Analytical Study of Giant Fluctuations and Temporal Intermittency

Sachdeva, Himani; Barma, Mustansir

doi:10.1007/s10955-013-0899-1

Cited by 8 publications

(4 citation statements)

References 44 publications

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“…Differences between systems would manifest themselves in the value of the dynamical exponent z, and the forms of the scaling functions. We expect this description to work for a number of systems which exhibit clustering such as inelastically colliding particles [29], aggregating clusters in open systems [30], particles driven by a spatially correlated Gaussian field leading to path coalescence [31,32] and the zero-range process [33], along with the physical systems they describe.…”

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confidence: 99%

Time evolution of intermittency in the passive slider problem

Singha

Barma

2018

Phys. Rev. E

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How does a steady state with strong intermittency develop in time from an initial state which is statistically random? For passive sliders driven by various fluctuating surfaces, we show that the approach involves an indefinitely growing length scale which governs scaling properties. A simple model of sticky sliders suggests scaling forms for the time-dependent flatness and hyperflatness, both measures of intermittency and these are confirmed numerically for passive sliders driven by a Kardar-Parisi-Zhang surface. Aging properties are studied via a two-time flatness. We predict and verify numerically that the time-dependent flatness is, remarkably, a nonmonotonic function of time with different scaling forms at short and long times. The scaling description remains valid when clustering is more diffuse as for passive sliders evolving through Edwards-Wilkinson driving or under antiadvection, although exponents and scaling functions differ substantially.

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confidence: 99%

Time evolution of intermittency in the passive slider problem

Singha

Barma

2018

Phys. Rev. E

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“…one can determine the stationary mass distribution at the origin as we demonstrated in section 2.4. (One can probably push this analysis and probe fluctuations, see [41] for a recent effort in this direction.) Our analysis in one dimension is exact, while the applicability of rate equation above the critical dimension is a rather subtle issue.…”

Section: Discussionmentioning

confidence: 99%

Aggregation driven by a localized source

Krapivsky

2015

J. Phys. A: Math. Theor.

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We study aggregation driven by a localized source of monomers. The densities become stationary and have algebraic tails far away from the source. We show that in a model with mass-independent reaction rates and diffusion coefficients, the density of monomers decays as r −β(d) in d dimensions.The decay exponent has irrational values in physically relevant dimensions: β(3) = ( √ 17 + 1)/2 and β(2) = √ 8. We also study Brownian coagulation with a localized source and establish the behavior of the total cluster density and the total number of of clusters in the system. The latter quantity exhibits a logarithmic growth with time.PACS numbers: 05.40.-a, 82.20.-w, 82.70.-y Equating the two asymptotic behaviors, r −2 ∼ Jr −1 , we estimate the location of the crossover region: r ∼ J −1 . The asymptotic (8) [resp. (10)] is therefore applicable when r J −1 [resp. r J −1 ].

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“…A similar model but with symmetric dynamics [21] of the particles was later studied and both studies saw the emergence of a new phase-the empty road (ER) phase with zero bulk density which was explained using a cluster analysis. With periodic boundary conditions and conserved particle numbers, the dynamics of these models can be mapped exactly to the chipping-diffusion-aggregation models (henceforth CDA models) [22][23][24][25][26]. The CDA models consider a lattice that allows occupancy of multiple particles at the same site.…”

Section: Introductionmentioning

confidence: 99%

The effect of boundaries and impurity on a system with non-local hop dynamics

Karthika¹,

Nagar²

2019

J. Phys. A: Math. Theor.

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We study a one-dimensional lattice model of particles which interact with each other via hard-core repulsion, and which can make long hops in addition to the usual nearest neighbour hopping dynamics. The parameter p gives the probability for long hops and the p = 0 limit leads to the well studied totally asymmetric simple exclusion process (TASEP). The first part of this study describes the combined effect of open boundaries and long hops on the steady state of the system. Apart from the usual low density (LD), high density (HD) and maximum current (MC) phases, the introduction of a finite p leads to a new possibility-an empty road (ER) phase with particles clearing out faster than they enter. The variation in the phase diagram with p is interesting, with the LD and MC phases vanishing at large values of p while the ER and HD phases divide the parameter space into 1/2. In the second part of this study, we look at the combined effect of long hops and static/dynamic impurities. The boundaries are taken to be periodic for simplicity. We see that the system with a static impurity and with 0 < p < 1 shows a phase transition from a shock phase characterised by finite densities on either side of the shock (HD–LD phase) to a phase where the density on one side of the shock is zero (HD-ER phase). We also study the effect of a dynamic impurity, introduced via a slow particle. Here, the system undergoes a phase transition from a homogeneous phase to a shock phase depending on the density, the speed of the particle, as well as the probability p. The shock phase dominates the phase diagram at large values of p. All our studies involve numerical simulations which are supported by mean field theory arguments. The mean field approximation works well qualitatively and correctly identifies the possible phases, while the quantitative agreement with numerics varies, depending on parameter values.

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Analytical Study of Giant Fluctuations and Temporal Intermittency

Cited by 8 publications

References 44 publications

Time evolution of intermittency in the passive slider problem

Time evolution of intermittency in the passive slider problem

Aggregation driven by a localized source

The effect of boundaries and impurity on a system with non-local hop dynamics

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