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Passive Sliders on Fluctuating Surfaces: Strong-Clustering States

Apoorva Nagar·Mustansir Barma·Satya N. Majumdar
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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.

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Apoorva Nagar, Mustansir Barma, Satya N. Majumdar. 2005-05-11. Passive Sliders on Fluctuating Surfaces: Strong-Clustering States. https://doi.org/10.1103/physrevlett.94.240601

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