Freezing transition in bi-directional CA model for facing pedestrian traffic

We present a bi-directional cellular automaton (CA) model for facing traffic of pedestrians on a wide passage. The excluded-volume effect and bi-directionality of facing traffic are taken into account. The CA model is not stochastic but deterministic. We study the jamming and freezing transitions when pedestrian density increases. We show that the dynamical phase transitions occur at three stages with increasing density. There exist four traffic states: the free traffic, jammed traffic 1, jammed traffic 2, and frozen state. At the frozen state, all pedestrians stop by preventing from going ahead each other. At three transitions, the pedestrian flow changes from the free traffic through the jammed traffic 1 and jammed traffic 2, to the frozen state.     

Effects of random biquadratic couplings in a spin-1 spin-glass model

A spin-1 model, appropriated to study the competition between bilinear (J _ij S _i S _j ) and biquadratic (K _ij S _i ² S _j ²) random interactions, both of them with zero mean, is investigated. The interactions are infinite-ranged and the replica method is employed. Within the replica-symmetric assumption, the system presents two phases, namely, paramagnetic and spin-glass, separated by a continuous transition line. The stability analysis of the replica-symmetric solution yields, besides the usual instability associated with the spin-glass ordering, a new phase due to the random biquadratic couplings between the spins. Received 18 May 1999 and Received in final form 20 October 1999     

Effect of gravitational force upon traffic flow with gradients

We study the effect of gravitational force upon traffic flow on a highway with sag, uphill, and downhill. We extend the optimal velocity model to take into account the gravitational force which acts on vehicles as an external force. We study the traffic states and jamming transitions induced by the slope of highway. We derive the fundamental diagrams (flow-density diagrams) for the traffic flow on the sag, the uphill, and downhill by using the extended optimal velocity model. We clarify where and when traffic jams occur on a highway with gradients. We show the relationship between densities before and after the jam. We derive the dependence of the fundamental diagram on the slope of gradients.     

Simon-Gutowitz bidirectional traffic model revisited

The Simon-Gutowitz bidirectional traffic model [P.M. Simon, H.A. Gutowitz, Phys. Rev. E 57 (1998) 2441] is revisited in this Letter. We found that passing cars get stuck with oncoming cars before returning to their home lanes. This provokes the occurrence of wide jams on both lanes. We have rectified the rules for lane changing. Then, the wide jams disappear and the revisited model can describe well the realistic bidirectional traffic.     

Fundamental diagram in traffic flow of mixed vehicles on multi-lane highway

We study the fundamental diagram for traffic flow of vehicular mixture on a multi-lane highway. We present the car-following model of multi-lane traffic in which slow and fast vehicles flow with changing lanes. We investigate the traffic states of the vehicular mixture under the periodic boundary. Two values of the current appear at a density and two current curves are obtained. Vehicles move with changing lanes in the traffic state of high current, while vehicles move without changing lanes in the traffic state of low current. They depend on the density, the fraction of slow vehicles, and the initial condition. In the high-current curve, the jamming transition between the free flow and the jammed state occurs at a low density. The fundamental diagrams (current-density diagrams) are shown for the single-lane, two-lane, three-lane, and four-lane traffics.     

Distributions of time- and distance-headways in the Nagel-Schreckenberg model of vehicular traffic: effects of hindrances

In the Nagel-Schreckenberg model of vehicular traffic on single-lane highways vehicles are modelled as particles which hop forward from one site to another on a one dimensional lattice and the inter-particle interactions mimic the manner in which the real vehicles influence each other's motion. In this model the number of empty lattice sites in front of a particle is taken to be a measure of the corresponding distance-headway (DH). The time-headway (TH) is defined as the time interval between the departures (or arrivals) of two successive particles recorded by a detector placed at a fixed position on the model highway. We investigate the effects of spatial inhomogeneities of the highway (static hindrances) on the DH and TH distributions in the steady-state of this model. Received: 2 March 1988 / Revised: 13 April 1998 / Accepted: 17 April 1998     

Lattice hydrodynamic model with bidirectional pedestrian flow

The two-dimensional lattice hydrodynamic model of traffic is extended to the two-dimensional bidirectional pedestrian flow via taking four types of pedestrians into account. The stability condition and the mKdV equation to describe the density wave of pedestrian congestion are obtained by linear stability and nonlinear analysis, respectively. In addition, there exist three phase transitions among the freely moving phase, the coexisting phase and the uniformly congested phase in the phase diagram. It can also be found that the critical point a_c refers to not only the fraction c₁ of the eastbound and westbound pedestrians, but also the fraction c₂ of the northbound and southbound pedestrians. However, the critical point a_c could not appear in the phase diagram and congested crowd at any time when two fractions are equal to same value of 0.5 (c₁=c₂=0.5). Furthermore, numerical simulation is carried out to examine the performance of such a model and the results show coincidence with the theory analysis results.     

Freezing transition in the mean-field approximation model of pedestrian counter flow

We study the freezing transition in the counter flow of pedestrians within the channel numerically and analytically. We present the mean-field approximation (MFA) model for the pedestrian counter flow. The model is described in terms of a couple of nonlinear difference equations. The excluded-volume effect and bi-directionality are taken into account. The fundamental diagrams (current-density diagrams) are derived. When pedestrian density is higher than a critical value, the dynamical phase transition occurs from the free flow to the freezing (stopping) state. The critical density is derived by using the linear stability analysis. Also, the velocity and current (flow) at the steady state are derived analytically. The analytical result is consistent with that obtained by the numerical simulation.     

Landau expansion for a metamagnetic model

We performed a detailed Landau expansion of the free energy for a metamagnetic model considering terms up to twelfth order. We obtained explicit expressions for the coefficients as a function of the temperature and the ratio between ferro- and antiferromagnetic interactions. We showed that a naive analysis based on the signs of these coefficients cannot always give us sufficient guarantee about the correctness of the phase diagram of the model. In these cases it is necessary to resort to the full expression of the free energy in order to characterize the nature of the phase transition. Received 28 November 2001     

Critical dynamics in clusters of noble gas atoms

The multi-fragmentation dynamics of noble gas atomic clusters is considered for different statistically distributed deposited energies. The conditions giving rise to the development of criticality in the cluster evolution are revealed from an analysis of the signals in the fragment mass distribution. The time dependence of the observables related to critical exponents is studied. It is demonstrated that in a certain regime the cluster exhibits a behavior which can be identified as the precursor of a second-order liquid-gas phase transition. Received 1st September 1998 and Received in final form 14 January 1999     

Density waves in traffic flow model with relative velocity

The car-following model of traffic flow is extended to take into account the relative velocity. The stability condition of this model is obtained by using linear stability theory. It is shown that the stability of uniform traffic flow is improved by considering the relative velocity. From nonlinear analysis, it is shown that three different density waves, that is, the triangular shock wave, soliton wave and kink-antikink wave, appear in the stable, metastable and unstable regions of traffic flow respectively. The three different density waves are described by the nonlinear wave equations: the Burgers equation, Korteweg-de Vries (KdV) equation and modified Korteweg-de Vries (mKdV) equation, respectively.     

Analysis of stability and density waves of traffic flow model in an ITS environment

By introducing relative velocities of arbitrary number of cars ahead into the full velocity difference models (FVDM), we present a forward looking relative velocity model (FLRVM) of cooperative driving control system. To our knowledge, the model is an improvement over the similar extension in the forward looking optimal velocity models (FLOVM), because it is more reasonable and realistic in implement of incorporating intelligent transportation system in traffic. Then the stability criterion is investigated by the linear stability analysis with finding that new consideration theoretically lead to the improvement of the stability of traffic flow, and the validity of our theoretical analysis is confirmed by direct simulations. In addition, nonlinear analysis of the model shows that the three waves: triangular shock wave, soliton wave and kink-antikink wave appear respectively in stable, metastable and unstable regions. These correspond to the solutions of the Burgers equation, Korteweg-de Vries (KdV) equation and modified Korteweg-de Vries (mKdV) equation.     

Full counting statistics of a general quantum mechanical variable

We present a quantum mechanical framework for defining the statistics of measurements of , A(t) being a quantum mechanical variable. This is a generalization of the so-called full counting statistics proposed earlier for DC electric currents. We develop an influence functional formalism that allows us to study the quantum system along with the measuring device while fully accounting for the back action of the detector on the system to be measured. We define the full counting statistics of an arbitrary variable by means of an evolution operator that relates the initial and final density matrices of the measuring device. In this way we are able to resolve inconsistencies that occur in earlier definitions. We suggest two schemes to observe the so defined statistics experimentally.Received: 30 June 2003, Published online: 15 October 2003PACS: 73.50.Td Noise processes and phenomena - 73.23.-b Electronic transport in mesoscopic systems - 74.40.+k Fluctuations (noise, chaos, nonequilibrium superconductivity, localization, etc.)     

Dynamics of selfavoiding tethered membranes. I. Model A dynamics (Rouse model)

The dynamical scaling properties of selfavoiding polymerized membranes with internal dimension D are studied using model A dynamics. It is shown that the theory is renormalizable to all orders in perturbation theory and that the dynamical scaling exponent z is given by . This result applies especially to membranes (D=2) but also to polymers (D=1). Received: 5 September 1997 / Accepted: 17 November 1997     

A simulation study of an asymmetric exclusion model with open and periodic boundaries for parallel dynamics

The effect of jumping rate probability on the phase diagram of an asymmetric exclusion model is studied by numerical simulations. Density, current and velocity of particles are calculated for parallel dynamics. In the open boundaries case for one species of particles (particles 1), a passage from first to second order transition occurs by decreasing the jumping rate. In the periodic boundaries case, by introducing another species of particle (particle 2) which plays the role of obstacle for particles 1, the average velocity of particles 1 increases with increasing the jumping rate for small density. While the average velocity of particle 2 decreases for small and intermediate densities. Received: 21 October 1997     

Transition from homogeneous to inhomogeneous flows in a lattice-gas binary mixture of slender particles

We study the unidirectional flow of a binary mixture of biased-random walkers on a square lattice under a periodic boundary. The lattice-gas mixture consists of two types of slender particles (walkers) which have different biases (drift coefficients). When the density is higher than a critical value, a dynamical transition occurs from the homogeneous flow to the inhomogeneous flow and clogging appears. The inhomogeneous state returns to the homogeneous congested flow with further increasing density. The clogging does not appear in the unidirectional flow of the conventional lattice-gas binary mixture of single-site particles. The jamming (clogging) transition is clarified for various sizes of slender particles.     

A new macro model with consideration of the traffic interruption probability

In this paper, we present a new macro model which involves the effects that the probability of traffic interruption has on the car-following behavior through formulating the inner relationship between micro and macro variables. Linear stability analysis shows that consideration of the traffic interruption probability can improve the stability of traffic flow if and only if the drivers’ reactive time required for adjusting their acceleration based on the traffic interruption probability p is not greater than that one based on the non-interruption probability 1−p. Numerical results verify that the new model can be used to analyze the effects of traffic interruption probability and traffic interruption on shock, rarefaction wave, small perturbation and uniform flow. The model has been applied in reproducing some complex traffic phenomena resulted by some traffic interruptions (e.g., signal light, pedestrian and tolling station).