Groups and interactions in data, networks and biology

Particle, kinetic, and hydrodynamic models of swarming and network traffic models

Jian-Guo Liu

Duke University

In this talk, I will present some rigorous results on coarse graining and closures from agent based models to kinetic models, and to hydrodynamical models for swarm and network traffic models. I will discuss phase transitions, panic behavior, and emergence of coherent states from a balance of competing influences such as focusing, concentration, or aggregation effects vs dispersing, defocusing, or fragmentation effects. I will connect the pressure, viscosity and capillarity in the derived hydrodynamic models to the order parameter, interaction frequency and interaction range among agents.