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We give a concise account on the derivation of hybrid quantum-classical models for stationary electron transport in graphene, in presence of sharp potential steps or barriers. A quantum region (an asymptotically thin strip around the potential step or barrier) is coupled through the quantum scattering data to a classical region, where electron transport is described in terms of semiclassical kinetic equations. The diffusive limit of the kinetic model is derived by means of the Hilbert expansion method, which requires the introduction of a boundary layer corrector and the discussion of a system of coupled Milne problems. [ABSTRACT FROM PUBLISHER]

We investigate the particle dynamics in a two-dimensional structure containing two different populations of particles. We consider the semiclassical high temperature limit of the particle gas. The particle motion is described at the hydrodynamic level. We show the existence of a regime, denoted as collimated beam limit, where the problem of the closure of the hydrodynamic moments hierarchy simplifies considerably. Some numerical experiments are presented in which our model is applied to the numerical simulation of a nanometric device based on a graphene sheet. [ABSTRACT FROM AUTHOR]