论文标题
自前线颗粒的大规模动力学在障碍物中移动：模型推导和模式形成
Large-scale dynamics of self-propelled particles moving through obstacles: model derivation and pattern formation
论文作者
论文摘要
我们通过集体移动的自旋转颗粒（SPP）和弹性束缚的障碍物的相互作用进行建模和研究模式。基于个体的模型的模拟至少显示了三种不同的大规模模式：行进乐队，步道和移动群集。这激发了宏观局部微分方程模型的推导，用于自行颗粒与障碍物之间的相互作用，为此我们假定较大的系绳刚度。结果是一个非线性，非本地部分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，并且允许从模型参数预测模式大小，则预期图案化。宏观方程表明，障碍物相互作用会引起短距离的SPP聚集，而不论障碍和SPP是有吸引力还是令人反感的。
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 non-linear, 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.
