Dynamics and transport in nonlinear symplectic map lattices

• Grant number: 23/16146-6
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: April 01, 2024
• Status: Discontinued
• Field of knowledge: Physical Sciences and Mathematics - Physics
• Principal Investigator: Iberê Luiz Caldas
• Grantee: Leonardo Costa de Souza
• Host Institution: Instituto de Física (IF). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated scholarship(s): 24/20417-8 - Dynamics of coupled symplectic map, BE.EP.PD

Abstract

This project proposes to investigate transport phenomena in Hamiltonian systems with a high degree of freedom. The study will focus on symplectic networks of maps coupled in a non-local manner, where the coupling strength follows a power-law dependence on the distance within the network. This investigation will encompass both twist maps and non-twist maps. We will analyze diffusion as a function of network size and coupling strength. Additionally, our investigation will explore the formation of orbit cluster regions, which represent spatial coherent structures emerging from the dynamical system. The cluster regions are associated with the stickiness of chaotic trajectories near persistent periodic islands. To quantify this stickiness, we will employ a recurrence time entropy approach. In order to, characterize the clustered orbits we will apply the weighted Birkhoff averages, a powerful method that allows orbits to be distinguished. Lastly, with this results will be possible to understand the similarities and differences between systems that obeys and violate the twist condition.

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

VIANA, RICARDO L.; MATHIAS, AMANDA C.; SOUZA, LEONARDO C.; HAERTER, PEDRO. Fractal structures in the chaotic advection of passive scalars in leaky planar hydrodynamical flows. Chaos, v. 34, n. 5, p. 12-pg., 2024-05-01. (23/16146-6)