Attitude equilibria of dual spin satellites subject to gravitational torques ofn bodies

We consider the motion of a dual spin satellite placed in the gravitational field of n material points, assuming that the satellite has no influence on the motion of these points. The main bodies are located at the libration points of the classical n bodies problem. We investigate the set of relative equilibria of the satellite. As in the elementary case of a gyrostat attracted by a single point, we show that this problem is equivalent to find the extremum of a quadratic function. We obtain all possible equilibria of the satellite by solving two algebraic equations. Sufficient conditions of stability of these relative equilibria are given.     

Trace-element-rich brines in eclogitic veins: implications for fluid composition and transport during subduction

Primary and pseudosecondary fluid inclusions occur in oscillatory-and sector-zoned omphacite in eclogitic veins from the Monviso ophiolitic complex in the Western Alps. The inclusions contain aqueous brines and daughter crystals of halite, sylvite, calcite, dolomite, albite, anhydrite and/or gypsum, barite, baddeleyite, rutile, sphene, Fe oxides, pyrite and monazite. This daughter mineral suite indicates high solubilites of Na, K, Ca, Mg, Fe, Zr, Ti, P, Ba, Ce, La, Th, and S species and provides direct evidence for transport of high-fieldstrenght, large-ion-lithophile, and light-rare-earth elements as dissolved species during subduction. Fluid-inclusion heterogeneities preserved within and between adjacent grains in the veins, however, suggest that the scale of fluid equilibration was small. A crack-seal geometry in some of the veins implies that fluid release in pulses rather than steady flow controlled mineral deposition and growth in the veins. From these observations, we develop a model of fluid release and entrapment in which pulses of fluid are associated in time with increments of shear and tensile failure; the rate of fluid release and the reduction in porosity both depend on the rate of plastic flow. Vein fluids may initially be derived from decreptitation of early fluid inclusions in the host eclogites, Small-scale fluid heterogeneities implied by the fluid inclusions in the veins are best interpreted in terms of limited fluid flow, and hence limited metasomatism. We conclude that element recycling into the mantle wedge during subduction will depend at least as strongly on fluid transport mechanisms as on element solubilities in the fluid phase. At Monviso, despite evidence for high trace element solubilities in saline brines, the elements were not removed from the downgoing slab prior to teaching depths of 40 km.     

Numerical investigation of all possible equilibria of dual spin satellites

This paper is the continuation of a previous work [6] in which we have obtained the set of all possible equilibria of a gyrostat satellite attracted by n points mass by solving two algebraical equations P₁=0 and P₂=0. It results that there is a maximum of 24 isolated equilibrium orientations for the satellite. Sufficient conditions of stability for these relative equilibria are given.Here we consider only the elementary case n=1. We show that the coefficients of the two algebrical equations depend on four parameters j₁, j₃, K and v². The two first parameters depend only on the direction of the internal angular momentum of the rotors, the third being only function of the principal moments of inertia of the satellite and the last parameter is a decreasing function of one of the components of . We show that the two polynomials P₁ and P₂ are unvariant within two transformations of the parameters j₁ and j₃. It is then possible to reduce the range of variation of these parameters.For some particular values of the parameters, it is possible to give the minimum number of real roots of equations P₁=0 and P₂=0. In general cases, a computing program is written to obtain the number of real roots of these equations according to the values of the parameters. We show that among the roots found, few of them corresponds to stable equilibrium orientations.     

Differential distribution of the two cryptic species, Pomatoschistus microps and P. marmoratus, in the lagoons of southern France, with an emphasis on the genetic organisation of P. microps

The presence and the distribution of two cryptic sedentary gobies, Pomatoschistus microps and Pomatoschistus marmoratus, were investigated in several lagoons stretching along the Golfe du Lion, southern France Mediterranean coast, and Corsica. Pomatoschistus microps is the only sedentary Pomatoschistus species in two shallow lagoons with large variations of salinity and temperature. In contrast, P. marmoratus, another sedentary species, can be found preferentially in a deep salty lagoon with small salinity variations. Both species occur sympatrically in the Rhone Delta and hybridise, producing fertile offspring. Using allozymes, competition, linked to fitness, is invoked to explain the distribution pattern of these sibling species.     

Correspondence between the distribution of hydrodynamic time parameters and the distribution of biological and chemical variables in a semi-enclosed coral reef lagoon

Hydrodynamic modeling can be used to spatially characterize water renewal rates in coastal ecosystems. Using a hydrodynamic model implemented over the semi-enclosed Southwest coral lagoon of New Caledonia, a recent study computed the flushing lag as the minimum time required for a particle coming from outside the lagoon (open ocean) to reach a specific station [Jouon, A., Douillet, P., Ouillon, S., Fraunié, P., 2006. Calculations of hydrodynamic time parameters in a semi-opened coastal zone using a 3D hydrodynamic model. Continental Shelf Research 26, 1395–1415]. Local e-flushing time was calculated as the time requested to reach a local grid mesh concentration of 1/e from the precedent step. Here we present an attempt to connect physical forcing to biogeochemical functioning of this coastal ecosystem. An array of stations, located in the lagoonal channel as well as in several bays under anthropogenic influence, was sampled during three cruises. We then tested the statistical relationships between the distribution of flushing indices and those of biological and chemical variables. Among the variables tested, silicate, chlorophyll a and bacterial biomass production present the highest correlations with flushing indices. Correlations are higher with local e-flushing times than with flushing lags or the sum of these two indices. In the bays, these variables often deviate from the relationships determined in the main lagoon channel. In the three bays receiving significant riverine inputs, silicate is well above the regression line, whereas data from the bay receiving almost insignificant freshwater inputs generally fit the lagoon channel regressions. Moreover, in the three bays receiving important urban and industrial effluents, chlorophyll a and bacterial production of biomass generally display values exceeding the lagoon channel regression trends whereas in the bay under moderate anthropogenic influence values follow the regressions obtained in the lagoon channel. The South West lagoon of New Caledonia can hence be viewed as a coastal mesotrophic ecosystem that is flushed by oligotrophic oceanic waters which subsequently replace the lagoonal waters with water considerably impoverished in resources for microbial growth. This flushing was high enough during the periods of study to influence the distribution of phytoplankton biomass, bacterial production of biomass and silicate concentrations in the lagoon channel as well as in some of the bay areas.     

A note on the correspondence between Mathieu's transformations and redundant variables in lagrangian mechanics

It is shown that, to any change of variables:q _i=q_i(r, t) (i=1,..., n; =1,...,n+m; mn) increasing the number of variables, it is possible to associate a Mathieu's transformation and conversely. The results are applied to the theory of the osculating plane of motion.

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Resumé On montre qu'à toute transformation:q _i=q_i(r, t)(i=1,..., n; =1,...,n+m; mn) augmentant le nombre de variables, on peut associer une transformation de Mathieu et réciproquement. Les résultats sont appliqués à la théorie du plan osculateur du mouvement.

     

An asymptotic solution for the stellar case of the planar Three-Body Problem

A simplified model of the planar Three-Body Problem is considered in which two particles, forming a close binary, orbit a distant point. A small parameter , related to the distance separating the binary and the remaining mass is defined. The time is eliminated from the equations of motion and an angular variable is used instead. A two-variable expansion procedure is used to find an asymptotic solution. The solution obtained is known completely up to the order ten in , and it is valid for almost arbitrary initial conditions. Specification of the initial conditions leads to a solution which is periodic with respect to a modified time variable.

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Résumé On considère un modèle simplifé du Problème Plan des Trois Corps, dans lequel deux particules, formant une binaire proche, sont en orbite par rapport à un troisième point éloigné des deux autres. On définit un petit paramètre , lié à la distance séparant la binaire de la particule restante. On élimine le temps des équations du mouvement et on utilise une variable angulaire comme nouvelle variable indépendante. Une méthode de développement à deux échelles est utilisée permettant d'obtenir une solution asymptotique du problème. La solution obtenue est connue complètement jusqu'àl'ordre dix en , et elle est valable pour des conditions initiales très générales. Pour des conditions initiales bien déterminées, on obtient une solution périodique par rapport à une nouvelle variable temporelle.

     

On the role of heat flow, lithosphere thickness and lithosphere density on gravitational potential stresses

Gravitational potential stresses (GPSt) are known to play a first-order role in the state of stress of the Earth's lithosphere. Previous studies focussed mainly on crust elevation and structure and little attention has been paid to modelling GPSt using realistic lithospheric structures. The aim of the present contribution is to quantify gravitational potential energies and stresses associated with stable lithospheric domains. In order to model realistic lithosphere structures, a wide variety of data are considered: surface heat flow, chemical depletion of mantle lithosphere, crustal thickness and elevation. A numerical method is presented which involves classical steady-state heat equations to derive lithosphere thickness, geotherm and density distribution, but additionally requires the studied lithosphere to be isostatically compensated at its base. The impact of varying surface and crustal heat flow, topography, Moho depth and crust density on the signs and magnitudes of predicted GPSt is systematically explored. In clear contrast with what is assumed in most previous studies, modelling results show that the density structure of the mantle lithosphere has a significant impact on the value of the predicted GPSt, in particular in the case of thick lithospheres. Using independent information from the literature, the method was applied to get insights in the state of stress of continental domains with contrasting tectono-thermal ages. The modelling results suggest that in the absence of tectonic stresses Phanerozoic and Proterozoic lithospheres are spontaneously submitted to compression whereas Archean lithospheres are in a neutral to slightly tensile stress state. These findings are in general in good agreement with global stress measurements and observed geoid undulations.