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Multifrequency control of Faraday wave patterns.

Chad M Topaz1, Jeff Porter, Mary Silber

  • 1Department of Mathematics, University of California-Los Angeles, Los Angeles, CA 90095, USA. topaz@ucla.edu

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 9, 2005
PubMed
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Manipulating Faraday wave patterns is possible by adjusting the harmonic content of the forcing function. Resonant triad interactions are key, with only a few frequencies and their phases significantly influencing pattern selection.

Area of Science:

  • Nonlinear Dynamics
  • Fluid Mechanics
  • Pattern Formation

Background:

  • Faraday waves exhibit complex patterns driven by periodic forcing.
  • Understanding pattern selection mechanisms is crucial for controlling fluid dynamics.

Purpose of the Study:

  • To investigate how harmonic content in forcing functions influences Faraday wave pattern formation.
  • To identify key resonant interactions governing pattern selection.

Main Methods:

  • Symmetry-based analysis under weak damping and forcing assumptions.
  • Investigation of resonant triad interactions between standing and damped modes.
  • Numerical simulations to validate results for larger damping and forcing values.

Main Results:

Related Experiment Videos

  • Harmonic content and relative phases of forcing functions critically affect pattern selection.
  • At most five frequencies significantly influence triad interactions.
  • Resonant triad interactions can either enhance or suppress pattern formation.

Conclusions:

  • The harmonic content of periodic forcing offers a method to control Faraday wave patterns.
  • The findings are applicable to both one-dimensional and two-dimensional patterns, including superlattices and quasipatterns.