gibson:teaching:spring-2012:iam950
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gibson:teaching:spring-2012:iam950 [2012/01/26 08:35] gibson |
gibson:teaching:spring-2012:iam950 [2012/02/08 10:25] (current) gibson [News] |
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| greg.chini@unh.edu, Kingsbury Hall W113 | greg.chini@unh.edu, Kingsbury Hall W113 | ||
| - | [[gibson:teaching:spring-2012:iam950:syllabus]] | + | **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 ====== | ||
| + | |||
| + | **3 Feb 2012:** {{:gibson:teaching:spring-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. | ||
| + | |||
| + | ====== Homework ====== | ||
| + | |||
| + | ^ # ^ due ^ notes ^ | ||
| + | | [[:gibson:teaching:spring-2012:iam95:HW1]] | | | | ||
| + | |||
| + | |||
| + | ====== General info ====== | ||
| + | **Syllabus:**[[gibson:teaching:spring-2012:iam950:syllabus | detailed & updated ]] {{:gibson:teaching:spring-2012:iam950syllabus.pdf|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 | ||
| + | * [[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 | ||
| + | |||
gibson/teaching/spring-2012/iam950.1327595713.txt.gz · Last modified: 2012/01/26 08:35 by gibson
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