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====== Research projects ======

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...

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 ======

  * 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





====== Blog of Blogs ======

^who ^repository ^edit file ^public  ^
|Borrero and Cvitanović  |svn://localhost:22369/halcrow/  |TEX/main.tex  |  |
|Elton                   |svn://localhost:22369/elton/ |blog/blog.tex  |[[http://ChaosBook.org/projects/Elton|ChaosBook.org/projects/Elton]]  |
|Gibson                  | | [[gtspring2009:research_projects:gibson:blog|gibson blog]] (on dokuwiki)   ||
|Siminos                 |svn://localhost:22369/siminos/  |blog/??      |  |
|Spieker                 |svn://localhost:22369/spieker/ |blog/blog.tex  |[[http://ChaosBook.org/projects/Spieker|ChaosBook.org/projects/Spieker]]  |

[[gtspring2009:foo]]
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