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Geometric erogdicity of a beadspring pair with stochastic Stokes forcing
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Mattingly, Jonathan C., McKinley, Scott A. and Pillai, Natesh S., 1981 (2009) Geometric erogdicity of a beadspring pair with stochastic Stokes forcing. Working Paper. Coventry: University of Warwick. Centre for Research in Statistical Methodology. (Working papers).

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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 whiteintime uid velocity fields. We follow previous work combining control theoretic arguments, Lyapunov functions, and hypoelliptic 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 LennardJones 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 > 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 
Date:  2009 
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Status:  Not Peer Reviewed 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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URI:  http://wrap.warwick.ac.uk/id/eprint/35202 
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