Eitan Tadmor, University of Maryland

A fascinating aspect of collective dynamics is self-organization of small scale interactions into high-order structures with larger-scale patterns. It is a characteristic feature of “social particles” which actively probe the environment and emerge in various types of clusters. In different contexts these clusters take the form of flocks, swarms, consensus, synchronized states etc.. In this talk I will survey recent mathematical developments in collective dynamics driven by alignment.   Alignment protocols   reflect the tendency of steering towards average headings, and are governed by different classes of pairwise communication kernels. A main question of interest is how different kernels affect the long-time, large-crowd dynamics. In particular, we discuss emergent behavior for a general class of pressure tensors without a closure assumption, proving the flocking of p-alignment hydrodynamics.

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