Research

Research interests

My current research field is mathematical modeling/analysis and numerical analysis of partial differential equations arising in rarefied gas (and gas-particles mixtures) and plasmas sciences.

Publications

Submitted papers
  • The Vlasov-Ampère system and the Bernstein-Landau paradox , with Bruno Després, Alexandre Rege, Ricardo Weder, submitted (2020). Arxiv.
  • Mathematical and numerical study of a dusty knudsen gas mixture : extension to non-spherical dust particles, submitted (2020). HAL.
Publications
  • A projection algorithm on the set of polynomials with two bounds, with Martin Campos-Pinto, Bruno Després, Maxime Herda, Numerical Algorithms, 2020. Publication.
  • Mathematical and Numerical study of a dusty knudsen gas mixture, with Francesco Salvarani, in Acta Applicandae Mathematicae, 2019. Publication, Bibtex
  • Algorithms for Positive Polynomial Approximation, with Martin Campos Pinto and Bruno Després. SIAM Jounal of Numerical Analysis, 2019. Publication, HAL.
  • From particle methods to forward-backward Lagrangian schemes, with Martin Campos Pinto. SMAI Journal of Computational Mathematics, 2018. Publication (open access).
  • Convergence of a linearly transformed particle method for aggregation equations, with Martin Campos Pinto, José Antonio Carrillo de La Plata, Young-Pil Choi, Numerische mathematik, 2018. Publication, pdf, Bibtex.
  • Uniform convergence of a linearly transformed particle method for the Vlasov-Poisson system, with Martin Campos Pinto, SIAM Journal on Numerical Analysis, 2016. HAL, Publication, Bibtex.
  • Enhanced convergence estimates for semi-lagrangian schemes Application to the Vlasov-Poisson equation, with Bruno Després and Michel Mehrenberger. SIAM Journal of Numerical Analysis, 2013. HAL, Publication.
  • Nonlinear stability of a Vlasov equation for magnetic plasmas, with Bruno Després, Benoît Perthame and Rémi Sentis. Kinetic and related Models, 2013. HAL, Publication
  • Kinetic Modelling of the Transport of Dust Particles in a Rarefied Atmosphere, with Stéphane Dellacherie and Jacques Segré. Mathematical Models and Methods in Applied Sciences, 2012. Preprint, Publication
  • Numerical Simulation By a Random Particle Method of Deuterium-Tritium Reactions in a Plasma, with C. Copol, S. Dellacherie, J.M Mounsamy. ESAIM PROCEEDINGS, 2012. HAL, Publication.
  • An Efficient Kinetic Model for Assemblies of Amyloid Fibrils and Its Application to Polyglutamine Aggregation, with S. Prigent, A. Ballesta, P. Gabriel, L.M. Tine, H. Rezaei and M. Doumic. Plos One, 2012.
  • Numerical approximation of Knudsen layer for the Euler-Poisson system, with N.Vauchelet, C. Besse, Th. Goudon, I. Lacroix-Violet,  J-P Dudon, L. Navoret. ESAIM PROCEEDINGS, 2011. HAL, Publication
  • Label structured cell proliferation models, with H.T. Banks, M. Doumic, K.L. Sutton, W.C. Thompson. Appl. Math. Lett., Vol. 23, No. 12, 1412--1415, 2010.
  • Small Mass Ratio Limit of Boltzmann Equations in the Context of the Study of Evolution of Dust Particles in a Rarefied Atmosphere, with L. Desvillettes. Journal of Statistical Physics, 2009. Publication.
  • Kinetic modelling and numerical simulations using particle methods for the transport of dust in a rarefied gas. American Institute of Physics. Proceeding of the 26 th symposium "Rarefied gas dynamics'' (RGD), 2008. HAL, Publication.
PhD thesis
My PhD thesis was dealing about a kinetic modelling of a rarefied spray.
I defended it on Novembre 29th, 2009. My PhD advisors were Laurent Desvillettes (previously at ENS Cachan, now at Université de Paris) and Stéphane Dellacherie.
Key words: Gas-particle mixture, kinetic modelling, Boltzmann equation, Vlasov equation, Povzner inequality, particle method, DSMC simulation.
Link to my manuscrit
More détails here (in french)

Habilitation à diriger des recherches
I defended my habilitation on January, 11th, about model development and analysis of numerical methods for kinetic problems arising from plasma physics and gas-particles flows.