Asymmetric simple exclusion process on a Cayley tree

Basu, Mahashweta; Mohanty, P. K.

doi:10.1088/1742-5468/2010/10/p10014

Cited by 15 publications

(25 citation statements)

References 17 publications

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“…(9) it follows that either ρ (2,3) bulk = ρ − (1/8) 0.146 and the defect chains C 2,3 are in the LD phase or ρ (2,3) bulk = ρ + (1/8) 0.854 and the defect chains C 2,3 are in the HD phase.…”

Section: A Mean-field Theorymentioning

confidence: 99%

“…The values of α * d and β * d are calculated from the finite-size numerical data for the local densities τ (1) L 1 , τ (4) 1 , τ (2,3) 1 and τ (2,3) L d using Eqs. (5) and (6) with J L = J MC = 1/4.…”

Section: A Mean-field Theorymentioning

confidence: 99%

“…However, in the presence of hard-core exclusion the collective behavior of such transportation networks is not yet well understood. Indeed, the role of junctions has been considered only recently in the example of simple networks involving no more than two junctions (see [1,2]) or in self-similar treelike topologies (see [3] and references therein).…”

Section: Introductionmentioning

confidence: 99%

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Position dependence of the particle density in a double-chain section of a linear network in a totally asymmetric simple exclusion process

Pesheva

Brankov²

2013

Phys. Rev. E

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We report here results on the study of the totally asymmetric simple exclusion process, defined on an open network, consisting of head and tail simple-chain segments with a double-chain section inserted in between. Results of numerical simulations for relatively short chains reveal an interesting feature of the network. When the current through the system takes its maximum value, a simple translation of the double-chain section forward or backward along the network leads to a sharp change in the shape of the density profiles in the parallel chains, thus affecting the total number of particles in that part of the network. In the symmetric case of equal injection and ejection rates α=β>1/2 and equal lengths of the head and tail sections, the density profiles in the two parallel chains are almost linear, characteristic of the coexistence line (shock phase). Upon moving the section forward (backward), their shape changes to the one typical for the high- (low-) density phases of a simple chain. The total bulk density of particles in a section with a large number of parallel chains is evaluated too. The observed effect might have interesting implications for the traffic flow control as well as for biological transport processes in living cells. An explanation of this phenomenon is offered in terms of a finite-size dependence of the effective injection and ejection rates at the ends of the double-chain section.

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Section: A Mean-field Theorymentioning

confidence: 99%

Section: A Mean-field Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Position dependence of the particle density in a double-chain section of a linear network in a totally asymmetric simple exclusion process

Pesheva

Brankov²

2013

Phys. Rev. E

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“…These systems allow additional motion of particles in the TASEPs and can be interpreted as networks of TASEPs and reservoirs, where each site in a lattice is connected with the particle reservoir or a site in a different TASEP. On the other hand, the TASEP on networks has been focused on recently [16][17][18][19]. The results have concluded that the dynamics of the system depends on structure of the networks.…”

Section: Introductionmentioning

confidence: 99%

A balance network for the asymmetric simple exclusion process

Ezaki

Nishinari

2012

J. Stat. Mech.

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We investigate a balance network of the asymmetric simple exclusion process (ASEP). Subsystems consisting of ASEPs are connected by bidirectional links with each other, which results in balance between every pair of subsystems. The network includes some specific important cases discussed in earlier works such as the ASEP with the Langmuir kinetics, multiple lanes and finite reservoirs. Probability distributions of particles in the steady state are exactly given in factorized forms according to their balance properties. Although the system has nonequilibrium parts, the expressions are well described in a framework of statistical mechanics based on equilibrium states. Moreover, the overall argument does not depend on the network structures, and the knowledge obtained in this work is applicable to a broad range of problems.

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“…However, very little analysis has been carried out for the transport of packets in tree-or river-like branching hierarchical networks [30]. In this paper, we explore the transport dynamics and statistics on a hierarchical regular 2D lattice model, two of its variants [31], and its critical case [32].…”

Section: Introductionmentioning

confidence: 99%

Transmission of packets on a hierarchical network: Statistics and explosive percolation

Kachhvah

Gupte

2012

Phys. Rev. E

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We analyze an idealized model for the transmission or flow of particles, or discrete packets of information, in a weight bearing branching hierarchical 2 − D networks, and its variants. The capacities add hierarchically down the clusters. Each node can accommodate a limited number of packets, depending on its capacity and the packets hop from node to node, following the links between the nodes. The statistical properties of this system are given by the Maxwell -Boltzmann distribution. We obtain analytical expressions for the mean occupation numbers as functions of capacity, for different network topologies. The analytical results are shown to be in agreement with the numerical simulations. The traffic flow in these models can be represented by the site percolation problem. It is seen that the percolation transitions in the 2−D model and in its variant lattices are continuous transitions, whereas the transition is found to be explosive (discontinuous) for the V − lattice, the critical case of the 2 − D lattice. The scaling behavior of the second order percolation case is studied in detail. We discuss the implications of our analysis.

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Asymmetric simple exclusion process on a Cayley tree

Cited by 15 publications

References 17 publications

Position dependence of the particle density in a double-chain section of a linear network in a totally asymmetric simple exclusion process

Position dependence of the particle density in a double-chain section of a linear network in a totally asymmetric simple exclusion process

A balance network for the asymmetric simple exclusion process

Transmission of packets on a hierarchical network: Statistics and explosive percolation

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