Emergence and self-organization in complex systems
Student No.:50
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)
Starting Date:2012-7-3
Ending Date:2012-8-14

Course description:


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