Phase transitions, hysteresis, and hyperbolicity for self-organized alignment dynamics
主 题: Phase transitions, hysteresis, and hyperbolicity for self-organized alignment dynamics
报告人: Professor Jian-Guo Liu (Duke University)
时 间: 2013-07-15 10:30-11:30
地 点: 理科一号楼1114 （数学所活动）
We provide a complete and rigorous description of phase transitions for kinetic models of self-propelled particles interacting through alignment. These models exhibit a competition between alignment and noise. Both the alignment frequency and noise intensity depend on a measure of the local alignment. We show that, in the spatially homogeneous case, the phase transition features (number and nature of equilibria, stability, convergence rate, phase diagram, hysteresis) are totally encoded in how the ratio between the alignment and noise intensities depend on the local alignment. In the spatially inhomogeneous case, we derive the macroscopic models associated to the stable equilibria and classify their hyperbolicity according to the same function. This is a joint work with Pierre Degond of University of Toulouse and Amic Frouvelle University of Paris Dauphine.