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This study reveals how random initial states evolve into intermittent steady states through a growing length scale. This scale governs intermittency measures like flatness, showing nonmonotonic time dependence.

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Area of Science:

  • Statistical physics
  • Complex systems dynamics
  • Surface growth phenomena

Background:

  • Understanding the emergence of complex patterns from simple initial conditions is a fundamental challenge.
  • Intermittency, characterized by bursts of activity, is observed in various physical and natural systems.
  • Passive sliders on fluctuating surfaces provide a tractable model for studying spatio-temporal pattern formation.

Purpose of the Study:

  • To elucidate the mechanism by which a steady state with strong intermittency develops from random initial conditions.
  • To identify the key scaling properties governing this developmental process.
  • To investigate the aging properties and time-dependent behavior of intermittency measures.

Main Methods:

  • Numerical simulations of passive sliders on fluctuating surfaces, including Kardar-Parisi-Zhang (KPZ) and Edwards-Wilkinson (EW) surfaces.
  • Development and analysis of a simple sticky slider model.
  • Calculation of time-dependent flatness and hyperflatness as measures of intermittency.
  • Study of aging properties using two-time flatness measurements.

Main Results:

  • The approach to an intermittent steady state is characterized by an indefinitely growing length scale that dictates scaling properties.
  • A simple sticky slider model predicts scaling forms for time-dependent flatness and hyperflatness, confirmed numerically for KPZ surfaces.
  • Time-dependent flatness exhibits nonmonotonic behavior with distinct scaling forms at short and long times.
  • The established scaling description holds for more diffuse clustering, as seen in EW driving or antiadvection, albeit with different exponents and functions.

Conclusions:

  • A universal mechanism involving a growing length scale governs the development of intermittency in passive slider systems.
  • Intermittency measures display complex, nonmonotonic time dependencies, indicating aging effects.
  • The findings provide a framework for understanding intermittency in diverse driven systems, with potential implications for surface growth and complex dynamics.