Scale-invariant density profiles of a dynamically extending TASEP

Department of Physics, BITS, Hyderabad Campus - Shameerpet, Hyderabad 500078, India and Institute of Physics - Sachivalaya Marg, Bhubaneswar 751005, India

Received: 30 November 2012
Accepted: 11 January 2013

Abstract

We study the implications of coupling Langmuir kinetics (LK) process with the dynamics of an extending lattice. The model that we consider couples a dynamically extending totally asymmetric exclusion process (TASEP) with the process of random attachment and detachment of particles in the bulk of the lattice. We explore a dynamical regime where the boundary processes of lattice extension and particle input compete with the bulk process of particle attachment and detachment. This competition leads to a scale-invariant density profile of particles when expressed in terms of the relative position in the growing lattice. It also leads to phase coexistence and shocks in the bulk of the lattice. We use a combination of mean-field (MF) analysis and Monte Carlo (MC) simulations to characterize the density profile in the growing lattice and construct a MF phase diagram. This study may be useful in the context of modeling transport and patterning in the growing biofilaments.