Large-Scale Dynamics of Self-propelled Particles Moving Through Obstacles: Model Derivation and Pattern Formation

Pedro Aceves-Sanchez (1) , Pierre Degond (2) , Eric E Keaveny (2) , Angelika Manhart (3) , Sara Merino-Aceituno (4) , Diane Peurichard (5)

1 NC State - North Carolina State University [Raleigh]
2 Imperial College London
3 UCL - University College of London [London]
4 University of Vienna [Vienna]
5 MAMBA - Modelling and Analysis for Medical and Biological Applications

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.

Mots clés: Self-propelled particles; Hydrodynamic limit; Pattern formation; Stability analysis; Gradient flow; Non-local interactions

Domaines: Mathématiques [math]

Pedro Aceves-Sanchez, Pierre Degond, Eric E Keaveny, Angelika Manhart, Sara Merino-Aceituno, et al.. Large-Scale Dynamics of Self-propelled Particles Moving Through Obstacles: Model Derivation and Pattern Formation. Bulletin of Mathematical Biology, 2020, 82 (10), pp.129. ⟨10.1007/s11538-020-00805-z⟩. ⟨hal-03138284⟩