A fourth-order solution of the ideal resonance problem

The second-order solution of the Ideal Resonance Problem, obtained by Henrard and Wauthier (1988), is developed further to fourth order applying the same method. The solutions for the critical argument and the momentum are expressed in terms of elementary functions depending on the time variable of the pendulum as independent variable. This variable is related to the original time variable through a Kepler-equation. An explicit solution is given for this equation in terms of elliptic integrals and functions. The fourth-order formal solution is compared with numerical solutions obtained from direct numerical integrations of the equations of motion for two specific Hamiltonians.     

Inland aeolian deposits of south‐west France: facies,stratigraphy and chronology

Archaeological investigations undertaken along a proposed highway together with the compilation of available geological and pedological data made it possible to give a first overview of the distribution of Pleistocene aeolian deposits in south‐west France. A chronological framework for deposition has been obtained using both radiocarbon (n = 24) and luminescence (n = 26) dating. It shows that aeolian transport was very active during the Late Pleniglacial, between 15 and ～23 ka, leading to sand emplacement over a 13 000‐m² area at the centre of the basin. The Pleniglacial coversands are typified by extensive fields of small transverse to barchanoid ridges giving way to sandsheets to the east. Subsequent aeolian phases, at ca. 12 ka (Younger Dryas) and 0.8–0.2 ka (Little Ice Age), correspond to the formation of more localized and higher, mainly parabolic dunes. At the southern and eastern margins of the coversand area, aeolian dust accumulated to form loess deposits, the thickness of which reaches ～3 m on the plateaus. Luminescence dates together with interglacial‐ranking palaeoluvisols between the loess units clearly indicate that these accumulations built up during the last two glacial–interglacial cycles. The chronology of sand and loess deposition thus appears to be consistent with that already documented for northern Europe. This suggests that it was driven by global climate changes in the northern hemisphere. The relatively thin aeolian deposits (and particularly loess) in south‐west France is thought to reflect both a supply‐limited system and a moister climate than in more northern and continental regions. Copyright © 2011 John Wiley & Sons, Ltd.     

Origin and tectonic significance of corundum–kyanite–sapphirine amphibolites from the Variscan French Massif Central

The contact zone between two major allochthonous lithotectonic units in the French Massif Central (FMC) is characterized by the presence of corundum‐bearing amphibolites associated with serpentinites, flaser‐gabbros, eclogites and granulites. These unusual amphibolites are best preserved in the Western FMC, where they are found within the lower oceanic crust of the Limousin ophiolite. Mineralogical observations and thermodynamic modelling of the spinel–corundum–sapphirine–kyanite amphibolites in the CMASH system show that they were formed at peak P–T conditions around 800 °C/10 kbar in response to near isothermal burial followed by a retrogressive anticlockwise path. Metamorphic reactions are controlled both by modification of P–T conditions and by local chemical changes linked to fluid infiltration. Pargasite growth has been enhanced by infiltration of Ca‐ and Al‐rich fluids whereas kyanite‐ and sapphirine‐forming reactions are partly controlled by local inputs of MgO–SiO₂ components, most probably during infiltration metasomatism. By analogy with worldwide ophiolites (Oman, Tethyan, Appalachian) and published numerical models, subduction of a still‐hot oceanic ridge is proposed to form these Al‐rich amphibolites from plagioclase‐rich troctolites. The trace‐element composition of high‐Ti, fine‐grained amphibolites (former fine‐grained Fe–Ti gabbros) adjacent to the corundum‐bearing ones, further indicates that the oceanic crust was initially created at a mid‐ocean ridge (rather than within a back‐arc basin), followed by the emplacement of supra‐subduction zone‐type magmas, probably due to intraoceanic subduction close to the ridge.     

Study of the soil–atmosphere moisture exchanges through convective drying tests in non‐isothermal conditions

This paper deals with the moisture exchanges occurring between soils and the surrounding atmosphere. Convective drying tests are performed on Awans silts at different drying temperatures and air relative humidities in order to reproduce the natural drying conditions. The experiments improve the understanding of the vapour transfers kinetics between the soil samples and the atmosphere. The experimental results are analysed assuming that the transfers take place in a boundary layer existing at the surface of the porous medium. The influence of the thermal conditions on the evaporation is also taken into account. In our model, coupled vapour and energy exchanges are controlled by mass and heat transfer coefficients characterizing the boundary layer. These coefficients are determined from the drying experiments. The modelling of the drying tests in non‐isothermal conditions is performed in order to validate the formulation of the vapour and heat exchanges. The numerical results present a good agreement with the kinetic of the materials desaturation determined during the tests. The analysis of the moisture transport mechanisms into the sample and at the boundary shows that at the beginning of the test, the drying is first achieved by the transport of moisture in its liquid form and its evaporation at the sample outer boundary in contact with the atmosphere. In a second step, vapour diffusion becomes predominant into the sample and it corresponds to the most important decrease of relative humidity. Copyright © 2009 John Wiley & Sons, Ltd.