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Suppressing Fermi acceleration in a two-dimensional non-integrable time-dependent oval-shaped billiard with inelastic collisions

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  • Oliveira, Diego F.M.
  • Leonel, Edson D.

Abstract

Some dynamical properties of a classical particle confined inside a closed region with an oval-shaped boundary are studied. We have considered both the static and time-dependent boundaries. For the static case, the condition that destroys the invariant spanning curves in the phase space was obtained. For the time-dependent perturbation, two situations were considered: (i) non-dissipative and (ii) dissipative. For the non-dissipative case, our results show that Fermi acceleration is observed. When dissipation, via inelastic collisions, is introduced Fermi acceleration is suppressed. The behaviour of the average velocity for both the dissipative as well as the non-dissipative dynamics is described using the scaling approach.

Suggested Citation

  • Oliveira, Diego F.M. & Leonel, Edson D., 2010. "Suppressing Fermi acceleration in a two-dimensional non-integrable time-dependent oval-shaped billiard with inelastic collisions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(5), pages 1009-1020.
    • Handle: RePEc:eee:phsmap:v:389:y:2010:i:5:p:1009-1020
    DOI: 10.1016/j.physa.2009.10.036
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    Citations

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    Cited by:

    1. Oliveira, Diego F.M. & Roberto Silva, Mario & Leonel, Edson D., 2015. "A symmetry break in energy distribution and a biased random walk behavior causing unlimited diffusion in a two dimensional mapping," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 436(C), pages 909-915.
    2. Oliveira, Diego F.M. & Leonel, Edson D., 2014. "Statistical and dynamical properties of a dissipative kicked rotator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 413(C), pages 498-514.
    3. Cetin, Kivanc & Tirnakli, Ugur & Oliveira, Diego F.M. & Leonel, Edson D., 2024. "Statistical mechanical characterization of billiard systems," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    4. Oliveira, Diego F.M. & Robnik, Marko & Leonel, Edson D., 2011. "Dynamical properties of a particle in a wave packet: Scaling invariance and boundary crisis," Chaos, Solitons & Fractals, Elsevier, vol. 44(10), pages 883-890.

    More about this item

    Keywords

    Fermi acceleration;

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