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Global ballistic acceleration in a bouncing-ball model.

Tiago Kroetz1, André L P Livorati2,3, Edson D Leonel3,4

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This summary is machine-generated.

This study reveals how accelerator modes drive particle velocity increases in a bouncing-ball model, leading to distinct growth regimes. Fractal basins of influence impact the system's average velocity.

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Area of Science:

  • Physics
  • Dynamical Systems
  • Chaos Theory

Background:

  • The bouncing-ball model is a classic system for studying chaotic dynamics.
  • Fermi acceleration describes particle energy increase through repeated collisions.

Purpose of the Study:

  • Investigate the phenomenon of ballistic velocity increase in a bouncing-ball model.
  • Characterize accelerator and deaccelerator modes and their impact on particle dynamics.

Main Methods:

  • Analytical determination of parameter sets for acceleration and deacceleration structures.
  • Analysis of phase space dynamics, including accelerator and deaccelerator modes.
  • Investigation of non-symplectic mapping effects on system behavior.

Main Results:

  • Identified accelerator modes causing regular, monotonic velocity increases.
  • Observed coexistence of regular and ballistic Fermi acceleration, defining two growth regimes.
  • Characterized deaccelerator modes and their relation to unstable points.
  • Found fractal basins of influence due to non-symplectic mapping, affecting average velocity.

Conclusions:

  • Accelerator modes are key to ballistic velocity increases in the bouncing-ball model.
  • The interplay of regular and ballistic Fermi acceleration creates complex dynamics.
  • Fractal basins of influence significantly impact the global average velocity.