Scaling invariance of the diffusion coefficient in a family of two-dimensional Hamiltonian mappings
Contribuinte(s) |
Universidade Estadual Paulista (UNESP) |
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Data(s) |
27/05/2014
27/05/2014
10/06/2013
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Resumo |
We consider a family of two-dimensional nonlinear area-preserving mappings that generalize the Chirikov standard map and model a variety of periodically forced systems. The action variable diffuses in increments whose phase is controlled by a negative power of the action and hence effectively uncorrelated for small actions, leading to a chaotic sea in phase space. For larger values of the action the phase space is mixed and contains a family of elliptic islands centered on periodic orbits and invariant Kolmogorov-Arnold-Moser (KAM) curves. The transport of particles along the phase space is considered by starting an ensemble of particles with a very low action and letting them evolve in the phase until they reach a certain height h. For chaotic orbits below the periodic islands, the survival probability for the particles to reach h is characterized by an exponential function, well modeled by the solution of the diffusion equation. On the other hand, when h reaches the position of periodic islands, the diffusion slows markedly. We show that the diffusion coefficient is scaling invariant with respect to the control parameter of the mapping when h reaches the position of the lowest KAM island. © 2013 American Physical Society. |
Identificador |
http://dx.doi.org/10.1103/PhysRevE.87.062904 Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, v. 87, n. 6, 2013. 1539-3755 1550-2376 http://hdl.handle.net/11449/75626 10.1103/PhysRevE.87.062904 WOS:000320166600014 2-s2.0-84879540770 2-s2.0-84879540770.pdf |
Idioma(s) |
eng |
Relação |
Physical Review E: Statistical, Nonlinear, and Soft Matter Physics |
Direitos |
closedAccess |
Palavras-Chave | #Area-preserving mappings #Chaotic orbits #Control parameters #Diffusion equations #Periodic orbits #Scaling invariance #Survival probabilities #Transport of particles #Hamiltonians #Mapping #Phase space methods #Two dimensional #Diffusion |
Tipo |
info:eu-repo/semantics/article |