Lecture 21
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PATTERN FORMING SYSTEMS — AN INTRODUCTION: This lecture introduces some of the canonical forms of linear instabilities that can occur in spatio-temporal systems.
Lecture 22
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LINEAR STABILITY AND ORDER PARAMETERS: This lecture introduces linear stability analysis for spatio-temporal systems, showing that multiscale perturbation theory provides an analytic approach for characterizing the dynamics.
Lecture 23
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ORDER PARAMETERS AND DOMINANT BALANCE: The multiple scale perturbation method using slow space and time scales allows us to characterize the onset of instability using an order parameter, or envelop equation, for determining the nonlinear evolution near a bifurcation point.
Lecture 24
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MODAL ANALYSIS AND MODE COUPLING: This lecture introduces the multiple scale method to modal analysis problems where the underlying dynamics is dominated by eigenfunctions of an underlying linear operator. Coupling can occur from forcing, nonlinearity, or non-orthogonal modes, leading to slow scale mode coupling dynamics.
Lecture 25
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DATA-DRIVEN DOMINANT BALANCE PHYSICS: This lecture by Jared Callahan highlights how emerging machine learning methods can be used to discovery dominant balance physics regimes.