A dynamically extending exclusion process

TL;DR

This paper introduces the dynamically extending exclusion process (DEEP), a novel non-equilibrium model with a growing lattice, analyzing its steady states, phase diagram, and shock dynamics, inspired by filamentous fungal growth.

Contribution

It presents the first detailed analysis of DEEP, including mean-field approximations and phase behavior, expanding the class of exclusion process models.

Findings

Discovery of a new phase with a receding shock

Identification of a phase where shock velocity is less than tip velocity

Elucidation of steady state behavior and phase diagram of DEEP

Abstract

An extension of the totally asymmetric exclusion process, which incorporates a dynamically extending lattice is explored. Although originally inspired as a model for filamentous fungal growth, here the dynamically extending exclusion process (DEEP) is studied in its own right, as a nontrivial addition to the class of nonequilibrium exclusion process models. Here we discuss various mean-field approximation schemes and elucidate the steady state behaviour of the model and its associated phase diagram. Of particular note is that the dynamics of the extending lattice leads to a new region in the phase diagram in which a shock discontinuity in the density travels forward with a velocity that is lower than the velocity of the tip of the lattice. Thus in this region the shock recedes from both boundaries.