HEX-TASEP: dynamics of pinned domains for TASEP transport on a periodic lattice of hexagonal topology

Embley, Ben; Parmeggiani, Andrea; Kern, Norbert

doi:10.1088/0953-8984/20/29/295213

Cited by 14 publications

(16 citation statements)

References 22 publications

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“…The value of τ is chosen short enough so as to probe the movement of the DW on mesoscopic time scales rather than probing only the mean-field density profile. Following the approach of [25] we choose for τ the smallest value which gives exactly one micro-domain wall (µDW) in the averaged profile. A µDW is defined as any point where the density crosses 0.5 (from above or below) between one lattice site and the next.…”

Section: Shock Phasementioning

confidence: 99%

Multiple phase transitions in a system of exclusion processes with limited reservoirs of particles and fuel carriers

2012

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The TASEP is a paradigmatic model from non-equilibrium statistical physics, which describes particles hopping along a lattice of discrete sites. The TASEP is applicable to a broad range of different transport systems, but does not consider the fact that in many such systems the availability of resources required for the transport is limited. In this paper we extend the TASEP to include the effect of a limited number of two different fundamental transport resources: the hopping particles, and the "fuel carriers", which provide the energy required to drive the system away from equilibrium. As as consequence, the system's dynamics are substantially affected: a "limited resources" regime emerges, where the current is limited by the rate of refuelling, and the usual coexistence line between low and high particle density opens into a broad region on the phase plane. Due to the combination of a limited amount of both resources, multiple phase transitions are possible when increasing the exit rate β for a fixed entry rate α. This is a new feature that can only be obtained by the inclusion of both kinds of limited resources. We also show that the fluctuations in particle density in the LD and HD phases are unaffected by fluctuations in the number of loaded fuel carriers, except by the fact that when these fuel resources become limited, the particle hopping rate is severely reduced.Multiple phase transitions in a TASEP with limited particles and fuel carriers

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Section: Shock Phasementioning

confidence: 99%

Multiple phase transitions in a system of exclusion processes with limited reservoirs of particles and fuel carriers

2012

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“…The motor proteins on cytoskeletal networks [5,6] provide one interesting example of such behavior. In order to clarify the effects of junctions, the TASEP has been studied in various systems consisting of coupled 1D segments, including open (i.e., connected to particle reservoirs) segments with a single junction [7], closed (i.e., conserving the particles) 1D loops with a single junction [8,9], closed 1D loops with a shortcut [10], periodic hexagonal lattices [11], and closed and directed random regular (CDRR) networks [12]. For lack of exact solutions, all these studies rely on the simplifying assumption that the correlations between each junction and its neighboring sites are negligible.…”

Section: Introductionmentioning

confidence: 99%

Effects of junctional correlations in the totally asymmetric simple exclusion process on random regular networks

Baek

Jeong

2014

Phys. Rev. E

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We investigate the totally asymmetric simple exclusion process on closed and directed random regular networks, which is a simple model of active transport in the one-dimensional segments coupled by junctions. By a pair mean-field theory and detailed numerical analyses, it is found that the correlations at junctions induce two notable deviations from the simple mean-field theory, which neglects these correlations: (1) the narrower range of particle density for phase coexistence and (2) the algebraic decay of density profile with exponent 1/2 even outside the maximal-current phase. We show that these anomalies are attributable to the effective slow bonds formed by the network junctions.

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“…Different versions of simple networks were studied in Refs. [4,5]. In the former reference two cases were investigated: (a) two vertices of degree 3, connected by three chains, one of which has the opposite direction to the remaining two (closed system), and (b) two vertices of degree 3, connected by two chains with the same direction; the remaining incoming and outgoing chains are coupled to * nina@imbm.bas.bg † brankov@theor.jinr.ru reservoirs with the same particle density (open counterpart).…”

Section: Introductionmentioning

confidence: 99%

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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HEX-TASEP: dynamics of pinned domains for TASEP transport on a periodic lattice of hexagonal topology

Cited by 14 publications

References 22 publications

Multiple phase transitions in a system of exclusion processes with limited reservoirs of particles and fuel carriers

Multiple phase transitions in a system of exclusion processes with limited reservoirs of particles and fuel carriers

Effects of junctional correlations in the totally asymmetric simple exclusion process on random regular networks

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

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