Nonconserving locally disordered exclusion process under constrained resources.

Abstract

Driven by transport processes in natural and man-made systems, we examine a locally disordered totally asymmetric simple exclusion process with Langmuir kinetics in a resource-constrained environment. The disorder is in the form of a defect that may bind to or unbind from a particular site and slows down the particle movement, when present on the lattice. Using a mean-field approach, we analyze the steady-state behavior of the model by computing density profiles and constructing phase diagrams in the α-β parameter space, thereby revealing a rich quantitative and qualitative phase structure. The impact of finite resources and Langmuir kinetics on the stationary properties of the system is analyzed by varying the filling factor and binding constant. Upon varying the filling factor, the results uncover several critical values where the phase diagram changes qualitatively and the resulting phase complexity varies nonmonotonically. As the binding constant is increased from small values, the phase structure evolves from a limited set of phases to maximal diversity at moderate values, before settling into a simplified regime at large values. An obstruction factor is introduced to capture the combined effects of defect density and the slowdown rate in order to incorporate the role of the dynamic defect. Owing to this combined effect, increasing the obstruction factor simplifies the phase diagram, suppressing Meissner-type phases and promoting high density and shock regimes. The mean-field predictions are verified through Monte Carlo simulations implemented via Gillespie algorithm.