کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
1155681 | 958757 | 2012 | 27 صفحه PDF | دانلود رایگان |
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.
Journal: Stochastic Processes and their Applications - Volume 122, Issue 12, December 2012, Pages 3953–3979