### Kinetic models in material science

**Tzavaras, A E ***(Maryland)*

Tuesday 07 September 2010, 15:30-16:10

Seminar Room 1, Newton Institute

#### 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).

#### Presentation

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