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.     

运用概率分布函数确定特高品位

地质品位是评价矿石质量的重要依据。样品的品位与频率的曲线为不对称的正态曲线时,通过对样品品位的数率统计,用正态分布积分函数计算某测定品位以上的样品在样本总体内允许出现的数量,确定其是否为特高品位。     

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。     

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.     

A dynamic network model for two‐phase immiscible flow

A dynamic pore‐scale network model is formulated for two‐phase immiscible flow. Interfaces are tracked through the pore throats using a modified Poiseuille equation, whereas special displacement rules are used at the pore bodies. The model allows interfaces to move over several pore‐lengths within a time step. Initial computational results are presented for a drainage experiment to demonstrate some of the features of the model. This revised version was published online in July 2006 with corrections to the Cover Date.     

西藏岗巴晚白垩世锶同位素曲线的地层学意义及问题讨论

地质历史时期古海洋中的锶同位素组成具有全球基本一致的演化规律 ,并主要受全球性海平面变化影响。根据从西藏岗巴宗山上白垩统剖面中 6 3个海相碳酸盐样品获得的锶同位素测试数据建立了锶同位素演化曲线 ,与北美同时代锶同位素曲线进行了对比 ,证明晚白垩世有一次全球性海平面升降事件 ,在宗山剖面宗山组近底部的年龄值为 89.4 Ma,并讨论了西藏岗巴宗山地区晚白垩世地层划分对比中的一些问题。     

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。     

夹层厚度对瑞利面波频散曲线的影响

文章以弹性波横波速度为参数,利用瑞利面波频散曲线的快速标量传递算法进行正演模拟计算,系统研究软弱层厚度对瑞利面波基阶模频散曲线的影响,分析和总结了频率与相速度（f-c）、频率与波数（f-k）、深度与相速度（h-c）等瑞利面波基阶模曲线随软弱层厚度变化的规律。     

SP anomaly over doable line of poles-interpretation through log curves

In the analysis and interpretation ofsp anomalies, two-dimensional finite sheet models are equated to the double line of poles. The profiles over such a model being asymmetric with a minor positive peak and a major negative peak, a double logarithmic curve matching technique simpler than that of Meiser is suggested in the paper for easy and unique solution for all values of depth, dip and length. This technique along with a few others have been tested on two profiles across the sulphide deposit from the Rakha Mines, Singhbhum copper belt, India.     

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.