Zone inhomogeneity with the random asymmetric simple exclusion process in a one-lane system

In this paper we use theoretical analysis and extensive simulations to study zone inhomogeneity with the random asymmetric simple exclusion process （ASEP）. In the inhomogeneous zone, the hopping probability is less than 1. Two typical lattice geometries are investigated here. In case A, the lattice includes two equal segments. The hopping probability in the left segment is equal to 1, and in the right segment it is equal to p, which is less than 1. In case B, there are three equal segments in the system; the hopping probabilities in the left and right segments are equal to 1, and in the middle segment it is equal to p, which is less than 1. Through theoretical analysis, we can discover the effect on these systems when p is changed.

Local inhomogeneity in totally asymmetric simple exclusion processes with different hopping rates

Local inhomogeneity in totally asymmetric simple exclusion processes （TASEPs） with different hopping rates was studied. Many biological and chemical phenomena can be described by these non-equilibrium processes. A simple approximate theory and extensive Monte Carlo computer simulations were used to calculate the steady-state phase diagrams and bulk densities. It is found that the phase diagram for local inhomogeneity in TASEP with different hopping rates p is qualitatively similar to homogeneous models. Interestingly, there is a saturation point pair （a＊, fl＊） for the system, which is decided by parameters p and q. There are three stationary phases in the system, when parameter p is fixed （i.e., p=0.8）, with the increase of the parameter q, the region of LD/LD and HD/HD phase increases and the HD/LD is the only phase which the region shrinks. The analytical results are in good agreement with simulations.

Existence of spontaneous symmetry breaking in two-lane totally asymmetric simple exclusion processes with an intersection

We study two-lane totally asymmetric simple exclusion processes(TASEPs)with an intersection.Monte Carlo simulations show that only symmetric phases exist in the system.To verify the existence of asymmetric phases,we carry out a cluster mean-field analysis.Analytical results show that the densities of the two upstream segments of the intersection site are always equal,which indicates that the system is not in asymmetric phases.It demonstrates that the spontaneous symmetry breaking does not exist in the system.The density profiles and the boundaries of the symmetric phases are also investigated.We find that the cluster mean-field analysis shows better agreement with simulations than the simple mean-field analysis where the correlation of sites is ignored.

Spectrum of the Open Asymmetric Simple Exclusion Process with Arbitrary Boundary Parameters

We study the one-dimensional asymmetric simple exclusion process （ASEP） with generic open boundaries （in- cluding current-counting deformation）, and obtain the exact solutions of this ASEP via the off-diagonal Bethe ansatz method. In particular, numerical results for the small size asymmetric simple exclusion process indicate that the spectrum obtained by the Bethe ansatz equations is complete. Moreover, we present the eigenvalue of the totally asymmetric exclusion process and the corresponding Bethe ansatz equations.

Successive defects asymmetric simple exclusion processes with particles of arbitrary size

This paper uses various mean-field approaches and the Monte Carlo simulation to calculate asymmetric simple exclusion processes with particles of arbitrary size in the successive defects system. In this system, the hopping probability p （p 〈 1） and the size d of particles are not constant, Through theoretical calculation and computer simulation, it obtains the exact theoretical results and finds that the theoretical results are in agreement with the computer simulation. These results are helpful in analysing the effect of traffic with different hopping probabilities p and sizes d of particle.

Symmetry phases of asymmetric simple exclusion processes on two lanes with an intersection

This paper studies two-lane asymmetric simple exclusion processes(ASEPs)with an intersection.In the upstream segments of the intersection,one particle can move to the next site with rate 1 if the site is empty,and the other particle can move forward with rate p in the sites of downstream segments.The parameter p can represent the rate of slowing of motion,and the parameter is introduced to investigate spontaneous symmetry breaking(SSB)phenomenon.Extensive Monte Carlo simulations are carried out.It is shown that three symmetric phases exist and the SSB does not exist in the system.Simple mean field approach in which correlation of sites is ignored is firstly adopted to analyze the system,and the system is divided into four independent segments.It is found that the analytical results deviate from the simulation ones,especially when p is small.In addition,the inexsitence of SSB can only be explained qualitatively.Motivated by this,we carry out the cluster mean field analysis in which correlation of five sites is considered.It is shown that densities of the two upstream segments are equal,which demonstrates that the SSB does not exist.It is also shown that,as expected,the cluster mean field analysis performs much better than the simple mean field analysis.

Asymmetric Coupling in Two-Lane Asymmetric Simple Exclusion Processes with Unequal Injection Rates: Effect of Different Hoping Rates

This paper investigates the effect of both unequal injection rates and different hopping rates on two-lane asymmetric simple exclusion processes(ASEPs) with asymmetric coupling. When the hopping rates of both lanes are different, the system includes six steady phases, however, when the hopping rates of both lanes are same, the seventh phase(MC, MC) will exist in the system. Interestingly, with different hopping rates of both lanes, the densities of the system cannot be influenced by the non-zero vertical transition rate. Our theoretical arguments are in well agreement with extensively performed Monte Carlo simulations.

Effect of unequal injection rates and different hopping rates on asymmetric exclusion processes with junction

In this paper, the effects of unequal injection rates and different hopping rates on the asymmetric simple exclusion process （ASEP） with a 2-input 1-output junction are studied by using a simple mean-field approach and extensive computer simulations. The steady-state particle currents, the density profiles, and the phase diagrams are obtained. It is shown that with unequal injection rates and different hopping rates, the phase diagram structure is qualitatively changed. The theoretical calculations are in good agreement with Monte Carlo simulations.

Effect of unequal injection rates on asymmetric exclusion processes with junction

In this paper, we investigate the effect of unequal injection rates on totally asymmetric simple exclusion processes （TASEPs） with a 2-input 1-output junction and parallel update. A mean-field approach is developed to deal with the junction that connects two sub-chains and the single main chain. We obtain the stationary particle currents, density profiles and phase diagrams. Interestingly, we find that the number of stationary-state phases is changeable depending on the value of a1 （a1 is the injection rate on the first sub-chain）. When a1 〉 1/3, there are seven stationary-state phases in the system, however when a1 〈 1/3, only six stationary-state phases exist in the system. The theoretical calculations are shown to be in agreement with Monte Carlo simulations.