A highly symmetric restricted nine-body problem and the linear stability of its relative equilibria

We study a highly symmetric nine-body problem in which eight positive masses, called the primaries, move four by four, in two concentric circular motions such that their configuration is always a square for each group of four masses. The ninth body being of negligible mass and not influencing the motion of the eight primaries. We assume all the nine masses are in the same plane and that the masses of the primaries are \(m_{1}=m_{2}=m_{3}=m_{4}=\tilde{m}\) and m ₅=m ₆=m ₇=m ₈=m and the radii associated to the circular motion of the bodies with mass \(\tilde{m}\) is λ∈[λ ₀,1] and for the bodies with mass m is 1. We prove the existence of central configurations which characterize such arrangement of the primaries and we study the influence of the parameter λ, the ratio of the radii of the two circles, on the masses m and \(\tilde{m}\) . We use a synodical system of coordinates to eliminate the time dependence on the equations of motion. We show the existence of equilibria solutions symmetrically distributed on the four quadrants and their dependence on the parameter λ. Finally, we show that there can be 13, 17 or 25 equilibria solutions depending on the size of λ and we investigate their linear stability.     

Spring drought prediction based on winter NAO and global SST in Portugal

The aim of this paper is to test the ability of neural network approaches to hindcast the spring standardized precipitation index on a 6‐month time scale (SPI6) in Portugal, based on winter large‐scale climatic indices. For this purpose, the linkage of the spring SPI time series with the winter North Atlantic Oscillation (NAO) and the sea surface temperature (SST) was investigated by means of maps of the correlation coefficient for the period from October 1910 to September 2004. The results indicate that the winter NAO is a good predictor for the SPI6 of the spring (SPI6 finishing in April, May and June, SPI6_April, SPI6_May and SPI6_June, respectively) for the northern, central and southern regions of Portugal. The winter SST1 (area of the Mediterranean Sea) must only be considered for the northern region, and the winter SST3 (area of the North Atlantic between Iberia and North America) only for the southern region. Spatial maps of predictive SPI6 for April, May and June were created and validated. The neural models explained more than 81% of the total variance for the SPI6_April and SPI6_May and more than 64% of the total variance for the SPI6_June. Probability maps were also developed considering the values predicted by the neural methods for the spring months and all drought categories (moderate, severe and extreme). These maps indicating the probability of droughts can provide valuable support for the integrated planning and management of water resources throughout Portugal. Copyright © 2012 John Wiley & Sons, Ltd.     

Cubic anomalies in the Wilkinson Microwave Anisotropy Probe

We perform a frequentist analysis of the bispectrum of the Wilkinson Microwave Anisotropy Probe first-year data. We find clear signal domination up to  ℓ≈ 200  , with overall consistency with Gaussianity, except for the following features. There is a flat patch (i.e. a low χ² region) in the same-ℓ components of the bispectrum spanning the range  ℓ= 32–62  ; this may be interpreted as ruling out Gaussianity at the 99.6 per cent confidence level. There is also an asymmetry between the north and south inter-ℓ bispectrum components at the 99 per cent confidence level. The preferred asymmetry axis correlates well with the  (ℓ, b ) = (57, 10)  direction quoted in the literature for asymmetries in the power spectrum and three-point correlation function. However, our analysis of the quadrupole (its bispectrum and principal axes) fails to make contact with previously claimed anomalies.     

The complete bispectrum of COBE-DMR four-year maps

We extend a previous bispectrum analysis of the COBE -DMR four-year maps, allowing for the presence of correlations between all possible angular scales. For reasons of presentation we restrict ourselves to triplets of modes symmetrically arranged, but with larger and larger ℓ separation. We find that the non-Gaussian signal found earlier for bispectrum components including adjacent modes does not extend to triplets of modes with larger separations. Indeed for all separations Δℓ>1 we find that the COBE -DMR data are very Gaussian. The implication seems to be that the previously detected non-Gaussian scale–scale correlation falls off very quickly with mode separation.     

Governance and effects of marine reserves in the Gulf of California,Mexico

We trace the evolution, governance, and effects of three marine reserve (no-take zones) initiatives in the Gulf of California, Mexico: Loreto Bay National Park, Puerto Peñasco, and San Pedro Mártir Island Biosphere Reserve. Preliminary monitoring results, although highly variable, are encouraging for conservation and fisheries management. However, open access situations and differing conceptions among local stakeholders and government concerning access rights to fishing grounds, coupled with limited support for surveillance and lags between local and government institutional arrangements and interests, are the main constraints for the success of these and future reserves in the region. We discuss the main social–ecological feedbacks at play and the implications of our findings within a regional context.     

Selection and scaling of earthquake records in assessment of structures in low-to-moderate seismicity zones

The behaviour of a building during an earthquake depends on many factors including the characteristics of the ground motion, the configuration and dynamic characteristics of the structure, the hysteretic behaviour of the structural components, the building's non-structural parts, and the local soil behaviour. When conducting seismic assessment studies, controlling the first factor involves selecting and scaling appropriate earthquake records. It is a common practice to scale the records to fit a target acceleration response S_a determined from a pre-determined spectrum or attenuation law. In doing so, two key-problems must be faced: (i) the value adopted for the “effective” period T₁,which lengthens as the structure enters the non-linear range, and (ii) the reliability of the reference value adopted for S_a(T₁). In this work, the influence of selecting appropriate values for these two parameters—T₁ and S_a(T₁)—on the response of the building is investigated from the study of two structures, of 4 and 8 stories. The study does not focus on evaluating a particular seismic code; rather, it uses a European attenuation model as the target spectrum. Non-linear dynamic response analyses are carried out to investigate the Collapse Prevention State of these structures subjected to records representative of a Performance-based Earthquake Engineering level characterized by 2% exceedence in 50 years with 2475 years of return time. The records are selected from a database of European earthquakes, and the failure of the structures is evaluated by statistical means. From the results of the analyses, it is proposed that in seismic assessment studies the reference period for scaling should be 1.1 times the fundamental period of the structure, and at least 30 records should be used to guarantee reliable results.     

Distribution patterns of macrobenthic species in relation to organic enrichment within aquaculture earthen ponds

The relationship between organic enrichment and macrobenthic colonization patterns was investigated during an 8-month period in Diplodus sargus (white seabream) production ponds. A stratified sampling design was applied and each pond was divided into three zones: water entrance (WE); central (C); and automatic feeder zones (AF). Generally, the number of species and Shannon–Wiener diversity increased from the WE to the AF zone. Abundance did not present a clear trend. The recently developed marine biotic index (AMBI) was applied and showed to be sufficiently robust to discriminate, within a relatively small area, differences in macrobenthic communities due to organic enrichment. Nevertheless, caution is advised when applying this index or others based on ecological group’s assignment, as the classification of a certain area may differ when allocating a certain species to an unsuitable group. This is particularly evident when common species are involved.