Asymmetric simple exclusion process on chains with a shortcut

Abstract

We consider the asymmetric simple exclusion process (TASEP) on an open network consisting of three consecutively coupled macroscopic chain segments with a shortcut between the tail of the first segment and the head of the third one. The model was introduced by Y.-M. Yuan et al. [J. Phys. A 40, 12351 (2007)] to describe directed motion of molecular motors along twisted filaments. We report here unexpected results which revise the previous findings in the case of maximum current through the network. Our theoretical analysis, based on the effective rates' approximation, shows that the second (shunted) segment can exist in both low- and high-density phases, as well as in the coexistence (shock) phase. Numerical simulations demonstrate that the last option takes place in finite-size networks with head and tail chains of equal length, provided the injection and ejection rates at their external ends are equal and greater than one-half. Then the local density distribution and the nearest-neighbor correlations in the middle chain correspond to a shock phase with completely delocalized domain wall. Upon moving the shortcut to the head or tail of the network, the density profile takes a shape typical of a high- or low-density phase, respectively. Surprisingly, the main quantitative parameters of that shock phase are governed by a positive root of a cubic equation, the coefficients of which linearly depend on the probability of choosing the shortcut. Alternatively, they can be expressed in a universal way through the shortcut current. The unexpected conclusion is that a shortcut in the bulk of a single lane may create traffic jams.

On the appearance of traffic jams in a long chain with a shortcut in the bulk

“…In the former case the molecular motors walk along a filament which is twisted so that a motor may jump with probability q between two sites, which are far away along the filament but close in real space. Model A was reexamined in our recent paper [23]. It turned out that the authors of Ref.…”

“…In the former case the molecular motors walk along a filament which is twisted so that a motor may jump with probability q between two sites, which are far away along the filament but close in real space. Model A was reexamined in our recent paper [28]. It turned out that the authors of the former work used an unfounded approximation due to which the coexistence phase in the shunted chain, in the case of maximum current through the network, was not detected.…”

“…(b) To check on the considered family of networks with arbitrary length of the shortcut the predicted by the Domain Wall Theory (DWT) [32,33] universal dependence of the main features of the shock phase in the shunted segment on the current through the shortcut, see our conjecture in [28]. (c) To study in detail, the statistical properties at the junction points from the viewpoint of the conditions for applicability of the DWT, and to explain the distortion of the density profiles in the head and tail segments, resulting from the presence of a shortcut.…”

One-dimensional irreversible aggregation with dynamics of a totally asymmetric simple exclusion process

“…Presently, ASEP and TASEP are paradigmatic models for understanding a variety of nonequilibrium phenomena. Devised to model kinetics of protein synthesis [27], TASEP and its numerous extensions have found many applications to vehicular traffic flow [28][29][30], biological transport [31][32][33][34][35][36], one-dimensional surface growth [37,38], forced motion of colloids in narrow channels [39,40], spintronics [41], current through chains of quantum dots [42], etc. Notably, traffic-like collective motion is found also at different levels of all biological systems.…”

MPA for TASEP with a generalized update on a ring

“…biological transport [9][10][11][12][13][14][15][16], one-dimensional surface growth [17,18], forced motion of colloids in narrow channels [19,20], spintronics [21], transport of "data packets" on the Internet [22], current through chains of quantum dots [23], limit order market [24], to mention some.…”