Time evolution of intermittency in the passive slider problem

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.