Approximate general solution of 2-degrees of freedom dynamical systems using `les solutions precieuses'

This paper presents the procedure of a computational scheme leading to approximate general solution of the axi-symmetric,2-degrees of freedom dynamical systems. Also the results of application of this scheme in two such systems of the non-linear double oscillator with third and fifth order potentials in position variables. Their approximate general solution is constructed by computing a dense set of families of periodic solutions and their presentation is made through plots of initial conditions. The accuracy of the approximate general solution is defined by two error parameters, one giving a measure of the accuracy of the integration and calculation of periodic solutions procedure, and the second the density in the initial conditions space of the periodic solutions calculated. Due to the need to compute families of periodic solutions of large periods the numerical integrations were carried out using the eighth order, variable step, R-K algorithm, which secured for almost all results presented here conservation of the energy constant between 10^-9 and 10^-12 for single runs of any and all solutions. The accuracy of the approximate general solution is controlled by increasing the number of family curves and also by `zooming' into parts of the space of initial conditions. All families of periodic solutions were checked for their stability. The computation of such families within areas of `deterministic chaos' did not encounter any difficulty other than poorer precision. Furthermore, on the basis of the stability study of the computed families, the boundaries of areas of `order' and `chaos' were approximately defined. On the basis of these results it is concluded that investigations in thePoincaré sections have to disclose 3 distinct types of areas of `order' and 2 distinct types of areas of `chaos'. Verification of the `order'/`chaos' boundary calculation was made by working out several Poincaré surfaces of sections. This revised version was published online in July 2006 with corrections to the Cover Date.     

Numerical Investigation of the Galactic Problem by Computing Families of Periodic Solutions

The galactic dynamical system expressed by a third-order axisymmetric polynomial potential is investigated numerically by computing periodic solutions. We define as Sthe compact set of initial conditions generating bounded motions, and as S ^p , with S ^p ? S, the countable set of all initial conditions generating periodic solutions. Then, we consider the subsets S _s ^p and S _a ^p of S ^p , where S _s ^p ∪ S _a ^p = S ^p , S _s ^p S _a ^p = Ø, the first of which corresponds to symmetric periodic solutions, and the second to asymmetric solutions. Then, we approximate the set S _s ^p , leaving treatment of the set S _a ^p of asymmetric solutions for a future publication. The set S _s ^p is known to be dense in S (‘Last Geometric Theorem of Poincar;’, Birkhoff, 1913). Using a computer programme capable to locate all elements of the set S _s ^p that generate symmetric periodic solutions that re-enter after intersecting the axis of symmetry from 1 to ntimes. The results of the approximation of S _s ^p in the total domain and in the sample sub-domains of zooming, we present in graphical form as family curves in the (x, C) plane. The solutions located with the largest periods re-enter after 440 galaxy revolutions while the families calculated fully (initial conditions, period, energy, stability co-efficient) include solutions that re-enter after 340 galaxy revolutions. To advance further the approximation of the set S _s ^p thus obtained, we applied the same procedure inside eight sub-domains of the domain Sinto which we ‘zoomed’ through selection of finer search steps and double maximum periods. The family curves thus calculated presented in the (x, C) plane do not intersect anywhere in some sub-domains and their pattern resembles that of laminar flow. In other sub-domains, however, we found family curves from which branching families emanate. The concepts of completeand non-completeapproximation of S _s ^p in sub-domains of laminar and sub-domains with branching family curves, respectively, is introduced. Also, the concept of basic family of order1, 2, ..., n, are defined. The morphology of individual periodic solutions of all families is investigated, and the types of envelopes found are described. The approximate set S _s ^p was also checked by computing Poincar; sections for energy values corresponding to the mean energy range of the eight sub-domains of zooming mentioned above. These sections show that most parts of the compact domain in Sgenerating non-periodic but bounded solutions correspond to with well-shaped tori that intersect the x-axis, a fact that implies that dominant to exclusive type of periodic solutions are the symmetric ones with two normal crossings of this axis. The presence of non-symmetric periodic solutions as well as of chaotic regions is encountered. All calculations reported here were performed using the variable step R-K 8th-order direct integration and setting the allowable energy variation Δ C= |C _start? C _end| < 10^?13. The output, consisting of many thousands of families and their properties (initial conditions, morphology, stability, etc.), is stored in a directory entitled ‘Atlas of the Symmetric Periodic Solution of the Galactic Motion Problem’.     

Discovery of Potassium-Bearing Cuttings from the Well Yangta 4 in the Kuqa Depression and Seam Division

正The world petroleum exploration suggests that,about70%of the world’s potash resources were discovered during oil and gas exploration(Zheng et al.,2007).The Kuqa depression in the Tarim basin is abundant with petroleum exploration data,and     

Quasi indicatrix approach for distortion visualization and analysis for map projections

Tissot’s indicatrix or ellipse of distortion is a diagram that is the projection of an infinitesimal circle on the original surface. It is normally an ellipse of which elongation depends on the amount of distortion caused by map projection. It provides a medium for analyzing existing projections and developing new ones. The ellipse can be scaled and depicted on the map for visualization purposes. This paper presents an alternative approach, in which the projection of a finite small circle on the sphere is used. Its projection is normally an ellipse that can be very close to Tissot’s indicatrix, and is called quasi indicatrix, here. Its parameters can be derived from the forward projection equations without using partial derivatives. Therefore, it is a useful and practical approach from a programmer’s point of view. The quasi indicatrix approach is also numerically tested on Aitoff–Hammer projection with a set of points. The indicatrix parameters obtained by using this approach deviate 0.5% from the ground truths at most, being the average less than 0.2%.     

碱式水解法提取红土分子化石: 以安徽宣城更新世网纹红土为例

红土中种类丰富的分子化石为红土古生态研究提供了直接证据, 但较低含量的分子化石限制了传统索氏抽提方法的推广应用.本次研究尝试性地运用碱式水解法提取安徽宣城更新世红土中的分子化石, 在25g样品中检测到了含量明显、种类丰富的有机物, 且该方法可以显著地降低空白污染, 这说明碱式水解法在分子化石含量低的地质体(如红土) 研究中具有一定的应用潜力.本次研究检测出除了传统索式抽提得到的正构烷烃、脂肪酸、脂肪醇等以外, 还提取到了二元羧酸这一重要化合物, 它的存在为网纹红土可能形成于多水环境提供了新的证据.测试样品中各类分子化石组合信息显示出红土有机物以微生物为主的来源特征, 表明网纹红土形成过程受到了微生物活动的影响, 同时伴有大量低等菌、藻来源有机质的输入, 初步结果为红土形成环境研究提供了新的证据.      

内蒙古及东北地区古冻土及古环境考察研究新进展

中国北方地区保留了晚更新世以来大量的冰缘遗迹. 在气候变化背景下, 在寒区和干旱区分别出现冰缘地貌、正逆向沙化等问题, 综合不同区域的地质遗迹, 从时间上的对应关系可进一步分析气候环境变化问题. 2008年5-7月调查中, 在鄂尔多斯和大同地区分别发现了新的砂楔和土楔;在大兴安岭生态定位研究站设立了8个钻孔和2套自动气象站, 开启了冻土、湿地、 积雪研究以及现代陆面过程对下伏冻土影响的研究;在黄岗梁地区新发现了一个冻融褶皱;调查了松嫩沙地古沙丘及古土壤活动与冻土进退的关系;发现小兴安岭地区冻土退化显著, 岛状冻土散布于海拔相对较高的地区;三江平原西部农业开发强烈改变了地表覆盖, 冻土温度升高显著, 冻土上限下降明显, 甚至厚度较薄的冻土消失. 后期工作希望通过综合、集成分析以上结果, 探讨我国北方地区晚更新世/全新世的冻土南界及环境变迁.     

Geoheritage importance of stratigraphic type sections,type localities and reference sites—review,discussion and protocols for geoconservation

Equivalent in principle to type localities and type specimens in biology and paleontology, geological type sections and type localities, whether for sedimentary, metamorphic or igneous units, are critically important sites as long-term reference and research localities and for geo-education of students. Unlike type specimens that are housed in museums or established institutions of learning, most geological type sections and localities are in field settings and, if they are not located in National Parks or other reserves with some legislated protection, run the risk of being destroyed, inundated, buried by earthworks or otherwise modified. The history of the geological sciences in Australia is such that a number of type localities, or stratigraphic type sections, have been destroyed by local government actions, or developers through lack of knowledge of their importance, or lack of knowledge of their existence. Examples of the severe modification or loss of type sections include those of the Maxicar beds, the Tims Thicket Limestone and the Eaton Sand. The UK, a leader in the field of Geoconservation and with a number of global stratotype section and point locations as well as many other type sections identified within its borders, provides models for preserving and managing important geological sites and type sections. Whole-of-government and local governments are involved in the registering and protection of important geological sites. Aspects of the UK model may be adapted to help secure geological type sections and localities in Australia. While some type sections and heritage localities are already protected, to improve the level of protection for more sites we propose a long-term, multi-pronged approach: creation of an inventory of all nominated locations; registration of appropriate sites at Local, State or Federal government levels, where current legislation allows; education of landowners and land managers, both government and non-government to highlight the importance of type sections to science; and securing more geological type sections and localities in some form of reserve.     

黄河（山东段）悬河稳定性评价

通过黄河（山东段）悬河稳定性影响因素分析,各河段都有决口失稳的可能。该文从区域地壳稳定性、堤基稳定性、河道稳定性3个方面,采用模糊数学综合评判法进行悬河稳定性评价,对河段可能出现的失稳或决口险点及其可能造成的危害性进行分析和预测,初步确定了10处地质险段。     

薄片显微描绘和自动图像分析技术在岩石学定量评价中的应用

用显微镜描绘技术在绘图纸上绘出线条清晰,反差很大的岩石薄片手绘图像,再将手绘图像通过电视摄像机（ＣＣＤ）输入到计算机自动图像系统中处理,可以取得组成岩石主要矿物的密度分布、粒度、形状及空间分布模式,揭示岩石特征,为岩石学定量研究提供参数。     

太湖地区多剖面地层学分析与良渚期环境事件

太湖地区多剖面地层学分析和环境考古研究表明:本区良渚期为全新世大暖期中气候逐渐向干凉转变的时期,但大部分时间里仍略比今天暖湿。良渚期末气候走入低谷并剧烈波动,良渚期侵蚀面反映一次较长时间的海面下降过程,气候剧烈波动的转型期与海面下降至低海面过程相一致。此时本区洪积层、埋藏遗址及遗址地层中文化间歇层等发育皆反映古洪水泛滥事件的存在;而良渚期侵蚀面上的铁锰结核聚集现象及现没于水下的众多良渚期开挖的古井等遗迹还反映出这一时期也曾发生过气候干燥事件。分析认为良渚文化繁荣发展期陆地面积扩大,气候略好于今天;而良渚文化衰亡期则处于4300~3800aB. P.间的水、旱灾丛生的低海面气候异常期。