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Title: Self-similar transport in incomplete chaos

Abstract

Particle chaotic dynamics along a stochastic web is studied for three-dimensional Hamiltonian flow with hexagonal symmetry in a plane. Two different classes of dynamical motion, obtained by different values of a control parameter, and corresponding to normal and anomalous diffusion, have been considered and compared. It is shown that the anomalous transport can be characterized by powerlike wings of the distribution function of displacement, flights which are similar to Levy flights, approximate trappings of orbits near the boundary layer of islands, and anomalous behavior of the moments of a distribution function considered as a function of the number of the moment. The main result is related to the self-similar properties of different topological and dynamical characteristics of the particle motion. This self-similarity appears in the Weierstrass-like random-walk process that is responsible for the anomalous transport exponent in the mean-moment dependence on [ital t]. This exponent can be expressed as a ratio of fractal dimensions of space and time sets in the Weierstrass-like process. An explicit form for the expression of the anomalous transport exponent through the local topological properties of orbits has been given.

Authors:
 [1]; ;  [2]
  1. Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, New York 10012 (United States) Physics Department, New York University, 4 Washington Place, New York, New York 10003 (United States)
  2. Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, New York 10012 (United States)
Publication Date:
OSTI Identifier:
6278306
DOE Contract Number:  
FG02-86ER53223; FG02-92ER54184
Resource Type:
Journal Article
Journal Name:
Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; (United States)
Additional Journal Information:
Journal Volume: 48:3; Journal ID: ISSN 1063-651X
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; STOCHASTIC PROCESSES; DIFFUSION; DISTRIBUTION FUNCTIONS; FLUID FLOW; FRACTALS; HEXAGONAL CONFIGURATION; THREE-DIMENSIONAL CALCULATIONS; CONFIGURATION; FUNCTIONS; 661300* - Other Aspects of Physical Science- (1992-)

Citation Formats

Zaslavsky, G M, Stevens, D, and Weitzner, H. Self-similar transport in incomplete chaos. United States: N. p., 1993. Web. doi:10.1103/PhysRevE.48.1683.
Zaslavsky, G M, Stevens, D, & Weitzner, H. Self-similar transport in incomplete chaos. United States. doi:10.1103/PhysRevE.48.1683.
Zaslavsky, G M, Stevens, D, and Weitzner, H. Wed . "Self-similar transport in incomplete chaos". United States. doi:10.1103/PhysRevE.48.1683.
@article{osti_6278306,
title = {Self-similar transport in incomplete chaos},
author = {Zaslavsky, G M and Stevens, D and Weitzner, H},
abstractNote = {Particle chaotic dynamics along a stochastic web is studied for three-dimensional Hamiltonian flow with hexagonal symmetry in a plane. Two different classes of dynamical motion, obtained by different values of a control parameter, and corresponding to normal and anomalous diffusion, have been considered and compared. It is shown that the anomalous transport can be characterized by powerlike wings of the distribution function of displacement, flights which are similar to Levy flights, approximate trappings of orbits near the boundary layer of islands, and anomalous behavior of the moments of a distribution function considered as a function of the number of the moment. The main result is related to the self-similar properties of different topological and dynamical characteristics of the particle motion. This self-similarity appears in the Weierstrass-like random-walk process that is responsible for the anomalous transport exponent in the mean-moment dependence on [ital t]. This exponent can be expressed as a ratio of fractal dimensions of space and time sets in the Weierstrass-like process. An explicit form for the expression of the anomalous transport exponent through the local topological properties of orbits has been given.},
doi = {10.1103/PhysRevE.48.1683},
journal = {Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; (United States)},
issn = {1063-651X},
number = ,
volume = 48:3,
place = {United States},
year = {1993},
month = {9}
}