Abstract. This paper is devoted to the analysis of a numerical scheme for the coagulation and fragmentation equation. A time explicit finite volume scheme is developed, based on a conservative formulation of the equation. It is shown to converge under a stability condition on the time step, while a first order rate of convergence is established and an explicit error estimate is given. Finally, several numerical simulations are performed to investigate the gelation phenomenon and the long time behavior of the solution.

By following a strategy introduced in previous works, quantum extensions of the classical electron-phonon scattering operator are deduced from first principles. These quantum collision operators satisfy a quantum H-theorem and relax towards quantum equilibria. Then, under an assumption of dominant elastic interactions, a hierarchy of quantum spherical harmonic expansion (SHE) models is derived by a diffusive approximation of collisional Wigner equations. These models are proven entropic and their expansions into powers of the reduced Planck constant ℏ are calculated, leading to ℏ2 corrections for the classical SHE model.

Dans une approche clinique, instrumentée par la théorie anthropologique du didactique, nous étudions l’appropriation différenciée d’un outil d’analyse des enseignements par les membres d’un réseau de conseillers pédagogiques (CP) de l’enseignement supérieur1. Nous construisons un modèle praxéologique de référence de cet outil, au moyen duquel nous analysons certaines de ses mises en œuvre « non conformes ». L’analyse permet de supposer que l’existence d’intérêts divergents des différents conseillers pédagogiques, liés à des positions institutionnelles différentes, est l’un des facteurs explicatifs de l’apparition de différences dans l’appropriation de l’outil d’analyse. Ceci illustre le fait que la construction de la profession de CP est certainement liée à la production d’un intérêt spécifique de CP.

SUMMARYIn this paper, we give the rigorous derivation of a di usion model for semiconductor devices, the starting point being a microscopic description of electron transport by means of a kinetic equation of Boltzmann type. The limit of a small mean free path at a large time leads to a di usion equation of 'SHE' type (spherical harmonics expansion). We deal with a collision operator that models interactions between electron and phonons. This induces a peculiar form for the di usion tensor: electron-phonon collisions happen to be discontinuous in energy and inelastic, and, as a consequence, the di usion tensor appears as an inÿnite dimensional matrix.