Department of Mathematics, North Carolina State University, Raleigh, NC, 27695, USA.
Department of Mathematics, Imperial College London, London, SW7 2AZ, UK.
Bull Math Biol. 2020 Sep 25;82(10):129. doi: 10.1007/s11538-020-00805-z.
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.
我们对通过集体运动的自主粒子（SPP）与弹性束缚障碍物相互作用产生的图案进行建模和研究。基于个体的模拟揭示了至少三种独特的大尺度模式：移动带、轨迹和移动团簇。这促使我们推导出一个用于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，我们假设系绳的刚度很大。结果是一个非线性、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，就会出现图案形成，并且可以根据模型参数预测图案的大小。宏观方程表明，障碍物相互作用会引起短程 SPP 聚集，而与障碍物和 SPP 是吸引还是排斥无关。
