报告题目: |
Dynamics of Orientational Alignment and Phase Transition |
报告人: |
Prof. Jian-Guo Liu |
|
Duke University and Tsinghua University
|
报告时间: |
2010-11-18 15:00 |
报告地点: |
理科楼1304报告厅 |
主办单位: |
数学科学系 |
简介: |
Phase transition of directional field appears in some physical and biological systems such as ferromagnetism near Currie temperature, flocking dynamics near critical mass of self propelled particles. Dynamics of orientational alignment associated with the phase transition can be effectively described by a mean field kinetic equation. The natural free energy of the kinetic equation is non-convex with a minimizer level set consisting of a sphere at super-critical case, a typic spontaneous symmetry breaking behavior in physics. In this talk, I will present some analytical results on this dynamics equation of orientational alignment and exponential convergence rate to the equilibria for both supper and sub critical cases, as well at algebraic convergence rate at the critical case. A new entropy and spontaneous symmetry breaking analysis played an important role in our analysis. This is a joint work with Pierre Degond and Amic Frouvelle. |
|
