IMA Postdoc Seminar (February 3, 2009)

Speaker: Wei Xiong (IMA)

Title: Hydrodynamics of particles immersed in a thermally fluctuating, viscous, incompressible fluid

Abstract: My current work concerns the hydrodynamics of particles immersed in a thermally fluctuating, viscous, incompressible fluid. The governing equations stipulate conservation of momentum in the fluid, conservation of linear and angular momentum of the particle, and no-slip boundary conditions on the boundary of the particle. Is there existence and uniqueness for the solution? What are the limit theorems when time goes to infinity? These problems not only provide more detailed study of physical Brownian motions but also give a testing ground for the techniques in stochastic partial differential equations.

In this talk, I will focus on particles passively advected by the fluid. I will give existence and uniqueness results for passive particles (point particles as well as finite size particles) immersed in the fluid, and I will give limit theorems when the time goes to infinity. Also, I will give numerical simulations of the motion of the particle in the case of deterministic forcing, and a numerical scheme for the stochastic forcing case.