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Lattice Model to Derive the Fluctuating Hydrodynamics of Active Particles with Inertia
A Manacorda1,2, A Puglisi2
1Dipartimento di Fisica, Sapienza Università di Roma, piazzale A. Moro 2, 00185 Roma, Italy.
Abstract:
We derive the hydrodynamic equations with fluctuating currents for the density, momentum, and energy fields for an active system in the dilute limit. In our model, nonoverdamped self-propelled particles (such as grains or birds) move on a lattice, interacting by means of aligning dissipative forces and excluded volume repulsion. Our macroscopic equations, in a specific case, reproduce a transition line from a disordered phase to a swarming phase and a linear dispersion law accounting for underdamped wave propagation. Numerical simulations up to a packing fraction ∼10% are in fair agreement with the theory, including the macroscopic noise amplitudes. At a higher packing fraction, a dense-diluted coexistence emerges. We underline the analogies with the granular kinetic theories, elucidating the relation between the active swarming phase and granular shear instability.
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