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Geometric erogdicity of a bead-spring pair with stochastic Stokes forcing
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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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Official URL: http://www2.warwick.ac.uk/fac/sci/statistics/crism...
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: |
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| Volume: | Vol.2009 | ||||
| Number: | No.13 | ||||
| Number of Pages: | 26 | ||||
| Status: | Not Peer Reviewed | ||||
| Access rights to Published version: | Open Access (Creative Commons) | ||||
| Date of first compliant deposit: | 1 August 2016 | ||||
| Date of first compliant Open Access: | 1 August 2016 |
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