An Incompressible Three-Dimensional Multiphase Particle-in-Cell Model for Dense Particle Flows

A three-dimensional, incompressible, multiphase particle-in-cell method is presented for dense particle flows. The numerical technique solves the governing equations of the fluid phase using a continuum model and those of the particle phase using a Lagrangian model. Difficulties associated with calculating interparticle interactions for dense particle flows with volume fractions above 5% have been eliminated by mapping particle properties to an Eulerian grid and then mapping back computed stress tensors to particle positions. A subgrid particle, normal stress model for discrete particles which is robust and eliminates the need for an implicit calculation of the particle normal stress on the grid is presented. Interpolation operators and their properties are defined which provide compact support, are conservative, and provide fast solution for a large particle population. The solution scheme allows for distributions of types, sizes, and density of particles, with no numerical diffusion from the Lagrangian particle calculations. Particles are implicitly coupled to the fluid phase, and the fluid momentum and pressure equations are implicitly solved, which gives a robust solution.     

Effect of relevant umklapp process on the two-leg Hubbard ladder with a half-filled band under pressure

By means of perturbative renormalization approach we study the effect of relevant umklapp process on dimensional crossover caused by interladder one particle hopping in weakly coupled two-leg Hubbard ladders with a half filled-band. We found that a crossover takes place at a finite value which increases as the amplitude of umklapp process increases. For the system undergoes a phase transition to the spin density wave phase (SDW) via the two particle hopping process, while for the system undergoes a crossover to the two dimensional Fermi liquid phase via one particle hopping process. Received 25 December 1998     

Theoretical vs. empirical classification and prediction of congested traffic states

Starting from the instability diagram of a traffic flow model, we derive conditions for the occurrence of congested traffic states, their appearance, their spreading in space and time, and the related increase in travel times. We discuss the terminology of traffic phases and give empirical evidence for the existence of a phase diagram of traffic states. In contrast to previously presented phase diagrams, it is shown that “widening synchronized patterns” are possible, if the maximum flow is located inside of a metastable density regime. Moreover, for various kinds of traffic models with different instability diagrams it is discussed, how the related phase diagrams are expected to approximately look like. Apart from this, it is pointed out that combinations of on- and off-ramps create different patterns than a single, isolated on-ramp.     

Phase diagram of Bose-Fermi mixtures in one-dimensional optical lattices

The ground state phase diagram of the one-dimensional Bose-Fermi Hubbard model is studied in the canonical ensemble using a quantum Monte Carlo method. We focus on the case where both species have half filling in order to maximize the pairing correlations between the bosons and the fermions. In case of equal hopping we distinguish among phase separation, a Luttinger liquid phase, and a phase characterized by strong singlet pairing between the species. True long-range density waves exist with unequal hopping amplitudes.     

The phase diagram and the pathway of phase transitions for traffic flow in a circular one-lane roadway

This paper demonstrates that patient driving habits lead to homogenous congested flow while impatient driving habits lead to wide-moving jam flow in the high density region based on the numerical simulation of the intelligent driver model proposed by M.Treiber [M. Treiber, A.Hennecke, D. Helbing, Phys. Rev. E 62 (2) (2000), 1805-1824]. In a circular one lane traffic system which includes homogeneous drivers, we obtain the stable condition of homogenous flow and the phase diagram of traffic flow based on the linearization analysis. The phase diagram shows three possible pathways of phase transition along with the increase of global density: from the homogenous free flow to the homogenous congested flow directly, from the homogenous free flow to the synchronized flow then to the homogenous congested flow, or from the homogenous free flow to synchronized flow then to the wide-moving jam flow. The paper also analyzes the traffic flow including heterogenous drivers, and the results indicate that homogenous congested flow will lose its stability when the proportion of impatient drivers reaches a critical value and some new kinds of traffic flow emerge: wide-moving jam flow or a mixture of synchronized flow and wide-moving jam flow.     

速度限制对交通流的影响

运用元胞自动机模型研究单车道路面上设立限速区对交通流的影响.计算机模拟结果显示,在交通流与密度的基本图中存在饱和交通流量,其大小取决于限速区的最大速度.限速区的设立导致不同相的分离.在确定性的模型中,当车辆密度较低时,存在两种不同的自由流相;而当车辆密度较高时,出现最大交通流相和自由流相.在随机模型中,车辆密度较高时,出现最大交通流相-堵塞相-自由流.对交通流以及临界密度等量给出一些解析结果.     

Compositional dependence of the electrical conductivity of calcium vanadate glassy semiconductors

Scanning electron microscopy (SEM), X- ray diffraction (XRD), density (d), oxygen molar volume (V_m) and dc conductivity of different compositions of calcium vanadate glasses are reported. SEM exhibits a surface without any presence of a microstructure which is a characteristic of the amorphous phase. The overall features of these XRD curves confirm the amorphous nature of the present glasses. Density was observed to decrease with an increase in V₂O₅ content. The experimental results were analyzed with reference to theoretical models existing in the literature. It has been observed that the high-temperature conductivity data are consistent with Mott's nearest-neighbor hopping model. However, both Mott variable-range hopping (VRH) and Greaves intermediate range hopping models are found to be applicable. The hopping at high temperatures in the calcium vanadate glasses occurs by non-adiabatic process in contrast to the vanadate glasses formed with conventional network formers. The hopping model of Schnakenberg can predict the temperature dependence of the conductivity data. The percolation model of Triberis and Friedman applied to the small polaron hopping (SPH) regime is also consistent with data. The various model parameters such as density of states, hopping energy, etc., obtained from the best fits were found to be consistent with the glass compositions.     

元胞自动机交通流模型的相变特性研究

系统地研究 VDR模型和T²模型在不同车流密度时车辆位置的相关性. 通过VDR模型、BJH模型和T²模型的序参量计算，确定在这三个模型中车流从自由流动到阻塞的相变特性，结果发现引入慢启动规则后，在不同的延迟概率和最大速度情况下，将引起交通相变特性的改变. 关键词： 交通流 元胞自动机 相关函数 序参量     

A theoretical model for uni-directional ant trails

A theoretical model of uni-directional ant traffic, motivated by the motion of ants in trail is proposed. Two different type of ants, one of which smells very well and the other does not, are considered. The flux of ants in this model is investigated as functions of the probability of evaporation rate of pheromone. The obtained results indicate that the mean velocity of the ants varies non-monotonically with their density. In addition, it is observed that phase transition in the flux and the mean velocity vs. density occurs at certain density for a fixed evaporation rate. The effective hopping probability is investigated as well depending on the evaporation rate of pheromone. It is worth to note that the proposed model can be generalized for vehicular traffic on freeways.     

The ground state of the two-leg Hubbard ladder a density-matrix renormalization group study

We present density-matrix renormalization group results for the ground state properties of two-leg Hubbard ladders. The half-filled Hubbard ladder is an insulating spin-gapped system, exhibiting a crossover from a spin liquid to a band insulator as a function of the interchain hopping matrix element. When the system is doped, there is a parameter range in which the spin gap remains. In this phase, the doped holes from singlet pairs and the pair field and the “4k_F” density correlations associated with pair-density fluctuations decay as power laws, while the “2k_F” charge density wave correlations decay exponentially. We discuss the behavior of the exponents of the pairing and density correlations within this spin-gapped phase. Additional one-band Luttinger liquid phases which occur in the large interband hopping regime are also discussed.     

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).     

Vehicular motion in counter traffic flow through a series of signals controlled by a phase shift

We study the dynamical behavior of counter traffic flow through a sequence of signals (traffic lights) controlled by a phase shift. There are two lanes for the counter traffic flow: the first lane is for east-bound vehicles and the second lane is for west-bound vehicles. The green-wave strategy is studied in the counter traffic flow where the phase shift of signals in the second lane has opposite sign to that in the first lane. A nonlinear dynamic model of the vehicular motion is presented by nonlinear maps at a low density. There is a distinct difference between the traffic flow in the first lane and that in the second lane. The counter traffic flow exhibits very complex behavior on varying the cycle time, the phase difference, and the split. Also, the fundamental diagram is derived by the use of the cellular automaton (CA) model. The dependence of east-bound and west-bound vehicles on cycle time, phase difference, and density is clarified.     

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.     

Exploring jamming transitions and density waves in bidirectional pedestrian traffic

In this paper we propose a two-dimensional lattice hydrodynamic model considering path change in the bidirectional flow of pedestrians on the road. The stability condition and the mKdV equation describing the density wave of pedestrian traffic jamming are obtained by linear stability and nonlinear analyses. The phase diagram produced from these analyses indicates that the phase transition occurs amongst the freely moving phase, the coexisting phase and the uniformly congested phase below the critical point a_c. Additionally the results reveal the existence of a critical magnitude of path change (γ_c). Once the magnitude of path change exceeds the critical value, it gives rise to unstable density waves. Moreover, numerical simulations are performed and the results are in accordance with the theoretical analyses.     

Phase diagrams properties of the mixed traffic flow on a crossroad

Based on the Ishibashi and Fukui crossroad traffic flow model [Y. Ishibashi and M. Fukui. J. Phys. Soc. Japan. 70 (2001) 2793], mixed traffic flow (i.e., the fast and slow vehicles with different maximum velocities are mixed) is investigated in this work. According to the numerical simulation results and the principle for constructing the phase diagram, phase diagrams for mixed traffic flow are constructed. It is noted that the topology of these phase diagrams is similar to that of phase diagrams for homogeneous vehicles (which refers to slow vehicles only). From the phase diagrams, it is evident that mixed traffic flow is influenced by the mixing rate f (fraction of slow and fast vehicles) in regions II and V, but not in other regions. Although a mixture of fast and slow vehicles is introduced in the crossroad traffic flow model, the separation between phases in the phase diagrams remains linear. For a given q (the vehicle density on the northbound road), one flow plateau appears in regions IIx or IVy, while two maximum flow plateaus appear in region V in each of the phase diagrams. The maximum flow values in region V reflect the maximum traffic capacity for the traffic system as defined in this work. Since mixed traffic flow is a common phenomenon in real traffic, this work may offer help in real traffic simulations and traffic management.     

Modeling Three-Dimensional Multiphase Flow Using a Level Contour Reconstruction Method for Front Tracking without Connectivity

Three-dimensional multiphase flow and flow with phase change are simulated using a simplified method of tracking and reconstructing the phase interface. The new level contour reconstruction technique presented here enables front tracking methods to naturally, automatically, and robustly model the merging and breakup of interfaces in three-dimensional flows. The method is designed so that the phase surface is treated as a collection of physically linked but not logically connected surface elements. Eliminating the need to bookkeep logical connections between neighboring surface elements greatly simplifies the Lagrangian tracking of interfaces, particularly for 3D flows exhibiting topology change. The motivation for this new method is the modeling of complex three-dimensional boiling flows where repeated merging and breakup are inherent features of the interface dynamics. Results of 3D film boiling simulations with multiple interacting bubbles are presented. The capabilities of the new interface reconstruction method are also tested in a variety of two-phase flows without phase change. Three-dimensional simulations of bubble merging and droplet collision, coalescence, and breakup demonstrate the new method's ability to easily handle topology change by film rupture or filamentary breakup. Validation tests are conducted for drop oscillation and bubble rise. The susceptibility of the numerical method to parasitic currents is also thoroughly assessed.     

Traffic states and fundamental diagram in cellular automaton model of vehicular traffic controlled by signals

We present a cellular automaton (CA) model for vehicular traffic controlled by traffic lights. The CA model is not described by a set of rules, but is given by a simple difference equation. The vehicular motion varies highly with both signals’ characteristics and vehicular density. The dependence of tour time on both cycle time and vehicular density is clarified. In the dilute limit of vehicles, the vehicular motion is compared with that by the nonlinear-map model. The fundamental diagrams are derived numerically. It is shown that the fundamental diagram depends highly on the signals’ characteristics. The traffic states are shown for various values of cycle time in the fundamental diagram. We also study the effect of a slow vehicle on the traffic flow.     

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.     

Structure and magnetostriction of RFex (1.6 ? x ? 2.0) and R(Fe1−yTiy)1.8 (y ? 0.2) alloys (RDy0.65Tb0.25Pr0.1)

Structure, Curie temperature and magnetostriction of RFe_x (1.6 ? x ? 2.0) and R(Fe_1−yTi_y)_1.8 (y ? 0.2) alloys (RDy_0.65Tb_0.25Pr_0.1) have been investigated using optical microscopy, X-ray diffraction, AC initial susceptibility and standard strain gauge techniques. The homogenized RFe_x alloys are found to be essentially single phase in the range of 1.8 ? x ? 1.85. The second phase is a rare-earth-rich phase when x ? 1.8, and (Dy, Tb, Pr)Fe₃ phase when x ? 1.85. X-ray diffraction indicates that the R(Fe_1−yTi_y)_1.8 alloys contain a small amount of Fe₂Ti phase when y ? 0.05, which increases with the increment of Ti content. The Curie temperature of R(Fe₁−_yTi_y)_1.8 alloys slightly enhances with increasing Ti concentration when y ? 0.05, then remains almost unchanged in the range of 0.05 ? y ? 0.20. The magnetostriction of RFe_x alloys is improved when x ? 1.80 and reduced by increasing Fe content when x ? 1.85. The magnetostriction of R(Fe_1−yTi_y)_1.8 alloys is lowered by increasing Ti content.