Bruno Pinçon

Selective focusing on small scatterers in acoustic waveguides using time reversal mirrors

We investigate the acoustic selective focusing properties of time reversal in a two-dimensional acoustic waveguide. A far-field model of the problem is proposed in the time-harmonic case. In order to tackle the question of selective focusing, we derive an asymptotic model for small scatterers. We show that in the framework of this limit problem, approximate eigenvectors of the time reversal operator can be obtained when the number of propagating modes of the waveguide is large enough. This result provides, in particular, a mathematical justification of the selective focusing properties observed experimentally. Some numerical experiments on selective focusing are presented.

Locomotion of articulated bodies in an ideal fluid: 2d model with buoyancy, circulation and collisions

Articulated solid bodies (ASB) is a basic model for the study of shape-changing underwater vehicles made of rigid parts linked together by pivoting joints. In this paper we study the locomotion of such swimming mechanisms in an ideal fluid. Our study ranges over a wide class of problems: several ASBs can be involved (without being hydrodynamically decoupled), the fluid-bodies system can be partially or totally confined and fluid circulation, buoyancy force and possible collisions between bodies are taken into account. We derive the Euler–Lagrange equation governing the dynamics of the system, study its well-posedness and describe a numerical scheme implemented in a Matlab toolbox (Biohydrodynamics Toolbox).

Far Field Modeling of Electromagnetic Time Reversal and Application to Selective Focusing on Small Scatterers

A time harmonic far field model for closed electromagnetic time reversal mirrors is proposed. Then, a limit model corresponding to small perfectly conducting scatterers is derived. This asymptotic model is used to prove the selective focusing properties of the time reversal operator. In particular, a mathematical justification of the decomposition of the time reversal operator (DORT) method is given for axially symmetric scatterers.

SINGULARITIES OF STATIONARY SOLUTIONS TO THE VLASOV-POISSON SYSTEM IN A POLYGON

We present an existence result for the stationary Vlasov--Poisson system in a bounded domain of~

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Stationary Solutions to the Vlasov-Poisson System

, with more general hypotheses than considered so far in the literature. In particular, we prove the equivalence of the kinetic approach (which consists in looking for the equilibrium distribution function) and the potential approach (where the unknown is the electrostatic potential at equilibrium). We study the dependence of the solution on parameters such as the total mass of the distribution, or those entering in the boundary conditions of the potential. Focusing on the case of a plane polygon, we study the singular behavior of the solution near the reentrant corners, and examine the dependence of the singularity coefficients on the parameters of the problem. Numerical experiments illustrate and confirm the analysis.