Phase Transition Dynamics

1. Front Matter

   Pages i-xxii

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2. Introduction to Dynamic Transitions

   • Tian Ma, Shouhong Wang

   Pages 1-24

3. Dynamic Transition Theory

   • Tian Ma, Shouhong Wang

   Pages 25-121

4. Equilibrium Phase Transition in Statistical Physics

   • Tian Ma, Shouhong Wang

   Pages 123-248

5. Fluid Dynamics

   • Tian Ma, Shouhong Wang

   Pages 249-372

6. Geophysical Fluid Dynamics and Climate Dynamics

   • Tian Ma, Shouhong Wang

   Pages 373-446

7. Dynamical Transitions in Chemistry and Biology

   • Tian Ma, Shouhong Wang

   Pages 447-525

8. Back Matter

   Pages 527-555

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This book is an introduction to a comprehensive and unified dynamic transition theory for dissipative systems and to applications of the theory to a range of problems in the nonlinear sciences. The main objectives of this book are to introduce a general principle of dynamic transitions for dissipative systems, to establish a systematic dynamic transition theory, and to explore the physical implications of applications of the theory to a range of problems in the nonlinear sciences. The basic philosophy of the theory is to search for a complete set of transition states, and the general principle states that dynamic transitions of all dissipative systems can be classified into three categories: continuous, catastrophic and random. The audience for this book includes advanced graduate students and researchers in mathematics and physics as well as in other related fields.

• Nonlinear Sciences
• Phase Transition Dynamics
• dissipative partial differential equations
• time-dependent Ginzburg-Landau superconductivity model
• partial differential equations
• fluid- and aerodynamics

From the book reviews:

“The goals of this interesting book are to derive a general principle of dynamic transitions for dissipative systems and to establish a systematic dynamic transition theory for a wide range of problems in the nonlinear sciences. … The intended audience for this book includes students and researchers working on nonlinear problems in physics, meteorology, oceanography, biology, chemistry, and the social sciences.” (Carlo Bianca, Mathematical Reviews, December, 2014)

“This is a clearly written book on numerous types of phase transitions taken in a broad sense when a dynamical dissipative system transforms from one physical state into another. … The book is a very useful literature not only for the professionals in the field of dynamic systems and phase transitions but also for graduate students due to its interdisciplinary coverage and state-of-the-art level.” (Vladimir Čadež, zbMATH, Vol. 1285, 2014)

• Department of Mathematics, Sichuan University, Sichuan, People's Republic of China

  Tian Ma

• Department of Mathematics, Indiana University, Bloomington, USA

  Shouhong Wang

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