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Shouhong Wang

2010-12-30
14:00:00 - 15:00:00

308 , Mathematics Research Center Building (ori. New Math. Bldg.)

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, using the Landau's mean field theory and the Le Chatelier principle, a dynamic model for the gas-liquid phase transitions is established, and the model 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. In addition, the study suggests an asymmetry principle of fluctuations, which we also discover in phase transitions for ferromagnetic systems.
The analysis is based on the dynamic transition theory we have developed recently 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.