Hex-Tasep : Dynamics of Pinned Domains for Tasep transport on a Periodic Lattice of Hexagonal Topology
Résumé
We investigate a totally asymmetric simple exclusion process (TASEP) on a periodic hexagonal lattice with a single unit cell. We first explain the resulting stationary density profiles and the resulting fundamental current–density relation in terms of mean-field arguments. For intermediate overall densities, transport through one of the segments saturates in a maximum current phase, whereas the others develop domain walls of fixed height but fluctuating position. Via kinetic Monte Carlo simulations we focus on and fully characterize their non-equilibrium and stochastic phenomenology. We invoke a picture of anticorrelated domain wall dynamics, which we visualize as a diffusing obstruction of constant size (‘jam'). The role of the boundary conditions is discussed by comparing the periodic lattice carrying a fixed number of particles to a system coupled to reservoirs at open boundaries which is periodic only on average. We highlight the differences in their dynamics based on a novel visualization of domain wall motion at an intermediate ‘mesoscopic' timescale.