Diffusion phenomena in a mixed phase space

Author(s)

Palmero, Matheus S. ^{[1, 2, 3]} ; Diaz, Gabriel I. ^[1] ; McClintock, Peter V. E. ^[3] ; Leonel, Edson D. ^[2]

Affiliation

^[1] Univ Sao Paulo, Inst Fis, Rua Matao, Tr R 187, BR-05314970 Sao Paulo, SP - Brazil

^[2] UNESP Univ Estadual Paulista, Dept Fis, Ave 24A, 1515, Bela Vista, BR-13506900 Rio Claro, SP - Brazil

^[3] Univ Lancaster, Dept Phys, Lancaster LA1 4YW - England

• Document type: Journal article
• Source: Chaos; v. 30, n. 1 JAN 2020.
• Web of Science Citations: 0

Abstract

We show that, in strongly chaotic dynamical systems, the average particle velocity can be calculated analytically by consideration of Brownian dynamics in a phase space, the method of images, and the use of the classical diffusion equation. The method is demonstrated on the simplified Fermi-Ulam accelerator model, which has a mixed phase space with chaotic seas, invariant tori, and Kolmogorov-Arnold-Moser islands. The calculated average velocities agree well with numerical simulations and with an earlier empirical theory. (AU)

• FAPESP's process: 16/15713-0 - Scaling laws associated with a symmetry-break in the probability distribution function in a set of dynamical systems
• Grantee: Matheus Palmero Silva
• Support Opportunities: Scholarships abroad - Research Internship - Master's degree
• FAPESP's process: 14/27260-5 - Scaling laws associated to a symmetry-break in the energy distribution in a set of dynamical systems: application to discrete mappings
• Grantee: Matheus Palmero Silva
• Support Opportunities: Scholarships in Brazil - Master
• FAPESP's process: 17/14414-2 - Scaling investigation in dynamical systems
• Grantee: Edson Denis Leonel
• Support Opportunities: Regular Research Grants