In this article an anisotropic interaction model avoiding collisions is proposed. Starting point is a general isotropic interacting particle system, as used for swarming or follower-leader dynamics. An anisotropy is induced by rotation of the force vector resulting from the interaction of two agents. In this way the anisotropy is leading to a smooth evasion behaviour. In fact, the proposed model generalizes the standard models, and compensates their drawback of not being able to avoid collisions. Moreover, the model allows for formal passage to the limit 'number of particles to infinity', leading to a mesoscopic description in the mean-field sense. Possible applications are autonomous traffic, swarming or pedestrian motion. Here, we focus on the latter, as the model is validated numerically using two scenarios in pedestrian dynamics. The first one investigates the pattern formation in a channel, where two groups of pedestrians are walking in opposite directions. The second experiment considers a crossing with one group walking from left to right and the other one from bottom to top. The well-known pattern of lanes in the channel and travelling waves at the crossing can be reproduced with the help of this anisotropic model at both, the microscopic and the mesoscopic level. In addition, the 'right-before-left' and 'left-before-right' rule appear intrinsically for different anisotropy parameters.

中文翻译：

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避免碰撞的各向异性相互作用模型

本文提出了一种避免碰撞的各向异性相互作用模型。起点是一般的各向同性相互作用粒子系统，用于群体或跟随者-领导者动力学。各向异性是由两种药物相互作用产生的力矢量旋转引起的。这样，各向异性导致平滑的回避行为。实际上，所提出的模型对标准模型进行了概括，并弥补了它们无法避免冲突的缺点。此外，该模型允许形式传递到极限“无穷大的粒子数”，从而导致在平均场意义上进行介观描述。可能的应用是自动交通，人群拥挤或行人运动。在这里，我们将重点放在后者上，因为在行人动力学中使用两种情况对模型进行了数值验证。第一个研究通道的模式形成，其中两组行人以相反的方向行走。第二个实验考虑的是一个交叉路口，一组从左到右行走，另一组从下到上行走。借助这种各向异性模型，可以在微观和介观两个层面上再现通道中的车道和交叉口的行波模式。另外，对于不同的各向异性参数，“左前右”和“右前左”规则在本质上出现。借助这种各向异性模型，可以在微观和介观两个层面上再现通道中的车道和交叉口的行波模式。另外，对于不同的各向异性参数，“左前右”和“右前左”规则在本质上出现。借助这种各向异性模型，可以在微观和介观两个层面上再现通道中的车道和交叉口的行波模式。另外，对于不同的各向异性参数，“左前右”和“右前左”规则在本质上出现。