Time evolution of intermittency in the passive slider problem

TL;DR

This paper investigates how intermittency develops over time in passive slider systems driven by fluctuating surfaces, revealing a growing length scale and non-monotonic flatness behavior confirmed through numerical simulations.

Contribution

It introduces a scaling framework for the time evolution of intermittency in passive sliders, validated by numerical results for various surface driving mechanisms.

Findings

Scaling forms for flatness and hyperflatness are confirmed numerically.

Time-dependent flatness exhibits non-monotonic behavior with different regimes.

Scaling description applies across different driving conditions with varying exponents.

Abstract

How does a steady state with strong intermittency develop in time from an initial state which is statistically random? For passive sliders driven by various fluctuating surfaces, we show that the approach involves an indefinitely growing length scale which governs scaling properties. A simple model of sticky sliders suggests scaling forms for the time-dependent flatness and hyperflatness, both measures of intermittency and these are confirmed numerically for passive sliders driven by a Kardar-Parisi-Zhang surface. Aging properties are studied via a two-time flatness. We predict and verify numerically that the time-dependent flatness is, remarkably, a non-monotonic function of time, with different scaling forms at short and long times. The scaling description remains valid when clustering is more diffuse as for passive sliders evolving through Edwards-Wilkinson driving or under antiadvection, although exponents and scaling functions differ substantially.