Exclusive Queueing Process with Discrete Time

In a recent study (Arita in Phys. Rev. E 80(5):051119, 2009), an extension of the M/M/1 queueing process with the excluded-volume effect as in the totally asymmetric simple exclusion process (TASEP) was introduced. In this paper, we consider its discrete-time version. The update scheme we take is the parallel one. A stationary-state solution is obtained in a slightly arranged matrix product form of the discrete-time open TASEP with the parallel update. We find the phase diagram for the existence of the stationary state. The critical line which separates the parameter space into regions with and without the stationary state can be written in terms of the stationary current of the open TASEP. We calculate the average length of the system and the average number of particles.     

Fluctuations in the Weakly Asymmetric Exclusion Process with Open Boundary Conditions

We investigate the fluctuations around the average density profile in the weakly asymmetric exclusion process with open boundaries in the steady state. We show that these fluctuations are given, in the macroscopic limit, by a centered Gaussian field and we compute explicitly its covariance function. We use two approaches. The first method is dynamical and based on fluctuations around the hydrodynamic limit. We prove that the density fluctuations evolve macroscopically according to an autonomous stochastic equation, and we search for the stationary distribution of this evolution. The second approach, which is based on a representation of the steady state as a sum over paths, allows one to write the density fluctuations in the steady state as a sum over two independent processes, one of which is the derivative of a Brownian motion, the other one being related to a random path in a potential.     

Spontaneous symmetry breaking in asymmetric exclusion process with constrained boundaries and site sharing: A Monte Carlo study

This paper investigates the two species totally asymmetric simple exclusion process (TASEP) with constrained boundaries and site sharing in a one-lane system. The model is reminiscent of pedestrian traffic crossing a narrow pathway in both directions. In boundaries, particles can enter the system only if the corresponding sites are empty. The new aspect of this study compared to previous two species TASEP models is that the oppositely moving particles do not exchange their positions each other but by sharing the same site. Monte Carlo simulations have shown that the spontaneous symmetry breaking is observed in high-low-density phase and asymmetric low-low-density phase. The flipping processes are also observed in both phases. The maximal current phase appears for sufficiently large sharing probability. Histograms of two species of particles and average currents are computed. The results are also compared with the Bridge model [Evans et al., Phys. Rev. Lett. 74 (1995) 208] which means that two species of particles can exchange their positions with a certain probability when they meet together. It is shown that our model exhibits higher current than that in the Bridge model.     

Instability transitions and ensemble equivalence in diffusive flow

We investigate the critical behavior of one-dimensional (1D) stochastic flow with competing nonlocal and local hopping events, in context of the totally asymmetric simple exclusion process (TASEP) with a defect site in a 1D closed chain. The defect site can effectively generate various boundary conditions, controlling the total number of particles in the system. Both open and periodic-like setups exhibit dynamic instability transitions from a populated finite density phase to an empty road (ER) phase as the nonlocal hopping rate increases. In the stationary populated phase, strong clustering promoted by nonlocal skids drives such transitions and determines their scaling properties. By static and dynamic simulations, we locate such transition points, and discuss their nature and scaling properties. In the open TASEP variant, we numerically establish that the instability transition into the ER phase is second order in the regime where the entry point reservoir controls the current, while it is first order in the regime where the bulk controls the current. Since it is well known that such transitions are absent in the periodic TASEP variant, we compare our results in the open setup with those in the periodic-like setup, and discuss the issue of the ensemble equivalence. Finally, the same discussion is extended to the symmetric cases.      

Correlated noises in an absorptive optical bistable model

We study the steady state properties of an absorptive optical bistable model in the presence of correlated noises. Based on the corresponding Fokker-Planck equation the steady state solution of the probability distribution and the average value of the transmitted light have been investigated. We have found that fluctuations of the input light amplitude improve the transmitted light and an optimized value exists for the fluctuations of the population difference at which the transmitted light takes its maximum value. The correlation between the two noises reduce the transmitted light and the noises in the model can induce a phase transition.     

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     

Dynein-Inspired Multilane Exclusion Process with Open Boundary Conditions

Motivated by the sidewise motions of dynein motors shown in experiments, we use a variant of the exclusion process to model the multistep dynamics of dyneins on a cylinder with open ends. Due to the varied step sizes of the particles in a quasi-two-dimensional topology, we observe the emergence of a novel phase diagram depending on the various load conditions. Under high-load conditions, our numerical findings yield results similar to the TASEP model with the presence of all three standard TASEP phases, namely the low-density (LD), high-density (HD), and maximal-current (MC) phases. However, for medium- to low-load conditions, for all chosen influx and outflux rates, we only observe the LD and HD phases, and the maximal-current phase disappears. Further, we also measure the dynamics for a single dynein particle which is logarithmically slower than a TASEP particle with a shorter waiting time. Our results also confirm experimental observations of the dwell time distribution: The dwell time distribution for dyneins is exponential in less crowded conditions, whereas a double exponential emerges under overcrowded conditions.     

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. 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.     

Defect-induced transitions in synchronous asymmetric exclusion processes

The effects of a single local defect in synchronous asymmetric exclusion processes are investigated via theoretical analysis and Monte Carlo simulations. Our theoretical analysis shows that there are four possible stationary phases, i.e., the (low density, low density), (low density, high density), (high density, low density) and (high density, high density) in the system. In the (high density, low density) phase, the system can reach a maximal current which is determined by the local defect, but independent of boundary conditions. A phenomenological domain wall approach is developed to predict dynamic behavior at phase boundaries. The effects of defective hopping probability p on density profiles and currents are investigated. Our investigation shows that the value of p determines phase transitions when entrance rate α and exit rate β are fixed. Density profiles and currents obtained from theoretical calculations are in agreement with Monte Carlo simulations.     

Structure of Liquid‐Sheet Sprays

Spray characteristics and their spatial distribution have been investigated experimentally for sprays generated by the breakup of thin liquid sheets in co‐flowing air streams. The spray characteristics such as droplet mean and fluctuation velocity and Sauter mean diameter have been measured by using phase Doppler anemometry under various liquid and air flow conditions at the nozzle exit. The results show that at a given spray cross section the droplet axial mean velocity has a maximum value at the spray center, and decreases towards the edge of the spray; whereas the Sauter mean diameter has a minimum value at the center and increases monotonically towards the spray periphery. Data analysis indicates that sufficiently downstream of the nozzle exit the droplet mean velocity attains a jet‐like self‐similar distribution in the transverse direction, and such universal distribution is also observed for the turbulent fluctuation velocity and turbulent intensity, although it is achieved further downstream compared to the mean velocity profile. The Sauter mean diameter at the spray center has a complex variation in the downstream direction due to secondary atomization at high air velocity near the nozzle exit and droplet entrainment, migration and possible coalescence farther downstream.     

Self-consistent interpretation of the 2D structure of the liquid Au82Si18 surface: bending rigidity and the Debye-Waller effect

The structural and mechanical properties of 2D crystalline surface phases that form at the surface of liquid eutectic Au82Si18 are studied using synchrotron x-ray scattering over a large temperature range. In the vicinity of the eutectic temperature the surface consists of a 2D atomic bilayer crystalline phase that transforms into a 2D monolayer crystalline phase during heating. The latter phase eventually melts into a liquidlike surface on further heating. We demonstrate that the short wavelength capillary wave fluctuations are suppressed due to the bending rigidity of 2D crystalline phases. The corresponding reduction in the Debye-Waller factor allows for measured reflectivity to be explained in terms of an electron density profile that is consistent with the 2D surface crystals.     

Quantum fluctuation driven first-order phase transition in weak ferromagnetic metals

In a local Fermi liquid (LFL), we show that there is a line of weak first-order phase transitions between the ferromagnetic and paramagnetic phases due to purely quantum fluctuations. We predict that an instability towards superconductivity is only possible in the ferromagnetic state. At T?=?0 we find a point on the phase diagram where all three phases meet and we call this a quantum triple point (QTP). A simple application of the Gibbs phase rule shows that only these three phases can meet at the QTP. This provides a natural explanation of the absence of superconductivity at this point coming from the paramagnetic side of the phase diagram, as observed in the recently discovered ferromagnetic superconductor, UGe ₂.     

Exact relaxation in a class of nonequilibrium quantum lattice systems

A reasonable physical intuition in the study of interacting quantum systems says that, independent of the initial state, the system will tend to equilibrate. In this work we introduce an experimentally accessible setting where relaxation to a steady state is exact, namely, for the Bose-Hubbard model quenched from a Mott quantum phase to the free strong superfluid regime. We rigorously prove that the evolving state locally relaxes to a steady state with maximum entropy constrained by second moments--thus maximizing the entanglement. Remarkably, for this to be true, no time average is necessary. Our argument includes a central limit theorem and exploits the finite speed of information transfer. We also show that for all periodic initial configurations (charge density waves) the system relaxes locally, and identify experimentally accessible signatures in optical lattices as well as implications for the foundations of statistical mechanics.     

Charge Stripes Due to Electron Correlations in the Two-Dimensional Spinless Falicov—Kimball Model

We calculate the restricted phase diagram for the Falicov–Kimball model on a two-dimensional square lattice. We consider the limit where the average conduction electron density is equal to the average localized electron density, which is the limit related to the S _z =0 states of the Hubbard model. After considering over 20,000 different candidate phases (with a unit cell of 16 sites or less) and their thermodynamic mixtures, we find only about 100 stable phases in the ground-state phase diagram, where the ground state is usually the phase separated mixture of two or three stable phases, that often have different electron densities than in the Maxwell-constructed mixture. We analyze these phases to describe where stripe phases occur and relate these discoveries (were appropriate) to the physics behind stripe formation in the Hubbard model.     

决定论性逐步加速交通流模型的渐近稳态行为

研究Nagel-Schreckenberg(NS)交通流元胞自动机模型在不考虑车辆随机延迟情况下的决定论性模型的基本图,即渐近稳态的车流平均速度作为车辆密度的函数关系．证明决定论性NS模型,在车流的自组织作用下,其渐近稳态的基本图,与决定论性Fukui-Ishibashi(FI)交通流模型的基本图完全相同．这个结果表明,若把FI交通流模型中的车辆突然加速方式（即车辆速度可以在仅仅一个时步内加速到其最高速限M或前方空距所允许的最大速度）,改变为车辆逐步加速方式（车辆速度在每一时步中最多仅能增加一个速度单位）,则车辆的自组织相互作用,并不会改变其车流的长时间渐近稳态行为． 关键词：     

Regular and Chaotic Spatiotemporal Patterns in a Model of Slime Mold Aggregation

In this paper we proposed a spatial modulated two-variable Martiel-Goldbeter model to describe the complex spatiotemporal disorder dynamical behavior during development of Dictyostelium discoideum strain FR17. As the nonlinear modulated parameter A and diffusion coefficient E varied, the system shows: 1) multiperiodic phase, 2) co-existence phase of chaotic and multi-periodic state, 3) spatiotemporal chaotic phase, 4) co-existence phase of chaotic, multi-periodic and steady state, and 5) co-existence phase of chaotic and steady state. These phases can be described by spatiotemporal power spectra, pattern distribution function and Lyapunov spectra. We believed that the complex spatiotemporal disorder dynamical behavior during development of Dictyosteliurn discoideum strain FR17 is a spatiotemporal chaotic state.     

Phase Diagram of a Two-Species Lattice Model with a Linear Instability

We discuss the properties of a one-dimensional lattice model of a driven system with two species of particles in which the mobility of one species depends on the density of the other. This model was introduced by Lahiri and Ramaswamy ( Phys . Rev. Lett ., 79 , 1150 (1997)) in the context of sedimenting colloidal crystals, and its continuum version was shown to exhibit an instability arising from linear gradient couplings. In this paper we review recent progress in understanding the full phase diagram of the model. There are three phases. In the first, the steady state can be determined exactly along a representative locus using the condition of detailed balance. The system shows phase separation of an exceptionally robust sort, termed strong phase separation, which survives at all temperatures. The second phase arises in the threshold case where the first species evolves independently of the second, but the fluctuations of the first influence the evolution of the second, as in the passive scalar problem. The second species then shows phase separation of a delicate sort, in which long-range order coexists with fluctuations which do not damp down in the large-size limit. This fluctuation-dominated phase ordering is associated with power law decays in cluster size distributions and a breakdown of the Porod law. The third phase is one with a uniform overall density, and along a representative locus the steady state is shown to have product measure form. Density fluctuations are transported by two kinematic waves, each involving both species and coupled at the nonlinear level. Their dissipation properties are governed by the symmetries of these couplings, which depend on the overall densities. In the most interesting case, the dissipation of the two modes is characterized by different critical exponents, despite the nonlinear coupling.     

开放四能级系统中相对位相对探测响应的影响

利用具有自发辐射诱导相干开放四能级系统的定态数值解,从不同角度分析了探测场和驱动场之间的相对位相Φ对探测场增益(吸收)以及粒子数差的影响.研究结果表明：通过对相对位相的控制,可以实现探测场无反转增益和色散的周期性放大和减弱,并能得到无吸收高色散;Φ=α的色散曲线与Φ=α+π/2的增益曲线相似;在探测场共振条件下,适当调节相对位相,可以使无反转激光（LWI）增益达到最大.还研究了粒子注入和退出速率的变化对位相相关的LWI增益的调制作用.     

垂直转子轴式黏性泵内部流动LBM模拟

为了对垂直转子轴式黏性泵内部流动规律进行研究,采用格子Boltzmann法(LBM)对该泵模型全流场进行了数值模拟。采用具有二阶精度的弯曲固壁边界条件和基于插值公式的移动固壁边界条件,对具有圆形、矩形及方形等3种不同截面形状转轴的模型泵内部定常与非定常流动进行了计算,得到了模型泵体出口剖面处x方向速度分量平均值。结果表明,具有圆形截面形状转轴的泵送效果较另两种截面形状的转轴为佳,计算所得的出口剖面处x方向速度分量平均值与文献中实验结果吻合良好。