Spurious phase in a model for traffic on a bridge

Exclusion processes on a roundabout traffic model with constrained resources

Motivated by the vehicular traffic phenomenon at roundabouts, we examine how the limited availability of resources affects the movement of two distinct types of particles on bidirectional lanes connected by two bridges, with each bridge specifically designated for the transportation of one species. To provide a theoretical ground for our findings, we employ a mean-field framework and successfully validate them through dynamic Monte Carlo simulations. Based on the theoretical analysis, we analytically derive various stationary properties, such as the particle densities, phase boundaries, and particle currents, for all the possible symmetric as well as asymmetric phases. The qualitative as well as quantitative behavior of the system is significantly affected by the constraint on the number of resources. The complexity of the phase diagram shows a nonmonotonic behavior with an increasing number of particles in the system. Analytical arguments enable the identification of several critical values for the total number of particles, leading to a qualitative change in the phase diagrams. The interplay of the finite resources and the bidirectional transport yields unanticipated and unusual features such as back-and-forth transition, the presence of two congested phases where particle movement is halted, as well as shock phases induced by boundaries and the bulk of the system. Also, it is found that spontaneous symmetry-breaking phenomena are induced even for very few particles in the system. Moreover, we thoroughly examine the location of shocks by varying the parameters controlling the system's boundaries, providing insights into possible phase transitions.

Interplay of reservoirs in a bidirectional system

Motivated by the interplay of multiple species in several real world transport processes, we propose a bidirectional totally asymmetric simple exclusion process with two finite particle reservoirs regulating the inflow of oppositely directed particles corresponding to two different species. The system's stationary characteristics, such as densities, currents, etc., are investigated using a theoretical framework based on mean-field approximation and are supported by extensive Monte Carlo simulations. The impact of individual species populations, quantified by filling factor, has been comprehensively analyzed considering both equal and unequal conditions. For the equal case, the system exhibits the spontaneous symmetry-breaking phenomena and admits both symmetric as well as asymmetric phases. Moreover, the phase diagram exhibits a different asymmetric phase and displays a nonmonotonic variation in the number of phases with respect to the filling factor. For unequal filling factors, the phase schema can display at most five phases including a phase that shows maximal current for one of the species.

Exclusion process with scaled resources: Delocalized shocks and interplay of reservoirs

In this paper we study a conserved system comprised of two directed lanes having identical dynamics and two reservoirs with scaled resources that are strategically connected to the boundaries of the lanes, forming a ringlike structure. The steady-state properties of the system have been analyzed in the framework of mean-field theory. Our findings display a rich behavior, emphasizing the nontrivial effects of incorporating two reservoirs. As a consequence, two distinct phases that admit delocalized shocks emerge and occupy a significant region in the phase diagram. Moreover in one of theses phases, each lane admits a delocalized shock whose movements are perfectly synchronized. In another phase, the single shock in the system may traverse both lanes or remain restricted to a single lane, depending upon the size of the system. All the findings are validated by Monte Carlo simulations.

Far-from-equilibrium bidirectional transport system with constrained entrances competing for pool of limited resources

Motivated by the wide occurrence of limited resources in many real-life systems, we investigate two-lane totally asymmetric simple exclusion process with constrained entrances under finite supply of particles. We analyze the system within the framework of mean-field theory and examine various complex phenomena, including phase separation, phase transition, and symmetry breaking. Based on the theoretical analysis, we analytically derive the phase boundaries for various symmetric as well as asymmetric phases. It has been observed that the symmetry-breaking phenomenon initiates even for very small number of particles in the system. The phases with broken symmetry originates as shock-low density phase under limited resources, which is in contrast to the scenario with infinite number of particles. As expected, the symmetry breaking continues to persist even for higher values of system particles. Seven stationary phases are observed, with three of them exhibiting symmetry-breaking phenomena. The critical values of a total number of system particles, beyond which various symmetrical and asymmetrical phases appear and disappear are identified. Theoretical outcomes are supported by extensive Monte Carlo simulations. Finally, the size-scaling effect and symmetry-breaking phenomenon on the simulation results have also been examined based on particle density histograms.

Dynamical phase transitions in totally asymmetric simple exclusion processes with two types of particles under periodically driven boundary conditions

Driven diffusive systems have provided simple models for nonequilibrium systems with nontrivial structures. Steady-state behavior of these systems with constant boundary conditions have been studied extensively. Comparatively less work has been carried out on the responses of these systems to time-dependent parameters. We report the modifications to the probability density function of a two-particle exclusion model in response to a periodically changing perturbation to its boundary conditions. The changes in the shape of the distribution as a function of the frequency of the perturbation contains considerable structure. A dynamical phase transition in which the system response changes abruptly as a function of perturbation frequency was observed. We interpret this structure to be a consequence of the existence of a typical time scale associated with the dynamics of density shock profiles within the system.

Unusual shock wave in two-species driven systems with an umbilic point

Using dynamical Monte Carlo simulations we observe the occurrence of an unexpected shock wave in driven diffusive systems with two conserved species of particles. This U shock is microscopically sharp, but does not satisfy the usual criteria for the stability of shocks. Exact analysis of the large-scale hydrodynamic equations of motion reveals the presence of an umbilical point which we show to be responsible for this phenomenon. We prove that such an umbilical point is a general feature of multispecies driven diffusive systems with reflection symmetry of the bulk dynamics. We argue that a U shock will occur whenever there are strong interactions between species such that the current-density relation develops a double well and the umbilical point becomes isolated.

Weakening interaction suppresses spontaneous symmetry breaking in two-channel asymmetric exclusion processes

This paper has studied spontaneous symmetry breaking (SSB) phenomenon in two types of two-channel asymmetric simple exclusion processes (ASEPs). One common feature of the two systems is that interactions for each species of particle happen at only one site, and the system reduces to two independent ASEPs when interaction vanishes. It is shown that with the weakening of interaction, the SSB is suppressed. More interestingly, the SSB disappears before the interaction is eliminated. Our work thus indicates that local interaction has to be strong enough to produce SSB. The mean-field analysis has been carried out, and the results are consistent with the simulation ones.

Spontaneous symmetry breaking and periodic structure in a multilane system

We study a multilane totally asymmetric simple exclusion process (TASEP) with narrow entrances under parallel update. The narrow entrances are modeled in this way: the entry of a particle is not allowed if the exit site of the previous lane is occupied. It is shown the results depend on the number of lanes, n. If n is an even number, the results are essentially the same as n=2: two symmetry-breaking phases--i.e., a high-density-low-density (HD-LD) phase and an asymmetric low-density-low-density phase--are identified. In contrast, if n is an odd number, a periodic structure is observed and the period is found to be proportional to the lane number n and system size L. It is also found when the injection rate alpha=1 that the seesaw phase observed in the case of n=2 disappears and the HD-LD phase or symmetric LD phase appears. Some mean-field calculations are also presented. We show that it is not possible to have high densities in two successive lanes and also not possible to have high density in one lane and low densities in all other lanes. For odd n, we have obtained the period T and it is in good agreement with simulations for a small removal rate beta, but deviates from simulation results for large beta because correlation is neglected in the mean-field approximation.