Fils et méthodes d'éléments finis pour les équations de Maxwell. Le modèle de Holland revisité

Notre étude porte sur l'incorporation de fils minces dans les formulations volumiques des équations de Maxwell. Nous construisons un modèle basé sur une approximation quasi-statique du champ électrique au voisinage du fil. Ce modèle correspond à un problème mathématique bien posé car conservant une énergie. Il s' écrit sous la forme d' un problème d' évolution variationnel et se prête donc bien à une discrétisation par éléments finis en espace et différences finies en temps. Nous choisissons des éléments finis et une technique d'assemblage qui redonnent le schéma de Yee en l'absence du fil et proposons deux schémas de discrétisation en temps pour les termes additionnels dus au fil. Le premier redonne le schéma aux différences finies proposé par Holland et qui est très utilisé dans les codes industriels. Notre modèle est donc le cadre mathématique sous-jacent du schéma de Holland. Le second est un schéma original qui présente l' avantage d'être stable sous la condition de stabilité usuelle, c' est à dire indépendamment de la présence ou de la grosseur du fil. Il est donc une alternative intéressante au schéma de Holland qui souffre de problème de stabilité. L' étude est complétée par la détermination de l' inductance artificielle optimale qui est un paramètre clé de la méthode. Une formule explicite est donnée dans le cas d'un fil parallèle aux axes du maillage. Les résultats des expériences numériques confirment nos conclusions théoriques. Signalons pour finir une retombée intéressante par elle-même de notre travail qui est la déterminat- ion du comportement asymptotique de la fonction de Green de l' équation d'Helmholtz bidimensionnelle discrétisée avec un laplacien à cinq points

Fictitious Domain Method for Unsteady Problems: Application to Electromagnetic Scattering

In this work, we present and implement a fictitious domain method for time dependent problems of scattering by obstacles. We focus our attention on the case of 2D electromagnetic waves and perfectly conducting boundaries. Such a method allows us to work with uniform meshes for the electric field, independently of the geometry of the obstacle, the boundary condition being taken into account via the introduction of a Lagrange multiplier that can be interpreted as a surface current. After a brief description of the method and a presentation of its main properties, we show the superiority in terms of accuracy of this new method over the method that consists in using a staircase like approximation of the boundary

Interior penalty discontinuous Galerkin method for coupled elasto-acoustic media

We introduce a high order interior penalty discontinuous Galerkin scheme for the nu- merical solution of wave propagation in coupled elasto-acoustic media. A displacement formulation is used, which allows for the solution of the acoustic and elastic wave equations within the same framework. Weakly imposing the correct transmission condition is achieved by the derivation of adapted numerical fluxes. This generalization does not weaken the discontinuous Galerkin method, thus hp-non-conforming meshes are supported. Interior penalty discontinuous Galerkin methods were originally developed for scalar equations. Therefore, we propose an optimized formulation for vectorial equations more suited than the straightforward standard transposition. We prove consis- tency and stability of the proposed schemes. To study the numerical accuracy and convergence, we achieve a classic plane wave analysis. Finally, we show the relevance of our method on numerical experiments

Acoustic propagation in a vortical homentropic flow

This paper is devoted to the theoretical and the numerical studies of the radiation 4 of an acoustic source in a general homentropic flow. As a linearized model, we consider Goldstein's 5 Equations, which extend the usual potential model to vortical flows. The equivalence between 6 Linearized Euler's Equations with general source terms and Goldstein's Equations is established, 7 and the relations between unknowns, in each model, are analysed. A closed-form relation between 8 the hydrodynamic phenomena and the acoustics is derived. Finally, numerical results are presented 9 and the relevance of using Goldstein's Equations compared to the potential model is illustrated

Acoustic propagation in a vortical homentropic flow

This paper is devoted to the theoretical and the numerical studies of the radiation 4 of an acoustic source in a general homentropic flow. As a linearized model, we consider Goldstein's 5 Equations, which extend the usual potential model to vortical flows. The equivalence between 6 Linearized Euler's Equations with general source terms and Goldstein's Equations is established, 7 and the relations between unknowns, in each model, are analysed. A closed-form relation between 8 the hydrodynamic phenomena and the acoustics is derived. Finally, numerical results are presented 9 and the relevance of using Goldstein's Equations compared to the potential model is illustrated

11th Applied isotope geochemistery conference AIG-11

36Cl measurements in groundwaters of the deep confined aquifer of the Lake Chad Basin (LCB) were performed in order to constrain groundwater geochemical ages and residence times. Twenty-seven wells were sampled in Nigeria, Niger and Chad in the southern parts of the large (700 000 km2) multilayered aquifer of the LCB. 36Cl/Cl values range between 11±1.10-15 to 148±8.10-15 at/at. The highest ratios are observed near the recharge zone of the Nigerian part of the Continental Terminal aquifer, while the lowest ones are found in wells located near the southern fringe of the present-day lake Chad. Chloride concentrations are low (below 100 mg/l) and not correlated to the 36Cl/Cl values, indicating negligible dissolution of evaporites in most samples. Reliable 36Cl ages can be calculated along the different flow paths investigated, suggesting residence times of the deep groundwaters larger than 300 000 years. These results are consistent with new AMS-14C data below the detection limit but are in contradiction with previous 14C data obtained in the area

Effects of a soluble dietary fibre NUTRIOSE® on colonic fermentation and excretion rates in rats

The resistant dextrin NUTRIOSE®, developed from starch, is expected to act as a prebiotic. The aim of this study was to determine the effects of NUTRIOSE® on cecal parameters, short-chain fatty acid (SCFA) concentrations, and fecal excretion in rats. In an initial experiment, twenty-four male Fischer F344 rats were randomly assigned to one of the following four treatments for 14 days: G0 (control diet), G2.5 (control diet + 2.5% of dextrin), G5 (control diet + 5% of dextrin), and G10 (control diet + 10% of dextrin). After 14 days, total cecal weight, cecal content, and cecal wall weight were significantly increased in G5 and G10 compared to G0. At the same time, cecal pH was significantly lower in G10 compared to G0. Total SCFA concentration was significantly higher in G10 than in G5, G2.5, and G0, and significantly higher in G5 than in G0. Acetate, butyrate, and propionate concentrations were significantly increased in G5 and G10 compared to the controls. In a second trial based on a similar design, eighteen male Fischer F344 rats were treated with a control diet supplemented with 5% of dextrin or 5% of fructo-oligosaccharide. The results obtained with NUTRIOSE® were similar to those obtained with the fructo-oligosaccharide. In a third experiment, two groups of 5 Fischer F344 rats were orally treated with 100 and 1,000 mg/kg NUTRIOSE®, respectively, and from 18% to 25% of the dextrin was excreted in the feces. The results of these three studies show that the consumption of NUTRIOSE®, by its effects on total cecal weight, cecal content, cecal wall weight, pH, and SCFA production, could induce healthy benefits since these effects are reported to be prebiotic effects

Characterizing, modelling and understanding the climate variability of the deep water formation in the North-Western Mediterranean Sea

Observing, modelling and understanding the climate-scale variability of the deep water formation (DWF) in the North-Western Mediterranean Sea remains today very challenging. In this study, we first characterize the interannual variability of this phenomenon by a thorough reanalysis of observations in order to establish reference time series. These quantitative indicators include 31 observed years for the yearly maximum mixed layer depth over the period 1980–2013 and a detailed multi-indicator description of the period 2007–2013. Then a 1980–2013 hindcast simulation is performed with a fully-coupled regional climate system model including the high-resolution representation of the regional atmosphere, ocean, land-surface and rivers. The simulation reproduces quantitatively well the mean behaviour and the large interannual variability of the DWF phenomenon. The model shows convection deeper than 1000 m in 2/3 of the modelled winters, a mean DWF rate equal to 0.35 Sv with maximum values of 1.7 (resp. 1.6) Sv in 2013 (resp. 2005). Using the model results, the winter-integrated buoyancy loss over the Gulf of Lions is identified as the primary driving factor of the DWF interannual variability and explains, alone, around 50 % of its variance. It is itself explained by the occurrence of few stormy days during winter. At daily scale, the Atlantic ridge weather regime is identified as favourable to strong buoyancy losses and therefore DWF, whereas the positive phase of the North Atlantic oscillation is unfavourable. The driving role of the vertical stratification in autumn, a measure of the water column inhibition to mixing, has also been analyzed. Combining both driving factors allows to explain more than 70 % of the interannual variance of the phenomenon and in particular the occurrence of the five strongest convective years of the model (1981, 1999, 2005, 2009, 2013). The model simulates qualitatively well the trends in the deep waters (warming, saltening, increase in the dense water volume, increase in the bottom water density) despite an underestimation of the salinity and density trends. These deep trends come from a heat and salt accumulation during the 1980s and the 1990s in the surface and intermediate layers of the Gulf of Lions before being transferred stepwise towards the deep layers when very convective years occur in 1999 and later. The salinity increase in the near Atlantic Ocean surface layers seems to be the external forcing that finally leads to these deep trends. In the future, our results may allow to better understand the behaviour of the DWF phenomenon in Mediterranean Sea simulations in hindcast, forecast, reanalysis or future climate change scenario modes. The robustness of the obtained results must be however confirmed in multi-model studies