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.     

The Piànico tephra: an early Middle Pleistocene record of intraplate volcanism in the Mediterranean

ABSTRACT Distal tephra are a valuable record of the volcano-tectonic evolution of an area under study. Here, we document the case of the Early Middle Pleistocene rhyolitic tephra of Piànico, discovered in the Southern Italian Alps. The geochemical characteristics of Piànico are unique among the distal tephra outcropping in Italy and indicate an intraplate volcanism at the source. The alkali composition and trace elements show a striking resemblance with the rhyolitic complex of the Euganean Hills, located 170 km from Piànico. However, these rhyolites are much older (Oligocene). Alternatively, the source of this intraplate volcanic episode could be located in the southern Tyrrhenian Sea.     

Fluid-mineral equilibria in a hydrothermal system,Roosevelt hot springs,Utah

The availability of fluids and drill cuttings from the active hydrothermal system at Roosevelt Hot Springs allows a quantitative comparison between the observed and predicted alteration mineralogy, calculated from fluid-mineral equilibria relationships. Comparison of all wells and springs in the thermal area indicates a common reservoir source, and geothermometer calculations predict its temperature to be higher ($\text{288°C ± 10°}$) than the maximum measured temperature of 268°C.The composition of the deep reservoir fluid was estimated from surface well samples, allowing for steam loss, gas release, mineral precipitation and ground-water mixing in the well bore. This deep fluid is sodium chloride in character, with approximately 9700 ppm dissolved solids, a pH of 6.0, and gas partial pressures of O₂ ranging from 10^?32 to 10^?35 atm, CO₂ of 11 atm, H₂S of 0.020 atm and CH₄ of 0.001 atm.Comparison of the alteration mineralogy from producing and nonproducing wells allowed delineation of an alteration pattern characteristic of the reservoir rock. Theoretical alteration mineral assemblages in equilibrium with the deep reservoir fluid, between 150° and 300°C, in the system Na₂O-K₂O-CaO-MgO-FeO-Fe₂O₃-Al₂O₃-H₄SiO₄-H₂O-H₂S-CO₂-HCl, were calculated. Minerals theoretically in equilibrium with the calculated reservoir fluid at $\text{>240°C}$ include sericite, K-feldspar, quartz, chalcedony, hematite, magnetite and pyrite. This assemblage corresponds with observed higher-temperature ($\text{>210°C}$) alteration assemblage in the deeper parts of the producing wells. The presence of montmorillonite and mixed-layer clays with the above assemblage observed at temperatures <210°C corresponds with minerals predicted to be in equilibrium with the fluid below 240°C.Alteration minerals present in the reservoir rock that do not exhibit equilibrium with respect to the reservoir fluid include epidote, anhydrite, calcite and chlorite. These may be products of an earlier hydrothermal event, or processes such as boiling and mixing, or a result of errors in the equilibrium calculations as a result of inadequate thermochemical data.     

Soil-erosion assessment at basin scale through 137Cs content analysis based on pedo-morphological units

Soil loss evaluation by means of radioisotopic content measurements represents a promising technique, half-way between field surveys and theoretical models, which still suffers from its practical limits when applied at basin scale. A main limit is represented by the costs of field investigations and laboratory investigations on the high number of soil samples required by a traditional sampling scheme, such as regular grid or transects. A non-conventional soil sampling scheme was tested with the aim to consider a relative scanty number of soil samples and to verify the feasibility of this technique on large areas. This scheme was based on the hypothesis that land analysis and classification could point out areas characterised by homogeneous behaviour with respect to the ¹³⁷Cs deposition and transmission model. A Geographic Information System (GIS)-aided procedure allowed to classify the selected basin area in pedo-morphological units, representative of the different pedologic, morphologic and land-use conditions, to locate few sampling points for each unit. Outcomes pointed out a low correlation between ¹³⁷Cs contents and soil physical and compositional characteristics. Nevertheless, the isotopic methodology allowed to estimate a total soil loss value at basin scale almost consistent with both observed data, given by reservoir sedimentation measurements and estimates from the application of the RUSLE model. Thus, the results can be considered encouraging and they allow to deem that the isotopic methodology can be refined in order to account for erosion and deposition processes even at river basin scale and with a limited number of soil samples.