Explore a comprehensive lecture on emergent behavior in collective dynamics, delivered by Eitan Tadmor at the 2022 Virtual Joint Mathematics Meetings. Delve into various examples of emergence involving living agents and collective dynamics, covering fundamental concepts such as alignment, opinion dynamics, flocking, swarming, and synchronization. Examine the role of communication kernels, anticipation in alignment, and the 3 Zone model. Investigate questions about alignment dynamics, large-time behavior, and graph connectivity. Analyze emergent behavior instability, large crowd dynamics, hydrodynamic descriptions, and energy fluctuations. Discover the implications of short-range interactions and topological kernels. Gain insights into how different fields approach collective dynamics, with a focus on the role of empirical data in biology.
Overview
Syllabus
Intro
Examples of emergence with living agents
Examples of emergence in collective dynamics
Fundamentals
Alignment - a paradigm for pairwise interactions
Opinion Dynamics
Rating
Flocking
Swarming
Synchronization
The role communication kernels
Communication kernels (-) - where do they come from
Models of collective dynamics
Anticipation breeds alignment
Collective dynamics — the 3 Zone model
3Zone protocol: on the role of alignment
Questions about alignment dynamics
Large time behavior and connectivity of graph dynamics
Emergent behavior — instability
Large crowd dynamics N
Hydrodynamic description
Energy fluctuations
Hydrodynamic Alignment
Short range interactions - topological kernels
Collective dynamics — different questions arise in different fields
Collective dynamics - different questions and tools arise in different fields Biology - The role of empirical data
Taught by
Joint Mathematics Meetings
