2020/03/09 by Roman Shvydkoy, Eitan Tadmor, Shvydkoy, Roman +1
Biochemistry, Genetics and Molecular Biology · Engineering · Social Sciences · #35Q35 #76N10 #92D25 #Adaptation and Self-Organizing Systems (nlin.AO) #Analysis of PDEs (math.AP) #Diffusion and Search Dynamics #Evolutionary Game Theory and Cooperation #FOS: Mathematics #FOS: Physical sciences #Slime Mold and Myxomycetes Research
paper · pdf · doi:10.48550/arxiv.2003.04489
openalex publication_date 2020/03/09 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
We study the multi-scale description of large-time collective behavior of\nagents driven by alignment. The resulting multi-flock dynamics arises naturally\nwith realistic initial configurations consisting of multiple spatial scaling,\nwhich in turn peak at different time scales. We derive a `master-equation'\nwhich describes a complex multi-flock congregations governed by two\ningredients: (i) a fast inner-flock communication; and (ii) a slow(-er)\ninter-flock communication. The latter is driven by macroscopic observables\nwhich feature the up-scaling of the problem. We extend the current mono-flock\ntheory, proving a series of results which describe rates of multi-flocking with\nnatural dependencies on communication strengths. Both agent-based, kinetic, and\nhydrodynamic descriptions are considered, with particular emphasis placed on\nthe discrete and macroscopic descriptions.\n