主 题: Introduction to Dynamic Transition Theory and its Applications
报告人: Prof. Shouhong Wang (美国Indiana 大学数学系)
时 间: 2009-11-24、25日共两次报告,时间及地点相
地 点: 理科一号楼 1418
In these two talks, I shall present a brief overview of the dynamic transition theory developed recently by Ma and myself, and its applications. The main philosophy of the theory is to search for the full set of transition states, giving a complete characterization on stability and transition. The set of transition states --physical "reality"-- is represented by a local attractor. Following this philosophy, the dynamic transition theory is developed to identify the transition states and to classify them both dynamically and physically. The theory has a wide range of applications in both equilibrium and nonequilibrium phase transitions.
In the first talk, I shall focus on the introduction of the dynamic transition theory, including 1) the new classification scheme of phase transitions, 2) strategies for center manifold reductions, and 3) systematic approaches to classify the transitions.
In the second talk, to demonstrate the wide range of applications of the theory, I shall study the phase separation of binary systems modeled by the Cahn-Hilliard equation. If time permits, I shall discuss applications to superconductivity and superfluidity as well. In these applications, the study leads to some specific physical predictions, which are otherwise unknown from both the physical and mathematical points of view. For example, as a physical prediction, we derive the existence of a new superfluid phase C for liquid helium-3.