报告人： 汪守宏教授

地  点： 管研楼1611

Talk 1:

时   间： 5月22日下午 3:30-4:30

题   目： Dynamic Transition Theory and Gas-Liquid Transitions

摘   要:   In this talk, I shall present an example demonstrating the symbiotic interplay between advanced mathematics and physics -- the development of new mathematics under close links to the physics and in return its application to the physics for a better understanding and new predictions to the underlying physical phenomena.

The gas-liquid transition is one of the most basic problems in equilibrium phase transitions. In the pressure-temperature phase diagram, the gas-liquid coexistence curve terminates at a critical point C, also called the Andrews critical point. It is, however, still an open question why the Andrews critical point exists and what is the order of transition going beyond this critical point. To answer this basic question, a new dynamic model is established, and is consistent with the van der Waals equation in steady state level. With this dynamic model, we are able to derive a theory on the Andrews critical point C: 1) the critical point is a switching point where the phase transition changes from the first order with latent heat to the third order, and 2) the liquid-gas phase transition going beyond Andrews point is of the third order.

This clearly explains why it is hard to observe the liquid-gas phase transition near the critical point.

The study is based on the development of a new dynamic transition theory with the philosophy to search the complete set of transition states. The theory has been applied to a wide range of nonlinear problems.  This is joint with Tian Ma.

Talk 2:

时  间：  5月24日下午4:30-5:30

题  目：  Stability and Transitions in Fluid Dynamics

摘  要：  In this talk, I shall address two types of transitions in fluid dynamics -- the transition in the physical spaces and the dynamic transition in the phase space. The study is based on the geometric theory of incompressible flows and the dynamic transition theory for nonlinear dynamical systems. To demonstrate the main ideas, we focus on two examples: 1) the dynamic transition and pattern formation of the Benard convection, and 2) the formation of the Taylor vortices. These have become over the years a paradigm of instabilities, bifurcations, structure formation, and chaotic behavior in fluid dynamics as well as in physical systems in general. In particular, for the Taylor problem, contrary to what is commonly believed, we show tha  the  the Taylor vortices  do not appear after the first dynamical bifurcation, and they appear only when the Taylor number is further increased to cross another critical value so that a structural bifurcation occurs. This structural bifurcation corresponds to the boundary-layer and interior separations of the flow structure in the physical space. 

主办单位：

中国科学技术大学数学科学学院

国家数学与交叉科学中心合肥分中心

欢迎感兴趣的师生参加！