Existence of dynamical hull functions with two variables for the ac-driven Frenkel-Kontorova model

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:255

Article

Qin, Wen-Xin

关键词: Dynamical hull function;    Frenkel-Kontorova model;    Incommensurate structures;    Mode locking;    Monotone system;   

DOI  :  10.1016/j.jde.2013.07.050

来源: Elsevier

【 摘 要 】

In this paper we are concerned with the dynamics of incommensurate structures in the overdamped limit case of the Frenkel-Kontorova model with periodic driving force. We show in the infinite-dimensional phase space, there exists an ordered circle, on which both the Poincare map and the space shift map induce orientation preserving circle homeomorphisms with rotation numbers rho and omega respectively, the latter characterizing the mean spacing of particles. Furthermore, we prove that the average velocity P for the particle chain with irrational omega exists and (v) over bar = rho/T, where T denotes the period of the driving force, and it is continuous and nondecreasing with respect to F, the average of the external driving force. If the shift map on the invariant ordered circle is ergodic, we demonstrate the existence of two-variable dynamical hull functions and that there are no mode locking behaviors. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free