Publications

  1. Continuum dynamics of the intention field under weakly cohesive social interactions, Pierre Degond, Jian-Guo Liu and Thomas Tardiveau, Math. Models Methods Appl. Sci. accepted, (2016). Arxiv version.
  2. A new flocking model through body attitude coordination (with Pierre Degond, Imperial College London, and Amic Frouvelle, Universite Paris Dauphine). Math. Models Methods Appl. Sci., accepted, (2016). Arxiv version.
  3. Isotropic Wave Turbulence with simplified kernels: existence, uniqueness and mean-field limit for a class of instantaneous coagulation-fragmentation processes, 2015. Arxiv version.
    • The isotropic 4-wave kinetic equation is considered in its weak formulation us- ing model (simplified) homogeneous kernels. Existence and uniqueness of solutions is proven in a particular setting where the kernels have a rate of growth at most linear. We also consider finite stochastic particle systems undergoing instantaneous coagulation- fragmentation phenomena and give conditions in which this system approximates the solution of the equation (mean-field limit).
  4. Anomalous transport in FPU-β chains (with Antoine Mellet) at the Journal of Statistical Physics, 2015. Arxiv version, journal version.
    • Abstract: This paper is devoted to the derivation of a macroscopic fractional diffusion equation describing heat transport in an anharmonic chain. More precisely, we study here the so-called FPU- β chain, which is a very simple model for a one-dimensional crystal in which atoms are coupled to their nearest neighbors by a harmonic potential, weakly perturbed by a quartic potential. The starting point of our mathematical analysis is a kinetic equation: Lattice vibrations, responsible for heat transport, are modeled by an interacting gas of phonons whose evolution is described by the Boltzmann phonon equation. Our main result is the rigorous derivation of an anomalous diffusion equation starting from the linearized Boltzmann phonon equation.
  5.  Kinetic derivation of fractional Stokes and Stokes-Fourier systems (with Sabine Hittmeir), Kinetic and Related models, 2015. Arxiv version, journal version.
    • Abstract: In recent works it has been demonstrated that using an appropriate rescaling, linear Boltzmann-type equations give rise to a scalar fractional diffusion equation in the limit of a small mean free path. The equilibrium distributions are typically heavy-tailed distributions, but also classical Gaussian equilibrium distributions allow for this phenomena if combined with a degenerate collision frequency for small velocities. This work aims to an extension in the sense that a linear BGK-type equation conserving not only mass, but also momentum and energy, for both mentioned regimes of equilibrium distributions is considered. In the hydrodynamic limit we obtain a fractional diffusion equation for the temperature and density making use of the Boussinesq relation and we also demonstrate that with the same rescaling fractional diffusion cannot be derived additionally for the momentum. But considering the case of conservation of mass and momentum only, we do obtain the incompressible Stokes equation with fractional diffusion in the hydrodynamic limit for heavy-tailed equilibria.
    • Slides presentation
  6. From Boltzmann to incompressible Navier-Stokes in Sobolev spaces with polynomial weight (with Marc Briant and Clément Mouhot). Arxiv version.
    • Abstract: We study the Boltzmann equation on the d-dimensional torus in a perturbative setting around a global equilibrium under the Navier-Stokes linearisation. We use a recent functional analysis breakthrough to prove that the linear part of the equation generates a C0-semigroup with exponential decay in Lebesgue and Sobolev spaces with polynomial weight, independently on the Knudsen number. Finally we show a Cauchy theory and an exponential decay for the perturbed Boltzmann equation, uniformly in the Knudsen number, in Sobolev spaces with polynomial weight. The polynomial weight is almost optimal and furthermore, this result only requires derivatives in the space variable and allows to connect to solutions to the incompressible Navier-Stokes equations in these spaces.
  7.  An iterative algorithm for homology computation on simplicial shapes.Dobrina Boltcheva; David Canino; Sara Merino Aceituno; Jean-Claude Léon; Leila De Floriani; Franck Hétroy. Computer-Aided Design, Elsevier, 2011, 43 (11), pp. 1457-1467. Journal version.