Mattingly, Jonathan C., McKinley, Scott A. and Pillai, Natesh S. (2009) Geometric erogdicity of a bead-spring pair with stochastic Stokes forcing. Working Paper. Coventry: University of Warwick. Centre for Research in Statistical Methodology. Working papers, Vol.2009 (No.13).

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Abstract

We consider a simple model for the
uctuating hydrodynamics of a
exible 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
uid velocity field. This is a generalization of previous models which
have used linear spring forces as well as white-in-time
uid 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.

Item Type:	Working or Discussion Paper (Working Paper)
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Statistics
Library of Congress Subject Headings (LCSH):	Hydrodynamics, Ergodic theory, Stokes flow
Series Name:	Working papers
Publisher:	University of Warwick. Centre for Research in Statistical Methodology
Place of Publication:	Coventry
Official Date:	2009
Dates:	Date Event 2009 Published
Volume:	Vol.2009
Number:	No.13
Number of Pages:	26
Status:	Not Peer Reviewed
Access rights to Published version:	Open Access

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