Collaborative Research: Phantom traffic jams, continuum modeling, and connections with detonation wave theory

即使在没有任何类型的障碍物的情况下，最初均匀的交通流量也会变得不均匀，从而导致“幻影”交通拥堵的形成。幻象交通拥堵可以解释为在某些类型的宏观交通模型中发生的不稳定。在适当的条件下，如果交通密度超过一个临界阈值，小的扰动就会放大并发展成非线性行波。这些被称为干扰波的交通波是在现实中观察到的，并已在实验中重现。在本项目中，建立并开发了反应气体动力学中干扰波与爆震波之间的数学类比：幻象交通堵塞是流体运动中的不稳定性的类比，而干扰波是爆震波的类比。利用燃烧理论中的Zel‘dovich-von Neumann-Doering理论，这种类比可以预测干扰子的准确形状和传播速度。分析中的一个关键特征是存在一个音速点，它充当一个事件视界(类似于发生在黑洞中的视界)，信息无法传播通过。对交通波进行了理论分析和数值模拟研究。一个特别的目标是充分了解幽灵交通拥堵，以便制定有效的对策。‘幽灵交通拥堵’是指在道路上没有瓶颈、障碍物或任何可识别的原因的情况下，自发发生的车辆交通的轻微拥堵。观察表明，均匀的车流会产生不均匀，从而导致行驶中的交通堵塞。这些交通堵塞波会强制执行意想不到的刹车动作，从而给司机和材料带来压力，浪费燃料并增加污染，是潜在车辆碰撞的热点。在本项目中，研究了幻象交通拥堵和干扰的行为。建立了交通模型与气体动力学、水力学和天体物理学之间的理论类比，并将其用于促进对交通流的理解。这些连接提供了对可能发生幻象交通拥堵的情况的洞察，并允许预测由此产生的干扰的形状和速度。对幽灵交通拥堵的基本了解是制定适当对策以避免或改善它们的关键一步。制定有效的方法来管理或防止幽灵交通拥堵，可能会对减少燃料消耗和污染产生重大影响。将被纳入模型并进行研究的两种可能的策略是：在单个车辆上安装辅助驾驶装置，以及在高速公路上自适应控制限速。这项研究的一个重要组成部分是理论分析和数值实验之间的相互作用。这个项目的研究涉及三个国际合作，以及研究生和本科生的研究项目。

Initially homogeneous traffic flow can become inhomogeneous even in the absence of obstructions of any kind, leading to the formation of ''phantom'' traffic jams. Phantom traffic jams can be explained as instabilities that occur in certain types of macroscopic traffic models. Under appropriate conditions, if the traffic density exceeds a critical threshold value, small perturbations amplify and grow into nonlinear traveling waves. These traffic waves, called jamitons, are observed in reality and have been reproduced experimentally. In this project, a mathematical analogy between jamitons and detonation waves in reacting gas dynamics is established and exploited: phantom traffic jams are the analogs of instabilities in the fluid's motion, and jamitons are the analogs of detonation waves. Using the Zel'dovich-von Neumann-Doering theory from combustion theory, the analogy allows the prediction of the exact shape and travel velocity of the jamitons. A key feature in the analysis is the presence of a sonic point, which acts as an event horizon (similar to the one that occurs in a black hole) across which information cannot propagate. Traffic waves are studied theoretically and by numerical simulations. A particular goal is to understand phantom traffic jams well enough to allow the development of effective countermeasures.A ''phantom'' traffic jam is a small congestion in vehicular traffic that occurs spontaneously, in the absence of bottlenecks, obstacles, or any discernible causes on the road. Observations show that uniform traffic flow can develop inhomogeneities, which turn into traveling traffic jams. These traffic jam waves (''jamitons'') enforce unexpected braking maneuvers, and thus impose stress on drivers and materials, waste fuel and increase pollution, and are hot spots for potential vehicle collisions. In this project, the behavior of phantom traffic jams and jamitons is studied. Theoretical analogies between traffic modeling and gas dynamics, hydraulics, and astrophysics, are established and used to advance the understanding of traffic flow. These connections yield insight into the situations under which phantom traffic jams can occur, and allow the prediction of the shape and velocity of the resulting jamitons. A fundamental understanding of phantom traffic jams is a key step in devising appropriate countermeasures to avoid or ameliorate them. The development of effective ways to manage or prevent phantom traffic jams could have a considerable impact on the reduction of fuel consumption and pollution. Two possible strategies that will be incorporated into the models and investigated are: assisted driving devices in the individual vehicles, and adaptively controlled speed limits on highways. A crucial component of this study is the interplay between theoretical analysis and numerical experiments. The research in this project involves three international collaborations, as well as graduate and undergraduate research projects.