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 \(L_5\).     

Assessing future risk: quantifying the effects of sea level rise on storm surge risk for the southern shores of Long Island, New York

Sea level rise threatens to increase the impacts of future storms and hurricanes on coastal communities. However, many coastal hazard mitigation plans do not consider sea level rise when assessing storm surge risk. Here we apply a GIS-based approach to quantify potential changes in storm surge risk due to sea level rise on Long Island, New York. We demonstrate a method for combining hazard exposure and community vulnerability to spatially characterize risk for both present and future sea level conditions using commonly available national data sets. Our results show that sea level rise will likely increase risk in many coastal areas and will potentially create risk where it was not before. We find that even modest and probable sea level rise (.5 m by 2080) vastly increases the numbers of people (47% increase) and property loss (73% increase) impacted by storm surge. In addition, the resulting maps of hazard exposure and community vulnerability provide a clear and useful example of the visual representation of the spatial distribution of the components of risk that can be helpful for developing targeted hazard mitigation and climate change adaptation strategies. Our results suggest that coastal agencies tasked with managing storm surge risk must consider the effects of sea level rise if they are to ensure safe and sustainable coastal communities in the future.     

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.     

Spatial control of groundwater contamination,using principal component analysis

A study on the geochemistry of groundwater was carried out in a river basin of Andhra Pradesh to probe into the spatial controlling processes of groundwater contamination, using principal component analysis (PCA). The PCA transforms the chemical variables, pH, EC, Ca²⁺, Mg²⁺, Na⁺, K⁺, HCO \(_3^- \) , Cl^?, SO \(_4^{2-} \) , NO \(_3^-\) and F^?, into two orthogonal principal components (PC1 and PC2), accounting for 75% of the total variance of the data matrix. PC1 has high positive loadings of EC, Na⁺, Cl^?, SO \(_4^{2-} \) , Mg²⁺ and Ca²⁺, representing a salinity controlled process of geogenic (mineral dissolution, ion exchange, and evaporation), anthropogenic (agricultural activities and domestic wastewaters), and marine (marine clay) origin. The PC2 loadings are highly positive for HCO \(_3^- \) , F^?, pH and NO \(_3^- \) , attributing to the alkalinity and pollution controlled processes of geogenic and anthropogenic origins. The PC scores reflect the change of groundwater quality of geogenic origin from upstream to downstream area with an increase in concentration of chemical variables, which is due to anthropogenic and marine origins with varying topography, soil type, depth of water levels, and water usage. Thus, the groundwater quality shows a variation of chemical facies from Na⁺ > Ca²⁺ > Mg²⁺ > K⁺: HCO \(_3^- \) > Cl^? > SO \(_4^{2-}>\) NO \(_3^- \) > F^?at high topography to Na⁺ > Mg²⁺ > Ca²⁺ > K⁺: Cl^? > HCO \(_3^- \) > SO \(_4^{2-}>\) NO \(_3^- \) > F^? at low topography. With PCA, an effective tool for the spatial controlling processes of groundwater contamination, a subset of explored wells is indexed for continuous monitoring to optimize the expensive effort.     

Inclusions in diamonds from the K14 and K10 kimberlites, Buffalo Hills, Alberta, Canada: diamond growth in a plume?

Analyses of mineral inclusions, carbon isotopes, nitrogen contents and nitrogen aggregation states in 29 diamonds from two Buffalo Hills kimberlites in northern Alberta, Canada were conducted. From 25 inclusion bearing diamonds, the following paragenetic abundances were found: peridotitic (48%), eclogitic (32%), eclogitic/websteritic (8%), websteritic (4%), ultradeep? (4%) and unknown (4%). Diamonds containing mineral inclusions of ferropericlase, and mixed eclogitic-asthenospheric-websteritic and eclogitic-websteritic mineral associations suggests the possibility of diamond growth over a range of depths and in a variety of mantle environments (lithosphere, asthenosphere and possibly lower mantle).

Eclogitic diamonds have a broad range of C-isotopic composition (δ¹³C=−21‰ to −5‰). Peridotitic, websteritic and ultradeep diamonds have typical mantle C-isotope values (δ¹³C=−4.9‰ av.), except for two ¹³C-depleted peridotitic (δ¹³C=−11.8‰, −14.6‰) and one ¹³C-depleted websteritic diamond (δ¹³C=−11.9‰). Infrared spectra from 29 diamonds identified two diamond groups: 75% are nitrogen-free (Type II) or have fully aggregated nitrogen defects (Type IaB) with platelet degradation and low to moderate nitrogen contents (av. 330 ppm-N); 25% have lower nitrogen aggregation states and higher nitrogen contents (30% IaB; <1600 ppm-N).

The combined evidence suggests two generations of diamond growth. Type II and Type IaB diamonds with ultradeep, peridotitic, eclogitic and websteritic inclusions crystallised from eclogitic and peridotitic rocks while moving in a dynamic environment from the asthenosphere and possibly the lower mantle to the base of the lithosphere. Mechanisms for diamond movement through the mantle could be by mantle convection, or an ascending plume. The interaction of partial melts with eclogitic and peridotitic lithologies may have produced the intermediate websteritic inclusion compositions, and can explain diamonds of mixed parageneses, and the overlap in C-isotope values between parageneses. Strong deformation and extremely high nitrogen aggregation states in some diamonds may indicate high mantle storage temperatures and strain in the diamond growth environment. A second diamond group, with Type IaA–IaB nitrogen aggregation and peridotitic inclusions, crystallised at the base of the cratonic lithosphere. All diamonds were subsequently sampled by kimberlites and transported to the Earth's surface.     

Comparison of the high-pressure schist belts of New Caledonia and Sanbagawa,Japan

The high-pressure schist terranes of New Caledonia and Sanbagawa were developed along the oceanic sides of sialic forelands by tectonic burial metamorphism. The parent rocks were chemically similar, as volcanic-sedimentary trough or trench sequences, and metamorphic temperatures in both belts were 250° to 600° C. From phase equilibria curves, total pressures were higher for New Caledonia (6–15 kb) than for Sanbagawa (5–11 kb) and the estimated thermal gradients were 7–10° C/km and 15° C/km respectively.PT paths identify the higher pressure in New Caledonia (P differences 2 kb at 300° C and 4 kb at 550° C) with consequent contrast in progressive regional metamorphic zonation for pelites in the two areas: lawsonite-epidote-omphacite (New Caledonia) and chlorite-garnet-biotite (Sanbagawa). In New Caledonia the Na-amphibole is dominantly glaucophane and Na-pyroxenes associated with quartz are Jadeite (Jd_95–100) and omphacite; in Sanbagawa the amphibole is crossite or riebeckite and the pyroxene is omphacite (Jd₅₀). For both areas, garnet rims show increase in pyrope content with advancing grade, but Sanbagawa garnets are richer in almandine. Progressive assemblages within the two belts can be equated by such reactions as:New Caledonia Sanbagawa glaucophane+paragonite+H₂Oalbite+chlorite+quartz glaucophane+epidote+H₂Oalbite+chlorite+actinolite and the lower pressure Japanese associations appear as retrogressive phases in the New Caledonia epidote and omphacite zones.The contrasts inPT gradient, regional zonation and mineralogy are believed due to differences in the tectonic control of metamorphic burial: for New Caledonia, rapid obduction of an upper sialic plate over an inert oceanic plate and sedimentary trough; and for Sanbagawa, slower subduction of trench sediments beneath a relatively immobile upper plate.     

School vulnerability to disaster: examination of school closure,demographic, and exposure factors in Hurricane Ike’s wind swath

Damage and destruction to schools from climate-related disasters can have significant and lasting impacts on curriculum and educational programs, educational attainment, and future income-earning potential of affected students. As such, assessing the potential impact of hazards is crucial to the ability of individuals, households, and communities to respond to natural disasters, extreme events, and economic crises. Yet, few studies have focused on assessing the vulnerability of schools in coastal regions of the USA. Using Hurricane Ike’s tropical storm wind swath in the State of Texas as our study area, we: (1) assessed the spatial distribution patterns of school closures and (2) tested the relationship between school closure and vulnerability factors (namely physical exposure and school demographics) using zero-inflated negative binomial regression models. The regression results show that higher probabilities of hurricane strikes, more urbanized school districts, and school districts located in coastal counties on the right side of Ike’s path have significant positive associations with an increase in the number of school closure days. Socioeconomic characteristics were not significantly associated with the number of days closed, with the exception of proportion of Hispanic youth in schools, a result which is not supported by the social vulnerability literature. At a practical level, understanding how hurricanes may adversely impact schools is important for developing appropriate preparedness, mitigation, recovery, and adaptation strategies. For example, school districts on the right side of the hurricane track can plan in advance for potential damage and destruction. The ability of a community to respond to future natural disasters, extreme events, and economic crises depends in part on mitigating these adverse effects.     

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.     

Policy responses to informality in urban Africa: the example of Maputo,Mozambique

In the global South informality constitutes one of the leading issues for urban policy makers. The planning challenges around informality are particularly relevant in urban Africa as most Africans make their livelihoods in the informal economy. This paper examines issues of state policy responses to informality through the lens of street traders. Under scrutiny are policy responses towards street trading in Mozambique’s capital, Maputo, a city that has experienced the advance of informalization. It is argued that the dominant approach towards informal trading across urban Africa is of a ‘sanitising’ policy response by the local state which is rooted upon traditions of modernist urban planning in search of ‘ordered development’. The research discloses that in Maputo national and municipal authorities have adopted a more tolerant approach to the informal economy, mainly because it provides a livelihood to so many of the city’s poor and because of potential social unrest likely to be triggered by a repressive approach. In Maputo the core narrative is of an urban informal economy viewed by officials as an important livelihood for the city’s poor, albeit one which is subject both to periodic harassment and encouragement to ‘formalize’. The analysis represents a contribution to the expanding corpus of writings on Africa’s informalising cities and specifically concerning policy responses towards street trading.