Activity drives self-assembly of passive soft inclusions in active nematics

Active nematics are out-of-equilibrium systems in which energy injection at the microscale drives emergent collective behaviors, from spontaneous flows to active turbulence. While the dynamics of these systems have been extensively studied, their potential for controlling the organization of embedded soft particles remains largely unexplored. Here, we investigate how passive droplets suspended in an active nematic fluid self-organize under varying activity levels and packing fractions. Through numerical simulations, we uncover a rich phase diagram featuring dynamic clustering, activity-induced gelation, and a novel activity-driven deformability-induced phase separation regime where activity stabilizes dense droplet assemblies. We find that droplet deformability plays a key role in enabling this regime, as it allows droplets to absorb the stress exerted by the surrounding active fluid. Crucially, we demonstrate that temporal modulation of activity enables precise control over structural morphological transitions. Our results suggest new routes to design adaptive smart materials with tunable microstructure and dynamics, bridging active nematics with applications in programmable colloidal assembly and bio-inspired material design.