Passive Sliders on Fluctuating Surfaces: Strong-Clustering States

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.

To be published in Physical Review Letters

References in corpus (4)

• Particles and fields in fluid turbulence
• Passive Sliders on Growing Surfaces and (anti-)Advection in Burger's Flows
• Passive Random Walkers and River-like Networks on Growing Surfaces
• Dynamics of a passive sliding particle on a randomly fluctuating surface

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