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Part 0. Introduction

Wed 01/25 intro, pictures, taxonomy, themes, goals, questions

Mon 01/30 linear stability, S-H, types I,II,III, super and subcritical
Wed 02/01 numerical simulation methods

Part I. Weakly nonlinear patterns

Mon 02/06 nonlinear saturation and mode reduction/slaving
Wed 02/08 amplitude eqns (1d) for type I instab (S-H)

Mon 02/13 applications of amplitude eqns: long-wavelength and secondary instabilities, fronts/ramps
Wed 02/15

Mon 02/20 Kuramoto-Sivashinsky dynamics
Wed 02/22

Part II. Strongly nonlinear patterns

Mon 02/27 linear WKB theory (oscillators and waves)
Wed 02/29 weakly nonlinear WKB theory (dispersive waves)

Mon 03/05 strongly nonlinear WKB theory: complex S-H eqn
Wed 03/07 phase-diffusion theory

Spring Break: Mon 03/12–Fri 03/16

Mon 03/19 amplitude eqns for type II systems with long-wavelength neutral modes
Wed 03/21 mean-drift and goldstone modes

Part III. Spatio-temporal patterns in shear flows

Mon 03/19 intro: pipe, plane couette, boundary-layer
Wed 03/21 symmetries, subcricitality, linear stability of laminar flow

Mon 03/26 self-sustaining processes
Wed 03/28 far-from laminar equilibria & traveling waves

Mon 04/02 periodic orbits
Wed 04/04 spatially localized solutions

Part IV. Periodic orbit theory

Mon 04/09 motivation, outline
Wed 04/11 perron-frobenius

Mon 04/16 cycle expansion
Wed 04/18

Mon 04/23
Wed 04/25

Mon 04/30 Homogenization of the K-S eqn
Wed 05/02

Mon 05/07

gibson/teaching/spring-2012/iam950/syllabus.txt · Last modified: 2012/01/25 13:13 by gibson