| Abstract: |
| Phase transition is a universal phenomena of Nature. The central problem in statistical physics and in nonlinear sciences is on phase transitions. All phase transitions in Nature that we have encountered can be classified into the following two types: 1) dynamical phase transitions, and
2) topological phase transitions (TPTs), also called the pattern formation transitions.
The notion of dynamic phase transition is applicable to all dissipative systems, including nonlinear dissipative systems in statistical physics, fluid dynamics, atmospheric and oceanic sciences, biological and chemical systems etc. The systematic dynamic transition theory and its various applications are synthesized in [1].
TPTs are entirely different from dynamic phase transitions. Intuitively speaking, a TPT refers to the change of the topological structure in the physical space as certain system control parameter crosses a critical threshold. The notion of TPTs is originated from the pioneering work by J. Michael Kosterlitz and David J. Thouless, where they identified a completely new type of phase transitions in two-dimensional systems where topological defects play a crucial role. With this work, they received 2016 Nobel prize in physics.
In this talk, we review recent theories developed by the authors on both dynamic phase transitions and topological phase transitions. The theories are then applied to boundary layer and interior separation phenomena in geophysical fluid dynamics, including the wind-drivern circulation and tropical cyclones.
[1] Tian Ma and Shouhong Wang, Phase Transition Dynamics, Springer-Verlag, November, 2013, XX, 555 pp. 153 illus., 2 illus. in color, 2013
[2] Tian Ma and Shouhong Wang, Geometric Theory of Incompressible Flows with Applications to Fluid Dynamics, AMS Mathematical Surveys and Monographs Series, vol. 119, 2005, 234 pp.
[3] Tian Ma and Shouhong Wang, Topological Phase Transitions I: Quantum Phase Transitions, 2017, Hal-01651908
[4] Tian Ma and Shouhong Wang, Topological Phase Transitions II: Spiral Structure of Galaxies, 2017, Hal-01671178
[5] Tian Ma and Shouhong Wang, Topological Phase Transition III: Solar Surface Eruptions and Sunspots, 2017, Hal-01672381
[6] Tian Ma and Shouhong Wang, Topological Phase Transitions IV: Dynamic Theory of Boundary-Layer Separations, 2017, Hal-01672759
[7] Ruikuan Liu, Tian Ma, Shouhong Wang and Jiayang Yang, Topological Phase Transition V: Interior Separations and Cyclone Formation Theory, 2017, Hal-01673496
[8] Ruikuan Liu, Tian Ma, Shouhong Wang and Jiayang Yang, Dynamic Theory of Fluctuations And Critical Exponents of Thermodynamic Phase Transitions, 2017, Hal-01674269 |
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