71 citations · 176 across the 14 of their papers we have counts for
18 papers
Machine Learning Methods for Autonomous Ordinary Differential Equations
Maxime Bouchereau, Philippe Chartier, Mohammed Lemou +1
Ordinary Differential Equations are generally too complex to be solved analytically. Approximations thereof can be obtained by general purpose numerical methods. However, even thou…
Uniformly accurate schemes for drift--oscillatory stochastic differential equations
Ibrahim Almuslimani, Philippe Chartier, Mohammed Lemou +1
In this work, we adapt the {\em micro-macro} methodology to stochastic differential equations for the purpose of numerically solving oscillatory evolution equations. The models we…
Symplectic Learning for Hamiltonian Neural Networks
Marco David, Florian Méhats
Machine learning methods are widely used in the natural sciences to model and predict physical systems from observation data. Yet, they are often used as poorly understood "black b…
Nonlinear instability of inhomogeneous steady states solutions to the HMF Model
Mohammed Lemou, Ana Maria Luz, Florian Méhats
In this work we prove the nonlinear instability of inhomogeneous steady states solutions to the Hamiltonian Mean Field (HMF) model. We first study the linear instability of this mo…
Stable Ground States for the HMF Poisson Model
Marine Fontaine, Mohammed Lemou, Florian Méhats
In this paper we prove the nonlinear orbital stability of a large class of steady states solutions to the Hamiltonian Mean Field (HMF) system with a Poisson interaction potential.…
Averaging of nonlinear Schrödinger equations with strong magnetic confinement
Rupert L. Frank, Florian Méhats, Christof Sparber
We consider the dynamics of nonlinear Schrödinger equations with strong constant magnetic fields. In an asymptotic scaling limit the system exhibits a purely magnetic confinement,…
Averaging of highly-oscillatory transport equations
Philippe Chartier, Nicolas Crouseilles, Mohammed Lemou
In this paper, we develop a new strategy aimed at obtaining high-order asymptotic models for transport equations with highly-oscillatory solutions. The technique relies upon recent…
Uniformly accurate time-splitting methods for the semiclassical Schrödinger equation Part 1 : Construction of the schemes and simulations
Philippe Chartier, Loïc Le Treust, Florian Méhats
This article is devoted to the construction of new numerical methods for the semiclassical Schrödinger equation. A phase-amplitude reformulation of the equation is described where…
Uniformly accurate numerical schemes for the nonlinear Dirac equation in the nonrelativistic limit regime
Mohammed Lemou, Florian Méhats, Xiaofei Zhao
We apply the two-scale formulation approach to propose uniformly accurate (UA) schemes for solving the nonlinear Dirac equation in the nonrelativistic limit regime. The nonlinear D…
Uniformly accurate time-splitting methods for the semiclassical linear Schr{ö}dinger equation
Philippe Chartier, Loïc Le Treust, Florian Méhats
This article is devoted to the construction of numerical methods which remain insensitive to the smallness of the semiclassical parameter for the linear Schr{ö}dinger equation in t…
The quantum Liouville-BGK equation and the moment problem
Florian Méhats, Olivier Pinaud
This work is devoted to the analysis of the quantum Liouville-BGK equation. This equation arises in the work of Degond and Ringhofer on the derivation of quantum hydrodynamical mod…
Dimension reduction for dipolar Bose-Einstein condensates in the strong interaction regime
Weizhu Bao, Loïc Le Treust, Florian Méhats
We study dimension reduction for the three-dimensional Gross-Pitaevskii equation with a long-range and anisotropic dipole-dipole interaction modeling dipolar Bose-Einstein condensa…
The fermionic King model
Pierre-Henri Chavanis, Mohammed Lemou, Florian Méhats
We study the fermionic King model which may provide a relevant model of dark matter halos. The exclusion constraint can be due to quantum mechanics (for fermions such as massive ne…
Models of dark matter halos based on statistical mechanics: II. The fermionic King model
Pierre-Henri Chavanis, Mohammed Lemou, Florian Méhats
We discuss the nature of phase transitions in the fermionic King model which describes tidally truncated quantum self-gravitating systems. This distribution function takes into acc…
Models of dark matter halos based on statistical mechanics: I. The classical King model
Pierre-Henri Chavanis, Mohammed Lemou, Florian Méhats
We consider the possibility that dark matter halos are described by the Fermi-Dirac distribution at finite temperature. This is the case if dark matter is a self-gravitating quantu…
Solving highly-oscillatory NLS with SAM: numerical efficiency and geometric properties
Philippe Chartier, Norbert J. Mauser, Florian Méhats +1
In this paper, we present the Stroboscopic Averaging Method (SAM), recently introduced in [7,8,10,12], which aims at numerically solving highly-oscillatory differential equations.…
Analysis of models for quantum transport of electrons in graphene layers
Raymond El Hajj, Florian Méhats
We present and analyze two mathematical models for the self consistent quantum transport of electrons in a graphene layer. We treat two situations. First, when the particles can mo…
A boundary matching micro/macro decomposition for kinetic equations
Mohammed Lemou, Florian Méhats
We introduce a new micro/macro decomposition of collisional kinetic equations which naturally incorporates the exact space boundary conditions. The idea is to write the distributio…