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


===== Ideas for research projects =====

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.

==== Projects that can be executed with channelflow.org "as is" ====

  - 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. 

==== Other open projects ====

  - 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

===== Hiccups =====

(latest posts at the top)

{{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//

{{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. 

{{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]].

{{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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