Emergent behavior in swarming hydrodynamics

Abstract: I will discuss recent developments in our study of swarming dynamics. A main question of interest is the emergent behavior which we characterize by spectral analysis, covering different classes of long-range and short-range communication kernels. These include examples of metric-based and topologically-based kernels, and kernels derived from a unified paradigm of anticipation. In the canonical case of metric-based short-range kernels, we derive lower-bounds on the spectral gap, independent of thermal equilibrium (no closure for the pressure), which yield an emergent behavior of non-vacuous smooth solutions. The latter are known to exist in one- and two space dimensions and we settle the question of existence for arbitrary dimension.

MathematicsPhysics

Audience: researchers in the topic

Nečas Seminar on Continuum Mechanics

Series comments: This seminar was founded on December 14, 1966.

Faculty of Mathematics and Physics, Charles University, Sokolovská 83, Prague 8. If not written otherwise, we will meet on Mondays at 15:40 in lecture hall K3 (2nd floor).