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gtspring2009:research_projects [2009/01/12 05:39] predrag removed blog list from the research page |
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- | ====== Research projects ====== | ||
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- | Need to ponder a rational division between what goes into the communal blog, and | ||
- | what stays in individual blogs. Predrag leans 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 this area... | ||
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- | John Gibson comment: Maybe we could 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. | ||
- | ====== Ideas for research projects ====== | ||
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- | * 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. | ||
- | * 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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