When characteristic transport lengthscales approach the molecular mean free path associated with the particular transport carrier, macroscopic closures (e.g. Fourier's Law) and associated macroscopic descriptions fail. In these regimes, kinetic theory approaches, for example, the Boltzmann transport equation, may be used. In this group we use theoretical approaches including simulation, to study transport at small scales for a number of applications. Recent work has focused on nanoscale gas transport, as well as nanoscale solid-state heat transfer as mediated by phonons.

*Figure Caption: The figure shows cutout of a three-dimensional simulation of phonon-mediated heat transfer in porous silicon. Arrows show the heat flux vector field.*

The complexity associated with Boltzmann equation makes efficient numerical solution methods very important, while the high dimensionality associated with the carrier distribution function as well as the importance of advection as the ballistic regime is approached, make particle simulation methods the tool of choice. Our group focuses on the development of efficient simulation methods for addressing current and future simulation needs in the area of nanoscale particle transport.