Collision Operators for Mesoscale Simulations of Flocks*

Flocking is the quintessential example of emergent collective behaviour in active systems, seen across scales from bacterial dynamics to drone swarms. The agent-based Vicsek model, and its hydrodynamic limit, continue revealing exciting physics, including new non-equilibrium phases. However, understanding and simulating flocks at the mesoscale, i.e., between the microscopic and hydrodynamic limits, remains a significant challenge. We utilize the Multi-Particle Collision Dynamics framework and develop a set of collision operators to simulate flocking at the mesoscale. Comparing the scalar order parameters, density fluctuations, and autocorrelation functions to those obtained from agent-based models, we show that our proposed operators reproduce the dynamics and out-of-equilibrium phases of the Vicsek model and its variants. We expect our algorithm to reveal exciting dynamics at the mesoscale between micro and macroscopic limits of flocking, offer a pathway to coarse-graining other active systems, and allow extensions to more complex flocking behaviours.