A dynamically extending exclusion process

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.

20 pages, 12 figures

References in corpus (13)

• Nonequilibrium Steady States of Matrix Product Form: A Solver's Guide
• Phase transitions in an exactly soluble one-dimensional exclusion process
• Phase Coexistence in Driven One Dimensional Transport
• Physics of Transport and Traffic Phenomena in Biology: from molecular motors and cells to organisms
• Traffic of molecular motors through tube-like compartments
• Shock formation in an exclusion process with creation and annihilation
• Localization of shocks in driven diffusive systems without particle number conservation
• Collective dynamics of molecular motors pulling on fluid membranes
• A model of hyphal tip growth involving microtubule-based transport
• Filament depolymerization by motor molecules
• Nonequilibrium Criticality at Shock Formation in Steady States
• Dynamic Boundaries in Asymmetric Exclusion Processes
• Disorder and non-conservation in a driven diffusive system

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• Dynamical phase transition of a 1D transport process including death
• Exclusion in a priority queue
• Density profiles of the exclusive queueing process
• Self-organized system-size oscillation of a stochastic lattice-gas model
• Length regulation of microtubules by molecular motors: Exact solution and density profiles
• Critical behavior of the exclusive queueing process
• Simplest nonequilibrium phase transition into an absorbing state
• Effective ergodicity breaking in an exclusion process with varying system length
• Exclusion process on an open lattice with fluctuating boundaries
• Data-Driven Optimal Closures for Mean-Cluster Models: Beyond the Classical Pair Approximation
• On the Diffusion of Sticky Particles in 1D