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Title: An Investigation of Chaotic Diffusion in a Family of Hamiltonian Mappings Whose Angles Diverge in the Limit of Vanishingly Action

Abstract

The chaotic diffusion for a family of Hamiltonian mappings whose angles diverge in the limit of vanishingly action is investigated by using the solution of the diffusion equation. The system is described by a two-dimensional mapping for the variables action, I, and angle, θ and controlled by two control parameters: (i) ϵ, controlling the nonlinearity of the system, particularly a transition from integrable for ϵ=0 to non-integrable for ϵ≠0 and; (ii) γ denoting the power of the action in the equation defining the angle. For ϵ≠0 the phase space is mixed and chaos is present in the system leading to a finite diffusion in the action characterized by the solution of the diffusion equation. The analytical solution is then compared to the numerical simulations showing a remarkable agreement between the two procedures.

Authors:
 [1]
  1. UNESP - Univ Estadual Paulista, Departamento de Física (Brazil)
Publication Date:
OSTI Identifier:
22788348
Resource Type:
Journal Article
Journal Name:
Journal of Statistical Physics
Additional Journal Information:
Journal Volume: 170; Journal Issue: 1; Other Information: Copyright (c) 2018 Springer Science+Business Media, LLC, part of Springer Nature; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0022-4715
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ANALYTICAL SOLUTION; CHAOS THEORY; COMPARATIVE EVALUATIONS; COMPUTERIZED SIMULATION; DIFFUSION EQUATIONS; HAMILTONIANS; MAPPING; NONLINEAR PROBLEMS; PHASE SPACE; PHASE TRANSFORMATIONS; SCALING LAWS; TWO-DIMENSIONAL CALCULATIONS

Citation Formats

Leonel, Edson D., E-mail: edleonel@rc.unesp.br, and Kuwana, Célia M. An Investigation of Chaotic Diffusion in a Family of Hamiltonian Mappings Whose Angles Diverge in the Limit of Vanishingly Action. United States: N. p., 2018. Web. doi:10.1007/S10955-017-1920-X.
Leonel, Edson D., E-mail: edleonel@rc.unesp.br, & Kuwana, Célia M. An Investigation of Chaotic Diffusion in a Family of Hamiltonian Mappings Whose Angles Diverge in the Limit of Vanishingly Action. United States. https://doi.org/10.1007/S10955-017-1920-X
Leonel, Edson D., E-mail: edleonel@rc.unesp.br, and Kuwana, Célia M. 2018. "An Investigation of Chaotic Diffusion in a Family of Hamiltonian Mappings Whose Angles Diverge in the Limit of Vanishingly Action". United States. https://doi.org/10.1007/S10955-017-1920-X.
@article{osti_22788348,
title = {An Investigation of Chaotic Diffusion in a Family of Hamiltonian Mappings Whose Angles Diverge in the Limit of Vanishingly Action},
author = {Leonel, Edson D., E-mail: edleonel@rc.unesp.br and Kuwana, Célia M.},
abstractNote = {The chaotic diffusion for a family of Hamiltonian mappings whose angles diverge in the limit of vanishingly action is investigated by using the solution of the diffusion equation. The system is described by a two-dimensional mapping for the variables action, I, and angle, θ and controlled by two control parameters: (i) ϵ, controlling the nonlinearity of the system, particularly a transition from integrable for ϵ=0 to non-integrable for ϵ≠0 and; (ii) γ denoting the power of the action in the equation defining the angle. For ϵ≠0 the phase space is mixed and chaos is present in the system leading to a finite diffusion in the action characterized by the solution of the diffusion equation. The analytical solution is then compared to the numerical simulations showing a remarkable agreement between the two procedures.},
doi = {10.1007/S10955-017-1920-X},
url = {https://www.osti.gov/biblio/22788348}, journal = {Journal of Statistical Physics},
issn = {0022-4715},
number = 1,
volume = 170,
place = {United States},
year = {2018},
month = {1}
}