Publications

Philippe Chartier, Michel Koskas, Mohammed Lemou, Florian Méhats (2024). Homomorphic sign evaluation using functional bootstrapping with a RNS representation of integers.

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Philippe Chartier, Michel Koskas, Mohammed Lemou, Florian Méhats (2024). Fully Homomorphic Encryption on large integers.

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Samuel Guilluy, Florian Méhats, Billal Chouli (2024). Boolean Ring of Blackening Operators and applications to Representation Learning.

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Marco David, Florian Méhats (2023). Symplectic learning for Hamiltonian neural networks. Journal of Computational Physics.

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Maxime Bouchereau, Philippe Chartier, Mohammed Lemou, Florian Méhats (2023). Machine Learning Methods for Autonomous Ordinary Differential Equations. arXiv preprint arXiv:2304.09036.

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Samuel Guilluy, Florian Méhats, Billal Chouli (2023). Constituency Tree Representation for Argument Unit Recognition. Proceedings of the 10th Workshop on Argument Mining.

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Tom Laborde, Alexandre Gensse, Philippe Chartier, Mohammed Lemou, Florian Méhats, Fabien Chaillan, Clément Gicquel (2023). Application du chiffrement fonctionnel sur données confidentielles pour la conception de modèles d'apprentissage automatique. Conference on Artificial Intelligence for Defense.

Ibrahim Almuslimani, Philippe Chartier, Mohammed Lemou, Florian Méhats (2022). Uniformly accurate schemes for drift--oscillatory stochastic differential equations. Applied Numerical Mathematics.

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Philippe Chartier, Mohammed Lemou, Florian Méhats, Xiaofei Zhao (2022). Derivative-free high-order uniformly accurate schemes for highly oscillatory systems. IMA Journal of Numerical Analysis.

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Philippe Chartier, Nicolas Crouseilles, Mohammed Lemou, Florian Méhats, Xiaofei Zhao (2020). Uniformly accurate methods for three dimensional Vlasov equations under strong magnetic field with varying direction. SIAM Journal on Scientific Computing.

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Mohammed Lemou, Ana Maria Luz, Florian Méhats (2020). Nonlinear instability of inhomogeneous steady states solutions to the HMF Model. Journal of Statistical Physics.

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Philippe Chartier, Nicolas Crouseilles, Mohammed Lemou, Florian Méhats (2020). Averaging of highly-oscillatory transport equations. Kinetic and Related Models.

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Philippe Chartier, Mohammed Lemou, Florian Méhats, Gilles Vilmart (2020). A new class of uniformly accurate numerical schemes for highly oscillatory evolution equations. Foundations of Computational Mathematics.

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Nicolas Crouseilles, Shi Jin, Mohammed Lemou, Florian Méhats (2020). A micro-macro method for a kinetic graphene model in one space dimension. Multiscale Modeling & Simulation.

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Philippe Chartier, Loı̈c Le Treust, Florian Méhats (2019). Uniformly accurate time-splitting methods for the semiclassical linear Schrödinger equation. ESAIM: Mathematical Modelling and Numerical Analysis.

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Philippe Chartier, Nicolas Crouseilles, Mohammed Lemou, Florian Méhats, Xiaofei Zhao (2019). Uniformly accurate methods for Vlasov equations with non-homogeneous strong magnetic field. Mathematics of Computation.

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Marine Fontaine, Mohammed Lemou, Florian Méhats (2019). Stable Ground States for the HMF Poisson Model. Annales de l’Institut Henri Poincaré (C) Non Linear Analysis.

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Philippe Chartier, Mohammed Lemou, Florian Méhats, Gilles Vilmart (2019). Highly oscillatory problems with time-dependent vanishing frequency. SIAM Journal on Numerical Analysis.

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Nicolas Crouseilles, Mohammed Lemou, Florian Méhats, Xiaofei Zhao (2017). Uniformly accurate Particle-in-Cell method for the long time solution of the two-dimensional Vlasov--Poisson equation with uniform strong magnetic field. Journal of Computational Physics.

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Mohammed Lemou, Florian Méhats, Xiaofei Zhao (2017). Uniformly accurate numerical schemes for the nonlinear dirac equation in the nonrelativistic limit regime. Communications in Mathematical Sciences.

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Florian Méhats, Olivier Pinaud (2017). The quantum Liouville--BGK equation and the moment problem. Journal of Differential Equations.

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Florian Méhats, Nicolas Raymond (2017). Strong confinement limit for the nonlinear Schrödinger equation constrained on a curve. Annales Henri Poincaré.

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Mohammed Lemou, Ana Maria Luz, Florian Méhats (2017). Nonlinear Stability Criteria for the HMF Model. Archive for Rational Mechanics and Analysis.

Philippe Chartier, Mohammed Lemou, Florian Méhats (2017). Highly-oscillatory evolution equations with multiple frequencies: averaging and numerics. Numerische Mathematik.

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Weizhu Bao, Loı̈c Le Treust, Florian Méhats (2017). Dimension reduction for dipolar Bose-Einstein condensates in the strong interaction regime. Kinetic and Related Models.

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Philippe Chartier, Florian Méhats, Mechthild Thalhammer, Yong Zhang (2017). Convergence of multi-revolution composition time-splitting methods for highly oscillatory differential equations of Schrödinger type. ESAIM: Mathematical Modelling and Numerical Analysis.

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Rupert L Frank, Florian Méhats, Christof Sparber (2017). Averaging of nonlinear Schrödinger equations with strong magnetic confinement. Communications in Mathematical Sciences.

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Stéphane Balac, Arnaud Fernandez, Fabrice Mahé, Florian Méhats, Rozenn Texier-Picard (2016). The Interaction Picture method for solving the generalized nonlinear Schrödinger equation in optics. ESAIM: Mathematical Modelling and Numerical Analysis.

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Philippe Chartier, Norbert J Mauser, Florian Méhats, Yong Zhang (2016). Solving highly-oscillatory NLS with SAM: numerical efficiency and long-time behavior. Discrete Contin. Dyn. Syst. Ser. S.

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Philippe Chartier, Florian Méhats, Mechthild Thalhammer, Yong Zhang (2016). Improved error estimates for splitting methods applied to highly-oscillatory nonlinear Schrödinger equations. Mathematics of Computation.

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Florian Méhats, Christof Sparber (2016). Dimension reduction for rotating Bose-Einstein condensates with anisotropic confinement. Discrete and Continuous Dynamical Systems-Series A.

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Clotilde Fermanian Kammerer, Florian Méhats (2016). A kinetic model for the transport of electrons in a graphene layer. Journal of Computational Physics.

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Philippe Chartier, Nicolas Crouseilles, Mohammed Lemou, Florian Méhats (2015). Uniformly accurate numerical schemes for highly oscillatory Klein--Gordon and nonlinear Schrödinger equations. Numerische Mathematik.

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François Castella, Ph Chartier, Florian Méhats, Ander Murua (2015). Stroboscopic averaging for the nonlinear Schrödinger equation. Foundations of Computational Mathematics.

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Luigi Barletti, Méhats Florian, Negulescu Claudia, Possanner Stefan, others (2015). Numerical study of a quantum-diffusive spin model for two-dimensional electron gases. Communications in Mathematical Sciences.

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Pierre-Henri Chavanis, Mohammed Lemou, Florian Méhats (2015). Models of dark matter halos based on statistical mechanics: The fermionic King model. Physical Review D.

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Pierre-Henri Chavanis, Mohammed Lemou, Florian Méhats (2015). Models of dark matter halos based on statistical mechanics: The classical King model. Physical Review D.

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Weizhu Bao, Loı̈c Le Treust, Florian Méhats (2015). Dimension reduction for anisotropic Bose--Einstein condensates in the strong interaction regime. Nonlinearity.

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Florian Méhats, Yannick Privat, Mario Sigalotti (2014). On the controllability of quantum transport in an electronic nanostructure. SIAM Journal on Applied Mathematics.

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Raymond El Hajj, Florian Méhats (2014). Analysis of models for quantum transport of electrons in graphene layers. Mathematical Models and Methods in Applied Sciences.

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Nicolas Crouseilles, Mohammed Lemou, Florian Méhats (2013). Asymptotic preserving schemes for highly oscillatory Vlasov--Poisson equations. Journal of Computational Physics.

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Christophe Besse, Rémi Carles, Florian Méhats (2013). An asymptotic preserving scheme based on a new formulation for NLS in the semiclassical limit. Multiscale Modeling & Simulation.

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Mohammed Lemou, Florian Méhats, Cyril Rigault (2012). Stable Ground States and Self-Similar Blow-Up Solutions for the Gravitational Vlasov--Manev System. SIAM Journal on Mathematical Analysis.

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Mohammed Lemou, Florian Méhats, Pierre Raphaël (2012). Orbital stability of spherical galactic models. Inventiones mathematicae.

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Mohammed Lemou, Florian Méhats (2012). Micro-macro schemes for kinetic equations including boundary layers. SIAM Journal on Scientific Computing.

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Patrick Gérard, Florian Méhats (2011). The Schrödinger--Poisson system on the sphere. SIAM journal on mathematical analysis.

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Naoufel Ben Abdallah, Yongyong Cai, François Castella, Florian Méhats (2011). Second order averaging for the nonlinear Schrödinger equation with strongly anisotropic potential. Kinetic and related models.

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Florian Méhats, Olivier Pinaud (2011). A problem of moment realizability in quantum statistical physics. Kinet. Relat. Models.

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Mohammed Lemou, Florian Méhats, Pierre Raphaël (2011). A new variational approach to the stability of gravitational systems. Communications in mathematical physics.

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Mohammed Lemou, Florian Méhats (2011). A boundary matching micro/macro decomposition for kinetic equations. Comptes Rendus. Mathématique.

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Luigi Barletti, Florian Méhats (2010). Quantum drift-diffusion modeling of spin transport in nanostructures. Journal of mathematical physics.

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Pierre Carcaud, Pierre-Henri Chavanis, Mohammed Lemou, Florian Méhats (2010). Evaporation law in kinetic gravitational systems described by simplified Landau models. Discrete and Continuous Dynamical Systems - B.

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Stéphane Brull, Florian Méhats (2010). Derivation of viscous correction terms for the isothermal quantum Euler model. ZAMM-Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik: Applied Mathematics and Mechanics.

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Florian Méhats, Olivier Pinaud (2010). An inverse problem in quantum statistical physics. Journal of Statistical Physics.

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Naoufel Ben Abdallah, François Castella, Fanny Delebecque-Fendt, Florian Méhats (2009). The strongly confined Schrödinger--Poisson system for the transport of electrons in a nanowire. SIAM Journal on Applied Mathematics.

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Mohammed Lemou, Florian Méhats, Pierre Raphaël (2009). Stable ground states for the relativistic gravitational Vlasov--Poisson system. Communications in Partial Differential Equations.

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Fanny Delebecque-Fendt, Florian Méhats (2009). An effective mass theorem for the bidimensional electron gas in a strong magnetic field. Communications in Mathematical Physics.

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Mohammed Lemou, Florian Méhats, Pierre Raphaël (2009). A new variational approach to the stability of gravitational systems. Comptes Rendus Mathématique.

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Naoufel Ben Abdallah, François Castella, Florian Méhats (2008). Time averaging for the strongly confined nonlinear Schrödinger equation, using almost-periodicity. Journal of Differential Equations.

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Mohammed Lemou, Florian Méhats, Pierre Raphaël (2008). The orbital stability of the ground states and the singularity formation for the gravitational Vlasov Poisson system. Archive for rational mechanics and analysis.

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Mohammed Lemou, Florian Méhats, Pierre Raphaël (2008). Structure of the linearized gravitational Vlasov--Poisson system close to a polytropic ground state. SIAM journal on mathematical analysis.

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Mohammed Lemou, Florian Méhats, Pierre Raphaël (2008). Stable self-similar blow up dynamics for the three dimensional relativistic gravitational Vlasov-Poisson system. Journal of the American Mathematical Society.

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Grégoire Allaire, Anton Arnold, Thomas Yizhao Hou, Pierre Degond, Samy Gallego, Florian Méhats, Christian Ringhofer (2008). Quantum hydrodynamic and diffusion models derived from the entropy principle. Quantum Transport: Modelling, Analysis and Asymptotics—Lectures given at the CIME Summer School held in Cetraro, Italy September 11–16, 2006.

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Mohammed Lemou, Florian Méhats, Pierre Raphaël (2007). Uniqueness of the critical mass blow up solution for the four dimensional gravitational Vlasov--Poisson system. Annales de l’Institut Henri Poincaré C, Analyse non linéaire.

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Pierre Degond, Samy Gallego, Florian Méhats (2007). On quantum hydrodynamic and quantum energy transport models. Communications in Mathematical Sciences.

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Pierre Degond, Samy Gallego, Florian Méhats (2007). Isothermal quantum hydrodynamics: derivation, asymptotic analysis, and simulation. Multiscale Modeling & Simulation.

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Pierre Degond, Samy Gallego, Florian Méhats (2007). An entropic quantum drift-diffusion model for electron transport in resonant tunneling diodes. Journal of Computational Physics.

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Pierre Degond, Samy Gallego, Florian Méhats (2007). An asymptotic preserving scheme for the Schrödinger equation in the semiclassical limit. Comptes Rendus Mathematique.

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J-P Bourgade, Pierre Degond, Florian Méhats, Christian Ringhofer (2006). On quantum extensions to classical spherical harmonics expansion/Fokker-Planck models. Journal of mathematical physics.

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Naoufel Ben Abdallah, Florian Méhats, Géraldine Quinio (2006). Global existence of classical solutions for a Vlasov-Schrödinger-Poisson system. Indiana University mathematics journal.

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N Ben Abdallah, Florian Méhats, Nicolas Vauchelet (2006). Diffusive transport of partially quantized particles: existence, uniqueness and long-time behaviour. Proceedings of the Edinburgh Mathematical Society.

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Florian Méhats (2006). Analysis of a quantum subband model for the transport of partially confined charged particles. Monatshefte für Mathematik.

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Naoufel Ben Abdallah, Florian Méhats, Claudia Negulescu (2006). Adiabatic quantum-fluid transport models. Communications in Mathematical Sciences.

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Naoufel Ben Abdallah, Florian Méhats, Christian Schmeiser, Rada M Weishäupl (2005). The nonlinear Schrödinger equation with a strongly anisotropic harmonic potential. SIAM journal on mathematical analysis.

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Naoufel Ben Abdallah, Florian Méhats (2005). Semiclassical analysis of the Schrödinger equation with a partially confining potential. Journal de mathématiques pures et appliquées.

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Pierre Degond, Florian Méhats, Christian Ringhofer (2005). Quantum hydrodynamic models derived from the entropy principle. Contemporary Mathematics.

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Pierre Degond, Florian Méhats, Christian Ringhofer (2005). Quantum energy-transport and drift-diffusion models. Journal of statistical physics.

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Naoufel Ben Abdallah, Florian Méhats, Olivier Pinaud (2005). On an open transient Schrödinger--Poisson system. Mathematical Models and Methods in Applied Sciences.

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Naoufel Ben Abdallah, Florian Méhats (2005). On a Vlasov–Schrödinger–Poisson Model. Communications in Partial Differential Equations.

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Samy Gallego, Florian Méhats (2005). Entropic discretization of a quantum drift-diffusion model. SIAM journal on numerical analysis.

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Naoufel Ben Abdallah, Florian Méhats, Olivier Pinaud (2005). Adiabatic Approximation of the Schrödinger--Poisson System with a Partial Confinement. SIAM journal on mathematical analysis.

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Samy Gallego, Florian Méhats (2004). Numerical approximation of a quantum drift-diffusion model. Comptes rendus. Mathématique.

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Naoufel Ben Abdallah, Florian Méhats, Nicolas Vauchelet (2004). A note on the long time behavior for the drift-diffusion-Poisson system. Comptes Rendus Mathematique.

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Florian Méhats (2002). Convergence of a numerical scheme for a nonlinear oblique derivative boundary value problem. ESAIM: Mathematical Modelling and Numerical Analysis.

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Naoufel Ben Abdallah, Florian Méhats, Nicolas Vauchelet (2002). Analysis of a drift-diffusion-Schrödinger--Poisson model. Comptes Rendus Mathematique.

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Annalisa Ambroso, Florian Méhats, Pierre-Arnaud Raviart (2001). On singular perturbation problems for the nonlinear Poisson equation. Asymptotic Analysis.

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Naoufel Ben Abdallah, Pierre Degond, Florian Méhats (1999). The Child--Langmuir asymptotics for magnetized flows. Asymptotic Analysis.

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Florian Méhats, Jean-Michel Roquejoffre (1999). A nonlinear oblique derivative boundary value problem for the heat equation Part 2: Singular self-similar solutions. Annales de l’Institut Henri Poincaré C.

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Florian Méhats, Jean-Michel Roquejoffre (1999). A nonlinear oblique derivative boundary value problem for the heat equation Part 1: Basic results. Annales de l’Institut Henri Poincaré C.

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Florian Méhats (1998). The Child--Langmuir asymptotics applied to a bipolar diode. Mathematical methods in the applied sciences.

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Naoufel Ben Abdallah, Pierre Degond, Florian Méhats (1998). Mathematical models of magnetic insulation. Physics of plasmas.

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Florian Méhats, Jean-Michel Roquejoffre (1995). Un problème d'évolution avec condition aux limites non linéaire. Comptes rendus de l’Académie des sciences. Série 1, Mathématique.