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.     

Évolution de l'onde semi-diurne M2 de la marée à Brest de 1846 à 2005

The work of searching, recovering and quality control of ancient sea-level measurements at Brest is presented. This work enables us to complete a study carried out by Cartwright in 1972, which showed a decrease in the tidal M2 semi-diurnal amplitude of 1% per century. After including these ancient data, as well as the last four decades of observations in the analysis, our results show an increase of the amplitude of M2 after 1960 and a decrease before 1880, suggesting a long-period oscillation rather than a steady secular trend. To cite this article: N. Pouvreau et al., C. R. Geoscience 338 (2006).     

Impacts of Holocene climatic variations on alluvial fan activity below snowpatches in subarctic Québec

In the Lake Guillaume-Delisle area of subarctic Québec, storm-generated alluvial fans have been active sporadically throughout the Holocene. In this study, we propose that the persistence of late-lying snowpatches in fan catchments during Holocene cold episodes promoted alluvial fan activity by lowering the precipitation threshold required to trigger a torrential event. This hypothesis was tested by characterizing the depositional processes responsible for alluvial fan formation below snowpatches, and by reconstructing the Holocene alluvial fan activity. Stratigraphic and sedimentary analyses conducted on seven alluvial fans revealed that they were deposited by torrential activity leading to waterlaid, transient, or hyperconcentrated deposition. The chronology of the storm-generated alluvial fans — based on 22 radiocarbon dates — indicates that torrential activity was enhanced during the cooler Late Holocene (i.e., after ca. 3500 cal. yr BP). Snowier winters and cooler summers were beneficial to nival activity, allowing the persistence of larger snowpatches throughout the summer and fall seasons. Rainfall-induced thaw of such snowpatches during rainstorm events is inferred to have contributed to alluvial fan activity by increasing water availability. Three peaks of alluvial activity occurred during the Late Holocene (2950–2750, 1900–1400, and 800–300 cal. yr BP) and are indicative of increased storminess resulting in higher fan activity. Increased fan activity during cooler episodes was concurrent with increased runoff activity in the immediate pronival area. This stresses the importance of nivation below snowpatches and pinpoints the role of nivation in enhancing geomorphological activity during period of cooler and more humid climate in subarctic environments.     

Surface temperature differences between minerals in crystalline rocks: Implications for granular disaggregation of granites through thermal fatigue

Thermal expansion differences between minerals within rocks under insolation have previously been assumed to drive breakdown by means of granular disaggregation. However, there have been no definitive demonstrations of the efficacy of this weathering mechanism. Different surface temperatures between minerals should magnify thermal expansion differences, and thus subject adjacent minerals to repeated stresses that might cause breakdown through fatigue failure. This work confirms the existence of surface temperature differences between minerals in granitic rocks under simulated short-term temperature fluctuations so as to discriminate their potential for initiating granular disaggregation. The influence of colour, as a surrogate for albedo, and crystal size, as a function of thermal mass are specifically identified because of their ease of quantification. Four rock types with a range of these properties were examined, and subjected to repeated short-term temperature cycles by radiative heating and cooling under laboratory conditions. Results show that while albedo is the main control for overall and individual maximum temperatures, crystal size is the main factor controlling higher temperature differences between minerals. Thus, stones with large differences of mineral sizes can undergo magnified stresses due to thermal expansion differences.     

The Vigny limestones: a record of Palaeocene (Danian) tectonic-sedimentary events in the Paris Basin

Danian marine sedimentation in the Paris Basin occurred between two major erosional phases. The earlier was responsible for the stripping of presumably deposited Maastrichtian sediments and of a variable thickness of Campanian chalk. The later occurred during the late Palaeocene and resulted in the erosion of almost all Danian deposits, which are now limited to small and scattered outcrops. One of these outcrops corresponds to reefal and peri‐reefal limestones of middle to late Danian age, exposed in the quarries of Vigny (NW of Paris). Danian deposits here show intricate relations with the surrounding Campanian chalk. Danian sedimentation was contemporaneous with faulting, which generated signifiant sea‐floor relief and resulted in contrasting depositional areas: topographic highs with coralgal reefs, and depressions where calcirudite channel fill accumulated. Normal faulting occurred along WNW–ESE master faults. The generation of submarine fault scarps gave rise to various types of gravity‐driven phenomena, including the sliding and slumping of large blocks of reefal limestone and the deposition of carbonate debris flows. Along with the redeposition of the Danian carbonates, flows of fluidized and reworked Campanian chalk resulted from the peculiar physical properties of the undercompacted chalks. Erosion and faulting occurred predominantly during the Palaeocene and represent a major episode in the physiographic evolution of the Paris Basin.     

Up to what temperature is petroleum stable? New insights from a 5200 free radical reactions model

The discovery of crude oils and condensates at ever higher temperatures casts doubt on the validity of the usual geochemical modelling approach, that uses empirical reactions and rate constants. The solution used to account for such a high thermal stability is presently to adjust the rate parameters, but the physical meaning and scientific value of such a strategy can be questioned. We have developed a mechanistic model consisting of 5200 lumped free radical reactions to describe the thermal evolution of a mixture of 52 organic species meant to represent light petroleum. Rate constants used are those available in the literature or estimated using well established thermochemistry-reactivity correlations. Chemical structures included in the model are linear, branched and cyclic hydrocarbons, hydro- and alkyl-aromatics, PAHs, and three heteroatomic compounds. Reactions include cracking and alkylation chains and inhibiting and accelerating reactions from the various reactants. This model has been applied to several mixtures with various proportions of reaction inhibitors and accelerators, and to a composition representing a light mature oil. From the results obtained, we conclude that mature oils will be stable up to 240–260 °C, depending on their composition, and that the thermal cracking of oil to gas is not possible under reasonable basin conditions. The kinetics of petroleum cracking are thus much slower than generally recognized.     

Premier pôle paléomagnétique,d'âge Moscovien contraint par un test du pli,obtenu dans le bassin d'Illizi (Craton saharien,Algérie)First palaeomagnetic pole,of Moscovian age constrained by a fold test,in the Illizi Basin (Saharan Craton,Algeria)

Palaeomagnetic study, carried out in the Moscovian (～305 Ma) formation in the Edjeleh anticline, shows the existence of three magnetisation components. Two of them are probably Cenozoic and Permian remagnetisations. The third component determined by both well defined ChRMs and remagnetisation circles analysis passes the fold test. Because the folding started before or during the Stephano-Autunian, this third component is the primary magnetisation. Its palaeomagnetic pole (28.3°S, 58.9°E), close to other poles from the Saharan platform obtained from neighbouring periods but without palaeomagnetic tests, confirms the age of these last data. To cite this article: B. Bayou et al., C. R. Geoscience 334 (2002) 81–87.     

Sediment yield and storage variations in the Négron River catchment (south western Parisian Basin,France) during the Holocene period

In the Négron River catchment area (162 km²), surface‐sediment stores are composed of periglacial calcareous ‘grèze’ (5 × 10⁶ t) and loess (21 × 10⁶ t), and Holocene alluvium (12·6 × 10⁶ t), peat (0·6 × 10⁶ t) and colluvium (18·5 × 10⁶ t). Seventy‐five per cent of the Holocene sediments is stored along the thalwegs. Present net sediment yield, calculated from solid discharge at the Négron outlet, is low (0·6 t km^?2 a^?1) due to the dominance of carbonate rocks in the catchment. Mean sediment yield during the Holocene period is 7·0 t km^?2 a^?1 from alluvium stores and 7·6 t km^?2 a^?1 from colluvium stores. Thus, the gross sediment yield during the Holocene period is about 18·7 t km^?2 a^?1 and the sediment delivery ratio 3 per cent. The yield considerably varies from one sub‐basin to another (3·9 to 24·5 t km^?2 a^?1) according to lithology: about 25 per cent and 50 per cent of initial stores of periglacial grèze and loess respectively were reworked during the Holocene period. Sediment yield has increased by a factor of 6 in the last 1000 years, due to the development of agriculture. The very high rate of sediment storage on the slope during that period (88 per cent of the yield) can be accounted for by the formation of cultivation steps (‘rideaux’). It is predicted that the current destruction of these steps will result in a sediment wave reaching the valley floors in the coming decades. Subboreal and Subatlantic sediments and pollen assemblages in the Taligny marsh, where one‐third of the alluvium is stored, show the predominant influence of human activity during these periods in the Négron catchment. Copyright © 2002 John Wiley & Sons, Ltd.     

Fracturation d'âge Aptien supérieur sur la bordure orientale de la plate-forme arabique (Haushi-Huqf,Oman)Aptian faulting (Shu'aiba Formation) on the eastern edge of the Arabian Platform (Haushi-Huqf,Oman)

In the Haushi-Huqf (Eastern Central Oman) as in other parts of the Arabian platform, a major sedimentary break is recorded between the Early Aptian carbonates (Shu'aiba Formation) and the Albian orbitolinid-rich marls (Nahr Umr Formation). The unconformity corresponds to a succession of events: (1) a brusque interruption of the regressive sequence of the Shu'aiba limestone (algae and small rudistid build-ups); (2) a stratigraphic gap related to the Late Aptian; (3) the development of a thick ferruginous crust (hardground) that covered the top surface of the Shu'aiba; the hardground is related to a forced flooding surface; (4) the Shu'aiba was rapidly drowned and buried under the Nahr Umr marls. Moreover, the Shu'aiba limestone was subject to faulting NW–SE-trending normal faults before lithification and formation of the ferruginous crust. The faulting episode is clearly dated: post-Early Aptian and pre-Albian. The signification of the faulting remains hypothetical. The syndiagenetic NW–SE normal faults may correspond to ‘en echelon’ faults, combined with transcurrent fault movements (for example the Haushi-Nafun Fault). The possible causes of these intra-platform transcurrent movements are discussed. To cite this article: C. Montenat, P. Barrier, C. R. Geoscience 334 (2002) 781–787.