Active Brownian Particles with Alignment

Active Brownian particles (ABP) self-propel at speed v₀ and undergo rotational diffusion D_r. Alignment interaction J couples orientations: polar (J favors parallel) vs nematic (J favors ±parallel). The order-disorder transition is driven by J/D_r. Polar order → flocking; nematic order → lanes with ±½ topological defects (half-integer charges arise from the ℤ₂ symmetry). Motility contrast (Δv): fast movers in a slow background undergo motility-induced aggregation — a distinct mechanism from MIPS. Defects in nematic active matter are motile: +½ defects move in the direction of their cusp; −½ defects are stationary in passive nematics but advect in active ones.