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Related Experiment Videos

Geometric diagnostics of complex patterns: spiral defect chaos.

Hermann Riecke1, Santiago Madruga

  • 1Engineering Science and Applied Mathematics, Northwestern University, Evanston, Illinois 60208, USA.

Chaos (Woodbury, N.Y.)
|April 8, 2006
PubMed
Summary

This study introduces an automated method to quantify spiral patterns in complex systems. The findings reveal how fluid properties and heating influence spiral characteristics in Rayleigh-Benard convection.

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Area of Science:

  • Complex systems analysis
  • Fluid dynamics
  • Pattern formation

Background:

  • Spiral patterns are prevalent across physical, chemical, and biological systems.
  • Quantitative characterization of spiral elements in complex patterns is challenging.

Purpose of the Study:

  • To develop an automated approach for quantitatively characterizing spiral-like elements in complex stripe-like patterns.
  • To apply this method to analyze spiral defect chaos in Rayleigh-Benard convection.

Main Methods:

  • An automated method was developed to identify spiral tip location, arc length, and winding number.
  • The approach also quantifies pattern components (Betti number of order 1), size, and shape.
  • The method was applied to spiral defect chaos in thermally driven Rayleigh-Benard convection.

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Main Results:

  • Spiral arc length decreases with lower Prandtl numbers and increased heating.
  • Spiral winding number shows nonmonotonic behavior with heating and depends strongly on the Prandtl number.
  • Large spirals (Pr > 1) exhibit a three-peak distribution for length and winding number, while small Prandtl numbers yield compact patterns.

Conclusions:

  • The developed automated method effectively quantifies spiral characteristics in complex patterns.
  • Fluid properties (Prandtl number) and heating significantly influence spiral formation and morphology in Rayleigh-Benard convection.
  • The study provides insights into the statistical distribution of spiral features, differentiating between high and low Prandtl number regimes.