Abstract not found

the entropy principle

Abstract not found

Abstract not found

In this paper, we propose a model to describe the transport of trapped particles in a surface potential. It is derived from a microscopic (kinetic) description of particle motion in the potential subject to collisions with the solid surface. Under specific hypotheses on the collision operator and adequate time and space rescaling, the kinetic model is formally shown to converge to a diffusion equation in position-energy space known in the literature as the SHE model (for Spherical Harmonics Expansion). The model applies to several practical situations in semiconductor and plasma physics. Key words: Botzmann equation, Diffusion equation, Spherical Harmonics Expansion, Semiconductors, Plasmas, Surface collisions. AMS Subject classification: 35Q20, 76P05, 82A70, 78A35, 41A60 Acknowledgements: The author would express his gratitude to J. P. Boeuf for having suggested this problem and provided encouragements and references. This work has been supported by the TMR network No. ERB FMBX CT97 ...

We first establish a quantum microscopic scattering matrix model in multidimensional wave-vector space, which relates the phase space density of each superlattice cell with that of the neighbouring cells. Then, in the limit of a large number of cells, a SHE (Spherical Harmonics Expansion)-type model of diffusion equations for the particle number density in the position-energy space is obtained. The crucial features of diffusion constants on retaining the memory of the quantum scattering characteristics of the superlattice elementary cell (like e.g. transmission resonances) are shown in order. Two examples are treated with the analytically computation of the diffusion constants. Key words: superlattices, scattering matrix model, diffusion approximation, spherical harmonics expansion, drift-diffusion, energy transport, transmission resonance.

We review a few problems issued from the modeling of the transport of charged particles, subject to the influence of given or self-consistent electric fields. We describe some of the mathematical methods introduced to deal with these problems.

in a surface potential

Summary. This paper reports on recent developments in diffusive limits of kinetic systems. Usually, collision operators in kinetic theory exhibit multiple relaxation scales and before a full relaxation towards a Maxwellian equilibrium has been achieved, the system passes through a series of states that can be described by partial equilibria. The paper describes various models describing the dynamics of these partial equilibria, namely the SHE (Spherical Harmonics Expansion) and the ET (Energy Transport) models. Various examples of applications of these models to plasma problems are presented. Acknowledgements: Work partially supported by the Commissariat l’Energie Atomique and by Centre National d’Etudes Spatiales

Abstract. The quasineutral limit of compressible Navier-Stokes-Poisson system with heat conductivity and general (ill-prepared) initial data is rigorously proved in this paper. It is proved that, as the Debye length tends to zero, the solution of the compressible Navier-Stokes-Poisson system converges strongly to the strong solution of the incompressible Navier-Stokes equations plus a term of fast singular oscillating gradient vector fields. Moreover, if the Debye length, the viscosity coefficients and the heat conductivity coefficient independently go to zero, we obtain the incompressible Euler equations. In both cases the convergence rates are obtained. 1.