Spontaneous pulsing states in an active particle system

Abstract

We study a two-lane two-species exclusion process inspired by Lin et al. (C. Lin et al. J. Stat. Mech., 2011), that exhibits a non-equilibrium pulsing phase. Particles move on two parallel one-dimensional tracks, with one open and one reflecting boundary. The particle type defines the hopping direction. When only particles hopping towards the open end are allowed to change lane, the system exhibits a phase transition from a low density phase to a pulsing phase depending on the ratio between particle injection and type-changing rate. This phase transition can be observed in the stochastic model as well as in a mean-field description. In the low density phase, the density profile can be predicted analytically. The pulsing phase is characterised by a fast filling of the system and - once filled - by a slowly backwards moving front separating a decreasing dense region and an expanding low density region. The hopping of the front on the discrete lattice is found to create density oscillations, both, in time and space. By means of a stability analysis we can predict the structure of the dense region during the emptying process, characterised by exponentially damped perturbations, both at the open end and near the moving front.

28 pages, 15 figures

References in corpus (8)

• Diffusive transport without detailed balance in motile bacteria: Does microbiology need statistical physics?
• Collective motion and nonequilibrium cluster formation in colonies of gliding bacteria
• The Totally Asymmetric Simple Exclusion Process with Langmuir Kinetics
• Traffic of molecular motors through tube-like compartments
• A model of hyphal tip growth involving microtubule-based transport
• Exclusion Processes with Internal States
• Phase diagram of two-lane driven diffusive systems
• Non-equilibrium phase transitions in tubulation by molecular motors

Cited by in corpus (4)

• Steady state, relaxation and first-passage properties of a run-and-tumble particle in one-dimension
• Two-lane totally asymmetric simple exclusion process with extended Langmuir kinetics
• Interference of two co-directional exclusion processes in the presence of a static bottleneck: a biologically motivated model
• A biologically motivated three-species exclusion model: effects of leaky scanning and overlapping genes on initiation of protein synthesis