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

即使没有任何类型的障碍物，最初均匀的交通流也可能变得不均匀，从而导致形成“幻影”交通拥堵。虚拟交通拥堵可以解释为某些类型的宏观交通模型中出现的不稳定性。在适当的条件下，如果交通密度超过临界阈值，小的扰动就会放大并成长为非线性行波。这些交通波被称为 jamitons，在现实中被观察到并已通过实验再现。在该项目中，建立并利用了反应气体动力学中的贾米顿和爆震波之间的数学类比：虚拟交通堵塞是流体运动中不稳定性的类比，而贾米顿是爆炸波的类似物。利用燃烧理论中的泽尔多维奇-冯·诺伊曼-多林理论，该类比可以预测 Jamitons 的确切形状和行进速度。分析中的一个关键特征是存在声波点，它充当事件视界（类似于黑洞中发生的事件视界），信息无法在其中传播。通过理论和数值模拟研究交通波。一个特定的目标是充分了解虚拟交通拥堵，以便制定有效的对策。“虚拟”交通拥堵是指在道路上没有瓶颈、障碍物或任何明显原因的情况下自发发生的车辆交通小拥堵。观察表明，均匀的交通流可能会产生不均匀性，从而导致交通拥堵。这些交通拥堵波（“jamitons”）会强制执行意想不到的制动操作，从而给驾驶员和材料带来压力，浪费燃料并增加污染，并且是潜在车辆碰撞的热点。在这个项目中，研究了虚拟交通拥堵和干扰的行为。交通建模与气体动力学、水力学和天体物理学之间的理论类比被建立并用于增进对交通流的理解。这些连接可以深入了解可能发生虚拟交通拥堵的情况，并可以预测由此产生的拥堵的形状和速度。对虚拟交通拥堵的基本了解是制定适当对策以避免或改善这些拥堵的关键步骤。开发有效的方法来管理或预防虚拟交通拥堵可能会对减少燃料消耗和污染产生相当大的影响。将纳入模型并进行研究的两种可能的策略是：单个车辆中的辅助驾驶设备，以及高速公路上的自适应控制速度限制。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。该项目的研究涉及三个国际合作以及研究生和本科生研究项目。

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.