Reservoir crowding in a resource-constrained exclusion process with a dynamic defect.

Abstract

To understand the complicated transport processes that occur in biological and physical systems, we investigate a constrained totally asymmetric simple exclusion process with a stochastic defect particle. The defect particle might randomly emerge or vanish, resulting in a dynamic defect, and slows down the flow of moving particles when attached to the lattice. Using a mean-field technique, we examine the steady-state characteristics and boundary-layer analysis is provided to comprehend the properties of finite system. In a simplification, our theoretical method unifies three different parameter used to define the defect dynamics into one parameter termed the obstruction factor. It is found that the defect kinetics lead to emergence of phases where the current is defect restricted. The system shows nine phases overall, including bulk-induced and boundary-induced shock phases, with the phase schema showing no more than eight phases depending on the dynamics. We found that variation of obstruction does not lead to qualitative transition in the system, whereas the change in constraint on total particles affect the system qualitatively. All the theoretical outcomes have been validated using extensive Monte Carlo simulations.