Traffic jams and ordering far from thermal equilibrium

The recently suggested correspondence between domain dynamics of traffic models and the asymmetric chipping model is reviewed. It is observed that in many cases traffic domains perform the two characteristic dynamical processes of the chipping model, namely chipping and diffusion. This correspondence indicates that jamming in traffic models in which all dynamical rates are non-deterministic takes place as a broad crossover phenomenon, rather than a sharp transition. Two traffic models are studied in detail and analyzed within this picture.     

元胞自动机交通流模型的相变特性研究

系统地研究 VDR模型和T²模型在不同车流密度时车辆位置的相关性. 通过VDR模型、BJH模型和T²模型的序参量计算，确定在这三个模型中车流从自由流动到阻塞的相变特性，结果发现引入慢启动规则后，在不同的延迟概率和最大速度情况下，将引起交通相变特性的改变. 关键词： 交通流 元胞自动机 相关函数 序参量     

Multiscaling at Point J: jamming is a critical phenomenon

We analyze the jamming transition that occurs as a function of increasing packing density in a disordered two-dimensional assembly of disks at zero temperature for "Point J" of the recently proposed jamming phase diagram. We measure the total number of moving disks and the transverse length of the moving region, and find a power law divergence as the packing density increases toward a critical jamming density. This provides evidence that the T=0 jamming transition as a function of packing density is a second order phase transition. Additionally, we find evidence for multiscaling, indicating the importance of long tails in the velocity fluctuations.     

Jamming percolation and glass transitions in lattice models

A new class of lattice gas models with trivial interactions but constrained dynamics is introduced. These models are proven to exhibit a dynamical glass transition: above a critical density rhoc ergodicity is broken due to the appearance of an infinite spanning cluster of jammed particles. The fraction of jammed particles is discontinuous at the transition, while in the unjammed phase dynamical correlation lengths and time scales diverge as exp[C(rhoc-rho)-mu]. Dynamic correlations display two-step relaxation similar to glass formers and jamming systems.     

Mixtures of anisotropic and spherical colloids: Phase behavior, confinement, percolation phenomena and kinetics

Purely entropic systems such as suspensions of hard rods, platelets and spheres show rich phase behavior. Rods and platelets have successfully been used as models to predict the equilibrium properties of liquid crystals for several decades. Over the past years hard particle models have also been studied in the context of non-equilibrium statistical mechanics, in particular regarding the glass transition, jamming, sedimentation and crystallization. Recently suspensions of hard anisotropic particles also moved into the focus of materials scientists who work on conducting soft matter composites. An insulating polymer resin that is mixed with conductive filler particles becomes conductive when the filler percolates. In this context the mathematical topic of connectivity percolation finds an application in modern nano-technology. In this article, we briefly review recent work on the phase behavior, confinement effects, percolation transition and phase transition kinetics in hard particle models. In the first part, we discuss the effects that particle anisotropy and depletion have on the percolation transition. In the second part, we present results on the kinetics of the liquid-to-crystal transition in suspensions of spheres and of ellipsoids.     

Phase diagrams in unidirectionally coupled map lattice for open traffic flow

The jamming transition from the free traffic to the oscillatory traffic is investigated with the unidirectionally coupled map lattice model which has the hyperbolic tangent local map. Spatio-temporal structures in the jamming transition are found with the use of numerical simulation. The traffic states are studied for both constant and noisy boundary conditions. We show the phase diagrams of different kinds of congested traffic. It is found that the noise at the boundary has an important effect on the traffic states. The traffic behavior in the coupled map lattice model exhibits a jamming transition similar to that found in the car-following model.     

Mechanical, vibrational, and dynamical properties of amorphous systems near jamming

Amorphous systems undergo the jamming transition when the density increases, temperature drops, or external shear stress decreases, as described by the jamming phase diagram which was proposed to unify different processes such as the glass transition, random close packing, and yielding under shear stress. At zero temperature and shear stress, the jamming transition occurs at a critical density at Point J. In this paper, we review recent studies of the material properties of marginally jammed solids and the glassy dynamics in the vicinity of Point J. As the only singular point in the jamming phase diagram, Point J exhibits special criticality in both mechanical and vibrational quantities. Dynamics approaching the glass transition in the vicinity of Point J show critical scalings, suggesting that the molecular glass transition and the colloidal glass transition are equivalent in the hard sphere limit. All these studies shed light on the long-standing puzzles of the glass transition and unusual properties of amorphous solids.     

Analytic approach to the critical density in cellular automata for traffic flow

The jamming transition in the stochastic traffic cellular automaton of Nagel and Schreckenberg [J. Phys. I 2, 2221 (1992)] is examined. We argue that most features of the transition found in the deterministic limit do not persist in the presence of noise, and suggest instead to define the transition to take place at that critical density rho(c) at which a large initial jam just fails to dissolve. We show that rho(c)=v(J)/(v(J)+v(F)), where v(F) is the velocity of noninteracting vehicles and v(J) is the speed of the dissolution wave moving into the jam. An approximate analytic calculation of v(J) in the framework of a simple renormalization scheme is presented, which explicitly displays the effect of the interaction between vehicles during the acceleration stage of the Nagel-Schreckenberg rules with maximum velocity v(max)>1. The analytic prediction is compared to numerical simulations. We find a remarkable correspondence between the analytic expression for v(J) and a phase diagram obtained numerically by Lübeck et al.     

Multiple jamming transitions in traffic flow

The effect of accelerating stepwise on the jamming transition is investigated in the extended car-following model. The optimal velocity function is modified to take into account accelerating stepwise vehicles. It is shown that the multiple phase transitions occur on varying the car density. The multiple transitions change with the delay time. The flow-density curves and the velocity-headway curves are presented for various delay times. It is also shown that the multiple jamming transition lines are consistent with the neutral stability curves. The jamming transitions are closely related with the turning points of the optimal velocity function.     

Microscopic mean-field theory of the jamming transition

Dense particle packings acquire rigidity through a nonequilibrium jamming transition commonly observed in materials from emulsions to sandpiles. We describe athermal packings and their observed geometric phase transitions by using equilibrium statistical mechanics and develop a fully microscopic, mean-field theory of the jamming transition for soft repulsive spherical particles. We derive analytically some of the scaling laws and exponents characterizing the transition and obtain new predictions for microscopic correlation functions of jammed states that are amenable to experimental verifications and whose accuracy we confirm by using computer simulations.     

Self-Organization and Phase Transition in Two-Dimensional Traffic-Flow Model

An analytical investigation is made on two-dimensional traffic-flow model with alternative movement and exclude-volume effect between right and up arrows. Several exact results are obtained, including the upper critical density above which there are only jamming configurations, and the lower critical density below which there are only moving configurations. The observed jamming transition takes place at another critical density p_c(N), which is in the intermediate region between the lower and upper critical densities. This transition is suggested to be a second-order phase transition, the order parameter is found. The nature of self-organization, ergodicity breaking and synchronization are discussed. Comparison with the sandpile model is made.     

The green wave model of two-dimensional traffic: Transitions in the flow properties and in the geometry of the traffic jam

We carried out computer simulations to study the green wave model (GWM), the parallel updating version of the two-dimensional traffic model of Biham et al. The better convergence properties of the GWM together with a multi-spin coding technique enabled us to extrapolate to the infinite system size which indicates a nonzero density transition from the free flow to the congested state (jamming transition). In spite of the sudden change in the symmetry of the correlation function at the transition point, finite size scaling and temporal scaling seems to hold, at least above the threshold density. There is a second transition point at a density deep in the congested phase where the geometry of the cluster of jammed cars changes from linear to branched: Just at this transition point this cluster has fractal geometry with dimension 1.58. The jamming transition is also described within the mean field approach.     

开放边界条件下改进的Nagel-Schreckenberg交通流模型的研究

在开放边界条件下,采用改进的NagelSchreckenberg交通流模型,数值模拟了在不同参数下的交通流基本图,结果表明,改进的NagelSchreckenberg模型的交通流量较原来的模型有明显提高,并分析和讨论了从自由运动相转化为最大流量相或从阻塞相转化为自由运动相的特性及其临界点变化规律 关键词： 元胞自动机 交通流 开放边界条件 相变     

Topological invariants for phase transition points of one-dimensional Z<Subscript>2</Subscript> topological systems

We study topological properties of phase transition points of two topologicallynon-trivial Z₂ classes (D and DIII) in one dimension byassigning a Berry phase defined on closed circles around the gap closing points in theparameter space of momentum and a transition driving parameter. While the topologicalproperty of the Z₂ system is generally characterized by aZ₂topological invariant, we identify that it has a correspondence to the quantized Berryphase protected by the particle-hole symmetry, and then give a proper definition of Berryphase to the phase transition point. By applying our scheme to some specific models ofclass D and DIII, we demonstrate that the topological phase transition can be wellcharacterized by the Berry phase of the transition point, which reflects the change ofBerry phases of topologically different phases across the phase transition point.     

Isoenergetic jamming transition in particle-filled systems

A full understanding of the jamming transition remains elusive, but recent advances which draw upon the common features of frustrated systems are encouraging. Herein, we show that, for mixtures of oil and silica particles, the dependence of the dejamming stress on filler volume fraction, phi is consistent with the shape of a reported jamming phase diagram [Trappe, Nature (London) 411, 772 (2001)]. We discover for the first time, however, that the role of phi disappears when mechanical energy input, defined as stress multiplied by strain, is used instead of stress as the critical parameter. We also examine literature results for aqueous suspensions of boehmite alumina powders, latex dispersions of polystyrene particles, and carbon black-filled elastomers in order to illustrate the universality of our finding. This study provides evidence for a thermodynamic interpretation of the jamming transition.     

Effects of short-range attraction on Jamming transition

Enormous progresses to understand the jamming transition have been driven via simulating purely repulsive particles which were somehow idealized in the past two decades. While the attractive systems are both theoretical and practical compared with repulsive systems. By studying the statistics of rigid clusters, we find that the critical packing fraction φ_c varies linearly with attraction μ for different system sizes when the range of attraction is short. While for systems with long-range attractions, however, the slope of φ_c appears significantly different, which means that there are two distinct jamming scenarios. In this paper, we focus our main attention on short-range attractions scenario and define a new quantity named "short-range attraction susceptibility" χ_p, which describes the degree of response of the probability of finding jammed states pjto short-range attraction strength μ. Our central results are that χ_p diverges in the thermodynamic limit as χ_p ∝|φ-φ_c~∞|~(-γ_p), where φ_c~∞ is the packing fraction at the jamming transition for the infinite system in the absence of attraction. χ_p obeys scaling collapse with a scaling function in both two and three dimensions, illuminating that the jamming transition can be considered as a phase transition as proposed in previous work.     

Cooperative Behavior of Kinetically Constrained Lattice Gas Models of Glassy Dynamics

Kinetically constrained lattice models of glasses introduced by Kob and Andersen (KA) are analyzed. It is proved that only two behaviors are possible on hypercubic lattices: either ergodicity at all densities or trivial non-ergodicity, depending on the constraint parameter and the dimensionality. But in the ergodic cases, the dynamics is shown to be intrinsically cooperative at high densities giving rise to glassy dynamics as observed in simulations. The cooperativity is characterized by two length scales whose behavior controls finite-size effects: these are essential for interpreting simulations. In contrast to hypercubic lattices, on Bethe lattices KA models undergo a dynamical (jamming) phase transition at a critical density: this is characterized by diverging time and length scales and a discontinuous jump in the long-time limit of the density autocorrelation function. By analyzing generalized Bethe lattices (with loops) that interpolate between hypercubic lattices and standard Bethe lattices, the crossover between the dynamical transition that exists on these lattices and its absence in the hypercubic lattice limit is explored. Contact with earlier results are made via analysis of the related Fredrickson--Andersen models, followed by brief discussions of universality, of other approaches to glass transitions, and of some issues relevant for experiments.     

Lattice model for colloidal gels and glasses

We study a lattice model of attractive colloids. It is exactly solvable on sparse random graphs. As the pressure and temperature are varied, it reproduces many characteristic phenomena of liquids, glasses, and colloidal systems such as ideal gel formation, liquid-glass phase coexistence, jamming, or the re-entrance of the glass transition.     

Critical scaling in linear response of frictionless granular packings near jamming

We study the origin of the scaling behavior in frictionless granular media above the jamming transition by analyzing their linear response. The response to local forcing is non-self-averaging and fluctuates over a length scale that diverges at the jamming transition. The response to global forcing becomes increasingly nonaffine near the jamming transition. This is due to the proximity of floppy modes, the influence of which we characterize by the local linear response. We show that the local response also governs the anomalous scaling of elastic constants and contact number.     

Spiral model, jamming percolation and glass-jamming transitions

The Spiral Model (SM) corresponds to a new class of kinetically constrained models introduced in joint works with Fisher [9,10] which provide the first example of finite dimensional models with an ideal glass-jamming transition. This is due to an underlying jamming percolation transition which has unconventional features: it is discontinuous (i.e. the percolating cluster is compact at the transition) and the typical size of the clusters diverges faster than any power law, leading to a Vogel-Fulcher-like divergence of the relaxation time. Here we present a detailed physical analysis of SM, see [6] for rigorous proofs.