Passive Sliders on Fluctuating Surfaces: Strong-Clustering States

Nagar, Apoorva; Barma, Mustansir; Majumdar, Satya N.

doi:10.1103/physrevlett.94.240601

Cited by 30 publications

(45 citation statements)

References 16 publications

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“…To find the latter, we simulated a surface with height field h(r, t) evolving according to KPZ dynamics, and evaluated the density using the equilibrium weight ρ(r, t) = e −βh(r,t) /Z. As shown in [10], the results with β = 4 agree with the autocorrelation function in the nonequilibrium system, apart from a numerical factor.…”

Section: The Density-density Correlation Functionmentioning

confidence: 76%

“…Does the phenomenon survive in higher dimensions? These questions will be addressed in a subsequent paper [16], where it will be shown that the steady state is of the SCS kind in all these cases, even though the degree of clustering differs from one case to another.…”

Section: Future Workmentioning

confidence: 97%

“…The divergence indicates formation of clusters while the scaling of r with L implies that the clusters are typically separated from each other by a distance that scales with the system size. A brief account of some of our our results has appeared in [10].…”

Section: Introductionmentioning

confidence: 97%

“…Specifically, we study and characterize the steady state properties of passive, non-interacting particles sliding on a fluctuating surface and subject to noise [9,10]. The surface is the autonomously evolving field and the particles slide downwards along the local slope.…”

Section: Introductionmentioning

confidence: 99%

“…One can also consider dropping the nonlinear term itself; this leads to the Edwards-Wilkinson (EW) equation for surface growth. The problems of KPZ anti-advection and passive sliders on an Edwards Wilkinson surface are interesting in themselves and will be addressed in a subsequent paper [16].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

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

2006

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We study the clustering of passive, non-interacting particles moving under the influence of a fluctuating field and random noise, in one dimension. The fluctuating field in our case is provided by a surface governed by the Kardar-Parisi-Zhang (KPZ) equation and the sliding particles follow the local surface slope. As the KPZ equation can be mapped to the noisy Burgers equation, the problem translates to that of passive scalars in a Burgers fluid. We study the case of particles moving in the same direction as the surface, equivalent to advection in fluid language. MonteCarlo simulations on a discrete lattice model reveal extreme clustering of the passive particles. The resulting Strong Clustering State is defined using the scaling properties of the two point densitydensity correlation function. Our simulations show that the state is robust against changing the ratio of update speeds of the surface and particles. In the equilibrium limit of a stationary surface and finite noise, one obtains the Sinai model for random walkers on a random landscape. In this limit, we obtain analytic results which allow closed form expressions to be found for the quantities of interest. Surprisingly, these results for the equilibrium problem show good agreement with the results in the non-equilibrium regime.

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Section: The Density-density Correlation Functionmentioning

confidence: 76%

Section: Future Workmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

2006

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Analytical Study of Giant Fluctuations and Temporal Intermittency

Sachdeva

Barma

2013

J Stat Phys

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We study analytically giant fluctuations and temporal intermittency in a stochastic onedimensional model with diffusion and aggregation of masses in the bulk, along with influx of single particles and outflux of aggregates at the boundaries. We calculate various static and dynamical properties of the total mass in the system for both biased and unbiased movement of particles and different boundary conditions. These calculations show that (i) in the unbiased case, the total mass has a non-Gaussian distribution and shows giant fluctuations which scale as system size (ii) in all the cases, the system shows strong intermittency in time, which is manifested in the anomalous scaling of the dynamical structure functions of the total mass. The results are derived by taking a continuum limit in space and agree well with numerical simulations performed on the discrete lattice. The analytic results obtained here are typical of the full phase of a more general model with fragmentation, which was studied earlier using numerical simulations.

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Universality Classes in Two-Component Driven Diffusive Systems

2015

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We study time-dependent density fluctuations in the stationary state of driven diffusive systems with two conserved densities ρ λ . Using Monte-Carlo simulations of two coupled single-lane asymmetric simple exclusion processes we present numerical evidence for universality classes with dynamical exponents z = (1 + √ 5)/2 and z = 3/2 (but different from the Kardar-Parisi-Zhang (KPZ) universality class), which have not been reported yet for driven diffusive systems. The numerical asymmetry of the dynamical structure functions converges slowly for some of the non-KPZ superdiffusive modes for which mode coupling theory predicts maximally asymmetric z-stable Lévy scaling functions. We show that all universality classes predicted by mode coupling theory for two conservation laws are generic: They occur in two-component systems with nonlinearities in the associated currents already of the minimal order ρ 2 λ ρ µ . The macroscopic stationary current-density relation and the compressibility matrix determine completely all permissible universality classes through the mode coupling coefficients which we compute explicitly for general two-component systems.

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Passive Sliders on Fluctuating Surfaces: Strong-Clustering States

Cited by 30 publications

References 16 publications

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

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

Analytical Study of Giant Fluctuations and Temporal Intermittency

Universality Classes in Two-Component Driven Diffusive Systems

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