## Phase Transition DynamicsThis 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. |

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### Contents

1 | |

25 | |

3 Equilibrium Phase Transition in Statistical Physics | 123 |

4 Fluid Dynamics | 249 |

5 Geophysical Fluid Dynamics and Climate Dynamics | 373 |

6 Dynamical Transitions in Chemistry and Biology | 447 |

Appendix A | 526 |

541 | |

552 | |

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### Common terms and phrases

asymptotically stable attractor attractor bifurcation boundary condition Boussinesq equations center manifold function classical complex eigenvalues consider constant convection critical point critical Rayleigh number defined density derive Dirichlet boundary condition dissipative systems divu domain dynamic transition theory eigenvalue problem eigenvectors ENSO equilibrium phase transitions flow following assertions hold free energy Ginzburg–Landau given global attractor Hadley cell Hence homeomorphic hyperbolic regions jump transition Lemma length scale linear liquid metastable Neumann boundary condition nondegenerate nondimensional nonlinear oceanic open sets oscillation parabolic region periodic orbit periodic solution perturbation phase diagram phase transition Physical Conclusion Proof of Theorem prove real eigenvalues reduced equation saddle-node bifurcation satisfies shown in Fig singular points singular separation stable manifold steady-state solutions structure shown superconducting superfluid Taylor number Taylor problem topological structure topologically equivalent Type unstable vector field Walker circulation Wang zero