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Theory and methods are applicable to a wide range of scientific problems
Provides a thorough introduction to dynamic transition theory for nonlinear partial differential equations
Mathematical discussion of dynamic transition theory is developed with attention to physics
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.
User’s Guide.- General Theory of Phase Transition Dynamics.- Dynamic Transition Theory.- Equilibrium Phase Transition in Statistical Physics.- Fluid Dynamics.- Geophysical Fluid Dynamics and Climate Dynamics.- Dynamical Transitions in Chemistry and Biology.- References.