Scaling and Condensation of Dry Active Matter Around Circular Obstacles

Abstract: Active Brownian particles confined to rigid substrates are known to accumulate near rigid boundaries and, under suitable conditions, undergo motility-induced phase separation (MIPS). A particularly intriguing manifestation of this behavior is the formation of self-sustained vortices around circular obstacles, which act as localized nucleation sites for particle aggregation. While several dynamical properties of such vortices have been previously characterized, their behavior in the thermodynamic limit remains largely unexplored. Here, we investigate how the mass and spatial extent of a dry active-matter vortex scale with system size. Using numerical simulations of repulsive active Brownian Particles interacting with a fixed circular obstacle, we measure the vortex mass, mean radius, and maximum radius as functions of the global area fraction, obstacle size, and system size. We find two distinct scaling regimes. At low densities, the vortex remains localized and its characteristic properties saturate as the system size increases. Above a critical density, however, the vortex mass grows extensively with the total number of particles, while its spatial dimensions scale linearly with the system size, indicating the emergence of an obstacle-stabilized condensed state.