Institute for applied mathematics

B08 – Screening in interacting particle systems

In this project we study effective properties of some specific particle systems in which screening effects play a crucial role. By screening we understand the phenomenon that interactions between particles that are in principle long-range are screened by neighbouring particles within a certain effective interaction range. The two examples we consider are a dilute system of solid particles in a Stokes flow and coarsening systems with local interactions respectively.

For particles in a Stokes flow we propose to rigorously prove Einstein's law that gives a formula for the effective viscosity in suspensions. In contrast  to previous work we plan to take in particular the evolution of particles into account. We will also investigate the rigorous derivation of kinetic models and plan to address the so-called Caflish-Luke paradox. For all these tasks it will be essential to understand the screening effect in Stokes flows.

We also plan to study coarsening systems with local interactions that serve as toy-problems for more complex coarsening phenomena such as grain growth. In such systems it does not seem possible to describe the statistics of a large system by an evolution equation for the particle number density deduced via a mean-field type or a kinetic type of argument. Instead we plan to develop methods to characterize initial data for which the system develops a universal long-time behaviour.

Name Institute Location Phone
Niethammer, BarbaraIAMEn60/2.0392216niethammer@iam.uni-bonn.de
Velázquez, Juan JoséIAMEn60/2.02362378velazquez@iam.uni-bonn.de

Contact

Coordinator: Prof. Dr. Stefan Müller
Chief Administrator: sfb1060(at)iam.uni-bonn.de
Imprint

Funded by

since 01.01.2013

Mailing address

SFB 1060
University of Bonn
Endenicher Allee 60
D-53115 Bonn / Germany