We model and study the patterns created through the interaction of collectively moving self-propelled particles (SPPs) and elastically tethered obstacles. Simulations of an individual-based model reveal at least three distinct large-scale patterns: travelling bands, trails and moving clusters. This motivates the derivation of a macroscopic partial differential equations model for the interactions between the self-propelled particles and the obstacles, for which we assume large tether stiffness. The result is a coupled system of nonlinear, non-local partial differential equations. Linear stability analysis shows that patterning is expected if the interactions are strong enough and allows for the predictions of pattern size from model parameters. The macroscopic equations reveal that the obstacle interactions induce short-ranged SPP aggregation, irrespective of whether obstacles and SPPs are attractive or repulsive. Electronic supplementary material The online version of this article (10.1007/s11538-020-00805-z) contains supplementary material, which is available to authorized users.

中文翻译：

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自推进粒子穿过障碍物的大规模动力学：模型推导和模式形成

我们对通过集体移动的自推进粒子 (SPP) 和弹性拴系障碍物的相互作用创建的模式进行建模和研究。基于个体的模型的模拟揭示了至少三种不同的大规模模式：旅行带、轨迹和移动集群。这激发了自推进粒子和障碍物之间相互作用的宏观偏微分方程模型的推导，为此我们假设系绳刚度很大。结果是非线性、非局部偏微分方程的耦合系统。线性稳定性分析表明，如果相互作用足够强并且允许根据模型参数预测图案大小，则可以预期图案化。宏观方程表明障碍物相互作用引起短程 SPP 聚集，无论障碍和 SPP 是有吸引力的还是令人厌恶的。电子补充材料本文的在线版本（10.1007/s11538-020-00805-z）包含补充材料，可供授权用户使用。