Motions close to escapes in the rhomboidal four body problem

In this work we study escape and capture orbits in the planar rhomboidal 4-body problem in a level of constant negative energy. There are only two different values of the masses here. By using numerical analysis, we show certain transversal intersections of the invariant manifolds of parabolic orbits. We then introduce Symbolic Dynamics when the mass ratio is small, and when it is close to one. In the first case the escapes or captures predominate in the direction of one of the diagonals of the rhombus, while in the second case we find solutions escaping or being captured in the direction of both possible diagonals.     

The Anisotropic Schwarzschild-Type Problem, Main Features

The two-body problem associated to an anisotropic Schwarzschild-type field is being tackled. Both the motion equations and the energy integral are regularized via McGehee-type transformations. The regular vector field exhibits nice symmetries that form a commutative group endowed with an idempotent structure. The physically fictitious flows on the collision and infinity manifolds, as well as the local flows in the neighbourhood of these manifolds, are fully described. Homothetic, spiral, and oscillatory orbits are pointed out. Some features of the global flow are depicted for all possible levels of energy. For the negative-energy case, few things have been done. The positive-energy global flow does not have zero-velocity curves; every orbit is of the type ejection – escape or capture – collision. In the zero-energy case, the collision and infinity manifolds have a very similar structure. The existence of eight trajectories that connect the equilibria on these manifolds is proved. The projectability of the zero-energy global flow completes the full understanding of the problem in this case.     

The complete SRSS modal combination rule

The complete Square‐Root‐of‐Sum‐of‐Squares (c‐SRSS) modal combination rule is presented. It expresses the structural response in terms of uncoupled SDOF modal responses, yet accounting fully for modal response variances and cross‐covariances. Thus, it is an improvement over the classical SRSS rule which neglects contributions from modal cross‐covariances. In the c‐SRSS rule the spectral moments of the structural response are expressed rigorously in terms of the spectral moments of uncoupled modal responses and of some coefficients that can be computed straightforwardly as a function of modal frequencies and damping, without involving the computation of cross‐correlation coefficients between modal responses. An example shows an application of the c‐SRSS rule for structural systems with well separated and closely spaced modal frequencies, subjected to wide‐band and narrow‐band excitations. Comparisons with response calculations using the SRSS and the Complete Quadratic Combination rules are given and discussed in detail. Based on the c‐SRSS rule a response spectrum formulation is introduced to estimate the maximum structural response. An example considering a narrow‐band excitation from the great Mexico earthquake of September 19, 1985, is given and the accuracy of the response spectrum formulation is examined. Copyright © 2010 John Wiley & Sons, Ltd.     

An Analytical Model for Hydraulic Fracturing in Shallow Bedrock Formations

A theoretical method is proposed to estimate post‐fracturing fracture size and transmissivity, and as a test of the methodology, data collected from two wells were used for verification. This method can be employed before hydrofracturing in order to obtain estimates of the potential hydraulic benefits of hydraulic fracturing. Five different pumping test analysis methods were used to evaluate the well hydraulic data. The most effective methods were the Papadopulos‐Cooper model (1967), which includes wellbore storage effects, and the Gringarten‐Ramey model (1974), known as the single horizontal fracture model. The hydraulic parameters resulting from fitting these models to the field data revealed that as a result of hydraulic fracturing, the transmissivity increased more than 46 times in one well and increased 285 times in the other well. The model developed by dos Santos (2008) , which considers horizontal radial fracture propagation from the hydraulically fractured well, was used to estimate potential fracture geometry after hydrofracturing. For the two studied wells, their fractures could have propagated to distances of almost 175 m or more and developed maximum apertures of about 2.20 mm and hydraulic apertures close to 0.30 mm. Fracturing at this site appears to have expanded and propagated existing fractures and not created new fractures. Hydraulic apertures calculated from pumping test analyses closely matched the results obtained from the hydraulic fracturing model. As a result of this model, post‐fracturing geometry and resulting post‐fracturing well yield can be estimated before the actual hydrofracturing.     

Periodic orbits for a class of galactic potentials

In this work, applying general results from averaging theory, we find periodic orbits for a class of Hamiltonian systems H whose potential models the motion of elliptic galaxies.     

Diatom assemblages from surface sediments of the Río de la Plata estuary,Uruguay

The Río de la Plata estuary (RdlP) exhibits environmental gradients associated with the freshwater input and oceanic water intrusion. The aim of this study was to assess diatom species distribution in surface sediment samples related to such environmental gradients. The internal section of RdlP was dominated by Aulacoseira spp., Eunotia spp., Staurosirella martyi, Actinocyclus normanii and Thalassiosira baltica, indicatives of low salinity levels and high trophic conditions, associated with the riverine and estuarine regimes. The external section was dominated by Coscinodiscus radiatus, Thalassiosira spp., Paralia sulcata, Cyclotella striata, among other marine taxa, indicatives of high salinity and low trophic conditions, associated with the influence of the Southwestern Atlantic Ocean. Furthermore, the intermediate section presents a mixture of both diatom groups representing mixing conditions. The observed diatom species groups capture fairly well the RdlP environmental variability and can be reliably used for paleoenvironmental studies in this and other similar estuarine systems.     

Coupling patterns between para‐glacial and permafrost degradation responses in Antarctica

The recently deglaciated environments in maritime permafrost regions are usually affected by very active paraglacial processes. Elephant Point is an ice‐free area of 1.16 km2 located in the SW of Livingston island (South Shetland Islands, Antarctica). Between 1956–2010 the retreat of the ice cap covering most part of this island has exposed 17.3% of the land surface in this peninsula. Two geomorphological units were identified in this new ice‐free area: a moraine extending from the western to the eastern coastlines and a relatively flat proglacial surface. The glacier in 1956 sat in contact with the northern slope of the moraine, but its accelerated retreat ‐ in parallel to the warming trend recorded in the Antarctic Peninsula ‐ left these areas free of glacier ice. Subsequently, the postglacial evolution was controlled by the relaxation phase typical of paraglacial systems. The typology and intensity of geomorphological processes show a significantly different dynamics between the southern and northern slopes of the moraine. This pattern is related to the different stage of paraglacial adjustment in both slopes. In the southern side, on coarser sediments, pronival ramparts, debris flows and alluvial fans are distributed, with a low to moderate activity of slope processes. In the northern side, mass wasting processes are extremely active on fine‐grained unconsolidated sediments. Ice‐rich permafrost is being degraded by thermokarst processes. Landslides and mudflows transfer large amounts of sediments down‐slope. The surface affected by retrogressive‐thaw slumps in the moraine has been quantified in 24,172 m2, which accounts for 9.6% of its surface. The abundance of kettle‐lakes is also indicative of the degradation of the ground ice. Paraglacial processes are expected to continue in the moraine and proglacial area in the near future, although their intensity and duration will depend on the magnitude and rate of future climate trends in the northern Antarctic Peninsula. Copyright © 2015 John Wiley & Sons, Ltd.     

Anomalous Diffuse CO2 Emissions at the Masaya Volcano (Nicaragua) Related to Seismic-Volcanic Unrest

Anomalous changes in the diffuse emission of carbon dioxide within the Masaya caldera have been observed before two seismic events that occurred at 10 and 30 km from the observation site. Their epicenters are located, respectively, south of Managua in Las Colinas (4.3 magnitude) and the Xiloa caldera (3.6 magnitude), in 2002 and 2003, recorded by the geochemical station located at El Comalito, Masaya volcano (Nicaragua). Anomalous increases were observed, which occurred around 50 and 8 days before the main seismic event that took place in Las Colinas, and 4 days before the seismic swarm at the Xiloa caldera, with a maximum CO₂ efflux of 9.3 and 10.7 kg m^?2 day^?1, respectively. The anomalous CO₂ efflux increases remained after filtering with multiple regression analysis was applied to the CO₂ efflux time series, which indicated that atmospheric variables, during the first 4 months, explained 23 % CO₂ variability, whereas, during the rest of the time series, CO₂ efflux values are poorly controlled with only 6 %. The observed anomalies of the diffuse CO₂ emission rate might be related to pressure changes within the volcanic–hydrothermal system and/or to geostructural changes in the crust due to stress/strain changes caused before and during the earthquakes’ formation, and seem not to be related to the activity of the main crater of Masaya volcano.