Kramers escape rate in nonlinear diffusive media.
In this paper, we study nonlinear Kramers problem by investigating overdamped systems ruled by the one-dimensional nonlinear Fokker-Planck equation. We obtain an analytic expression for the Kramers escape rate under quasistationary conditions by employing a metastable potential and its predictions are in excellent agreement with numerical simulations. The results exhibit the anomalies due to the nonlinearity in W that the escape rate grows with D and drops as mu becomes large at a fixed D. Indeed, particles in the subdiffusive media (mu>1) can escape over the barrier only when D is above a critical value, while this confinement does not exist in the superdiffusive media (mu<1).
JiangLin
Zhao
Z
Institute of Mechanics (IMECH), Chinese Academy of Sciences, Beijing, 100080, China. ydqc@eyou.com
Bao
Jing-Dong
JD
Wenping
Gong
G
D000465:Algorithms; D002627:Chemistry, Physical / Q000379:methods*; D004058:Diffusion; D004735:Energy Transfer; D008956:Models, Chemical; D008958:Models, Molecular; D015233:Models, Statistical; D008962:Models, Theoretical; D017711:Nonlinear Dynamics; D013269:Stochastic Processes; D013816:Thermodynamics; D013997:Time Factors