Figure 1

Schematic illustration of a TASEP segment with open boundary conditions. The attempt rate for a particle to enter is $\alpha$, and the exit rate $\beta$. Particles hop from left to right, and interact through their excluded volume. We use $p=1$ throughout.Reuse & Permissions

Figure 2

Phase diagram of a single TASEP segment with open boundary conditions. According to the entry (exit) rates $\alpha$ ($\beta$), one of three transport regimes is established: in the LD (low density) phase the current is entry limited, in HD (high density) it is exit limited, and in MC (maximum current) it is bulk limited. LD-HD represents coexisting phases, separated by a domain wall.Reuse & Permissions

Figure 3

Schematic illustration of TASEP on a closed-loop (figure-of-eight) topology. Particles interact through excluded volume. The effective entrance rate $\alpha$ and exit rate $\beta$ are set through the density at the junction $\tilde{\rho }$ (see main text).Reuse & Permissions

Figure 4

Current $\tilde{J}$ through a junction shared by $N$ loops, as a function of the overall density $\rho$. Lines are mean-field predictions, symbols are results from kinetic Monte Carlo simulations. We superpose data obtained with segments of length $L=100$ (open symbols) and $L=1000$ (full symbols) in order to illustrate how finite size effects reduce with segment size.Reuse & Permissions

Figure 5

Maximum (plateau) currents as a function of the number of segments sharing a junction. The saturation is due to the fact that the increased transport capacity through extra segments is progressively compensated by an increased blockage at the junction site. Data points are from simulation ($L=100$ sites per segment), the solid line is the mean-field prediction [Eq. (4)].Reuse & Permissions

Figure 6

Currents at the junction and in the bulk of each loop for a fourfold topology with four distinct (nondegenerate) bias parameters (${\sigma }_1=\frac{10}{20}$, ${\sigma }_2=\frac{6}{20}$, ${\sigma }_3=\frac{3}{20}$, ${\sigma }_4=\frac{1}{20}$). The currents through individual loops progressively saturate, starting from the one with the strongest bias. At high density, the bias becomes futile, i.e., all loops carry the same current, despite the bias.Reuse & Permissions

Figure 7

Junction occupancy $\tilde{\rho }$ as a function of the overall density for a fourfold topology with four distinct (nondegenerate) bias parameters (same parameters as Fig. 6). The four successive plateaus are labeled by the associated bias parameters $\sigma \in \{{\sigma }_1,...,{\sigma }_4\}$. The associated density ranges are ${\overline{P}}^{\left(\sigma \right)}=[{\rho }_{-}^{\left(\sigma \right)},{\rho }_{+}^{\left(\sigma \right)}]$, whereas the subsequent range between successive plateaus are denoted as $P^{\left(\sigma \right)}=[{\rho }_{+}^{\left(\sigma \right)},{\rho }_{*}^{\left(\sigma \right)}]$; see Appendix [and in particular Eqs. (B3) and (B4)] for the corresponding expressions.Reuse & Permissions

Figure 8

Junction current $\tilde{J}$ versus overall density $\rho$, here for a fivefold loop ($N=5$), for various pumping rates $\nu$. The pumping initially raises the plateau current while reducing the relevant density zone. The underlying LD-HD phase is ultimately reduced to the single point $\rho =1/2$, where it corresponds to a MC phase. This happens at a pumping rate ${\nu }^{*}=N$, and further pumping no longer increases the current. Deviations from predictions are attributable to finite size effects (data are for segments of length $L=100$), as discussed before.Reuse & Permissions

Figure 9

Density at the junction $\tilde{\rho }$ versus overall density $\rho$, for a fivefold topology ($N=5$). For the saturated pumping regime, the mean-field results do not reproduce Monte Carlo data for densities around half-filling ($\rho =1/2$), a discrepancy which is attributed to the presence of the MC phase (see discussion in the text). In the regime of efficient pumping ($\nu \le N$), the small discrepancies from mean field predictions are finite size effects.Reuse & Permissions

Figure 10

Role of pumping on the effective rates, represented on the phase diagram for a twofold topology, without pumping ($\nu =1$) and with pumping ($\nu =5)$ and with the borderline value ($\nu =2$) for which we cross over from efficient to saturated pumping. Shown are the successive points representing the successive pairs of effective rates $(\alpha ,\beta )$ as the overall density $\rho$ is progressively increased. The slope is $-N/\nu$, and therefore decreases as the pumping rate increases. Above the threshold ${\nu }^{*}=N$, the effective rates ($\alpha ,\beta )$ cross the MC zone. The notation $X$:$Y$ indicates the phase in either loop, whereas $X$-$Y$ stands for the coexistence of two phases on the same segment, where they are separated by a domain wall.Reuse & Permissions

Figure 11

Local density at the junction and at the neighboring sites as a function of the overall density, for pumping rates $\nu =1,2,5$ on a twofold topology. “Entry” stands for the entry site of the segments (directly fed from the junction site), whereas “exit” stands for the exit sites, i.e., the last sites in the segment, which feed the junction. Without pumping, the bottleneck effect is apparent in that the exit of segments is more likely to be occupied than the entrance sites. With $\nu =5$ the entrance sites are fuller, whereas the exit sites (and in particular the junction) are depopulated. This is characteristic for the effect of pumping. Dashed lines are mean-field predictions; continuous lines are refined mean-field predictions taking into account boundary layer effects on the boundary sites, as discussed in the text. See Appendix for the fully detailed expressions used to plot the graphs.Reuse & Permissions

Figure 12

Complete phase diagram of a twofold loop. Phase space parameters are the pumping rate $\nu$ and the overall density $\rho$. Depending on the pumping rate we distinguish the regimes of (i) weak pumping ($0<\nu <\frac{1}{{\sigma }_1}$), intermediate pumping ($\frac{1}{{\sigma }_1}<\nu <\frac{1}{{\sigma }_2}$), and strong pumping ($\frac{1}{{\sigma }_2}<\nu$). (a) Strong bias, (b) intermediate bias, (c) vanishing bias, for comparison with the above figures. Note that the scale of the $\nu$ axes differs between these figures.Reuse & Permissions

Figure 13

Current at the junction $\tilde{J}$ versus overall density $\rho$ in a twofold topology of $L=100$ sites, with bias 0.9: 0.1. Several pumping rates are shown for comparison ($\nu =1,5,13)$.Reuse & Permissions

Figure 14

Currents at the junction and in the bulk of each loop versus the overall density $\rho$ in a twofold loop of $L=100$ sites, bias 0.9:0.1. Parameters for the graphs have been chosen to represent the respective regimes of pumping. Note that the scales are not the same for all subfigures, in order to ensure visibility. Deviations from mean-field predictions arise in the disfavored loop, but are attributed to the presence of the MC phase in the favored loop (see discussion in the text).Reuse & Permissions

Figure 15

Local density at the junction and at its neighboring sites, the entry and exit sites for the segments, as a function of the overall density. We have analyzed a twofold loop with a bias of 0.9:0.1; simulations are for segments of length $L=100$. The dashed lines indicate straightforward mean-field predictions, the continuous lines are the improved predictions from refined arguments acknowledging the particular role of the boundary sites. See Appendix for details of mean-field predictions (some refined arguments are used again).Reuse & Permissions