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Suppressing Fermi acceleration in two-dimensional driven billiards.

Edson D Leonel1, Leonid A Bunimovich

  • 1Departamento de Estatística, Matemática Aplicada e Computação-IGCE-UNESP-Univ Estadual Paulista, Rio Claro, SP, Brazil.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 28, 2010
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Summary
This summary is machine-generated.

This study investigates particle dynamics in a dissipative oval billiard with a moving boundary. Results show different velocity decay patterns based on dissipation, with a phase transition observed in some cases.

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Area of Science:

  • Physics
  • Nonlinear Dynamics
  • Statistical Mechanics

Background:

  • Investigating particle dynamics in confined systems is crucial for understanding energy transfer and chaotic behavior.
  • Dissipative systems, where energy is lost over time, exhibit complex behaviors influenced by boundary conditions and interaction laws.
  • Billiard models provide simplified yet powerful frameworks for studying classical mechanics and statistical properties.

Purpose of the Study:

  • To analyze the behavior of particles within an oval-shaped billiard with a periodically moving boundary.
  • To explore the effects of velocity-dependent dissipation on particle dynamics.
  • To identify and characterize phase transitions related to energy gain in dissipative systems.

Main Methods:

  • Simulating particle trajectories in a 2D oval billiard with a time-dependent boundary.
  • Implementing three distinct forms of velocity-dependent dissipation: linear (F∝-V), quadratic (F∝-V^2), and power-law (F∝-V^δ, 1<δ<2).
  • Employing scaling laws to analyze phase transitions and determine critical exponents.

Main Results:

  • Observed linear, exponential, and power-law decay of particle velocity depending on the dissipation type.
  • Identified a phase transition from limited to unlimited energy gain for quadratic and power-law dissipation.
  • Found critical exponents in the quadratic case matching those of the dissipative bouncer model, indicating universality.

Conclusions:

  • Dissipation significantly alters particle velocity decay, with distinct behaviors for different power laws.
  • A universal phase transition exists in certain dissipative billiard systems, linking different models.
  • The study confirms the suppression of unlimited energy growth across all investigated dissipation types.