Séminaire de mathématiques appliquées (archives)

The motivation of this work is the detection of cerebrovascular accidents by microwave tomographic imaging. This requires the solution of an inverse problem based on a minimization algorithm with successive solutions of a direct problem such as the modeling of a whole-microwave measurement system. The feasibility of this type of imaging is conditioned on one hand by an accurate reconstruction of the material properties of the propagation medium and on the other hand by a considerable reduction of simulation time. Fulfilling these two requirements will enable a very rapid and accurate diagnosis.

A new numerical scheme to compute isothermal and unsteady flow of an incompressible viscoplastic Bingham medium will be presented. The main difficulty, for both theoretical and numerical approaches, is due to the non-differentiability of the plastic part of the stress tensor in regions where the rate-of-strain tensor vanishes. This is handled by reformulating the definition of the plastic stress tensor in terms of a projection. A new time scheme, based on the classical incremental projection method for the Newtonian Navier-Stokes equations, is proposed. The plastic tensor is treated implicitly in the first sub-step of the projection scheme and is computed by using a fixed point procedure.

During this talk, we will focus on the problem of testing the equality of metric measure spaces (mm-spaces) up to an isomorphism (a measure-preserving isometry), giving samples on these spaces. For this purpose, we introduce a new shape signature, the distance-to-a-measure signature, which is a probability measure on R+ built from the mm-space of interest. To reach our goal, we use bootstrap methods, involving Wasserstein metrics.

Le résumé est visible ici.

Les methodes dite hypocoercives permettent de montrer le retour exponentiel en temps vers l'equilibre Maxwellien pour une grande classe d'equations cinétiques inhomogènes. Elles sont basées sur des estimations de type commutateurs d'inspiration microlocale. Nous montrerons dans cet exposé que ces methodes permettent egalement de montrer le retour vers l'equilibre pour des nouveaux schemas cinetiques semi-discrets ou discrets, meme s'il n'y plus de commutateurs au sens continu du terme et que la notion meme d'equilibre est ambigue. Nous en profiterons pour parler egalement du cas coercif (homogene) qui est une des premieres etapes non triviale de l'analyse discrete.

Euler equations for compressible flows treats pressure as a scalar quantity. However, for several applications this description of pressure is not suitable. Many extended model based on the higher moments of Boltzmann equations are considered to overcome this issue. One such model is Ten-moment Gaussian closure equations, which treats pressure as symmetric tensor.

Dans cet exposé, nous nous intéresserons à la résolution numérique d'équations de convection-diffusion non-linéaires munies de conditions de flux nuls ou/et Dirichlet non-homogènes au bord. Pour une certaine classe de non-linéarités, ces équations admettent une large gamme d'entropies relatives assurant la convergence de la solution en temps long vers l'état stationnaire.