Kinetic formulation and global existence for the Hall-Magneto-hydrodynamics system

This paper deals with the derivation and analysis of the the Hall Magneto-Hydrodynamic equations. We first provide a derivation of this system from a two-fluids Euler-Maxwell system for electrons and ions, through a set of scaling limits. We also propose a kinetic formulation for the Hall-MHD equations which contains as fluid closure different variants of the Hall-MHD model. Then, we prove the existence of global weak solutions for the incompressible viscous resistive Hall-MHD model. We use the particular structure of the Hall term which has zero contribution to the energy identity. Finally, we discuss particular solutions in the form of axisymmetric purely swirling magnetic fields and propose some regularization of the Hall equation

On the regularity criterion of weak solution for the 3D viscous Magneto-hydrodynamics equations

We improve and extend some known regularity criterion of weak solution for the 3D viscous Magneto-hydrodynamics equations by means of the Fourier localization technique and Bony's para-product decomposition.Comment: 13page

Weak and strong solutions of equations of compressible magnetohydrodynamics

International audienceThis article proposes a review of the analysis of the system of magnetohydrodynamics (MHD). First, we give an account of the modelling asumptions. Then, the results of existence of weak solutions, using the notion of renormalized solutions. Then, existence of strong solutions in the neighbourhood of equilibrium states is reviewed, in particular with the method of Kawashima and Shizuta. Finally, the special case of dimension one is highlighted : the use of Lagrangian coordinates gives a simpler system, which is solved by standard techniques

A comparison of homogenization and standard mechanics analyses for periodic porous composites

Composite material elastic behavior has been studied using many approaches, all of which are based on the concept of a Representative Volume Element (RVE). Most methods accurately estimate effective elastic properties when the ratio of the RVE size to the global structural dimensions, denoted here as ν, goes to zero. However, many composites are locally periodic with finite ν. The purpose of this paper was to compare homogenization and standard mechanics RVE based analyses for periodic porous composites with finite ν. Both methods were implemented using a displacement based finite element formulation. For one-dimensional analyses of composite bars the two methods were equivalent. Howver, for two- and three-dimensional analyses the methods were quite different due to the fact that the local RVE stress and strain state was not determined uniquely by the applied boundary conditions. For two-dimensional analyses of porous periodic composites the effective material properties predicted by standard mechanics approaches using multiple cell RVEs converged to the homogenization predictions using one cell. In addition, homogenization estimates of local strain energy density were within 30% of direct analyses while standard mechanics approaches generally differed from direct analyses by more than 70%. These results suggest that homogenization theory is preferable over standard mechanics of materials approaches for periodic composites even when the material is only locally periodic and ν is finite.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/47812/1/466_2004_Article_BF00369853.pd

Sensibilisation de l'avalanche du thulium par l'erbium dans LiYF4_4

A par* de l'étude expérimentale d'un cristal de LiYF4 : 1,8% Tm et contenant une très faible concentration d'erbium, nous analysons les effets, sur la luminescence bleue (480 nm) du thulium, des transferts d'énergie entre les deux ions Tm$^{3+}$ et Er'". Notre étude, qui est à la fois spectroscopique et cinétique, est basée sur la méthode d'excitation sélective avec un laser accordable émettant dans le rouge (650 nm). Nous montrons ainsi que, malgré quelques effets négatifs, ces transferts qui existent dans les deux sens, peuvent avoir un effet sensibilisateur positif pour l'avalanche de photons, à condition que l'erbium reste faiblement concentré

Measurement of textile materials thermal properties

The determination of thermal properties of textile materials is difficult and subject to errors. Here we used two experimental methods. A PhotoPyroElectric method (Front PPE configuration with a modulated heat flow imposed on the surface of the sensor) and a commercial device (Alambeta) based the hot plate method. Two theorical approaches for the latter device were used. We tested the two methods on different textile materials (cotton, modal, wool and spacer). We observe good agreement between thermal conductivities measured with the two methods

Traitement des signaux de contrôle par courants de foucault : Coopération numérique/symbolique

La coopération entre la programmation procédurale, 'le "numérique", et la programmation déclarative, le "symbolique", permet de conférer à des systèmes de traitement de l'information une autonomie remarquable vis-à-vis de décisions complexes traditionnellement prises par des humains. Nous illustrons notre propos dans le contexte du contrôle par courants de Foucault des tubes de générateurs de vapeur avec les résultats de la maquette logicielle Extracsion®