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 \(L_5\).     

Temporal–spatial variability of atmospheric and hydrological natural disasters during recent 500 years in Inner Mongolia,China

Natural Hazards - Inner Mongolia, located in the northern China, is a natural disaster-prone region. This study is dedicated to making a comprehensive and quantitative analysis of the...     

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.     

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.     

A Note on Reviving the Goddard Satellite-Based Surface Turbulent Fluxes （GSSTF） Dataset

Accurate sea surface flux measurements are crucial for understanding the global water and energy cycles. The oceanic evaporation, which is a major component of the global oceanic fresh water flux, is useful for predicting oceanic circulation and transport. The global Goddard Satellite-based Surface Turbulent Fluxes Version-2 (GSSTF2; July 1987--December 2000) dateset that was officially released in 2001 has been widely used by scientific community for global energy and water cycle research, and regional and short period data analyses. We have recently been funded by NASA to resume processing the GSSTF dataset with an objective of continually producing a uniform dataset of sea surface turbulent fluxes, derived from remote sensing data. The dataset is to be reprocessed and brought up-to-date (GSSTF2b) using improved input datasets such as a recently upgraded NCEP/DOE sea surface temperature reanalysis, and an upgraded surface wind and microwave brightness temperature V6 dataset (Version 6) from the Special Sensor Microwave Imager (SSM/I) produced by Remote Sensing Systems (RSS). A second new product (GSSTF3) is further proposed with a finer temporal (12-h) and spatial (0.25^ox0.25^o) resolution. GSSTF2b (July 1987--December 2008) and GSSTF3 (July 1999--December 2009) will be released for the research community to use by late 2009 and early 2011, respectively.     

综合气象观测系统业务运行综合评估技术研究

综合气象观测网运行监控系统是我国气象探测设备运行保障的实时业务系统.文章以装备技术保障工程理论为基础,按可靠性、维修性、保障性、业务性、经济性等多个范畴,从装备运行状态、装备性能参数、探测数据质量、通信传输、供应保障、维护维修等方面,提出了针对我国综合气象观测网中各类设备的运行、维护和保障等工作进行综合评估的技术方法,...