| Full text | |
| Author(s): |
Mendez-Bermudez, J. A.
[1]
;
Martinez-Mendoza, A. J.
[1]
;
Livorati, Andre L. P.
[2]
;
Leonel, Edson D.
[3, 2]
Total Authors: 4
|
| Affiliation: | [1] Benemerita Univ Autonoma Puebla, Inst Fis, Puebla 72570 - Mexico
[2] UNESP Univ Estadual Paulista, Dept Fis, BR-13506900 Rio Claro, SP - Brazil
[3] Abdus Salam Int Ctr Theoret Phys, I-34151 Trieste - Italy
Total Affiliations: 3
|
| Document type: | Journal article |
| Source: | Journal of Physics A-Mathematical and Theoretical; v. 48, n. 40 OCT 9 2015. |
| Web of Science Citations: | 3 |
| Abstract | |
The escape of particles from the phase space produced by a two-dimensional, nonlinear and area-preserving, discontinuous map is investigated by using both numerical simulations and the explicit solution of the corresponding diffusion equation. The mapping, given in action-angle variables, is parameterized by K, which controls a transition from integrability to non-integrability. We focus on the two dynamical regimes of the map: slow diffusion (K < K-c) and quasilinear diffusion (K > K-c) regimes, separated by the critical parameter value K-c = 1. When a hole is introduced in the action axis, we find the histogram of escape times P-E(n) and the survival probability of particles P-S(n) to be scaling invariant in both the slow and the quasilinear diffusion regimes, with scaling laws proportional to the corresponding diffusion coefficients, namely, proportional to K-5/2 and K-2, respectively. Our numerical simulations agree remarkably well with the analytical results obtained from the explicit solution of the diffusion equation, hence giving robustness to the escape formalism. (AU) | |
| FAPESP's process: | 14/25997-0 - Complex networks: a random matrix approach |
| Grantee: | Francisco Aparecido Rodrigues |
| Support Opportunities: | Research Grants - Visiting Researcher Grant - International |
| FAPESP's process: | 13/14655-9 - Dynamical and statistical properties of nonlinear discontinuous maps |
| Grantee: | Edson Denis Leonel |
| Support Opportunities: | Research Grants - Visiting Researcher Grant - International |
| FAPESP's process: | 12/23688-5 - Exponents and scaling laws, phase transitions and transport properties of time dependent systems |
| Grantee: | Edson Denis Leonel |
| Support Opportunities: | Regular Research Grants |
| FAPESP's process: | 14/25316-3 - Investigation of transport and diffusion properties of particles using escape formalism for time-dependent systems |
| Grantee: | André Luís Prando Livorati |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |