Dynamical and transport properties in conservative and dissipative dynamical systems

• Grant number: 13/22764-2
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: March 01, 2014
• End date: February 28, 2017
• Field of knowledge: Physical Sciences and Mathematics - Physics - General Physics
• Principal Investigator: Edson Denis Leonel
• Grantee: Diogo Ricardo da Costa
• Host Institution: Instituto de Geociências e Ciências Exatas (IGCE). Universidade Estadual Paulista (UNESP). Campus de Rio Claro. Rio Claro , SP, Brazil

Abstract

In this Post-Doctorate project we will study some dynamical and transport properties in conservative and dissipative dynamical systems. Part of the project will be dedicated to study the bouncer, Fermi-Ulam or billiard models, where the moving wall is given by the Van der Pol, Duffing, Van der Pol-Duffing or Rayleigh-Duffing equations. We will show analytical and numerically that the critical exponents do not depend on the time dependent function proposed for a system, where we will study the Fermi-Ulam model and waveguide in a generalized form and a general mapping that reproduces different critical exponents, where a connection to the standard mapping will be done. The critical exponents for some kinds of pulsating billiards will also be analyzed. We will study elliptic-oval and triangle/circular billiards with a dispersing mechanism, that are a generalization of the annular and Sinai billiards. Elliptic, triangle/circle or parabolic oval rotating billiards will also be studied, seeking to discover if they satisfy the LRA conjecture. A mushroom billiard and its properties will also be subject of this project. It will be shown that is possible to obtain 3-dimensional parameter spaces, for example, the generalized logistic mapping or the Fermi-Ulam with different dissipation mechanisms. Some optical-chaotic billiards shall be analyzed, and finally, for the circle/triangle billiard or even the parabolic oval we will study the influence of a gravitational field and the time-dependence in the boundary. The obtained results will contribute in a positive form to the advance of the acknowledgement in this field of research.

Scientific publications

(7)

(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)

DA COSTA, DIOGO RICARDO; DETTMANN, CARL P.; LEONEL, EDSON D.. Transport and dynamical properties for a bouncing ball model with regular and stochastic perturbations. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, v. 20, n. 3, p. 871-881, MAR 2015. (12/18962-0, 13/22764-2)

HANSEN, MATHEUS; DA COSTA, DIOGO R.; OLIVEIRA, DIEGO F. M.; LEONEL, EDSON D.. Statistical properties for a dissipative model of relativistic particles in a wave packet: A parameter space investigation. Applied Mathematics and Computation, v. 238, p. 387-392, JUL 1 2014. (13/01449-1, 12/23688-5, 12/18962-0, 13/22764-2)

HANSEN, MATHEUS; DA COSTA, DIOGO RICARDO; CALDAS, IBERE L.; LEONEL, EDSON D.. Statistical properties for an open oval billiard: An investigation of the escaping basins. CHAOS SOLITONS & FRACTALS, v. 106, p. 355-362, JAN 2018. (17/14414-2, 12/23688-5, 13/22764-2, 14/00334-9, 11/19296-1)

DA COSTA, DIOGO RICARDO; DETTMANN, CARL P.; LEONEL, EDSON D.. Circular, elliptic and oval billiards in a gravitational field. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, v. 22, n. 1-3, p. 731-746, MAY 2015. (12/18962-0, 13/22764-2, 12/23688-5)

DA COSTA, DIOGO RICARDO. A dissipative Fermi-Ulam model under two different kinds of dissipation. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, v. 22, n. 1-3, p. 1263-1274, MAY 2015. (13/22764-2)

LADEIRA, DENIS GOUVEA; LEONEL, EDSON D.. Dynamics of a charged particle in a dissipative Fermi-Ulam model. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, v. 20, n. 2, p. 546-558, FEB 2015. (12/18962-0, 13/22764-2)

DA COSTA, DIOGO RICARDO; DETTMANN, CARL P.; DE OLIVEIRA, JULIANO A.; LEONEL, EDSON D.. Dynamics of classical particles in oval or elliptic billiards with a dispersing mechanism. Chaos, v. 25, n. 3, MAR 2015. (12/23688-5, 14/18672-8, 12/18962-0, 13/22764-2)