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Coupled instabilities drive quasiperiodic order-disorder transitions in Faraday waves

Valeri Frumkin*,†

Shreyas Gokhale*,‡

  • Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

  • Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

  • *These authors contributed equally to this work.
  • †valerafr@mit.edu
  • ‡gokhales@mit.edu

Phys. Rev. E 108, L012601 – Published 17 July, 2023

DOI: https://doi.org/10.1103/PhysRevE.108.L012601

Abstract

We present an experimental study of quasiperiodic transitions between a highly ordered square-lattice pattern and a disordered, defect-riddled state, in a circular Faraday system. We show that the transition is driven initially by a long-wave amplitude modulation instability, which excites the oscillatory transition phase instability, leading to the formation of dislocations in the Faraday lattice. The appearance of dislocations dampens amplitude modulations, which prevents further defects from being created and allows the system to relax back to its ordered state. The process then repeats itself in a quasiperiodic manner. Our experiments reveal an unexpected mechanism for temporal quasiperiodicity that results from a coupling between two distinct instabilities on the route to chaos.

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