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

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Mattingly, Jonathan C. ; McKinley, Scott A. ; Pillai, Natesh S. (2009)
  • Publisher: University of Warwick. Centre for Research in Statistical Methodology
  • Subject: QA

We consider a simple model for the \ud uctuating hydrodynamics of a \ud exible polymer\ud 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\ud stochastic Stokes \ud uid velocity field. This is a generalization of previous models which\ud have used linear spring forces as well as white-in-time \ud uid velocity fields.\ud We follow previous work combining control theoretic arguments, Lyapunov functions, and hypo-elliptic diffusion theory to prove exponential convergence via a Harris\ud chain argument. To this, we add the possibility of excluding certain "bad" sets in phase\ud space in which the assumptions are violated but from which the systems leaves with a\ud controllable probability. This allows for the treatment of singular drifts, such as those\ud derived from the Lennard-Jones potential, which is an novel feature of this work.
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