2008
DOI: 10.1088/0953-8984/20/29/295213
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HEX-TASEP: dynamics of pinned domains for TASEP transport on a periodic lattice of hexagonal topology

Abstract: We investigate a totally asymmetric simple exclusion process (TASEP) on a periodic hexagonal lattice with a single unit cell. We first explain the resulting stationary density profiles and the resulting fundamental current–density relation in terms of mean-field arguments. For intermediate overall densities, transport through one of the segments saturates in a maximum current phase, whereas the others develop domain walls of fixed height but fluctuating position. Via kinetic Monte Carlo simulations we focus on… Show more

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Cited by 14 publications
(16 citation statements)
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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%
“…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%
“…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%
“…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%