Differences

This shows you the differences between two versions of the page.

--- gtspring2009:howto:poincare [2009/03/20 08:30]
gibson created
+++ gtspring2009:howto:poincare [2010/02/02 07:55] (current)
@@ Line 2: / Line 2: @@
 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  =====
@@ Line 40: / Line 41: @@
    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,
+   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.
+This produces data directories data-12696, etc. I made symbolic links to these directories with simpler
+labels to make some future processing simpler.
+   ln -s data-11268 data-a
+   ln -s data-12696 data-b
 ===== Compute the Poincare crossings =====
-[[gtspring2009:howto: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
-where e(θ) = e0 cos θ + e1 sin θ, and where u(t) is always mapped into a canonical 1st quadrant
+where e(θ) = e0 cos θ + e1 sin θ, and where u(t) is always mapped into a canonical 1st quadrant defined by
+(u(t), etx) ≥ 0 and (u(t), etz) ≥ 0. Here etx and etz are τx and τz antisymmetric basis vectors. In my calculations
+I chose these to be the τx and τz antisymmetric basis vectors of the EQ2 translation basis described in our 2008
+JFM paper.
+To compile eq2poincare.cpp, use this {{gtspring2009:howto:poincare:makefile.txt}}. Edit the Makefile to so that CHANNELDIR
+is set to you channelflow installation
+  CHANNELDIR = /home/gibson/channelflow-1.3.5
+then run "make eq2poincare.x". Then execute
+  eq2poincare.x -d data-a -o section-pi4 --theta 0.7854 -tag a -T0 0 -T1 400 etx etz e0 e1 EQ2.ff
+That will produce files uM0a.ff, uP0a.ff, uM1a.ff, uP1a.ff in directory section-pi4/. The P/M indicates
+whether (u(t) - EQ2, e(θ)) is increasing (P) or decreasing (M) at the crossing. The following integer
+indicates the number of the crossing (incremented once per M,P pair), and the 'a' is a label indicating
+which trajectory the crossing came from.
+The point of this crazy labeling scheme is that it gives the right lexical ordering to the filenames of
+multiple crossings of multiple trajectories. For example, after computing the crossings of all trajectories
+using the bash-for loop
+   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.

channelflow.org

User Tools

Site Tools

Differences

Page Tools