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Multiscale models in social (networks) applications, eventually combining mean-field and kinetic equations with either microscopic
or macroscopic objects, are approaches of strongly increasing importance and high potential for future quantitative research.
Typically, individual-based models need to be intelligently coarse grained
to translate the relevant microstructure information to a mesoscopic (Boltzmann-level) or to a macroscopic (continuum) level.
Considering a minimal discrete ODE model for colective motion (crowd evacuation) scenario, I address following basic questions: (i) What is the natural scaling for the averaging? (ii) How much microstructural information needs to be kept to capture the specific individual-level interaction responsible for the formation and propagation of the macroscopically-observed pattern (for instance, lane formation in pedestrian counterflow). (iii) What are the main microscopic interactions responsible for the macroscopic cross-diffusion transport mechanism sometimes arising in pedestrian's motion? |
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