Mass transport perspective on an accelerated exclusion process: Analysis of augmented current and unit-velocity phases

Abstract

In an accelerated exclusion process (AEP), each particle can "hop" to its adjacent site if empty as well as "kick" the frontmost particle when joining a cluster of size ≤ max. With various choices of the interaction range, max, we find that the steady state of AEP can be found in a homogeneous phase with augmented currents (AC) or a segregated phase with holes moving at unit velocity (UV). Here we present a detailed study on the emergence of the novel phases, from two perspectives: the AEP and a mass transport process (MTP). In the latter picture, the system in the UV phase is composed of a condensate in coexistence with a fluid, while the transition from AC to UV can be regarded as condensation. Using Monte Carlo simulations, exact results for special cases, and analytic methods in a mean field approach (within the MTP), we focus on steady state currents and cluster sizes. Excellent agreement between data and theory is found, providing an insightful picture for understanding this model system.

Accelerated transport and growth with symmetrized dynamics

“…The value of ρ for the emergence of the UV phase depends on the value of the control parameter max , the range (see below for its definition) of the kick interaction. In the definition of the AEP model the particle-vacancy symmetry is broken, but the dynamics can be nevertheless successfully understood by considering the concerted motion of vacancies for large values of max [17]. In the present work we further generalize the TASEP to include a "draw" (from behind) interaction, to restore the particle-vacancy symmetry.…”

“…Very recently, an accelerated exclusion process (AEP) was developed and analyzed by Dong et al [16,17]. In the AEP a particle hopping into a (particle) cluster "kicks" the frontmost particle of that cluster one site forward.…”

“…In Refs. [16] and [17] this is argued to lead via condensation to the existence of a novel "unit velocity" (UV) phase with the particle current J = 1 − ρ for particle densities ρ > 1/2. The value of ρ for the emergence of the UV phase depends on the value of the control parameter max , the range (see below for its definition) of the kick interaction.…”

“…Macroscopic quantities of interest, including the current through the system and its fluctuations, as well as configurational properties, such as the dynamics of the largest cluster and the condensation transition, have been of a renewed interest for various generalizations [6][7][8][9][10][11][12][13][14][15][16][17] of the basic TASEP model, many of them interesting, e.g., from the point of view of RNA transcription, jamming of traffic flow, phase separation, and growth phenomena.…”

Totally asymmetric exclusion process fed by using a non-Poissonian clock

“…Macroscopic quantities of interest, in particular the particle density and current and their fluctuations as well as configurational properties, such as the dynamics of the largest cluster and the condensation transition, have been of renewed interest for various generalizations [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] of the basic TASEP model, many of them interesting, e.g., from the point of view of RNA transcription, jamming of traffic flow, phase separation, and growth phenomena.…”