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.     

Recurrent mesoproterozoic continental magmatism in South-Central Norway

We report U–Pb dates and Lu–Hf isotope data, obtained by LAM-ICPMS, for zircons from metamorphic rocks of the Setesdalen valley, situated in the Telemark block south of the classic Telemark region of southern Norway. The samples include infracrustal rocks from the metamorphic basement, metaigneous rocks and metasediments from the Byglandsfjorden supracrustal cover sequence, and metaigneous rocks which intruded the whole succession. The main crustal evolution took place from 1,550–1,020 Ma, beginning with the emplacement of juvenile tonalitic melts; the contribution of older crustal material increased with time. Around 1,320 Ma, further addition of juvenile material occurred, involving both mafic and felsic melts, metamorphism and deformation. Acid magmas with high FeO*/MgO were intruded at 1,215 Ma, coinciding with underplating elsewhere in South Norway. The period starting at 1,215 Ma is represented by supracrustal rocks, principally metarhyolites with minor mafic material and immature sediments of the Byglandsfjorden Group. The crust generation processes ended with the intrusion of diorites and granodiorites at 1,030 Ma, late in the Sveconorwegian orogeny. Regional processes of metamorphism and deformation (around 1,290 and 1,000 Ma) can be related to the assembly of Rodinia. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

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.     

致密砂岩层内强钙质胶结物成因机制及其意义——以鄂尔多斯盆地三叠系延长组长7油层组为例

通过岩心和薄片观察,利用荧光显微镜、阴极发光显微镜、同位素质谱仪、冷热台等设备,对鄂尔多斯盆地长7油层组强钙质胶结砂岩及其附近含油砂岩开展研究。结果表明：钙质胶结是致密砂岩储层含油非均质性的主要因素,胶结期次主要为一期;簇同位素揭示该期钙质胶结物的形成温度为18~42℃,对应地质时代为中晚三叠世—中侏罗世,为早成岩期产物,推测与盆地早期小规模构造运动相关;相邻的含油砂岩中油气包裹体伴生的同期盐水包裹体的均一化温度为90~120℃,结合盆地模拟揭示油气主要为一期充注,充注期为100~130 Ma,处于早白垩世;长7油层组不含油致密砂岩内钙质胶结物形成时间早于含油砂岩内石油的充注时间。     

蓝细菌聚金作用实验研究

蓝细菌聚金实验研究表明:①不同的生物由于生化组分的差异,其富金能力不同,低等蓝细菌生物比动物细胞富金能力强;②金在细胞中的分布与其各部分生化组成(也就是生物配体)密切相关;③金离子进入细胞不是一种简单的扩散作用,而是通过细胞膜界面两侧物质之间的交换而实现的,蓝细菌活体聚金机理主要是参与生命活动的吸收作用;④在较高温热水环境中微生物对成矿最显着。     

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.