International Journal of Modern Physics C

This paper investigates the factors influencing the spread of popular topic competition from the perspective of propagation dynamics. The popularity of a topic is directly influenced by the level of people’s interest in it. The rarity, deviation and type can influence the level of interest in such topics. In addition, the topic publisher also has an impact on the competitive dissemination of the topic. The higher the rank of the original publisher is, the easier it spreads. Compared with small bloggers without fans, it is easier to attract people’s attention, and the heat of the topic will rise faster. The results show that the rarer the topic, the greater the deviation from reality, and the more followers the originator has, the more competitive it is.

The speed limit signs can be used to enhance traffic safety, nevertheless, the large differences between the speed of vehicles provoked by the speed limit zone (SLZ) may increase the dissipation of energy caused by the deceleration of vehicles. In this paper, the effect of the SLZ on traffic flow and energy dissipation is investigated based on a cellular automaton model that considers the three traffic phases (free flow, synchronized flow and wide moving jams). It is found that the throughput and the energy dissipation depend strongly on the length of the SLZ as well as on the speed adopted inside the SLZ. The microscopic effect of the SLZ is also studied. The dependence of the density and the length of platoons induced by the SLZ were evaluated. The characteristic of the traffic flow can be also evaluated with the energy dissipation. For high densities, the effect of the SLZ becomes seldom on the flow, however, the energy dissipation shows salient features, which can be used as an indicator of traffic phases.

We investigate the statistical properties of multi-scale regression model based on detrending moving average (DMA). The performance of the multi-scale regression estimator based on DMA is evaluated by varying the length, distribution and structure for different position parameters. Using different position parameters for the detrending windows in simulation, we find that the variance of the estimated regression coefficients for position parameter $\theta =0.5$ is the smallest. By changing series length, distribution and structure, the estimated regression coefficients are stably near the theoretical values. The method is applied to analyze the dependence of inter-earthquakes time (IET) on inter-earthquakes distances (IED) between consecutive earthquakes in the California region. Results suggest that the cross-correlation between the IET and IED series is statistically significant. Scale-dependent statistic of estimated DMA multi-scale regression coefficient demonstrates significant dependence between IET and IED series.

Network topology is the basic for the development of traffic management and control. In a road network, bayonets with installation of surveillance facilities are key components to recognize traffic congestion from time to time. Therefore, identifying the essential bayonets in a road network becomes one of the most efficient ways to alleviate traffic congestion for traffic engineers and transport department. To do so, this paper aims to propose a novel sorting algorithm based on similarity measurements and traffic flow information to efficiently identify key bayonets in road networks. Our research results show that by analyzing the bayonet data in a fixed period of time in a medium-sized city of China, we have successfully identified the location of key bayonet points. Most of these key bayonet points are closed to residential areas and important traffic stations. The rank of these bayonet points can help the city managers better understand the topological characteristics of the road network as well as the propagation of congestion so as to make the traffic policies or control strategies for traffic congestion alleviation.

A modified continuum traffic flow model is established in this paper based on an extended car-following model considering driver’s reaction time and distance. The linear stability of the model and the Korteweg–de Vries (KdV) equation describing the density wave of traffic flow in the metastable region are obtained. In the new model, the relaxation term and the dissipation term exist at the same time, thus the type and stability of equilibrium solution of the model can be analyzed on the phase plane. Based on the equilibrium point, the bifurcation analysis of the model is carried out, and the existence of Hopf bifurcation and saddle-node bifurcation is proved. Numerical simulations show that the model can describe the complex nonlinear dynamic phenomena observed in freeway traffic, such as local cluster effect. Various bifurcations of the model, such as Hopf bifurcation, saddle-node bifurcation, Limit Point bifurcation of cycles, Cusp bifurcation and Bogdanov–Takens bifurcation, are also obtained by numerical simulations, and the traffic behaviors of some bifurcations are studied. The results show that the numerical solution is consistent with the analytical solution. Consequently, some nonlinear traffic phenomena can be analyzed and predicted from the perspective of global stability.

In this paper, a high-order hybrid method for solving compressible two-phase fluid flow, including cavitation, is presented. In this regard, assuming pressure and temperature equilibrium, mass and heat transfer between the different phases are modeled. In this work, the CRMWENOZ method, which is a new combination of compact and weighted essentially non-oscillatory (WENO) methods and is more accurate than conventional methods, is presented. The new high-order hybrid method aims to predict the density and the pressure discontinuities in two-phase flow by combining the CRMWENOZ high-order method and an adaptive moving mesh technique. For this purpose, the adaptive moving mesh partial differential equation (MMPDE) method would also improve the accuracy of results by concentrating on the grid nodes in high-gradient regions for transient flows. Applying the CRMWENOZ method alongside MMPDE and using the fifth-order Radau method for time discretization lead to a substantial improvement in the accuracy of simulation, particularly near the liquid–gas interfaces. The accuracy of the proposed hybrid method was compared to other studies’ predictions of one-dimensional (1D) expansion and shock tube problems containing two-phase flow with and without cavitation. The results showed that the hybrid method presented was more accurate than the usual two-phase flow methods while using a reasonable amount of computer resources.

With the increasing complexity and demand for transportation networks, effective routing planning has attracted more and more attention. Different modes of transportation, such as the airplane, railway and so on, work together, forming a multi-modal transportation network. Therefore, this paper studies the routing and congestion problems in the multi-modal transportation network, and shows how to increase the network capacity as much as possible while saving time and economic costs, so as to avoid congestion and realize the effective use of different modes of transportation. This paper simulates the influence of two main factors on the network capacity, the parameter which shows the importance between time costs and economic costs, and the difference between different transportation modes. The results show the change of the network capacity when the time cost and economic cost are of different importance. There exists a critical point that can balance time costs and economic costs, so as to maximize network capacity. Then this paper further finds out the method of estimating the condition when the network takes the maximum capacity through theoretical analysis.

By incorporating the interruption probability effect, this paper provides a novel lattice hydrodynamic model for two lanes. The two-lane stability is investigated from linear stable analysis, which implies that the interruption probability effect can extend the stable region in the two-lane system. Moreover, the density waves and the hysteresis loops shrink from simulation tests as the intensity of the interruption probability effect increases, which indicates that the interruption probability effect strengthens the two-lane stability. More importantly, the fuel consumption and emissions fall down clearly with the interruption probability effect increasing on two lanes according to simulation tests.

Legendre polynomials’ first derivatives have been used as the basis function via the pseudo-Galerkin spectral method. Operational matrices for derivatives have been used and extended to deal with the system of ordinary differential-algebraic equations. An algorithm via those matrices has been designed. The accuracy and efficiency of the proposed algorithm had been shown by two techniques, theoretically, via the boundedness of the approximated expansion and numerically through numerical examples.

Understanding, predicting and controlling the motion of the solid particles became active research topics, like debris flows, sand storms, transport of volcanic ash, coal combustion, drug delivery and steel making. Thus, the motion of a neutrally buoyant elliptical particle in a double-lid-driven square cavity is studied with the lattice Boltzmann method, where the effects of the initial position, Reynolds number and aspect ratio are studied. The square cavity is divided into two parts by the two primary vortexes, and the motion of the elliptical particle is determined by the interaction of the two primary vortexes. The limit cycle is sensitive to the initial position of the elliptical particle, namely, placing the elliptical particle at different positions initially, the motion of the elliptical particle exhibits different modes. Especially, the elliptical particle is apt to cross the horizontal centerline of the square cavity at moderate Reynolds numbers. The effect of the Reynolds number on the motion of the elliptical particle is significant, with the increase of the Reynolds number, the effects of the two primary vortexes on the motion of the elliptical particle are different, which affects the trajectory of the elliptical particle fundamentally. With the increase of the aspect ratio, the elliptical particle becomes flatter, the hydrodynamic force and torque acting on the elliptical particle become unbalanced and the elliptical particle no longer moves along the 8-like limit cycle.

Multi-scale behaviors emerge in financial markets as complex systems. In this study, we intended to employ multi-scale Shannon entropy to trace the information transition of these phenomena, at different levels of Tehran stock market index (TEDPIX). The obtained results show that, in various magnitude scales and time scales, entropy Granger-causes TEDPIX index in terms of linear and nonlinear aspects. The results revealed that Granger causalities exist between entropy and TEDPIX. The causalities were linear in monthly (noise), quarterly (noise), semi-yearly (noise) and yearly (useful information) time spans; on the other hand, in quarterly (useful information) time span, the causalities were nonlinear. In this regard, one can conclude that entropy would be able to predict the market’s behavior.

The essence of traffic congestion is a kind of bifurcation behavior incurred by the loss of stability in the traffic flow from the perspective of system stability. Therefore, researching the bifurcation characteristics of traffic flow can provide some new methods for relieving the traffic congestion. In this paper, we study the bifurcation dynamic behavior and the bifurcation conditions of traffic flow based on Kühne’s continuum traffic flow model. We discussed the types and stabilities of the equilibrium solutions and proved the existence conditions of some bifurcation of the model. Then various bifurcations of the system are found by numerical simulation and the stability catastrophic behaviors initiated by some bifurcation in traffic flow are investigated. Combined with the measured data, we study the actual traffic flow bifurcation phenomena and analyze the internal reasons for the stability catastrophic behavior of traffic flow passed by the bifurcation point. The nonlinear characteristics and formation mechanism of traffic flow phenomena are revealed from a new perspective. It may help to design the corresponding control schemes for preventing and alleviating traffic congestion.

Fresnel diffraction is a fundamental wave phenomenon happening near the shadow boundary behind a large opaque object. Previously, it was studied for the case of diffraction at large apertures in a black screen. In this paper, we investigate this phenomenon for perfectly conducting cylinders with large cross-sections. First, this theory is developed for the circular cylinders, then extended to the cylinders of arbitrary shape. It is shown that Fresnel diffraction can be interpreted as interference of the shadow radiation with the incident wave. Analytical equations and numerical data are provided and discussed in detail.

One of the problems in the numerical analysis of solutions is the nonlinear variable-order fractional convection-diffusion equations for nonsmooth solutions. We offer a numerical technique based on the shifted Legendre Gauss-Lobatto collocation and the shifted Chebyshev Gauss-Radau collocation to solve the problem. The technique with shifted Legendre Gauss-Lobatto and shifted Chebyshev Gauss-Radau nodes is applied to diminish nonlinear variable-order fractional convection-diffusion equations to an easily-solvable system of algebraic equations. Besides, we give numerical test examples to show that the approach can preserve the nonsmooth solution of the underlying problems.