标题： 二阶宏观交通模型中jamitons的相互作用 显示英文标题

标题： Interaction of jamitons in second-order macroscopic traffic models

摘要： Jamitons是某些二阶车辆交通宏观模型中出现的自维持行波解。 出现jamiton的一个必要条件是局部交通密度破坏所谓的次特征条件。 该条件指出，使用相同期望速度函数形成的相应一阶Lighthill-Whitham-Richards（LWR）模型的特征速度被相应二阶模型的特征速度所包围。 研究了交通流二阶模型中jamitons碰撞现象，特别是二阶Aw-Rascle-Zhang（ARZ）交通模型[A. Aw, M. Rascle,{\it SIAM J. Appl.\ Math.} {\bf 60} (2000) 916--938; H. M. Zhang,{\it 交通研究B卷} {\bf 36} (2002) 275--290]的情况。 首先定义了一个相容性条件，以选择可以相互碰撞的jamitons。 jamitons的碰撞会产生一个新的jamiton，其速度与初始速度不同。 观察到，出口速度使测试jamiton的速度和碰撞jamitons的初始速度平滑化。 其他性质如出口jamitons的振幅、长度和最大密度也得到了探讨。在振幅和最大出口密度的情况下，结果表明，在广泛的声速密度范围内，出口值超过或等于输入值。 另一方面，产生的jamiton比进入的jamitons更长。 最后，探讨了各种驾驶员反应时间的行为。 结果表明，某些性质不依赖于该时间，例如振幅、出口速度或最大密度，而出口长度则依赖于驾驶员反应时间。 显示英文摘要

摘要： Jamitons are self-sustained traveling wave solutions that arise in certain second-order macroscopic models of vehicular traffic. A necessary condition for a jamiton to appear is that the local traffic density breaks the so-called sub-characteristic condition. This condition states that the characteristic velocity of the corresponding first-order Lighthill-Whitham-Richards (LWR) model formed with the same desired speed function is enclosed by the characteristic speeds of the corresponding second-order model. The phenomenon of collision of jamitons in second-order models of traffic flow is studied analytically and numerically for the particular case of the second-order Aw-Rascle-Zhang (ARZ) traffic model [A.\ Aw, M.\ Rascle, {\it SIAM J.\ Appl.\ Math.} {\bf 60} (2000) 916--938; H.\ M.\ Zhang, {\it Transp.\ Res.\ B} {\bf 36} (2002) 275--290]. A compatibility condition is first defined to select jamitons that can collide each other. The collision of jamitons produces a new jamiton with a velocity different from the initial ones. It is observed that the exit velocities smooth out the velocity of the test jamiton and the initial velocities of the jamitons that collide. Other properties such as the amplitude of the exit jamitons, lengths, and maximum density are also explored.In the cases of the amplitude and maximum exit density it turns out that over a wide range of sonic densities, the exit values exceed or equal the input values. On the other hand, the resulting jamiton has a greater length than the incoming ones. Finally, the behavior for various driver reaction times is explored. It is obtained that some properties do not depend on that time, such as the amplitude, exit velocity, or maximum density, while the exit length does depend on driver reaction time.