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Nonreciprocal wave scattering on nonlinear string-coupled oscillators.

Stefano Lepri1, Arkady Pikovsky2

  • 1Consiglio Nazionale delle Ricerche, Istituto dei Sistemi Complessi, via Madonna del Piano 10, I-50019 Sesto Fiorentino, Italy.

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This study explores wave scattering in a string with nonlinear oscillators, demonstrating non-reciprocal transmission. The system exhibits unique behaviors like chaotic diode effects, offering potential for novel modulators.

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Area of Science:

  • Nonlinear Dynamics
  • Wave Scattering
  • Mechanical Metamaterials

Background:

  • Investigates wave propagation in a string system coupled with nonlinear lumped oscillators.
  • Models the system as a driven-dissipative neutral delay differential equation.
  • Highlights the role of nonlinearity in creating directional asymmetry.

Purpose of the Study:

  • Analyze non-reciprocal wave scattering in a nonlinear string-oscillator system.
  • Explore the emergence of periodic, quasiperiodic, and chaotic scattering regimes.
  • Identify potential applications as non-reciprocal modulators and a "chaotic diode".

Main Methods:

  • Utilizes the amplitude equation approach for approximate analysis of periodic regimes.
  • Employs numerical simulations of the full delay differential equation system.
  • Investigates Hopf bifurcations to understand modulator behavior.

Main Results:

  • Demonstrates non-reciprocal scattering due to nonlinear oscillators.
  • Identifies periodic scattering regimes via Hopf bifurcations, acting as a non-reciprocal modulator.
  • Reveals complex dynamics including quasiperiodic and chaotic scattering, and a "chaotic diode" effect.

Conclusions:

  • The nonlinear string-oscillator system exhibits directional asymmetry in wave transmission.
  • The system can function as a non-reciprocal modulator and a "chaotic diode".
  • Nonlinear dynamics lead to complex scattering phenomena with potential device applications.