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.

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.

Syllabus: detailed & updated course announcement (PDF)

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
• Chaos: Classical and Quantum, Predrag Cvitanovi\'c et. al, www.chaosbook.org, 2011.
• Linear and Nonlinear Waves, Gerald Whitham, Wiley \& Sons, 1973