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Scarred patterns in surface waves.

A Kudrolli1, M C Abraham, J P Gollub

  • 1Department of Physics, Haverford College, Haverford, Pennsylvania 19041, USA. ukudrolli@clarku.edu

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 20, 2001
PubMed
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Surface waves in stadium billiards exhibit scarred patterns due to quantum chaos. Nonlinearity and boundary effects influence wave behavior, leading to suppressed or enhanced modes along specific periodic orbits.

Area of Science:

  • Nonlinear dynamics
  • Wave phenomena
  • Quantum chaos

Background:

  • Chaotic ray dynamics in bounded systems can lead to scarred wave patterns.
  • Faraday waves exhibit nonlinear behavior beyond their instability threshold.

Purpose of the Study:

  • Investigate the interplay between boundaries and nonlinearity in surface wave patterns.
  • Explore mode selection and pattern formation in a stadium billiard geometry.

Main Methods:

  • Experimental investigation of parametrically forced surface waves (Faraday waves).
  • Systematic scan of wave patterns across different driving accelerations.
  • Characterization of spatiotemporal chaos using pattern entropy.

Main Results:

Related Experiment Videos

  • Observed a subset of linear modes, enhanced along periodic ray orbits, while others were suppressed.
  • Identified time-independent scarred patterns and asymmetric/disordered states near onset.
  • Characterized spatiotemporal chaos via pattern entropy, noting reduced pattern change near ordered states.

Conclusions:

  • Nonlinearity and boundary conditions significantly influence wave pattern formation in chaotic systems.
  • Observed phenomena align with predictions regarding boundary dissipation and Lyapunov exponents.
  • Complex, symmetric patterns can emerge even in chaotic regimes.