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Transport, escape of particles and dynamical properties of some non-linear mappings

Grant number: 12/18962-0
Support type:Scholarships abroad - Research Internship - Doctorate
Effective date (Start): February 01, 2013
Effective date (End): July 31, 2013
Field of knowledge:Physical Sciences and Mathematics - Physics - General Physics
Principal Investigator:Edson Denis Leonel
Grantee:Diogo Ricardo da Costa
Supervisor abroad: Carl Dettmann
Home Institution: Instituto de Física (IF). Universidade de São Paulo (USP). São Paulo , SP, Brazil
Local de pesquisa : University of Bristol, England  

Abstract

We will investigate some escape and dynamical properties for an ensemble of non-interacting particles moving in closed domains. When a holeor a escape region is introduced in the phase space, the histogram for the number of particles that escaped, which is scaling invariant, grows rapidly reaching a maximum and tends to zero for long enough time. The systems proposed here have a mixed phase space, containing KAM islands, chaotic seas and invariant spanning curves (ISC). Considering the position of the hole as proprotional to the first ISC, we can find some critical exponents, confirming a scaling invariance. In this project we consider anoval/elliptic billiard that contains a small circle in the horizontal axis, which is a generalization of the annular and Sinai billiards. Another problem of our interest is the characterization of the families of marginally unstable periodic orbits (MUPOs) in mushroom billiard, considering circular and elliptical hats. We therefore will try to obtain the dimension of the set without MUPOs as a function of the base length $r$, and the presence of stickiness in mushroooms without these MUPOs. As we know the curve $y=x^4$ has curvature that approaches zero at the point $x=0$, and so violates the strict focussing property. This meansthere may be trajectories that are sticky to the extent that they have an infinite number of regular collisions in a finite time. We propose toinvestigate its properties and effect on the dynamics of the whole billiard. The last problem that we propose is to investigate the resulting stickiness and its effect on the dynamics of the whole billiard in a cusp composed for a dispersing and focusing edge (it is made considering two non-concentric circles). In this case, there may be an unbounded number of collisions in a finite time as the trajectory enters the region between the two circles. (AU)

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. 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. Web of Science Citations: 0.
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. Web of Science Citations: 3.
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. Web of Science Citations: 10.
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. Web of Science Citations: 5.
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. Web of Science Citations: 4.
DA COSTA, DIOGO RICARDO; CALDAS, IBERE L.; LEONEL, EDSON D. Phase space properties and chaotic transport for a particle moving in a time dependent step potential well. Applied Mathematics and Computation, v. 236, p. 215-228, JUN 1 2014. Web of Science Citations: 2.
DA COSTA, DIOGO RICARDO; OLIVEIRA, DIEGO F. M.; LEONEL, EDSON D. Dynamical and statistical properties of a rotating oval billiard. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, v. 19, n. 6, p. 1926-1934, JUN 2014. Web of Science Citations: 0.

Please report errors in scientific publications list by writing to: cdi@fapesp.br.