Classical Scattering and Block Regularization for the Homogeneous Central Field Problem

The present paper offers an alternative point of view of block regularization for the motion of a particle in a central potential field of the form –x ^–, where x is the distance between the particle and the source and some positive real number.Working in the physical space, we consider the scattering angle determined by the path of the particle as a function of angular momentum. We prove that a particle flow is passing over the collision singularity preserving differentiability with respect to initial data if and only if = 2(1–1/n), n positive integer, n 2.This result coincides with the outcome of block regularization applied by McGehee to the same dynamical problem. We discuss that this identity was to expect since both methods target the same physical constraint over the flow.     

The content of some microelements in mineral waters from Covasna and Harghita Romanian districts

Using two analytical techniques, CSV/ASV and ICP–AES, the concentration of some microelements (lead, zinc, manganese) in mineral waters from the Covasna and Harghita districts of Romania were determined. The optimum parameters for the voltammetric determination of manganese, copper, zinc and lead were established (electrolyte, deposition time, pulse duration, pulse amplitude, etc.) and then the content of these elements in twelve samples of mineral water were determined. The results obtained by both techniques led to the conclusion that the concentration of microelements in mineral waters from Covasna and Harghita districts is connected to the mineral content underground.     

On the restricted three body problem with oblate primaries

We present a study of the Lagrangian triangular equilibria in the planar restricted three body problem where the primaries are oblate homogeneous spheroids steadily rotating around their axis of symmetry and whose equatorial planes coincide throughout their motion.     

The end of the Great Khersonian Drying of Eurasia: Magnetostratigraphic dating of the Maeotian transgression in the Eastern Paratethys

Central Eurasia underwent significant palaeoclimatic and palaeogeographic transformations during the middle to late Miocene. The open marine ecosystems of the Langhian and Serravallian seas progressively collapsed and were replaced in the Tortonian by large endorheic lakes. These lakes experienced major fluctuations in water level, directly reflecting the palaeoclimatic conditions of the region. An extreme lowstand of the Eastern Paratethys lake (?300 m) during the regional Khersonian stage reveals a period of intensely dry conditions in Central Eurasia causing a fragmentation of the Paratethys region. This period of “Great Drying” ended by a climate change towards more humid conditions at the base of the Maeotian stage, resulting in a large transgressive event that reconnected most of the Paratethyan basins. The absence of a robust time frame for the Khersonian–Maeotian interval hampers a direct correlation with the global records and complicates a thorough understanding of the underlying mechanisms. Here we present a new chronostratigraphic framework for the Khersonian and Maeotian deposits of the Dacian Basin of Romania, based on integrated magneto‐biostratigraphic studies on long and continuous sedimentary successions. We show the dry climate conditions in the Khersonian start at 8.6–8.4 Ma. The Khersonian/Maeotian transition is dated at 7.65–7.5 Ma, several million years younger than previous estimates. The Maeotian transgression occurs later (7.5–7.4 Ma) in more marginal and shallower basins, in agreement with the time transgressive character of the flooding. In addition, we date a sudden water level drop of the Eastern Paratethys lake, the Intra‐Maeotian Event (IME), at 6.9 Ma, and hypothesize that this corresponds to a reconnection phase with the Aegean basin of the Mediterranean. Finally, we discuss the potential mechanisms explaining the particularities of the Maeotian transgression and conclude that the low salinity and the seemingly “marine influxes” most likely correspond to episodes of intrabasinal mixing in a gradual and pulsating transgressive setting.     

The Schwarzschild Problem in Astrophysics

The Schwarzschild problem (the two-body problem associated to apotential of the form A/r + B/r³ has been qualitativelyinvestigated in an astrophysical framework, exemplified by two likelysituations: motion of a particle in the photogravitational field ofan oblate, rotating star, or in that of a star which generates aSchwarzschild field. Using McGehee-type transformations, regularizedequations of motion are obtained, and the collision singularity isblown up and replaced by the collision manifold (a torus)pasted on the phase space. The flow on is fullycharacterized. Then, reducing the 4D phase space to dimension 2, theglobal flow in the phase plane is depicted for all possible values ofthe energy and for all combinations of nonzero A and B. Eachphase trajectory is interpreted in terms of physical motion,obtaining in this way a telling geometric and physical picture of themodel.