Localization of shocks in driven diffusive systems without particle number conservation

Abstract

We study the formation of localized shocks in one-dimensional driven diffusive systems with spacially homogeneous creation and annihilation of particles (Langmuir kinetics).We show how to obtain hydrodynamic equations which describe the density profile in systems with uncorrelated steady state as well as in those exhibiting correlations. As a special example of the latter case the Katz-Lebowitz-Spohn model is considered. The existence of a localized double density shock is demonstrated for the first time in one-dimensional driven diffusive systems. This corresponds to phase separation into regimes of three distinct densities, separated by localized domain walls. Our analytical approach is supported by Monte-Carlo simulations.

Weakly coupled, antiparallel, totally asymmetric simple exclusion processes

“…S(ρ(x, τ )) ≡ 0) [17]. Under these circumstances, the TASEP has a product measure stationary state and the current-density relationship is simply J(ρ) = ρ(1 − ρ), hence the currents in the two lanes are given as…”

“…Inspired by the traffic of cytoskeletal motors [11], such models were introduced where a totally asymmetric exclusion process is coupled to a finite compartment where the motion of particles is diffusive [12,13,14]. Recently, the attention has turned to exclusion processes endowed with various types of reactions which violate the conservation of particles in the bulk [15,16,17,18,19,20,21,22,23,24,25,26,27,28]. The simplest one among these models is the TASEP with "Langmuir kinetics", where particles are created and annihilated also at the bulk sites of the system [16]-a process, which may serve as a simplified model for the cooperative motion of molecular motors along a filament from which motors can detach and attach to it again.…”

Traffic of single-headed motor proteins KIF1A: Effects of lane changing

“…Since no estimate of ω f l+ and ω f l− are available, we use ω f l+ = ω f l− = ω f l and vary the single parameter ω f l /ω f over a wide range to explore the consequences of different rates of lane changing. The flux per lane (obtained from (8)) and the average density ρ (given by (6)) are plotted against ω f l /ω f in Fig. 2 for several different values of ω s /ω f and compared with the corresponding simulation data.…”

“…Each subunit of a protofilament is a 8 nm heterodimer of α-β tubulins and provides a specific binding site for a single head of a kinesin motor. Often many kinesins move simultaneously along a given MT; because of close similarities with vehicular traffic [3], the collective movement of the molecular motors on a MT is sometimes referred to as molecular motor traffic [4,5,6,7,8].…”

“…Each subunit of a protofilament is a 8 nm heterodimer of α-β tubulins and provides a specific binding site for a single head of a kinesin motor. Often many kinesins move simultaneously along a given MT; because of close similarities with vehicular traffic [3], the collective movement of the molecular motors on a MT is sometimes referred to as molecular motor traffic [4,5,6,7,8].The effects of lane changing on the flow properties of vehicular traffic has been investigated extensively using particle-hopping models [3] which are, essentially, appropriate extensions of the totally asymmetric simple exclusion process (TASEP) [9,10,11]. Models of multi-lane TASEP, where the particles can occasionally change lane, have also been investigated analytically [12,13].…”