gtspring2009:research_projects
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| - | ====== Research projects ====== | ||
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| - | ===== Ideas for research projects ===== | ||
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| - | Please pick a project (or add your own project, if not in the list), write your name next to it with a | ||
| - | link to your blog, where you describe your goals in detail. | ||
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| - | ==== Projects that can be executed with channelflow.org "as is" ==== | ||
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| - | - Search for equilibria of plane Couette with isotropy group | ||
| - | that is currently unexplored, in particular the ?? isotropy described in "[[http://www.scribd.com/full/4929920?access_key=key-28bjtf1f3w5j7pq0ef7h|Halcrow et al. on symmetries of plane Couette]]." | ||
| - | - Look for equilibria, traveling waves, and periodic orbits of plane Couette in isotropy groups that are currently unexplored. | ||
| - | - Systemize the computation of periodic orbits by considering how unstable manifolds of different solutions (nearly) map onto each other. | ||
| - | - Search for more heteroclinic connections, particularly connections to solutions with greater than 1d unstable manifolds. | ||
| - | - Do a more thorough bifurcation analysis of existing solutions. | ||
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| - | ==== Other open projects ==== | ||
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| - | - Look for equilibria, traveling waves, and periodic orbits of plane Couette in isotropy groups that are currently unexplored. | ||
| - | - Do numerical studies of lifetime of transients. | ||
| - | - Look at state-space structure as a function of Reynolds number, starting from our current state-space portraits and heteroclinic connections. Can we understand transient lifetimes as a function of Reynolds from changes in state space structure? | ||
| - | - Related to above, try to understand via state-space structure why turbulent lifetime increases dramatically when Lz goes from <latex> 1.2 \pi </latex> to <latex> 1.75 \pi </latex> | ||
| - | - Construct a control system using linearizations about a set of periodic orbits with blowing/sucking boundary conditions for control. This has a lot of parts, should probably start with just one part e.g. linearizing about a periodic orbit | ||
| - | - Try to hit various lower-branch equilibria using small perturbations of the laminar state as initial conditions, or make a close pass and then shoot towards turbulence along the lower branch's unstable manifold. Initial condition would be a Stokes-mode [v,w](y,z) roll plus a perturbation with streamwise (x) variation. | ||
| - | - Compute subharmonic instabilities of existing solutions | ||
| - | - Try to construct new solutions as subharmonic perturbations of spatially doubled (tripled,...) solutions | ||
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| - | ===== Hiccups ===== | ||
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| - | (latest posts at the top) | ||
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| - | {{gtspring2009:pc.jpg }} Let's agree on all graphics being *.png - that works for both the dokuwiki and pdflaTeX. | ||
| - | See [[gtspring2009:howto:format#figures|How to format figures]]. --- //[[predrag.cvitanovic@physics.gatech.edu|Predrag Cvitanovic]] 2009-02-27 13:29// | ||
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| - | {{gtspring2009:gibson.png?24}} Let people experiment with the dividing line. The | ||
| - | overhead of blogging via latex and subversion is large enough to slow down my research, | ||
| - | deter me from blogging things that I should blog, and commenting on others' blogs, and | ||
| - | keeping a current PDF on the web of my blog was such a hassle I never did it (should have | ||
| - | used a cron job). This motivated me to start a latex-enabled wiki. On the downside, blogging via wiki | ||
| - | would take us further away from publication readiness. The web and the wiki prefer | ||
| - | pixel-oriented graphics like PNG and JPEG rather than postscript or PDF, for example. | ||
| - | But in my experience blogging figures good enough for publication is a waste of time | ||
| - | (getting the fonts, axes, labels, etc just right is very time-consuming --I spend at | ||
| - | least a couple hours for every published figure), and the text of a paper is very different | ||
| - | from what you write when you're trying to make sense of new ideas. That said, I'm not sure | ||
| - | that blogging via wiki is right, so I support letting people experiment. | ||
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| - | {{gtspring2009:pc.jpg }} I lean toward putting most text into individual | ||
| - | blogs (easiest to migrate to publications), and putting updates as what the study group | ||
| - | might want to read into [[:gtspring2009|study group main page]]. | ||
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| - | {{gtspring2009:gibson.png?24}} Need to ponder a rational division between what goes into the communal blog, and | ||
| - | what stays in individual blogs. | ||
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