Phase-space approach to dynamical density functional theory
We consider a system of interacting particles subjected to Langevin inertial dynamics and derive the governing time-dependent equation for the one-body density. We show that, after suitable truncations of the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy, and a multiple time scale analysis, we obtain a self-consistent equation involving only the one-body density. This study extends to arbitrary dimensions previous work on a one-dimensional fluid and highlights the subtelties of kinetic theory in the derivation of dynamical density functional theory.
Publisher Summary With respect to the quality problems of groundwater, the streamlines and travel times in a flow region should be assessed. Especially in flow problems in the vertical plane, that is, underneath a waste disposal, the presence of inhomogeneities, such as clay layers, is very important. This chapter presents a method for the calculation of the stream function all through the flow domain based upon the finite-element method. In this flow domain, which is divided in elements with various transmissivities, internal sources or sinks may be present. Also, the porous medium can be anisotropic.