Approach to Equilibrium of a Body Colliding Specularly and Diffusely with a Sea of Particles

Abstract

We consider a rigid body acted upon by two forces, a constant force and the collective force of interaction with a continuum of particles. We assume that some of the particles that collide with the body reflect elastically (specularly), while others reflect probabilistically with some probability distribution K. We find that the rate of approach of the body to equilibrium is O(t-3-p) in three dimensions where p can take any value in (0, 2], depending on K. © 2013 Springer-Verlag Berlin Heidelberg.