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Related Experiment Videos

Slow relaxation in weakly open rational polygons.

Valery B Kokshenev1, Eduardo Vicentini

  • 1Departamento de Física, Universidade Federal de Minas Gerais, ICEx, Caixa Postal 702, CEP 30123-970, Belo Horizonte, Minas Gerais, Brazil.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 26, 2003
PubMed
Summary

This study reveals two distinct decay pathways in polygonal billiards, differentiating between regular sliding orbits and chaotic excitations arising from vertex effects. These findings clarify complex dynamics in nonintegrable systems.

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From ballistic to Brownian motion through enhanced diffusion in vertex-splitting polygonal and disk-dispersing Sinai billiards.

Physical review. E, Statistical, nonlinear, and soft matter physics·2002

Area of Science:

  • Mathematical Physics
  • Dynamical Systems
  • Statistical Mechanics

Background:

  • Polygonal billiards are simplified models for studying complex dynamical systems.
  • Understanding boundary effects is crucial for analyzing particle behavior in confined spaces.
  • Nonintegrable systems exhibit complex, often chaotic, dynamics.

Purpose of the Study:

  • To investigate the interplay between regular and irregular boundary effects in rational polygonal billiards.
  • To analyze the decay dynamics and establish relaxation channels.
  • To characterize the late-time survival probability S(m) as a function of time t.

Main Methods:

  • Analysis of decay dynamics through late-time survival probability S(m) ~ t(-delta).
  • Identification and characterization of distinct slow relaxation channels.

Related Experiment Videos

  • Examination of the conditions under which secondary relaxation channels become active.

    • Main Results:

    • Two distinct slow relaxation channels were identified.
    • A primary universal channel with delta=1 corresponds to the relaxation of regular sliding orbits.
    • A secondary channel with delta>1 opens when m>P(m)/Delta, linked to vertex order-disorder effects and chaoticlike excitations.

    Conclusions:

    • The study establishes two fundamental decay mechanisms in polygonal billiards.
    • The findings highlight the significant role of vertex geometry in system dynamics.
    • This work provides insights into the relaxation processes in nonintegrable dynamical systems.