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Nonlinear Hydrodynamic Modeling: A Mathematical Introduction

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Cover of 'Nonlinear Hydrodynamic Modeling: A Mathematical Introduction'

Table of Contents

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    Book Overview
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    Chapter 1 Modeling: A strategy for understanding
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    Chapter 2 A simple nonlinear model of convection
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    Chapter 3 From the equations of motion to spectral models
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    Chapter 4 Linear stability analysis
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    Chapter 5 Bifurcation analysis of stationary solutions
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    Chapter 6 Typical branching forms: Stationary solutions
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    Chapter 7 The expected branching solution: Preferred wavelengths
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    Chapter 8 Identifying crucial parameters with contact catastrophe theory
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    Chapter 9 Hierarchies of transitions: Secondary branching
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    Chapter 10 Alexander-Yorke Continuation: Numerically finding all the stationary solutions in a spectral model
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    Chapter 11 Typical branching forms: Periodic solutions
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    Chapter 12 The expected branching solution: Preferred wavelengths and orientations
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    Chapter 13 On computing the branching direction of bifurcating periodic solutions
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    Chapter 14 Bifurcation analysis of periodic solutions
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    Chapter 15 The transition to turbulence
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    Chapter 16 Diagnosing the structures of attractors
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    Chapter 17 Introduction to topological hydrodynamics
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    Chapter 18 Modeling and metamodeling
Attention for Chapter 9: Hierarchies of transitions: Secondary branching
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