Analytic study of the three-urn model for separation of sand

Shim, Gyoung Moo; Park, B. Y.; Noh, Jae Dong; Lee, Hoyun

doi:10.1103/physreve.70.031305

Cited by 18 publications

(27 citation statements)

References 11 publications

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“…7 are given in Table II. Additionally we can observe the different values of the constant prefactors a in the scaling law (6). For asymmetric dynamics, the coarsening time scale is roughly an order of magnitude faster for strongly asymmetric dynamics p left ≤ 0.75 compared with weakly asymmetric dynamics.…”

Section: A Zrpmentioning

confidence: 87%

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Dynamics of condensate formation in stochastic transport with pair-factorized steady states: Nucleation and coarsening time scales

Nagel

Janke

2016

Phys. Rev. E

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Driven diffusive systems such as the zero-range process (ZRP) and the pair-factorized steady states (PFSS) stochastic transport process are versatile tools that lend themselves to the study of transport phenomena on a generic level. While their mathematical structure is simple enough to allow significant analytical treatment, they offer a variety of interesting phenomena. With appropriate dynamics, the ZRP and PFSS models feature a condensation transition where, for a supercritical density, the translational symmetry breaks spontaneously and excess particles form a single-site or spatially extended condensate, respectively. In this paper we numerically study the typical time scales of the two stages of this condensation process: Nucleation and coarsening. Nucleation is the first stage of condensation where the bulk system relaxes to its stationary distribution and droplet nuclei form in the system. These droplets then gradually grow or evaporate in the coarsening regime to coalesce in a single condensate when the system finally relaxes to the stationary state. We use the ZRP condensation model to discuss the choice of the estimation method for the nucleation time scale and present scaling exponents for the ZRP and PFSS condensation models with respect to the choice of the typical droplet nuclei mass. We then proceed to present scaling exponents in the coarsening regime of the ZRP for partially asymmetric dynamics and the PFSS model for symmetric and asymmetric dynamics.

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Section: A Zrpmentioning

confidence: 87%

“…This is achieved by counting the number of droplets that have at least the typical mass (threshold mass) at every time in the trajectory and computing its average over many trajectories. The scaling exponent is then determined visually for the best data collapse assuming the power law (6).…”

Section: Nucleationmentioning

confidence: 99%

Dynamics of condensate formation in stochastic transport with pair-factorized steady states: Nucleation and coarsening time scales

Nagel

Janke

2016

Phys. Rev. E

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“…Furthermore, as cases with L = 2, 3 [5,6,7,8,9,10,11] are already solved we focus on the general case with at least moderate L and large N ≫ 1 particle number. …”

Section: The Modelmentioning

confidence: 99%

“…In the case of exclusion models, it was proved [12] that the correspondence to an already solved model, namely the zero-range process [11] can be of great help, as many results can be obtained directly.…”

Section: Introductionmentioning

confidence: 99%

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Analytic study of clustering in shaken granular material using zero-range processes

Török

2005

Physica A: Statistical Mechanics and its Applications

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Zero-Range Process with Open Boundaries

2005

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We calculate the exact stationary distribution of the one-dimensional zero-range process with open boundaries for arbitrary bulk and boundary hopping rates. When such a distribution exists, the steady state has no correlations between sites and is uniquely characterized by a space-dependent fugacity which is a function of the boundary rates and the hopping asymmetry. For strong boundary drive the system has no stationary distribution. In systems which on a ring geometry allow for a condensation transition, a condensate develops at one or both boundary sites. On all other sites the particle distribution approaches a product measure with the finite critical density ρ c . In systems which do not support condensation on a ring, strong boundary drive leads to a condensate at the boundary. However, in this case the local particle density in the interior exhibits a complex algebraic growth in time. We calculate the bulk and boundary growth exponents as a function of the system parameters.

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Analytic study of the three-urn model for separation of sand

Cited by 18 publications

References 11 publications

Dynamics of condensate formation in stochastic transport with pair-factorized steady states: Nucleation and coarsening time scales

Dynamics of condensate formation in stochastic transport with pair-factorized steady states: Nucleation and coarsening time scales

Analytic study of clustering in shaken granular material using zero-range processes

Zero-Range Process with Open Boundaries

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