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Double milling in self-propelled swarms from kinetic theory
We present a kinetic theory for swarming systems of
interacting, self-propelled discrete particles. Starting from the
Liouville equation for the many-body problem we
derive a kinetic equation for the single particle probability
distribution function and the related macroscopic hydrodynamic equations.
General solutions include flocks of constant density and fixed
velocity and other non-trivial morphologies such as compactly
supported rotating mills. The kinetic theory approach leads us to the
identification of macroscopic structures otherwise not recognized as
solutions of the hydrodynamic equations, such as double mills of two
superimposed flows. We find the conditions allowing for the
existence of such solutions and compare to the case of single
mills.