Investigation of anomalous transport and diffusion for time-dependent dynamical systems

• Grant number: 15/26699-6
• Support Opportunities: Scholarships abroad - Research Internship - Post-doctor
• Start date: July 01, 2016
• End date: December 31, 2016
• Field of knowledge: Physical Sciences and Mathematics - Physics - General Physics
• Principal Investigator: Edson Denis Leonel
• Grantee: André Luís Prando Livorati
• Supervisor: Carl Philip Dettmann
• Host Institution: Instituto de Geociências e Ciências Exatas (IGCE). Universidade Estadual Paulista (UNESP). Campus de Rio Claro. Rio Claro , SP, Brazil
• Institution abroad: University of Bristol, England
• Associated to the scholarship: 14/25316-3 - Investigation of transport and diffusion properties of particles using escape formalism for time-dependent systems, BP.PD

Abstract

In this project we aim to investigate some properties of anomalous transport and diffusion for some dynamical system with mixed phase space.In such systems, the stickiness phenomenon, briefly described here as orbits that get trapped around stability islands for finite times, can play different roles in the dynamics. We intent to study the behavior of the survival probability, related with some leaking variable in the phase space, and characterize the influence of the anomalous diffusion and transport, with the position and/or size of the leaking,and also with control parameters. Since there is a lack of analytical treatment of these anomalous behavior in the literature, we intent to doextensive numerical simulations, followed by an attempt to describe analytically the behavior of the survival probability for different combinations of control parameters and leak position and/or size. We expect to obtain original results, and bring some more light to these problemsinvolving stickiness phenomenon in general and among these dynamical systems. Also, the stickiness phenomenon has interpretation and applicationsin different areas of science as Astronomy, Hydrodynamics, Acoustic, Biology, Plasmas, among others

Scientific publications

(5)

(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)

LIVORATI, ANDRE L. P.; KROETZ, TIAGO; DETTMANN, CARL P.; CALDAS, IBERE L.; LEONEL, EDSON D.. Transition from normal to ballistic diffusion in a one-dimensional impact system. Physical Review E, v. 97, n. 3, MAR 9 2018. (17/14414-2, 15/26699-6, 14/25316-3)

PALMERO, MATHEUS S.; LIVORATI, ANDRE L. P.; CALDAS, IBERE L.; LEONEL, EDSON D.. Ensemble separation and stickiness influence in a driven stadium-like billiard: A Lyapunov exponents analysis. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, v. 65, p. 248-259, DEC 2018. (17/14414-2, 14/25316-3, 12/23688-5, 12/00556-6, 15/26699-6, 11/19296-1)

LIVORATI, ANDRE L. P.; KROETZ, TIAGO; DETTMANN, CARL P.; CALDAS, IBERE L.; LEONEL, EDSON D.. Transition from normal to ballistic diffusion in a one-dimensional impact system. PHYSICAL REVIEW E, v. 97, n. 3, p. 9-pg., 2018-03-09. (17/14414-2, 14/25316-3, 15/26699-6)

LIVORATI, ANDRE L. P.. Dynamics and scaling properties for a one-dimensional impact system with two periodically vibrating walls. Physics Letters A, v. 381, n. 28, p. 2214-2221, JUL 25 2017. (15/26699-6, 14/25316-3)

LIVORATI, ANDRE L. P.; PALMERO, MATHEUS S.; DIAZ-, I, GABRIEL; DETTMANN, CARL P.; CALDAS, IBERE L.; LEONEL, EDSON D.. Investigation of stickiness influence in the anomalous transport and diffusion for a non-dissipative Fermi-Ulam model. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, v. 55, p. 225-236, FEB 2017. (14/25316-3, 12/23688-5, 15/26699-6, 14/27260-5)