KIT

Abstract

I will review some recent works on the derivation and study of kinetic models in a context of material science problems:

(i) the derivation of kinetic equations from a class of particle systems that describes theories for crystalline interfaces. In this line of work we derive the macroscopic limits of theories that describe crystal interfaces starting from models at the nanoscale from the perspective of kinetic theory. (joint work with Dio Margetis, Univ. of Maryland)

(ii) the study of certain kinetic equations that appear in modeling sedimentation for dilute suspensions for rigid rods. Here, we study a class of models introduced by Doi and describing suspensions of rod{like molecules in a solvent uid. Such models couple a microscopic Fokker-Planck type equation for the probability distribution of rod orientations to a macroscopic Stokes ow. We show that steady states can have discontinuous solutions analogous to the ones studied in the context for macroscopic viscoelastic models (e.g. for Oldroyd-B models) and spurt phenomena or shear bands in that context. Also, that the long-time behavior of the sedimentating ow is approximated in a diusive scaling by the Keller-Segel model. (joint work with Ch. Helzel, U. Bochum and F. Otto, Leipzig).