Speaker
Description
Almost universally, individual agents in collectives of active particles require time to examine their surroundings and form an appropriate response. Examples of when perception and actuation delays significantly affect system dynamics can be found in living organisms, robotic collectives, communication networks, and cellular processes like biopolymer assembly and migration. Still, theoretical descriptions of these systems often neglect the delays for mathematical simplicity. In particular, formulating a field theory of many-body systems interacting with time delay is an open problem.
Here, we investigate the applicability of spin-wave approximation to particle active matter models featuring delays. These models include the Vicsek and the more recent Inertial Spin Model (ISM), with the former neglecting and the latter accounting for orientational inertia. Our work introduces two levels of spin-wave approximation: discrete network and the continuum limit. The Vicsek model shows a good agreement with both types of approximation, provided that local perturbations remain within certain bounds. Conversely, the ISM exhibits satisfactory agreement only at the network level. Our findings represent a step towards a comprehensive hydrodynamic theory for delayed active many-particle models.
