Geometric ergodicity of a bead-spring pair with stochastic Stokes forcing


Journal Article

We consider a simple model for the fluctuating hydrodynamics of a flexible polymer in a 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. In addition we allow the possibility of excluding certain "bad" sets in phase space in which the assumptions are violated but from which the system leaves with a controllable probability. This allows for the treatment of singular drifts, such as those derived from the Lennard-Jones potential, which is a novel feature of this work. © 2012 Elsevier B.V. All rights reserved.

Full Text

Duke Authors

Cited Authors

  • Mattingly, JC; McKinley, SA; Pillai, NS

Published Date

  • December 1, 2012

Published In

Volume / Issue

  • 122 / 12

Start / End Page

  • 3953 - 3979

International Standard Serial Number (ISSN)

  • 0304-4149

Digital Object Identifier (DOI)

  • 10.1016/

Citation Source

  • Scopus