gtspring2009:howto:poincare
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gtspring2009:howto:poincare [2009/03/20 08:59] gibson |
gtspring2009:howto:poincare [2010/02/02 07:55] (current) |
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| around the Nagata EQ2 upper branch. This is procedure is too special-case and | around the Nagata EQ2 upper branch. This is procedure is too special-case and | ||
| - | kludgy to put in channelflow documentation. | + | kludgy to put in channelflow documentation. It is a horrific mixture of general-purpose |
| + | channnnelflow utilities, specialized channelflow programs, Unix utilities, and bash | ||
| + | shell programming. | ||
| ===== Integrate perturbations ===== | ===== Integrate perturbations ===== | ||
| Line 40: | Line 41: | ||
| couette -T0 0 -T1 400 -o data-11268 eq2_11268e0.ff | couette -T0 0 -T1 400 -o data-11268 eq2_11268e0.ff | ||
| - | couette -T0 0 -T1 400 -o data-12696 eq2_11268e0.ff | + | couette -T0 0 -T1 400 -o data-12696 eq2_12696e0.ff |
| ... | ... | ||
| Instead of typing each of these out, you can use a bash for-loop, | Instead of typing each of these out, you can use a bash for-loop, | ||
| - | for i in eq2_*eo.ff ; do tag=${i#eq2_} ; couette -T0 0 -T1 400 -o data-${tag%.e0.ff} $i ; done | + | for i in eq2_*e0.ff ; do tag=${i#eq2_} ; couette -T0 0 -T1 400 -o data-${tag%.e0.ff} $i ; done |
| The ${...} stuff is bash string manipulation syntax to extract the numerical part of the input file names. | The ${...} stuff is bash string manipulation syntax to extract the numerical part of the input file names. | ||
| Line 56: | Line 57: | ||
| ===== Compute the Poincare crossings ===== | ===== Compute the Poincare crossings ===== | ||
| - | [[gtspring2009:howto:poincare:eq2poincare.cpp]] is a special program I wrote to compute crossings of a Poincare section defined by | + | {{gtspring2009:howto:poincare:eq2poincare.cpp}} is a special program I wrote to compute crossings of a Poincare section defined by |
| (u(t) - EQ2, e(θ)) == 0 | (u(t) - EQ2, e(θ)) == 0 | ||
| Line 65: | Line 66: | ||
| JFM paper. | JFM paper. | ||
| - | To compile eq2poincare.cpp, use this [[gtspring2009:howto:poincare:Makefile]]. Edit the Makefile to so that CHANNELDIR | + | To compile eq2poincare.cpp, use this {{gtspring2009:howto:poincare:makefile.txt}}. Edit the Makefile to so that CHANNELDIR |
| is set to you channelflow installation | is set to you channelflow installation | ||
| Line 85: | Line 86: | ||
| for i in data-[a-p] ; do tag=${i#data-} ; eq2poincare.x -d data-$tag -o section-pi4 --theta 0.7854 -tag ${tag} -T0 0 -T1 400 etx etz e0 e1 EQ2.ff; done | for i in data-[a-p] ; do tag=${i#data-} ; eq2poincare.x -d data-$tag -o section-pi4 --theta 0.7854 -tag ${tag} -T0 0 -T1 400 etx etz e0 e1 EQ2.ff; done | ||
| + | The files in directory section-pi4 will be ordered in increasing distance along the unstable manifold. | ||
| + | gibson@tansen$ ls section-foo-pi4/ | ||
| + | crossingtimes-a.asc uM0d.ff uM1g.ff uM3a.ff uM4d.ff uP0h.ff uP2b.ff uP3e.ff | ||
| + | crossingtimes-b.asc uM0e.ff uM1h.ff uM3b.ff uM4e.ff uP0i.ff uP2c.ff uP3f.ff | ||
| + | crossingtimes-c.asc uM0f.ff uM1i.ff uM3c.ff uM4f.ff uP1a.ff uP2d.ff uP3g.ff | ||
| + | crossingtimes-d.asc uM0g.ff uM2a.ff uM3d.ff uM4g.ff uP1b.ff uP2e.ff uP3h.ff | ||
| + | crossingtimes-e.asc uM0h.ff uM2b.ff uM3e.ff uM4h.ff uP1c.ff uP2f.ff uP4a.ff | ||
| + | crossingtimes-f.asc uM0i.ff uM2c.ff uM3f.ff uP0a.ff uP1d.ff uP2g.ff uP4b.ff | ||
| + | crossingtimes-g.asc uM1a.ff uM2d.ff uM3g.ff uP0b.ff uP1e.ff uP2h.ff uP4c.ff | ||
| + | crossingtimes-h.asc uM1b.ff uM2e.ff uM3h.ff uP0c.ff uP1f.ff uP2i.ff uP4d.ff | ||
| + | crossingtimes-i.asc uM1c.ff uM2f.ff uM3i.ff uP0d.ff uP1g.ff uP3a.ff uP4e.ff | ||
| + | uM0a.ff uM1d.ff uM2g.ff uM4a.ff uP0e.ff uP1h.ff uP3b.ff uP4f.ff | ||
| + | uM0b.ff uM1e.ff uM2h.ff uM4b.ff uP0f.ff uP1i.ff uP3c.ff uP4g.ff | ||
| + | uM0c.ff uM1f.ff uM2i.ff uM4c.ff uP0g.ff uP2a.ff uP3d.ff uP4h.ff | ||
| + | etc. | ||
| | | ||
| + | ===== Project the crossing points ===== | ||
| + | |||
| + | Next we project the crossing points of the Poincare section using the channelflow ''projectfields'' utility. | ||
| + | |||
| + | projectfields -b basis-EQ2ef/ -Nb 4 -or EQ2.ff -o portrait-pi4 section-pi4/*.ff | ||
| + | |||
| + | The above command assumes you have put the basis vectors e0,e1,e2,e3 into a directory named basis-EQ2ef/; | ||
| + | if not you might use '-b .' instead. | ||
| + | |||
| + | This creates a new directory 'portrait-pi4' containing ASCII files uM0a.asc, uM0b.asc, ..., each of which | ||
| + | contains four numbers corresponding to the projection of the fields in uM0a.ff, etc onto the four basis vectors | ||
| + | e0,e1,e2,e3. E.g. | ||
| + | |||
| + | | ||
| + | gibson@tansen$ cat portrait-pi4/uM0a.asc | ||
| + | % e0 e1 e2 e3 | ||
| + | -9.6755005579877134e-06 9.6754650183359171e-06 3.8296888337351566e-10 -2.5429703558485441e-08 | ||
| + | |||
| + | It's easier to plot this data if it's in one file and in the right order. To do that, we strip out the | ||
| + | comments with ''grep'' and save the results to two files. | ||
| + | |||
| + | gibson@tansen$ grep -v -h ^% portrait-foo-pi4/uM*.asc > uM.asc | ||
| + | gibson@tansen$ grep -v -h ^% portrait-foo-pi4/uP*.asc > uP.asc | ||
| + | |||
| + | That produces two files of incoming/outgoing crossings that can be plotted with matlab or whatever. | ||
| + | |||
| + | |||
| + | | ||
gtspring2009/howto/poincare.1237564780.txt.gz · Last modified: 2009/03/20 08:59 by gibson
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