Asymmetric coupling in two-lane simple exclusion processes: Effect of unequal injection rates

This Letter investigates the effect of unequal injection rates on two-lane simple exclusion processes with asymmetric coupling. It is a generalization of the work of Pronina and Kolomeisky [E. Pronina, A.B. Kolomeisky, Physica A 372 (2006) 12], in which the injection rates of two lanes are equal. With the injection rate α₁ increases, the (1,LD), (1,HD), (1,MC) and (MC,MC) phase region do not change, while the (LD,0) phase regions shrink and the (HD,0) and (MC,0) phase regions expand. Interestingly, domain walls are observed in both lanes when the system is in the (MC,MC) phase. However, the unequal injection rates have little effect on the domain wall dynamics. The phase diagram and the density profiles are investigated by using Monte Carlo simulations and mean-field approximation. The analytical results are in good agreement with simulations.     

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.     

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.     

Asymmetric Effects on Escape Rates of Bistable System

The asymmetric effects on the escape rates from the stable states x_± in the bistable system are analyzed. The results indicate that the multiplicative noise and the additive noise always enhance the particle escape from stable states x_± of bistable. However, the asymmetric parameter r enhances the
particle escape from stable state x₊, and holds back the particle escape from stable state x_-.     

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.     

Modelling Asymmetric Unemployment Dynamics: The Logarithmic-Harmonic Potential Approach

Asymmetric behaviour has been documented in unemployment rates which increase quickly in recessions but decline relatively slowly during expansions. To model such asymmetric dynamics, this paper provides a rigorous derivation of the asymmetric mean-reverting fundamental dynamics governing the unemployment rate based on a model of a simple labour supply and demand (fundamental) relationship, and shows that the fundamental dynamics is a unique choice following the Rayleigh process. By analogy, such a fundamental can be considered as a one-dimensional overdamped Brownian particle moving in a logarithmic–harmonic potential well, and a simple prototype of stochastic heat engines. The solution of the model equation illustrates that the unemployment rate rises faster with more flattened potential well of the fundamental, more ample labour supply, and less anchored expectation of the unemployment rate, suggesting asymmetric unemployment rate dynamics in recessions and expansions. We perform explicit calibration of both the unemployment rate and fundamental dynamics, confirming the validity of our model for the fundamental dynamics.     

Phase Separation in a Bidirectional Two-Lane Asymmetric Exclusion Process

This paper studies a bidirectional two-lane asymmetric exclusion process, in which particles move in opposite direction on the two lanes. Interaction between the two lanes is implemented as follows: particle hops with rate p when there is a particle at the same site in the other lane, otherwise it hops with rate 1. It is shown that under periodic boundary conditions, a plateau will form on the fundamental diagram if p<1. This plateau corresponds to a phase separation phenomenon. We have compared the phase separation with those reported in previous works, and it is shown that the mechanism of phase separation in our model is different from previous ones. A possible phase separation mechanism is proposed, i.e., the system always tries to maximize the probability that particles could hop with rate 1. A simple mean field approximation and a 2-cluster mean field approach have been applied to calculate the steady current. It is shown that the results of the 2-cluster mean field approach are much closer to the simulations.     

Dynamics of a Tagged Particle in the Asymmetric Exclusion Process with the Step Initial Condition

The one-dimensional totally asymmetric simple exclusion process (TASEP) is considered. We study the time evolution property of a tagged particle in the TASEP with the step initial condition. Calculated is the multi-time joint distribution function of its position. Using the relation of the dynamics of the TASEP to the Schur process, we show that the function is represented as the Fredholm determinant. We also study the scaling limit. The universality of the largest eigenvalue in the random matrix theory is realized in the limit. When the hopping rates of all particles are the same, it is found that the joint distribution function converges to that of the Airy process after the time at which the particle begins to move. On the other hand, when there are several particles with small hopping rate in front of a tagged particle, the limiting process changes at a certain time from the Airy process to the process of the largest eigenvalue in the Hermitian multi-matrix model with external sources.     

强光场中原子的电离速率

以静态场隧道电离为基础,在准静态近似的条件下,对描述强光场中原子及其各阶离子电离的电离速率进行了较为系统的总结,纠正了早期对隧道电离的电离速率公式进行讨论并且后来的计算中被广泛引用的文献「１０」中公式的错误,地部分稀有气体原子及其各了子在线偏振、圆偏振强光场中的了速度及相应的阈值光强进行了比较。     

Exact Determination of the Phase Structure of a Multi-Species Asymmetric Exclusion Process

We consider a multi-species generalization of the Asymmetric Simple Exclusion Process on an open chain, in which particles hop with their characteristic hopping rates and fast particles can overtake slow ones. The number of species is arbitrary and the hopping rates can be selected from a discrete or continuous distribution. We determine exactly the phase structure of this model and show how the phase diagram of the 1-species ASEP is modified. Depending on the distribution of hopping rates, the system can exist in a three-phase regime or a two-phase regime. In the three-phase regime the phase structure is almost the same as in the one species case, that is, there are the low density, the high density and the maximal current phases, while in the two-phase regime there is no high-density phase.     

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.     

Asymmetric twin-field quantum key distribution with both statistical and intensity fluctuations

Twin-field quantum key distribution(TF-QKD) is a disruptive innovation which is able to overcome the rate-distance limit of QKD without trusted relays. Since the proposal of the first TF-QKD protocol, theoretical and experimental breakthroughs have been made to enhance its ability. However, there still exist some practical issues waiting for settlement. In this paper, we examine the performances of asymmetric TF-QKD protocol with unstable light sources and limited data sizes. The statistical fluctuations of the parameters are estimated employing Azuma's inequality. Through numerical simulations, we compare the secret key rates of the asymmetric TF-QKD protocol with different data sizes and variant intensity fluctuation magnitudes. Our results demonstrate that both statistical and intensity fluctuations have significant impacts on the performance of asymmetric TF-QKD.     

Electrofluorescence polarity in a molecular diode

The kinetic equations describing the transmission of an electron in the molecular compound “electrode 1–molecule–electrode 2” (1M2 system) are derived using the method of a nonequilibrium density matrix. The steady-state transmission regime is considered, for which detailed analysis of the kinetics of electrofluorescence formation in systems with symmetric and asymmetric couplings between the molecule and the electrodes is carried out. It is shown that the optically active state of the molecule is formed as a result of electron hops between the molecule and each of the electrodes, as well as due to inelastic interelectrode tunneling of the electron. The electrofluorescence power for a molecular diode (asymmetric 1M2 system) depends on the polarity of the voltage bias applied to the electrodes. The polarity is explained using a model in which the optically active part of the molecule (chromophore group) is represented by the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO). Two mechanisms of the emergence of polarity are revealed. One mechanism is associated with nonidentical Stark shifts of the HOMO and LUMO levels relative to the Fermi levels of the electrodes. The second mechanism is associated with the fact that the rates of an electron hopping between HOMO (LUMO) and one of the electrodes are much higher than the rates of such a hopping with the other electrode. The conditions in which each mechanism can be implemented experimentally are indicated.     

A Cellular Automaton Model for Two-Lane Traffic

We present some long time limit properties of a cellular automaton that models traffic of cars on a (infinite) two-lane road. This model, called TL184, is a natural generalization of the cellular automaton classified as 184 by Wolfram (to be abbreviated by CA184) and studied before as a model for one-lane traffic. TL184 models cars' motions on each lane by particles that interact via the CA184 rules, and cars' lane changes by a possibility for particles to flip from one CA184 to another. We calculate the infinite-time limit of the particle current in TL184, starting from a translation invariant measure, and use this result to show how the possibility of lane changes may enhance the current of cars in TL184 compared to that in a corresponding model of two non-interacting one-lane roads. We provide examples which demonstrate that even though the rules that regulate lane changes are completely symmetric, the system does not evolve to an equipartition of cars among both lanes from a given initially asymmetric distribution; moreover, the asymptotic car velocities and currents may be different on different lanes. We also show that, for a particular class of initial distributions, the asymptotic car density on a lane may be a non-monotonic function of the initial car density on this lane. Finally, we derive the current-density relation for an extended continuous-time version of TL184 with asymmetric lane-changing rules.     

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.     

Integral Formulas for the Asymmetric Simple Exclusion Process

In this paper we obtain general integral formulas for probabilities in the asymmetric simple exclusion process (ASEP) on the integer lattice with nearest neighbor hopping rates p to the right and q = 1−p to the left. For the most part we consider an N-particle system but for certain of these formulas we can take the limit. First we obtain, for the N-particle system, a formula for the probability of a configuration at time t, given the initial configuration. For this we use Bethe Ansatz ideas to solve the master equation, extending a result of Schütz for the case N = 2. The main results of the paper, derived from this, are integral formulas for the probability, for given initial configuration, that the m ^th left-most particle is at x at time t. In one of these formulas we can take the limit, and it gives the probability for an infinite system where the initial configuration is bounded on one side. For the special case of the totally asymmetric simple exclusion process (TASEP) our formulas reduce to the known ones.     

Asymmetric heat conduction in nonlinear lattices

In this Letter, we conduct an extensive study of the two-segment Frenkel-Kontorova model. We show that the rectification effect of the heat flux reported in recent literature is possible only in the weak interfacial coupling limit. The rectification effect will be reversed when the properties of the interface and the system size change. These two types of asymmetric heat conduction are governed by different mechanisms though both are induced by nonlinearity. An intuitive physical picture is proposed to interpret the reversal of the rectification effect. Since asymmetric heat conduction depends critically on the properties of the interface and the system size, it is probably not an easy task to fabricate a thermal rectifier or thermal diode in practice.     

Asymmetric confinement in a doubly modulated bistable device

A Brownian particle hopping in a symmetric double-well potential may be statistically confined into a single well by the simultaneous action of two periodic input signals, one tilting the minima, the other one modulating the barrier height. Such a basic mechanism for asymmetric confinement can be conveniently maximized by tuning the input signal parameters (frequencies, phase lag, amplitudes), thus leading to a resonant localization of the particle in a target potential well.     

Asymmetric exclusion model with two species: Spontaneous symmetry breaking

A simple two-species asymmetric exclusion model is introduced. It consists of two types of oppositely charged particles driven by an electric field and hopping on an open chain. The phase diagram of the model is calculated in the meanfield approximation and by Monte Carlo simulations. Exact solutions are given for special values of the parameters defining its dynamics. The model is found to exhibit two phases in which spontaneous symmetry breaking takes place, where the two currents of the two species are not equal.     

Towards a Model for Protein Production Rates

In the process of translation, ribosomes read the genetic code on an mRNA and assemble the corresponding polypeptide chain. The ribosomes perform discrete directed motion which is well modeled by a totally asymmetric simple exclusion process (TASEP) with open boundaries. Using Monte Carlo simulations and a simple mean-field theory, we discuss the effect of one or two “bottlenecks” (i.e., slow codons) on the production rate of the final protein. Confirming and extending previous work by Chou and Lakatos, we find that the location and spacing of the slow codons can affect the production rate quite dramatically. In particular, we observe a novel “edge” effect, i.e., an interaction of a single slow codon with the system boundary. We focus in detail on ribosome density profiles and provide a simple explanation for the length scale which controls the range of these interactions. PACS numbers: 05.70.Ln, 64.90.+b, 87.14.Gg