不等边基四边形的等距曲线设计

根据等距曲线的成形原理和几何特性,讨论了在有条件下的不等边基四边形等距曲线设计以及基四边形边长和形状的变化对等距曲线的影响,阐述了等距曲线的图形设计原则、轮廓曲线作图方法并加以证明,从而确定了不等边基四边形的设计作图范围和应用特性,扩展了机械传动机构型面联接中的等距曲线设计途径和方法。     

The general solution of the HENON–HEILES problem

The general solution of the Henon–Heiles system is approximated inside a domain of the (x, C) of initial conditions (C is the energy constant). The method applied is that described by Poincaré as ‘the only “crack” permitting penetration into the non-integrable problems’ and involves calculation of a dense set of families of periodic solutions that covers the solution space of the problem. In the case of the Henon–Heiles potential we calculated the families of periodic solutions that re-enter after 1–108 oscillations. The density of the set of such families is defined by a pre-assigned parameter ε (Poincaré parameter), which ascertains that at least one periodic solution is computed and available within a distance ε from any point of the domain (x, C) for which the approximate general solution computed. The approximate general solution presented here corresponds to ε = 0.07. The same solution is further improved by “zooming” into four square sub-domain of (x, C), i.e. by computing sufficient number of families that reduce the density parameter to ε = 0.003. Further zooming to reduce the density parameter, say to ε = 10⁻⁶, or even smaller, although easily performable in both areas occupied by stable as well as unstable solutions, was found unnecessary. The stability of all members of each and all families computed was calculated and presented in this paper for both the large solution domain and for the sub-domains. The correspondence between areas of the approximate general solution occupied by stable periodic solutions and Poincaré sections with well-aligned section points and also correspondence between areas occupied by unstable solutions and Poincaré sections with randomly scattered section points is shown by calculating such sections. All calculations were performed using the Runge-Kutta (R-K) 8th order direct integration method and the large output received, consisting of many thousands of families is saved as “Atlas of the General Solution of the Henon–Heiles Problem,” including their stability and is available at request. It is concluded that approximation of the general solution of this system is straightforward and that the chaotic character of its Poincaré sections imposes no limitations or difficulties.     

The Homoclinic Tangle of A 1:2 Resonance in a 2-D Hamiltonian System

We study in great detail the geometry of the homoclinic tangle, with respect to the energy, corresponding to an unstable periodic orbit of type 1:2, on a surface of section representing a 2-D Hamiltonian system. The tangle consists of two resonance areas, in contrast with the tangles of type-l or -{l, m, k, x = 0} considered in previous studies, that consist of only one resonance area. We study the intersections of the inner and outer lobes of the same resonance area and of the two resonance areas. The intersections of the lobes follow certain rules. The detailed study of these rules allows us to derive quantitative relations about the number of intersections and to understand the complex behavior of the higher order lobes by studying the lower order lobes. We find 1st, 2nd, 3rd, etc. order intersections formed by lobes making 1, 2, 3, etc. turns around an island. After a sufficiently high order of iterations a lobe may intersect its image and thus produce a Poincaré recurrence. Numerical results for a wide interval of energies are presented. The number of intersections changes through tangencies. In any finite interval of the energy between two tangencies of 1st order, an infinite number of higher order tangencies occur and thus, according to the Newhouse theorem, there exist nearby islands of stability.     

A study on the bio-hydro mechanical effects of the tree roots on the Agaclı coal reclaimed – forested land

The research area that is in the north of Istanbul (Turkey) and it is a land of open pit coal mining residuals reclaimed and turned to forest in 1988–1989. The materials that are open pit mine spoils are formed by sandy loam, sandy clay loam, heavy loam and clay (noncalcareous Pliocene I sediments). Pseudoacacia (Robinia pseudoacacia), Maritima Pine (Pinus pinaster) and Stone Pine (Pinus pinea) are planted on these materials. The aims of this research were to determine the strength of the material provided by tree roots and evaluate the performance of the forestation practices at lands especially where open pit coal mining spoil (residual) materials piled up. The research has been performed at two stages. The first one was hydro-mechanical effect concerned about material moisture depletion as a result of transpiration and the second one was bio-mechanical effects due to strength parameters of the roots and their growth pattern within the material. All results were evaluated in relation to tensile strength and displacement curves due to pre and post failure behaviors of materials and root systems. The results showed the increase of the displacement of the material was the significant indicator of the bio-mechanics tensile strength of the material provided by the tree roots. The fast growing type of tree roots have stabilized the material up to a depth for 80–100 cm by covering the coal residual materials within 12 years.     

关于倾斜脉的重力异常公式及理论曲线正误的商榷

本文着重讨论了重力勘探教材中关于倾斜脉的△g、V_(xz)、V_(zz)理论公式及二次微商理论曲线的正误问题。文中给出了无限延深倾斜脉的准确的 V_(xz)及 V_(zz)理论曲线,并且指出应该充分地利用 V_(xz)V_(zz)异常特征解释推断脉的倾向.     

从高密度电阻率法数据中抽取电测深曲线进行解释

对于碳酸盐岩地层中的多层岩溶、溶洞洞高较小或顺层岩溶,直接从高密度电阻率拟断面图和反演电阻率断面图上难以将其区分。通过从高密度电法数据中抽取电测深曲线,对一系列测点的电测深视电阻率曲线进行解释,同时结合其视电阻率拟断面图和反演电阻率断面图作出推断,能有效地将上述岩溶进行区分。在湖南省某高速公路跨线桥墩台桩基工程基础勘探中的实践表明,使用该方法可获得较好的地质解释效果。     

黏土中自升式钻井船插桩对邻近桩基影响的分析方法

自升式钻井船是广泛用于浅、中水域油气资源开发的重要设施,经常紧邻固定式导管架平台进行作业。钻井船插桩就位过程中大量土体被排开,挤土效应会导致邻近导管架平台桩基承受很大的附加荷载,影响平台的正常设计性能,该效应在黏土中尤为显著。针对黏土中钻井船插桩对邻近桩基的影响这一实际问题,现有规范和分析方法存在明显不足。为此,建立了一套数值分析方法,把这一复杂问题分解成相对独立、简单的两个方面进行分析：一是采用任意拉格朗日-欧拉（ALE）数值方法,计算自由场地插桩周围土体产生的位移场;二是利用桩基水平力与位移关系曲线,即P-Y曲线,采用杆系-土弹簧的传统方法计算土体位移产生的桩体加载。通过与已有离心试验数据的比较,验证了该方法的可靠性和适用性。研究揭示了自由场地土体的变形模式和流动机制,阐明了由于插桩邻近桩基产生的附加荷载变化规律,特别是发现了黏土变形参数 对插桩引起的自由场地土体位移场有显著影响,但对插桩引起的桩基加载影响较小。最后,针对导管架对桩基的桩头约束条件和插桩及导管架自身对桩基的线性叠加加载适用性问题给出了详细说明。     

辉绿岩裂缝对其磁组构的影响

磁组构是由岩石中磁性矿物定向分布而产生的组构特征,因此磁组构分析是研究岩石组构常用的技术手段,它具有 见效快、灵敏度高、无损样品等特点,近年来得到广泛应用。然而在磁组构研究工作中钻取定向样品或定向手标本时,常 常会遇到天然样品含有裂缝且裂缝中充填大量近地表沉积物和自生矿物。本文针对辉绿岩裂缝充填物对其磁组构结果的影 响程度做了详细研究,选用160个含裂缝的辉绿岩岩芯定向样品,通过对比去除裂缝充填物前后的磁组构变化,发现实验 前后所有样品磁化率大小变化率平均值<1%,磁组构方向变化平均值<1°,因此认为辉绿岩裂缝物质对其磁组构影响甚微。 矿物学和岩石磁学分析表明裂隙充填物主要为石英、长石,以及少量赤铁矿、黄铁矿和绿泥石等表生矿物。而辉绿岩的携 磁矿物主要是亚铁磁性的磁铁矿,其磁化率强度约为同等质量裂缝填充物的30倍,致使辉绿岩中的裂隙充填物对磁组构的 影响很小。