Emergent motion of condensates in mass-transport models

Hirschberg, Ori; Mukamel, David; Schütz, Gunter M.

doi:10.1103/physreve.87.052116

Cited by 7 publications

(22 citation statements)

References 33 publications

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“…First, the site carrying the maximal number of particles moves unidirectionally, in the same direction as hopping particles. The motion of the condensate is similar to the "slinky"-like motion of a non-Markovian model [30,31] or a generalization of ZRP to non-factorizing probabilities [32]. Second, the evolution speeds up in time; the condensate moves faster and faster as it gains particles, see also Fig.…”

Section: Explosive-condensation Rates Given By Equation (38)mentioning

confidence: 80%

Condensation in stochastic mass transport models: beyond the zero-range process

Evans¹,

Waclaw²

2014

J. Phys. A: Math. Theor.

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We consider an extension of the zero-range process to the case where the hop rate depends on the state of both departure and arrival sites. We recover the misanthrope and the target process as special cases for which the probability of the steady state factorizes over sites. We discuss conditions which lead to the condensation of particles and show that although two different hop rates can lead to the same steady state, they do so with sharply contrasting dynamics. The first case resembles the dynamics of the zero-range process, whereas the second case, in which the hop rate increases with the occupation number of both sites, is similar to instantaneous gelation models. This new "explosive" condensation reveals surprisingly rich behaviour, in which the process of condensate's formation goes through a series of collisions between clusters of particles moving through the system at increasing speed. We perform a detailed numerical and analytical study of the dynamics of condensation: we find the speed of the moving clusters, their scattering amplitude, and their growth time. We finally show that the time to reach steady state decreases with the size of the system. Condensation in stochastic mass transport models: beyond the zero-range process

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Section: Explosive-condensation Rates Given By Equation (38)mentioning

confidence: 80%

Condensation in stochastic mass transport models: beyond the zero-range process

Evans¹,

Waclaw²

2014

J. Phys. A: Math. Theor.

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“…For the same reason the model eludes solution by Bethe ansatz. In possible further studies, the conditions for the existence of real condensation transition and the behavior of the condensate in various modified TASEP models, including those with open boundaries, are of interest [9,14].…”

Section: Discussionmentioning

confidence: 99%

“…Macroscopic quantities of interest, including the current through the system and its fluctuations, as well as configurational properties, such as the dynamics of the largest cluster and the condensation transition, have been of a renewed interest for various generalizations [6][7][8][9][10][11][12][13][14][15][16][17] of the basic TASEP model, many of them interesting, e.g., from the point of view of RNA transcription, jamming of traffic flow, phase separation, and growth phenomena.…”

Section: Introductionmentioning

confidence: 99%

Accelerated transport and growth with symmetrized dynamics

Merikoski

2013

Phys. Rev. E

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In this paper we consider a model of accelerated dynamics with the rules modified from those of the recently proposed [Dong et al., Phys. Rev. Lett. 109, 130602 (2012)] accelerated exclusion process (AEP) such that particle-vacancy symmetry is restored to facilitate a mapping to a solid-on-solid growth model in 1 + 1 dimensions. In addition to kicking a particle ahead of the moving particle, as in the AEP, in our model another particle from behind is drawn, provided it is within the "distance of interaction" denoted by max . We call our model the doubly accelerated exclusion process (DAEP). We observe accelerated transport and interface growth and widening of the cluster size distribution for cluster sizes above max , when compared with the ordinary totally asymmetric exclusion process (TASEP). We also characterize the difference between the TASEP, AEP, and DAEP by computing a "staggered" order parameter, which reveals the local order in the steady state. This order in part explains the behavior of the particle current as a function of density. The differences of the steady states are also reflected by the behavior of the temporal and spatial correlation functions in the interface picture.

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“…Macroscopic quantities of interest, in particular the particle density and current and their fluctuations as well as configurational properties, such as the dynamics of the largest cluster and the condensation transition, have been of renewed interest for various generalizations [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] of the basic TASEP model, many of them interesting, e.g., from the point of view of RNA transcription, jamming of traffic flow, phase separation, and growth phenomena.…”

Section: Introductionmentioning

confidence: 99%

Totally asymmetric exclusion process fed by using a non-Poissonian clock

Merikoski

2015

Phys. Rev. E

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Totally asymmetric exclusion process fed by using a non-Poissonian clock Merikoski, Juha Merikoski, J. (2015). Totally asymmetric exclusion process fed by using a nonPoissonian clock. Physical review E, 91 (6), 062101. doi:10.1103/PhysRevE.91.062101 2015PHYSICAL REVIEW E 91, 062101 (2015) Totally asymmetric exclusion process fed by using a non-Poissonian clock In this article we consider the one-dimensional totally asymmetric open-boundary exclusion process fed by a process with power-law-distributed waiting times. More specifically, we use a modified Pareto distribution to define the jump rate for jumps into the system. We then characterize the propagation of fluctuations through the system by kinetic Monte Carlo simulations and by numerical evaluation of the steady-state partition function.

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Emergent motion of condensates in mass-transport models

Cited by 7 publications

References 33 publications

Condensation in stochastic mass transport models: beyond the zero-range process

Condensation in stochastic mass transport models: beyond the zero-range process

Accelerated transport and growth with symmetrized dynamics

Totally asymmetric exclusion process fed by using a non-Poissonian clock

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