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.     

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.     

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.     

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.     

Traffic flow on a toll highway with electronic and traditional tollgates

We study the traffic states and jams occurring in traffic flow on a two-lane toll highway with electronic and manual (traditional) tollgates. The electronic and manual collection vehicles sort themselves into their respective lanes at low density, while they mix at each tollgate at high density. We derive the fundamental diagrams (flow-density diagrams) for the electronic and manual collection vehicles. The traffic states change with increasing density and varying the ratio. Dynamical phase transitions occur. It is shown that the fundamental diagrams for the two tollgates depend greatly on the density and fraction of both vehicles.     

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.     

Traffic states induced by slowdown sections on two-lane highway

We study the traffic states and jams occurring on a two-lane highway with a few slowdown sections. We derive the fundamental diagrams (flow-density diagrams). The fundamental diagrams on first and second lanes depend highly on the configuration of slowdown sections. The occupancy fraction of vehicles on first and second lanes varies with configuration of slowdown sections and also changes with density for the definite configuration. When a jam is formed on a lane, the flow (current) saturates on the lane. The saturated flow is given by the maximal value of the current of the slowdown section. The relationship between the densities before and after the jam is derived analytically. The dependence of jam lengths on density is derived numerically and analytically.     

Discretization effect in a multi-grid egress model

In the traditional egress model based on cellular automata, building spaces are divided into discrete grids, the size of which is usually as large as that of a pedestrian. In order to explore the influences of the grid size on the evacuation results, we studied the evacuation process using a multi-grid egress model. In the multi-grid model, a finer grid is used and each pedestrian occupies n×n basic grids. It is found that if the pedestrian always moves one grid at each time step, the evacuation time increases with the decrease of the grid size, and reaches a stable, grid-independent value when the grid size is small enough. Another factor which influences the evacuation results is the length of the time step. It is found that with the increasing length of the time step, the evacuation time has a tendency to increase but endures complex changes. The differences between the single-grid model and multi-grid model may be due to two main reasons. First, in the multi-grid model, the pedestrians are out of alignment so that there are patches of unusable empty spaces as they are smaller in size than a pedestrian. Second, in the multi-grid model, pedestrians tend to reach the exit at the same time, leading to more serious conflicts among pedestrians.     

Simulation of pedestrian flow on square lattice based on cellular automata model

Simulations of two-way and four-way pedestrian flow on the square lattice for small systems will be presented based on cellular automata (CA) in this paper. For the reason that the decision-making process of pedestrians in their movements is complex and intelligent, pedestrian movement is more flexible and adaptive to dynamic conditions than vehicular flow. First, a special technique will be introduced to simplify tactically the process into the interaction of four dynamic parameters, which can reflect the pedestrian judgment on the surrounding conditions and decide the pedestrian's choice of action such as moving ahead, stopping to wait, position exchange, lane switching, back stepping, etc. Second, the simulation method and the relationships of velocity-density and flow-density will be studied and analyzed. It is found that there are phase transitions at the critical density point and at different phases the relationships of velocity-density and flow-density are different from each other. Moreover, the different weight coefficients of four dynamic parameters affect the simulation results of these two models.     

Simulation of pedestrian counter-flow with right-moving preference

People prefer to walk on the right-hand side of the road for physical and social reasons. In this paper, pedestrian counter-flow in a channel is simulated with the Cellular Automata (CA) Model, with focus on right-preference. Two types of pedestrians are taken into account, walking leftward and rightward along the channel. Circular and open boundaries are adopted respectively. The right-preference intensity, k, is introduced, defined as the ratio of the right-moving probability to left-moving probability. In simulations, the dynamical transition between fluid and jammed phase is presented. With a fixed k, the critical density is independent of the channel size. According to research results on physiology and sociology [O. Guentuerkuen, Nature 421 (2003) 711; M. Reiss, G. Reiss, Percept. Mot. Skill 85 (1997) 569; M.C. Corballis, Psychol. Rev. 104 (1997) 714], k=1,2,8 have been discussed, and k=8 is satisfied in this work. Furthermore, simulation results are compared with the ideal calculation, and other researchers’ experiments [M. Isobe, T. Adachi, T. Nagatani, Physica A 336 (2004) 638]. It is found that right-preference is effective when the density is below critical. The model is shown to be useful to simulate and analyze this situation numerically.     

Second-order phase transition in two-dimensional cellular automaton model of traffic flow containing road sections

Two-dimensional cellular automaton model has been broadly researched for traffic flow, as it reveals the main characteristics of the traffic networks in cities. Based on the BML models, a first-order phase transition occurs between the low-density moving phase in which all cars move at maximal speed and the high-density jammed phase in which all cars are stopped. However, it is not a physical result of a realistic system. We propose a new traffic rule in a two-dimensional traffic flow model containing road sections, which reflects that a car cannot enter into a road crossing if the road section in front of the crossing is occupied by another car. The simulation results reveal a second-order phase transition that separates the free flow phase from the jammed phase. In this way the system will not be entirely jammed (“don’t block the box” as in New York City).     

Topological Properties of Urban Public Traffic Networks in Chinese Top-Ten Biggest Cities

We investigate the topological characteristics of complex networks as exemplified by the urban public traffic network （UPTN） in Chinese top-ten biggest cities. It is found that the UPTNs have small world behaviour, by the examination of their topological parameters. The quantitative analysis of the transport efficiency of the UPTNs reveals their higher local efficiency El and lower global efficiency Eg, which coincide well with the status quo of those Chinese cities still at their developing stage. Furthermore, the topological properties of efficiency in the UPTNs are also examined, and the findings indicate that, on the one hand, the UPTNs show robustness to random attacks and frangibility to malicious attacks on a global scale; on the other hand, the interrelation between UPTN efficiency and network motifs deserves our attention. The motifs which interrelate the UPTN efficiency are always triangular-formed patterns, e.g. motifs ID 238, ID 174 and ID 102, etc.     

Monte Carlo investigation of the phase transition in the 2D Potts model with open boundary conditions

Finite size effects on the phase transition in the 2D Potts model with open boundary conditions are studied with Wang-Landau Monte Carlo simulations. We show the lattice size dependent cross-over from first order to continuous phase transition and discuss it in terms of surface induced disorder and size dependence of the latent heat.     

Magnetic properties of an anti-ferromagnetic and ferrimagnetic mixed spin-1/2 and spin-5/2 Ising model in the longitudinal magnetic field within the effective-field approximation

The magnetic properties of an anti-ferromagnetic and ferrimagnetic mixed spin-1/2 and spin-5/2 Ising model with a crystal field in a longitudinal magnetic field on the honeycomb (z=3) and square lattice (z=4) are studied by using the effective-field theory with correlations. The ground state phase diagram of the model is obtained in the longitudinal magnetic field (h) and a single-ion potential or crystal-field interaction (Δ) plane. We also investigate the thermal variations of the sublattice and total magnetizations, and present the phase diagrams in the (Δ/|J|, ) plane. The phase diagrams have one, two or even three compensation temperatures depending on the values of the crystal-field interaction. Moreover, the susceptibility, internal energy and specific heat of the system are numerically examined, and some interesting phenomena in these quantities are found due to the applied longitudinal magnetic field.     

A stochastic multi-cluster model of freeway traffic

A stochastic approach based on the Master equation is proposed to describe the process of formation and growth of car clusters in traffic flow in analogy to usual aggregation phenomena such as the formation of liquid droplets in supersaturated vapour. By this method a coexistence of many clusters on a one-lane circular road has been investigated. Analytical equations have been derived for calculation of the stationary cluster distribution and related physical quantities of an infinitely large system of interacting cars. If the probability per time (or p) to decelerate a car without an obvious reason tends to zero in an infinitely large system, our multi-cluster model behaves essentially in the same way as a one-cluster model studied before. In particular, there are three different regimes of traffic flow (free jet of cars, coexisting phase of jams and isolated cars, highly viscous heavy traffic) and two phase transitions between them. At finite values of p the behaviour is qualitatively different, i.e., there is no sharp phase transition between the free jet of cars and the coexisting phase. Nevertheless, a jump-like phase transition between the coexisting phase and the highly viscous heavy traffic takes place both at and at a finite p. Monte-Carlo simulations have been performed for finite roads showing a time evolution of the system into the stationary state. In distinction to the one-cluster model, a remarkable increasing of the average flux has been detected at certain densities of cars due to finite-size effects. Received 17 September 1999     

Deceleration in advance in the Nagel-Schreckenberg traffic flow model

Based on the Nagel-Schreckenberg model, we study the impact of deceleration in advance on the dynamics of traffic flow. In the process of deceleration in advance, the effect of reaction delay and the effect of expectation are considered respectively. The traffic flow properties are studied by analyzing the fundamental diagram, spatio-temporal patterns, distance headway distribution and car accidents. The simulation results show that reaction delay brings complex traffic flow patterns and expectation makes the serious car accidents rarely happen.     

Finite-size-induced transition in ensemble of globally coupled oscillators

The collective behavior of overdamped nonlinear noise-driven oscillators coupled via mean field is investigated numerically. When a coupling constant is increased, a transition in the dynamics of the mean field is observed. This transition scales with the number of oscillators and disappears when this number tends to infinity. Analytical arguments explaining the observed scaling are presented.     

Performance characteristic of a Stirling refrigeration cycle in micro/nano scale

The aim of the paper is to present the performance characteristics of a Stirling refrigeration cycle in micro/nano scale, in which the working substance of cycle is an ideal Maxwellian gas. Due to the quantum boundary effect on the gas particles confined in the finite domain, the cycle no longer possesses the condition of perfect regeneration. The inherent regenerative losses, the refrigeration heat and coefficient of performance (COP) of the cycle are derived. It is found that, for the micro/nano scaled Stirling refrigeration cycle devices, the refrigeration heat and COP of cycle all depend on the surface area of the system (boundary of cycle) besides the temperature of the heat reservoirs, the volume of system and other parameters, while for the macro scaled refrigeration cycle devices, the refrigeration heat and COP of cycle are independent of the surface area of the system. Variations of the refrigeration heat ratio r_R and the COP ratio r_ε with the temperature ratio τ and volume ratio r_V for the different surface area ratio r_A are examined, which reveals the influence of the boundary of cycle on the performance of a micro/nano scaled Stirling refrigeration cycle. The results are useful for designing of a micro/nano scaled Stirling cycle device and may conduce to confirming experimentally the quantum boundary effect in the micro/nano scaled devices.     

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 ease of un-subeonscious 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.     

Performance analysis of a thermosize micro/nano heat engine

In a recent paper [A. Sisman, I. Muller, Phys. Lett. A 320 (2004) 360] the thermodynamic properties of ideal gases confined in a narrow box were examined theoretically. The so-called “thermosize effects” similar to thermoelectric effects, such as Seebeck-like thermosize effect, Peltier-like thermosize effect and Thomson-like thermosize effect, were analyzed. Like the thermoelectric generator, based on the thermosize effects we have established a model of micro/nano scaled ideal gas heat engine cycle which includes two isothermal and two isobaric processes. The expressions of power output and efficiency of this cycle in the two cases of reversible and irreversible heat exchange are derived and the optimal performance characteristics of the heat engine is discussed by some numerical example. The results obtained here will provide theoretical guidance for the design of micro/nano scaled device.