arXiv subjects

Edson D. Leonel

Publications and source records attributed to Edson D. Leonel.

60 records · Page 4Linked to original sources

arXiv2010

Asymmetric transport in the bouncer model: Mixed, time dependent, noncompact dynamics

We consider time-dependence of dynamical transport, following a recent study of the stadium billiard in which classical transmission and reflection probabilities were shown to exhibit exponential or algebraic decay depending on the choice of the lead or "hole". The system considered here is much more general, having a generic mixed phase space structure, time-dependence of the dynamics, and Fermi acceleration (trajectories with unbounded velocity). We propose an efficient numerical scheme for this model, observe the asymmetric transport effect, and discuss observed stretched exponential decays.

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arXiv2010

Fermi acceleration and suppression of Fermi acceleration in a time-dependent Lorentz Gas

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.

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arXiv2009

A bouncing ball model with two nonlinearities: a prototype for Fermi acceleration

Some dynamical properties of a bouncing ball model under the presence of an external force modeled by two nonlinear terms are studied. The description of the model is made by use of a two dimensional nonlinear measure preserving map on the variables velocity of the particle and time. We show that raising the straight of a control parameter which controls one of the nonlinearities, the positive Lyapunov exponent decreases in the average and suffers abrupt changes. We also show that for a specific range of control parameters, the model exhibits the phenomenon of Fermi acceleration. The explanation of both behaviours is given in terms of the shape of the external force and due to a discontinuity of the moving wall's velocity.

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arXiv2009

Breaking down the Fermi acceleration with inelastic collisions

The phenomenon of Fermi acceleration is addressed for a dissipative bouncing ball model with external stochastic perturbation. It is shown that the introduction of energy dissipation (inelastic collisions of the particle with the moving wall) is a sufficient condition to break down the process of Fermi acceleration. The phase transition from bounded to unbounded energy growth in the limit of vanishing dissipation is characterized.

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arXiv2009

Corrugated waveguide under scaling investigation

Some scaling properties for classical light ray dynamics inside a periodically corrugated waveguide are studied by use of a simplified two-dimensional nonlinear area-preserving map. It is shown that the phase space is mixed. The chaotic sea is characterized using scaling arguments revealing critical exponents connected by an analytic relationship. The formalism is widely applicable to systems with mixed phase space, and especially in studies of the transition from integrability to non-integrability, including that in classical billiard problems.

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arXiv2004

The Fermi-Ulam Accelerator Model Under Scaling Analysis

The chaotic low energy region of the Fermi-Ulam simplified accelerator model is characterised by use of scaling analysis. It is shown that the average velocity and the roughness (variance of the average velocity) obey scaling functions with the same characteristic exponents. The formalism is widely applicable, including to billiards and to other chaotic systems.

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