MW 2:10-3:30pm Kingsbury N204
Prof. John Gibson, Mathematics and Statistics
firstname.lastname@example.org, Kingsbury Hall N309E
Prof. Greg Chini, Mechanical Engineering
email@example.com, Kingsbury Hall W113
abstract: This course examines the theory of bifurcations, pattern formation, and spatiotemporal chaos in systems governed by time-dependent nonlinear partial differential equations. We begin with comparatively well-developed theories and simple model systems (e.g. 1-dimensional nonlinear PDEs) and progresses by stages of increasing complexity to the culminating problem of coherent structures and turbulence in the Navier-Stokes equations. The goal is to give advanced graduate students the proper analytic and conceptual background for research in the dynamics of unstable spatio-temporal patterns in turbulent shear flows.
3 Feb 2012: ks_cnab2.m Matlab source code for time-integration of Kuramoto-Sivashinksy eqn.
26 Jan 2012: Please read the Introduction of Cross and Greenside for Monday 30 Jan. I have placed a few xeroxed copies place on the bookshelf outside my Kingsbury N309E. Please borrow for a few hours or overnight and return a.s.a.p. so that others have a chance to read. But also please order and purchase the book for use throughout the semester.
Primary text: Pattern Formation and Dynamics in Nonequilibrium Systems, Michael Cross and Henry Greenside, Cambridge University Press, 2009.