The capacity drop caused by the combined effect of the intersection and the bus stop in a CA model

The aim of this work is to investigate the combined effect of the signalized intersection and its near-by bus stop, by using a two-lane CA model. Four cases that the stop locates upstream or downstream the intersection, and ones with the special stop lane or not are considered. The effect of the distance L_D between the stop and the intersection on the capacity is studied, with respect to the traffic light cycle T and the bus dwell time T_s. It is found that acting as a bottleneck, the bus stop near the intersection causes the drop of the capacity. The negative effect only appears below a critical point L_Dc, which is related to the T and the T_s in no stop lane cases. The larger T and T_s have the tendency to create the higher loss of the capacity. While for stop lane cases, the critical value L_Dc changes little. Comparisons among four cases suggest that the special stop lane can effectively enhance the capacity, and the downstream stops perform better than the upstream ones at small L_D or small T or large T_s. The results imply that the capacity can be maximized by adjusting both the position of the bus stop and the cycle time, or adding a special stop lane. These findings may be useful to offer scientific guidance for the management and the design of traffic networks.     

Performance of Wang-Landau algorithm in continuous spin models and a case study: Modified XY-model

Performance of Wang-Landau (WL) algorithm in two continuous spin models is tested by determining the fluctuations in energy histogram. Finite size scaling is performed on a modified XY-model using different WL sampling schemes. Difficulties faced in simulating relatively large continuous systems using WL algorithm are discussed.     

MC-simulation of the 3D,q=3 Potts model

We consider theq=3 Potts model in three dimensions by Monte Carlo simulations. The microcanonical density of states is calculated as a function of the internal energy of the system. We extrapolate the data for the simulated finite systems to the thermo-dynamic limit and find a discontinuous phase transition. This method is checked in the two-dimensional case, where exact results are known.     

How the on-ramp inflow causes bottleneck

We study traffic dynamics in a simple system with three open boundaries. Traffic patterns in steady states are mainly controlled by boundary conditions. There are three distinct phases in the entire parameter space. We construct a phase diagram and develop a mean-field theory to derive the phase regimes. The influences of speed limit are also discussed. We identify three kinds of on-ramp bottleneck: localized bottleneck in free flow, severe bottleneck in congestion, and extended bottleneck in rush hours. The first two are steady and the third is dynamical. The on-ramp bottleneck can be enhanced significantly by the dynamical effects of rush hours.     

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).     

First order phase transitions in the canonical and the microcanonical ensemble

In the canonical ensemble any singularity of a thermodynamic function at a temperatureT _c is smeared over a temperature range of orderT _T /N. Therefore it is rather difficult to distinguish between a discontinuous and a continuous phase transition on the basis of numerical data obtained for finite systems in the canonical ensemble. It is demonstrated for four model systems that this problem cannot be circumvented by considering higher cumulants of the energy distribution or cumulant ratios. On the other hand, the distinction between first and a second order phase transition is rather direct if based on the microcanonical density of states which is readily obtainable in the dynamical ensemble.     

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).     

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.     

Statistical features of traffic flow on urban freeways

Urban freeways play an important role in urban traffic networks. Compared with highway traffic, urban freeway traffic has different characteristics, such as denser on- and off-ramps, more complex road conditions, and lower velocity limits. Until now, however, there has been no comprehensive analysis of urban traffic flow. In this paper, through an analysis of the density dependence of velocity distribution, we investigate the fundamental velocity-density relationships of urban freeways, compare them with those of highway traffic, and explain them using existing traffic flow theories.     

Phase diagram of the two-dimensional ferromagnetic three-color Ashkin-Teller model

In the present work we study the critical properties of the ferromagnetic three-color Ashkin-Teller model (3AT) by means of a Migdal-Kadanoff renormalization group approach on a diamond-like hierarchical lattice. The analysis of the fixed points and flux diagram of the recursion relations is used to determine the corresponding phase diagram (including its symmetry properties) and critical exponents. Our numerical results show the presence of four universality classes, three of them are associated to the Potts model with q=2, 4 and 6 states. Finally, a connection between our findings and some known results from the literature is presented.     

The Korteweg-de Vries soliton in the lattice hydrodynamic model

The lattice hydrodynamic model is not only a simplified version of the macroscopic hydrodynamic model, but is also closely connected with the microscopic car following model. The modified Korteweg-de Vries (mKdV) equation about the density wave in congested traffic has been derived near the critical point since Nagatani first proposed it. But the Korteweg-de Vries (KdV) equation near the neutral stability line has not been studied, which has been investigated in detail in the car following model. So we devote ourselves to obtaining the KdV equation from the lattice hydrodynamic model and obtaining the KdV soliton solution describing the traffic jam. Numerical simulation is conducted, to demonstrate the nonlinear analysis result.     

The “backward looking” effect in the lattice hydrodynamic model

The novel lattice hydrodynamic model is presented by incorporating the “backward looking” effect. The stability condition for the the model is obtained using the linear stability theory. The result shows that considering one following site in vehicle motion leads to the stabilization of the system compared with the original lattice hydrodynamic model and the cooperative driving lattice hydrodynamic model. The Korteweg-de Vries (KdV, for short) equation near the neutral stability line is derived by using the reductive perturbation method to show the traffic jam which is proved to be described by KdV soliton solution obtained from the KdV equation. The simulation result is consistent with the nonlinear analysis.     

Effect of real-time information upon traffic flows on crossing roads

The effect of real-time information on the traffic flows of the crossing roads is studied by simulations based on a cellular automaton model. At the intersection, drivers have to enter a road of a shorter trip-time, by making a turn if necessary, as indicated on the information board. Dynamics of the traffic are expressed as a return map in the density-flow space. The traffic flow is classified into six phases, as a function of the car density. It is found that such a behavior of drivers induces too much concentration of cars on one road and, as a result, causes oscillation of the flow and the density of cars on both roads. The oscillation usually results in a reduced total flow, except for the cases of high car density.     

The inverse excitation-induced abnormal spiral wave

The effects of a local constant forcing on spiral waves in two-dimensional excitable media described by Bär model are investigated. A constant external forcing is imposed on the core of spiral wave, leading to parameter variability of a medium. It is found that the forcing can significantly alter the shape and rotation period of spiral wave when the values of related parameters are properly chosen. The change of wave structure is attributed to the transition from normal excitation to inverse excitation in the forced medium. An abnormal spiral wave with a very thick spiral arm has been observed. The physical mechanism underlying these phenomena is theoretically analyzed.     

A kinetic model for the premelting of a crystalline structure

An analytical kinetic approach to examine the premelting phenomenon is suggested by using a first passage time analysis. Premelting is considered to occur when the time of formation of a Frenkel type defect in the surface monolayer becomes sufficiently small. The mean time of defect formation on the surface lattice, i.e., the mean time necessary for a selected (surface-located) molecule to leave its lattice site and form a Frenkel defect, is calculated by using a first passage time analysis. The model is illustrated by numerical calculations for a crystalline structure composed of molecules interacting via the Lennard-Jones (LJ) potential. The lattice vectors in the plane parallel to the free surface of the crystal were assumed to be equal (to the lattice parameter) and the angle between them was varied. The model predictions of the Tammann temperature (of premelting) are very sensitive to the parameters of the LJ potential. In all the cases considered, the temperature dependence of the mean first passage time has two clearly distinct regimes: at low temperatures the dependence is sharp and at high temperatures it is weak.     

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.     

Phase separation of binary systems

In this paper, three physical predictions on the phase separation of binary systems are derived based on a dynamic transition theory developed recently by the authors. First, the order of phase transitions is precisely determined by the sign of a nondimensional parameter K such that if K>0, the transition is first order with latent heat and if K<0, the transition is second order. Here the parameter K is defined in terms of the coefficients in the quadratic and cubic nonlinear terms of the Cahn-Hilliard equation and the typical length scale of the container. Second, a phase diagram is derived, characterizing the order of phase transitions, and leading in particular to a prediction that there is only a second-order transition for molar fraction near 1/2. This is different from the prediction made by the classical phase diagram. Third, a TL-phase diagram is derived, characterizing the regions of both homogeneous and separation phases and their transitions.     

Topological Effects on the Performance of Transportation Networks

We investigate the influence of the network topology on the performance （characterized by the total system cost and maximal tratffic volume） of transportation networks, where the weights are not static （constant）, but dynamic （a function of the flow on the link）. Four classes of networks are used in the simulation, including regular networks, random networks, small-world networks and scale-free networks. The initial simulation results show that topologies play important roles on the performance of transportation networks, and random networks have better performance than other networks. Also, we find that there are distinct difference of the link flow distribution for various networks in both the distribution function form and the span between the minimum and the maximum of the link flow, explaining the difference of the performance among distinct networks. These findings will be useful in network design problems of transportation systems.