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 \(L_5\).     

Earthquakes in Switzerland and surrounding regions during 2006

This report of the Swiss Seismological Service summarizes the seismic activity in Switzerland and surrounding regions during 2006. During this period, 572 earthquakes and 91 quarry blasts were detected and located in the region under consideration. Of these earthquakes, two occurred in conjunction with the construction of the new Gotthard railway tunnel and 165 were induced artificially by the stimulation of a proposed geothermal reservoir beneath the city of Basel. With 20 events with M _L ≥ 2.5, five of which were artificially induced, the seismic activity in the year 2006 was far below the average over the previous 31 years. Nevertheless, six events were felt by the public, most prominently the strongest of the induced Basel events (M _L 3.4), which caused some non-structural building damage. Noteworthy are also the two earthquakes near Cortaillod (M _L 3.2), on the shore of Lake Neuchatel, and in Val Mora (M _L 3.5), between the Engadin and Val Müstair, as well as the 42 aftershocks of the M _L 4.9 Vallorcine earthquake, between Martigny and Chamonix, of September 2005. Editorial handling: Stefan Bucher     

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.     

南极半岛周边海域表层沉积物粒度分布特征及其环境指示意义

基于南极半岛周边海域表层沉积物调查以及收集的资料,并通过分析表层沉积物粒度数据研究沉积物类型和分布特征,探讨沉积物的变化规律。南极半岛周边海域的沉积物类型比较丰富,主要分为四大类:砾质、砂质、粉砂质以及泥质沉积物;根据不同的水深和地貌单元可分为陆架(或岛架)碎屑沉积物、陆坡(或岛坡)沉积物和深海沉积物。研究区沉积物属于冰海沉积物,并可划分为残副冰碛物和混合副冰碛物。沉积物的搬运介质以冰川、冰筏为主,海流对沉积物的影响较为明显,沉积物类型随地形变化而呈有规律的分布。     

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.     

Comparison of two drought indices in studying regional meteorological drought events in China

The composite-drought index (CI), improved weighted average of precipitation index (IWAP), and the objective identification technique for regional extreme events (OITREE) were employed to detect China's regional meteorological drought events (CRMDEs) during 1961–2010. Compared with existing references, CI and IWAP both showed strong ability in identifying CRMDEs. Generally, the results of CI and IWAP were consistent, especially for extreme and severe CRMDEs. During 1961–2010, although the frequencies of extreme and severe CRMDEs based on CI and IWAP both showed weak decreasing trends, the two mean-integrated indices both showed increasing but not significant trends. However, the results of IWAP were more reasonable than CI’s in two aspects. Firstly, the monthly frequency of extreme and severe CRMDEs based on IWAP showed a clear seasonal variation, which coincided with the seasonal variation of the East Asian monsoon over central–eastern China, whereas the frequency based on CI presented a much weaker seasonal variation. Secondly, the two sets of results were sometimes inconsistent with respect to the start and end times of a CRMDE, and CRMDEs based on CI generally showed two unreasonable phenomena: (1) under non-drought conditions, a severe drought stage could suddenly occur in a large area; and (2) during the following period, drought could alleviate gradually in cases of non-precipitation. Comparative analysis suggested that the IWAP drought index possesses obvious advantages in detecting and monitoring regional drought events.     

Geological Characteristics and Stability Evaluation of Wanjia Middle School Slope in Wenchuan Earthquake Area

To investigate the formation mechanism and the stability of Wanjia middle school slope in Wenchuan Earthquake Area, the macroscopic geological characteristics and the failure process of the landslide are researched by engineering geology analysis method, limit equilibrium method, and finit element method. The results show that after the Wenchuan Earthquake, retaining walls, houses and other infrastructure on the foot of Wanjia middle school slope were severely destroyed, 10 cm wide tension fracture appeared at the trailing edge of the slope. Wanjia middle school slope is a type of medium-sized soil landslide. The area of the deformation body is about 19,314 m², the total volume of the deformation body is about 23 × 10⁴ m³. There may be two potential sliding surfaces in the unstable slope: shallow and deep landslide. The analysis results of the limit equilibrium method and the finite element method show that: under dead weight, dead weight + rainstorm, dead weight + earthquake conditions, the plastic zone occurs mainly at the middle part or the trailing edge of the slope, and it doesn’t fully cut through the deep landslide body, so the deep landslide is stable. However, under rainstorm or earthquake conditions, the plastic zone almost completely cut thorough the shallow landslide body, it shows that the shallow landslide is in the understable–basic stable state. It is found that the results of finite element method is concordant with the results of the limit equilibrium method (F _s = 1.06–1.29, the shallow landslide is in the basic stable–stable state). The calculation results show that shallow landslides are likely to occur in Wanjia middle school slope during a rainstorm or an earthquake, so monitoring and control of the slope should be strengthened. The shallow landslide should be managed by some measures, such as anti slide pile retaining structures and drainage works, and the dangerous rock bodies on the slope surface should be cleaned up.     

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.     

Spatial decision support applications based on three-dimensional city models

The basic mathematic models, such as the statistic model, the time-serial model, the spatial dynamic model etc., and some typical analysis methods based on 3DCM are proposed and discussed. A few typical spatial decision making methods integrating the spatial analysis and the basic mathematical models are also introduced, e.g. visual impact assessment, dispersion of noise immissions, base station plan for wireless communication. In addition, a new idea of expectation of further applications and add-in-value service of 3DCM is promoted. As an example, the sunshine analysis is studied and some helpful conclusions are drawn.