Mathematical Problems in Engineering
Volume 2009 (2009), Article ID 513023, 9 pages
Research Article

Dissipation Effects in the Ratchetlike Fermi Acceleration

Departamento de Física, Universidade Federal do Paraná, 81531-980 Curitiba, PR, Brazil

Received 23 April 2009; Accepted 29 June 2009

Academic Editor: Edson Denis Leonel

Copyright © 2009 Cesar Manchein and Marcus W. Beims. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Ac-driven asymmetric pulses can be used to control the Fermi acceleration between three different motions, A: the accelerated mode, D: the decelerated mode, and H: the hyperaccelerated mode. In this paper we show that dissipation strongly affects the particles velocity, reducing the possibility for an accurate control of the dynamics. The saturation time, where the mean velocity starts to be constant due to dissipation, decays with a power law ~γβ, where γ is the dissipation parameter and β is close to 1. The value of the saturated mean velocity also decays with a power law with exponent β~ 0.6 for case H, and β~ 0.3 for case A. In case D this velocity is almost constant for small dissipations.