Sur un modèle de type Borgnakke—Larsen conduisant à des lois d'énergie non linéaires en température pour les gaz parfaits polyatomiques
Formal passage from kinetic theory to incompressible Navier–Stokes equations for a mixture of gases
We present in this paper the formal passage from a kinetic model to the incompressible Navier−Stokes equations for a mixture of monoatomic gases with different masses. The starting point of this derivation is the collection of coupled Boltzmann equations for the mixture of gases. The diffusion coefficients for the concentrations of the species, as well as the ones appearing in the equations for velocity and temperature, are explicitly computed under the Maxwell molecule assumption in terms of the...
Characterization of collision kernels
In this paper we show how abstract physical requirements are enough to characterize the classical collision kernels appearing in kinetic equations. In particular Boltzmann and Landau kernels are derived.
About estimates for the spatially homogeneous Boltzmann equation
A proof of the smoothing properties of the positive part of Boltzmann's kernel.
We give two direct proofs of Sobolev estimates for the positive part of Boltzmann's kernel. The first deals with a cross section with separated variables; no derivative is needed in this case. The second is concerned with a general cross section having one derivative in the angular variable.
Characterization of collision kernels
In this paper we show how abstract physical requirements are enough to characterize the classical collision kernels appearing in kinetic equations. In particular Boltzmann and Landau kernels are derived.
Derivation of a homogenized two-temperature model from the heat equation
This work studies the heat equation in a two-phase material with spherical inclusions. Under some appropriate scaling on the size, volume fraction and heat capacity of the inclusions, we derive a coupled system of partial differential equations governing the evolution of the temperature of each phase at a macroscopic level of description. The coupling terms describing the exchange of heat between the phases are obtained by using homogenization techniques originating from [D. Cioranescu, F. Murat,...
Exponential convergence to equilibrium via Lyapounov functionals for reaction-diffusion equations arising from non reversible chemical kinetics
We show that the entropy method, that has been used successfully in order to prove exponential convergence towards equilibrium with explicit constants in many contexts, among which reaction-diffusion systems coming out of reversible chemistry, can also be used when one considers a reaction-diffusion system corresponding to an irreversible mechanism of dissociation/recombination, for which no natural entropy is available.
A vectorizable simulation method for the Boltzmann equation
Exponential convergence to equilibrium Lyapounov functionals for reaction-diffusion equations arising from non reversible chemical kinetics
We show that the entropy method, that has been used successfully in order to prove exponential convergence towards equilibrium with explicit constants in many contexts, among which reaction-diffusion systems coming out of reversible chemistry, can also be used when one considers a reaction-diffusion system corresponding to an irreversible mechanism of dissociation/recombination, for which no natural entropy is available.
A Coherent Derivation of an Average Ion Model Including the Evolution of Correlations Between Different Shells
We propose in this short note a method enabling to write in a systematic way a set of refined equations for average ion models in which correlations between populations are taken into account, starting from a microscopic model for the evolution of the electronic configuration probabilities. Numerical simulations illustrating the improvements with respect to standard average ion models are presented at the end of the paper.
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