Phase Transition in Dynamical Systems: Defining Classes of Universality for Two-Dimensional Hamiltonian Mappings via Critical Exponents
Contribuinte(s) |
Universidade Estadual Paulista (UNESP) |
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Data(s) |
30/09/2013
20/05/2014
30/09/2013
20/05/2014
01/01/2009
|
Resumo |
Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) 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. Copyright (C) 2009 Edson D. Leonel. |
Formato |
22 |
Identificador |
http://dx.doi.org/10.1155/2009/367921 Mathematical Problems In Engineering. New York: Hindawi Publishing Corporation, p. 22, 2009. 1024-123X http://hdl.handle.net/11449/24944 10.1155/2009/367921 WOS:000271739500001 WOS000271739500001.pdf |
Idioma(s) |
eng |
Publicador |
Hindawi Publishing Corporation |
Relação |
Mathematical Problems in Engineering |
Direitos |
openAccess |
Tipo |
info:eu-repo/semantics/article |