Title: Effective Diffusive Behavior for Passive Tracers and Inertial  
Particles: Homogenization and Numerical Algorithms

Abstract:  In this talk we will present results concerning the large  
scale long time behaviour of particles moving in a periodic (random) 
velocity field subject to molecular diffusion. The particle can be 
considered massless (passive tracer) or  not (inertial particle). In 
both cases the large scale long time behavior of the particle is 
described
by a Brownian motion with an effective diffusivity matrix K. 
We then  present some numerical algorithms concerning the calculation of 
the effective diffusivity in the limit of vanishing molecular diffusion 
(stochastic geometric integrators).  
We end the talk by studying the case where the driving noise is no 
longer white but colored and study the effects of this change to the 
effective diffusivity matrix.