(joint work with Hersir Sigurgeirsson, SCCM, Stanford)

The aim of this work is to find a mathematical model for the motion of particles in a turbulent velocity field, consistent with experimental observations about particle distributions; and then to use this model to study the effect of particle collisions on particle distributions.

We describe a mathematical model in which the velocity field is modelled as a Gaussian random field, and the particles are assumed to move according to Stokes' law. The velocity field may then be viewed as the solution of a stochastic PDE. An algorithm for the time-integration of the coupled stochastic PDE-ODE is described, including the handling of collisions. Some analysis of the cost of collision detection is also presented.

The model is analyzed in the framework of random dynamical systems and shown to be well-posed; in addition a random attractor is shown to exist. By a combination of numerical simulation, exploiting the existence of a random attractor, and some analysis when a natural scale separations occur, the particle distributions are studied, with and without collisions.