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Localized Faraday patterns under heterogeneous parametric excitation.

Héctor Urra1, Juan F Marín1, Milena Páez-Silva1

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Heterogeneous forcing of Faraday waves creates localized patterns and alters instability onset. This study explores localized wave patterns using nonlinear Schrödinger equations and Gaussian forcing profiles.

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Area of Science:

  • Nonlinear dynamics
  • Fluid mechanics
  • Wave phenomena

Background:

  • Faraday waves typically emerge from uniform forcing.
  • Uniform excitation is not always feasible in real-world systems.

Purpose of the Study:

  • Investigate the impact of heterogeneous forcing on Faraday waves.
  • Analyze the formation of localized wave patterns and changes in instability onset.

Main Methods:

  • Experimental observation of Faraday waves under localized vibrations.
  • Theoretical analysis using the parametrically driven and damped nonlinear Schrödinger equation.
  • Modeling energy injection with a Gaussian spatial profile.

Main Results:

  • Localized subharmonic wave patterns form under finite-region vibrations.
  • The onset of the Faraday instability is modified by heterogeneous forcing.
  • Theoretical predictions align well with experimental results for large Gaussian decay length scales.

Conclusions:

  • Heterogeneous forcing is a viable method to generate localized Faraday wave patterns.
  • The nonlinear Schrödinger equation effectively models these localized patterns.
  • Theoretical models accurately predict experimental outcomes under specific conditions.