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Singular scaling functions in clustering phenomena

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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.

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Authors and Affiliations

  1. Department of Theoretical Physics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai, 400005, India

    M. Barma

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  1. M. Barma
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Barma, M. Singular scaling functions in clustering phenomena. Eur. Phys. J. B 64, 387–393 (2008). https://doi.org/10.1140/epjb/e2008-00118-9

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  • DOI: https://doi.org/10.1140/epjb/e2008-00118-9

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