Geometric ergodicity of a bead-spring pair with stochastic Stokes forcing
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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.
Published Version (Please cite this version)10.1016/j.spa.2012.07.003
Publication InfoMattingly, Jonathan Christopher; McKinley, Scott A; & Pillai, NS (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 http://hdl.handle.net/10161/9524.
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James B. Duke Professor
Jonathan Christopher Mattingly grew up in Charlotte, NC where he attended Irwin Ave elementary and Charlotte Country Day. He graduated from the NC School of Science and Mathematics and received a BS is Applied Mathematics with a concentration in physics from Yale University. After two years abroad with a year spent at ENS Lyon studying nonlinear and statistical physics on a Rotary Fellowship, he returned to the US to attend Princeton University where he obtained a PhD in Applied and