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Front depinning by deterministic and stochastic fluctuations: A comparison.

A J Alvarez-Socorro1, Marcel G Clerc1, M A Ferré1

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Deterministic fluctuations in many-body systems can pin fronts, unlike Gaussian noise. This study reveals a complex, fractal-like pinning-depinning transition in phase turbulence, offering a new characterization for driven dissipative systems.

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Area of Science:

  • Statistical Physics
  • Complex Systems
  • Nonlinear Dynamics

Background:

  • Driven dissipative many-body systems are modeled using macroscopic variables with fluctuations accounting for microscopic details.
  • Front dynamics in such systems are influenced by various types of fluctuations, impacting phenomena like pinning and depinning.

Purpose of the Study:

  • To investigate the effect of deterministic fluctuations from phase turbulence on front dynamics.
  • To analyze the pinning-depinning transition in the presence of deterministic fluctuations and compare it to noise-driven systems.

Main Methods:

  • Modeling front dynamics under deterministic fluctuations derived from phase turbulence.
  • Derivation of an equation for front position, characterized as an overdamped system with a ratchet potential and chaotic forcing.
  • Transformation of the derived equation into a linear parametrically driven oscillator with chaotic frequency.

Main Results:

  • Deterministic fluctuations can lead to front pinning, a behavior contrasting with systems exhibiting Gaussian white noise.
  • The pinning-depinning transition in the deterministic case is robust but exhibits a complex, fractal-like structure in parameter space.
  • Noise-driven front propagation shows a washed-out pinning-depinning transition, unlike the deterministic case.

Conclusions:

  • A novel characterization of the pinning-depinning transition in parameter space is provided for deterministic fluctuation systems.
  • The derived model, an oscillator with chaotic forcing, offers an unambiguous description of this transition.
  • Deterministic fluctuations present distinct front dynamics and transition behaviors compared to stochastic (noise-driven) systems.