2019/11/25 by Daniel Lear, Roman Shvydkoy · 25 citations
Computer Science · Earth and Planetary Sciences · Mathematics · Physics and Astronomy · #Classical mechanics #Collective motion #Computer science #Context (archaeology) #Convergence (economics) #Distributed Control Multi-Agent Systems #Euler's formula #Flock #Flocking (texture) #Geology #Geometry #Marine and coastal ecosystems #Mathematical analysis #Mathematics #Micro and Nano Robotics #Physics #Stability (learning theory) #Traveling wave #Vector field #math.AP
paper · pdf · doi:10.2140/apde.2022.15.175
published in Analysis & PDE 15(1), 175-196 (Mathematical Sciences Publishers) · 18 pages
arxiv created 2019/11/25 · openalex publication_date 2022/03/16 · arxiv updated 2022/03/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In this note we reveal new classes of solutions to hydrodynamic Euler alignment systems governing collective behavior of flocks. The solutions describe unidirectional parallel motion of agents, and are globally well-posed in multi-dimensional settings subject to a threshold condition similar to the one dimensional case. We develop the flocking and stability theory of these solutions and show long time convergence to traveling wave with rapidly aligned velocity field. In the context of multi-scale models introduced in \citeST-multi our solutions can be superimposed into Mikado formations -- clusters of unidirectional flocks pointing in various directions. Such formations exhibit multiscale alignment phenomena and resemble realistic behavior of interacting large flocks.