Course Syllabus
Course Information
Harvard College/GSAS: 80719 |
Fall 2017-18 |
Brian F. Farrell |
Location: Geological Museum 418 (FAS) Meeting Time: Tuesday, Thursday 10:00am - 11:29am Exam Group: |
An introduction to the ideas and approaches to dynamics of generalized stability theory. Topics include autonomous and non-autonomous operator stability, stochastic turbulence models and linear inverse models. Students will learn the concepts behind non-normal thinking and how to apply these ideas in their daily intellectual life. |
Note: Given in alternate years. |
Prerequisite: Applied Math 105 |
Topic Descriptions and Links to Lecture Notes:
Overview of the concepts of stability theory and generalized stability theory.
GST for autonomous operators: the initial value problem, SVD of the propagator, solution for the optimal excitation at initial time and the evolved optimal, relation between eigenfunction-based and SVD-based analysis of stability, use of penalty functions to constrain an optimization, the numerical and spectral abscissa and the global optimal, the pseudospectrum and the issue of the ill-conditioned nature of an eigenfunction-based representation of the stability of non-normal dynamical systems.
Reynolds matrix example of optimal excitation at initial time.
GST for autonomous operators that are continuously excited. Frequency domain analysis, the resolvent and the optimal structure and response for excitation at a chosen frequency. The distinction between resonant response in a normal system and the response of a non-normal system - the concept of the equivalent normal system. Using stochastic excitation white in space and time to study the dynamical operator. Time domain analysis of a continuously forced system - the optimal excitation and response functions for a continuously excited operator.
Example of GST time and frequency based analysis applied to the Reynolds matrix in which the non-normality of the matrix is controlled by the parameter .
GST time and frequency based analysis applied to baroclinic wave dynamics using the Eady model of baroclinc wave dynamics.
GST applied to non-autonomous operators and the stability of linear time-dependent dynamical systems.
Parametric instability of time dependent systems with harmonic and stochastic fluctuation.
Parametric instability of atmospheric flows. The Eady model example.
Linear inverse theory.
Course Summary:
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