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.     

Effect of looking backward on traffic flow in a cooperative driving car following model

An extended car following model is proposed by incorporating intelligent transportation system and the backward looking effect under certain condition in traffic flow. The neutral stability condition of this model is obtained by using the linear stability theory. The results show that anticipating the behavior of vehicles preceding and following one vehicle could lead to appreciable stabilization of traffic system. From the simulation of space-time evolution of the vehicle headways, it is shown that the traffic jam could be suppressed efficiently via taking into account the information about the motion of two preceding vehicles and one following vehicle, and the analytical result is consistent with the simulation one.     

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.     

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.     

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.     

A new method to study phase transition in 3D Heisenberg model

It is shown that partial entropy, which is the classical analog of von Neumann entropy in quantum theory, is an effective tool to study the thermodynamic phase transitions in the physical systems. This method captures the intrinsic characters of critical fluctuations and does not need the pre-assumed order parameter. As an example, the finite temperature phase transition in the quantum three-dimensional spin-1/2 Heisenberg model is studied, where the stochastic series expansion quantum Monte Carlo method with operator-loop update is used. It is found that close to the critical temperature, the derivative of partial entropy displays a maximum value and shows finite size scaling behaviors, from which the critical temperature and critical exponents are determined.     

Nonequilibrium phase transition in the kinetic Ising model on a two-layer square lattice under the presence of an oscillating field

The nonequilibrium or dynamic phase transitions are studied, within a mean-field approach, in the kinetic Ising model on a two-layer square lattice consisting of spin- 1/2 ions in the presence of a time varying (sinusoidal) magnetic field has been studied by using Glauber-type stochastic dynamics. The dynamic equations of motion are obtained in terms of the intralayer coupling constants J₁ and J₂ for the first and second layer, respectively, and interlayer coupling constant J₃ between these two layers. The nature (first- or second-order) of the transitions is characterized by investigating the behavior of the thermal variations of the dynamic order parameters. The dynamic phase transitions are obtained and the dynamic phase diagrams are constructed in the plane of the reduced temperature versus the amplitude of the magnetic field and found fourteen fundamental types of phase diagrams. Phase diagrams exhibit one, two or three dynamic tricritical points for various values of J₂/|J₁| and J₃/|J₁|. Besides the paramagnetic (p), ferromagnetic (f) and compensated (c) phases, there were the f+c,f+sf,c+sf,af+p,m+p,f+m and c+af, where the af, sf and m are the antiferromagnetic, surface ferromagnetic and mixed phases respectively. Coexistence phase regions also exist in the system.     

Dynamic compensation temperature in the kinetic spin-1 Ising model in an oscillating external magnetic field on alternate layers of a hexagonal lattice

The dynamic behavior of a two-sublattice spin-1 Ising model with a crystal-field interaction (D) in the presence of a time-varying magnetic field on a hexagonal lattice is studied by using the Glauber-type stochastic dynamics. The lattice is formed by alternate layers of spins σ=1 and S=1. For this spin arrangement, any spin at one lattice site has two nearest-neighbor spins on the same sublattice, and four on the other sublattice. The intersublattice interaction is antiferromagnetic. We employ the Glauber transition rates to construct the mean-field dynamical equations. Firstly, we study time variations of the average magnetizations in order to find the phases in the system, and the temperature dependence of the average magnetizations in a period, which is also called the dynamic magnetizations, to obtain the dynamic phase transition (DPT) points as well as to characterize the nature (continuous and discontinuous) of transitions. Then, the behavior of the total dynamic magnetization as a function of the temperature is investigated to find the types of the compensation behavior. Dynamic phase diagrams are calculated for both DPT points and dynamic compensation effect. Phase diagrams contain the paramagnetic (p) and antiferromagnetic (af) phases, the p+af and nm+p mixed phases, nm is the non-magnetic phase, and the compensation temperature or the L-type behavior that strongly depend on the interaction parameters. For D<2.835 and H₀>3.8275, H₀ is the magnetic field amplitude, the compensation effect does not appear in the system.     

Partition function zeros of the antiferromagnetic Ising model on triangular lattice in the complex temperature plane for nonzero magnetic field

The grand partition functions Z(T,B)$Z(T,B)$ of the Ising model on L×L$L\times L$ triangular lattices with fully periodic boundary conditions, as a function of temperature T and magnetic field B  , are evaluated exactly for L<12$L<12$ (using microcanonical transfer matrix) and approximately for L?12$L?12$ (using Wang–Landau Monte Carlo algorithm). From Z(T,B)$Z(T,B)$, the distributions of the partition function zeros of the triangular-lattice Ising model in the complex temperature plane for real B≠0$B\ne 0$ are obtained and discussed for the first time. The critical points aN(x)$a_N(x)$ and the thermal scaling exponents yt(x)$y_t(x)$ of the triangular-lattice Ising antiferromagnet, for various values of x=e−2βB$x=e^{-2\beta B}$, are estimated using the partition function zeros.     

Magnetic phase diagram of the Ca1−xMnxO systems

The magnetic properties of the Ca_1−xMn_xO systems in the range 0?x?1 have been studied by mean field theory and high-temperature series expansions (HTSEs). By using the first theory, we have evaluated the nearest neighbour and the next-neighbour super-exchange interaction J₁(x) and J₂(x) respectively, in the range 0.45?x?1. The corresponding classical exchange energy for magnetic structure is obtained for the Ca_1−xMn_xO systems. The HTSEs combined with the Padé approximants (PA) method is applied to the Ca_1−xMn_xO systems; we have obtained the magnetic phase diagrams (TN or TSG versus dilution x) in the range 0?x?1. The obtained theoretical results are in agreement with experimental ones obtained by magnetic measurements. The critical exponents associated with the magnetic susceptibility (γ) and the correlation lengths (ν) are deduced in the range 0?x?1.     

Random bond Potts model: The test of the replica symmetry breaking

The averaged spin-spin correlation function squared is calculated for the ferro-magnetic random bond Potts model in two dimensions. The technique being used is the renormalization group plus conformal field theory. The results are of the E-expansion type fixed point calculation, E being the deviation of the central charge (or the number of components) of the Potts model from the Ising model value. Calculations are done both for the replica symmetric and the replica symmetry broken fixed points. The results obtained allow for numerical simulation tests to decide between the two different criticalities of the random bond Potts model.     

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.     

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.     

Universal amplitudes and profiles for critical adsorption

The analysis of published experimental data for seven different binary liquid mixtures allows us to test the concept of universality for critical phenomena at interfaces and to compare the values of three independent universal surface amplitudes with theoretical predictions. In spite of uncomfortable large experimental error bars in the case of one surface amplitude we find agreement for five different systems and disagreement for two. For the other two surface amplitudes we obtain a marginal agreement between theory and experiment which is impeded by the lack of experimental error bars. We also test the scaling functions for critical adsorption. In view of the complexity of the data analysis the agreement between theory and experiment is satisfactory and encouraging. Experimental improvements are suggested in order to obtain more stringent tests.Dedicated to H. Wagner on the occasion of his 60th birthday     

Monte Carlo study of the change of critical temperature in a diluted Ising model due to configuration disorder

Monte Carlo simulations on a diluted Ising Hamiltonian were used to obtain the susceptibility of virtual binary samples (conformed by ferromagnetic atoms and non-magnetic atoms) on a bcc lattice. Samples size of L=10$L=10$ were constructed with different configuration order using random mixtures. The susceptibility curves illustrate that the critical temperature decreases when the disorder in the samples increase. From fittings of the exchange interaction versus the concentration of non-magnetic atoms it was possible to reasonably describe the magnetic phase diagram of the Fe_1−qAlq${\mathrm{Fe}}_{1-q}{\mathrm{Al}}_q$ alloys.     

Classical two-site fidelity and quantum phase transitions in the Ising model and the extended Hubbard model

In this Letter, the classical two-site-ground-state fidelity (CTGF) is exploited to identify quantum phase transitions (QPTs) for the transverse field Ising model (TFIM) and the one-dimensional extended Hubbard model (EHM). Our results show that the CTGF exhibits an abrupt change around the regions of criticality and can be used to identify QPTs in spin and fermionic systems. The method is especially convenient when it is connected with the density-matrix renormalization group (DMRG) algorithm.     

Excitations in the dilute lattice model: , and mass spectra

On the basis of features observed in the exact perturbation approach solution for the eigenspectrum of the dilute A₃ model, we propose expressions for excitations in the dilute A₄ and A₆ models. Principally, we require that these expressions satisfy the appropriate inversion relations. We demonstrate that they give the expected E₇ and E₆ mass spectra, and universal amplitudes, and agree with numerical expressions for the eigenvalues. Received: 17 February 1998 / Accepted: 30 April 1998     

Renormalized vertex modification of Hall conductivity for dilute magnetic alloys

By means of the renormalized vertex procedure for the motion of Green's function developed by the authors, the vertex function of magnetic alloys, based on thes-d exchange interaction, is solved exactly and the corresponding Hall conductivity tensors are obtained. It is found that the value of the renormalized Hall conductivity is (1+h ²)^–1 times less than that before the renormalization (hereh is a reduced magnetic field). It is shown that the renormalized modification of the conductivity is very important in the cases with not too weak external magnetic field and slow relaxation time.     

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.     

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.