On the period of the periodic orbits of the restricted three body problem

We will show that the period T of a closed orbit of the planar circular restricted three body problem (viewed on rotating coordinates) depends on the region it encloses. Roughly speaking, we show that, \(2 T=k\pi +\int _\Omega g\) where k is an integer, \(\Omega \) is the region enclosed by the periodic orbit and \(g:{\mathbb {R}}^2\rightarrow {\mathbb {R}}\) is a function that only depends on the constant C known as the Jacobian constant; it does not depend on \(\Omega \). This theorem has a Keplerian flavor in the sense that it relates the period with the space “swept” by the orbit. As an application we prove that there is a neighborhood around \(L_4\) such that every periodic solution contained in this neighborhood must move clockwise. The same result holds true for \(L_5\).     

Late Carboniferous porphyry copper mineralization at La Voluntad,Neuquén,Argentina: Constraints from Re–Os molybdenite dating

The La Voluntad porphyry Cu–Mo deposit in Neuquén, Argentina, is one of several poorly known porphyry-type deposits of Paleozoic to Early Jurassic age in the central and southern Andes. Mineralization at La Voluntad is related to a tonalite porphyry from the Chachil Plutonic Complex that intruded metasedimentary units of the Piedra Santa Complex. Five new Re–Os molybdenite ages from four samples representing three different vein types (i.e., quartz–molybdenite, quartz–sericite–molybdenite and quartz–sericite–molybdenite ± chalcopyrite–pyrite) are identical within error and were formed between ~312 to ~316 Ma. Rhenium and Os concentrations range between 34 to 183 ppm and 112 to 599 ppb, respectively. The new Re–Os ages indicate that the main mineralization event at La Voluntad, associated to sericitic alteration, was emplaced during a time span of 1.7 ± 3.2 Ma and that the deposit is Carboniferous in age, not Permian as previously thought. La Voluntad is the oldest porphyry copper deposit so far recognized in the Andes and indicates the presence of an active magmatic arc, with associated porphyry style mineralization, at the proto-Pacific margin of Gondwana during the Early Pennsylvanian.     

Well placement optimization subject to realistic field development constraints

This work considers the well placement problem in reservoir management and field development optimization. In particular, it emphasizes embedding realistic and practical constraints into a mathematical optimization formulation. Such constraints are a prerequisite for the wider use of mathematical optimization techniques in well placement problems, since constraints are a way to incorporate reservoir engineering knowledge into the problem formulation. There are important design limitations that are used by the field development team when treating the well placement problem, and these limitations need to be articulated and eventually formalized within the problem before conducting the search for optimal well placements. In addition, these design limitations may be explicit or implicit. In this work, various design limitations pertaining to well locations have been developed in close collaboration with a field operator on the Norwegian Continental Shelf. Moreover, this work focuses on developing constraint-handling capability to enforce these various considerations during optimization. In particular, the Particle Swarm Optimization (PSO) algorithm is applied to optimize for the well locations, and various practical well placement constraints are incorporated into the PSO algorithm using two different constraint-handling techniques: a decoder procedure and the penalty method. The decoder procedure maps the feasible search space onto a cube and has the advantage of not requiring parameter tuning. The penalty method converts the constrained optimization problem into an unconstrained one by introducing an additional term, which is called a penalty function, to the objective function. In contrast to the penalty method, only feasible solutions are evaluated in the decoder method. Through numerical simulations, a comparison between the penalty method and the decoder technique is performed for two cases. We show that the decoder technique can easily be implemented for the well placement problem, and furthermore, that it performs better than the penalty method in most of the cases.     

中国古代牧业社会骨制品的初步考察:以新疆巴里坤石人子沟遗址为例

考古遗址出土骨制品的研究对于揭示古代社会的动物资源获取和利用、手工业生产、社会组织结构等问题具有重要意义。国内骨制品研究目前多集中在农业区域,这些研究为探讨新石器时代至青铜时代的动物使用及其与社会发展、早期国家形成的关系等问题作出了重要贡献。然而,针对牧业社会骨制品的考察十分缺乏。新疆哈密地区巴里坤草原分布有大量古代牧业文化遗址,石人子沟遗址（43°31'12.8"~43°34'28.9"N,93°13'44.8"~93°16'49.1"E）是其中一处青铜时代晚期至铁器时代早期的大型聚落。本文从动物考古学视角研究该遗址2006年至2011年发掘出土的426件骨制品。结果显示,石人子沟遗址骨制品的原料主要为以羊（Ovis aries/Capra hircus）、马（Equus caballus）为主的家养动物和以鹿（Cervidae）为主的野生动物,其中羊的比例最高（69.7%）,鹿（13.8%）、马（2.3%）次之,这与中原地区青铜时代农业文化遗址的骨制品多以牛为原料的情况明显不同。羊在骨制品原料中占绝对多数且大量使用羊距骨制品的现象是对石人子沟遗址以牧业为主的生业经济方式的直接反映。石人子沟遗址不同类型骨制品的制作各具特点,但整体表现出"省时省力"的特点,即对使用部位细致打磨,对非使用部位仅做简单处理。与中原地区商周时期大型制骨作坊规范化、规模化、产业化的骨器生产不同,石人子沟遗址未见专门的制骨场所,骨制品生产的操作链条也并不完整。遗址的骨制品生产可能是以家庭为单元进行的,产品的专业化、精细化程度也相对较低。该研究填补了我国古代牧业文化遗址出土骨制品动物考古学专门研究的空白,为进一步探究我国古代不同区域、不同生业经济基础下的制骨手工业面貌提供了重要资料。

     

Broad search for unstable resonant orbits in the planar circular restricted three-body problem

Unstable resonant orbits in the circular restricted three-body problem have increasingly been used for trajectory design using optimization and invariant manifold techniques. In this study, several methods for computing these unstable resonant orbits are explored including grid searches, flyby maps, and continuation. Families of orbits are computed focusing on orbits with multiple loops near the secondary in the Jupiter–Europa system, and their characteristics are explored. Different parameters such as period and stability are examined for each set of resonant orbits, and the continuation of several specific orbits is explored in more detail.     

整体最小二乘的迭代解法

在引入整体最小二乘平差准则的基础上,推导了整体最小二乘的迭代解法;同时,引入多元函数隐函数求导的方法以确定未知参数对观测数据的线性信息,解决了整体最小二乘下的精度评定问题。给出了运用新的解法在拟合函数确定以及坐标转换参数确定等方面的应用实例,验证了新算法的可行性。     

The Analysis of Three Dimensional FEM for Interaction of the Gravity-arch Dam and Complex Ground at Geheyan,Qingjiang River

This paper introduces the analysis of three dimensional finite element method for the gravity-arch dam building on the complex ground. The foundation rock of dip and strain-slip, three faults, two weak intercalations and etc. arc considered in this calculation model. Water static pressure, gravity of dam, uplift, temperature stress and so on are computed, including three dimensional osmotic and temperature fields in the foundation. The range of calculation model is about 1400×900×600m2 . There are 1845 elements of all kinds, 3280 nodes in the network of finite element. The superlax iterative method is used to solve, and three dimensional perspective and software of after treatment are applied in analyses. The dimension of this computation is large, various results of treating complex problems are reasonable. The important basis has applied to designing unit. The computation is important practical significance for Geheyan Dam which is being built.     

聂尔库组植物化石新材料及其地层意义

聂尔库组分布于辽宁东北部新宾县南杂木一带的苏子河盆地,为一套河湖相砂页岩沉积。该组含有较丰富的动、植物化石,但由于系统采集和研究不够,自建组以来,在地层时代和对比方面迄今仍是众说纷云。作者通过系统采集,共获植物亿石12属13种,化石组合面貌与英国威尔登植物群可以比较;与辽西的海州组、辽北—吉中营城组、黑龙江东部的穆棱组植物组合亦很相似,其时代大体相当于早白垩世尼殴克姆晚期。文中对我国首次发现的属种作了描述。     

Non-Linear Theory and Power-Law Models for Information Integration and Mineral Resources Quantitative Assessments

Singular physical or chemical processes may result in anomalous amounts of energy release or mass accumulation that, generally, are confined to narrow intervals in space or time. Singularity is a property of different types of non-linear natural processes including cloud formation, rainfall, hurricanes, flooding, landslides, earthquakes, wildfires, and mineralization. The end products of these non-linear processes can be modeled as fractals or multifractals. Hydrothermal processes in the Earth’s crust can result in ore deposits characterized by high concentrations of metals with fractal or multifractal properties. Here we show that the non-linear properties of the end products of singular mineralization processes can be applied for prediction of undiscovered mineral deposits and for quantitative mineral resource assessment, whether for mineral exploration or for regional, national and global planning for mineral resource utilization. In addition to the general theory and framework for the non-linear mineral resources assessment, this paper focuses on several power-law models proposed for characterizing non-linear properties of mineralization and for geoinformation extraction and integration. The theories, methods, and computer system discussed in this paper were validated using a case study dealing with hydrothermal Au mineral potential in southern Nova Scotia, Canada.     

A simplified method for analyzing the fundamental frequency of monopile supported offshore wind turbine system design

Preliminary design of offshore wind turbines requires high precision simplified methods for the analysis of the system fundamental frequency. Based on the Rayleigh method and Lagrange's Equation, this study establishes a simple formula for the analysis of system fundamental frequency in the preliminary design of an offshore wind turbine with a monopile foundation. This method takes into consideration the variation of cross-section geometry of the wind turbine tower along its length, with the inertia moment and distributed mass both changing with diameter. Also the rotational flexibility of the monopile foundation is mainly considered. The rigid pile and elastic middle long pile are calculated separately. The method is validated against both FEM analysis cases and field measurements, showing good agreement. The method is then used in a parametric study, showing that the tower length Lt, tower base diameter d0, tower wall thickness δt, pile diameter db and pile length Lb are the major factors influencing the fundamental frequency of the offshore wind turbine system. In the design of offshore wind turbine systems, these five parameters should be adjusted comprehensively. The seabed soil condition also needs to be carefully considered for soft clay and loose sand.