A mathematical model for Tsunami generation using a conservative velocity-pressure hyperbolic system

By using the Hugoniot curve in detonics as a Riemann invariant of a velocity-pressure model, we get a conservative hyperbolic system similar to the Euler equations. The only differences are the larger value of the adiabatic constant (= 8.678 instead of 1.4 for gas dynamics) and the mass density replaced by a strain density depending on the pressure. The model is not homogeneous since it involves a gravity and a friction term. After the seismic wave reaches up the bottom of the ocean, one gets a pressure wave propagating toward the surface, which is made of a frontal shock wave followed by a regular decreasing profile. Since this regular profile propagates faster than the frontal shock waves, the amplitude of the pressure wave is strongly reduced when reaching the surface. Only in the case of a strong earth tremor the residual pressure wave is still sufficient to generate a water elevation with a sufficient wavelengths enable to propagate as a SaintVenant water wave and to become a tsunami when reaching the shore. We describe the construction of the model and the computation of the wave profile and discuss about the formation or not of a wave

Sound travellingwaves in wind instruments as solutions to non linear homogeneous gas dynamics equations

The sound propagation is usually described by a linear homogeneous wave equation, though the air flow in a duct is described by the gas dynamics equations, using a variable cross section, which corresponds to a non linear non homogneous system. The aim of this paper is to exhibit a common periodic solution to both models, with several free parameters such as frequency or amplitude, able to represent any sound. By taking in account a friction term linked to the material (wood or brass for instance) of the duct, it is possible to build an analytic such solution when the cross section fullfills some condition which corresponds exactly to the general shape of the wind instruments. The conclusion is that in the wind intruments, the shape brings the linearity

Tenders for European cereal export refunds : a structural approach

Diffusion du document : INRA Station d'Economie et Sociologie rurales 65 rue de Saint-Brieuc 35042 Rennes Cedex (FRA)Les restitutions à l'exportation de céréales européennes sont majoritairement attribuées par voie d'adjudication. La théorie des enchères est appliquée aux stratégies d'offre de prix d'achat de stocks d'intervention de blé tendre par les opérateurs. Ceci permet de caractériser le comportement de ces derniers, face à un tel instrument de régulation des marchés. La spécification et la méthode d'estimation des stratégies d'offre optimales sont développées sous deux hypothèses contrastées, relatives aux évaluations individuelles des céréales par ces opérateurs. Il s'agit des paradigmes de "valeurs privées" et de "valeur commune". Une hypothèse peu restrictive conduit à une forme réduite des modèles dont l'estimation est relativement simple, hormis quelques calculs additionnels nécessaires à une caractérisation complète des distributions latentes correspondant à chaque paradigme. Les résultats empiriques permettent finalement de conclure aux deux éléments suivants : d'une part l'hypothèse de valeur commune est la plus appropriée, ce qui signifie que les comportements des agents sont dictés par une référence unique sur le marché mondial, d'autre part la procédure d'adjudication utilisée par la Commission européenne se montre efficace, puisque les exportateurs ne tireraient pratiquement aucune rente lors de l'achat des stocks d'intervention

Water clustering in polychloroprene

Water sorption has been studied gravimetrically for polychloroprene rubber samples, first at a fixed hygrometric ratio (98% HR) and several temperatures (25, 40, 60 and 80 °C) for samples of 1.8 and 3.8 mm thickness (Constant Temperature and Hygrometry, CTH experiments), then at fixed temperature (40 °C) and several hygrometric ratios ranging from 0 to 95% HR on samples of 0.1 mm thickness (DVS experiments). CTH experiments reveal an abnormal sorption behavior: after an apparently fickian transient period, the water absorption continues at almost constant rate, no equilibrium is observed after more than 2500 h, whatever the temperature. DVS experiments reveal a very low Henry's solubility but the formation of clusters at water activities higher than 40%. The water diffusivity is almost independent of activity below 50% HR and decreases rapidly when activity increases above 50%. Contrary to CTH experiments, equilibrium is reached in DVS and the difference is not simply linked to the well-known effect of sample thickness on diffusion rate. The results allow hypotheses such as hydrolysis or osmotic cracking to explain the abnormal sorption phenomenon to be rejected. It is suggested that clusters could be polymer-water complexes having a linear/branched structure able to grow without phase separation that could explain the reversibility of sorption-desorption cycles. The difference of behavior between thin 0.1 mm and thicker 1.8 or 3.8 mm samples could be due to an effect of swelling stresses

Oxidation of unvulcanized, unstabilized polychloroprene: A kinetic study

Thermal oxidation in air at atmospheric pressure, in the 80-140 °C temperature range and in oxygen at 100 °C in the 0.02-3 MPa pressure range, of unvulcanized, unstabilized, unfilled polychloroprene (CR) has been characterized using FTIR and chlorine concentration measurement. The kinetic analysis was focused on double bond consumption. A mechanistic scheme involving unimolecular and bimolecular hydroperoxide decomposition, oxygen addition to alkyl radicals, hydrogen abstraction on allylic methylenes, alkyl and peroxyl additions to double bonds and terminations involving alkyl and peroxy radicals was elaborated. The corresponding rate constants were partly extracted from the literature and partly determined from experimental data using the kinetic model derived from the mechanistic scheme in an inverse approach. Among the specificities of polychloroprene, the following were revealed: The rate of double bond consumption is a hyperbolic function of oxygen pressure that allows a law previously established for the oxidation of saturated substrates to be generalized. CR oxidation is characterized by the absence of an induction period that reveals the instability of hydroperoxides. The kinetic analysis also reveals that peroxyl addition is faster than hydrogen abstraction but slower in CR than in common hydrocarbon polydienes

LITTO D- A Seamless Digital Terrain Model

The French National Geographic Institute (IGN) and the French Naval Hydrographie and Oceanographic Office (SHOM) were tasked by the Prime Minister to combine efforts to produce a seamless, precise topographic and bathymetric model, of the entire French coast. The Litto3D project was then created to meet more than one hundred requirements expressed by coastal managers and by users of geo-referenced data. An initial laser survey was conducted in the Golfe du Morbihan, Brittany and was used to generate a precise DTM. This experiment enabled SHOM and IGN to develop a methodology applicable everywhere and by everyone.El Primer Ministro encomendô al Instituto Geogrâfico Francés (IGN) y al Servicio Hidrogrâfico y Oceanogrâfico de la Marina Francesa (SHOM) la tarea de combinar sus esfuerzos para producir un modelo topogrâfico y batimétrico uniforme y preciso de la totalidad de la costa francesa. Fue creado enfonces el proyecto “Litto3D", para satisfacer mas de un centenar de requerimientos expresados por los administradores costeros y por los usuarios de datos geo-referenciados. Se efectuô un levantamiento inicial por laser en el “Golfe du Morbihan", en Bretaha, que fue utilizado para generar un DTM preciso. Este experimento permitiô al SHOM y al IGN desarrollar una metodologia aplicable en todas partes y por cada persona.L'Institut géographique nationale (IGN) et le Service hydrographique et océanographique de la marine française (SHOM) ont été chargés par le Premier Ministre de mettre en commun leurs efforts pour produire un modèle continu, à topographie et bathymétrie de précision, de l’ensemble des côtes de la France. Le projet Litto3D a donc été mis sur pied afin de répondre à plus d'une centaine de demandes formulées par des gestionnaires côtiers et par les utilisateurs de données géo-référenciées. Un premier levé laser a été effectué dans le golfe du Morbihan, en Bretagne, et a servi à produire des DTM précis. Cette expérience a permis au SHOM et à l'IGN de mettre au point une méthodologie appliquée partout et par tout le monde

Role of strain induced crystallization and oxidative crosslinking in fracture properties of rubbers

Tensile properties and crack propagation properties, especially critical strain energy release rate in mode I, GIC, have been used to investigate fracture properties of elastomers and their relationships with microstructure. These investigations were mainly based on a series of comparisons: first, the behaviour of polychloroprene rubber (CR), undergoing stress hardening due to strain induced crystallization (SIC) and oxidative crosslinking (OCL) was compared with that of chlorinated polyethylene (CPE), which undergoes SIC but not OCL, and with a polyurethane based on hydroxyl terminated polybutadiene (PU) which undergoes OCL but not SIC. Comparisons were also made on CR between fracture behaviour at ambient temperature, where SIC occurs and at 100°C where there is no SIC. Finally, oxidative crosslinking was used to vary in a continuous way the crosslink density in CR and PU, in order to evaluate the role of crosslinking in fracture behaviour. The results reveal the strong contribution of SIC to fracture strength. Crosslinking, even at low conversion, inhibits SIC which explains the sharp decrease of CR toughness in the early period of exposure to oxidation. When SIC has disappeared, it is possible to appreciate the effect of crosslinking on fracture behaviour. This effect, as evaluated from the density of deformation energy at rupture in tension or from GIC value, is almost negligible while the sample modulus increases regularly as a consequence of crosslinking. It appears that the toughness remains almost constant because it is under the influence of two contradictory phenomena: the negative effect of a reduction of ultimate elongation and the positive effect of a modulus increase. Such behaviour can be explained in terms of heterogeneous distribution of the lengths of elastically active chains. After long exposure, the sample behaviour becomes brittle, very high modulus values indicate that the samples approach, presumably in a heterogeneous way, the glassy state