Understanding totally asymmetric simple-exclusion-process transport on networks: Generic analysis via effective rates and explicit vertices

Abstract

In this paper we rationalize relevant features of totally asymmetric simple-exclusion processes on topologies more complex than a single segment. We present a mean-field framework, exploiting the previously introduced notion of effective rates, which we express in terms of the average particle density on explicitly introduced junction sites. It allows us to construct the phase behavior as well as the current-density characteristic from well-known results for a linear totally asymmetric simple-exclusion-process segment in a very systematic and generic way. We validate the approach by studying a fourfold vertex in all variations in the number of entering/exiting segments and compare our predictions to simulation data. Generalizing the notion of particle-hole symmetry to take into account the topology at a junction shows that the average particle density at the junction constitutes a relevant directly observable parameter which gives detailed insight into the transport process. This is illustrated by a complete study of a simple network with figure-of-eight topology. Finally we generalize the approach to handle rate bias at a junction and discuss the surprisingly rich phenomenology of a biased figure-of-eight structure. This example highlights that the proposed framework is generic and readily extends to other topologies.

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

“…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).…”

“…In Ref. [5] graphs containing vertices of degree 4 and out-degrees 1, 2, and 3 were considered. The notion of particle-hole symmetry in the presence of a junction was carefully analyzed and an appropriate interpretation on the microscopic level was given.…”

A balance network for the asymmetric simple exclusion process

“…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.…”

Position-Induced Phase Change in a TASEP with a Double-Chain Section (a Model of Biological Transport)

“…Our goal here is to present a study of the effects, arising in TASEP, defined on a simple example of such a network: a linear chain of attachment sites with a double-chain defect inserted in it [25]. For other studies of TASEP on topologies more complex than a single segment see [26,27,28,29]. Recently, applications to biological transport have motivated generalizations of the TASEP to cases when the entry rate is chosen to depend on the number of particles in the reservoir (TASEP with finite resources) [30,31].…”