Jam Clusters Research Articles

Sticky Matters: Jamming and Rigid Cluster Statistics with Attractive Particle Interactions.

While the large majority of theoretical and numerical studies of the jamming transition consider athermal packings of purely repulsive spheres, real complex fluids and soft solids generically display attraction between particles. By studying the statistics of rigid clusters in simulations of soft particles with an attractive shell, we present evidence for two distinct jamming scenarios. Strongly attractive systems undergo a continuous transition in which rigid clusters grow and ultimately diverge in size at a critical packing fraction. Purely repulsive and weakly attractive systems jam via a first-order transition, with no growing cluster size. We further show that the weakly attractive scenario is a finite size effect, so that for any nonzero attraction strength, a sufficiently large system will fall in the strongly attractive universality class. We therefore expect attractive jamming to be generic in the laboratory and in nature.

Characterizing and distinguishing free and jammed traffic flows from the distribution and correlation of experimental speed data

From a physics point of view, the emergence of a traffic jam is considered to be a dynamical phase transition. To verify this, we performed a series of circuit experiments. In previous work, Tadaki et al (2013 New J. Phys 15 103034), we confirmed the occurrence of this phase transition and estimated the critical density between free and jammed flows by analyzing the fundamental diagram. In this paper, we characterize and distinguish free and jammed flows, beyond the analyses of fundamental diagrams, according to the distribution and correlation of experimental speed data. We find that the speed in free flow does not correlate and its distribution has a narrow single peak at the average. The distribution of speed in jammed flow has two peaks or a single broad peak. The two peaks indicate the car speeds inside and outside of jam clusters. The broad single peak appears as a result of the appearance and disappearance of jam clusters. We also find that the formation of jam clusters induces a long correlation in speed. We can identify the size of jam clusters and the relative distance between coexisting jam clusters from this speed correlation.

Phase transition in 2D partially asymmetric simple exclusion process with two species

The dynamics of two species of particles undergoing asymmetric simple exclusion process (ASEP) on the 2D lattice are investigated in this paper. A sharp transition from moving phase to jamming phase was shown under periodic boundary conditions. We have developed a mean field analysis for the moving phase by extending the method of [] and this produces good agreement with simulation results. Two types of jamming phase were observed. In the first type of jamming phase, some particles at the border of the jamming cluster could move back and forth due to the ASEP rule. The first type of jamming phase reduces to the 1D ASEP with a barrier at the boundary of the lattice. We also have analyzed the average hops for the first type of jamming phase by analyzing the 1D ASEP model. The analytical results agree with the simulation results well. Under open boundary conditions, the system exhibits two phases when forward hopping probability q is larger than 0.5. The particles form a wall at the entrance when q is smaller than 0.5. The dependence of the average velocity, the density and the flow rate on the injection probability in the moving phase have also been obtained through mean field analysis.

Effect of overpasses in the Biham-Middleton-Levine traffic flow model with random and parallel update rule

The effect of overpasses in the Biham-Middleton-Levine traffic flow model with random and parallel update rules has been studied. An overpass is a site that can be occupied simultaneously by an eastbound car and a northbound one. Under periodic boundary conditions, both self-organized and random patterns are observed in the free-flowing phase of the parallel update model, while only the random pattern is observed in the random update model. We have developed mean-field analysis for the moving phase of the random update model, which agrees with the simulation results well. An intermediate phase is observed in which some cars could pass through the jamming cluster due to the existence of free paths in the random update model. Two intermediate states are observed in the parallel update model, which have been ignored in previous studies. The intermediate phases in which the jamming skeleton is only oriented along the diagonal line in both models have been analyzed, with the analyses agreeing well with the simulation results. With the increase of overpass ratio, the jamming phase and the intermediate phases disappear in succession for both models. Under open boundary conditions, the system exhibits only two phases when the ratio of overpasses is below a threshold in the random update model. When the ratio of the overpass is close to 1, three phases could be observed, similar to the totally asymmetric simple exclusion process model. The dependence of the average velocity, the density, and the flow rate on the injection probability in the moving phase has also been obtained through mean-field analysis. The results of the parallel model under open boundary conditions are similar to that of the random update model.

Shortcomings of the bond orientational order parameters for the analysis of disordered particulate matter

Local structure characterization with the bond-orientational order parameters q(4), q(6), ... introduced by Steinhardt et al. [Phys. Rev. B 28, 784 (1983)] has become a standard tool in condensed matter physics, with applications including glass, jamming, melting or crystallization transitions, and cluster formation. Here, we discuss two fundamental flaws in the definition of these parameters that significantly affect their interpretation for studies of disordered systems, and offer a remedy. First, the definition of the bond-orientational order parameters considers the geometrical arrangement of a set of nearest neighboring (NN) spheres, NN(p), around a given central particle p; we show that the choice of neighborhood definition can have a bigger influence on both the numerical values and qualitative trend of q(l) than a change of the physical parameters, such as packing fraction. Second, the discrete nature of neighborhood implies that NN(p) is not a continuous function of the particle coordinates; this discontinuity, inherited by q(l), leads to a lack of robustness of the q(l) as structure metrics. Both issues can be avoided by a morphometric approach leading to the robust Minkowski structure metrics q(l)'. These q(l)' are of a similar mathematical form as the conventional bond-orientational order parameters and are mathematically equivalent to the recently introduced Minkowski tensors [G. E. Schröder-Turk et al., Europhys. Lett. 90, 34001 (2010); S. Kapfer et al., Phys. Rev. E 85, 030301(R) (2012)].

JAMMING TRANSITION OF POINT-TO-POINT TRAFFIC THROUGH CO-OPERATIVE MECHANISMS

We study the jamming transition of two-dimensional point-to-point traffic through co-operative mechanisms (DCM) using computer simulation. We propose two decentralized co-operative mechanisms CM which are incorporated into the point-to-point traffic models: stepping aside (CM-SA) and choosing alternative routes (CM-CAR). Incorporating CM-SA is to prevent a type of ping-pong jumps from happening when two objects standing face-to-face want to move in opposite directions. Incorporating CM-CAR is to handle the conflict when more than one object competes for the same point in parallel update. We investigate and compare four models mainly from fundamental diagrams, jam patterns and the distribution of co-operation probability. It is found that although it decreases the average velocity a little, the CM-SA increases the critical density and the average flow. Despite increasing the average velocity, the CM-CAR decreases the average flow by creating substantially vacant areas inside jam clusters. We investigate the jam patterns of four models carefully and explain this result qualitatively. In addition, we discuss the advantage and applicability of decentralized co-operation modeling.

Effect of following strength on pedestrian counter flow

This paper proposes a modified lattice gas model to simulate pedestrian counter flow by considering the effect of following strength which can lead to appropriate responses to some complicated situations. Periodic and open boundary conditions are adopted respectively. The simulation results show that the presented model can reproduce some essential features of pedestrian counter flows, e.g., the lane formation and segregation effect. The fundamental diagrams show that the complete jamming density is independent of the system size only when the width W and the length L are larger than some critical values respectively, and the larger asymmetrical conditions can better avoid the occurrence of deadlock phenomena. For the mixed pedestrian flow, it can be found that the jamming cluster is mainly caused by those walkers breaking the traffic rules, and the underlying mechanism is analysed. Furthermore, the comparison of simulation results and the experimental data is performed, it is shown that this modified model is reasonable and more realistic to simulate and analyse pedestrian counter flow.

SUBCONSCIOUS EFFECT ON PEDESTRIAN COUNTER FLOW IN A MODIFIED LATTICE GAS MODEL WITH THE VARIABLE TRANSITION PROBABILITY

Pedestrian behavioral modeling is an important topic to reproduce rich pedestrian dynamics phenomena. In this paper, a modified lattice gas model is proposed to simulate pedestrian counter flow under periodic boundary conditions by considering the variable transition probability, which can quantitatively describe complex human subconscious behaviors and distinguish the individual and common characteristics of pedestrians. Four types of walkers are involved in the model, and their dynamical characteristics are discussed in some complex situations. The simulation results show that the presented model can reproduce some essential features of pedestrian counter flows, such as the lane formation, segregation effect and phase separation. For the mixed pedestrian flows, the comparison between the subconscious behaviors of obeying the traffic rules and those of breaking the traffic rules indicates that the former could effectively reduce the occurrence of jam cluster. In addition, it is found that with increase of the strength of drift D1, the jam transition threshold decreases. Finally, the simulation results are compared with our previous study (see Ref. 32). It is shown that the mean velocity and the mean flow are always larger at the free moving phase, and the underlying mechanism is discussed in detail.

Metastability in the formation of an experimental traffic jam

We show detailed data about the process of jam formation in a traffic experiment on a circuit without any bottlenecks. The experiment was carried out using a circular road on a flat ground. At the initial stage, vehicles are running homogeneously distributed on the circuit with the same velocity, but roughly 10 min later a traffic jam emerges spontaneously on the circuit. In the process of the jam formation, we found a homogeneous flow with large velocity is temporarily realized before a jam cluster appears. The instability of such a homogeneous flow is the key to understanding jam formation.

Analysis of pedestrian dynamics in counter flow via an extended lattice gas model

The modeling of human behavior is an important approach to reproduce realistic phenomena for pedestrian flow. In this paper, an extended lattice gas model is proposed to simulate pedestrian counter flow under the open boundary conditions by considering the human subconscious behavior and different maximum velocities. The simulation results show that the presented model can capture some essential features of pedestrian counter flows, such as lane formation, segregation effect, and phase separation at higher densities. In particular, an interesting feature that the faster walkers overtake the slower ones and then form a narrow-sparse walkway near the central partition line is discovered. The phase diagram comparison and analysis show that the subconscious behavior plays a key role in reducing the occurrence of jam cluster. The effects of the symmetrical and asymmetrical injection rate, different partition lines, and different combinations of maximum velocities on pedestrian flow are investigated. An important conclusion is that it is needless to separate faster and slower pedestrians in the same direction by a partition line. Furthermore, the increase of the number of faster walkers does not always benefit the counter flow in all situations. It depends on the magnitude and asymmetry of injection rate. And at larger maximum velocity, the obtained critical transition point corresponding to the maximum flow rate of the fundamental diagram is in good agreement with the empirical results.

Subconscious Effect on Pedestrian Counter Flow

We propose an extended lattice gas model with different maximum velocities to simulate pedestrian counter flow by considering the subconscious behaviour of walkers. Four types of walkers including faster right walkers, slower right walkers, faster left walkers and slower left walkers are involved in the simulation. The simulation results show that our model can capture some essential features of pedestrian counter flows, such as the lane formation, segregation effect and phase separation at higher densities. We also find that the subconscious effect can reduce the occurrence of jam cluster evidently compared with the case of un-subconscious effect. At large maximum velocity, the critical density corresponding to the maximum flow rate of the fundamental diagram is in good agreement with the empirical results.

Traffic jams without bottlenecks—experimental evidence for the physical mechanism of the formation of a jam

A traffic jam on a highway is a very familiar phenomenon. From the physical viewpoint, the system of vehicular flow is a non-equilibrium system of interacting particles (vehicles). The collective effect of the many-particle system induces the instability of a free flow state caused by the enhancement of fluctuations, and the transition to a jamming state occurs spontaneously if the average vehicle density exceeds a certain critical value. Thus, a bottleneck is only a trigger and not the essential origin of a traffic jam. In this paper, we present the first experimental evidence that the emergence of a traffic jam is a collective phenomenon like ‘dynamical’ phase transitions and pattern formation in a non-equilibrium system. We have performed an experiment on a circuit to show the emergence of a jam with no bottleneck. In the initial condition, all the vehicles are moving, homogeneously distributed on the circular road, with the same velocity. The average density of the vehicles is prepared for the onset of the instability. Even a tiny fluctuation grows larger and then the homogeneous movement cannot be maintained. Finally, a jam cluster appears and propagates backward like a solitary wave with the same speed as that of a jam cluster on a highway.

Sidle effect on pedestrian counter flow

We study the behavior of walkers sidling through the crowd in the counter flow of pedestrian. When a walker enters the crowd, he turns himself sidelong to avoid a collision and edge through the crowd. The biased random walk model is extended to take into account the sidle effect. We present three models. The first model is for the pedestrians, which walk normally face to face. In the second model, pedestrian walks only sideways. In the third model, a walker turns himself sidelong if he enters the crowd, edges through the crowd, and returns normal walk if congestion disappears. It is shown that the walking sideways is faster than the normal walk, reduces the congestion, and the jamming transition point becomes lower than that of the normal walk. The jam cluster oscillates highly around the channel center near the jamming transition point in the third model.

Asymmetric Optimal Velocity Model

The optimal velocity (OV) model is one of the car-following traffic flow models, which can reproduce some observed features. The acceleration and braking abilities are symmetrically introduced into the OV model, besides the asymmetry in real vehicles. We introduce the asymmetry between acceleration and braking through the susceptibility in the OV model. As a result, the density contrast becomes large between inside and outside of jam clusters. Jam clusters propagate slower than in the symmetric case.

Random walk theory of jamming in a cellular automaton model for traffic flow

The jamming behavior of a single lane traffic model based on a cellular automaton approach is studied. Our investigations concentrate on the so-called VDR model which is a simple generalization of the well-known Nagel–Schreckenberg model. In the VDR model one finds a separation between a free flow phase and jammed vehicles. This phase separation allows to use random walk like arguments to predict the resolving probabilities and lifetimes of jam clusters or disturbances. These predictions are in good agreement with the results of computer simulations and even become exact for a special case of the model. Our findings allow a deeper insight into the dynamics of wide jams occuring in the model.

Optimal velocity model for traffic flow

We present the Optimal Velocity (OV) model for traffic flow, which shows spontaneous formation of a jam cluster. We investigate the phase diagram and the general bound of induced time delay which plays an essential role in the jam flow solution.

Distribution of Jam Clusters in a Two-Dimensional Cellular Automaton Traffic Flow Model with Open Boundaries

The distribution of jam clusters in a two-dimensional cellular automaton model of traffic flow with open boundaries is investigated by computer simulation. The size distribution of jam clusters obeys the power law of the injection rate in the high-injection-rate region. The total number of unmoved cars in jam clusters shows a sharp transition at the critical injection rate and can be an adequate order parameter describing the phase transition with the emergence of a traffic jam.

Particle hopping models and traffic flow theory.

This paper shows how particle hopping models fit into the context of traffic flow theory. Connections between fluid-dynamical traffic flow models, which derive from the Navier-Stokes-equations, and particle hopping models are shown. In some cases, these connections are exact and have long been established, but have never been viewed in the context of traffic theory. In other cases, critical behavior of traffic jam clusters can be compared to instabilities in the partial differential equations. Finally, it is shown how this leads to a consistent picture of traffic jam dynamics.

Evolution of Traffic Jam in Traffic Flow Model

Traffic flow is simulated in a three-state cellular automaton model. In a two-dimensional cell without a crashed car, the ensemble average of the velocity of the cars is enhanced by the self-organization in the low-density phase of cars. In the high-density phase above p =0.5 of car density, the velocity is decreased and the system then degenerates into a global jamming phase in which all cars are stopped. A crashed car provides the seed of a jamming cluster, which grows into a global traffic jam even in the low-density phase. The growth of the jamming cluster is studied, and the time dependence of the number of jamming cars and the scaling law for the cell sizes are discussed.