Publisher's Note: Fermi acceleration on the annular billiard [Phys. Rev. E 73, 066229 (2006)]

Carvalho, R. Egydio de; Souza, F. Caetano; Leonel, Edson D.

doi:10.1103/physreve.74.019904

Cited by 16 publications

(35 citation statements)

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“…In the eccentric and pulsating scenario, as the total particle energy E as p θ are no longer preserved and the mechanism of indefinite energy growth (FA) has been already reported in previous works [3,4]. Now we are going to study the effects of the magnetic field on the phenomenon of FA.…”

Section: Results Discussion and Conclusionmentioning

confidence: 99%

“…This study is a natural sequence of previous papers [3,4,[20][21][22][23], but in the present work, we now consider a charged particle, which beyond being subject to the dynamic conditions of the PAB, is also subjected to the action of a constant magnetic field perpendicularly orientated in relation to the plane of the billiard. This system will be called as magnetic pulsating annular billiard (MPAB).…”

Section: The Magnetic Billiardmentioning

confidence: 99%

“…In the particular focus of this work, the mechanism of FA has been noticed in the stadiumlike billiard [2,9,11,12], in the annular billiard [3,4,10], in the one-dimensional stochastic Fermi-Ulam billiard [5,6], in the elliptical billiard [7,8], in the Sinai's billiard [9,11], and in the Lorentz gas-like billiard [16]. Recent results on FA associated with the interaction of charge particles with magnetic islands or mirrors have also been reported [14,15,17,18].…”

Section: Introductionmentioning

confidence: 99%

“…It is a two-dimensional system limited by two breathing circular boundaries of radius R(t) and r(t) (R > r) [3,4]. The distance between both centers is the eccentricity δ, which plays the role of perturbation parameter.…”

Section: Introductionmentioning

confidence: 99%

“…In recent years, several studies have been developed in order to show dynamical properties which could contribute for inducing or suppressing Fermi acceleration (FA), which can be named as indefinite energy growth [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. The Loskutov-Ryabov-Akinshin conjecture says that a chaotic regime observed in static billiards is a sufficient condition to find FA when a periodic time-dependent perturbation is added on the billiard boundaries [1].…”

Section: Introductionmentioning

confidence: 99%

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Tunable Fermi acceleration in a nondissipative driven magnetic billiard

et al. 2014

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We study the effect of a constant magnetic field on the dynamics of a system that may present Fermi acceleration (FA). The model in consideration is the nondissipative annular billiard with breathing boundaries. There is a field threshold, from which the mechanism of FA can be deactivated. The presence of the magnetic field curves the particle trajectories and for some combinations of the parameters FA is totally, and nontrivially, suppressed without considering any kind of dissipation.

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Section: Results Discussion and Conclusionmentioning

confidence: 99%

Section: The Magnetic Billiardmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Tunable Fermi acceleration in a nondissipative driven magnetic billiard

et al. 2014

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Hidden High Period Accelerator Modes in a Bouncer Model

Kroetz

Livorati

Leonel

et al. 2015

Springer Proceedings in Physics

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We characterized the influence of high period accelerator modes in the global dynamics of a non-dissipative Bouncer model. The dynamics of the system was investigated considering both complete and simplified approaches. Evaluating the average of the velocity over large ensembles of initial conditions for the complete mapping, we obtained particular ranges of the control parameter where high period accelerating structures are located. The position, influence and shape of the accelerator modes were obtained considering the symplectic mapping. Our results, lead us to infer that even for high period and less influent accelerator modes, the dynamics is globally affected for long time series, causing an anomalous diffusion, in compare with the regular Fermi acceleration. 1 Introduction Modelling of dynamical systems, has been one of the most embracing area of interest among physicists and mathematicians is the past decades [1-5]. Low-dimensional systems in particular, despite the simple modelling, are very suitable to study and to investigate chaotic properties in their phase space [1-5]. These systems can present a very complex dynamics leading to a rich variety of nonlinear phenomena, considering either dissipative and non-dissipative dynamics [1-5].

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