Crises in a dissipative bouncing ball model

Livorati, André L. P.; Caldas, Iberê L.; Dettmann, Carl P.; Leonel, Edson D.

doi:10.1016/j.physleta.2015.09.016

Cited by 16 publications

(9 citation statements)

References 57 publications

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“…For the nondissipative version, the system basically behaves like the standard map in a local approximation [2,9], where some of the previous findings concerning the ballistic transport and accelerator modes (AMs) in the standard map serve as the motivation background for this paper [29][30][31][32][33][34][35]. Yet, despite the simple dynamics, interesting applications for this system can be found in dynamic stability in human performance [36], vibration waves in a nanometric-sized mechanical contact system [37], granular materials [38], experimental devices concerning normal coefficient of restitution [39], mechanical vibrations [40,41], anomalous transport and diffusion [42], thermodynamics [43], crisis between chaotic attractors [44], and chaos control [45], among others [46,47].…”

Section: Introductionmentioning

confidence: 99%

Transition from normal to ballistic diffusion in a one-dimensional impact system

et al. 2018

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We characterize a transition from normal to ballistic diffusion in a bouncing ball dynamics. The system is composed of a particle, or an ensemble of noninteracting particles, experiencing elastic collisions with a heavy and periodically moving wall under the influence of a constant gravitational field. The dynamics lead to a mixed phase space where chaotic orbits have a free path to move along the velocity axis, presenting a normal diffusion behavior. Depending on the control parameter, one can observe the presence of featured resonances, known as accelerator modes, that lead to a ballistic growth of velocity. Through statistical and numerical analysis of the velocity of the particle, we are able to characterize a transition between the two regimes, where transport properties were used to characterize the scenario of the ballistic regime. Also, in an analysis of the probability of an orbit to reach an accelerator mode as a function of the velocity, we observe a competition between the normal and ballistic transport in the midrange velocity.

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Section: Introductionmentioning

confidence: 99%

Transition from normal to ballistic diffusion in a one-dimensional impact system

et al. 2018

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“…As an illustration we have marked two points in red. The (+) point corresponds to N = 4, while the (*) point to N = 19. larger chaotic attractor as a parameter is varied [11][12][13]. This process occurs mainly when the basin boundary of each attractor collide, so that an orbit moves chaotically back and forth from one region to the other [14].…”

Section: Case C: Alternating Chaotic Regionsmentioning

confidence: 99%

Forcing the escape: Partial control of escaping orbits from a transient chaotic region

Alfaro¹,

Capeáns²,

Sanjuán³

2021

Preprint

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A new control algorithm based on the partial control method has been developed. The general situation we are considering is an orbit starting in a certain phase space region Q having a chaotic transient behavior affected by noise, so that the orbit will definitely escape from Q in an unpredictable number of iterations. Thus, the goal of the algorithm is to control in a predictable manner when to escape. While partial control has been used as a way to avoid escapes, here we want to adapt it to force the escape in a controlled manner. We have introduced new tools such as escape functions and escape sets that once computed makes the control of the orbit straightforward. We have applied the new idea to three different cases in order to illustrate the various application possibilities of this new algorithm.

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“…In this section we will describe the model under study, so called Fermi-Ulam model (FUM), which consists of the motion of a free particle that suffers elastic collisions with two heavy walls, where one of them is said to be fixed at x = l, and the other one is periodic oscillating around x = 0 . Dissipation could be introduced in the system via inelastic collisions [39] where a damping coefficient can be considered on the walls [40] . Also, kinetic friction [41] and in flight dissipation [42] can be introduced as well.…”

Section: The Model the Mapping And Chaotic Propertiesmentioning

confidence: 99%

Investigation of stickiness influence in the anomalous transport and diffusion for a non-dissipative Fermi–Ulam model

Livorati

Palmero

Díaz-I

et al. 2018

Communications in Nonlinear Science and Numerical Simulation

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We study the dynamics of an ensemble of non interacting particles constrained by two infinitely heavy walls, where one of them is moving periodically in time, while the other is fixed. The system presents mixed dynamics, where the accessible region for the particle to diffuse chaotically is bordered by an invariant spanning curve. Statistical analysis for the root mean square velocity, considering high and low velocity ensembles, leads the dynamics to the same steady state plateau for long times. A transport investigation of the dynamics via escape basins reveals that depending of the initial velocity ensemble, the decay rates of the survival probability present different shapes and bumps, in a mix of exponential, power law and stretched exponential decays. After an analysis of step-size averages, we found that the stable manifolds play the role of a preferential path for faster escape, being responsible for the bumps and different shapes of the survival probability.

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Crises in a dissipative bouncing ball model

Cited by 16 publications

References 57 publications

Transition from normal to ballistic diffusion in a one-dimensional impact system

Transition from normal to ballistic diffusion in a one-dimensional impact system

Forcing the escape: Partial control of escaping orbits from a transient chaotic region

Investigation of stickiness influence in the anomalous transport and diffusion for a non-dissipative Fermi–Ulam model

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