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Fabrication and Testing of Microfluidic Optomechanical Oscillators
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Complex mode dynamics of coupled wave oscillators.

T J Alexander1, D Yan2, P G Kevrekidis2

  • 1School of Physical, Environmental and Mathematical Sciences, University of New South Wales, Canberra, Australia 2600.

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|February 4, 2014
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Summary
This summary is machine-generated.

Localized nonlinear waves in periodic potentials behave like coupled oscillators. Their dynamics exhibit complex phenomena, including chaotic oscillations and Josephson-like effects, accurately modeled by a discrete system.

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Area of Science:

  • Nonlinear dynamics
  • Wave physics
  • Condensed matter physics

Background:

  • Periodic potentials host localized wave phenomena.
  • Coupled oscillator systems exhibit rich dynamics.
  • Understanding wave behavior in potentials is crucial for quantum and classical systems.

Purpose of the Study:

  • To investigate the oscillatory behavior of nonlinear coherent waves in periodic potentials.
  • To model these waves as coupled oscillators.
  • To explore the transition from small to large amplitude excitations and associated complex dynamics.

Main Methods:

  • Analysis of nonlinear coherent waves in periodic potentials.
  • Identification of small-amplitude oscillation modes.
  • Extension of analysis to large amplitude regimes.
  • Development and application of a discrete model with nearest-neighbor coupling.

Main Results:

  • Nonlinear coherent waves in periodic potentials act as coupled wave oscillators.
  • Small-amplitude modes extend to large amplitudes, with some persisting.
  • Complex behaviors observed include Josephson-like oscillation breakdown, mode destabilization, and chaotic oscillations.
  • A discrete model with nearest-neighbor coupling accurately describes the system dynamics.

Conclusions:

  • Localized nonlinear waves in periodic potentials can be effectively treated as coupled oscillators.
  • The system exhibits complex nonlinear dynamics, including chaos, at large amplitudes.
  • A discrete lattice model provides an accurate description of these wave oscillator dynamics.