11 octobre 2018

S.V. Raghurama Rao (Department of Aerospace Engineering, Indian Institute of Science, Bangalore)
A Lattice Boltzmann Relaxation Scheme for Compressible Flows

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Lieu : IMO, Salle 3L8

Résumé : Traditional Lattice Boltzmann Method (LBM) is limited to incompressible flows, due to a built-in low Mach number expansion of the equilibrium distribution. A Lattice Boltzmann Relaxation Scheme for compressible flows is presented. The equilibrium distributions are simple functions of conserved variables and fluxes, avoiding low Mach number limitation. The results are presented for 1-D and 2-D Euler equations. New approaches are also introduced to approximate viscous Burgers equation.

A Lattice Boltzmann Relaxation Scheme for Compressible Flows  Version PDF

Valentina Franceschi (Orsay)
Essential self-adjointness of Sub-elliptic Laplacians

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Lieu : salle 2L8 (IMO, bâtiment 307)

Résumé : The aim of this seminar is to present recent results about essential self-adjointness of sub-elliptic laplacians. These are hypoelliptic operators defined on a manifold M, that are naturally associated to a geometric structure on it. In the case when such a structure is Riemannian and complete, the associated Laplace-Beltrami operator is indeed essentially self-adjoint. This amounts to say that the solutions to the Schrödinger equation on M are well defined without imposing any boundary conditions. Our purpose is to address the case when the structure is sub-Riemannian : this can be thought of as a generalization of the Riemannian case, under anisotropic constraints on the directions of motion on M. In particular, singularities may appear, encoded in the blow up of an intrinsic measure, whose definition depends only on the geometry. In this case the problem is still open and a standing conjecture, formulated by Boscain and Laurent, asserts that the sub-elliptic Laplacian is essentially self-adjoint. We will explain our results supporting the conjecture and underline the cases that are not included in our analysis. In collaboration with D. Prandi (CNRS, CentraleSupélec, Giffes-sur-Yvette, France) and L. Rizzi (CNRS & Institut Fourier, Grenoble, France)

Notes de dernières minutes : Café culturel assuré à 13h par Konstantin Pankrashkin

Essential self-adjointness of Sub-elliptic Laplacians  Version PDF