Effect of Weak Non-Conservative Dynamics on Pattern Formation in Scalar Active Matter

Abstract

Biological systems such as bacteria and cells undergo growth or degradation, resulting in weak violations of mass conservation. We investigate how such weak non-conservative dynamics affect phase separation in scalar active matter by incorporating a reaction term into a minimal continuum model. Through numerical simulations and linear stability analysis, we show that even weak non-conservative reactions arrest coarsening and stabilize nonequilibrium microphase-separated states. With increasing activity, the system undergoes a morphological transition from interconnected labyrinthine patterns to worm-like structures and eventually to isolated droplets. Quantitative analysis of the correlation function and static structure factor reveals a well-defined steady-state characteristic length. Qualitative analysis of the resulting phases shows that the non-conservative reaction primarily promotes microphase separation and enhances local hexagonal ordering, while activity predominantly controls the domain morphology. Our results demonstrate that weak violations of mass conservation fundamentally alter the nonlinear coarsening dynamics of active phase separation and provide a minimal framework for understanding pattern formation in related systems.