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.     

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.     

Intraseasonal SST-precipitation relationship and its spatial variability over the tropical summer monsoon region

The SST-precipitation relationship in the intraseasonal variability (ISV) over the Asian monsoon region is examined using recent high quality satellite data and simulations from a state of the art coupled model, the climate forecast system version 2 (CFSv2). CFSv2 demonstrates high skill in reproducing the spatial distribution of the observed climatological mean summer monsoon precipitation along with its interannual variability, a task which has been a conundrum for many recent climate coupled models. The model also exhibits reasonable skill in simulating coherent northward propagating monsoon intraseasonal anomalies including SST and precipitation, which are generally consistent with observed ISV characteristics. Results from the observations and the model establish the existence of spatial variability in the atmospheric convective response to SST anomalies, over the Asian monsoon domain on intraseasonal timescales. The response is fast over the Arabian Sea, where precipitation lags SST by ~5 days; whereas it is slow over the Bay of Bengal and South China Sea, with a lag of ~12 days. The intraseasonal SST anomalies result in a similar atmospheric response across the basins, which consists of a destabilization of the bottom of the atmospheric column, as observed from the equivalent potential temperature anomalies near the surface. However, the presence of a relatively strong surface convergence over the Arabian Sea, due to the presence of a strong zonal gradient in SST, which accelerates the upward motion of the moist air, results in a relatively faster response in terms of the local precipitation anomalies over the Arabian Sea than over the Bay of Bengal and South China Sea. With respect to the observations, the ocean–atmosphere coupling is well simulated in the model, though with an overestimation of the intraseasonal SST anomalies, leading to an exaggerated SST-precipitation relationship. A detailed examination points to a systematic bias in the thickness of the mixed layer of the ocean model, which needs to be rectified. A too shallow (deep) mixed layer enhances (suppress) the amplitude of the intraseasonal SST anomalies, thereby amplifying (lessening) the ISV and the active-break phases of the monsoon in the model.     

The December 4, 1983 to February 18, 1984 eruption of Piton de la Fournaise (La Reunion, Indian Ocean): Description and interpretation

On December 4, 1983 an eruption started at vents located 1.5 km southwest of the summit of Piton de la Fournaise at the base of the central cone. After 31 months of quiescence this was one of the longest repose period in the last fifty years. The eruption had two phases: December 4 to January 18 and January 18 to February 18. Phase 1 produced about 8 × 10⁶ m³ of lava and Phase II about 9 × 10⁶ m³. The erupted lava is an aphyric basalt whose mineralogical and geochemical composition is close to that of other lavas emitted since 1977.The precursors of the December 4 outbreak were limited to two-week shallow (1.5–3 km) seismic crisis of fewer than 50 events. No long-term increase was noted in the local seismicity which is very quiet during repose periods and no long-term ground inflation preceded the eruption. Outbreaks of Phases I and II were preceded by short (2.5 hours and 1.5 hours) seismic swarms corresponding to the rise of magma toward the surface from a shallow reservoir. Large ground deformation explained by the emplacement of the shallow intrusions, was recorded during the seismic swarms. A summit inflation was observed in early January, before the phase II outbreak, while the phase I eruption was still continuing.Piton de la Fournaise volcanological observatory was installed in 1980. Seismic and ground deformation data now available for a period of 4 years including the 1981 and the 1983–1984 eruptions, allow us to describe the physical behavior of the volcano during this period. These observations lead us to propose that the magma transfer from deep levels to the shallow magma reservoir is not a continuous process but a periodic one and that the shallow magma reservoir was not resupplied before the 1981 and 1983–1984 eruptions. Considerations on the eruptive history and the composition of recent lavas indicate that the reservoir was refilled in 1977.     

Bias in hydraulic head measurements from multilevel vibrating-wire piezometers with excessively permeable backfill

Hydrogeology Journal - An extensive network of multilevel vibrating-wire piezometers (VWP) was recently created to monitor the spatial and temporal variation of pore pressure (and hydraulic head)...     

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.     

Subhaloes in scale-free cosmologies

We explore the dependence of the subhalo mass function on the spectral index n of the linear matter power spectrum using scale-free Einstein-de Sitter simulations with   n =−1  and −2.5. We carefully consider finite volume effects that may call into question previous simulations of   n < −2  power spectra. Subhaloes are found using a 6D friends-of-friends algorithm in all haloes originating from high-σ peaks. For   n =−1  , we find that the cumulative subhalo mass function is independent of the parameters used in the subhalo finding algorithm and is consistent with the subhalo mass function found in Λ cold dark matter (ΛCDM) simulations. In particular, the subhalo mass function is well fit by a power-law with an index of  α=−0.9  , that is the mass function has roughly equal mass in subhaloes per logarithmic interval in subhalo mass. Conversely, for   n =−2.5  , the algorithm parameters affect the subhalo mass function since subhaloes are more triaxial with less well-defined boundaries. We find that the index α is generally larger with  α≳−0.75  . We infer that although the subhalo mass function appears to be independent of n so long as   n ≳−2  , it begins to flatten as   n →−3  . Thus, the common practice of using  α≈−1.0  may greatly overestimate the number of subhaloes at the smallest scales in the CDM hierarchy.     

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.