Florian Méhats

Publications

Warning: this list has not been updated since end of 2019.
I am actually on leave from the University of Rennes 1 as Research Associate at Ravel Technologies.

Submitted for publication

► Nonlinear instability of inhomogeneous steady states solutions to the HMF Model (with M. Lemou and A. M. Luz). Preprint

► A micro-macro method for a kinetic graphene model in one-space dimension (with N. Crouseilles, S. Jin and M. Lemou). Preprint

Published or accepted papers

2019

► Highly-oscillatory problems with time-dependent vanishing frequency (with P. Chartier, M. Lemou and G. Vilmart), to appear in SIAM J. Numer. Anal. Preprint

2017

► Uniformly accurate Particle-In-Cell method for the long time two-dimensional Vlasov-Poisson equation with strong magnetic field (with N. Crouseilles, M. Lemou and X. Zhao), J. Comput. Phys. 346 (2017), 172-190. Preprint

► Convergence of multi-revolution composition time-splitting methods for highly oscillatory differential equations of Schrödinger type (with P. Chartier, M. Thalhammer and Y. Zhang), ESAIM:M2AN 51 (2017), no. 5, 1859-1882. Preprint

► Uniformly accurate numerical schemes for the nonlinear Dirac equation in the nonrelativistic limit regime (with M. Lemou and X. Zhao), Commun. Math. Sci. 15 (2017), no. 4, 1107-1128. Preprint

► Uniformly accurate forward semi-Lagrangian methods for highly oscillatory Vlasov-Poisson equations (with N. Crouseilles, M. Lemou and X. Zhao), SIAM Multiscale Model. Simul. 15 (2017), no. 2, 723-744. Preprint

► Dimension reduction for dipolar Bose-Einstein condensates in the strong interaction regime (with W. Bao and L. Le Treust), Kinetic and Related Models, 10 (2017), no.3, 553-571. Preprint

► Nonlinear stability criteria for the HMF model (with M. Lemou and A. M. Luz), Arch. Rational Mech. Anal. 224 (2017), no. 2, 353-380. Preprint

► Highly-oscillatory evolution equations with multiple frequencies: averaging and numerics (with P. Chartier and M. Lemou), Numer. Math. 136 (2017), no. 4, 907-939. Preprint

2016

► Dimension reduction for rotating Bose-Einstein condensate with anisotropic confinement (with C. Sparber), DCDS-A 36 (2016), no. 9, 5097-5118. Preprint

► Strong confinement limit for the nonlinear Schrödinger equation constrained on a curve (with N. Raymond) to appear in Ann. Henri Poincaré. Preprint

► Improved error estimates for splitting methods applied to highly-oscillatory nonlinear Schrödinger equations (with P. Chartier, M. Thalhammer and Y. Zhang), Math. of Comp. 85 (2016), 2863-2885. Preprint

► The Interaction Picture method for solving the generalized nonlinear Schrödinger equation in optics (with S. Balac, A. Fernandez, F. Mahé and R. Texier-Picard), M2AN Math. Model. Numer. Anal. 50 (2016) 945-964. Preprint

► Solving highly-oscillatory NLS with SAM: numerical efficiency and long-time behavior (with P. Chartier, N. Mauser and Y. Zhang), to appear in DCDS-S. Preprint

2015

► Models of dark matter halos based on statistical mechanics: II. The fermionic King model (with P.-H. Chavanis and M. Lemou), Phys. Rev. D 92 (2015), 123527. Preprint

► Models of dark matter halos based on statistical mechanics: I. The classical King model (with P.-H. Chavanis and M. Lemou), Phys. Rev. D 91 (2015), 063531. Preprint

► Dimension reduction for anisotropic Bose-Einstein condensates in the strong interaction regime (with W. Bao and L. Le Treust), Nonlinearity 28 (2015), no. 3, 755. Preprint

► Stroboscopic averaging for the nonlinear Schrödinger equation (with F. Castella, P. Chartier and A. Murua), Found. Comput. Math 15 (2015), no. 2, 519–559. Preprint

► Numerical study of a quantum-diffusive spin model for two-dimensional electron gases (with L. Barletti, C. Negulescu and S. Possanner), Comm. Math. Sci. 13, (2015), 1347--1378. Preprint

► Uniformly accurate numerical schemes for highly oscillatory Klein-Gordon and nonlinear Schrödinger equations (with P. Chartier, N. Crouseilles and M. Lemou), Numer. Math. 129 (2015), no. 2, 211-250. Preprint

2014

► On the controllability of quantum transport in an electronic nanostructure (with Y. Privat and M. Sigalotti), SIAM J. Appl. Math, 74 (2014), no. 6, 1870–1894. Preprint

► Analysis of models for quantum transport of electrons in graphene layers (with R. El Hajj), Math. Models Methods Appl. Sci. 24, (2014), no. 11, 2287-2310. Preprint

2013

► An asymptotic preserving scheme based on a new formulation for NLS  in the semiclassical limit (with C. Besse and R. Carles), SIAM Multiscale Model. Simul. 11 (2013), no. 4, 1228-1260. Preprint

► Asymptotic preserving schemes for highly oscillatory Vlasov-Poisson equations (with N. Crouseilles and M. Lemou), J. Comp. Phys. 248 (2013) 287–308. Preprint

2012

► Micro-macro schemes for kinetic equations including boundary layers (with M. Lemou), SIAM J. Sci. Comp. 34 (2012), no. 6, 134–760. Preprint

► Stable ground states and self-similar blow-up solutions for the gravitational Vlasov-Manev system (with M. Lemou and C. Rigault), SIAM J. Math. Anal. 44 (2012), no. 6, 3928-3968. Preprint

► Orbital stability of spherical galactic models (with M. Lemou and P. Raphaël), Inventiones Math. 187 (2012) 145–194. Preprint

2011

► Second order averaging for the nonlinear Schrödinger equation with strong anisotropic potential (with N. Ben Abdallah, Y. Cai and F. Castella), Kinet. Relat. Models, 4 (2011), no. 4, 831-856. Preprint

► A problem of moment realizability in quantum statistical physics (with O. Pinaud), Kinet. Relat. Models, 4 (2011), no. 4, 1143-1158. Preprint

► A boundary matching  micro/macro decomposition for kinetic equations (with M. Lemou), C. R. Acad. Sci. Paris, Ser. I 349 (2011) 479–484. Preprint

► The Schrödinger Poisson system on the sphere (with P. Gérard), SIAM J. Math. Anal. 43 (2011), no.3, 1232–1268. Preprint

► A new variational approach to the stability of gravitational systems (with M. Lemou and P. Raphaël), Comm. Math. Phys. 302 (2011), 161–224. Preprint

2010

► An inverse problem in quantum statistical physics (with O. Pinaud), J. Stat. Phys. 140 (2010), no. 3, 565–602. Preprint

► Evaporation law in kinetic gravitational systems described by simplified Landau models (with P. Carcaud, P.-H. Chavanis and M. Lemou), Discrete Contin. Dyn. Syst. B 14 (2010), no. 3, 907–934.  Preprint

► Quantum drift-diffusion modeling of spin transport in nanostructures (with L. Barletti), J. Math. Phys. 51 (2010), 053304. Preprint

► Derivation of viscous correction terms for the isothermal quantum Euler model (with S. Brull), Z. Angew. Math. Mech. 90 (2010), no. 3, 219 – 230. Preprint

2009

► A new variational approach to the stability of gravitational systems (with M. Lemou and P. Raphaël), C. R. Math. Acad. Sci. Paris 347  (2009),  no. 15–16, 979-984.

► An effective mass theorem for the bidimensional electron gas in a strong magnetic field (with F. Delebecque-Fendt), Comm. Math. Phys. 292 (2009), no. 3, 829–870. Preprint

► Stable ground states for the relativistic gravitational Vlasov-Poisson system (with M. Lemou and P. Raphaël), Comm. Partial Diff. Eq. 34 (2009), no. 7, 703–721. Preprint

► The strongly confined Schrödinger-Poisson system for the transport of electrons in a nanowire (with N. Ben Abdallah, F. Castella and F. Delebecque-Fendt), SIAM J. Appl. Math. 69 (2009), no. 4, 1162–1173. Preprint

2008

► Stable self-similar blow up dynamics for the three dimensional relativistic gravitational Vlasov-Poisson system (with M. Lemou and P. Raphaël), J. Amer. Math. Soc. 21 (2008), 1019-1063. Preprint

► Time averaging for the strongly confined nonlinear Schrödinger equation, using almost periodicity (with N. Ben Abdallah and F. Castella), J. Diff. Eq. 245, (2008), no 1, 154-200. Preprint

► Structure of the linearized gravitational Vlasov-Poisson system close to a polytropic ground state (with M. Lemou and P. Raphaël), SIAM J. Math. Anal. 39 (2008), no. 6, 1711-1739. Preprint

► On the orbital stability of the ground states and the singularity formation for the gravitational Vlasov Poisson system (with M. Lemou & P. Raphaël), Arch. Ration. Mech. Anal. 189 (2008), no. 3, 425-468. Preprint

2007

► On Quantum Hydrodynamic and Quantum Energy Transport Models (with P. Degond & S. Gallego), Commun. Math. Sci. 5 (2007), no. 4, 887-908. Preprint

► An asymptotic preserving scheme for the Schrödinger equation in the semiclassical limit (with P. Degond & S. Gallego), C. R. Math. Acad. Sci. Paris 345 (2007), no. 9, 531--536. Preprint

► Uniqueness of the critical mass blow up solution for the four dimensional gravitational Vlasov-Poisson system (with M. Lemou and P. Raphaël), Ann. I. H. Poincaré - AN 24 (2007) 825--833. Preprint

► Isothermal quantum hydrodynamics: derivation, asymptotic analysis and simulation (with P. Degond & S. Gallego), SIAM Multiscale Model. Simul.  6 (2007), no. 1, 246-272. Preprint

► An entropic Quantum Drift-Diffusion model for electron transport in resonant tunneling diodes (with P. Degond & S. Gallego), J. Comput. Phys. 221 (2007), 226-249. Preprint

2006

► Quantum hydrodynamic and diffusion models derived from the entropy principle (with P. Degond, S. Gallego and C. Ringhofer), lecture notes of a course by P. Degond at Cetraro, september 2006.

► On quantum extensions to classical Spherical Harmonics Expansion / Fokker-Planck models (with J.-P. Bourgade, P. Degond & C. Ringhofer), J. Math. Phys. 47 (2006), no. 4, 043302. Preprint

► Adiabatic quantum fluid transport models (with N. Ben Abdallah & C. Negulescu), Comm. Math. Sci.  4 (2006), no. 3, 621--650. Preprint

► Diffusive transport of partially quantized particles: Existence, uniqueness and long time behaviour (with N. Ben Abdallah and N. Vauchelet), Proc. of the Edinburgh Math. Soc. 49 (2006), 513--549. Preprint

► Analysis of a quantum subband model for the transport of partially confined charged particles,  Monatsh. Math. 147 (2006), 43-73. Preprint

► Global existence of classical solutions for a Vlasov-Schrödinger-Poisson system (with N. Ben Abdallah & G. Quinio), Indiana Univ. Math. J. 55 (2006), no. 4, 1423--1448. Preprint

2005

► Entropic discretization of a quantum drift-diffusion model (with S. Gallego), SIAM J. Numer. Anal. 43 (2005), no. 5, 1828-1849. Preprint

► Quantum Energy-Transport and Drift-Diffusion models (with P. Degond & C. Ringhofer), J. Stat. Phys. 118 (2005), no. 3-4, 625-665. Preprint

► Quantum hydrodynamic model derived from the entropy principle (with P. Degond & C. Ringhofer), Contemp. Math. 371 (2005), 107-131. Preprint

► Adiabatic approximation of the Schrödinger-Poisson system with a partial confinement (with N. Ben Abdallah & O. Pinaud), SIAM J. Math. Anal. 36 (2005), no. 3, 986-1013. Preprint

► The nonlinear Schrödinger equation with strong anisotropic harmonic potential (with N. Ben Abdallah, C. Schmeiser & R. M. Weishäupl), SIAM J. Math. Anal., 37 (2005), no. 1, 189-199. Preprint

► On an open transient Schrödinger-Poisson system (with N. Ben Abdallah & O. Pinaud), Math. Models Methods Appl. Sci. 15 (2005), 667--688. Preprint

► Semiclassical Analysis of the Schrödinger equation with a partially confining potential (with N. Ben Abdallah), J. Math. Pures Appl. 84 (2005), 580-614. Preprint

► On the orbital stability of the ground states and the singularity formation for the gravitational Vlasov Poisson system (with M. Lemou and P. Raphaël), C. R. Math. Acad. Sci. Paris 341 (2005), no. 4, 269-274. Preprint

2004

► On a Vlasov-Schrödinger-Poisson model (with N. Ben Abdallah), Comm. Partial Differential Equations 29 (2004), no. 1-2, 173-206. Preprint

► A note on the long time behavior for the Drift-Diffusion-Poisson system  (with N. Ben Abdallah & N. Vauchelet), C. R. Acad. Sci. Paris, Ser. I 339 (2004), 683-688. Preprint

► Numerical approximation of a quantum drift-diffusion model (with S. Gallego), C. R. Acad. Sci. Paris, Ser. I 339 (2004), 519-524. Preprint

2002

► Convergence of a numerical scheme for a nonlinear oblique derivative boundary value problem, M2AN: Math. Model Numer. Anal. 36 (2002), no. 6, 1111--1132. Preprint

► Analysis of a Drift-Diffusion-Schrödinger-Poisson model (with N. Ben Abdallah & N. Vauchelet), C. R. Acad. Sci. Paris Sér. I  335 (2002), 1007-1012. Preprint

2001

► On singular perturbation problems for the nonlinear Poisson equation (with A. Ambroso & P.-A. Raviart), Asymptot. Anal. 25 (2001), no. 1, 39-91. Preprint

1999

► A nonlinear oblique derivative boundary value problem for the heat equation. Part 2: Singular selfsimilar solutions (with J.-M. Roquejoffre), Ann. Inst. H. Poincaré Anal. Non Linéaire 16 (1999), no. 6, 691-724. Preprint

► A nonlinear oblique derivative boundary value problem for the heat equation. Part 1: Basic results (with J.-M. Roquejoffre), Ann. Inst. H. Poincaré Anal. Non Linéaire 16 (1999), no. 2, 221-253. Preprint

► The Child-Langmuir asymptotics for magnetized flows (with N. Ben Abdallah & P. Degond), Asymptot. Anal. 20 (1999), no. 2, 97-132. Preprint

1998

► Mathematical models for magnetic insulation (with N. Ben Abdallah & P. Degond), Phys. Plasmas 5 (1998), no. 5, 1522-1534. Preprint

► The Child-Langmuir asymptotics applied to a bipolar diode, Math. Methods Appl. Sci. 21 (1998), no. 12, 1115-1148. Preprint

1995

► Un problème d'évolution avec condition aux limites non linéaire (with J.-M. Roquejoffre), C. R. Acad. Sci. Paris Sér. I Math. 321 (1995), no. 10, 1319-1322.

PhD thesis and Habilitation thesis

► Etude mathématique et analyse asymptotique de modèles quantiques : transport, confinement et collisions, HDR soutenue le 23 novembre 2004 à l'Université Toulouse 3.

► Etudes de problèmes aux limites en Physique du Transport des Particules Chargées, Thèse soutenue le 9 décembre 1997 à l'Ecole polytechnique.

Proceedings

► A Drift-Diffusion subband model for the double-gate MOSFET (with N. Ben Abdallah, P. Pietra & N. Vauchelet), 5th IEEE Conference on Nanotechnology, Nagoya, July 11-15, 2005.

► Numerical discretization of a fully Quantum Drift-Diffusion model (with P. Degond & S. Gallego), Computational Fluid and Solid Mechanics 2005, K. J. Bathe Ed., Elsevier. Proceedings Third MIT Conference on Fluid and Solid Mechanics, June 14-17, 2005.

► Simulation of 2D quantum transport in ultrashort DG-MOSFETs : a fast algorithm using subbands (with N. Ben Abdallah, E. Polizzi, M. Mouis), Simulation of Semiconductor Processes and Devices, 2003. SISPAD 2003. International Conference on 3-5 Sept. 2003, 267-270.