Fractional diffusion limit of a linear Boltzmann model with reflective boundaries in a half-space

We investigate the fractional diffusion limit of a Linear Boltzmann equation with heavy-tailed velocity equilibrium in a half-space with Maxwell boundary conditions. We derive a new confined version of the fractional Laplacian and show uniqueness of weak solutions to the associated non-local diffusion equation. This paper extends previous results of L. Cesbron, A. Mellet and M. Puel [5] on the same kinetic model with diffusive boundary conditions

On the derivation of non-local diffusion equations in confined spaces

The subject of the thesis is the derivation of non-local diffusion equations from kinetic models with heavy-tailed equilibrium in velocity. We are particularly interested in confining the kinetic equations and developing methods that allow us, from the confined kinetic models, to derive confined versions of non-local diffusion equations.European Research Council Grant ERC-2011-StG Mathematical Topics of Kinetic Theor

Dérivation d'équations de diffusion non-locale dans des espaces confinés

The subject of the thesis is the derivation of non-local diffusion equations from kinetic models with heavy-tailed equilibrium in velocity. We are particularly interested in confining the kinetic equations and developing methods that allow us, from the confined kinetic models, to derive confined versions of non-local diffusion equations.Le sujet de cette thèse est la dérivation d'équations de diffusion non-locale à partir de modèles cinétiques dont l'équilibre en vitesse est une distribution à queue lourde. On s'intéressera tout particulièrement au confinement des équations cinétiques et au développement de méthodes qui permettent de dériver, à partir de ces modèles cinétiques confinés, des versions confinées d'équations de diffusion non-locale

On a Vlasov-Fokker-Planck equation for stored electron beams

In this paper we study a self-consistent Vlasov-Fokker-Planck equations which describes the longitudinal dynamics of an electron bunch in the storage ring of a synchrotron particle accelerator. We show existence and uniqueness of global classical solutions under physical hypotheses on the initial data. The proof relies on a mild formulation of the equation and hypoelliptic regularization estimates. We also address the problem of the long-time behavior of solutions. We prove the existence of steady states, called Haissinski solutions, given implicitly by a nonlinear integral equation. When the beam current (i.e. the nonlinearity) is small enough, we show uniqueness of steady state and local asymptotic nonlinear stability of solutions in appropriate weighted Lebesgue spaces. The proof is based on hypocoercivity estimates. Finally, we discuss the physical derivation of the equation and its particular asymmetric interaction potential

Global well-posedness of Vlasov-Poisson-type systems in bounded domains

In this paper we prove global existence of classical solutions to the Vlasov–Poisson and ionic Vlasov–Poisson models in bounded domains. On the boundary, we consider the specular reflection boundary condition for the Vlasov equation and either homogeneous Dirichlet or Neumann conditions for the Poisson equations.ISSN:1948-206XISSN:2157-504

A highly conserved toxo1 haplotype directs resistance to toxoplasmosis and its associated caspase-1 dependent killing of parasite and host macrophage.

International audienceNatural immunity or resistance to pathogens most often relies on the genetic make-up of the host. In a LEW rat model of refractoriness to toxoplasmosis, we previously identified on chromosome 10 the Toxo1 locus that directs toxoplasmosis outcome and controls parasite spreading by a macrophage-dependent mechanism. Now, we narrowed down Toxo1 to a 891 kb interval containing 29 genes syntenic to human 17p13 region. Strikingly, Toxo1 is included in a haplotype block strictly conserved among all refractory rat strains. The sequencing of Toxo1 in nine rat strains (5 refractory and 4 susceptible) revealed resistant-restricted conserved polymorphisms displaying a distribution gradient that peaks at the bottom border of Toxo1, and highlighting the NOD-like receptor, Nlrp1a, as a major candidate. The Nlrp1 inflammasome is known to trigger, upon pathogen intracellular sensing, pyroptosis programmed-cell death involving caspase-1 activation and cleavage of IL-1β. Functional studies demonstrated that the Toxo1-dependent refractoriness in vivo correlated with both the ability of macrophages to restrict T. gondii growth and a T. gondii-induced death of intracellular parasites and its host macrophages. The parasite-induced cell death of infected macrophages bearing the LEW-Toxo1 alleles was found to exhibit pyroptosis-like features with ROS production, the activation of caspase-1 and IL1-β secretion. The pharmacological inactivation of caspase-1 using YVAD and Z-VAD inhibitors prevented the death of both intravacuolar parasites and host non-permissive macrophages but failed to restore parasite proliferation. These findings demonstrated that the Toxo1-dependent response of rat macrophages to T. gondii infection may trigger two pathways leading to the control of parasite proliferation and the death of parasites and host macrophages. The NOD-like receptor NLRP1a/Caspase-1 pathway is the best candidate to mediate the parasite-induced cell death. These data represent new insights towards the identification of a major pathway of innate resistance to toxoplasmosis and the prediction of individual resistance