Competition between suppression and production of Fermi acceleration

Ladeira, Denis Gouvêa; Leonel, Edson D.

doi:10.1103/physreve.81.036216

Cited by 11 publications

(6 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It is relevant to recall that, by the use of scaling arguments, the universality of the ratio I 2 n /I 2 0 was deduced in [10,12,[37][38][39]; there, n CO was also reported to be proportional to I 2 0 K −2 , in agreement with Eq. (25).…”

supporting

confidence: 77%

Analytical description of critical dynamics for two-dimensional dissipative nonlinear maps

2016

Self Cite

View full text Add to dashboard Cite

The critical dynamics near the transition from unlimited to limited action diffusion for two families of well known dissipative nonlinear maps, namely the dissipative standard and dissipative discontinuous maps, is characterized by the use of an analytical approach. The approach is applied to explicitly obtain the average squared action as a function of the (discrete) time and the parameters controlling nonlinearity and dissipation. This allows to obtain a set of critical exponents so far obtained numerically in the literature. The theoretical predictions are verified by extensive numerical simulations. We conclude that all possible dynamical cases, independently on the map parameter values and initial conditions, collapse into the universal exponential decay of the properly normalized average squared action as a function of a normalized time. The formalism developed here can be extended to many other different types of mappings therefore making the methodology generic and robust.

show abstract

supporting

confidence: 77%

Analytical description of critical dynamics for two-dimensional dissipative nonlinear maps

2016

Self Cite

View full text Add to dashboard Cite

show abstract

“…However, the introduction of inelastic collision is enough to suppress Fermi acceleration. Results considering also the one dimension Fermi-Ulam model under an external force of type sawtooth [31] under effects of dissipation generated from a sliding of a body against a rough surface has also been considered. The external perturbation of sawtooth type was chosen because the oscillating wall always gives energy to the particle after collisions.…”

Section: Introductionmentioning

confidence: 99%

Fermi acceleration and its suppression in a time-dependent Lorentz gas

Oliveira

Vollmer

Leonel³

2011

Physica D: Nonlinear Phenomena

Self Cite

View full text Add to dashboard Cite

We study some dynamical properties of a Lorentz gas. We have considered both the static and time dependent boundary. For the static case we have shown that the system has a chaotic component characterized with a positive Lyapunov Exponent. For the time-dependent perturbation we describe the model using a four-dimensional nonlinear map. The behaviour of the average velocity is considered in two situations (i) non-dissipative and (ii) dissipative. Our results show that the unlimited energy growth is observed for the non-dissipative case. However, when dissipation, via damping coefficients, is introduced the senary changes and the unlimited engergy growth is suppressed. The behaviour of the average velocity is described using scaling approach.

show abstract

“…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. However, in this paper we will consider only the conservative version, where the collision with both walls are completely elastic.…”

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

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Competition between suppression and production of Fermi acceleration

Cited by 11 publications

References 23 publications

Analytical description of critical dynamics for two-dimensional dissipative nonlinear maps

Analytical description of critical dynamics for two-dimensional dissipative nonlinear maps

Fermi acceleration and its suppression in a time-dependent Lorentz gas

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

Contact Info

Product

Resources

About