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This paper is devoted to the formulation and numerical solution by Monte Carlo (MC) methods of an optimal control problem governed by the linear space-homogeneous Keilson-Storer (KS) master equation. The KS master equation is a representative model of the class of linear Boltzmann equations with many applications ranging from spectroscopy to transport theory. The purpose of the optimal control in the collision kernel of this model is to drive an ensemble of particles to acquire a desired mean velocity and to achieve a desired final velocity configuration. For this purpose, a KS optimality system characterizing the solution of the proposed optimal control problem is derived and used to construct a gradient-based optimization strategy in the framework of MC methods. This task requires to accommodate the resulting adjoint KS model in a form that is consistent with the kinetic formulation. Results of numerical experiments successfully validate the proposed control framework. [ABSTRACT FROM AUTHOR]

Graphene has attracted the attention of several researchers because of its peculiar features. In particular, the study of charge transport in graphene is challenging for future electron devices. Usually, the physical description of electron flow in graphene given by the semiclassical Boltzmann equation is considered to be a good one. However, due to the computational complexity, its use in simulation tools is not practical and, as already done for traditional semiconductors such as Si or GaAs, simpler models are warranted. Here we will assess the validity of a class of hydrodynamical models based on the maximum entropy principle (MEP), by comparing, in the case of suspended monolayer graphene, the direct solution of the semiclassical Boltzmann equation for electrons, obtained by employing a discontinuous Galerkin approach, with the MEP distribution function. A reasonable agreement is observed. [ABSTRACT FROM AUTHOR]