Passive Sliders on Fluctuating Surfaces: Strong-Clustering States

TL;DR

This paper investigates the clustering behavior of particles sliding on a fluctuating surface governed by the KPZ equation, revealing strong clustering and singular scaling functions through simulations and analytic results.

Contribution

It provides new insights into particle clustering on fluctuating surfaces, combining Monte Carlo simulations with analytic solutions for related random walk problems.

Findings

Particles cluster very strongly, with correlation functions diverging at small scales.

Scaling functions for clustering are singular and system-size dependent.

Analytic results for the Sinai problem match simulation findings.

Abstract

We study the clustering properties of particles sliding downwards on a fluctuating surface evolving through the Kardar-Parisi-Zhang equation, a problem equivalent to passive scalars driven by a Burgers fluid. Monte Carlo simulations on a discrete version of the problem in one dimension reveal that particles cluster very strongly: the two point density correlation function scales with the system size with a scaling function which diverges at small argument. Analytic results are obtained for the Sinai problem of random walkers in a quenched random landscape. This equilibrium system too has a singular scaling function which agrees remarkably with that for advected particles.