Consensus and flocking: self-organized dynamics from particle to hydrodynamic descriptions
Eitan Tadmor,  University of Maryland

Self-organized dynamics is driven by ?rules of engagement", which  describe how each agent interacts with its neighbors. They consist of  long-term attraction, mid-range alignment and short-range repulsion. Many  self-propelled models are driven by the balance between these three forces,  which yield emerging structures of interest. Examples range from consensus  of voters and traffic flows to the formation of flocks of birds or school of  fish, tumor growth etc.

We introduce a new particle-based model, driven by self-alignment, which  addresses several drawbacks of existing models for self-organized dynamics.  The model is independent of the number of agents:  only their geometry in phase space is involved. We will explain the emerging consensus and  unconditional flocking behavior in the proposed model in the presence of  non-symmetric interactions which decay sufficiently slow, and discuss the  difficulties with tracing graph connectivity otherwise.  The methodology carries over from particle to kinetic and hydrodynamic  descriptions.