Narrow Results

We study the effects of on-ramp and off-ramp to the traffic flow in a cellular automaton. The stochastic noise and the extended hopping are included. The phase diagram is obtained. Three distinct phases are observed. The density profiles are analyzed. In the maximum current phase, standing traffic jams emerge in the upstream of the on-ramp. A region of free flow is observed in the downstream of the off-ramp. In between the ramps, a scaled density profile is observed in one branch and a phase separation is observed in the other branch.

The kinetics of irreversible dimer–dimer reaction of the type A₂+B₂→2AB has already been studied through Monte Carlo simulation via a model based on Langmuir–Hinshelwood (thermal) mechanism. The results of this study are well known. There is single transition point (y_C) at y_B=0.5 (where y_B is partial pressure of B₂ dimer in gas phase), which separates the two poisoned states from each other. Here, we have studied this reaction on the basis of a nonthermal model, which involves the precursor motion of B₂ molecule. The most interesting feature of this model is that it yields a steady reactive window. The phase diagram is similar to the ZGB model. The reactive window is separated by continuous and discontinuous irreversible phase transitions. The width of the reactive window depends upon the mobility of the precursors. The dependence of production rate on partial pressure of B₂ is shown by simple mathematical equations in our model. Some interesting results are observed when reaction between precursors and chemisorbed B atoms is considered.

We have investigated the effects of the Eley–Rideal (ER) process on the phase diagram of the Langmuir–Hinshelwood (LH) type monomer–dimer (CO–O₂) catalytic reaction on (001) surface and subsurface of a simple cubic structure. With the consideration of a new pathway in which a dimer is adsorbed in such a way that it takes one surface site whereas second site may be from a surface or from a subsurface, a situation close to experiments is observed, i.e., with slight introduction of the monomer (CO), the production of AB₂ starts. In this case, the qualitative trend of surface oxygen coverage is consistent with the experimental situation.

The three-dimensional BC model is simulated on a cellular automaton which improved from the Creutz cellular automaton for simple cubic lattice. The phase diagram characterizing phase transition of the model is obtained for a comparison with those obtained from other calculations. The simulations confirm the existence of a tricritical point at which the phase transition changes from second-order to first-order at D/J =2.82. For the determined of the tricritical point, the thermodynamics quantities are computed using two different procedures which is called as the standard and the cooling algorithm for the anisotropy parameter values in the interval 3≥D/J≥-8. The simulations indicates that the cooling algorithm is a suitable procedure for the calculations near the first-order phase transition region, and the cooling rate is an important parameter in the determining of the phase boundary. The estimated critical temperatures for D/J =0 and 2.82 are compatible with the series expansion results.

A Monte Carlo Simulation study of the monomer dimer (CO–NO) heterogeneous catalytic reaction on body-centered cubic structure (BCC) is presented. The effect of Eley–Rideal (ER), diffusion of nitrogen and carbon monoxide on the phase diagram is investigated. The steady reactive state is observed while using Langmuir–Hinsehelwood (LH) mechanism. Whenever the ER mechanism is included in our simulation, the production of CO₂ starts as soon as y_CO departs from zero, which is consistent with the experimental results. The ER mechanism does not affect the production of N₂. The effect of diffusion of CO and N are found very little on the steady state reactive region where the concentration of CO is very high.

The spin-1 Ising (BEG) model has been simulated on a cellular automaton improved from the Creutz cellular automaton (CCA) for a face-centered cubic lattice. The simulations have been made in the 0 ≤ d = D/J ≤ 7 and -1.25 < k = K/J ≤ 0 parameter region. In this region, the ground state diagram (k, d) has ferromagnetic and perfect zero ordering regions. The ferromagnetic ordering region separates into four regions which exhibit different phase transition types as the first order, the second order, the reentrant, the double-reentrant and the successive phase transitions. The simulation results show that the model has the tricritical points, the critical end points and the bicritical points on the (kT_C/zJ, d) and (kT_C/zJ, k) planes as indicated by the Mean Field approximation results.

The spin-1 Ising Blume–Emery–Griffiths (BEG) model has been simulated using a cellular automaton (CA) algorithm improved from the Creutz cellular automaton (CCA) for a face-centered-cubic (fcc) lattice. The ground state diagram (k, d) of the fcc BEG model has ferromagnetic (F), quadrupolar (Q), and staggered quadrupolar (SQ) structure regions. The simulations have been made in the SQ region for the parameter values in the intervals -24 ≤ d = D/J < 0 and -3 ≤ k = K/J ≤ 0. The phase diagrams on the (kT_C/J, d) and the (kT_C/J, k) planes have been obtained through k = -3 and d = -4 lines, respectively. The SQ region separates into five regions (A₃ B(a), A₃ B(f), AB (type-I), AB (type-II), and AB₃(f)) which have the different stoichiometric Cu–Au type structures.

We study totally asymmetric simple exclusion process (TASEP) where particles move on a single-chain lattice which diverges into two parallel lattice branches. At the branching point, the particles move to one of the two branches with equal rate r/2. The phase diagram and density profiles are investigated by using mean-field approximation and Monte Carlo simulations. It is found that the phase diagram can be classified into three regions at any value of r. However, a threshold is identified. In cases of r > r_c and r < r_c, the phase diagram exhibits qualitatively different phases. The analytical results are in good agreement with the results of Monte Carlo simulations.

We propose Asymmetric Simple Exclusion Processes to analyze the traffic states around a T-shaped intersection. The system consists of six roadways connected by the intersection. There are nine control-parameters separated into three categories: injection α_i, removal β_i, and turning P_i, (where i = 1, 2, 3). As these nine parameters change, traffic states on each roadway reveal a two-phase transition: free flow (F) and jam (J). Together, there can be 64 (=2⁶) possible combinations for the traffic phases. We observe 63 distinct phases. We analyze three major causes of congestion:

(1) increase of traffic demand simulated by injection α_i;

(2) decrease of roadway capacity simulated by removal β_i;

(3) redistribution of traffic pattern simulated by turning P_i.

In case (1), congestion can be confined to the roadways heading toward the intersection. In case (2), spillovers can be observed and congestion will pervade the whole system. In case (3), congestion can be triggered by both increasing P_i and decreasing P_i. The phase diagram can be a convenient tool to summarize the results of numerical simulations. We also compare the unsignalized intersection to an intersection regulated by traffic signals. We find that the operation of traffic signals is very inefficient in resolving the congestion around a T-shaped intersection.

We describe a systematic method for complete enumeration of configuration classes (CCs) of the spin-1/2 Ising model in the energy-magnetization plane. This technique is applied to the antiferromagnetic (AF) Ising model in an external magnetic field on the square lattice, which is simulated using the tomographic entropic sampling (TES) algorithm. We estimate the number of configurations, Ω(E,m,L), and related microcanonical averages, for all allowed energies E and magnetizations m for L = 10 to 30, with ΔL = 2. With prior knowledge of the CCs, we can be sure that all allowed classes are sampled during the simulation. Complete enumeration of CCs also enables us to use the final estimate of Ω(E,m,L) to obtain good initial estimates, Ω₀(E,m,L′), for successive system sizes (L′ > L) through a two-dimensional interpolation. Using these results we calculate canonical averages of the thermodynamic quantities of interest as continuous functions of temperature T and external field h. In addition, we determine the critical line in the h-T plane using finite-size scaling analysis, and compare these results with several approximate theoretical expressions.

Different types of the lattice spin systems with the competing interactions have rich and interesting phase diagrams. In this study a system with competing nearest-neighbor interaction J₁, prolonged next-nearest-neighbor interaction J_p and ternary prolonged interaction J_tp is considered on a Cayley tree of arbitrary order k. To perform this study, an iterative scheme is developed for the corresponding Hamiltonian model. At finite temperatures several interesting properties are presented for typical values of α = T/J₁, β = −J_p/J₁ and γ = -J_tp/J₁. This study recovers as particular cases, previous work by Vannimenus¹ with γ = 0 for k = 2 and Ganikhodjaev et al.² in the presence J₁, J_p, J_tp with k = 2. The variation of the wavevector q with temperature in the modulated phase and the Lyapunov exponent associated with the trajectory of our iterative system are studied in detail.

Traffic flow at a single crossroad consisting of two perpendicular one-lane roads, treated earlier by Ishibashi and Fukui [J. Phys. Soc. Jpn.70, 2793 (2001); 70, 3747 (2001)], has been studied on the basis of the local occupation probability method. However, in this work, based on the novel theoretical analysis and computer simulations, we have studied this crossroad traffic model again and presented the same phase diagrams of traffic flow in the case of various maximum vehicle velocities. We have also derived the flow formulas in all regions in the phase diagrams, which are in good agreement with computer simulation results. Compared with the previous local occupation probability method, our analytical way is simpler and may be widely used for other traffic bottlenecks research.

The car-following model is extended to take into account the characteristics of mixed traffic flow containing fast and slow vehicles. We conduct the linear stability analysis to the extended model with finding that the traffic flow can be stabilized with the increase of the percentage of the slow vehicle. It also can be concluded that the stabilization of the traffic flow closely depends on not only the average value of two maximum velocities characterizing two vehicle types, but also the standard deviation of the maximum velocities among all vehicles, when the percentage of the slow vehicles is the same as that of the fast ones. With increase of the average maximum velocity, the traffic flow becomes more and more unstable, while the increase of the standard deviation takes negative effect in stabilizing the traffic system. The direct numerical results are in good agreement with those of theoretical analysis. Moreover, the relation between the flux and the traffic density is investigated to simulate the effects of the percentage of slow vehicles on traffic flux in the whole density regions.

The carbon structures of phases A and B of methane are investigated through classical molecular dynamics simulations using optimized potentials for liquid simulations all-atom force fields as well as ReaxFF reactive force fields. Both final thermodynamic states were obtained by the proper ramping of temperature and pressure through well-known regions of methane’s phase diagram using the isothermal–isobaric (NPT) ensemble. Our calculated structures are in good agreement with very recent experimental data. The knowledge of these phases is the basis for the study of methane at high pressures.

For the purposes of optimizing traffic flow composed of different types of vehicles, it is important to understand the interactions between them. This paper proposes a cellular automata model to investigate a bidirectional two-lane traffic flow under the periodic boundary condition. The vehicle flux and the phase diagrams of the system in the (${\rho }_1,{\rho }_2$) space are constructed by applying two different overtaking models (symmetric, asymmetric). The inter-lane correlation and the overtaking frequency are also studied. The simulation results show that the variation of the density of one lane has an apparent influence on the traffic of the adjacent lane. Furthermore, it is found that the phase diagram on both models is classified into several regions. Thus, for the symmetric model, as the overtaking probability increases, the traffic on the system becomes better. Likewise, the results also indicate that the asymmetric model can effectively enhance the traffic capacity and alleviate the congested state.

In this paper, we propose a stochastic cellular automata (CA) model to study traffic dynamic at a single-lane traffic circle of $N$ entry/exit points. The boundaries are controlled by the injecting rates ${\alpha }_1$, ${\alpha }_2$ and the extracting rate $\beta$. Both the cases with and without the splitter islands of width $L_{sp}$ are considered. The phase diagrams in the space ${(\alpha }_1\beta )$ are constructed and the density profiles are also investigated. The variation of the phase diagram with the traffic circle size $(L)$, the number of entry point $(N)$, and the time needed for drivers to change their exit willingly $(T_{\mathrm{\text{exit}}})$ is studied. The results show that the phase diagram in both cases consists essentially of three phases namely free flow, congestion and gridlock. However, the large sized traffic circle shows better performance in the free flow phase, in contrary, the increase of $N$ enlarges the congestion and the gridlock phases. We have also found that the decrease of $T_{\mathrm{\text{exit}}}$ enhances the traffic flow situation in the traffic circle. Furthermore, as the $L_{sp}$ increases, the free flow phase enlarges while the congestion and gridlock ones shrink.

In this paper, we present a cellular automata model to depict the traffic characteristics at such a nonsignalized $T$-shaped intersection in the presence of pedestrian crossings. The vehicular traffic flow characteristics with different parameters are studied. Throughput, phase diagrams, space-time and density profiles are built to point various traffic states and the phase transition features. The principal finding of the simulation are as follows: (1) The presence of crossing pedestrians has a significant influence on the vehicular traffic and the system performance, (2) The intersection capacity has a close relevance with the state of the weaving section. The smaller the interactions are at the weaving section, the higher the capacity and (3) In order to have a higher system ability, the crosswalk location should not be far from the yield line of the weaving section.

In this paper, we propose a stochastic cellular automata model to study the traffic behavior at a single-lane roundabout. Vehicles can enter the interior lane or exit from it via $N$ intersecting lane, the boundary conditions are stochastic. The traffic is controlled by a self-organized scheme. It has turned out that depending on the rules of insertion to the roundabout, five distinct traffic phases can appear, namely, free flow, congestion, maximum current, jammed and gridlock. The transition between the free flow and the gridlock is forbidden. The density profiles are used to study the traffic pattern at the interior lane of the roundabout. In order to quantify the interactions between vehicles in the interior lane of the roundabout, the velocity correlation coefficient (VCC) is also studied. Besides, the spatiotemporal diagrams corresponding to the entry/exit lanes are derived numerically. Furthermore, we have investigated the effect of displaying signal ($P_{\mathrm{\text{In}}})$, as the $P_{\mathrm{\text{In}}}$ decreases, the maximum current increases at the expense of the free flow and the jamming phase. Finally, we have investigated the effect of the braking probability $P$ on the interior lane of the roundabout. We have found that the increase of $P$ raises the spontaneous jam formation on the ring. Thus, enlarges the maximum current and the jamming phase while the free flow phase decreases.

Using the Nagel-Schreckenberg model, we investigate the flow characteristics in a traffic circle system, where the entry lanes are controlled by traffic lights operating in a fixed-time ($T)$. We considered four different strategies to control traffic coming from $N$ entry lanes. We found that depending on the strategy used, four distinct traffic phases can appear in the circulating lane of the traffic circle, namely free flow, congestion, maximum current, and gridlock. Also, we investigate the origin of the gridlock phase in both cases (i.e. with/without traffic lights). Furthermore, the lengths of queues of stopped vehicles in the entry lanes were studied. We found that the traffic flow behavior on the exit/entry lanes depends strongly on the flow characteristics at the circulating lane as well as traffic lights strategy. To improve the operation of the traffic circle system, we have studied the time delay between the traffic lights to switch where all entry lanes go red, which allowing vehicles to clear the circulating lane.

In this work, we have performed Monte Carlo simulations to study phase transitions in a mixed spin-1 and spin-3/2 Ising ferrimagnetic system on the square and cubic lattices and with two different single-ion anisotropies. These lattices are divided in two interpenetrating sublattices with spins $S^A=1$ (states $\pm 1$ and 0) on the sublattice $A$ and $S^B=3∕2$ (states $\pm 3∕2$, $\pm 1∕2$) on the sublattice $B$. We have used single-ion anisotropies $D_A$ and $D_B$ acting on the sites of the sublattice $A$ and $B$, respectively. We have determined the phase diagrams of the model in the temperature $T$ vs. the single-ion anisotropies strength $D_A$ and $D_B$ plane and shown that the system exhibits both second- and first-order phase transitions. This system also displays compensation points for some values of the anisotropies.