The motivation of the current paper is to provide a detailed review of crucial topics in micro-
and nanoscale gas flows, ie, velocity slip and temperature jump phenomena and their …

ABSTRACT We review Monte Carlo methods for solving the Boltzmann equation for
applications to small-scale transport processes, with particular emphasis on nanoscale heat …

We present an efficient particle method for solving the Boltzmann equation. The key
ingredients of this work are the variance reduction ideas presented in Baker and …

Due to the rapid advances in micro-electro-mechanical systems (MEMS), the study of
microflows becomes increasingly important. Currently, the molecular-based simulation …

The flow of a rarefied gas in a rectangular enclosure due to the motion of the upper wall is
solved over the whole range of the Knudsen number. The formulation is based on the two …

The formation and propagation of singularities for the Boltzmann equation in bounded
domains has been an important question in numerical studies as well as in theoretical …

Evaporative mass flux is governed by the interfacial state of liquid and vapor phases. For
closely similar pressures and mass fluxes of liquid water into its own vapor, the discontinuity …

We present a deviational Monte Carlo method for solving the Boltzmann-Peierls equation
with ab initio 3-phonon scattering, for temporally and spatially dependent thermal transport …

Evaporation is a physical phenomenon with fundamental significance to both nature and
technology ranging from plant transpiration to DNA engineering. Various analytical and …

A memory reduction technique is proposed for solving stationary kinetic model equations. As
implied by an integral solution of the stationary kinetic equation, a velocity distribution …