Time evolution of intermittency in the passive slider problem

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.

5 pages 6 figures

References in corpus (5)

• Burgers Turbulence
• Phase segregation of passive advective particles in an active medium
• Violation of Porod law in a freely cooling granular gas in one dimension
• Aging dynamics of non-linear elastic interfaces: the Kardar-Parisi-Zhang equation
• Glassy dynamics, aging and thermally activated avalanches in interface pinning at finite temperatures

Cited by in corpus (5)

• Clustering, intermittency and scaling for passive particles on fluctuating surfaces
• Response to a small external force and fluctuations of a passive particle in a one-dimensional diffusive environment
• Comment on "Replica Symmetry Breaking in Trajectories of a Driven Brownian Particle"
• Reply to Comment on "Replica symmetry breaking in trajectories of a driven Brownian particle"
• A Novel Mechanism of Ordering in a Coupled Driven System: Vacancy Induced Phase Separation