Geometric erogdicity of a bead-spring pair with stochastic Stokes forcing
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...
We consider a simple model for the
uctuating hydrodynamics of a
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
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 > 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|
|Number of Pages:||26|
|Status:||Not Peer Reviewed|
|Access rights to Published version:||Open Access|
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