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.
|Velázquez, Juan José||IAM||En60email@example.com|