A note concerning the 2:1 and the 3:2 resonances in the asteroid belt

The dynamical behavior of asteroids inside the 2:1 and 3:2 commensurabilities with Jupiter presents a challenge. Indeed most of the studies, either analytical or numerical, point out that the two resonances have a very similar dynamical behavior. In spite of that, the 3:2 resonance, a little outside the main belt, hosts a family of asteroids, called the Hildas, while the 2:1, inside the main belt, is associated to a gap (the Hecuba gap) in the distribution of asteroids.In his search for a dynamical explanation for the Hecuba gap, Wisdom (1987) pointed out the existence of orbits starting with low eccentricity and inclination inside the 2:1 commensurability and going to high eccentricity, and thus to possible encounters with Mars. It has been shown later (Henrard et al.), that these orbits were following a path from the low eccentric belt of secondary resonances to the high eccentric domain of secular resonances. This path crosses a bridge, at moderate inclination and large amplitude of libration, between the two chaotic domains associated with these resonances.The 3:2 resonance being similar in many respects to the 2:1 resonance, one may wonder whether it contains also such a path. Indeed we have found that it exists and is very similar to the 2:1 one. This is the object of the present paper.     

A Time Monte Carlo method for addressing uncertainty in land-use change models

One of the main objectives of land-use change models is to explore future land-use patterns. Therefore, the issue of addressing uncertainty in land-use forecasting has received an increasing attention in recent years. Many current models consider uncertainty by including a randomness component in their structure. In this paper, we present a novel approach for tuning uncertainty over time, which we refer to as the Time Monte Carlo (TMC) method. The TMC uses a specific range of randomness to allocate new land uses. This range is associated with the transition probabilities from one land use to another. The range of randomness is increased over time so that the degree of uncertainty increases over time. We compare the TMC to the randomness components used in previous models, through a coupled logistic regression-cellular automata model applied for Wallonia (Belgium) as a case study. Our analysis reveals that the TMC produces results comparable with existing methods over the short-term validation period (2000–2010). Furthermore, the TMC can tune uncertainty on longer-term time horizons, which is an essential feature of our method to account for greater uncertainty in the distant future.     

Environmental impact of an urban landfill on a coastal aquifer (El Jadida, Morocco)

The El Jadida landfill is one among many uncontrolled dumping sites in Morocco with no bottom liner. About 150 tons/day of solid wastes from mixed urban and industrial origins are placed directly on the ground. At the site of this landfill, the groundwaters circulate deeply (10–15 m) in the Cenomanian rock (calcareous–marl), which is characterised by an important permeability from cracks. The soil is sand–clay characterized by a weak coefficient of retention.The phreatic water ascends to the bottom of three quarries, which are located within the landfill. These circumstances, along with the lack of a leachate collection system, worsen the risks for a potential deterioration of the aquifer.To evaluate groundwater pollution due to this urban landfill, piezometric level and geochemical analyses have been monitored since 1999 on 60 wells. The landfill leachate has been collected from the three quarries that are located within the landfill. The average results of geochemical analyses show an important polluant charge vehiculed by landfill leachate (chloride = 5680 mg l⁻¹, chemical oxygen demand = 1000 mg l⁻¹, iron = 23 000 μg l⁻¹). They show also an important qualitative degradation of the groundwater, especially in the parts situated in the down gradient area and in direct proximity to the landfill. In these polluted zones, we have observed the following values: higher than 4.5 mS cm⁻¹ in electric conductivity, 1620 and 1000 mg l⁻¹ respectively in chlorides and sulfate (), 15–25 μg l⁻¹ in cadmium, and 60–100 μg l⁻¹ in chromium. These concentrations widely exceed the standard values for potable water.Several determining factors in the evolution of groundwater contamination have been highlighted, such as (1) depth of the water table, (2) permeability of soil and unsaturated zone, (3) effective infiltration, (4) humidity and (5) absence of a system for leachate drainage. So, to reduce the pollution risks of the groundwater, it is necessary to set a system of collection, drainage and treatment of landfill leachates and to emplace an impermeable surface at the site of landfill, in order to limit the infiltration of leachate.     

Chromospheric inhomogeneities in sunspot umbrae

The properties of rapidly changing inhomogeneities visible in the H and K lines above sunspot umbrae are described. We find as properties for these ‘Umbral Flashes’:

1. A lifetime of 50 sec. The light curve is asymmetrical, the increase is faster than the decrease in brightness.
2. A diameter ranging from the resolution limit up to 2000 km.
3. A tendency to repeat every 145 sec.
4. A ‘proper motion’ of 40 km/sec generally directed towards the penumbra.
5. A Doppler shift of 6 km/sec.
6. A magnetic field of 2100 G.
7. A decrease in this field of 12 G/sec. This decrease is probably related to the flash motion.
8. At any instant an average of 3–5 flashes in a medium-sized umbra. A weak feature often persists in the umbra after the flash. This post-flash structure initially shows a blue shift, but 100–120 sec after the flash, it shows a rapid red shift just before the flash repeats.

     

Properties of unstable waves in the lower St Lawrence Estuary

Abstract

The lower St Lawrence Estuary is an interesting case amongst estuaries in that it is wide enough to accommodate the development of mesoscale unstable waves and eddies. These features are generated by the runoff‐driven jet along this body's south shore. We present data yielding estimates of the length, time and velocity scales of these unstable disturbances. To relate these quantities to the dynamics we employ a 2‐layer quasigeos‐trophic instability model featuring realistic lateral shear. All model runs show short time and length scales, e‐folding periods of less than 10 days and wavelengths less than 50 km.     

Seismic scattering and shallow structure of the moon in oceanus procellarum

Long, reverberating trains of seismic waves produced by impacts and moonquakes may be interpreted in terms of scattering in a surface layer overlying a non-scattering elastic medium. Model seismic experiments are used to qualitatively demonstrate the correctness of the interpretation. Three types of seismograms are found, near impact, far impact and moonquake. Only near impact and moonquake seismograms contain independent information. Details are given in the paper of the modelling of the scattering processes by the theory of diffusion.Interpretation of moonquake and artificial impact seismograms in two frequency bands from the Apollo 12 site indicates that the scattering layer is 25 km thick, with a Q of 5000. The mean distance between scatterers is approximately 5 km at 25 km depth and approximately 2 km at 14 km depth; the density of scatterers appears to be high near the surface, decreasing with depth. This may indicate that the scatterers are associated with cratering, or are cracks that anneal with depth. Most of the scattered energy is in the form of scattered surface waves.Communication presented at the Lunar Science Institute Conference on Geophysical and Geochemical Exploration of the Moon and Planets, January 10–12, 1973.     

Fluid inclusions in granulites, granulitized eclogites and garnet clinopyroxenites from the Dabie–Sulu terranes, eastern China

Minor granulites (believed to be pre-Triassic), surrounded by abundant amphibolite-facies orthogneiss, occur in the same region as the well-documented Triassic high- and ultrahigh-pressure (HP and UHP) eclogites in the Dabie–Sulu terranes, eastern China. Moreover, some eclogites and garnet clinopyroxenites have been metamorphosed at granulite- to amphibolite-facies conditions during exhumation. Granulitized HP eclogites/garnet clinopyroxenites at Huangweihe and Baizhangyan record estimated eclogite-facies metamorphic conditions of 775–805 °C and ≥15 kbar, followed by granulite- to amphibolite-facies overprint of ca. 750–800 °C and 6–11 kbar. The presence of (Na, Ca, Ba, Sr)-feldspars in garnet and omphacite corresponds to amphibolite-facies conditions. Metamorphic mineral assemblages and P–T estimates for felsic granulite at Huangtuling and mafic granulite at Huilanshan indicate peak conditions of 850 °C and 12 kbar for the granulite-facies metamorphism and 700 °C and 6 kbar for amphibolite-facies retrograde metamorphism. Cordierite–orthopyroxene and ferropargasite–plagioclase coronas and symplectites around garnet record a strong, rapid decompression, possibly contemporaneous with the uplift of neighbouring HP/UHP eclogites.

Carbonic fluid (CO₂-rich) inclusions are predominant in both HP granulites and granulitized HP/UHP eclogites/garnet clinopyroxenites. They have low densities, having been reset during decompression. Minor amounts of CH₄ and/or N₂ as well as carbonate are present. In the granulitized HP/UHP eclogites/garnet clinopyroxenites, early fluids are high-salinity brines with minor N₂, whereas low-salinity fluids formed during retrogression. Syn-granulite-facies carbonic fluid inclusions occur either in quartz rods in clinopyroxene (granulitized HP garnet clinopyxeronite) or in quartz blebs in garnet and quartz matrices (UHP eclogite). For HP granulites, a limited number of primary CO₂ and mixed H₂O–CO₂(liquid) inclusions have also been observed in undeformed quartz inclusions within garnet, orthopyroxene, and plagioclase which contain abundant, low-density CO₂±carbonate inclusions. It is suggested that the primary fluid in the HP granulites was high-density CO₂, mixed with a significant quantity of water. The water was consumed by retrograde metamorphic mineral reactions and may also have been responsible for metasomatic reactions (“giant myrmekites”) occurring at quartz–feldspar boundaries. Compared with the UHP eclogites in this region, the granulites were exhumed in the presence of massive, externally derived carbonic fluids and subsequently limited low-salinity aqueous fluids, probably derived from the surrounding gneisses.     

On the maintenance of the axisymmetric part of the flow in the atmosphere

Summary The maintenance of the axisymmetric component of the flow in the atmosphere is investigated by means of a steady-state, quasi-geostrophic formulation of the meteorological equations. It is shown that the meridional variations in the time-averaged axisymmetric variables can be expressed as the sum of three contributions, one being due to the eddy heat transport, another to the eddy momentum transport, and a third to the convective-radiative equilibrium temperature which enters the problem through the specification of a Newtonian form of diabatic heating. The contributions by the large scale eddies are evaluated through the use of observed values for the eddy heat and momentum transports.The contributions from each of the three forcing mechanisms to the temperature and zonal wind fields are invstigated individually and found to be of about equal importance. The sum of the three contributions are also presented for the temperature, the zonal wind, the stream function associated with the mean meridional circulation and the corresponding vertical motion. Although the results fail to reproduce the main observed features of the lower stratosphere, they are found to be in good agreement with observations in the middle latitude troposphere. At any pressure level, for example, the computed mean zonal wind has a jet-like profile and the axis of the jet is found to slope to the south with height, as observed in the atmosphere.Based in part on a thesis submitted by the first author as partial fulfillment of the requirements for the Ph.D. degree at the University of Michigan. — Publication No. 194 from the Department of Meteorology and Oceanography, The University of Michigan.     

The high-pressure assemblages at Milos,Greece

Metamorphic rocks at Milos are known in small outcrops beneath the volcanic formations, as xenoliths in the Traphores volcanic breccia and as pebbles in the Paleochora Quaternary deposits. These rocks seem to belong to three different metamorphic units which probably have intricate relationships in the basement: — the eclogites unit shows garnetjadeite or garnet-omphacite primary associations, with apparently late crystallization of lawsonite phenoblasts an recrystallization features at relatively low temperatures; — the glaucophane schist unit exhibits Jadeite+quartz or glaucophane+lawsonite primary mineralogy; — the greenschist facies unit shows low-pressure main assemblages, most generally developed after high-pressure events. The two former units involve tholeiitic meta-igneous rocks, having been spilitized before metamorphism; they generally suffered more or less advanced recrystallization features in the low-pressure field of the greenschist facies. The third unit shows only meta-sedimentary rocks, with the sole exception of one single meta-doleritic pebble having calk-alkaline affinities.Petrological and mineralogical studies, based upon 15 bulk-rock compositions and 178 probe-analysed data points, lead to suspect at least 2, perhaps 3, different metamorphic events rather than one single metamorphic evolution, to account for the 3 U distinguished. From the observation of the mineralogical assemblages and their evolution, the former events (stages 1 and 2) could be related to rapid subduction of ocean-floor or back-arc basalts, whereas, during the latter event (stage 3), the rocks experienced crystallization conditions involving both decreasing pressures and increasing temperatures.     

Tidal evolution of hierarchical and inclined systems

We investigate the dynamical evolution of hierarchical three-body systems under the effect of tides, when the ratio of the orbital semi-major axes is small and the mutual inclination is relatively large (greater than 20°). Using the quadrupolar non-restricted approximation for the gravitational interactions and the viscous linear model for tides, we derive the averaged equations of motion in a vectorial formalism which is suitable to model the long-term evolution of a large variety of exoplanetary systems in very eccentric and inclined orbits. In particular, it can be used to derive constraints for stellar spin-orbit misalignment, capture in Cassini states, tidal-Kozai migration, or damping of the mutual inclination. Because our model is valid for the non-restricted problem, it can be used to study systems of identical mass or for the outer restricted problem, such as the evolution of a planet around a binary of stars. Here, we apply our model to various situations in the HD 11964, HD 80606, and HD 98800 systems.