Publications

Acoustics

On the sound speed in two-fluid mixtures and the implications for CFD model validation

Study of the propagation of sound in a single non-ideal fluid originates with Stokes in 1845 and Kirchhoff in 1868. The situation is much more complex in the case of two-fluid flow, both from the physical point of view, as the configuration of the…

Saad Benjelloun, Jean-Michel Ghidaglia

Analysis of PDEs

On the Cauchy Problem for the Muskat Equation. II: Critical Initial Data

Thomas Alazard, Quoc-Hung Nguyen

Annals of PDE - 2021

Acoustics

On the dispersion relation for compressible Navier-Stokes Equations

In this paper we revisit the classical sound dispersion and attenuation theory due to Stokes [5], 1845, and Kirchhoff [3], 1868, for the propagation of sound in non-ideal fluids. In particular we reformulate the analysis due to Fletcher[2], 1974,…

Saad Benjelloun, Jean-Michel Ghidaglia

Analysis of PDEs

Quasilinearization of the 3D Muskat equation, and applications to the critical Cauchy problem

We exhibit a new decomposition of the nonlinearity for the Muskat equation and use it to commute Fourier multipliers with the equation. This allows to study solutions with critical regularity. As a corollary, we obtain the first well-posedness…

Thomas Alazard, Quoc-Hung Nguyen

Analysis of PDEs

On the dynamics of the roots of polynomials under differentiation

This article is devoted to the study of a nonlinear and nonlocal parabolic equation introduced by Stefan Steinerberger to study the roots of polynomials under differentiation; it also appeared in a work by Dimitri Shlyakhtenko and Terence Tao on…

Thomas Alazard, Omar Lazar, Quoc-Hung Nguyen

Analysis of PDEs

Cauchy theory for the water waves system in an analytic framework

In this paper we consider the Cauchy problem for gravity water waves, in a domain with a flat bottom and in arbitrary space dimension. We prove that if the data are of size $\varepsilon$ in a space of analytic functions which have a holomorphic…

Thomas Alazard, Nicolas Burq, Claude Zuily

Mathematics

KFC: A clusterwise supervised learning procedure based on the aggregation of distances

Sothea Has, Aurélie Fischer, Mathilde Mougeot

Journal of Statistical Computation and Simulation - 2021

Mathematics

IMODAL: creating learnable user-defined deformation models

A natural way to model the evolution of an object (growth of a leaf for instance) is to estimate a plausible deforming path between two observations. This interpolation process can generate deceiving results when the set of considered deformations…

Leander Lacroix, Benjamin Charlier, Alain Trouvé, Barbara Gris

CVPR 2021 - IEEE/CVF Conference on Computer Vision and Pattern Recognition - 2021

Artificial Intelligence

Environnement immersif et interaction haptique

Luba Tchertanov, Maxim Stoliarchuk, Alain Trouvé

Mokrane Bouzeghoub - 2021

Sensory Organs

Pseudo-Gaze Deviation Resulting From Positive Angle Kappa and Esotropia

Abstract: A 6-year-old boy was referred for constant right gaze deviation. Rather than a gaze deviation, he constantly seemed to look on the left side of any displayed target. Examination revealed the association of a highly positive angle Kappa and…

Maxence Rateaux, Marie-Andrée Espinasse-Berrod, Chloé Couret, Dominique Bremond-Gignac, Matthieu Robert

Journal of Neuro-Ophthalmology - 2021