We derive a hydrodynamic description of metric-free active matter: starting from self-propelled particles aligning with neighbors defined by “topological” rules, not metric zones—a situation advocated recently to be relevant for bird flocks, fish schools, and crowds—we use a kinetic approach to obtain well-controlled nonlinear field equations. We show that the density-independent collision rate per particle characteristic of topological interactions suppresses the linear instability of the homogeneous ordered phase and the nonlinear density segregation generically present near threshold in metric models, in agreement with microscopic simulations.

• Received 30 March 2012

DOI:https://doi.org/10.1103/PhysRevLett.109.098101