  Active matter is not only indispensable to our understanding of diverse
biological processes, but also provides a fertile ground for discovering novel
physics. Many emergent properties impossible for equilibrium systems have been
demonstrated in active systems. These emergent features include
motility-induced phase separation, long-ranged ordered (collective motion)
phase in two dimensions, and order-disorder phase co-existences (banding and
reverse-banding regimes). Here, we unify these diverse phase transitions and
phase co-existences into a single formulation based on generic hydrodynamic
equations for active fluids. We also reveal a novel co-moving co-existence
phase and a putative novel critical point.
