Coupling of two asymmetric exclusion processes with open boundaries

We study the dynamics of a coupled two-channel ASEP in which intra-channel transition rates are dependent on the configuration of neighboring channel. The binding constant k$k$, which signifies the ratio of inter-channel transition rates, is introduced and the symmetric and asymmetric coupling conditions are analyzed for different values of k$k$. The vertical cluster mean-field theory is used to study the system behavior exactly in strong coupling conditions and approximately in intermediate coupling conditions. Additionally, the consequences of particular dynamics such as totally asymmetric simple exclusion process (TASEP), partially asymmetric simple exclusion process (PASEP) and symmetric simple exclusion process (SSEP) in either one or both channels are investigated. It is found that the transition rates have a significant influence on both the qualitative and quantitative nature of the phase diagrams. The mathematical computation shows how the number of phases varies from 3 via 6 to 7 under different environments. Interestingly, in the fully asymmetric coupling case, the results are found to be independent of the magnitude of non-zero vertical transition rate. Our theoretical arguments are in well agreement with extensively performed Monte-Carlo simulation results.     

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 α₁ (α₁ is the injection rate on the first sub-chain). When α₁ > 1/3, there are seven stationary-state phases in the system, however when α₁< 1/3, only six stationary-state phases exist in the system. The theoretical calculations are shown to be in agreement with Monte Carlo simulations.     

Strong Asymmetric Coupling of Two Parallel Exclusion Processes

This paper studies asymmetric strong coupling effect in two parallel exclusion processes, which is a generalization of previous works of Kolomeisky group (Pronina and Kolomeisky in Physica A 372:12, 2006; Tsekouras and Kolomeisky in J. Phys. A 41:465001, 2008). It is shown that with different configurations of hopping rates, the two-lane system exhibits diverse phase diagram and density profiles. Specifically, it shows how the phase diagram changes from having seven phases, via six phases, to three phases. Moreover, it shows that the phase diagram could have only one phase, which exhibits quadrilateral or triangular density profile. The vertical cluster mean-field approach is used to get the stationary-state bulk densities and phase diagrams. Extensively Monte Carlo simulations are carried out, and theoretical predictions are in excellent agreement with simulation results.     

Asymmetric exclusion processes with site sharing in a one-channel transport system

This Letter investigates two-species totally asymmetric simple exclusion process (TASEP) with site sharing in a one-channel transport system. In the model, different species of particles may share the same sites, while particles of the same species may not (hard-core exclusion). The site-sharing mechanism is applied to the bulk as well as the boundaries. Such sharing mechanism within the framework of the TASEP has been largely ignored so far. The steady-state phase diagrams, currents and bulk densities are obtained using a mean-field approximation and computer simulations. The presence of three stationary phases (low-density, high-density, and maximal current) are identified. A comparison on the stationary current with the Bridge model [M.R. Evans, et al., Phys. Rev. Lett. 74 (1995) 208] has shown that our model can enhance the current. The theoretical calculations are well supported by Monte Carlo simulations.     

The robustness in dynamics of out of equilibrium bidirectional transport systems with constrained entrances

Macroscopic and microscopic long-distance bidirectional transfer depends on connections between entrances and exits of various transport mediums. Persuaded by the associations, we introduce a small system module of Totally Asymmetric Simple Exclusion Process including oppositely directed species of particles moving on two parallel channels with constrained entrances. The dynamical rules which characterize the system obey symmetry between the two species and are identical for both the channels. The model displays a rich steady-state behavior, including symmetry breaking phenomenon. The phase diagram is analyzed theoretically within the mean-field approximation and substantiated with Monte Carlo simulations. Relevant mean-field calculations are also presented. We further compared the phase segregation with those observed in previous works, and it is examined that the structure of phase separation in proposed model is distinguished from earlier ones. Interestingly, for phases with broken symmetry, symmetry with respect to channels has been observed as the distinct particles behave differently while the similar type of particles exhibits the same conduct in the system. For symmetric phases, significant properties including currents and densities in the channels are identical for both types of particles. The effect of symmetry breaking occurrence on the Monte Carlo simulation results has also been examined based on particle density histograms. Finally, phase properties of the system having strong size dependency have been explored based on simulations findings.     

Superfluidity in many fermion systems: Exact renormalisation group treatment

The application of the exact renormalisation group to symmetric as well as asymmetric many-fermion systems with a short-range attractive force is studied. Assuming an ansatz for the effective action with effective bosons, describing pairing effects, a set of approximate flow equations for the effective coupling including boson and fermionic fluctuations has been derived. The phase transition to a phase with broken symmetry is found at a critical value of the running scale. The mean-field results are recovered if boson-loop effects are omitted. The calculations with two different forms of the regulator are shown to lead to similar results. We find that, being quite small in the case of the symmetric many-fermion system the corrections to mean-field approximation become more important with increasing mass asymmetry.     

Activated Random Walkers: Facts, Conjectures and Challenges

We study a particle system with hopping (random walk) dynamics on the integer lattice ? ^d . The particles can exist in two states, active or inactive (sleeping); only the former can hop. The dynamics conserves the number of particles; there is no limit on the number of particles at a given site. Isolated active particles fall asleep at rate λ>0, and then remain asleep until joined by another particle at the same site. The state in which all particles are inactive is absorbing. Whether activity continues at long times depends on the relation between the particle density ζ and the sleeping rate λ. We discuss the general case, and then, for the one-dimensional totally asymmetric case, study the phase transition between an active phase (for sufficiently large particle densities and/or small λ) and an absorbing one. We also present arguments regarding the asymptotic mean hopping velocity in the active phase, the rate of fixation in the absorbing phase, and survival of the infinite system at criticality. Using mean-field theory and Monte Carlo simulation, we locate the phase boundary. The phase transition appears to be continuous in both the symmetric and asymmetric versions of the process, but the critical behavior is very different. The former case is characterized by simple integer or rational values for critical exponents (β=1, for example), and the phase diagram is in accord with the prediction of mean-field theory. We present evidence that the symmetric version belongs to the universality class of conserved stochastic sandpiles, also known as conserved directed percolation. Simulations also reveal an interesting transient phenomenon of damped oscillations in the activity density.     

Effects of detachment and size of particles in totally asymmetric simple exclusion processes

In this article, the effects of irreversible detachments of particles in totally asymmetric simple exclusion processes (TASEPs) with extended particles which occupy more than one lattice site, are investigated. First, an approximate mean-field theory is used to calculate phase diagrams and density profiles. The results show that the detachment and the size of the particles have distinct effects on the stationary phases in the two sublattices divided by the detachment, especially in the mc/hd and the hd/hd phase. Here, symbols “mc”, “hd”, and “ld” are initials of maximal current, high density, and low density, respectively, and “mc/hd” represents the stationary state that the left sublattice is in the maximum-current (mc) phase while the right sublattice is in the high density (hd) phase. When the detachment rate is very large, there are four stationary phases, including ld/ld, ld/hd, mc/ld, and mc/hd phases. When the value of the detachment rate is in the middle range, the hd/hd phase occurs, and hence there exist five stationary phases. When the rate is very small, the mc/hd phase disappears, and there are only four phases again. These theoretical results qualitatively and quantitatively agree with computer Monte Carlo simulations especially in the case of large value of the detachment rate.     

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.     

Totally asymmetric exclusion processes at constrained m-input n-output junction points

Totally asymmetric exclusion processes at constrained m-input n-output junction points under random update are studied by theoretical calculation and computer simulation in this paper. At the junction points, the hopping rate of particles from m-input parallel lattices to n-output parallel lattices is assumed to be equal to r/n （0 〈 r 〈 1 ）. The mean-field approach and Monte Carlo simulations show that the phase diagram can be classified into three regions at any value of r. More interestingly, there is a threshold rc = n（ 1 - √1 - m/n）/m. In the cases of r 〉 re and r 〈 rc, qualitatively different phases exist in the system. With the increase of the value of m/n, the regions of （LD, LD） and （MC, LD） or （HD, LD） decrease, and the （HD, HD） is the only phase that increases in the region （LD stands for low density, HD stands for high density, and MC for maximal current）. Stationary current and density profiles are calculated, showing that they are in good agreement with Monte Carlo simulations.     

Free cooling of the one-dimensional wet granular gas

The free cooling behavior of a wet granular gas is studied in one dimension. We employ a particularly simple model system in which the interaction of wet grains is characterized by a fixed energy loss assigned to each collision. Macroscopic laws of energy dissipation and cluster formation are studied on the basis of numerical simulations and mean-field analytical calculations. We find a number of remarkable scaling properties which may shed light on earlier unexplained results for related systems.     

The zone strong coupling two-channel totally asymmetric simple exclusion processes

This article investigates the zone strong coupling two-channel totally asymmetric simple exclusion processes (TASEPs). The study is based on Pronina and Kolomeisky’s work [J. Phys. A-Math. Gen. 37, 9907 (2004)], in which the coupling exists within two whole parallel channels. Zone strong coupling two-channel TASEPs focuses on the behavior and the effect of a particular segment rather than the whole channel. The study shows that there are five possible stationary phases; LD/LD, HD/HD, MC/LD, LD/HD, and MC/HD. The phase diagrams and the density profiles are investigated using computer Monte Carlo simulations and mean-field approximation. The outcomes of the simulations match agreeably with the analytical predictions.     

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.     

Aggregation kinetics in a model colloidal suspension

We present molecular dynamics simulations of aggregation kinetics in a colloidal suspension modeled as a highly asymmetric binary mixture. Starting from a configuration with largely uncorrelated colloidal particles the system relaxes by coagulation-fragmentation dynamics to a structured state of low-dimensionality clusters with an exponential size distribution. The results show that short-range repulsive interactions alone can give rise to so-called cluster phases. For the present model and probably other, more common colloids, the observed clusters appear to be equilibrium phase fluctuations induced by the entropic intercolloidal attractions.     

Theoretical investigation of synchronous totally asymmetric simple exclusion process on lattices with two consecutive junctions in multiple-input-multiple-output traffic system

In this paper, we study the dynamics of the synchronous totally asymmetric simple exclusion process (TASEP) on lattices with two consecutive junctions in a multiple-input-multiple-output (MIMO) traffic system, which consists of m sub-chains for the input and the output, respectively. In the middle of the system, there are N (nN synchronously increasing, the vertical phase boundary moves toward the right and the horizontal phase boundary moves toward the upside in the phase diagram. The boundary conditions of the system as well as the numbers of input and output determine the no-equilibrium stationary states, stationary-states phases, and phase boundaries. We use the results to compare with computer simulations and find that they are in very good agreement with each other.     

Strong Asymmetric Coupling of Two Parallel Exclusion Processes: Effect of Unequal Injection Rates

In this letter, strong asymmetric coupling of two parallel exclusion processes: effect of unequal injection rates will be investigated. It is a generalization of the work of Xiao et al. (Phys. Lett. A 8, 374 (2009)), in which the particles only move on two lanes with rate 1 toward right. We can obtain the diverse phase diagram and density profiles of the system. The vertical cluster mean-field approach and extensively Monte Carlo simulations are used to study the system, and theoretical predictions are in excellent agreement with simulation results.     

Ground state properties and potential energy surfaces of ~(270)Hs from multidimensionally-constrained relativistic mean field model

We study the ground state properties,potential energy curves and potential energy surfaces of the superheavy nucleus 270Hs by using the multidimensionally-constrained relativistic mean-field model with the efFective interaction PC-PK1.The binding energy,size and shape as well as single particle shell structure corresponding to the ground state of this nucleus are obtained.270Hs is well deformed and exhibits deformed doubly magic feature in the single neutron and proton level schemes.One-dimensional potential energy curves and two-dimensional potential energy surfaces are calculated for 270Hs with various spatial symmetries imposed.We investigate in detail the effects of the reflection asymmetric and tri axial distortions on the fission barrier and fission path of 270Hs.When the axial symmetry is imposed,the reflection symmetric and reflection asymmetric fission barriers both show a double-hump structure and the former is highe匚However,when tri axial shapes are allowed the reflection symmetric barrier is lowered very much and then the reflection symmetric fission path becomes favorable.     

Surface solitons in trilete lattices

Fundamental solitons pinned to the interface between three semi-infinite one-dimensional nonlinear dynamical chains, coupled at a single site, are investigated. The light propagation in the respective system with the self-attractive on-site cubic nonlinearity, which can be implemented as an array of nonlinear optical waveguides, is modeled by the system of three discrete nonlinear Schrödinger equations. The formation, stability and dynamics of symmetric and asymmetric fundamental solitons centered at the interface are investigated analytically by means of the variational approximation (VA) and in a numerical form. The VA predicts that two asymmetric and two antisymmetric branches exist in the entire parameter space, while four asymmetric modes and the symmetric one can be found below some critical value of the inter-lattice coupling parameter—actually, past the symmetry-breaking bifurcation. At this bifurcation point, the symmetric branch is destabilized and two new asymmetric soliton branches appear, one stable and the other unstable. In this area, the antisymmetric branch changes its character, getting stabilized against oscillatory perturbations. In direct simulations, unstable symmetric modes radiate a part of their power, staying trapped around the interface. Highly unstable asymmetric modes transform into localized breathers traveling from the interface region across the lattice without significant power loss.     

Spontaneous Breaking of Translational Invariance and Spatial Condensation in Stationary States on a Ring. II. The Charged System and the Two-Component Burgers Equations

We further study the stochastic model discussed in ref. 2 in which positive and negative particles diffuse in an asymmetric, CP invariant way on a ring. The positive particles hop clockwise, the negative counter-clockwise and oppositely-charged adjacent particles may swap positions. We extend the analysis of this model to the case when the densities of the charged particles are not the same. The mean-field equations describing the model are coupled nonlinear differential equations that we call the two-component Burgers equations. We find roundabout weak solutions of these equations. These solutions are used to describe the properties of the stationary states of the stochastic model. The values of the currents and of various two-point correlation functions obtained from Monte-Carlo simulations are compared with the mean-field results. Like in the case of equal densities, one finds a pure phase, a mixed phase and a disordered phase.