Asymmetric Simple Exclusion Process Research Articles

The effect of individual tendency on crowd evacuation efficiency under inhomogeneous exit attraction using a static field modified FFCA model

As an extension of the Asymmetric Simple Exclusion Process, the floor field cellular automata model has its specific advantages in reproducing crowd self-organized phenomena, embodying individual characteristics and reducing the computing complexity by translating the long-ranged interaction to local interaction. Evacuation from a room is an important part in the study of building evacuation. In our experiment and real life observation we found the exit attraction non-uniformity. To obtain the effect of individual tendency to the exit attraction center on the crowd evacuation efficiency, the static field is modified. Compared with the control group, the exit attraction non-uniformity has a disadvantage in the crowd evacuation efficiency. The position deviation between the exit geometric center and the exit attraction center delays the crowd evacuation by generating a local merging flow. In addition, the individual tendency also increases the crowd evacuation time by increasing the static field gradient to the attraction center, leading to a low usage efficiency of exits. Compared with the influence of other factors, the inhomogeneous exit attraction has an obvious effect on the crowd evacuation efficiency.

Exclusion processes on networks as models for cytoskeletal transport

We present a study of exclusion processes on networks as models for complex transport phenomena, and in particular for active transport of motor proteins along the cytoskeleton. Specifically, we focus on the totally asymmetric simple exclusion process (TASEP) as well as its generalizations including backstepping (partially asymmetric simple exclusion process (PASEP)) and exchange with a bulk concentration (TASEP with Langmuir kinetics (TASEP-LK)). We build on the previously used effective rate approach to establish a general methodology in terms of effective rate diagrams, which allows for a simple classification of the stationary transport state of the total network. This approach is general and reveals generic features of exclusion processes on networks. Based on the three examples considered here, we show that the classification can be made in terms of three qualitative different network regimes: a homogeneous regime, a heterogeneous network regime and a heterogeneous segment regime. Using parameters representative of real motor proteins, we show how the transitions between these regimes can be regulated through a variety of multi-scale factors, such as the interplay of exclusion interactions, the non-equilibrium nature of the transport process, motor processivity and the network topology. Using the equilibrium limits of PASEP and TASEP-LK, we also shed further light on the emergence of density heterogeneities in active transport phenomena.

Disordered exclusion process revisited: some exact results in the low-current regime

We study the steady state of the totally asymmetric simple exclusion process with inhomogeneous hopping rates associated with sites (site-wise disorder). Using the fact that the non-normalized steady-state weights, which solve the master equation, are polynomials in all the hopping rates, we propose a general method for calculating their first few lowest coefficients exactly. In the case of binary disorder where all slow sites share the same hopping rate r < 1, we apply this method to calculate the steady-state current up to the quadratic term in r for some particular disorder configurations. For the most general (non-binary) disorder, we show that in the low-current regime the current is determined solely by the current-minimizing subset of equal hopping rates, provided all other slow rates are much larger. Our approach can be readily applied to any other driven diffusive system with unidirectional hopping, if one can identify a hopping rate such that the current vanishes when this rate is set to zero.

Theoretical Analysis of Kinesin KIF1A Transport Along Microtubule

Recently, a three-state model is presented to describe the intracellular traffic of unconventional (single-headed) kinesin KIF1A [Phys. Rev. Lett. {\bf 95}, 118101 (2005)], in which each motor can bind strongly or weakly to its microtubule track, and each binding site of the track might be empty or occupied by one motor. As the usual two-state model, i.e. the totally asymmetric simple exclusion process (TASEP) with motor detachment and attachment, in steady state of the system, this three-state model also exhibits shock (or domain wall separating the high-density and low density phases) and boundary layers. In this study, using mean-field analysis, the conditions of existence of shock and boundary layers are obtained theoretically. Combined with numerical calculations, the properties of shock are also studied. This study will be helpful to understand the biophysical properties of the collective transport of kinesin KIF1A.

Position dependence of the particle density in a double-chain section of a linear network in a totally asymmetric simple exclusion process

We report here results on the study of the totally asymmetric simple exclusion process, defined on an open network, consisting of head and tail simple-chain segments with a double-chain section inserted in between. Results of numerical simulations for relatively short chains reveal an interesting feature of the network. When the current through the system takes its maximum value, a simple translation of the double-chain section forward or backward along the network leads to a sharp change in the shape of the density profiles in the parallel chains, thus affecting the total number of particles in that part of the network. In the symmetric case of equal injection and ejection rates α=β>1/2 and equal lengths of the head and tail sections, the density profiles in the two parallel chains are almost linear, characteristic of the coexistence line (shock phase). Upon moving the section forward (backward), their shape changes to the one typical for the high- (low-) density phases of a simple chain. The total bulk density of particles in a section with a large number of parallel chains is evaluated too. The observed effect might have interesting implications for the traffic flow control as well as for biological transport processes in living cells. An explanation of this phenomenon is offered in terms of a finite-size dependence of the effective injection and ejection rates at the ends of the double-chain section.

Scalar products of state vectors in totally asymmetric exactly solvable models on a ring

We consider exactly solvable, totally asymmetric models of the low-dimensional nonequilibrium physics on a ring, namely, the totally asymmetric simple exclusion process and the totally asymmetric simple zero range process. The quantum inverse method allows us to calculate the scalar products of state vectors of the models and to represent the answers in the determinantal form. It is shown that the eigenvectors of the models form a complete orthogonal basis. The projections of state vectors on stationary, time independent states are studied. Bibliography: 39 titles.

Calculation of correlation functions in totally asymmetric exactly solvable models on a ring

We consider exactly solvable totally asymmetric models of low-dimensional nonequilibrium statistical physics on a periodic chain, namely, the totally asymmetric simple exclusion process and the totally asymmetric simple zero-range process. We describe the method for calculating correlation functions for the models on a periodic lattice and represent scalar products of state vectors of the model as determinants.

TASEP on a Linear Network with a Bypass

The asymmetric simple exclusion process (TASEP) is one of the paradigmatic models for understanding the rich world of non-equilibrium phenomena. Interesting realizations of the process on networks with complex geometry have been initiated in ....

Motor-mediated bidirectional transport along an antipolar microtubule bundle: A mathematical model

Long-distance bidirectional transport of organelles depends on the coordinated motion of various motor proteins on the cytoskeleton. Recent quantitative live cell imaging in the elongated hyphal cells of Ustilago maydis has demonstrated that long-range motility of motors and their endosomal cargo occurs on unipolar microtubules (MTs) near the extremities of the cell. These MTs are bundled into antipolar bundles within the central part of the cell. Dynein and kinesin-3 motors coordinate their activity to move early endosomes (EEs) in a bidirectional fashion where dynein drives motility towards MT minus ends and kinesin towards MT plus ends. Although this means that one can easily assign the drivers of bidirectional motion in the unipolar section, the bipolar orientations in the bundle mean that it is possible for either motor to drive motion in either direction. In this paper we use a multilane asymmetric simple exclusion process modeling approach to simulate and investigate phases of bidirectional motility in a minimal model of an antipolar MT bundle. In our model, EE cargos (particles) change direction on each MT with a turning rate Ω and there is switching between MTs in the bundle at the minus ends. At these ends, particles can hop between MTs with rate q(1) on passing from a unipolar to a bipolar section (the obstacle-induced switching rate) or q(2) on passing in the other direction (the end-induced switching rate). By a combination of numerical simulations and mean-field approximations, we investigate the distribution of particles along the MTs for different values of these parameters and of Θ, the overall density of particles within this closed system. We find that even if Θ is low, the system can exhibit a variety of phases with shocks in the density profiles near plus and minus ends caused by queuing of particles. We discuss how the parameters influence the type of particle that dominates active transport in the bundle.

Matrix ansatz for the fluctuations of the current in the ASEP with open boundaries

The asymmetric simple exclusion process (ASEP) is one of the most extensively studied models in non-equilibrium statistical mechanics. The macroscopic particle current produced in its steady state is directly related to the breaking of detailed balance, and is therefore a physical quantity of particular interest. In this paper, we build a matrix product ansatz which allows us to access the exact statistics of the fluctuations of that current for finite sizes, as well as the probabilities of configurations conditioned on the mean current. We also show how this ansatz can be used for the periodic ASEP and how it translates into the language of the XXZ spin chain.

INVESTIGATION OF ASYMMETRIC SIMPLE EXCLUSION PROCESSES WITH ZONED INHOMOGENEITY AND ON-RAMP

In this paper, theoretical analysis and extensive simulations are used to investigate asymmetric simple exclusion processes (ASEPs) with zoned inhomogeneity and on-ramp in a single-lane system. There are five possible phase diagrams with different hopping rate p and on-ramp rate q. Interestingly, the MC/MC, MC/LD and MC/HD phase can exist in the phase diagram with different hopping rate p and on-ramp rate q. When the on-ramp rate is fixed, with the decreasing of hopping rate, the HD/HD phase shrinks, it implies the heavy traffic in the system.

The Bose Gas and Asymmetric Simple Exclusion Process on the Half-Line

In this paper we find explicit formulas for: (1) Green's function for a system of one-dimensional bosons interacting via a delta-function potential with particles confined to the positive half-line; and (2) the transition probability for the one-dimensional asymmetric simple exclusion process (ASEP) with particles confined to the nonnegative integers. These are both for systems with a finite number of particles. The formulas are analogous to ones obtained earlier for the Bose gas and ASEP on the line and integers, respectively. We use coordinate Bethe Ansatz appropriately modified to account for confinement of the particles to the half-line. As in the earlier work, the proof for the ASEP is less straightforward than for the Bose gas.

Position-Induced Phase Change in a TASEP with a Double-Chain Section (a Model of Biological Transport)

The totally asymmetric simple exclusion processes (TASEP) has beenused since 1968 to model different biochemical processes,including kinetics of protein synthesis, molecular motors traffic,collective effects in genetic transcription. Here, we considerTASEP defined on an open network consisting of simple head andtail chains with a double-chain section in-between. Our results of Monte Carlo simulations show a novel property of the model when the simple chains are in the maximum-current phase: upon moving the double-chain defect from the central position forward or backward along the network, keeping fixed the length of both the defect and the whole network, a position-induced phase change in the parallel defect chains takes place. This phenomenon is explained in terms of finite-size dependence of the effective injection and removal rates at the ends of the double-chain defect. Some implications of the results for molecular motors cellular transport along such networks are suggested. However, at present these are just speculations which need further examinations.

A balance network for the asymmetric simple exclusion process

We investigate a balance network for the totally asymmetric simple exclusion process (TASEP). Subsystems consisting of TASEPs are connected by bidirectional links with each other, which results in balance between every pair of subsystems. The network includes some specific important cases discussed in earlier works such as the TASEP with the Langmuir kinetics, multiple lanes and finite reservoirs. Probability distributions of particles in the steady state are exactly given in factorized forms according to their balance properties. Although the system has nonequilibrium parts, it is well described using expressions in a framework of statistical mechanics based on equilibrium states. Moreover, the overall argument does not depend on the network structures, and the knowledge obtained in this work is applicable to a broad range of problems.

Long time asymptotics of the totally asymmetric simple exclusion process

We study the long time asymptotics of the relaxation dynamics of the totally asymmetric simple exclusion process on a ring. Evaluating the asymptotic amplitudes of the local currents by the algebraic Bethe ansatz method, we find that the relaxation times starting from the step and alternating initial conditions are governed by different eigenvalues of the Markov matrix. In both cases, the scaling exponents of the leading asymptotic amplitudes with respect to the total number of sites are found to be −1. We also study the asymptotics of correlation functions such as the emptiness formation probability.

Exact Current Statistics of the Asymmetric Simple Exclusion Process with Open Boundaries

Nonequilibrium systems are often characterized by the transport of some quantity at a macroscopic scale, such as, for instance, a current of particles through a wire. The asymmetric simple exclusion process (ASEP) is a paradigm for nonequilibrium transport that is amenable to exact analytical solution. In the present work, we determine the full statistics of the current in the finite size open ASEP for all values of the parameters. Our exact analytical results are checked against numerical calculations using density matrix renormalization group techniques.

Current-activity versus local-current fluctuations in a driven flow with exclusion

We consider fluctuations of steady-state current activity, and of its dynamic counterpart, the local current, for the one-dimensional totally asymmetric simple exclusion process. The cumulants of the integrated activity behave similarly to those of the local current, except that they do not capture the anomalous scaling behavior in the maximal-current phase and at its boundaries. This indicates that the systemwide sampling at equal times, characteristic of the instantaneous activity, overshadows the subtler effects which come about from nonequal time correlations, and are responsible for anomalous scaling. We show that apparently conflicting results concerning asymmetry (skewness) of the corresponding distributions can in fact be reconciled, and that (apart from a few well-understood exceptional cases) for both activity and local current one has positive skew deep within the low-current phase, and negative skew everywhere else.

Hydrodynamic Limit for Weakly Asymmetric Simple Exclusion Processes in Crystal Lattices

We investigate the hydrodynamic limit for weakly asymmetric simple exclusion processes in crystal lattices. We construct a suitable scaling limit by using a discrete harmonic map. As we shall observe, the quasi-linear parabolic equation in the limit is defined on a flat torus and depends on both the local structure of the crystal lattice and the discrete harmonic map. We formulate the local ergodic theorem on the crystal lattice by introducing the notion of local function bundle, which is a family of local functions on the configuration space. The ideas and methods are taken from the discrete geometric analysis to these problems. Results we obtain are extensions of ones by Kipnis, Olla and Varadhan to crystal lattices.

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 (α*, β*) 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.

The Current Distribution of the Multiparticle Hopping Asymmetric Diffusion Model

In this paper we treat the \textit{multiparticle hopping asymmetric diffusion model} (MADM) on $\mathbb{Z}$ introduced by Sasamoto and Wadati in 1998. The transition probability of the MADM with $N$ particles is provided by using the Bethe ansatz. The transition probability is expressed as the sum of $N$-dimensional contour integrals of which contours are circles centered at the origin with restrictions on their radii. By using the transition probability we find $\mathbb{P}(x_m(t) =x)$, the probability that the $m$th particle from the left is at $x$ at time $t$. The probability $\mathbb{P}(x_m(t) =x)$ is expressed as the sum of $|S|$-dimensional contour integrals over all $S \subset \{1,...,N\}$ with $|S| \geq m$, and is used to give the current distribution of the system. The mapping between the MADM and the pushing asymmetric simple exclusion process (PushASEP) is discussed.