http://www.channelflow.org/dokuwiki/ 2012-02-05T00:50:24-08:00 http://www.channelflow.org/dokuwiki/ http://www.channelflow.org/dokuwiki/lib/tpl/default/images/favicon.ico text/html 2012-02-03T13:27:57-08:00 gibson http://www.channelflow.org/dokuwiki/doku.php?id=gibson:teaching:spring-2012:iam950&rev=1328304477&do=diff 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 PD… text/html 2012-01-25T13:13:51-08:00 gibson http://www.channelflow.org/dokuwiki/doku.php?id=gibson:teaching:spring-2012:iam950:syllabus&rev=1327526031&do=diff 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) text/html 2012-01-25T09:57:08-08:00 gibson http://www.channelflow.org/dokuwiki/doku.php?id=gibson&rev=1327514228&do=diff I am interested in turbulence and dynamical systems theory. The hope that dynamical systems theory could shed light on turbulence goes back some sixty years to Hopf. But it has proven difficult to translate Hopf's insights into concrete results, due to the very high (in principle infinite) dimensionality of the Navier-Stokes equations. text/html 2012-01-20T11:09:16-08:00 gibson http://www.channelflow.org/dokuwiki/doku.php?id=gibson:publications&rev=1327086556&do=diff [Geometry of turbulence in wall-bounded shear flows: periodic orbits] Predrag Cvitanović and John F. Gibson Physica Scripta (2010) 142 014007 [Snakes and ladders: localized solutions of plane Couette flow] Tobias M. Schneider, John F. Gibson, and John Burke Phys. Rev. Lett. (2010) 104 104501 (Cover Article, awarded Editor's Suggestion) text/html 2012-01-20T10:49:40-08:00 gibson http://www.channelflow.org/dokuwiki/doku.php?id=gibson:teaching&rev=1327085380&do=diff iam950 math527 math527 text/html 2011-12-13T17:03:03-08:00 ewg5 http://www.channelflow.org/dokuwiki/doku.php?id=gibson:teaching:fall-2011:math527&rev=1323824583&do=diff Lecture: McConnell 208, MWF 8:10a-9:00am Instructor: John F. Gibson. Office hours M 3-4pm, W 4-5pm, N309E Kingsbury Hall Teaching assistants: * Eric Laflamme (sections 1-3). Office hours M 10-11am, Tues 2-3pm, Kingsbury W353 * Evan Brand (sections 4-6). Office hours W 4-5pm, Thur 2-3pm, Kingsbury N316 text/html 2011-12-13T08:33:31-08:00 gibson http://www.channelflow.org/dokuwiki/doku.php?id=gibson:teaching:fall-2011:math527:exams&rev=1323794011&do=diff [ Exam #1 histogram] [ Exam #2 histogram] [ Exam #3 histogram] [ Exam #4 histogram]