Phase Transition in Dynamical Systems : Defining Classes of Universality for Two-Dimensional Hamiltonian Mappings via Critical Exponents
Author
Source
Mathematical Problems in Engineering
Issue
Vol. 2009, Issue 2009 (31 Dec. 2009), pp.1-22, 22 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2009-10-11
Country of Publication
Egypt
No. of Pages
22
Main Subjects
Abstract EN
A phase transition from integrability to nonintegrability in two-dimensional Hamiltonian mappings is described and characterized in terms of scaling arguments.
The mappings considered produce a mixed structure in the phase space in the sense that, depending on the combination of the control parameters and initial conditions, KAM islands which are surrounded by chaotic seas that are limited by invariant tori are observed.
Some dynamical properties for the largest component of the chaotic sea are obtained and described in terms of the control parameters.
The average value and the deviation of the average value for chaotic components of a dynamical variable are described in terms of scaling laws, therefore critical exponents characterizing a scaling function that describes a phase transition are obtained and then classes of universality are characterized.
The three models considered are: The Fermi-Ulam accelerator model, a periodically corrugate waveguide, and variant of the standard nontwist map.
American Psychological Association (APA)
Leonel, Edson Denis. 2009. Phase Transition in Dynamical Systems : Defining Classes of Universality for Two-Dimensional Hamiltonian Mappings via Critical Exponents. Mathematical Problems in Engineering،Vol. 2009, no. 2009, pp.1-22.
https://search.emarefa.net/detail/BIM-466401
Modern Language Association (MLA)
Leonel, Edson Denis. Phase Transition in Dynamical Systems : Defining Classes of Universality for Two-Dimensional Hamiltonian Mappings via Critical Exponents. Mathematical Problems in Engineering No. 2009 (2009), pp.1-22.
https://search.emarefa.net/detail/BIM-466401
American Medical Association (AMA)
Leonel, Edson Denis. Phase Transition in Dynamical Systems : Defining Classes of Universality for Two-Dimensional Hamiltonian Mappings via Critical Exponents. Mathematical Problems in Engineering. 2009. Vol. 2009, no. 2009, pp.1-22.
https://search.emarefa.net/detail/BIM-466401
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-466401