Phase transitions in the two-lane density difference lattice hydrodynamic model of traffic flow

In this paper, we derive the KdV equation from the two-lane lattice hydrodynamic traffic model considering density difference effect. The soliton solution is obtained from the KdV equation. Under periodical boundary, the KdV soliton of traffic flow is demonstrated by numerical simulation. The numerical simulation result is consistent with the nonlinear analytical result. Under open system, the density fluctuation of the downstream last one lattice is designed to explore the empirical congested traffic states. A phase diagram is presented which includes free traffic, moving localized cluster, triggered stop-and-go traffic, oscillating congested traffic, and homogeneous congested traffic. Finally, the spatiotemporal evolution of all the traffic states described in phase diagram are reproduced. Results suggest that the two-lane density difference hydrodynamic traffic model is suitable to describe the actual traffic.     

高架路匝道附近的交叉口交通流分析

考虑高架路匝道附近的交叉口交通流问题．所采用的模型是经修正的一维管流交通流模型,在运动方程中引入了弛豫项．基于该模型,对上海市内环线的武宁路匝道附近的交通流进行了案例分析,着重对主干道上的右转车辆干扰效应进行了数值模拟,所得结果与实测数据相当符合．分析表明,右转车辆对主干道的“挤压”效应是引起某些交叉口交通拥塞的重要原因,而设置在繁华路口的高架路匝道加剧了这种拥塞状况。     

Empirical test of a microscopic three-phase traffic theory

A review of dynamic nonlinear features of spatiotemporal congested patterns in freeway traffic is presented. The basis of the review is a comparison of theoretical features of the congested patterns that are shown by a microscopic traffic flow model in the context of the Kerner's three-phase traffic theory and empirical microscopic and macroscopic pattern characteristics measured on different freeways over various days and years. In this test of the microscopic three-phase traffic flow theory, a model of an "open" road is applied: Empirical time-dependence of traffic demand and drivers' destinations are used at the upstream model boundaries. At downstream model boundary conditions for vehicle freely leaving a modeling freeway section(s) are given. Spatiotemporal congested patterns emerge, develop, and dissolve in this open freeway model with the same types of bottlenecks as those in empirical observations. It is found that microscopic three-phase traffic models can explain all known macroscopic and microscopic empirical congested pattern features (e.g., probabilistic breakdown phenomenon as a first-order phase transition from free flow to synchronized flow, moving jam emergence in synchronized flow rather than in free flow, spatiotemporal features of synchronized flow and general congested patterns at freeway bottlenecks, intensification of downstream congestion due to upstream congestion at adjacent bottlenecks). It turns out that microscopic optimal velocity (OV) functions and time headway distributions are not necessarily qualitatively different, even if local congested traffic behavior is qualitatively different. Model performance with respect to spatiotemporal pattern emergence and evolution cannot be tested using these traffic characteristics. The reason for this is that important spatiotemporal features of congested traffic patterns are lost in these and many other macroscopic and microscopic traffic characteristics, which are widely used as the empirical basis for a test of traffic flow models. PACS: 89.40. + k, 47.54. + r, 64.60.Cn, 64.60.Lx     

A new lattice hydrodynamic model for two-lane traffic with the consideration of density difference effect

A new lattice hydrodynamic model for two-lane traffic flow is proposed by introducing the density difference effect (DDE). Using linear stability theory, stability condition of the presented model is obtained. Jamming transitions among the freely moving phase, the coexisting phase, and the uniform congested phase are investigated by employing nonlinear analysis. The modified KdV (mKdV) equation near the critical point is derived and the kink-antikink soliton solutions are obtained. Numerical simulations are presented to verify analytical results, showing that DDE can improve the stability of traffic flow effectively.     

On a closure of mass conservation equation and stability analysis in the mathematical theory of vehicular traffic flowSur une fermeture des équations de conservation de la masse et l'analyse de la stabilité dans la théorie mathématique de la circulation véhiculaire

This Note deals with the development of mathematical methods for the closure of the mass conservation equation for macroscopic hydrodynamical models of traffic flow on roads. The closure is obtained by a phenomenological model, relating the local mean velocity to local density earlier in time. An evolution equation is obtained for the flux and a stability analysis is performed; this qualitatively describes some features of congested flow. To cite this article: V. Coscia, C. R. Mecanique 332 (2004).     

基于元胞自动机模型的C型交织区交通流特性

根据C型双侧交织区的车辆换道特征建立相应的换道规则,采用多车道元胞自动机模型研究交织区系统的交通流特性. 通过数值模拟得到了不同交织区长度下的相图,表明当主路和匝道交通流均为自由流时,交织区长度对系统影响不大,但当主路或匝道拥挤时,交织区长度的增加可以明显改善入口匝道的交通流状况. 进一步讨论了主路畅通而交织流量较大情形下主路上的车辆密度、速度和换道频率分布,发现换道集中在合流区和分流区附近,并造成相应路段上的局部拥堵.      

受支架支撑的血管管壁变形及应力分析

为了计算动脉粥样硬化和局部斑块形成的堵塞对血管壁工作状态的影响,论文根据血液流动的连续性方程、运动方程,管壁的运动方程,在给定了血压波形函数的基础上,求得了狭窄血管管壁的径向位移及环向应力.分析了不同狭窄程度对血管壁变形及应力的影响;给出了不同狭窄情况下和局部斑块硬化程度不同时,血管植入支架所需的作用力;计算出植入支架后血管壁的径向位移及应力状态.论文的研究结果可供临床上对狭窄血管植入支架后的变形与受力分析及支架的正确安放参考;可避免发生堵塞严重或血管钙化时,由于安放支架不当而发生血管破裂的医疗事故.     

LAUNCH VEHICLE BUFFETING WITH AEROELASTIC COUPLING EFFECTS

Launch vehicle structural responses can couple with transonic flow state transitions at the nose of payload fairings. This self-sustained coupling yields a nonlinear equation of motion that can be analyzed using the force–response relationship and the periodicity condition. The traditional analysis approach for this phenomenon, however, linearizes the equation of motion by converting the alternating flow forces into an aerodynamic damping term and defines a stability criterion as the response amplitude that yields zero net system damping. This work clarifies the relationship between the present and traditional methods, and compares results and conclusions. The feasibility of modifying a launch vehicle response analysis of buffeting (random pressure fluctuations caused by turbulent flow) to include aeroelastic coupling effects is also explored. The aerodynamic stiffness and damping terms formulated herein are consistent with trends observed in wind-tunnel test data. It is shown, however, that the modified buffet analysis can be inaccurate, particularly when the aeroelastic coupling contribution does not dominate the system response.     

Mechanism of flow instability and transition to turbulence

In this paper, a new mechanism of flow instability and turbulence transition is proposed for wall bounded shear flows. It is stated that the total energy gradient in the transverse direction and that in the streamwise direction of the main flow dominate the disturbance amplification or decay. Thus, they determine the critical condition of instability initiation and flow transition under given initial disturbance. A new dimensionless parameter K for characterizing flow instability is proposed which is expressed as the ratio of the energy gradients in the two directions for the flow without energy input or output. It is suggested that flow instability should first occur at the position of K_max which may be the most dangerous position. This speculation is confirmed by Nishioka et al.'s experimental data. Comparison with experimental data for plane Poiseuille flow and pipe Poiseuille flow indicates that the proposed idea is really valid. It is found that the turbulence transition takes place at a critical value of K_max of about 385 for both plane Poiseuille flow and pipe Poiseuille flow, below which no turbulence will occur regardless the disturbance. More studies show that the theory is also valid for plane Couette flows which holds a critical value of K_max of about 370.     

Penetrative convection in thawing subsea permafrost

Penetrative convection is investigated in a porous medium bounded above by the ocean bed and below by the interface of the thawing permafrost ground. The thermal equation of state relating the density, temperature and salinity is assumed to be that of ocean water as proposed by the UNESCO formula. Employing the Boussinesq approximated Darcy-flow equations with such a realistic density formula in the buoyancy term, the problem of convective motion of brine is studied. Such convection flow is observed off the coast of Alaska. The field variables in question are the brine-velocity field, the temperature and the salinity, although we simplify the problem by imposing a temperature field that is linear in the depth variable. For this simplified system we study the continuous dependence of the velocity and salinity on the initial data, develop a linear instability analysis and, additionally, present a fully nonlinear three-dimensional stability analysis. This nonlinear analysis necessitates the introduction of a generalised energy (or Lyapunov function) due to the extra terms present in the realistic equation of state. Numerical results indicate that values of the critical Rayleigh numbers are smaller than when these extra terms are omitted. Received: March 10, 1997     

TDGL and mKdV equations for car-following model considering driver’s anticipation

Car-following models are proposed to describe the jamming transition in traffic flow on a highway. In this paper, a new car-following model considering the driver’s forecast effect is investigated to describe the traffic jam. The nature of the model is studied using linear and nonlinear analysis method. A thermodynamic theory is formulated to describe the phase transition and critical phenomenon in traffic flow and the time-dependent Ginzburg–Landau (TDGL) equation is derived to describe the traffic flow near the critical point. It is also shown that the modified Korteweg-de Veris (mKdV) equation is derived to describe the traffic jam. The connection between the TDGL and the mKdV equations is given.     

基于气液相界面捕捉的统一气体动理学格式

气液相界面运动的研究无论是在科学还是工程领域都是非常重要的. 其中, 非平衡流动的计算尤其受到关注. 基于此, 我们构造了捕捉气液相界面的统一气体动理学格式. 由于统一气体动理学格式将自由输运和粒子碰撞耦合起来更新宏观物理量和微观分布函数, 故而可以求解非平衡流动. 具体思路是, 通过将范德瓦尔斯状态方程所表达的非理想气体效应引入统一气体动理学格式之中来捕捉气液相界面, 两相的分离与共存通过范德瓦尔斯状态方程描述. 由于流体在椭圆区域是不稳定的, 因此气液相界面可以通过蒸发和凝结过程自动捕捉. 如此, 一个锋锐的相界面便可以通过数值耗散和相变而得到. 利用该方法得到麦克斯韦等面积律(Maxwell construction)对应的数值解, 并与其相应的理论解相比较, 二者符合良好. 而后, 通过对范德瓦尔斯状态方程所描述的液滴表面张力进行数值计算, 验证了Laplace定理. 此外, 通过模拟两个液滴的碰撞融合过程, 进一步证明了该格式的有效性. 但是, 由于范德瓦尔斯状态方程的特性, 其所构造的格式仅适用于液/气两相密度比小于5的情况.      

Shear-banding structure orientated in the vorticity direction observed for equimolar micellar solution

 The non-monotonic shear flow of a viscoelastic equimolar aqueous surfactant solution (cetylpyridinium chloride-sodium salicylate) is investigated rheologically and optically in a transparent strain-controlled Taylor Couette flow cell. As reported before, this particular wormlike micellar solution exhibits first a shear thinning and then a pronounced shear-thickening behavior. Once this shear-thickening regime is reached, a transient phase separation/shear banding of the solution into turbid and clear ring-like patterns orientated perpendicular to the vorticity axis, i.e., stacked like pancakes, is observed (Wheeler et al. 1998; Fischer 2000). The solution exhibit several unique features as no induction period of the shear induced phase, no structural build-up at the inner rotating cylinder, jumping pancake structure of clear and turbid ringlike phases, and oscillating shear stresses appear once the pancake structure is present. According to our analysis this flow phenomenon is not purely a mechanical or rheological driven hydrodynamic instability but one has to take into account structural changes of the oriented micellar aggregates (flow induced non-equilibrium phase transition) as proposed by several authors. Although this particular flow behavior and the underlying mixture of shear induced phases and mechanical instabilities is not fully understood yet, some classification characteristics based on a recent theoretical approach by Schmitt et al. (1995) and Porte et al. (1997) where a strong coupling between the flow instability (non-homogeneous flow profile due to the bands) and the structural changes causes the observed transient phenomena can be derived. In reference to the presented model the observed orientation of the rings is typical for complex fluids that undergo a spinodal phase separation coupled with a thermodynamic flow instability. In contrast to other shear banding phenomena, this one is observed in parallel plate, cone-plate, and Couette flow cell as well as under controlled stress and controlled rate conditions. Therefore, it adds an additional aspect to the present discussion on shear banding phenomena, i.e., the coupling of hydrodynamics and phase transition of rheological complex fluids. Received: 8 January 2001 Accepted: 15 May 2001     

Continuum modeling for two-lane traffic flow

In this paper, we study the continuum modeling of traffic dynamics for two-lane freeways. A new dynamics model is proposed, which contains the speed gradient-based momentum equations derived from a car-following theory suited to two-lane traffic flow. The conditions for securing the linear stability of the new model are presented. Numerical tests are carried out and some nonequilibrium phenomena are observed, such as small disturbance instability, stop-and-go waves, local clusters and phase transition. The project supported by the National Natural Science Foundation of China (70521001) The English text was polished by Yunming Chen.     

斜波压缩下锡的相变和层裂行为

获取不同热力学路径下锡的动态响应实验数据,是深入研究其相变和损伤物理过程的基础.利用小型磁驱装置CQ-4完成了金属锡的斜波加载实验,获取了锡含有相变和层裂损伤物理信息的实验数据.实验结果显示,在加载段锡依次经历了弹塑性转变和β-γ相变两种物理过程,屈服强度约0.194 GPa,相变压力随着锡厚度的增加从7.54 GPa减小到7.14 GPa.在卸载段出现了明显的层裂损伤,层裂强度约1.1 GPa,与相同加载压力下冲击实验结果有巨大差异,层裂片厚度约0.38 mm.结合由锡的多相Helmholtz自由能计算的多相状态方程、Hayes相变动力学方程和损伤度理论,对斜波压缩实验过程进行一维流体动力学数值模拟,计算结果可以很好描述锡的弹塑性转变、相变和层裂三个物理过程.     

The solid–fluid transition in a yield stress shear thinning physical gel

We present an experimental investigation of the solid–fluid transition in a yield stress shear thinning physical gel (Carbopol^® 940) under shear. Upon a gradual increase of the external forcing, we observe three distinct deformation regimes: an elastic solid-like regime (characterized by a linear stress–strain dependence), a solid–fluid phase coexistence regime (characterized by a competition between destruction and reformation of the gel), and a purely viscous regime (characterized by a power law stress-rate of strain dependence). The competition between destruction and reformation of the gel is investigated via both systematic measurements of the dynamic elastic moduli (as a function of stress, the amplitude, and temperature) and unsteady flow ramps. The transition from solid behavior to fluid behavior displays a clear hysteresis upon increasing and decreasing values of the external forcing. We find that the deformation power corresponding to the hysteresis region scales linearly with the rate at which the material is being forced (the degree of flow unsteadiness). In the asymptotic limit of small forcing rates, our results agree well with previous steady state investigations of the yielding transition. Based on these experimental findings, we suggest an analogy between the solid–fluid transition and a first-order phase transition, e.g., the magnetization of a ferro-magnet where irreversibility and hysteresis emerge as a consequence of a phase coexistence regime. In order to get further insight into the solid–fluid transition, our experimental findings are complemented by a simple kinetic model that qualitatively describes the structural hysteresis observed in our rheological experiments. The model is fairly well validated against oscillatory flow data by a partial reconstruction of the Pipkin space of the material’s response and its nonlinear spectral behavior.     

宏观交通流模型的余维2分岔分析

交通流特性是混合交通流建模的一个重要因素. 交通流模型中的分岔现象是导致复杂交通现象的因素之一. 交通流的分岔, 涉及复杂的动力学特征且研究较少. 因此, 提出了一个最优速度模型来研究驾驶员记忆对驾驶行为的影响. 基于带有记忆的最优速度连续交通流模型, 利用非线性动力学, 分析和预测了复杂交通现象. 推导了鞍结 (LP) 分岔存在条件, 并通过数值计算得到了余维1 Hopf (H) 分岔、LP分岔和同宿轨 (HC) 分岔以及余维2广义Hopf (GH) 分岔、尖点 (CP) 分岔和Bogdanov-Takens (BT) 分岔等多种分岔结构. 根据双参数分岔区域的特点, 研究了记忆参数对单参数分岔结构的影响, 分析了不同分岔结构对交通流的影响, 并用相平面描述了平衡点附近轨迹的变化特征. 选择Hopf分岔和鞍结分岔作为密度演化的起点, 描述了均匀流、稳定和不稳定的拥挤流以及走走停停现象. 结果表明, 驾驶员记忆对交通流的稳定性有重要影响; 动力学行为很好地解释了交通拥堵现象; 考虑余维2分岔的影响, 能更好地理解交通拥堵产生的根源, 并为制定有效抑制拥堵的方法提供一定的理论依据.      

Orientational phase transitions in systems of axially symmetric particles in steady elongational flow combined with potential fields

Effects of uniaxial elongational flow combined with an external potential field (electric, magnetic) on the isotropic-to-nematic phase transition are considered basing on the Onsager free energy approach and self-consistent field theory. Ellipsoidal particles of uniaxial symmetry subjected to dipole and quadruple fields are assumed. Mean-field potential of the interparticle interactions accounting for dipole and quadruple contributions is considered.The self-consistency equations include dipole and quadruple contributions of the external and mean-field potentials. The equilibrium thermodynamic potentials, critical conditions of phase instability, and phase equilibria are discussed.Example computations indicate that orientation of rigid, prolate particles in the elongational flow and/or an external potential field results in narrowing the range of phase instability, reducing the difference in orientational order between the phases in equilibrium, and shifting phase equilibria to smaller values of the interparticle interactions parameter.Uniaxial elongational flow contributes a potential with quadruple symmetry, additive to other quadruple terms of the external potential. Specific nature of the flow potential, different to the non-hydrodynamic potentials, is evident in the behaviour of internal energy and entropy. At the phase transitions, the flow contributes to the discontinuity of internal energy and entropy, a term originated from the activation energy of viscous motion.     

Coherent motion of turbulent thermal plume in stably stratified fluid

The purpose of this study is to clarify the existence of an ordered and large scale coherent motion in a turbulent plane thermal plume in a thermally-stable stratified fluid inside a comparatively large enclosure. First, the upper part of the thermal plume was carefully observed by a flow visualization. Secondly, a wave form of plume temperature variation was measured. Thirdly, a spectrum analysis was carried out on time series data of the thermal plume. Finally, physical characteristics were investigated on vortices in the thermal plume based on results of the wave form and the spectrum analysis of the plume temperature. As a result, the main conclusions are obtained as follows. (1) An existence of vortices near the upper part of the thermal plume was firstly found by careful flow visualization. (2) From the wave form of temperature variation and the spectrum analysis of the thermal plume, it was clarified that the vortices are generated in the transition state and are transported to the turbulent state. (3) The vortices are ordered and they behave as a large scale coherent motion in the turbulent thermal plume.