Transport of particles in chaotic seas

• Grant number: 22/03612-6
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: August 01, 2022
• End date: July 31, 2026
• Field of knowledge: Physical Sciences and Mathematics - Physics - General Physics
• Principal Investigator: Edson Denis Leonel
• Grantee: Daniel Borin
• Host Institution: Instituto de Geociências e Ciências Exatas (IGCE). Universidade Estadual Paulista (UNESP). Campus de Rio Claro. Rio Claro , SP, Brazil
• Associated scholarship(s): 24/06749-8 - Description of billiards transport properties through Tsallis statistics, BE.EP.DR

Abstract

The goal of the project consists in investigate some properties for the chaotic transport present in chaotic seas for discrete nonlinear mappings. The transport of particles is defined as a set of particles leaving from one specific region of the phase space to other defined region. It is known in the literature the absence of stability islands yields the survival probability to be described as an exponential while the existence of periodic regions changes such behavior to be characterized by a function with slower decay such as a power law or even a streched exponential. This reduction is linked to a dynamical trapping called as stickiness leading to an anomalous diffusion of the particles. One of the main goals of the project is to investigate the tranport of particles with main focus on the stickiness description. We use different approaches including numerical simulations and the solution of the diffusion equation in both retangular and polar coordinates near the periodic islands. We shall consider different mappings modeling several dynamical systems to investigate such properties including chaotic billiards. (AU)

Scientific publications

(6)

(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)

BORIN, DANIEL; LIVORATI, ANDRE LUIS PRANDO; LEONEL, EDSON DENIS. An investigation of the survival probability for chaotic diffusion in a family of discrete Hamiltonian mappings. CHAOS SOLITONS & FRACTALS, v. 175, p. 8-pg., 2023-10-01. (22/03612-6, 21/09519-5)

BORIN, DANIEL. Hurst exponent: A method for characterizing dynamical traps. PHYSICAL REVIEW E, v. 110, n. 6, p. 12-pg., 2024-12-31. (22/03612-6)

LIVORATI, ANDRE LUIS PRANDO; FABER, ANDRE PAGANOTTI; BORIN, DANIEL. Asymptotic convergence for the dynamics of a Duffing-like oscillator under scaling analyses. Chaos, v. 35, n. 1, p. 7-pg., 2025-01-01. (22/03612-6, 24/06749-8)

BORIN, DANIEL; DE BRITO, VINICIUS LOURENCO GARCIA; LEONEL, EDSON DENIS; HANSEN, MATHEUS. Buzz pollination: A theoretical analysis via scaling invariance. PHYSICAL REVIEW E, v. 110, n. 5, p. 6-pg., 2024-11-01. (22/03612-6, 21/09519-5)

BORIN, DANIEL. Caputo fractional standard map: Scaling invariance analyses. CHAOS SOLITONS & FRACTALS, v. 181, p. 5-pg., 2024-02-20. (22/03612-6)

SALES, MATHEUS ROLIM; BORIN, DANIEL; DA COSTA, DIOGO RICARDO; SZEZECH JR, JOSE DANILO; LEONEL, EDSON DENIS. An investigation of escape and scaling properties of a billiard system. Chaos, v. 34, n. 11, p. 11-pg., 2024-11-01. (22/03612-6, 23/08698-9, 19/14038-6)