Explicit spectral gap estimates for the linearized Boltzmann and Landau operators with hard potentials

This paper deals with explicit spectral gap estimates for the linearized Boltzmann operator with hard potentials (and hard spheres). We prove that it can be reduced to the Maxwellian case, for which explicit estimates are already known. Such a method is constructive, does not rely on Weyl's Theorem and thus does not require Grad's splitting. The more physical idea of the proof is to use geometrical properties of the whole collision operator. In a second part, we use the fact that the Landau operator can be expressed as the limit of the Boltzmann operator as collisions become grazing in order to deduce explicit spectral gap estimates for the linearized Landau operator with hard potentials

Modelling and numerical simulation of plasma flows with two-fluid mixing

13 pagesFor the modelling of plasma flows at very high temperature such the ones produced by laser beams, one must account for a bi-temperature compressible Euler system coupled to electron thermal conduction and radiative conduction. Moreover, mixing of two different fluids can occur, the two fluids occupying the same volume. For modelling such a phenomenon, instead of dealing with the conservation of mass, momentum and energy for each fluid, we propose here a simplified model which will be easier to implement in a multi-physics Lagrangian 2D code. The principle is to use a closure for expressing the relative velocity between the two fluids with the help of the gradient of the concentration. So, besides the classical system, the final model consists in a non-linear diffusion equation for the concentration and an equation for the mixing kinetic energy (analogous to the one used in turbulence models). We present also first numerical 2D simulations using this model

A model of biospray for the upper airways

We here deal with a model of therapeutic sprays for the upper airways. We aim to model both inhaled and injected sprays. We propose a numerical solver for the kinetic equation which underlies our model, using a particle method. Eventually, we present two numerical tests for simple geometries of the airways

TRY plant trait database – enhanced coverage and open access

Plant traits - the morphological, anatomical, physiological, biochemical and phenological characteristics of plants - determine how plants respond to environmental factors, affect other trophic levels, and influence ecosystem properties and their benefits and detriments to people. Plant trait data thus represent the basis for a vast area of research spanning from evolutionary biology, community and functional ecology, to biodiversity conservation, ecosystem and landscape management, restoration, biogeography and earth system modelling. Since its foundation in 2007, the TRY database of plant traits has grown continuously. It now provides unprecedented data coverage under an open access data policy and is the main plant trait database used by the research community worldwide. Increasingly, the TRY database also supports new frontiers of trait‐based plant research, including the identification of data gaps and the subsequent mobilization or measurement of new data. To support this development, in this article we evaluate the extent of the trait data compiled in TRY and analyse emerging patterns of data coverage and representativeness. Best species coverage is achieved for categorical traits - almost complete coverage for ‘plant growth form’. However, most traits relevant for ecology and vegetation modelling are characterized by continuous intraspecific variation and trait–environmental relationships. These traits have to be measured on individual plants in their respective environment. Despite unprecedented data coverage, we observe a humbling lack of completeness and representativeness of these continuous traits in many aspects. We, therefore, conclude that reducing data gaps and biases in the TRY database remains a key challenge and requires a coordinated approach to data mobilization and trait measurements. This can only be achieved in collaboration with other initiatives

Modélisation, étude mathématique et simulation des collisions

Benoît Desjardins, Examinateur, CEA/DAM Bruno Després, Rapporteur, CEA/DAM & Univ. Paris 6 Laurent Desvillettes, Directeur de Thèse, ENS CachanJean-Michel Ghidaglia, Président du jury, ENS CachanThierry Goudon, Rapporteur, Université Lille 1This thesis deals with the study of complex fluids in Fluid Mechanics, and particularly of sprays (i.e. particles in suspension in a surrounding fluid).The physical quantities are solutions of partial differential equations (PDE). The continuous phase (surrounding fluid) is described by Euler or Navier-Stokes type equations. The dispersed phase is described by a kinetic equation.The first part is devoted to a mathematical study of a coupling between a Vlasov equation, and the isentropic Euler equations, which appears in the modelling of thin sprays. We establish the existence for small time of a regular solution for the Vlasov-isentropic Euler system.Next, we write down the precise kernels corresponding to the complex phenomena of oscillations, breakup and collisions/coalescences.Then, we describe the numerical simulation of a kinetic-fluid coupling in an industrial code (Commissariat à l'Énergie atomique); we especially study the implementation of collisions in the code.A second model of breakup is also presented. This model is more adapted when droplets interact with a pressure wave and have an high Weber number.Finally, we give explicit estimates for the spectral gap of the linearized Boltzmann and Landau operators with hard potentials.Dans ce travail, nous nous intéressons à des problèmes issus de la Mécanique des Fluides et plus particulièrement au cas des aérosols (ou sprays, c'est-à-dire un ensemble de particules en suspension dans un fluide environnant). Les phénomènes physiques mis en jeu sont modélisés par des équations aux dérivées partielles (EDP). La phase continue (fluide environnant) est décrite par des équations issues de la mécanique des milieux continus de type Navier-Stokes ou Euler. La phase dispersée est décrite par une équation cinétique de type Boltzmann.Le premier résultat que nous présentons est consacré à l'étude mathématique d'un couplage entre une équation cinétique de type Vlasov et les équations d'Euler isentropiques. Ces équations modélisent un spray fin. Nous démontrons l'existence en temps petit d'une solution régulière pour le couplage Vlasov-Euler isentropique.Ensuite, nous présentons les équations précises relatives à la modélisation des collisions, coalescences et fragmentations dans un spray.Nous décrivons par la suite la simulation numérique du couplage fluide-cinétique dans un code industriel (Commissariat à l'Énergie Atomique), en particulier l'ajout des phénomènes de collisions.Un deuxième modèle de fragmentation est également présenté. Ce modèle est plus pertinent dans les cas où les particules de la phase dispersée ont un grand nombre de Weber.Enfin, nous présentons un résultat concernant une estimation explicite de trou spectral pour l'opérateur de Boltzmann avec potentiels durs linéarisé, et pour l'opérateur de Landau avec potentiels durs linéarisé

Modélisation, étude mathématique et simulation des collisions dans les fluides complexes

Nous nous intéressons à l'étude des aérosols (ou sprays, i.e. ensemble de particules en suspension dans un fluide environnant). La phase continue est décrite par des équations de type Navier Stokes ou Euler. La phase dispersée est décrite par une équation cinétique de type Boltzmann. Nous démontrons l'existence en temps petit d'une solution régulière pour le couplage Vlasov Euler isentropique. Nous présentons les équations précises relatives à la modélisation des collisions/coalescences/fragmentations dans un spray. Nous décrivons la simulation numérique du couplage fluide cinétique dans un code industriel (Commissariat à l'Énergie Atomique), en particulier l'ajout des phénomènes de collisions. Un deuxième modèle de fragmentation est présenté, plus pertinent dans les cas ou les particules ont un grand nombre de Weber. Enfin, nous présentons un résultat concernant, une estimation explicite de trou spectral pour les opérateurs de Boltzmann et de Landau avec potentiels durs linéarisésThis thesis deals with the study of sprays (i.e. particles in suspension in a surrounding fluid).The physical quantities are solutions of partial differential equations. The continuous phase is described by Euler or Navier Stokes type equations. The dispersed phase is described by a kinetic equation. We establish the existence for small tirne of a regular solution for the Vlasov isentropic Euler system. Next, we write clown the precise kernels corresponding to the complex phenomena of oscillations, breakup and collisions/coalescences. Then, we describe the numerical simulation of a kineticfluid coupling in an industrial code (Commissariat à l'Énergie atomique); we especially study the implementation of collisions in the code. A second model of breakup, more adapted when droplets interact with a pressure wave and have an high Weber number, is also presented. We give explicit estimates for the spectral gap of the linearized Boltzmann and Landau operators with hard potentialsCACHAN-ENS (940162301) / SudocSudocFranceF

Experimental investigation of waverier aerodynamic forces in supersonic and hypersonic slip regime

This paper presents an experimental investigation focused on aerodynamic forces of a waverider in supersonic and hypersonic slip regime. This study is carried out in the laboratory ICARE of CNRS with the wind tunnel named MARHy. This facility recreates supersonic and hypersonic rarefied flows thanks to different nozzles and a pumping unit able to stabilise low free flow pressure inside the testing chamber for several hours. The waverider investigated is a hypersonic glide vehicle which is optimized for a Mach number 10 and an altitude range between 40-50 km. During this experiment the waverider will be investigate for diffferent flows which are far from the initial optimized conditions. The objective is to investigate how viscous effects can impact the aerodynamic of waverider when these vehicles are not optimized for these conditions. Four supersonic rarefied flow allowed to investigate the impact of the variation of Mach number and free flow pressure on the maximum of Lift-to-Drag ratio. This parameter need to be maximise during a flight to travel the highest distance possible. Increase of Mach number and free flow pressure improve aerodynamic performance for supersonic flows. A fifth nozzle is investigated, it is an hypersonic rarefied flow which reproduce an extreme condition where the Mach number is maximum at high altitude so high viscous effects. For the hypersonic nozzle, aerodynamic performances are low and the behave of lift curve is abnormal compare to theory. Finally, maximums of Lift-to-Drag (L/D) ratio are compared to Knudsen number to establish a general trend of the variation of maximum of L/D ratio in function of a rarefaction parameter

ON THE CHAPMAN-ENSKOG ASYMPTOTICS FOR A MIXTURE OF MONOATOMIC AND POLYATOMIC RAREFIED GASES

International audienceIn this paper, we propose a formal derivation of the Chapman-Enskog asymptotics for a mixture of monoatomic and polyatomic gases. We use a direct extension of the model devised in [8, 16] for treating the internal energy with only one continuous parameter. This model is based on the Borgnakke-Larsen procedure [6]. We detail the dissipative terms related to the interaction between the gradients of temperature and the gradients of concentrations (Dufour and Soret effects), and present a complete explicit computation in one case when such a computation is possible, that is when all cross sections in the Boltzmann equation are constants