Publications [#213421] of Jonathan C. Mattingly

Papers Published

1. with Mattingly, Jonathan C. and McKinley, Scott A. and Pillai, Natesh S., Geometric ergodicity of a bead--spring pair with stochastic {S}tokes forcing, Stochastic Processes and their Applications, vol. 122 no. 12 (2012), pp. 3953--3979, ISSN 0304-4149 [MR2971721], [0902.4496]
   (last updated on 2012/12/18)

   Abstract:
   We consider a simple model for the fluctuating hydrodynamics of a flexible polymer in dilute solution, demonstrating geometric ergodicity for a pair of particles that interact with each other through a nonlinear spring potential while being advected by a stochastic Stokes fluid velocity field. This is a generalization of previous models which have used linear spring forces as well as white-in-time fluid velocity fields. We follow previous work combining control theoretic arguments, Lyapunov functions, and hypo-elliptic diffusion theory to prove exponential convergence via a Harris chain argument. To this, we add the possibility of excluding certain "bad" sets in phase space in which the assumptions are violated but from which the systems leaves with a controllable probability. This allows for the treatment of singular drifts, such as those derived from the Lennard-Jones potential, which is an novel feature of this work.