Asymmetric Simple Exclusion Process Research Articles

Multi species asymmetric simple exclusion process with impurity activated flips

We obtain an exact matrix product steady state for a class of multi species asymmetric simple exclusion process with impurities, under periodic boundary condition. Alongside the usual hopping dynamics, an additional flip dynamics is activated only in the presence of impurities. Although the microscopic dynamics renders the system to be non-ergodic, exact analytical results for observables are obtained in steady states for a specific class of initial configurations. Interesting physical features including negative differential mobility and transition of correlations from negative to positive with changing vacancy density, have been observed. We discuss plausible connections of this exactly solvable model with multi lane asymmetric simple exclusion processes as well as enzymatic chemical reactions.

Modeling and controlling congestion caused by a bottleneck in an overcrowded aquarium

In this study, we modeled a crowded aquarium using a modified totally asymmetric simple exclusion process and propose a new ticketing system with optimized input rates. We performed a case study for Kaiyukan, a large-scale aquarium in Japan, which encounters heavy congestion primarily caused by a bottleneck in the visitor traffic flow. Kaiyukan has a simple structure and is distinct in that visitors walk through a fixed one-way aisle, as opposed to a typical museum or aquarium layout where visitors can move freely through open areas. We investigated basic congestion features caused by the bottleneck using theoretical analysis and numerical simulations, and developed a new indicator to estimate congestion. Using the model and indicator, we developed a novel ticketing system designed to reduce congestion while preserving the maximum flow. The proposed system includes a 30 min break and indicated a better performance than the conventional method of aiming to maintain a constant input rate. The results indicate that Kaiyukan can reduce the number of visitors waiting and maintain its current daily attendance by introducing our ticketing system.

Asymmetrically coupled two lane totally asymmetric simple exclusion process with extended Langmuir kinetics

The proposed study is motivated by the transport phenomena where the particle hopping, attachment, and detachment dynamics rely on the occupancy state of the corresponding site on another lane. To depict this kind of scenario, we consider an open two-lane Totally Asymmetric Simple Exclusion Process with the presence of asymmetrically coupled and extended Langmuir kinetics regulations. We have analyzed the steady-state properties of the system by calculating characteristics including phase diagrams, density profiles, phase transitions, and finite size effect. The theoretical results are captured by utilizing the framework of a mean-field theory, and it is recognized that numerical findings match closely with the Monte Carlo simulation outcomes.

Modelling of transport processes: Theory and simulations

The transport processes, being a non-equilibrium system, have been a point of interest for physicists since many years revealing and explaining several unexpected effects. Such systems are often dealt with an archetypal model, known as totally asymmetric simple exclusion process, with two different types of boundary conditions: open and periodic. Moreover, these models are analyzed in two varieties of dynamics, random sequential and parallel updates, even at the micro level which play an important role in the global dynamics of the system. On contrary to the random sequential rule, the parallel updates introduce correlations in the system. Using theoretical and numerical methods in the framework based on mean-field approaches, the system properties are analyzed in both transient and steady state.•Both the updating rules are realized using Monte Carlo simulations.•In simplest form, mean-field approach ignores all the correlations and the results coincide with the random sequential update.•Correlations are induced in the system due to parallel update, therefore, a cluster mean-field theory is also discussed to handle them.

Optimization of transition behaviors in a two-lane system

Transitions between two lanes often have a significant impact on various forms of road traffic. To address this problem, we have developed a two-lane asymmetric simple exclusion process model and two hypothetical traffic control strategies, to simulate a futuristic scenario where the timing and location of transitions between two lanes are highly controlled. Various scenarios were proposed to study the effectiveness of these control strategies. An optimized control strategy, whose parameters were determined through an optimization algorithm, is confirmed to effectively maximize the average traffic flow. Consequently, we may identify suitable road sections and the corresponding timings of transitions to resolve congestion in this model.

Totally asymmetric simple exclusion process with local resetting and open boundary conditions

We study a totally asymmetric simple exclusion process with open boundary conditions and local resetting at the injection node. We investigate the stationary state of the model, using both mean–field (MF) approximation and kinetic Monte Carlo simulations, and identify three regimes, depending on the way the resetting rate scales with the lattice size. The most interesting regime is the intermediate resetting one, as in the case of periodic boundary conditions. In this regime we find pure phases and phase separation phenomena, including a low–density/high–density phase separation, which was not possible with periodic boundary conditions. We discuss density profiles, characterizing bulk regions and boundary layers, and nearest–neighbor covariances, finding a remarkable agreement between MF and simulation results. The stationary state phase diagram is mapped out analytically at the MF level, but we conjecture that it may be exact in the thermodynamic limit. We also briefly discuss the large resetting regime, which exhibits an inverse characteristic length scale diverging logarithmically with the lattice size.

Reentrance transition in two lane bidirectional transport system with bottlenecks

Inspired from the vehicular traffic scenarios, including the companionship of two consecutive speed bumps placed within a sufficient distance on the road, we investigate a bidirectional two-lane symmetrically coupled totally asymmetric simple exclusion process with two bottlenecks in the presence of Langmuir kinetics. The steady-state system dynamics in terms of density profiles, phase diagrams, phase transitions, and shock dynamics are investigated thoroughly, exploiting hybrid mean-field theory with various strengths of the bottleneck and lane changing rates which match well with Monte Carlo simulation outcomes. It has been detected that the qualitative and quantitative topology of phase diagrams crucially depend on bottleneck and lane switching rate, emanating in monotonic as well as non-monotonic alterations in the number of steady-state phases. We observe that the effect of the bottlenecks is weakened for the increasing values of the lane changing rate. The proposed study provides many novel mixed phases resulting in bulk-induced phase transitions. The interplay between bottlenecks, lane switching, bidirectional movement, and Langmuir kinetics produces unique phenomena, including reentrance transition and phase division of mixed shock region for comparatively lower lane switching rate.

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

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.

Derivation of the stochastic Burgers equation from totally asymmetric interacting particle systems

We consider equilibrium fluctuations for a class of totally asymmetric zero-range type interacting particle systems, which is particularly related to q-totally asymmetric simple exclusion processes (q-TASEPs). As a main result, we show that density fluctuation of our process converges to the stationary energy solution of the stochastic Burgers equation. Our proof is based on the second-order Boltzmann–Gibbs principle and a Taylor expansion argument.

The suppressed high density phase in three-lane asymmetric exclusion processes with narrow entrances

This paper studies totally asymmetric simple exclusion processes (TASEPs) on three lanes with narrow entrances. Three types of particles move on three parallel lanes, and changing lanes is forbidden. One particle cannot enter one lane if exit site of the neighboring lane is occupied. Simple mean field approach in which correlation of sites is ignored is firstly carried out in the analysis of the system. It is shown that high density is suppressed in the middle lane, and the other two lanes are always symmetric. In addition, the analysis indicates that there are only four phases in the system, and spontaneous symmetry breaking phenomenon does not exist. Extensive Monte Carlo simulations are carried out to confirm the analysis. However, the simple mean field analytical results of phases boundaries deviate that of simulations in the phase diagram. Motivated by this, cluster mean field approach is carried out, and correlations of vertical cluster sites are considered. It is found that the cluster mean field analysis performs much better than the simple mean field analysis.

Shock fluctuations in TASEP under a variety of time scalings

We consider the totally asymmetric simple exclusion process (TASEP) with two different initial conditions with shock discontinuities formed by blocks of fully packed particles. Initially a second class particle is at the left of a shock discontinuity. Using multicolored TASEP we derive exact formulas for the distribution of the second class particle and colored height functions. These are given in terms of the height function at different positions of a single TASEP configuration. We study the limiting distributions of second class particles (and colored height functions). The result depends on how the width blocks of particles scale with the observation time; we study a variety of such scalings.

Non-conserving exclusion process with a dynamic obstacle

Motivated by complex transport processes occurring in biological and physical systems, we study a non-conserving totally asymmetric simple exclusion process with a dynamic defect particle. The defect particle may appear or disappear stochastically and slows down the traffic of moving particles while bound to the lattice. We analyze the system in the context of mean-field approach, and investigate the steady state properties which exhibit a rich dynamic behavior. The theoretically obtained density profiles and current fully describe the phase diagram, further allowing to elucidate the effect of various dynamics individually. Depending upon non-conserving kinetics and defect dynamics, phase schema displays at most eighteen phases; in total, the system exhibits twenty-one phases. Several critical values of the kinetic rates that trigger a qualitative change in the phase diagrams are obtained using analytical arguments. The theoretical outcomes are validated through extensive Monte Carlo simulations.

Short-range and long-range correlations in driven dense colloidal mixtures in narrow pores.

The system of a driven dense colloid mixture in a tube with diameter comparable to particle size is modeled by a generalization of the asymmetric simple exclusion process (ASEP) model. The generalization goes in two directions: relaxing the exclusion constraint by allowing several (but few) particles on a site and by considering two species of particles, which differ in size and transport coefficients. We calculate the nearest-neighbor correlations using a variant of the Kirkwood approximation and show by comparison with numerical simulations that the approximation provides quite accurate results. However, for long-range correlations, we show that the Kirkwood approximation is useless, as it predicts exponential decay of the density-density correlation function with distance, while simulation data indicate that the decay is algebraic. For the one-component system, we show that the decay is governed by a power law with universal exponent close to 2. In the two-component system, the correlation function behaves in a more complicated manner: Its sign oscillates but the envelope decays again very slowly and the decay is compatible with a power law with an exponent somewhat lower than 2. Therefore, our generalization of the ASEP belongs to a different universality class from the ensemble of generalized ASEP models which are mappable to zero-range processes.

Hydrodynamics for One-Dimensional ASEP in Contact with a Class of Reservoirs

We study the hydrodynamic behaviour of the asymmetric simple exclusion process on the lattice of size n. In the bulk, the exclusion dynamics performs rightward flux. At the boundaries, the dynamics is attached to reservoirs. We investigate two types of reservoirs: (1) the reservoirs that are weakened by $$n^\theta $$ for some $$\theta <0$$ and (2) the reservoirs that create particles only at the right boundary and annihilate particles only at the left boundary. We prove that the spatial density of particles, under the hyperbolic time scale, evolves with the entropy solution to a scalar conservation law on [0, 1] with boundary conditions. The boundary conditions are characterised by the boundary traces [3, 17, 20] at $$x=0$$ and $$x=1$$ which take values from $$\{0,1\}$$ .

Role of extended coupling in bidirectional transport system.

Motivated by vehicular traffic phenomena, we study a bidirectional two-lane open totally asymmetric simple exclusion process with extended symmetric coupling conditions in the presence of Langmuir kinetics. The phase diagrams and density profiles are calculated utilizing mean-field theory for different lane-changing rates and are found to be in a good match with Monte Carlo simulation results. It has been observed that the qualitative topology of phase diagrams depends on the lane-switching rate significantly, resulting in nonmonotonic variations in the number of steady-state phases. The proposed model provides various mixed phases leading to bulk induced phase transitions. The interplay between bidirectional movement, extended coupling conditions, and Langmuir kinetics produces unusual phenomena, including a back-and-forth phase transition and partial phase division of the shock region for comparatively smaller values of the lane-changing rate. Moreover, we analyze the shock dynamics and calculate critical values for the lane-changing rate at which the phases appear or disappear.

A model of minimal entropy generation for cytoskeletal transport systems with multiple interacting motors

We study the steady-state rate of entropy generation for multiple interacting particles. The description used is based on the partially asymmetric exclusion process in a lattice with periodic boundary conditions. Our methodology shows that in the steady-state, the rate of entropy generation is directly proportional to the bulk drift and the applied driving force. Since in many cases the driving force is unknown or hard to determine. We circumvent this by deriving a lower bound for the entropy, resulting in an extended thermodynamic uncertainty relation for the asymmetric simple exclusion process. We systematically compared this bound with the actual entropy generation. Thus, we identify the force regimes, and particles’ density conditions where the entropy bound derived from this extended thermodynamic uncertainty relation is meaningful.

The role of extended range of interactions in the dynamics of interacting molecular motors

Motor proteins, also known as biological molecular motors, play important roles in various intracellular processes. Experimental investigations suggest that molecular motors interact with each other during the cellular transport, but the nature of such interactions remains not well understood. Stimulated by these observations, we present a theoretical study aimed to understand the effect of the range of interactions on dynamics of interacting molecular motors. For this purpose, we develop a new version of the totally asymmetric simple exclusion processes in which nearest-neighbor as well as the next nearest-neighbor interactions are taken into account in a thermodynamically consistent way. A theoretical framework based on a cluster mean-field approximation, which partially takes correlations into account, is developed to evaluate the stationary properties of the system. It is found that fundamental current–density relations in the system strongly depend on the strength and the sign of interactions, as well as on the range of interactions. For repulsive interactions stronger than some critical value, a mean-field theoretical approach predicts that increasing the range of interactions might lead to a change from unimodal to trimodal dependence in the flux-density fundamental diagram. However, it is not fully supported by extensive Monte Carlo computer simulations that test theoretical predictions. Although in most ranges of parameters a reasonable agreement between theoretical calculations and computer simulations is observed, there are situations when the cluster mean-field approach fails to describe properly the dynamics in the system. Theoretical arguments to explain these observations are presented. Our theoretical analysis clarifies the microscopic picture of how the range of interactions influences the dynamics of interacting molecular motors.

Nonequilibrium master equationfor interacting Brownian particles in a deep-well periodic potential.

Employing a creation and annihilation operator formulation, we derive an approximate many-body master equationdescribing discrete hopping from the more general continuous description of Brownian motion on a deep-well nonequilibrium periodic potential. The many-body master equationdescribes interactions of arbitrary strength and range arising from a "top-hat" two-body interaction potential. We show that this master equationreduces to the well-known asymmetric simple exclusion process and the zero range process in certain regimes. We also use the creation and annihilation operator formalism to derive results for the steady-state drift and the number fluctuations in special cases, including the unexplored limit of weak interparticle interactions.

Analytical investigation on totally asymmetric simple exclusion process with Langmuir kinetics and a parallel update with two sub-steps

Motivated by the fact that parallel update rules need to be employed to study the traffic dynamic of vehicles and pedestrians with bulk on-off ramps. This paper studies the totally asymmetric simple exclusion process (TASEP) with Langmuir kinetics and a parallel update with two sub-steps. Moreover, this new model can be analyzed analytically. Based on the mean-field method, the phase diagrams are obtained and the influences of model parameters are investigated. Compared to the system under the random update, there do not exist the phases related to the maximum current phase and Meissner phase in the system under the parallel update.

Quasi-static limit for the asymmetric simple exclusion

We study the one-dimensional asymmetric simple exclusion process on the lattice $\{1, \dots,N\}$ with creation/annihilation at the boundaries. The boundary rates are time dependent and change on a slow time scale $N^{-a}$ with $a>0$. We prove that at the time scale $N^{1+a}$ the system evolves quasi-statically with a macroscopic density profile given by the entropy solution of the stationary Burgers equation with boundary densities changing in time, determined by the corresponding microscopic boundary rates. We consider two different types of boundary rates: the "Liggett boundaries" that correspond to the projection of the infinite dynamics, and the reversible boundaries, that correspond to the contact with particle reservoirs in equilibrium. The proof is based on the control of the Lax boundary entropy--entropy flux pairs and a coupling argument.