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.     

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.     

Effective-field theory of the Ising model with three alternative layers on the honeycomb and square lattices

The Ising model with three alternative layers on the honeycomb and square lattices is studied by using the effective-field theory with correlations. We consider that the nearest-neighbor spins of each layer are coupled ferromagnetically and the adjacent spins of the nearest-neighbor layers are coupled either ferromagnetically or anti-ferromagnetically depending on the sign of the bilinear exchange interactions. We investigate the thermal variations of the magnetizations and present the phase diagrams. The phase diagrams contain the paramagnetic, ferromagnetic and anti-ferromagnetic phases, and the system also exhibits a tricritical behavior.     

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     

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.     

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.     

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.     

Two velocity difference model for a car following theory

In the light of the optimal velocity model, a two velocity difference model for a car-following theory is put forward considering navigation in modern traffic. To our knowledge, the model is an improvement over the previous ones theoretically, because it considers more aspects in the car-following process than others. Then we investigate the property of the model using linear and nonlinear analyses. The Korteweg-de Vries equation (for short, the KdV equation) near the neutral stability line and the modified Korteweg-de Vries equation (for short, the mKdV equation) around the critical point are derived by applying the reductive perturbation method. The traffic jam could be thus described by the KdV soliton and the kink-anti-kink soliton for the KdV equation and mKdV equation, respectively. Numerical simulations are made to verify the model, and good results are obtained with the new model.     

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).     

A renormalization-group analysis of a spin-1 Ising ferromagnet with competing crystal-field and repulsive biquadratic interactions

Phase diagrams have been produced and critical exponents calculated for a Blume-Emery-Griffiths system with competing biquadratic and crystal-field interactions with uniform ferromagnetic bilinear interactions. This competition directly effects the clustering and density of nonmagnetic impurities. These results have been produced using renormalization-group methods with a hierarchical lattice. A series of planes of constant, repulsive biquadratic coupling have been probed while varying the temperature and concentration of annealed vacancies in the system. The sinks have been analyzed and interpreted, and critical exponents calculated for the higher order transitions.     

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.     

The laws of establishing stationary composition in a droplet condensing in a binary vapor-gas environment

It is shown that the mole fractions of components within a droplet growing in an atmosphere of two condensing gases and a carrier gas approach their stationary values with a power-law behavior in time on a large scale and with exponential behavior on a small scale for both diffusion-controlled and free-molecular regimes of isothermal condensation. The parameters of the power and the exponential laws are specified for each regime of binary condensation and are linked to the thermodynamic and kinetic characteristics of condensing vapors and to the stationary mole fractions of the components in a growing binary droplet. The stationary composition of the solution within the droplet is shown to be established at a comparatively small relative increase of the droplet radius. A relaxation equation for the droplet composition at arbitrary initial deviations of mole fractions from their stationary values has been solved, and the limitations on the initial deviations allowing monotonic establishment of stationary composition in solution within a growing droplet have been considered.     

Phase transition and critical properties of spin-orbital interacting systems

Phase transition and critical properties of Ising-like spin-orbital interacting systems in 2-dimensional triangular lattice are investigated. We first show that the ground state of the system is a composite spin-orbital ferro-ordered phase. Though Landau effective field theory predicts the second-order phase transition of the composite spin-orbital order, however, the critical exponents obtained by the renormalization group approach demonstrate that the spin-orbital order-disorder transition is far from the second-order, rather, it is more close to the first-order. The unusual critical behavior near the transition point is attributed to the fractionalization of the composite order parameter.     

Finite size effects for the Ising model on random graphs with varying dilution

We investigate the finite size corrections to the equilibrium magnetization of an Ising model on a random graph with N nodes and N^γ edges, with 1<γ≤2. By conveniently rescaling the coupling constant, the free energy is made extensive. As expected, the system displays a phase transition of the mean-field type for all the considered values of γ at the transition temperature of the fully connected Curie-Weiss model. Finite size corrections are investigated for different values of the parameter γ, using two different approaches: a replica based finite N expansion, and a cavity method. Numerical simulations are compared with theoretical predictions. The cavity based analysis is shown to agree better with numerics.     

Analysis of car-following model considering driver’s physical delay in sensing headway

An extended car-following model is proposed by taking into account the delay of the driver’s response in sensing headway. The stability condition of this model is obtained by using the linear stability theory. The results show that the stability region decreases when the driver’s physical delay in sensing headway increases. The KdV equation and mKdV equation near the neutral stability line and the critical point are respectively derived by applying the reductive perturbation method. The traffic jams could be thus described by soliton solution and kink-antikink soliton solution for the KdV equation and mKdV equation respectively. The numerical results in the form of the space-time evolution of headway show that the stabilization effect is weakened when the driver’s physical delay increases. It confirms the fact that the delay of driver’s response in sensing headway plays an important role in jamming transition, and the numerical results are in good agreement with the theoretical analysis.     

A renormalization-group study of an Ising spin-glass with annealed vacancies

Systems driven and characterized by fluctuations in density and magnetization can be realistically modeled using the Blume–Emery–Griffiths model; a spin-1 Ising model with bilinear, biquadratic, and crystal-field interactions. In this study, renormalization-group techniques are used on an exactly solvable system in which frustration is present due to competing ferromagnetic and antiferromagnetic interactions. Thus, this calculation models a spin-glass system with annealed vacancies. To determine the effects of these competing bilinear interactions, an exactly solvable frustrated hierarchical model has been constructed, similar to those introduced to study spin glasses [S.R. McKay, A.N. Berker, S. Kirkpatrick, Phys. Rev. Lett. 48 (1982) 767]. Phase diagrams have been calculated for a series of planes of constant biquadratic coupling while varying the temperature and concentration of annealed vacancies in the system. In addition, a phase diagram was produced for constant concentration of annealed vacancies as the biquadratic coupling (i.e. clustering bias) was varied. Each phase diagram reveals three qualitatively unique basins of attraction, each corresponding to a phase distinguished by a unique renormalization-group trajectory. The sink of each trajectory is interpreted to determine the nature of each phase: dense paramagnetic, dilute paramagnetic and spin-glass.     

How heater filaments burn out: A new type of phase transitions

A simple model combining the most typical features of the physical phenomena involved in Ohmic heating of conductors is proposed. The instability associated with the one-dimensional Helmholtz equation used in the model sets in when boundary conditions are imposed at the ends of a section whose length coincides with the characteristic scale governing the change in the transport properties of the system. It has been found that this mechanism gives rise to formation of spatial structures as a result of a “dimensional” phase transition.     

A renormalization-group study into the effects of competing biquadratic and crystal-field interactions in the Blume–Emery–Griffiths model

The Blume–Emery–Griffiths model, a spin-1 Ising model with bilinear, biquadratic, and crystal field interactions, provides a general system for the analysis of systems driven by fluctuations in density and magnetization. In this study, we consider an exactly solvable system in which frustration is present due to competing biquadratic and crystal-field interactions. Thus, this calculation models a dilute ferromagnetic material with two types of nearest-neighbor site pairs, distinguished by whether or not simultaneous occupation is energetically favored. To determine the effects of this competition, we have constructed exactly solvable frustrated hierarchical models similar to those introduced to study spin glasses. The resulting phase diagrams reveal two distinct paramagnetic phases separated by a plane in parameter space in which the biquadratic interaction and crystal-field strength rescale chaotically. Each paramagnetic phase has a ferromagnetic complement in which the unique distribution of occupied sites possesses a net magnetization.     

The Glauber dynamics for a spin-1 metamagnetic Ising system with bilinear and biquadratic interactions

We present a study, within a mean-field approximation, of the dynamics of a spin-1 metamagnetic Ising system with bilinear and biquadratic interactions in the presence of a time-dependent oscillating external magnetic field. First, we employ the Glauber transition rates to construct the set of mean-field dynamic equations. Then, we study the time variation of the average order parameters to find the phases in the system. We also investigate the thermal behavior of dynamic order parameters to characterize the nature (first- or second-order) of the dynamic transitions. The dynamic phase transitions are obtained and the phase diagrams are constructed in two different the planes. The phase diagrams contain a disordered and ordered phases, and four different mixed phases that strongly depend on interaction parameters. Phase diagrams also display one or two dynamic tricritical points, a dynamic double critical end and dynamic quadruple points. A comparison is made with the results of the other metamagnetic Ising systems.     

Kinetics of a mixed spin-1/2 and spin-3/2 Ising ferrimagnetic model

We present a study, within a mean-field approach, of the kinetics of a mixed ferrimagnetic model on a square lattice in which two interpenetrating square sublattices have spins that can take two values, , alternated with spins that can take the four values, . We use the Glauber-type stochastic dynamics to describe the time evolution of the system with a crystal-field interaction in the presence of a time-dependent oscillating external magnetic field. The nature (continuous and discontinuous) of transition is characterized by studying the thermal behaviors of average order parameters in a period. The dynamic phase transition points are obtained and the phase diagrams are presented in the reduced magnetic field amplitude (h) and reduced temperature (T) plane, and in the reduced temperature and interaction parameter planes, namely in the (h, T) and (d, T) planes, d is the reduced crystal-field interaction. The phase diagrams always exhibit a tricritical point in (h, T) plane, but do not exhibit in the (d, T) plane for low values of h. The dynamic multicritical point or dynamic critical end point exist in the (d, T) plane for low values of h. Moreover, phase diagrams contain paramagnetic (p), ferromagnetic (f), ferrimagnetic (i) phases, two coexistence or mixed phase regions, (f+p) and (i+p), that strongly depend on interaction parameters.