The modelling and the numerical resolution of the electrical charging of a spacecraft in interaction with the Earth magnetosphere is considered. It involves the Vlasov-Poisson system, endowed with non standard boundary conditions. We discuss the pros and cons of several numerical methods for solving this system, using as benchmark a simple 1D model which exhibits the main difficulties of the original models.
We propose a hybrid classical-quantum model to study the motion of electrons in ultra-scaled confined nanostructures. The transport of charged particles, considered as one dimensional, is described by a quantum effective mass model in the active zone coupled directly to a drift-diffusion problem in the rest of the device. We explain how this hybrid model takes into account the peculiarities due to the strong confinement and we present numerical simulations for a simplified carbon nanotube.
In this work, we consider the computation of the boundary conditions for the linearized Euler–Poisson derived from the BGK kinetic model in the small mean free path regime. Boundary layers are generated from the fact that the incoming kinetic flux might be far from the thermodynamical equilibrium. In [2], the authors propose a method to compute numerically the boundary conditions in the hydrodynamic limit relying on an analysis of the boundary layers....
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