Three results are presented: First, we solve the problem of persistence of dissipation for reduction of kinetic models. Kinetic equations with thermodynamic Lyapunov functions are studied. Uniqueness of the thermodynamic projector is proven: There exists only one projector which transforms any...

In this paper, we introduce and discuss the passage to hy- drodynamic equations for kinetic models of conservative economies, in which the density of wealth depends on additional parameters, like the propensity to invest. As in kinetic theory of rarefied gases, the closure depends on the...

In this paper a convergence result for the BBGKY hierarchy to a Boltzmann-like equation, in the case of anelastic collision, is shown. Boltzmann-like equations are often used to model dissipative dynamical systems such as granular media. This convergence result aims to make a contribution...

We introduce non-perturbative analytical techniques for the derivation of the hydrodynamic manifolds from kinetic equations. The new approach is analogous to the Schwinger–Dyson equation of quantum field theories, and its derivation is demonstrated with the construction of the exact diffusion...

In this article we present a fluid dynamical model for the charge transport in semiconductors based on a recently found asymptotic solution of the semiconductor Boltzmann transport equation (BTE) for strong fields.

The controversial problem of the evolution of an isolated system with an internal adiabatic wall is investigated with the use of a simple microscopic model and the Boltzmann equation. In the case of two infinite volume one-dimensional ideal fluids separated by a piston whose mass is equal to the...

This paper is concerned with generalizations of the known local Lagrange formalism of first order. It will be applied to kinetic equations like the Fokker-Planck equation and the Boltzmann equation. In the latter case nonlocal methods are necessary from the very beginning. Nevertheless, in the...

We present a numerical study of the evolution of a wave packet in a nanoscale MOSFET featuring an ‘atomistic’ channel doping. Our two-dimensional Monte Carlo Wigner simulation results are compared against classical Boltzmann simulation results. We show that the quantum effects due to the...

In Monte Carlo (MC) simulations of semiconductor devices it is necessary to enhance the statistics in sparsely populated regions of interest. In this work the Monte Carlo method for stationary carrier transport, known as the Single-Particle MC method, is considered. It gives a solution to the...

A brief review of the semi-classical Monte Carlo method for semiconductor device simulation is given, covering the standard Monte Carlo algorithms, variance reduction techniques, the self-consistent solution, and the physical semiconductor model including band structure and scattering...