Since Stratton published his famous paper four decades ago, various transport models have
been proposed which account for the average carrier energy or temperature in one way or …

This paper proposes a survey and critical analysis focused on a variety of chemotaxis
models in biology, namely the classical Keller–Segel model and its subsequent …

The gas-kinetic numerical algorithm solving the Boltzmann model equation is extended and
developed to study the three-dimensional hypersonic flows of spacecraft re-entry into the …

In this paper we develop a deterministic high order accurate finite-difference WENO solver to
the solution of the 1-D Boltzmann–Poisson system for semiconductor devices. We follow the …

The Boltzmann equation for transport in semiconductors is projected onto spherical
harmonics in such a way that the resultant balance equations for the coefficients of the …

Kinetic equations contain uncertainties in their collision kernels or scattering coefficients,
initial or boundary data, forcing terms, geometry, etc. Quantifying the uncertainties in kinetic …

The numerical properties of a deterministic Boltzmann equation solver based on a spherical
harmonics expansion of the distribution function are analyzed and improved. A fully coupled …

Rapid plasma formation and evolution during high-power microwave (HPM) air breakdown
in an HPM device produce a macroscopic plasma shield to the microwave transmission …

Radiative heat transfer equations including heat conduction are considered in the small
mean free path limit. Rigorous results on the asymptotic procedure leading to the equilibrium …

In this paper we derive diffusive relaxation schemes for the linear semiconductor Boltzmann
equation that work in both the kinetic and diffusive regimes. Similar to our earlier approach …