Phase Transition Dynamics

Description

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. This second edition introduces a unified theory for topological phase transitions, provides a first-principle approach to statistical and quantum physics, and offers a microscopic mechanism of quantum condensates (Bose-Einstein condensation, superfluidity, and superconductivity). Reviews of first edition: “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) Front Matter ....Pages i-xxxi Introduction to Dynamic Transitions (Tian Ma, Shouhong Wang)....Pages 1-30 Dynamic Transition Theory (Tian Ma, Shouhong Wang)....Pages 31-127 Equilibrium Phase Transitions in Statistical Physics (Tian Ma, Shouhong Wang)....Pages 129-278 Fluid Dynamics (Tian Ma, Shouhong Wang)....Pages 279-403 Geophysical Fluid Dynamics and Climate Dynamics (Tian Ma, Shouhong Wang)....Pages 405-465 Dynamical Transitions in Chemistry and Biology (Tian Ma, Shouhong Wang)....Pages 467-529 Fundamental Principles of Statistical and Quantum Physics (Tian Ma, Shouhong Wang)....Pages 531-595 Quantum Mechanism of Condensates and High Tc Superconductivity (Tian Ma, Shouhong Wang)....Pages 597-638 Topological Phase Transitions (Tian Ma, Shouhong Wang)....Pages 639-717 Back Matter ....Pages 719-757