Localized Faraday patterns under heterogeneous parametric excitation

Abstract

Faraday waves are a classic example of a system in which an extended pattern emerges under spatially uniform forcing. Motivated by systems in which uniform excitation is not plausible, we study both experimentally and theoretically the effect of heterogeneous forcing on Faraday waves. Our experiments show that vibrations restricted to finite regions lead to the formation of localized subharmonic wave patterns and change the onset of the instability. The prototype model used for the theoretical calculations is the parametrically driven and damped nonlinear Schrödinger equation, which is known to describe well Faraday-instability regimes. For an energy injection with a Gaussian spatial profile, we show that the evolution of the envelope of the wave pattern can be reduced to a Weber-equation eigenvalue problem. Our theoretical results provide very good predictions of our experimental observations provided that the decay length scale of the Gaussian profile is much larger than the pattern wavelength.

10 pages, 9 figures, Accepted

References in corpus (1)

• Streaming patterns in Faraday waves

Cited by in corpus (8)

• Heterogeneity-stabilized homogeneous states in driven media
• Spatial asymmetries of resonant oscillations in periodically forced heterogeneous media
• Drift instabilities in localised Faraday patterns
• Self-organization in the one-dimensional Landau-Lifshitz-Gilbert-Slonczewski equation with non-uniform anisotropy fields
• Dissipative structures in a parametrically driven dissipative lattice: chimera, localized disorder, continuous-wave, and staggered state
• Spatial heterogeneity may form an inverse camel shape Arnol'd tongue in parametrically forced oscillations
• Breather bound states in a parametrically driven magnetic wire
• Ellipticity effects on diffusive magnon spin and heat transport in easy-plane ferromagnets