mKdV方程的双扭结单孤子及其稳定性研究

基于双曲函数法的思想,通过选择新的展开函数,得到了modified Korteweg-de Vries(mKdV)方程的几类精确解,其中一类为具有扭结—反扭结状结构的双扭结单孤子解.在不同的极限情况下,该解分别退化为mKdV方程的扭结状或钟状孤波解.文中对双扭结型孤子解的稳定性进行了数值研究,结果表明:在长波和短波简谐波扰动、钟型孤立波扰动与随机扰动下,该孤子均稳定.     

耦合KdV方程的双峰孤立子及其稳定性

利用扩展双曲函数法求解了耦合KdV方程,得到了6类精确解,其中一类为具有双峰状结构的单孤子解.在不同的极限情况下,该解分别退化为耦合KdV方程的扭结状或钟状孤波解.文中对双峰孤立波的稳定性进行了数值研究,结果表明:耦合KdV方程的双峰孤立波在长波小振幅扰动和小振幅钟型孤立波扰动下,均稳定. 关键词： 耦合KdV方程 双峰孤立子 稳定性     

多前车速度差的车辆跟驰模型的稳定性与孤波

通过线性稳定性分析,得到了多前车速度差模型的稳定性条件, 并发现通过调节多前车信息,使交通流的稳定区域明显扩大. 通过约化摄动方法 研究了该模型的非线性动力学特性:在稳定流区域,得到了描述密度波的Burgers方程;在交 通流的不稳定区域内,在临界点附近获得了描述车头间距的修正的Korteweg-de Vries (modified Korteweg-de Vries, mKdV)方程; 在亚稳态区域内,在中性稳定曲线附近获得了描述车头间距 的KdV方程. Burgers的孤波解、mKdV方程的扭结-反扭结波解及KdV方程的 孤波解描述了交通流堵塞现象.     

组合KdV方程的双扭结孤立波及其稳定性研究

利用扩展的双曲函数法得到了combined KdV-mKdV (cKdV)方程的几类精确解,其中一类为具有扭结—反扭结状结构的双扭结单孤子解.在不同的极限情况下,该解分别退化为cKdV方程的扭结状或钟状孤波解.理论分析表明,cKdV方程既有传播型孤立波解,也有非传播型孤立波解.文中对双扭结型孤立波解的稳定性进行了数值研究,结果表明,cKdV方程既存在稳定的双扭结型孤立波,也存在不稳定的双扭结型孤立波. 关键词： cKdV方程 双扭结单孤子 稳定性     

冲击压缩下物质黏性系数与冲击波阵面扰动衰减特性研究

为解决高温高压下物质黏性的测量问题,Sakharov曾提出一种冲击波小扰动实验方法,但人们一直未从理论上给出这类特定冲击波流场中扰动振幅衰减特性与黏性系数之间的量化关联.本文首次针对Mineev等的实验条件采用数值解方法定量地研究了金属铝(Al)中复杂流场演化过程、正弦形波阵面上相对扰动幅度的演化特征和它们的黏性效应,给出了相对扰动幅度衰减曲线的零点相对距离与黏性系数之间的定量关系.与Zaidel的均匀流场模型以及Miller等的非均匀流场模型相比,本文求解的流场演变问题已经接近实验的真实情况.利用本文数     

随机计及相对速度的交通流跟驰模型

从研究微观个体车辆行为出发，考虑车辆加速过程的不确定性，提出了随机计及相对速度的 交通流跟驰模型(SR-OV模型).对随机相对速度的跟驰模型的动力学方程进行稳定性分析，得 到与Bando跟驰模型不同的稳定性判据，其稳定性优于Bando模型.运用摄动理论分析交通过 程中密度波的变化，结果表明，在发生交通阻塞相变时，交通密度波以mKdV方程描述的扭结 -反扭结波演化.对随机相对速度跟驰模型进行数值模拟和分析，结果发现车流速度的变化小 于Bando模型的速度变化，而且与随机概率有关，当随机考虑相对速度的概率增大时，初始 的小扰动不会放大对车流产生影响，甚至长时间就消失，这与Bando模型完全不同.数值模拟 所得到的相图与解析解相符合,而且交通流稳定区域大于Bando模型.从车间距-速度演化图上 ，随着随机概率的增大，SR-OV模型在初始时存在的滞后现象，随着时间的增长，趋于稳定 状态后，滞后曲线收敛于一小区域，滞后效应被削弱.这完全不同于Bando模型，在Bando模 型中，滞后曲线由一点向外扩散，滞后曲线区域越来越大，车流趋于不稳定状态. 关键词： 交通流 跟驰模型 稳定性判据 相对速度     

最相邻后车综合信息对交通流不稳定性的影响分析

基于抑制交通流不稳定性所需的条件,分析司机后视获得的最相邻后车综合信息对交通流不稳定性的影响. 在司机关注前车信息概率大于关注后车信息概率与司机敏感系数大于0的现实条件下,解析分析以及仿真分析得到了以下结论:1)最相邻后车车头距信息减小了交通流的不稳定性,且关注概率越大,减小作用越大;跟驰车与最相邻后车的速度差信息增加了交通流的不稳定性,且关注概率越大,增加作用越大. 2)最相邻后车综合信息对交通流的不稳定性的减小作用大于增加作用,即最相邻后车综合信息减小了交通流的不稳定性. 3)司机距离差敏感系数越大,最相邻后车综合信息对交通流的不稳定性减小作用越大. 4)司机速度差敏感系数越大,最相邻后车综合信息对交通流的不稳定性增加作用越大. 关键词： 交通堵塞 交通流不稳定性 最相邻后车综合信息 跟驰模型     

船用核动力装置负荷切换控制动态仿真

本文以船用核动力装置为研究对象,建立了蒸汽发生器及二回路系统的数学模型及仿真模型.介绍了温度控制和切换控制两种核动力装置负荷协调控制策略,并进行了降负荷工况的仿真研究.研究表明:切换控制对系统参数扰动较大,但低负荷时系统参数皆小于温度控制,并且选取的切换点负荷越低,对系统参数的扰动越小,对系统的设备寿命及经济性有更好的...     

mBBM方程的双扭结孤立波及其动力学稳定性

采用双曲函数展开法得到Modified Benjamin-Bona-Mahony（mBBM）方程的一类扭结-反扭结状的双扭结孤立波解,在不同的极限情况下,此孤立波分别退化为mBBM方程的扭结状和钟状孤立波解.对双扭结型单孤子的结构特征进行分析,构造有限差分格式对其动力学稳定性进行数值研究.有限差分格式为两层隐式格式,在线性化意义下无条件稳定.数值结果表明mBBM方程的双扭结型单孤子在不同类型的扰动下均具有很强的稳定性.对双孤立波的碰撞进行数值模拟,发现既存在弹性碰撞也存在非弹性碰撞.     

大气湍流中光束束宽扩展和角扩展的比较研究

以厄米-双曲余弦-高斯（H-ChG）光束为例,对H-ChG光束通过大气湍流传输时的束宽扩展和角扩展做了详细研究.用相对束宽和相对角扩展代替束宽和角扩展来研究湍流对光束影响的灵敏程度.研究表明,折射率结构常数C²_n越小,光束束宽扩展和角扩展越小.有较大阶数m,n,较小参数Ω₀和束腰宽度w₀ H-ChG光束的角扩展受湍流影响较小.当传输距离足够远时,这一结论对H-ChG光束的束宽扩展也成立.当传输距离不长时,对H-ChG光束相对束宽随Ω₀和w₀的变化规律做了分析.用数值计算例做了说明,并对结果的正确性做了物理解释.厄米-高斯,双曲余弦高斯和高斯光束在大气湍流中的扩展可作为H-ChG光束的特例来处理. 关键词： 束宽扩展和角扩展 大气湍流 厄米-双曲余弦-高斯光束     

An extended smart driver model considering electronic throttle angle changes with memory

Based on the fact that the electronic throttle angle effect performs well in the traditional car following model,this paper attempts to introduce the electronic throttle angle into the smart driver model(SDM)as an acceleration feedback control term,and establish an extended smart driver model considering electronic throttle angle changes with memory(ETSDM).In order to show the practicability of the extended model,the next generation simulation(NGSIM)data was used to calibrate and evaluate the extended model and the smart driver model.The calibration results show that,compared with SDM,the simulation value based on the ETSDM is better fitted with the measured data,that is,the extended model can describe the actual traffic situation more accurately.Then,the linear stability analysis of ETSDM was carried out theoretically,and the stability condition was derived.In addition,numerical simulations were explored to show the influence of the electronic throttle angle changes with memory and the driver sensitivity on the stability of traffic flow.The numerical results show that the feedback control term of electronic throttle angle changes with memory can enhance the stability of traffic flow,which shows the feasibility and superiority of the proposed model to a certain extent.     

Congestion analysis of traffic networks with direction-dependant heterogeneity

Traffic flow directionality and network weight asymmetry are widespread notions in traffic networks. This paper investigates the influence of direction-dependant heterogeneity on traffic congestion. To capture the effect of the link directionality and link weight asymmetry, the heterogeneity indexes of complex networks and the traffic flow model are introduced. The numerical results show that the critical value of heterogeneity determines congestion transition processes. The congestion degree increases with heterogeneity when the network heterogeneity is at a subcritical region. A network is more tolerant of congestion if the heterogeneity of the network is smaller or larger than the critical value. Furthermore, when heterogeneity reaches the critical value, the average number of accumulated vehicles arrives at the maximum and the traffic flow is under a serious congestion state. A significant improvement on the tolerance to congestion of traffic networks can be made if the network heterogeneity is controlled within a reasonable range.     

高速跟驰交通流动力学模型研究

为研究道路交通中的高速跟驰物理现象,针对高速跟驰车辆特点,综合考虑了驾驶员换道决策行为以及随机慢化等因素,结合前景理论等方法,提出了一种用于模拟道路交通流中高速跟驰物理现象的动力学模型(简称HCCA模型).通过计算机数值模拟,研究了高速跟驰交通流物理现象演化机理及高速跟驰特性.结果表明:与对称的双车道元胞自动机动力学模型相比,本文建立的HCCA动力学模型能够再现道路高速跟驰物理现象,并得到了道路小间距高速跟驰率超过7%的结果与实测结果相符合,最后模拟得到了丰富的交通物理现象,再现了自由流、同步流及运动阻塞等复杂交通物理现象.     

Continuum modeling of cooperative traffic flow dynamics

This paper presents a continuum approach to model the dynamics of cooperative traffic flow. The cooperation is defined in our model in a way that the equipped vehicle can issue and receive a warning massage when there is downstream congestion. Upon receiving the warning massage, the (up-stream) equipped vehicle will adapt the current desired speed to the speed at the congested area in order to avoid sharp deceleration when approaching the congestion. To model the dynamics of such cooperative systems, a multi-class gas-kinetic theory is extended to capture the adaptation of the desired speed of the equipped vehicle to the speed at the downstream congested traffic. Numerical simulations are carried out to show the influence of the penetration rate of the equipped vehicles on traffic flow stability and capacity in a freeway.     

A new lattice model of traffic flow with the consideration of the driver?s forecast effects

In this Letter, a new lattice model is presented with the consideration of the driver?s forecast effects (DFE). The linear stability condition of the extended model is obtained by using the linear stability theory. The analytical results show that the new model can improve the stability of traffic flow by considering DFE. The modified KdV equation near the critical point is derived to describe the traffic jam by nonlinear analysis. Numerical simulation also shows that the new model can improve the stability of traffic flow by adjusting the driver?s forecast intensity parameter, which is consistent with the theoretical analysis.     

交通流双车跟驰模型与数值仿真

基于全速度差(FVD)模型,考虑双前车信息的影响,提出了交通流双车跟驰模型.通过线性稳定性分析,得到了改进模型的稳定性条件. 与FVD模型对比研究表明,改进模型的稳定区域有明显增加.数值模拟结果表明,改进模型通过调节次近邻前车信息,可以避免FVD模型中因为反应系数较小时出现负速度的缺陷.同时也表明次近邻前车对交通流存在不可忽视的影响. 关键词： 交通流 双车跟驰模型 模拟     

Modeling and analysis of car-following behavior considering backward-looking effect

The car-following behavior can be influenced by its driver’s backward-looking effect.Especially in traffic congestion,if vehicles adjust the headway by considering backward-looking effect,the stability of traffic flow can be enhanced.A model of car-following behavior considering backward-looking effect was built using visual information as a stimulus.The critical stability conditions were derived by linear and nonlinear stability analyses.The results of parameter sensitivity analysis indicate that the stability of traffic flow was enhanced by considering the backward-looking effect.The spatiotemporal evolution of traffic flow of different truck ratios and varying degrees of backward-looking effect was determined by numerical simulation.This study lays a foundation for exploring the complex feature of car-following behavior and making the intelligent network vehicles control rules more consistent with human driver habits.     

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.