Effect of coupling strength on a two-lane partially asymmetric coupled totally asymmetric simple exclusion process with Langmuir kinetics

Collective dynamics on constrained three-lane exclusion process

The motivation behind the proposed study stems from multilane traffic systems with finite availability of particles. Our investigation revolves around a totally asymmetric simple exclusion process incorporating a finite reservoir and the occurrence of lane-switching phenomena. The study delves into the system's characteristics, including phase diagrams, density profiles, phase transitions, finite-size effects, and shock positions. These analyses concern the number of particles within the system and various weak-coupling rates. The outcomes obtained from the generalized mean-field theory are cross-validated against the results derived from Monte Carlo simulations. In scrutinizing the system's dynamics, we observe several noteworthy observations. Notably, we identified critical mixed profiles featuring instances of double shocks. The system, intriguingly, demonstrates a transition known as reentrance transition. The study also reports a rare phenomenon, namely, the jumping effect within the shock profile, adding a layer of complexity to the system's behavior and proving the significance of limited resources.

Competition for resources in an exclusion model with biased lane-changing mechanism

The motivation for the proposed work is drawn from the attachment-detachment observed in biological and physical transport processes that entail finite resources. We investigate the influence of limited particle availability on particle dynamics within two parallel totally asymmetric simple exclusion lanes, with one lane incorporating only particle detachment and the other considering particle attachment. We establish a theoretical framework by employing vertical mean-field theory in conjunction with singular perturbation technique. The analytical findings are supported by numerical and stochastic validation using a finite-difference scheme and the Gillespie algorithm. By utilizing these approaches, we scrutinize various stationary properties, including particle densities, phase boundaries, and particle currents for both lanes. Our analysis reveals that the complexity of the phase diagram exhibits a nonmonotonic trend in the number of stationary phases as the particle count increases. Each phase diagram is constructed with respect to the intrinsic boundary parameters, illustrating both bulk and surface transitions occurring within the lanes. The interplay between finite resources and coupling mechanisms gives rise to two phases involving upward shock in one of the lanes, while two phases exhibit synchronized downward shock in both lanes. Finally, we delve into shock dynamics to comprehend critical phase transitions occurring in the system.

Asymmetric coupling induces two-directional reentrance transition in three-lane exclusion process

Inspired by vehicular traffic phenomena, we study a three-lane open totally asymmetric simple exclusion process with both-sided lane switching in the companionship of Langmuir kinetics. We calculate the phase diagrams, density profiles, and phase transitions through mean-field theory and successfully validate these findings with Monte Carlo simulation results. It has been found that both the qualitative and quantitative topology of phase diagrams crucially rely on the ratio of lane-switching rates called coupling strength. The proposed model has various unique mixed phases, including a double shock resulting in bulk-induced phase transitions. The interplay between both-sided coupling, third lane, and Langmuir kinetics produces unusual features, including a back-and-forth phase transition, also called a reentrance transition, in two directions for relatively nominal values of coupling strength. The presence of reentrance transition and peculiar phase boundaries leads to a rare type of phase division in which one phase lies entirely within another region. Moreover, we scrutinize the shock dynamics by analyzing four different types of shock and finite-size effects.

Particle creation and annihilation in a dynamically disordered totally asymmetric simple exclusion process

We study a single-channel dynamically disordered totally asymmetric simple exclusion process with bulk particle attachment and detachment. The continuum mean-field equations are derived and solved numerically to obtain steady-state phase diagrams and density profiles. The effects of various parameters, namely particle attachment rate, defect binding and unbinding rates, and binding constant, have been investigated. An increase in the attachment rate of particles reduces the number of steady-state phases, whereas a variation in defect binding and unbinding rates shifts the phase boundaries. One of the important consequences of introducing particle nonconserving dynamics is the appearance of shock in the steady state. The shock dynamics have been thoroughly examined and the defect strength is found to have a significant effect on the shock position. The mean-field solutions are validated using extensive Monte Carlo simulations.