Strong clustering of noninteracting, sliding passive scalars driven by fluctuating surfaces

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Apoorva Nagar,¹ Satya N. Majumdar,² and Mustansir Barma¹
¹Department of Theoretical Physics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400 005, India
²Laboratoire de Physique Theorique et Modeles Statistiques, Universit'e Paris-Sud, Bâtiment 100, Orsay, France

Received 25 October 2005; revised 20 April 2006; published 29 August 2006

Westudy the clustering of passive, noninteracting particles moving under theinfluence of a fluctuating field and random noise, in oneand two dimensions. The fluctuating field in our case isprovided by surfaces governed by the Kardar-Parisi-Zhang (KPZ) and theEdwards-Wilkinson (EW) equations, and the sliding particles follow the localsurface slope. As the KPZ equation can be mapped tothe noisy Burgers equation, the problem translates to that ofpassive scalars in a Burgers fluid. Monte Carlo simulations ondiscrete lattice models reveal very strong clustering of the passiveparticles for all sorts of dynamics under consideration. The resultingstrong clustering state is defined using the scaling properties ofthe two point density-density correlation function. Our simulations show thatthe state is robust against changing the ratio of updatespeeds of the surface and particles. We also solve therelated equilibrium problem of a stationary surface and finite noise,well known as the Sinai model for random walkers ona random landscape. For this problem, we obtain analytic resultswhich allow closed form expressions to be found for thequantities of interest. Surprisingly, these results for the equilibrium problemshow good agreement with the nonequilibrium KPZ problem.

URL:	http://link.aps.org/doi/10.1103/PhysRevE.74.021124
DOI:	10.1103/PhysRevE.74.021124
PACS:	05.40.-a; 47.40.-x; 02.50.-r; 64.75.+g 05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion 47.40.-x Compressible flows; shock waves 02.50.-r Probability theory, stochastic processes, and statistics 64.75.+g Solubility, segregation, and mixing; phase separation YEAR: 2006
KEYWORDS:	random noise, random processes, fluctuations, Monte Carlo methods, lattice theory

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Phys. Rev. E 74, 021124 (2006) [19 pages]

Strong clustering of noninteracting, sliding passive scalars driven by fluctuating surfaces

REFERENCES (35)

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A new free weekly publication from APS