This is an old revision of the document!
====== IAM 950: Spatiotemporal and turbulent dynamics ====== MW 2:10-3:30pm Kingsbury N204 Prof. John Gibson, Mathematics and Statistics\\ john.gibson@unh.edu, Kingsbury Hall N309E Prof. Greg Chini, Mechanical Engineering\\ greg.chini@unh.edu, 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. ====== News ====== **26 Jan 2012:** Please read the Introduction of Cross and Greenside for Monday. 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. ====== General info ====== [[gibson:teaching:spring-2012:iam950:syllabus | Detailed syllabus]] **Primary text:** //Pattern Formation and Dynamics in Nonequilibrium Systems//, Michael Cross and Henry Greenside, Cambridge University Press, 2009. **Supplementary texts:** * //Dissipative Structure & Weak Turbulence//, Paul Manneville, Academic Press, 1990. * //Instabilities, Chaos, and Turbulence//, Paul Manneville, Imperial College Press, 2010. * //Pattern Formation: An Introduction to Methods//, Rebecca Hoyle, Cambridge Texts in Applied Mathematics, 2006. * //Stability and Transition in Shear Flows//, Peter Schmid and Dan Henningson, Springer-Verlag, 2000. * //Turbulence, Coherent Structures, Dynamical Systems, and Symmetry//, Philip Holmes, John Lumley, and Gal Berkooz, Cambridge University Press, 1996 * [[http://www.chaosbook.org |Chaos: Classical and Quantum]], Predrag Cvitanovi\'c et. al, www.chaosbook.org, 2011. * //Linear and Nonlinear Waves//, Gerald Whitham, Wiley \& Sons, 1973
