Self-organized dynamics: aggregation and flocking
Dr. Changhui Tan
Department of Mathematics
Rice University
Abstract: Self-organized behaviors are commonly observed in nature and human societies, such as bird flocks, fish swarms and human crowds. In this talk, I will present some celebrated mathematical models, with simple small-scale interactions that lead to the emergence of global behaviors: aggregation and flocking. The models can be constructed through a multiscale framework: from microscopic agent-based dynamics, through kinetic mean-field descriptions, to macroscopic fluid systems. I will discuss some recent analytical, numerical and computational results on the derivation of the systems in different scales, global wellposedness theory, large time behaviors, as well as interesting connections to some classical equations in fluid mechanics.
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