Density waves in traffic flow model with relative velocity

The car-following model of traffic flow is extended to take into account the relative velocity. The stability condition of this model is obtained by using linear stability theory. It is shown that the stability of uniform traffic flow is improved by considering the relative velocity. From nonlinear analysis, it is shown that three different density waves, that is, the triangular shock wave, soliton wave and kink-antikink wave, appear in the stable, metastable and unstable regions of traffic flow respectively. The three different density waves are described by the nonlinear wave equations: the Burgers equation, Korteweg-de Vries (KdV) equation and modified Korteweg-de Vries (mKdV) equation, respectively.     

Analysis of stability and density waves of traffic flow model in an ITS environment

By introducing relative velocities of arbitrary number of cars ahead into the full velocity difference models (FVDM), we present a forward looking relative velocity model (FLRVM) of cooperative driving control system. To our knowledge, the model is an improvement over the similar extension in the forward looking optimal velocity models (FLOVM), because it is more reasonable and realistic in implement of incorporating intelligent transportation system in traffic. Then the stability criterion is investigated by the linear stability analysis with finding that new consideration theoretically lead to the improvement of the stability of traffic flow, and the validity of our theoretical analysis is confirmed by direct simulations. In addition, nonlinear analysis of the model shows that the three waves: triangular shock wave, soliton wave and kink-antikink wave appear respectively in stable, metastable and unstable regions. These correspond to the solutions of the Burgers equation, Korteweg-de Vries (KdV) equation and modified Korteweg-de Vries (mKdV) equation.     

Density waves in a traffic flow model with reaction-time delay

Density waves are investigated analytically and numerically in the optimal velocity model with reaction-time delay of drivers. The stability condition of this model is obtained by using the linear stability theory. The results show that the decrease of reaction-time delay of drivers leads to the stabilization of traffic flow. The Burgers, Korteweg-de Vries (KdV) and modified Korteweg-de Vries (mKdV) equations are derived to describe the density waves in the stable, metastable and unstable regions respectively. The triangular shock waves, soliton waves and kink-antikink waves appearing respectively in the three distinct regions are derived to describe the traffic jams. The numerical simulations are given.     

A study of solitary waves by He's semi-inverse variational principle

The dynamics of solitary waves in the presence of perturbation terms is studied in this paper with the aid of the semi-inverse variational principle. In this paper, shallow water waves as well as internal gravity waves in a density-stratified ocean are considered. These are respectively modeled by the Korteweg–de Vries equation as well as the compound Korteweg–de Vries equation. An analytical solution of the solitary wave is found in each case.     

Soliton and kink jams in traffic flow with open boundaries

Soliton density wave is investigated numerically and analytically in the optimal velocity model (a car-following model) of a one-dimensional traffic flow with open boundaries. Soliton density wave is distinguished from the kink density wave. It is shown that the soliton density wave appears only at the threshold of occurrence of traffic jams. The Korteweg-de Vries (KdV) equation is derived from the optimal velocity model by the use of the nonlinear analysis. It is found that the traffic soliton appears only near the neutral stability line. The soliton solution is analytically obtained from the perturbed KdV equation. It is shown that the soliton solution obtained from the nonlinear analysis is consistent with that of the numerical simulation.     

Nonlinear Waves in an Inhomogeneous Fluid Filled Elastic Tube

In a thin-walled, homogeneous, straight, long, circular, and incompressible fluid filled elastic tube, small but finite long wavelength nonlinear waves can be describe by a KdV (Korteweg de Vries) equation, while the carrier wave modulations are described by a nonlinear Schrödinger equation (NLSE). However if the elastic tube is slowly inhomogeneous, then it is found, in this paper, that the carrier wave modulations are described by an NLSE-like equation. There are soliton-like solutions for them, but the stability and instability regions for this soliton-like waves will change, depending on what kind of inhomogeneity the tube has.     

Density waves in a lattice hydrodynamic traffic flow model with the anticipation effect

By introducing the traffic anticipation effect in the real world into the original lattice hydrodynamic model, we present a new anticipation effect lattice hydrodynamic (AELH) model, and obtain the linear stability condition of the model by applying the linear stability theory. Through nonlinear analysis, we derive the Burgers equation and Korteweg-de Vries (KdV) equation, to describe the propagating behaviour of traffic density waves in the stable and the metastable regions, respectively. The good agreement between simulation results and analytical results shows that the stability of traffic flow can be enhanced when the anticipation effect is considered.     

Wave Breaking in a Class of Nonlocal Dispersive Wave Equations

Abstract

The Korteweg de Vries (KdV) equation is well known as an approximation model for small amplitude and long waves in di!erent physical contexts, but wave breaking phenomena related to short wavelengths are not captured in. In this work we consider a class of nonlocal dispersive wave equations which also incorporate physics of short wavelength scales. The model is identified by a renormalization of an infinite dispersive di!erential operator, followed by further specifications in terms of conservation laws associated with the underlying equation. Several well-known models are thus rediscovered. Wave breaking criteria are obtained for several models including the Burgers-Poisson system, the Camassa-Holm type equation and an Euler-Poisson system. The wave breaking criteria for these models are shown to depend only on the negativity of the initial velocity slope relative to other global quantities.     

The Effect of the Relative Velocity on Traffic Flow

The optimal velocity model of traffic is extended to take the relative velocity into account. The traffic behavior is investigated numerically and analytically with this model. It is shown that the car interaction with the relative velocity can effect the stability of the traffic flow and raise critical density. The jamming transition between the freely moving and jamming phases is investigated with the linear stability analysis and nonlinear perturbation methods. The traffic jam is described by the kink solution of the modified Korteweg--de Vries equation. The theoretical result is in good agreement with the simulation.     

A traffic flow lattice model considering relative current influence and its numerical simulation

<正>Based on Xue's lattice model,an extended lattice model is proposed by considering the relative current information about next-nearest-neighbour sites ahead.The linear stability condition of the presented model is obtained by employing the linear stability theory.The density wave is investigated analytically with the perturbation method.The results show that the occurrence of traffic jamming transitions can be described by the kink-antikink solution of the modified Korteweg-de Vries(mKdV) equation.The simulation results are in good agreement with the analytical results,showing that the stability of traffic flow can be enhanced when the relative current of next-nearest-neighbour sites ahead is considered.     

The Effect of the Relative Velocity on Traffic Flow

The optimal velocity model of traffc is extended to take the relative velocity into account. The traffcbehavior is investigated numerically and analytically with this model. It is shown that the car interaction with therelative velocity can effect the stability of the traffic flow and raise critical density. The jamming transition between thefreely moving and jamming phases is investigated with the linear stability analysis and nonlinear perturbation methods.The traffic jam is described by the kink solution of the modified Korteweg-de Vries equation. The theoretical result isin good agreement with the simulation.     

The KdV–Burgers equation in a new continuum model with consideration of driverʼs forecast effect and numerical tests

A new continuum traffic flow model is proposed based on an improved car-following model, which takes the driver?s forecast effect into consideration. The backward travel problem is overcome by our model and the neutral stability condition of the new model is obtained through the linear stability analysis. Nonlinear analysis shows clearly that the density fluctuation in traffic flow leads to a variety of density waves and the Korteweg–de Vries–Burgers (KdV–Burgers) equation is derived to describe the traffic flow near the neutral stability line. The corresponding solution for traffic density wave is also derived. Finally, the numerical results show that our model can not only reproduce the evolution of small perturbation, but also improve the stability of traffic flow.     

采用混合模型数值模拟从深海到浅海内波的传播

在南海东沙岛附近, 从MODIS遥感图像发现内波传播是从深海经陆架坡再到浅海, 由于深海和浅海环境条件的差异以及传播模型的适用条件不同, 因此 不能采用同一模型模拟内波的传播, 需用两种模型来分别模拟内波在深海和浅海中的传播. 采用差分法, 首先用非线性薛定谔方程模拟了深海内波的传播, 然后用EKdV方程模拟了内波在浅海中的继续传播. 模拟结果与实际的MODIS遥感内波图像相符合, 并与应用单一模型模拟结果相比, 混合模型模拟该海区的内波传播更接近遥感实测, 表明了混合模型的合理性.     

Solitary Density Waves for Improved Traffic Flow Model with Variable Brake Distances

Traffic flow model is improved by introducing variable brake distances with varying slopes.Stability of the traffic flow on a gradient is analyzed and the neutral stability condition is obtained.The KdV(Korteweg-de Vries)equation is derived the use of nonlinear analysis and soliton solution is obtained in the meta-stable region.Solitary density waves are reproduced in the numerical simulations.It is found that as uniform headway is less than the safety distance solitary wave exhibits upward form,otherwise it exhibits downward form.In general the numerical results are in good agreement with the analytical results.     

Nonlinear analysis of an improved continuum model considering mean-field velocity difference

Based on the velocity gradient model, an extended continuum model with consideration of the mean-field velocity difference is proposed in this paper. By using the linear stability theory, the linear stability criterion of the new model is gained, which proved that mean-field velocity difference has significant influence on stability of traffic flow. The KdV–Burgers equation is derived by using non-linear analysis method and the evolution of density wave near the neutral stability line is explored. Numerical simulations are carried out how mean-field velocity difference affect the stability of traffic flow, and energy consumption is also studied for this new macro model. At the same time, complicated traffic phenomena such as local cluster effects, shock waves and rarefaction waves can be reproduced in the new model by numerical simulation. Numerical results are consistent with the theoretical analysis, which indicates that the mean-field velocity difference not only suppresses traffic jam, but also depresses energy consumption.     

浅水体系中的多孤立波

形式分离变量法被推广应用于寻求不可积模型的多孤立波解.特别地,应用形式分离变量法于三个描述浅水体系的非线性方程:推广WhithamBroerKaup(WBK)方程、2+1维耦合KortewegdeVries(KdV)方程和1+1维耦合KdV方程,给出了这些体系的明显的解析的多孤立波解 关键词： 浅水体系 多孤立波 形式分离变量法 不可积模型     

Effect of Defects on the Spatial Localization of Nonlinear Acoustic Waves

A self-consistent mathematical model that includes equations of elasticity theory and kinetic equations for the density of different types of point defects is reduced to a nonlinear equation of evolution that combines the familiar Korteweg–de Vries–Burgers and Klein–Gordon equations of wave dynamics. Exact analytical solutions for this equation are found and analyzed.     

A new lattice hydrodynamic traffic flow model with a consideration of multi-anticipation effect

We present a new multi-anticipation lattice hydrodynamic model based on the traffic anticipation effect in the real world.Applying the linear stability theory,we obtain the linear stability condition of the model.Through nonlinear analysis,we derive the modified Korteweg-de Vries equation to describe the propagating behaviour of a traffic density wave near the critical point.The good agreement between the simulation results and the analytical results shows that the stability of traffic flow can be enhanced when the multi-anticipation effect is considered.     

Formation of freak waves in a soliton gas described by the modified Korteweg–de Vries equation

The nonlinear dynamics of multisoliton, differently polar fields is investigated within the framework of the modified Korteweg–de Vries equation. It is shown that the occurrence of abnormally large waves (freak waves) is possible in similar fields, which is associated with the modulation instability of cnoidal waves. The statistical moments of wave fields are investigated. It is shown that an increase in the coefficient of excess due to the interaction of solitons correlates with an increase in the probability of occurrence of freak waves. It is shown that the nonlinear interaction of differently polar solitons results in variation of the distribution functions of peak characteristics: the fraction of low-amplitude waves decreases, while that of the waves with large amplitudes increases. The dependence of the intensity of the density of the characteristics of the soliton gas is shown.     

考虑驾驶员预估效应的交通流格子模型与数值仿真

考虑驾驶员的预估效应对车流的影响,提出了一个改进的一维交通流格子模型.基于线性稳定性理论得到了该模型的线性稳定性判据;运用非线性分析方法导出了描述交通阻塞相变时的mKdV方程.应用数值仿真验证了mKdV方程的解,研究表明适当考虑车流中预估效应的作用能够增强交通流稳定性,从而能有效抑制交通阻塞的形成. 关键词： 预估效应 交通流 格子模型 数值仿真