Single to Double Mill Small Noise Transition via Semi-Lagrangian Finite Volume Methods

Understand

We show that double mills are more stable than single mills under stochastic perturbations in swarming dynamic models with basic attraction-repulsion mechanisms.

• In order to analyse accurately this fact, we will present a numerical technique for solving kinetic mean field equations for swarming dynamics.
• Numerical solutions of these equations for different sets of parameters will be presented and compared to microscopic and macroscopic results.
• As a consequence, we numerically observe a phase transition diagram in term of the stochastic noise going from single to double mill for small stochasticity fading gradually to disordered states when the noise strength gets larger.