| Grant number: | 13/22764-2 |
| Support type: | Scholarships in Brazil - Post-Doctorate |
| Effective date (Start): | March 01, 2014 |
| Effective date (End): | February 28, 2017 |
| Field of knowledge: | Physical Sciences and Mathematics - Physics - General Physics |
| Principal Investigator: | Edson Denis Leonel |
| Grantee: | Diogo Ricardo da Costa |
| Home 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. | |