A Lattice Boltzmann Method for Simulating Dry and Dense Active Fluids

Symmetry serves a foundational role in all areas of physics today. In classical many-body problems, by first clarifying the underlying symmetries of a system of interest, one can derive the hydrodynamic equations of motion that govern the dynamics of the system. Analysis of a hydrodynamic theory can elucidate the universal behavior exhibited by all generic systems respecting the prescribed set of symmetries; conversely, any particular many-body system defined by microscopic rules that respect the same set of symmetries can also be used to study the associated universal behavior in the hydrodynamic limit. An example of the latter is the use of lattice gas cellular automata to study the Navier-Stokes equations. Superseding the lattice gas cellular automata is the celebrated lattice Boltzmann method, which led to a drastic improvement in computational efficiency. Surprisingly, the development of a lattice Boltzmann method for dry active fluids is still lacking, which is what we accomplish here. We will demonstrate the usefulness of our approach by clarifying the phase behaviour of polar active fluids and motility-induced phase separation. In particular, we show that there are generically three distinct phases in polar active fluids separated by two discontinuous phase transitions.