Spontaneous filament formation and network self-assembly via active phase separation

We introduce Active Model H${}^{-}$, a scalar phase-field model of non-equilibrium phase separation in the overdamped hydrodynamic limit, and show that it produces filamentous networks with enhanced connections and arrested coarsening, a morphology not observed in existing scalar active field theories. Isolated filaments are unstable to spontaneous bending, and the resulting curvature drives self-propulsion towards the convex side, causing them to collide and assemble into a percolating network. The networks are locally non-equilibrium, with anomalously curved edges, disordered vertex angles and heterogeneous topological charge, yet recover Lewis’s law macroscopically. Under noise they show balanced break and reform dynamics.