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CNA Seminar/Colloquium/Joint Pitt-CNA Colloquium

Changhui Tan
University of Maryland
Title: Flocking dynamics in different scales

Abstract: Self-organized behavior is very common in nature and human societies. One widely discussed example is the flock formed by birds flying towards the same direction. Several models such as Cucker-Smale and Motsch-Tadmor are very successful in characterizing the flocking behavior. In this talk, we will discuss about flocking models in different scales, from agent-based models, through kinetic descriptions, to hydrodynamic systems. For kinetic representation, flocking is realized as a concentration in velocity variable. Several numerical methods will be introduced to deal with the delta-singularity. The macroscopic representation yields a very interesting fluid system: compressible Eulerian dynamics with nonlocal alignment. We show a critical threshold phenomenon for the fluid system. Under suitable initial conditions, the system has global strong solution, and it converges to a flock. On the other hand, another set of initial conditions will lead to a finite time break down of the system. We also add attraction-repulsion force to the system and study the long time behaviors.

Date: Tuesday, September 30, 2014
Time: 1:30 pm
Location: Wean Hall 7218
Submitted by:  David Kinderlehrer