Stochastic approach to diffusion inside the chaotic layer of a resonance
| Autor: | C. M. Giordano, P. M. Cincotta, Martin Federico Mestre, Armando Bazzani |
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| Přispěvatelé: | Martín F. Mestre, Armando Bazzani, Pablo M. Cincotta, Claudia M. Giordano |
| Jazyk: | angličtina |
| Rok vydání: | 2014 |
| Předmět: |
Ciencias Astronómicas
Integrable system Anomalous diffusion Ciencias Físicas FOS: Physical sciences stochastic perturbation Hamiltonian system purl.org/becyt/ford/1 [https] HAMILTONIAN SYSTEM Classical Transport Diffusion (business) fokker planck equation Symplectomorphism Physics Stochastic Analysis Methods Mathematical analysis purl.org/becyt/ford/1.3 [https] Standard map chaotic layers Nonlinear Sciences - Chaotic Dynamics Astronomía Diffusion process Phase space Chaotic Dynamics (nlin.CD) Numerical Simulations of Chaotic Systems CIENCIAS NATURALES Y EXACTAS |
| Zdroj: | SEDICI (UNLP) Universidad Nacional de La Plata instacron:UNLP CONICET Digital (CONICET) Consejo Nacional de Investigaciones Científicas y Técnicas instacron:CONICET |
| Popis: | We model chaotic diffusion in a symplectic four-dimensional (4D) map by using the result of a theorem that was developed for stochastically perturbed integrable Hamiltonian systems. We explicitly consider a map defined by a free rotator (FR) coupled to a standard map (SM). We focus on the diffusion process in the action I of the FR, obtaining a seminumerical method to compute the diffusion coefficient. We study two cases corresponding to a thick and a thin chaotic layer in the SM phase space and we discuss a related conjecture stated in the past. In the first case, the numerically computed probability density function for the action I is well interpolated by the solution of a Fokker-Planck (FP) equation, whereas it presents a nonconstant time shift with respect to the concomitant FP solution in the second case suggesting the presence of an anomalous diffusion time scale. The explicit calculation of a diffusion coefficient for a 4D symplectic map can be useful to understand the slow diffusion observed in celestial mechanics and accelerator physics. Instituto de Astrofísica de La Plata |
| Databáze: | OpenAIRE |
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