Analysis of Dynamics of Doi-Onsager Phase Transition
Seminar Room 1, Newton Institute
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. This problem was postulated by Onsager via minimization of a free energy and dynamically by Doi equation. It also appears in the mean-field equation of Vicsek model for flocking of birds. In this talk, I will present a new entropy for the Doi-Onsager equation which enable us to give a rigorous justification of this dynamics phase transition. This is a joint work with Pierre Degond and Amic Frouvelle.