Some problems on the classical n-body problem

Our idea is to imitate Smale’s list of problems, in a restricted domain of mathematical aspects of Celestial Mechanics. All the problems are on the n-body problem, some with different homogeneity of the potential, addressing many aspects such as central configurations, stability of relative equilibrium, singularities, integral manifolds, etc. Following Steve Smale in his list, the criteria for our selection are: (1) Simple statement. Also preferably mathematically precise, and best even with a yes or no answer. (2) Personal acquaintance with the problem, having found it not easy. (3) A belief that the question, its solution, partial results or even attempts at its solution are likely to have great importance for the development of the mathematical aspects of Celestial Mechanics.     

Airports and Environment: Proposal of Wastewater Reclamation at São Paulo International Airport

One way to reduce water consumption in urban areas is by using alternative sources of supply that can be provided by collecting rainwater and reusing wastewater for less restricted purposes. Thus, this study evaluated the characteristics of effluents produced by the wastewater treatment plant (WWTP) of São Paulo International Airport (SPIA), Brazil, in order to reuse it in non‐potable situations. The results achieved, indicated high efficiency in the biological system utilized by SPIA. The removal rates is equal to or >90% for most of the parameters analyzed, among them, fluoride, salinity, nitrite, nitrate, ammonium nitrogen, total nitrogen, phosphorus, sedimentable solids, turbidity, conductivity, apparent color, chemical oxygen demand, biochemical oxygen demand, total organic carbon, fecal coliforms, and oils and greases. Despite the final effluents were good enough to be launched in the local streams, they shall be submitted to a complementary treatment in order to fit some quality parameters to be reused for specific demands (landscape irrigation, toilet flushing, vehicle washing, fire fighting, and dust control).     

Monitoring of soil subsidence in urban and coastal areas due to groundwater overexploitation using GPS

The global positioning system (GPS) is widely used for determining the three-dimensional position of points on earth surface. In the last few years, its use has also been increasingly employed for obtaining vertical geometric coordinates, which associated with the orthometrical altitude of the point can be employed in various civil engineering applications, as has been seen in diverse localities throughout the world. The satisfactory performance of this technology for obtaining excellent precision in vertical coordinates demands some conditions, related to the satellites, such as transmission of signals and, principally, in the case of urbanized areas, the presence of obstructions in the proximity of the equipment, which interferes with the quality and quantity of the information collected. GPS is an efficient technique for the detection of small movements, including the monitoring of soil subsidence. The present article describes adequate forms of the use of GPS in such a way as to guarantee good precision of the resulting vertical coordinates, even under unfavorable situations, such as in coastal areas, where the reference networks for monitoring are implanted in only one of the sides of the point?Cobject region, which makes the situation more difficult and requires careful planning so that the use of GPS reaches the desired precision.     

Iridium enrichment and poor fractionation from gold, platinum and palladium in clausthalite (PbSe), Tilkerode, eastern Harz, Germany

Enrichments in platinum-group elements were found in clausthalite, PbSe, which occurs in carbonate–hematite veins hosted in black shale of Upper Wenlockian age in the eastern Harz, Germany. Spot measurements by laser ablation–quadrupole inductively coupled plasma mass spectrometry (LA–QICPMS) show that the clausthalite has Pt contents that average 0.459?ppm and range from 0.003 to 2.83?ppm. Other noble metals quantified in the present work include Au (0.226?ppm, 0.109–0.451?ppm), Ru (0.061?ppm, 0.006–0.264?ppm), Ir (0.071?ppm, 0.010–0.185?ppm), Pd (0.046?ppm, 0.017–0.107?ppm) and Os (0.010?ppm, <0.003–0.024?ppm). Elemental ratios of Au/Ir, Pd/Ir and Pt/Ir, the average values of which are respectively 4.6, 0.8, and 4.9, suggest that Au, Pd and Pt are poorly fractionated from Ir. The resulting Ir enrichment is unusual and should reflect a particularly soluble (and stable) aqueous complex of Ir in a highly oxidizing, low-temperature, Se-rich solution.     

Groundwater overexploitation and soil subsidence monitoring on Recife plain (Brazil)

Facing natural disasters is a priority challenge for cities, exacerbated by increases in urban population and climate change. Improving the resilience of cities is a critical need for the international community and especially for territories exposed to multiple risks, such as Chile. Although disasters are always tragic, the recovery and reconstruction post-disaster may provide a unique opportunity to prevent future suffering, enhancing the resilience of local communities. This paper presents the analysis of two Chilean reconstruction programmes applied in Mehuin and Dichato, after the earthquake and tsunami of 22 May 1960 and 27 February 2010, respectively. In both cases, reconstruction programmes were supported by the Chilean Government, but using different approaches: one focused on providing housing for people injured in the earthquake, while the other also included urban amenities and services. This article proposes an urban morphology analysis framework; in addition, it presents the assessment of the two case studies before and after a disaster, thus evaluating their resilience. By comparing urban morphology resilience pre- and post-disaster, a discussion about the effectiveness of two reconstruction approaches is presented. Finally, conclusions and recommendations to better integrate resilience into urban planning are proposed, with the aim of opening the discussion about how to make cities more resilient to natural disasters.     

Assessing estuarine environmental quality using fish-based indices: performance evaluation under climatic instability

The seasonal variation of five selected multimetric indices for the determination of the Ecological Quality Status (EQS) of transitional waters was evaluated, as well as the indices’ responses to an extreme drought event that occurred in 2005. The database used regards the Mondego River estuary, which was sampled from June 2003 to August 2006 on a monthly basis. Among the selected indices (EBI - Deegan et al. [Deegan, L., Finn, J.T., Ayvazlan, S.G., Ryder-Kieffer, C.A., Buonaccoesi, J., 1997. Development and validation of an Estuarine Biotic Integrity Index. Estuaries 30(3), 601-617], EDI - Borja et al. [Borja, A., Franco, J., Valencia, V., Bald, J., Muxika, I., Belzunce, M.J., Solaun, O., 2004. Implementation of the European Water Framework Directive from the Basque Country (northern Spain): a methodological approach. Marine Pollution Bulletin 48(3-4), 209-218], EFCI - Harrison and Whitfield [Harrison, T.D., Whitfield, A.K., 2004. A multi-metric fish index to assess the environmental condition of estuaries. Journal of Fish Biology 65, 683-710], EBI - Breine et al. [Breine, J.J., Maes, J., Quataert, P., Van den Bergh, E., Simoens, I., Van Thuyne, G., Belpaire, C., 2007. A fish-based assessment tool for the ecological quality of the brackish Scheldt estuary in Flanders (Belgium). Hydrobiologia 575, 141-159] and TFCI - Coates et al. [Coates, S., Waugh, A., Anwar, A., Robson, M., 2007. Efficacy of a multi-metric fish index as an analysis tool for the transitional fish component of the Water Framework Directive. Marine Pollution Bulletin 55, 225-240]), the EBI by Breine et al. (2007) was the only that evidenced clear interannual and seasonal variations. The EQS by the several indices ranged from “Low” to “High”, depending on the index considered, evidencing the high level of mismatch between indices. The results are discussed in the scope of the EU Water Framework Directive, regarding monitoring strategies, application of indices and EQS assessment.     

Landscape structure and use,climate, and water movement in the Mekong River basin

In this article the relative roles of precipitation and soil moisture in influencing runoff variability in the Mekong River basin are addressed. The factors controlling runoff generation are analysed in a calibrated macro‐scale hydrologic model, and it is demonstrated that, in addition to rainfall, simulated soil moisture plays a decisive role in establishing the timing and amount of generated runoff. Soil moisture is a variable with a long memory for antecedent hydrologic fluxes that is influenced by soil hydrologic parameters, topography, and land cover type. The influence of land cover on soil moisture implies significant hydrologic consequences for large‐scale deforestation and expansion of agricultural land. Copyright © 2007 John Wiley & Sons, Ltd.     

Morphological evolution of a complex drift-aligned prograded barrier

Prograded barriers are coastal landforms with a worldwide distribution that provide a paleoenvironmental record within a sequence of successive ridges and intervening swales. Most barriers with variable terrestrial morphologies, also known as complex barriers, have been poorly studied. At the main entrance of Western Port, a bay in southeastern Australia, a morphologically complex barrier was formed as a function of its somewhat sheltered position and orientation in relation to sporadic swells and tidal circulation. LiDAR-derived topography shows highly truncated and asymmetrical ridges both across and along the Somers–Sandy Point barrier plain. These uncommon morphologies are associated with an intricate hydrodynamic circulation subject to sporadic storms approaching at a sharp angle to the shoreline that eliminate a significant part of the sedimentary record but also redistribute vast quantities of sand to the downdrift shoreline, and a large and variable sandy bank that undergoes intense sediment movement. Optically stimulated luminescence (OSL) dating within a limited area on the western side revealed an age of ~2600 years for the innermost dated ridge, located about halfway across the plain. Significant erosion of the ridges' record occurred on the western side of the barrier between 2600 and 700 years ago and between 600 and 240 years ago, whereas undated ridges on the eastern side were preserved. This creates an opportunity for future research on past erosional events that would be of great value for coastal management and adaptation. Textural and elemental (XRF) sediment characteristics suggest that the type of material provided for barrier accretion remained the same throughout the late Holocene. Given the sustained growth of the barrier and other sandy parts of the bay, a net supply of marine sand from Bass Strait must have occurred. The proposed evolutionary model contributes to the understanding of the sediment budget for the bay as a whole.     

The masses in an isosceles solution of the three-body problem

A proof is given that the masses at the base of the triangle formed by the three particles of a three-body problem are necessarily equal. The proof uses only basic calculus.     

Nekton use of salt marsh creeks in the upper Tejo estuary

The use of the Tejo estuary, Portugal, salt marsh creeks by nekton was examined based on sampling surveys with a fyke net from September 1998 until August 2001. From the 20 taxa (14 fish species, 5 decapod crustacean species, and 1 cephalopod species) identified in the studied creeks, 16 were regularly caught throughout the sampling period. The shrimpPalaemonetes varians was the most numerically abundant species in the creeks, while the biomass was dominated by the mulletLiza ramada. The nekton assemblage was mainly represented by marine-estuarine opportunist species, comprising 85% of the total. A high seasonality was detected on the species abundance patterns: the most abundant species (P. varians, Crangon crangon, L. ramada, Pomatoschistus microps, Syngnathus sp., andAnguilla anguilla) occurred throughout the sampling period,Sardina pilchardus, Dicentrarchus, labrax, andAtherina boyeri were particularly abundant in spring and summer, andEngraulis encrasicholus, Liza aurata, Gambusia holbrooki, Palaemon longirostris, andPalaemon serratus were most abundant in autumn and winter.L. ramada occurred in the tidal creeks in high numbers during neap tides, while the majority of the remaining taxa were most abundant during spring tides, suggesting a differential pattern of habitat use occording to species.