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Non-uniform drag force on the Fermi accelerator model

Author

Listed:
  • Tavares, Danila F.
  • Leonel, Edson D.
  • Costa Filho, R.N.

Abstract

Some dynamical properties of a particle suffering the action of a generic drag force are obtained for a dissipative Fermi Acceleration model. The dissipation is introduced via a viscous drag force, like a gas, and is assumed to be proportional to a power of the velocity: F∝−vγ. The dynamics is described by a two-dimensional nonlinear area-contracting mapping obtained via the solution of Newton’s second law of motion. We prove analytically that the decay of high energy is given by a continued fraction which recovers the following expressions: (i) linear for γ=1; (ii) exponential for γ=2; and (iii) second-degree polynomial type for γ=1.5. Our results are discussed for both the complete version and the simplified version. The procedure used in the present paper can be extended to many different kinds of system, including a class of billiards problems.

Suggested Citation

  • Tavares, Danila F. & Leonel, Edson D. & Costa Filho, R.N., 2012. "Non-uniform drag force on the Fermi accelerator model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(22), pages 5366-5374.
    • Handle: RePEc:eee:phsmap:v:391:y:2012:i:22:p:5366-5374
    DOI: 10.1016/j.physa.2012.06.044
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    Keywords

    Fermi accelerator model; Damping forces;

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