Short-range interactions and the emergence of higher-order flocking structures
Eitan Tadmor, University of Maryland, USA
We discuss the large-time, large-crowd behavior of different models for flocking dynamics. The models are driven by different “rules of engagement” which quantify how each member of the flock interacts with its immediate neighbors.
We address two related central questions:
(i) How short-range interactions lead, over time, to the emergence of long-range patterns;
(ii) How the flocking behavior of large crowds is captured by their hydrodynamic description.
Here we introduce a new communication protocol which incorporates short-range kernels restricted to geometric balls and adapted to topological neighborhoods dictated by the local density inside these balls. We prove the unconditional emergence of flocking.