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We model and study the patterns created through the interaction ofcollectively moving self-propelled particles (SPPs) and elastically tetheredobstacles. Simulations of an individual-based model reveal at least threedistinct large-scale patterns: travelling bands, trails and moving clusters.This motivates the derivation of a macroscopic partial differential equationsmodel for the interactions between the self-propelled particles and theobstacles, for which we assume large tether stiffness. The result is a coupledsystem of non-linear, non-local partial differential equations. Linearstability analysis shows that patterning is expected if the interactions arestrong enough and allows for the predictions of pattern size from modelparameters. The macroscopic equations reveal that the obstacle interactionsinduce short-ranged SPP aggregation, irrespective of whether obstacles and SPPsare attractive or repulsive.

Large-scale dynamics of self-propelled particles moving through obstacles: model derivation and pattern formation