Approximate Solutions of the Equations of Motion of a Charged Particle in the Field of a Magnetic Dipole

Three differential equations of the first order (26)—(28) which determine the trajectory are deduced. An approximate integration by means of elementary functions yields a set of formulas (in chapt. 13. Conclusions) that give a „window”︁ in the sky inside of which the radiation point of a high energy cosmic ray (monotonely bent in the magnetic field) must lie.     

Amazonian floodplain water balance based on modelling and analyses of hydrologic and electrical conductivity data

In the Amazon basin, floodplains form a complex mosaic of freshwater systems with differing morphologies, resulting in varied inundation patterns and heterogeneous chemical and ecological characteristics. In this study, we focused on the Janauacá floodplain, a medium‐sized system (786 km², including the local watershed) located along the Solimões River. Based on in situ and satellite observations acquired from November 2006 to November 2011, we computed water fluxes between the mainstream and the floodplain and examined the temporal dynamics of floodplain storage from river flooding, rainfall, runoff, and exchanges with groundwater through bank seepage for the 5 years from 2006 to 2011. The mainstream was the main input of water to the flooded area, accounting on average for 93% of total water inputs by the end of the water year. Direct precipitation and runoff from uplands contributed less than or equal to 5% and 10%, respectively. The seepage contribution was less than 1%. Model uncertainties, evaluated using Monte Carlo analysis of the input data and model parameters, showed that all water fluxes were relatively well constrained except for outflow through seepage, which had a standard deviation across simulations greater than 60%. The water balance computation was verified using electrical conductivity as an assumed non‐reactive tracer. Except during periods of very low water, the simulated and measured conductivities agreed well. Moreover, conductivity data analysis confirmed that the Janauacá system can be considered homogeneous in terms of electrical conductivity for filling percentages equal to or greater than 40% (i.e., when the water level is above 19.5 m, generally from April to August) but presented large heterogeneities during the rest of the hydrological cycle.     

Interplanetary radar time delays in different theories of gravitation

The first order (in the massm of the central body) time delay is deduced for all theories of gravitation that satisfy the 3-dimensional principle of equivalence in the one-body problem. It is shown that the curvature of the light ray causes no first order time delay but that the first order time delay is sensitive to the non-linear term of a general metric when distancesr are measured by the periods of circular planetary orbits.     

L’ olistostrome coniacien de Lordat (Pyrénées ariégeoises) et son équivalent latéral de Vicdessos,témoins d’un nouveau bassin d’avant-pays au front nord de la Haute Chaîne Primaire

Résumé

De nouvelles datations et grade-datations fondées sur les Foraminifères planctoniques, ponctuellement identifiés en dépit d’un épimétamorphisme campanien, permettent de doubler voire à triper l’étendue du « sous-bassin » coniacien de Lordat (Zone des Écailles Bordières, Ariège), en partie calciturbiditique, aux dépens terrains jusqu’à présent tenus pour paléozoïques, tels ceux de l’ex-« Écaille paléozoïque de Lordat ». Ces derniers correspondent à des olistolithes de très grande taille au sein d’un vaste olistostrome (château de Lordat, ermitage de Saint-Pierre), lui-même inclus dans une épaisse série monoclinale, à dominante calcschisteuse, constituant un probable équivalent latéral du « Flysch à Fucoïdes ». Cette série déborde vers le Nord jusque sur la Zone Interne Métamorphique, comme le démontre l’âge néocrétacé du lambeau ex-paléozoïque de Carmilles, directement chevauché par le massif Primaire nord-pyrénéen de Saint-Barthélémy. Plus à l’Ouest, le « sous-bassin » de Vicdessos, prolongeant celui de Lordat, est constitué par une épaisse série également coniacienne, monoclinale, avec ses termes les plus récents vers le Nord, primitivement attribuée à un synclinorium subdivisé par des anticlinaux d’Urgo-Aptien qui sont en fait des intercalations plus calcaires dans le Crétacé supérieur. Le complexe coniacien partiellement turbiditique de Lordat-Vicdessos, subdivisé en au moins deux séquences tectono-sédimentaires de 3^e ordre, A et B, est interprété comme le remplissage de gouttières synclinales synsédimentaires successives d’un sous-bassin d’avant-pays, alimentées par l’érosion probablement sous-marine du front, migrant vers le Nord, de la Haute Chaîne Primaire organisée en anticlinaux d’amortissement (limités euxmêmes par des chevauchements synsédimentaires aveugles). Ce modèle de sous-bassin d’avant-pays s’insère parfaitement dans le schéma évolutif d’une chaîne interplaque en compression pendant tout le Crétacé supérieur et à double vergence, où se creuseraient, au Coniacien, sur une transversale N-S et de part et d’autre de la future Haute Chaîne en voie de structuration, au moins deux sousbassins liés à l’Europe (Lordat-Vicdessos et Nalzen I) et un sousbassin (San Gervas) lié à l’ibérie. © 2001 Éditions scientifiques et médicales Elsevier SAS     

Motor integrals of a generalized Kepler motion

The ordinary spinor differential Equation (20) of the unperturbed Kepler motion is obtained from the classical equation of motion (19) if one uses the spinor regularization (9) and postulates an essential subsidiary condition (10). A natural generalization for the Kepler motion follows by dropping this subsidiary conditions; it is the 8-parameter set of solutions of the spinor equation of motion (20). The sixteen natural extensive integrals (30)–(35) for this generalized Kepler motion are here deduced by means of the relativistic motors (2), (7) of the Spinor Ring Algebra. These integrals form, with respect to the Poisson bracket operation, a 15-dimensional Lie algebra (40)–(44), closely related to the Lie algebras in quantum mechanics.Dedicated to Professor G. Järnefelt on his 70th anniversary.     

On Spinor Equations of Motion and their “Possible Integrals”

The motion of one point mass of the classical mechanics is treated by means of the relativistic spinor regularization (KUSTAANHEIMO 1975). Most general spinor equations of motion (2.9)‒(2.10)and the differential equations(3.16)‒(3.25)for the “possible integrals” (3.2)‒(3.11)of these quations of motion are deduced. If the force is a superposition of a conservative central force and of another force perpendicular to radius vector and velocity (Chapter 4, Case D), then the theory yields scalar and spinor integrals (4.7), (4.10)‒(4.12), (4.14)‒(4.15), (4.17), (4.28) that enable a parametric representation of the orbit by quadratures, as soon as one solution of a RICCATI differential equation (4.33) has been found.     

Relativistic Spinor Linearization of the KEPLER Motion

A relativistically conformal mapping between pairs of spinors and relativistic motors with zero trace is given. The corresponding transformation of any equation of motion for a motor with zero trace into equations of motion for two spinors is deduced. It is shown that the spinors execute harmonic oscillations in the case of the unperturbed KEPLER motion.