Accueil Publications Curriculum Vitae Enseignement Liens

 

Florian Méhats

Publications

 

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





A new class of uniformly accurate numerical schemes for highly oscillatory evolution equations (with P. Chartier, M. Lemou and G. Vilmart), to appear in Found. Comput. Math. Preprint





Uniformly accurate methods for Vlasov equations with non-homogeneous strong magnetic field (with P. Chartier, N. Crouseilles, M. Lemou and X. Zhao), to appear in Math. of Comp. Preprint





Stable ground states for the HMF-Poisson model (with M. Fontaine and M. Lemou), Annales de l'Institut Henri Poincaré C, Analyse non linéaire 36 (2019), no. 1, 217-255. Preprint





Uniformly accurate time-splitting methods for the semiclassical linear Schrödinger equation. (with P. Chartier and L. Le Treust), to appear in ESAIM: Mathematical Modelling and Numerical Analysis. 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





Averaging of nonlinear Schrödinger equations with strong magnetic confinement (with R. L. Frank and C. Sparber), Commun. Math. Sci 15 (2017), no. 7, 1933-1945. Preprint




The quantum Liouville-BGK equation and the moment problem (with O. Pinaud), J. Diff. Eq. 263 (2017), no. 7, 3737-3787. 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



A kinetic model for the transport of electrons in a graphen layer (with C. Fermanian Kammerer), J. Comp. Phys. 327 (2016), 450-483. 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, 565602. 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, 907934.  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. 1516, 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, 829870. 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, 703721. 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, 11621173. 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.