Singular Scaling Functions in Clustering Phenomena

Abstract

We study clustering in a stochastic system of particles sliding down a fluctuating surface in one and two dimensions. In steady state, the density-density correlation function is a scaling function of separation and system size.This scaling function is singular for small argument -- it exhibits a cusp singularity for particles with mutual exclusion, and a divergence for noninteracting particles. The steady state is characterized by giant fluctuations which do not damp down in the thermodynamic limit. The autocorrelation function is a singular scaling function of time and system size. The scaling properties are surprisingly similar to those for particles moving in a quenched disordered environment that results if the surface is frozen.

8 pages, 3 figures, Invited talk delivered at Statphys 23, Genova, July 2007

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Cited by in corpus (4)

• The low noise phase of a 2d active nematic
• Scattering Properties of Paramagnetic Ground States in the Three-Dimensional Random-Field Ising Model
• Surface-Directed Spinodal Decomposition on Chemically Patterned Substrates
• Two-time correlation and occupation time for the Brownian bridge and tied-down renewal processes