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Nonergodicity, accelerator modes, and asymptotic quadratic-in-time diffusion in a class of volume-preserving maps

Mezić, Igor and Wiggins, Stephen (1995) Nonergodicity, accelerator modes, and asymptotic quadratic-in-time diffusion in a class of volume-preserving maps. Physical Review E, 52 (3). pp. 3215-3217. ISSN 1063-651X. http://resolver.caltech.edu/CaltechAUTHORS:MEZpre95

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Abstract

Using an elementary application of Birkhoff’s ergodic theorem, we give necessary and sufficient conditions for the existence of asymptotically n^2 diffusion (where n is an integer representing discrete time in the angle variables in a class of volume-preserving twist maps. We show that nonergodicity is the dynamical mechanism giving rise to this behavior. The influence of accelerator modes on diffusion is described. We discuss how additive noise changes the diffusive behavior and we investigate the effective-diffusivity dependence on bare diffusivity and accelerator modes. In particular, we find that the dependence of the effective-diffusivity coefficient on bare diffusivity is universal for small values of bare-diffusivity coefficient σ if asymptotic n^2 diffusion is present in the σ=0 case.


Item Type:Article
Additional Information:©1995 The American Physical Society Received 13 February 1995 This work was supported by the National Science Foundation, NSF ONR Grant No. N00014-89-J-3023 and AFOSR Grant No. AFOSR910241.
Record Number:CaltechAUTHORS:MEZpre95
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:MEZpre95
Alternative URL:http://dx.doi.org/10.1103/PhysRevE.52.3215
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:6432
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:08 Dec 2006
Last Modified:26 Dec 2012 09:21

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