灰岩、钙质含量较高的砂岩和粉砂岩及其混积岩为主;储集空间以溶蚀改造的裂缝和粒间溶蚀孔隙为特征,物性总体表现为低孔-特低孔、超低渗-非渗透;有利于形成储层的成岩作用是溶蚀和构造裂缝作用;储层形成机制可归纳为"岩性是基础,裂缝是条件,溶蚀是关键"。这可为区域中深层混积岩储层,乃至陆相湖泊混合沉积储层的研究与油气勘探开发提供借鉴与参考。     

模拟渗滤液作用下压实黏土的力学性质

垃圾填埋场中渗滤液的作用可能对压实黏土衬垫及地基土的力学性质产生一定的影响,但目前研究成果存在矛盾之处。以CaCl2溶液和苯酚溶液作为渗滤液中无机和有机污染物的代表,对添加10%钠基膨润土的压实黏土进行力学性质的试验研究。结果表明,（1）两种模拟渗滤液的作用使土的压缩性增强,抗剪强度降低。（2）苯酚对压实黏土力学性质的影响更为显著,不排水强度约为自来水和0.05molL-1CaCl2溶液的55%。（3）土样初始孔隙比相同时,溶液作用下扩散双电层变薄造成孔隙变大,可能是产生这种现象的主要原因。（4）模拟渗滤液的作用对压实黏土衬垫及地基土具有不利的影响。     

一个近似的VTI介质声波方程

声学近似是提高各向异性介质准纵波数值模拟和偏移处理计算速度的有效方法之一.为了获得VTI(具有垂直对称轴的横向各向同性)介质声波方程,根据VTI介质的精确相速度表达式,用待定系数法简化其中的根号项,得到一个近似相速度公式,由此公式通过反Fourier变换推导出一个时间二阶、空间四阶偏微分方程.定量相速度计算表明,当Thomsen参数ε=δ(即相应介质为椭圆各向异性介质)时,由该方程所确定的相速度是精确的;当ε≠δ时,该方程所确定的相速度随ε和δ差值的增大逐渐增加.该方程所确定的最大相速度百分比相对误差当ε=0.1、δ=0.2时为0.13%,当ε=0.8、δ=0.3时为-1.65%.有限差分数值模拟算例表明该方程是一个纯准纵波方程,其数值模拟波场快照中没有准横波.     

Whole mantle SH velocity model constrained by waveform inversion based on three-dimensional Born kernels

A whole mantle SH velocity model is obtained by using a unique data set and techniques. Body and surface waveforms including major and multi-orbit phases are used as a data set and are inverted by using 3-D Born kernels. The resultant model, SH18CE, reveals the different natures of the two major upwelling systems: the strong low velocity anomalies beneath Africa extend for more than 1000 km from the core–mantle boundary (CMB), whereas those beneath the Pacific are restricted to 300–400 km from the CMB. The results also show the variable natures of stagnant slabs on the 670 discontinuity around Japan: the depths of the strongest high velocity anomalies within the stagnant slabs are different region by region, which is consistent with the detailed delay time tomography model in this area.     

疏松砂岩稠油油藏出砂冷采机理及配套技术研究

稠油出砂冷采技术对地层原油含有溶解气的各类疏松砂岩稠油油藏具有较广泛的适应性，它通过大量砂子的产出和泡沫油的形成，获得较高的原油产量，河南油田于1996年在国内率先开展稠油出砂冷采技术调研及可行性研究，出砂冷采机理及配套工艺技术研究，并于1997年6月进入现场先导试验，矿场试验已展示出明显出砂冷采特征的G4906井，日产油量20t-30t，是常规开采和蒸汽吞吐的10倍和4倍以上，开采成本比蒸汽吞吐降低47%，出砂冷采工业化应用配套技术的形成和应用，将使国内及河南油田稠油资源利用程度进一步提高。     

Effects of Deicing-Salts on Heavy Metal Mobility Zum Einfluß von Streusalzen auf die Beweglichkeit von Schwermetallen

Heavy metal input into roadside soils and effects of deicing salts are often discussed as separate environmental problems. However, a relationship between salt input and heavy metal mobility has already been detected in laboratory tests. During a 2-year field study, the soil solution of a roadside soil was continuously sampled. The results of soil solution analysis not only showed a strong rise in deicing-salt related sodium, calcium and chloride concentrations, but also high zinc and cadmium values in winter and spring. Additional laboratory tests confirmed the mobilizing effects of salt solution which contained NaCl and CaCl₂. Cation exchange and the formation of chlorocomplexes are discussed as the responsible mechanisms.     

Prediction of limestone solution rates from rainfall and runoff data: Some comments

Recent work by Láng (1977) on solutional erosion rates in limestone drainage basins in relation to rainfall contains serious errors and has a questionable logical basis. Although much sounder, Smith and Atkinson's (1976) work on erosion rates in relation to runoff also requires modification as it greatly overestimates erosion rates in two areas of New Zealand. Greater resolution could probably be obtained by relating autogenic runoff to the rate of solution by autogenic waters and by computing separate relationships for areas where solution takes place under open and closed system equilibrium conditions. These factors should be taken into account in the experimental design of future studies.     

Comprehensive Development and Utilization of Saline Lake Groups in Dingbian,Shanxi Province of China

正The Dingbian Saline Lake groups are in Dingbian County,northwest of Shaanxi province,and located on the border area of the Loess Plateau and Maowusu Desert in Northern Shanxi.It's altitude is more than 1300m.The