Selfsimilar transport in incomplete chaos
Abstract
Particle chaotic dynamics along a stochastic web is studied for threedimensional 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 selfsimilar properties of different topological and dynamical characteristics of the particle motion. This selfsimilarity appears in the Weierstrasslike randomwalk process that is responsible for the anomalous transport exponent in the meanmoment dependence on [ital t]. This exponent can be expressed as a ratio of fractal dimensions of space and time sets in the Weierstrasslike process. An explicit form for the expression of the anomalous transport exponent through the local topological properties of orbits has been given.
 Authors:

 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)
 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:
 FG0286ER53223; FG0292ER54184
 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 1063651X
 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; THREEDIMENSIONAL CALCULATIONS; CONFIGURATION; FUNCTIONS; 661300*  Other Aspects of Physical Science (1992)
Citation Formats
Zaslavsky, G M, Stevens, D, and Weitzner, H. Selfsimilar transport in incomplete chaos. United States: N. p., 1993.
Web. doi:10.1103/PhysRevE.48.1683.
Zaslavsky, G M, Stevens, D, & Weitzner, H. Selfsimilar transport in incomplete chaos. United States. doi:10.1103/PhysRevE.48.1683.
Zaslavsky, G M, Stevens, D, and Weitzner, H. Wed .
"Selfsimilar transport in incomplete chaos". United States. doi:10.1103/PhysRevE.48.1683.
@article{osti_6278306,
title = {Selfsimilar 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 threedimensional 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 selfsimilar properties of different topological and dynamical characteristics of the particle motion. This selfsimilarity appears in the Weierstrasslike randomwalk process that is responsible for the anomalous transport exponent in the meanmoment dependence on [ital t]. This exponent can be expressed as a ratio of fractal dimensions of space and time sets in the Weierstrasslike 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 = {1063651X},
number = ,
volume = 48:3,
place = {United States},
year = {1993},
month = {9}
}