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

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2012-12-01

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Abstract

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.

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10.1016/j.spa.2012.07.003

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Mattingly, JC, SA McKinley and NS Pillai (2012). Geometric ergodicity of a bead-spring pair with stochastic Stokes forcing. Stochastic Processes and their Applications, 122(12). pp. 3953–3979. 10.1016/j.spa.2012.07.003 Retrieved from https://hdl.handle.net/10161/9524.

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