Mathematical Aspects of Collective Dynamics:
Kinetic Description and Fractional Diffusion

Flocking with compactly supported communication

Jan Peszek

University of Maryland


The talk addresses the issue of alignment of strong solutions to the Cucker-Smale flocking model with compactly supported interactions. Such interactions may produce dynamics, where distant agents do not communicate with each other at all, making alignment between them impossible. I will introduce a notion of ''chain connectivity'' that controls the distant interactions by interactions between the intermediate agents. The key factor is the chain connectivity propagates in time, provided that the intensity of the interactions is high enough. This way it is possible to control the global alignment through certain localized quantities. This method is flexible: it can be used with a variety of interaction kernels, in microscopic and macroscopic scale levels and periodic boundary conditions as well as compactly supported data in the real space of any dimension. The talk presents a joint work with Javier Morales and Eitan Tadmor.