Asymmetric Simple Exclusion Process Research Articles

Physical mechanisms in impacts of interaction factors on totally asymmetric simple exclusion processes

Exclusion processes are hot study issues in statistical physics and corresponding complex systems. Among fruitful exclusion processes, totally asymmetric simple exclusion process (namely, TASEP) attracts much attention due to its insight physical mechanisms in understanding such nonequilibrium dynamical processes. However, interactions among isolated TASEP are the core of controlling the dynamics of multiple TASEPs that are composed of a certain amount of isolated one-dimensional TASEP. Different from previous researches, the interaction factor is focused on the critical characteristic parameter used to depict the interaction intensity of these components of TASEPs. In this paper, a much weaker constraint condition [Formula: see text] is derived as the analytical expression of interaction factor. Self-propelled particles in the subsystem [Formula: see text] of multiple TASEPs can perform hopping forward at [Formula: see text], moving into the target site of the (i − 1)th TASEP channel at [Formula: see text] or updating into the (i + 1)th TASEP channel at [Formula: see text]. The comparison of this proposed interaction factor and other previous factors is performed by investigating the computational efficiency of obtaining analytical solutions and simulation ones of order parameters of the proposed TASEP system. Obtained exact solutions are observed to match well with Monte Carlo simulations. This research attempts to have a more comprehensive interpretation of physical mechanisms in the impact of interaction factors on TASEPs, especially corresponding to stochastic dynamics of self-propelled particles in such complex statistical dynamical systems.

Stochastic dynamics in nonequilibrium phase transitions of multiple totally asymmetric simple exclusion processes coupled with strong and weak interacting effects

Totally asymmetric simple exclusion process (TASEP) is an important stochastic dynamic process in the area of statistical physics, which can be used to model microscopic transport in nonequilibrium processes. Due to its rich stochastic dynamics and nonequilibrium phase transition mechanisms, the importance of TASEP in statistical physics is similar with that of Ising model, which has attracted many attentions. In this paper, multiple TASEPs are introduced and coupled with various strong and weak interacting effects of self-driven particles. Both strong and weak couplings are calculated by means of mean-field analyses and Monte Carlo simulations. Tremendous cluster dynamics, evolution law of topological structures of phase diagrams and mechanisms of shock evolution are found in thermodynamic limit of proposed particle system. Monte Carlo simulation results like phase boundaries are found to be a good match with mean-field analyses, which reflect the validity of the research. The research work will be conducive to exploring the mechanisms of stochastic dynamics in the process of nonequilibrium phase transitions of multi-body interacting particle systems.

Biologically motivated three-species exclusion model: Effects of leaky scanning and overlapping genes on initiation of protein synthesis.

The totally asymmetric simple exclusion process was originally introduced as a model for the trafficlike collective movement of ribosomes on a messenger RNA (mRNA) that serves as the track for the motorlike forward stepping of individual ribosomes. In each step, a ribosome elongates a protein by a single unit using the track also as a template for protein synthesis. But, prefabricated functionally competent ribosomes are not available to begin synthesis of protein; a subunit directionally scans the mRNA in search of the predesignated site where it is supposed to bind with the other subunit and begin the synthesis of the corresponding protein. However, because of "leaky" scanning, a fraction of the scanning subunits miss the target site and continue their search beyond the first target. Sometimes such scanners successfully identify the site that marks the site for initiation of the synthesis of a different protein. In this paper, we develop an exclusion model with three interconvertible species of hard rods to capture some of the key features of these biological phenomena and study the effects of the interference of the flow of the different species of rods on the same lattice. More specifically, we identify the mean time for the initiation of protein synthesis as appropriate mean first-passage time that we calculate analytically using the formalism of backward master equations. Despite the approximations made, our analytical predictions are in reasonably good agreement with the numerical data that we obtain by performing Monte Carlo simulations.

Dynamical phase behavior of the single- and multi-lane asymmetric simple exclusion process via matrix product states

The open asymmetric simple exclusion process (ASEP) has emerged as a paradigmatic model of nonequilibrium behavior, in part due to its complex dynamical behavior and wide physical applicability as a model of driven diffusion. We compare the dynamical phase behavior of the one-dimensional (1D) ASEP and the multi-lane ASEP, a previously unstudied extension of the 1D model that may be thought of as a finite-width strip of the fully two-dimensional (2D) system. Our characterization employs large deviation theory (LDT), matrix product states (MPS), and the density matrix renormalization group (DMRG) algorithm, to compute the current cumulant generating function and its derivatives, which serve as dynamical order parameters. We use this measure to show that when particles cannot exit or enter the lattice vertically, the phase behavior of the multi-lane ASEP mimics that of its 1D counterpart, exhibiting the macroscopic and microscopic signatures of the maximal current, shock, and high-density-low-density coexistence phases. Conversely, when particles are allowed to freely enter and exit the lattice, no such transition is observed. This contrast emphasizes the complex interplay between latitudinal and longitudinal hopping rates and the effect of current biasing. Our results support the potential of tensor networks as a framework to understand classical nonequilibrium statistical mechanics.

The exact phase diagram for a semipermeable TASEP with nonlocal boundary jumps

We consider a finite one-dimensional totally asymmetric simple exclusion process with four types of particles, , in contact with reservoirs. Particles of species 0 can neither enter nor exit the lattice, and those of species are constrained to lie at the first and last site. Particles of species 1 enter from the left reservoir into either the first or second site, move rightwards, and leave from either the last or penultimate site. Conversely, particles of species enter from the right reservoir into either the last or penultimate site, move leftwards, and leave from either the first or last site. This dynamics is motivated by a natural random walk on the Weyl group of type D. We compute the exact nonequilibrium steady state distribution using a matrix ansatz building on earlier work of Arita. We then give explicit formulas for the nonequilibrium partition function as well as densities and currents of all species in the steady state, and derive the phase diagram.

Limit law of a second class particle in TASEP with non-random initial condition

On considere le processus d’exclusion simple totalement asymetrique avec des condition initiales deterministes, densite $\lambda$ sur $\mathbb{Z}_{-}$ et $\rho$ sur $\mathbb{Z}_{+}$. Initialement on place une particule de deuxieme classe a l’origine. Si $\lambda<\rho$, un choc est cree et la particule de deuxieme classe le suit avec vitesse $1-\lambda-\rho$. Dans la limite $t\to\infty$, on demontre que les fluctuations de la position de la particule de deuxieme classe sont de l’ordre $t^{1/3}$ et on obtient sa loi limite. On determine aussi la loi limite du nombre de sauts faits par la particule de deuxieme classe jusqu’a l’instant $t$.

Theoretical study of network junction models for totally asymmetric exclusion processes with interacting particles

Biological transport phenomena frequently exhibit complex network behavior when several molecular fluxes converge to special junctions from which another fluxes move out in different directions. Similar behavior is also observed in vehicular transport. Stimulated by these observations, we developed a theoretical framework to investigate network junction models of totally asymmetric simple exclusion processes with interacting particles. Utilizing a two-site cluster mean field framework that takes into account some correlations in the system, stationary dynamic properties, such as phase diagrams, density profiles and correlations profiles, are explicitly evaluated. It is found that the number of stationary phases strongly depend on the number of segments that come and leave the network junction. The inter-particle interactions also have a strong effect of dynamic properties of the system. Our method can be extended to the systems with several junctions. All theoretical predictions are in good agreement with extensive Monte Carlo computer simulations.

Dynamical aspects of spontaneous symmetry breaking in driven flow with exclusion.

We present a numerical study of a two-lane version of the stochastic nonequilibrium model known as the totally asymmetric simple exclusion process. For such a system with open boundaries, and suitably chosen values of externally imposed particle injection (α) and ejection (β) rates, spontaneous symmetry breaking can occur. We investigate the statistics and internal structure of the stochastically induced transitions or "flips," which occur between opposite broken-symmetry states as the system evolves in time. From the distribution of time intervals separating successive flips, we show that the evolution of the associated characteristic times against externally imposed rates yields information regarding the proximity to a critical point in parameter space. On short timescales, we probe for the possible existence of precursor events to a flip between opposite broken-symmetry states. We study an adaptation of domain-wall theory to mimic the density reversal process associated with a flip.

The non-compact XXZ spin chain as stochastic particle process

In this note we relate the Hamiltonian of the integrable non-compact spin s XXZ chain to the Markov generator of a stochastic particle process. The hopping rates of the continuous-time process are identified with the ones of a q-Hahn asymmetric zero range model. The main difference with the asymmetric simple exclusion process, which can be mapped to the ordinary XXZ spin chain, is that multiple particles can occupy one and the same site. For the non-compact spin XXZ chain the associated stochastic process reduces to the multiparticle asymmetric diffusion model introduced by Sasamoto–Wadati.

Generalizations of TASEP in Discrete and Continuous Inhomogeneous Space

We investigate a rich new class of exactly solvable particle systems generalizing the Totally Asymmetric Simple Exclusion Process (TASEP). Our particle systems can be thought of as new exactly solvable examples of tandem queues, directed first- or last-passage percolation models, or Robinson-Schensted-Knuth type systems with random input. One of the novel features of the particle systems is the presence of spatial inhomogeneity which can lead to the formation of traffic jams. For systems with special step-like initial data, we find explicit limit shapes, describe hydrodynamic evolution, and obtain asymptotic fluctuation results which put the systems into the Kardar-Parisi-Zhang universality class. At a critical scaling around a traffic jam in the continuous space TASEP, we observe deformations of the Tracy-Widom distribution and the extended Airy kernel, revealing the finer structure of this novel type of phase transitions. A homogeneous version of a discrete space system we consider is a one-parameter deformation of the geometric last-passage percolation, and we obtain extensions of the limit shape parabola and the corresponding asymptotic fluctuation results. The exact solvability and asymptotic behavior results are powered by a new nontrivial connection to Schur measures and processes.

Bid-Based Priority Signal Control in a Connected Environment: Concept

Though the loss of time is considered equivalent to opportunity loss, little research has been conducted in the field of signal control that accounts for individual differences in subjective opportunity loss. Because bids reflect the subjective valuation of opportunity loss, this paper introduces the concept of a bid-based priority signal control that accommodates indeterministic characteristics of queue formation in a connected environment and addresses several key elements of such a concept. Within this conception, drivers can bid for their desired signal indication. Based on these bids, an algorithm extends a green interval as long as the cumulative opportunity loss observed in stopped movements remains less than the value that would be lost through the termination of that green interval. The effects of this new type of control on user benefit and queueing delay were assessed using the asymmetric simple exclusion process. Simulation results showed that the bid-based priority signal control produced a greater subjective user benefit when measured in relation to a pre-timed control with a similar green interval. In addition, the bid-based priority signal kept the average maximum queue length relatively equal to its pre-timed equivalent. The bid-based priority signal control also balanced out the expected values of user benefit in conflicting movements. Bid-based signal priority control was recommended for further study to investigate the effects of bidding distributions on effectiveness and queue length in high-fidelity microsimulations.

The q-Hahn PushTASEP

Abstract We introduce the $q$-Hahn PushTASEP—an integrable stochastic interacting particle system that is a three-parameter generalization of the PushTASEP, a well-known close relative of the TASEP (totally asymmetric simple exclusion process). The transition probabilities in the $q$-Hahn PushTASEP are expressed through the $_4\phi _3$ basic hypergeometric function. Under suitable limits, the $q$-Hahn PushTASEP degenerates to all known integrable (1+1)-dimensional stochastic systems with a pushing mechanism. One can thus view our new system as a pushing counterpart of the $q$-Hahn TASEP introduced by Povolotsky [37]. We establish Markov duality relations and contour integral formulas for the $q$-Hahn PushTASEP. In a $q\to 1$ limit of our process we arrive at a random recursion, which, in a special case, appears to be similar to the inverse-Beta polymer model. However, unlike in recursions for Beta polymer models, the weights (i.e., the coefficients of the recursion) in our model depend on the previous values of the partition function in a nontrivial manner.

Effect of hopping rates coupled with on-ramp on the phase diagrams of totally asymmetric simple exclusion process

In this paper, the effect of different hopping rates coupled with on-ramp on the phase diagrams has been investigated by totally asymmetric simple exclusion process (TASEP). The topology of phase diagrams on different hopping rates and on-ramp has been obtained. Additionally, the corresponding phase diagrams and the existing condition are given by approximate mean field theory, and the theoretical results agree well with Monte Carlo simulations.

Thermodynamic uncertainty for run-and-tumble–type processes

Thermodynamic uncertainty relations have emerged as universal bounds on current fluctuations in non-equilibrium systems. Here we derive a new bound for a particular class of run-and-tumble–type processes using the mathematical framework of renewal-reward theory which can be applied to both Markovian and non-Markovian systems. We demonstrate the results for selected single-particle models as well as a variant of the asymmetric simple exclusion process with collective tumbles. Our bound is relatively tight for a broad parameter regime and only requires knowledge of the statistics of run lengths and the mean entropy production rate of tumbles.

Global Density Profile For Particle Non-Conserving One Dimensional Transport From Renormalization Group Flows

The totally asymmetric simple exclusion process along with particle adsorption and evaporation kinetics is a model of boundary-induced nonequilibrium phase transition. In the continuum limit, the average particle density across the system is described by a singular differential equation involving multiple scales which lead to the formation of boundary layers (BL) or shocks. A renormalization group analysis is developed here by using the location and the width of the BL as the renormalization parameters. It not only allows us to cure the large distance divergences in the perturbative solution for the BL but also generates, from the BL solution, an analytical form for the global density profile. The predicted scaling form is checked against numerical solutions for finite systems.

Phase transitions in the ASEP and stochastic six-vertex model

In this paper, we consider two models in the Kardar–Parisi–Zhang (KPZ) universality class, the asymmetric simple exclusion process (ASEP) and the stochastic six-vertex model. We introduce a new class of initial data (which we call shape generalized step Bernoulli initial data) for both of these models that generalizes the step Bernoulli initial data studied in a number of recent works on the ASEP. Under this class of initial data, we analyze the current fluctuations of both the ASEP and stochastic six-vertex model and establish the existence of a phase transition along a characteristic line, across which the fluctuation exponent changes from $1/2$ to $1/3$. On the characteristic line, the current fluctuations converge to the general (rank $k$) Baik–Ben–Arous–Péché distribution for the law of the largest eigenvalue of a critically spiked covariance matrix. For $k=1$, this was established for the ASEP by Tracy and Widom; for $k>1$ (and also $k=1$, for the stochastic six-vertex model), the appearance of these distributions in both models is new.

The effect of boundaries and impurity on a system with non-local hop dynamics

We study a one-dimensional lattice model of particles which interact with each other via hard-core repulsion, and which can make long hops in addition to the usual nearest neighbour hopping dynamics. The parameter p gives the probability for long hops and the p = 0 limit leads to the well studied totally asymmetric simple exclusion process (TASEP). The first part of this study describes the combined effect of open boundaries and long hops on the steady state of the system. Apart from the usual low density (LD), high density (HD) and maximum current (MC) phases, the introduction of a finite p leads to a new possibility-an empty road (ER) phase with particles clearing out faster than they enter. The variation in the phase diagram with p is interesting, with the LD and MC phases vanishing at large values of p while the ER and HD phases divide the parameter space into 1/2. In the second part of this study, we look at the combined effect of long hops and static/dynamic impurities. The boundaries are taken to be periodic for simplicity. We see that the system with a static impurity and with 0 < p < 1 shows a phase transition from a shock phase characterised by finite densities on either side of the shock (HD–LD phase) to a phase where the density on one side of the shock is zero (HD-ER phase). We also study the effect of a dynamic impurity, introduced via a slow particle. Here, the system undergoes a phase transition from a homogeneous phase to a shock phase depending on the density, the speed of the particle, as well as the probability p. The shock phase dominates the phase diagram at large values of p. All our studies involve numerical simulations which are supported by mean field theory arguments. The mean field approximation works well qualitatively and correctly identifies the possible phases, while the quantitative agreement with numerics varies, depending on parameter values.

Totally asymmetric exclusion process with site-wise dynamic disorder

We propose an extension of the totally asymmetric simple exclusion process (TASEP) in which particles hopping along a lattice can be blocked by obstacles that dynamically attach/detach from lattice sites. The model can be thought as TASEP with site-wise dynamic disorder. We consider two versions of defect dynamics: (i) defects can bind to any site, irrespective of particle occupation, (ii) defects only bind to sites which are not occupied by particles (particle-obstacle exclusion). In case (i) there is a symmetric, parabolic-like relationship between the current and particle density, as in the standard TASEP. Case (ii) leads to a skewed relationship for slow defect dynamics. We also show that the presence of defects induces particle clustering, despite the translation invariance of the system. For open boundaries the same three phases as for the standard TASEP are observed, albeit the position of phase boundaries is affected by the presence of obstacles. We develop a simple mean-field theory that captures the model’s quantitative behaviour for periodic and open boundary conditions and yields good estimates for the current-density relationship, mean cluster sizes and phase boundaries. Lastly, we discuss an application of the model to the biological process of gene transcription.

Cluster mean-field dynamics in one-dimensional TASEP with inner interactions and Langmuir dynamics

In the area of statistical physics, totally asymmetric simple exclusion process (TASEP) is treated as one of the most important driven-diffusive systems. It contains profound non-equilibrium statistical physics mechanisms due to being the paradigm model like Ising model. Different with previous work, a one-dimensional TASEP coupled with inner interactions and Langmuir dynamics is taken into account. Weak coupled binding and unbinding rates are introduced in the proposed model. Bond breaking and making mechanisms of self-driven particles illustrating the unidirectional movement of protein motors are investigated by means of performing cluster mean-field analyses. Dynamics in the proposed system dominated by the competition between the attraction effect and the repulsion one are found to depend on the specific value of the interaction energy of these active particles. The research work will be helpful for understanding non-equilibrium statistical behaviors of interacting particle systems.

Multipoint distribution of periodic TASEP

The height fluctuations of the models in the KPZ class are expected to converge to a universal process. The spatial process at equal time is known to converge to the Airy process or its variations. However, the temporal process, or more generally the two-dimensional space-time fluctuation field, is less well understood. We consider this question for the periodic TASEP (totally asymmetric simple exclusion process). For a particular initial condition, we evaluate the multitime and multilocation distribution explicitly in terms of a multiple integral involving a Fredholm determinant. We then evaluate the large-time limit in the so-called relaxation time scale.