Derivatives of theH-function

The first two derivatives and the mixed derivative of theH-function with respect to the angular variable and the albedo of single scattering are studied in the case of isotropic scattering using the kernel approximation method. This allows to obtain simple formulae the accuracy of which is estimated to be very good in rather low orders of approximation. Some samples of numerical results are given with eight decimal accuracy.     

Relative current effect on short wave growth

Ocean Dynamics - Short waves growth is characterized by nonlinear and dynamic processes that couple ocean and atmosphere. Ocean surface currents can have a strong impact on short wave steepness and...     

Evaluation of Portuguese limestones’ susceptibility to salt mist through laboratory testing

The salt mist present in the coastal shoreline constitutes an important weathering agent of the building materials applied in these regions. Portugal has an extensive coastline, which has a high population density. It holds a long tradition in the use of stone as a building material, due to the abundance of this natural resource, but also because of its durability and beauty. Considering the main ornamental stones mined in Portugal, limestones are the most susceptible to the action of saline atmospheric aerosol, because, in most cases, they present open porosities higher than those of other stone types. This feature facilitates the penetration of saline aerosol in their structures. Six widely applied Portuguese limestones, with different technological properties, were selected for this study. After accessing their petrographic and main technological features, the limestones were submitted to salt mist test. The test method, established in the respective European standard, was complemented with further determinations (variation on water absorption and flexural strength after salt mist cycling). The results allowed evaluating the limestones’ suitability for the main types of applications and for specific usage conditions, within each one. Thus, it was possible to set the recommended uses for each limestone, in order to maximize its durability. Salt mist testing made possible to determine the limestones’ resistance to the climatic conditions of coastal areas. The detailed analysis of the salt mist results strengthens the knowledge that the open porosity plays a decisive role in the limestones’ behaviour to this test.     

Multidimensional simulations of radiative transfer in Type Ia supernovae

A three-dimensional Monte Carlo code for modelling radiation transport in Type Ia supernovae is described. In addition to tracking Monte Carlo quanta to follow the emission, scattering and deposition of radiative energy, a scheme involving volume-based Monte Carlo estimators is used to allow properties of the emergent radiation field to be extracted for specific viewing angles in a multidimensional structure. This eliminates the need to compute spectra or light curves by angular binning of emergent quanta. The code is applied to two test problems to illustrate consequences of multidimensional structure on the modelling of light curves. First, elliptical models are used to quantify how large-scale asphericity can introduce angular dependence to light curves. Secondly, a model which incorporates complex structural inhomogeneity, as predicted by modern explosion models, is used to investigate how such structure may affect light-curve properties.     

Qualitative study of the planar isosceles three-body problem

We consider the particular case of the planar three body problem obtained when the masses form an isosceles triangle for all time. Various authors [1, 2, 12, 8, 9, 13, 10] have contributed in the knowledge of the triple collision and of several families of periodic orbits in this problem. We study the flow on a fixed level of negative energy. First we obtain a topological representation of the energy manifold including the triple collision and infinity as boundaries of that manifold. The existence of orbits connecting the triple collision and infinity gives some homoclinic and heteroclinic orbits. Using these orbits and the homothetic solutions of the problem we can characterize orbits which pass near triple collision and near infinity by pairs of sequences. One of the sequences describes the regions visited by the orbit, the other refers to the behaviour of the orbit between two consecutive passages by a suitable surface of section. This symbolic dynamics which has a topological character is given in an abstract form and after it is applied to the isosceles problem. We try to keep globality as far as possible. This strongly relies on the fact that the intersection of some invariant manifolds with an equatorial plane (v=0) have nice spiraling properties. This can be proved by analytical means in some local cases. Numerical simulations given in Appendix A make clear that these properties hold globally.     

Analysis of some degenerate quadruple collisions

We consider the trapezoidal problem of four bodies. This is a special problem where only three degrees of freedom are involved. The blow up method of McGehee can be used to deal with the quadruple collision. Two degenerate cases are studied in this paper: the rectangular and the collinear problems. They have only two degrees of freedom and the analysis of total collapse can be done in a way similar to the one used for the collinear and isosceles problems of three bodies. We fully analyze the flow on the total collision manifold, reducing the problem of finding heteroclinic connections to the study of a single ordinary differential equation. For the collinear case, from which arises a one parameter family of equations, the analysis for extreme values of the parameter is done and numerical computations fill up the gap for the intermediate values. Dynamical consequences for possible motions near total collision as well as for regularization are obtained.Paper presented at the 1981 Oberwolfach Conference on Mathematical Methods in Celestial Mechanics.Dedicated to Prof. Szebehely on the occasion of his sixtieth birthday.     

Simulation of the hydrogeologic effects of oil-shale mining on the neighbouring wetland water balance: case study in north-eastern Estonia

The water balance of wetlands plays an integral role in their function. Developments adjacent to wetlands can affect their water balance through impacts on groundwater flow and increased discharge in the area, and they can cause lowering of the wetland water table. A 430 km² area was selected for groundwater modelling to asses the effect of underground mining on the water balance of wetlands in north-eastern Estonia. A nature conservation area (encompassing Selisoo bog) is within 3 km of an underground oil-shale mine. Two future mining scenarios with different areal extents of mining were modeled and compared to the present situation. Results show that the vertical hydraulic conductivity of the subsurface is of critical importance to potential wetland dewatering as a result of mining. Significant impact on the Selisoo bog water balance will be caused by the approaching mine but there will be only minor additional impacts from mining directly below the bog. The major impact will arise before that stage, when the underground mine extension reaches the border of the nature conservation area; since the restriction of activities in this area relates to the ground surface, the conservation area’s border is not sufficiently protective in relation to underground development.     

The 1909 Benavente (Portugal) earthquake: search for the source

The Lower Tagus River Valley has been affected by severe earthquakes comprising distant events, as in 1755, and local earthquakes, as in 1344, 1531, and 1909. The 1909 earthquake was located NE of Lisbon, near Benavente, causing serious damage and many losses. Mw 6.0 has been assessed for this earthquake and a reverse faulting focal mechanism solution has been calculated. Poor epicenter location, possible directivity and site effects, low fault slip rates, and the thick Cenozoic sedimentary cover make difficult correlation with regional structures. The focal mechanism indicates an ENE reverse fault as source, though it does not match any outcropping active structure suggesting that the event could have been produced by a blind thrust beneath the Cenozoic sedimentary fill. Hidden sources, inferred from seismic reflection data, are a possible NE structure linking the Vila Franca de Xira and the Azambuja faults, or the southern extension of the later. Evidence of surface rupturing is inhibited by the thick Holocene alluvial cover and the high fluvial sedimentation rate, though a slightly depressed area was identified in the Tagus alluvial plain W of Benavente which was investigated as possible geomorphic evidence of co-seismic surface deformation. A high-resolution seismic reflection profile was acquired across a 0.5 m high scarp at this site, and two trenches were opened across the scarp for paleoseismic research. Some deformation of dubious tectonic origin was found, requiring further studies.