|Emergence and self-organization in complex systems|
|Time：||Tue. 15:10-17:00 ; Fri. 10:10-12:00|
|Instructor：||Jian-Guo Liu [Duke University]|
|Place：||Lecture Hall, Floor 3, Jin Chun Yuan West Building (近春园西楼3层报告厅)|
Spontaneous emergence of coherent structure and self-organization as a result of simple local interactions between agents are one of the main characterizations for many biological, social and physical complex systems.
In this short course, I will present some mathematical tools to analysis emergence phenomena, particularly for phrase translation and self-organization.
I will also give some rigorous derivations of some macroscopic (kinetic and hydrodynamical) models from the microscopic dynamics (interacting particle system) at the agents level in these complex systems.
The subjects I will discuss are:
Cucker-Smale flocking dynamics and kinetic model.
Vicsek self-alignment model in particle system and kinetic modes
Generalized collisional invariants and derivation of hydrodynamical equations
Phrase translation for oriented interacting particle system and Onsager theory
Doi-Shelley kinetic models for bacterium swimming
Keller-Segel system in chemotaxis