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gtspring2009:spieker_blog [2009/04/08 08:58]
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gtspring2009:spieker_blog [2010/02/02 07:55] (current)
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-====== Dustin Spieker'​s ​Channelflow Blog ======+====== Dustin Spieker'​s ​blogs ====== 
 + 
 +**Possible Courses I'm considering for SP2010 (Recommendations would be appreciated)** 
 +  * Math 6646 - Numerical Methods for ODE'​s 
 +  * ME 7751 - Numerical Methods for Fluids 
 +  * Physics 8803 - Special Topics with Pablo Laguna (I think its a computational methods course)
  
 <​html>​ <​html>​
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 (append the latest posts to the bottom of appropriate section) (append the latest posts to the bottom of appropriate section)
-===== Getting started ===== 
- 
-:-) Got channelflow running on my linux machine. //​(1/​25/​2009)//​ 
- 
-:-) Ran through most of the commands in John Gibson'​s first tutorial and troubleshot the commands provided. //​(1/​25/​2009)//​ 
- 
-:-) Learned and implemented some of the rougher points of using this Wiki. //​(1/​25/​2009)//​ 
- 
- 
-===== Upper branch equilibrium,​ perturbed ===== 
- 
-Upper Branch Equilibrium evolution perturbed along eigenfunction 1. 
- 
-<​flashplayer width="​400"​ height="​320">​file=/​movies/​dspieker/​ubp01ef1.flv&​image=/​movies/​dspieker/​frame0.png&​repeat=none</​flashplayer>​ 
- 
-Upper Branch Equilibrium evolution perturbed in opposite direction. 
- 
-<​flashplayer width="​400"​ height="​320">​file=/​movies/​dspieker/​ubm01ef1.flv&​image=/​movies/​dspieker/​frame0.png&​repeat=none</​flashplayer>​ 
- 
-{{gtspring2009:​pc.jpg }}  
- //​Predrag to Dustin:// ​ 
-    * Had the same problem with [[http://​www.youtube.com/​watch?​v=YKaVJVHeDho|youtube]] - really kills the resolution (and John G would prefer Zappa). [[http://​www.flickr.com/​photos/​vasimos/​3249057643/​in/​photostream/​|flickr.com]] seems kinder to the videos, see [[gtspring2009:​research_projects:​siminos:​blog|Siminos blog]]. 8-)I don't think I'll use either website as a host anymore since John showed us how to host these on our blogs. ​ --- //​[[dustin.spieker@gatech.edu|Dustin Spieker]] 2009-02-05 06:07// 
-    * please can you crop it so it does not have all this area in the edges, as in [[gtspring2009:​howto:​format | How to format a movie]]? I need tightly cropped movies for [[http://​chaosbook.org/​tutorials/​index.html|ChaosBook/​tutorials pop-ups]]. Also, gray background is ugly - can you make it white? ​ 
- 
-8-) I'll work on both of these things. ​ I'm sure it just has to do with changing a little something in matlab, and I'll look into it.  --- //​[[dustin.spieker@gatech.edu|Dustin Spieker]] 2009-02-05 06:07// 
- 
-:-) Generated some state space trajectory plots and input dissipation plots using the tutorial John created on how to do so.  I will post some of them after I've tinkered a little bit.  --- //​[[dustin.spieker@gatech.edu|Dustin Spieker]] 2009-02-15 13:39// 
- 
-:-) Was able to post videos to my blog, obviously. ​ --- //​[[dustin.spieker@gatech.edu|Dustin Spieker]] 2009-02-20 16:26// 
- 
-:-) Compiled channelflow1.3.4 and it worked like a charm. --- //​[[dustin.spieker@gatech.edu|Dustin Spieker]] 2009-02-27 06:40// 
- 
-:-) It is worth noting that on my computer, it takes about 36 minutes to integrate a flow field 400 time steps, or about 6 seconds per time step.  Important to remember when budgeting time for script files. ​ Accordingly,​ I just sent about 10 GB of flow fields to be calculated for my Poincare Section, which should keep my computer busy until tomorrow. --- //​[[dustin.spieker@gatech.edu|Dustin Spieker]] 2009-03-09 15:00// 
- 
-===== Eigenvectors of the UB equilibrium ===== 
- 
-[[:​gtspring2009:​spieker_blog:​UB_eigenvectors:​first_try|First Attempt]] 
- 
-The following links are provided in order to maximize the aesthetics and bring out salient features of the eigenvectors,​ so that PC may more easily gauge what would be perfect for chaosbook, kinda like looking at paint chips: 
- 
-[[:​gtspring2009:​spieker_blog:​UB_eigenvectors:​color_scaling|Color Scaling]] 
- 
-[[:​gtspring2009:​spieker_blog:​UB_eigenvectors:​laminar|Laminar?​]] 
- 
- 
- 
- 
- 
-===== Goals ===== 
- 
-(In approximate order of importance) 
- 
-:-| Poincare sections, 'nuff said.  --- //​[[dustin.spieker@gatech.edu|Dustin Spieker]] 2009-02-20 16:26// 
- 
-:-| Port Channelflow to Mac so that I can run it on my laptop and provide a procedure for doing so. //​(1/​25/​2009)//​ 
-8-o Mac OS X is BSD Unix underneath. So channelflow installs on a Mac same as Linux if the prerequisite packages are installed. You can either install these packages with [[http://​www.finkproject.org/​|Fink]] or download the tar.gz files and compile them yourself. Fink should be much easier. Lina Kim at UC Santa Barbara M&AE uses channelflow on a Mac and has sent me some notes that I need to convert to documentation.... // John Gibson 2009-02-04 10:17// 
- 
-:-| Learn, Port, and Document the commands John Gibson provided for Matlab to Octave to help get everything running on free shareware. //​(1/​25/​2009)//​ 8-o That would be great. I don't think Octave graphics are up to the task, though. My guess is that integration with a Python plotting system is the best route to running on all free software. One possibility is Lawrence Livermore Lab's [[https://​wci.llnl.gov/​codes/​visit/​|VisIt]] system. // John Gibson 2009-02-04 10:07// 
- 
-:-| Work on my formatting for this page. //​(1/​25/​2009)//​ 
-===== Questions ​ ===== 
- 
-that arise from a fundamental lack of understanding:​ 
- 
-:?:  In the tutorial we went through on 1/20/2008, we only generated one eigenfunction for time considerations. ​ When I ran it on my own, I let the calculation run longer and it generated about 30 eigenfunctions before I wanted to move on.  How many of these eigenfunctions are worth generating for a particular solution and why? //​(1/​25/​2009)//​ 
- 
-:!: see [[chaosbook:​stability|ChaosBook.org blog for the answer]]. Time to read [[http://​chaosbook.org/​paper.shtml#​stability|Local stability]] and [[http://​chaosbook.org/​paper.shtml#​invariants|Cycle stability]]. Please enter comments/​edits/​questions into the appropriate chapter of the [[:​chaosbook|ChaosBook.org blog]]. 
- --- //​[[predrag.cvitanovic@physics.gatech.edu|Predrag Cvitanovic]] 2009-01-28 05:22// 
- 
-:?:  Hey John, I see you've posted a tutorial for Poincare sections. ​ If you have some or all of the code written, I'd like to see it if I might, so that I can start running it and seeing what it yields. ​ --- //​[[dustin.spieker@gatech.edu|Dustin Spieker]] 2009-02-25 15:16// 
- 
-:!:  Posted new {{downloads:​channelflow-1.3.4.tgz}} tarball with continuation and Poincare section 
-utilities. //John Gibson 2009-02-26 12:09 EST// 
- 
-:-) Hey John G., I've been going through the poincare section procedure, and I have hit a dead end.  I was wondering if you would be in Atlanta tomorrow to give me a quick hand with the compilation of eq2poincare.cpp?​ --- //​[[dustin.spieker@gatech.edu|Dustin Spieker]] 2009-03-23 14:57// 
- 
-{{gtspring2009:​gibson.png?​24}} Dustin: this is my fault. I had to modify some channelflow libraries and have not yet posted the new code as a tarball. I will do that by tomorrow a.m. at latest. It is available in svn right now. 
-I won't be in Atlanta tomorrow nor next week, but I hope to get a ticket for week after next. // John Gibson 2009-03-23 21:11 EST// 
- 
- 
-===== Pseudocodes ===== 
- 
-:-) Need to understand basis input so that I can input it in here. --- //​[[dustin.spieker@gatech.edu|Dustin Spieker]] 2009-02-24 06:13// 
- 
-:-) Added a [[gtspring2009:​howto|HowTo]] for writing script files. ​ Would like some feedback on that, so a user doesn'​t need to be so wary of doing what I said to do.  --- //​[[dustin.spieker@gatech.edu|Dustin Spieker]] 2009-02-26 06:02// 
- 
-== Recurrence plot: == 
- 
-  Inputs Needed: 
-  value for large time step = t 
-  value for smaller time step = T 
-  flowfield to compare = input.ff 
-  int index = 600; 
-  flowfield tmp = input.ff; 
-  Array Norms [index][index];​ 
-  ​ 
-  for (i = 0, i < index, i++){ 
-    for (j = 0, j < index, j++){ 
-      tmp.advance(T);​ 
-      Norms[i][j] = L2Dist (tmp, input); 
-    } 
-    input.advance(t) 
-    tmp = input; 
-  } 
- 
- 
- 
-== Poincare Section: == 
- 
-  Inputs Needed 
-  flowfield ff; 
-  value for the large advancing time step = t 
-  three eigenvectors = e1.ff, e2.ff, e3.ff 
-  const double time_step; 
-  ​ 
-  **Strobing Algorithm** 
-  ​ 
-  #//​Variables Needed// 
-  double tolerance; ​ /​*======>​ user defined*/ 
-  double distance; /​*======>​ distance between trajectory and */ 
-  int changed_sign;​ 
-  int time_sign = 1; 
-  double variable_time_step = time_step; 
-  int gol_i, gol_f, pom_i, pom_f /​*essentially booleans that tell whether the section has been crossed*/ 
-  ​ 
-  for(arguments){ /*this represents the main body of the poincare section code as it pertains to strobing*/ 
-    gol_i = ff.sign_in_a3_basis();​ 
-    ff.advance(time_step);​ 
-    gol_f = ff.sign_in_a3_basis();​ 
-    time_sign = gol_i * gol_f; 
-    ​ 
-    /*Actual Strobing (hopefully)*/​ 
-    if (gol_i * gol_f > 0){ 
-      cout >> "No Change";​ 
-    }else{ 
-      cout >> "​Crossed Section";​ 
-      variable_time_step = time_step / 2; 
-      time_sign = -1; 
-      while (distance >= tolerance){ 
-        pom_i = ff.sign_in_a3_basis();​ 
-        ff.advance(time_sign * variable_time_step);​ 
-        pom_f = ff.sign_in_a3_basis();​ 
-        time_sign = pom_i * pom_f; 
-        variable_time_step /= 2; 
-        distance = (Calculate diffence between 3rd eigenfunction distance of plane and trajectory);​ 
-      } 
-    }  ​ 
-  }    ​ 
- 
- 
-===== Hiccups ===== 
  
-{{gtspring2009:​gibson.png?​24 }}  Checked out Dustin'​s permission problems on the wiki. Dustin, you had two logins name registered, spieker ​and dspiekerShould probably choose one of them and remove the other. Discovered some robot registrations along the way, will probably have to enable captchas in the registration process. ​ --- // John Gibson 2009-02-04 12:12// +[[:gtspring2009:​spieker_blog:​daily_blog|Daily Blog:]] daily updates of the triumphs ​and failures.
-====== Project: Poincare sections and return maps ======+
  
-{{gtspring2009:​pc.jpg }} **most important:​** Compute an W03 cell unstable manifold Poincaré section and return map for the upper branch ​ solution. Place Gibson'​s new [[gtspring2009:​gibson:w03|periodic orbit P47.18 in the W03 cell]] on it.+[[:gtspring2009:​spieker_blog:First_Steps|Getting Started:]] my first dabbling with the program, probably not worth looking at.
  
-:-) I will take the W03 unstable manifold Poincaré section and return map for the upper branch project I have a feeling that I could readily jump into this one given the tools recently provided in channelflow-1.3.4. ​ --- //​[[dustin.spieker@gatech.edu|Dustin Spieker]] 2009-03-02 14:39//+[[:gtspring2009:​spieker_blog:​Eigenvectors|Eigenvectors:​]] from the UB eigenvectors ​for ChaosBook to tables of properties of the various eigenvectors.
  
-:-) Because of inherent symmetries of the problem that create four different representations of the same solution in +[[:​gtspring2009:​spieker_blog:​Spieker_PSection|Poincaré Sections:]] work so far on Poincaré sections.
-state space, we need to figure out a way to only count the crossings in one of the four subspaces, probably the  +
-canonical (no symmetry operations performed) subspace. ​ This creates a problem if two subsequent time steps cross the +
-poincare section AND from one subspace to another simultaneously. ​ Need to account for this. --- //[[dustin.spieker@gatech.edu|Dustin Spieker]] 2009-03-10 17:00//+
  
-:-) Right about the time I was finishing my first go around of making a Poincare Section of the UB unstable manifold, I looked at the homepage and saw that you, John G., had finished one.  Yours looked much better than the monstrosity my computer spit out.  I read over the considerations you made when constructing yours, and realized that I had made almost none, but rather blindly stumbled through the calculation with more or less arbitrary eigenvectors. ​ That's the bad news.  The good news is that I understood the considerations you took, and I am ready to give it another shot. --- //[[dustin.spieker@gatech.edu|Dustin Spieker]] 2009-03-18 09:32//+[[:​gtspring2009:​spieker_blog:​Continuations:​Lx|Continuations:​]] Streamwise continuations,​ the summer of 2009.
  
-:-) Second Try, something is still up, but at least my new plots are somewhat prettier. ​ More on analysis of the plots in a few minutes.+[[:gtspring2009:​spieker_blog:​correlationfcts|Correlation Functions]]
  
-{{:​gtspring2009:​psplot1_try2.png|}} +[[:​gtspring2009:​spieker_blog:fokkerplanck|Fokker-Planck Equation]]
-{{:​gtspring2009:​psplot2_try2.png|}} +
-{{:​gtspring2009:psplot3_try2.png|}}+
  
-So, I only used the generic poincare.cpp to obtain these results, so none of the symmetries have been factored out.  Something is inconsistent between ​[[gtspring2009:​gibson:w03#​more_poincare_sections|John G's]] representation and mine of the (u,e0) vs. (u,e1) plot which will need further investigation,​ and once I put up my method, John G. will be able to shed some light on my problem. ​ I was unable to connect the points together because of how I constructed my data files and fed them into matlab, yet another manifestation of my lack of knowledge in matlab. ​ More to come... --- //​[[dustin.spieker@gatech.edu|Dustin Spieker]] 2009-04-07 14:12//+[[:gtspring2009:​spieker_blog:Itano|Itano Visualization]]
  
-[[gtspring:​spieker_blog:​try_2proc|Procedure Followed]]+[[:​gtspring2009:​spieker_blog:​near_wall|Near Wall]]
  
-My current focuses are now to get eq2poincare.cpp working in synch with channelflow,​ changing the mixing angle (<​latex>​\theta</​latex>​) between e0 and e1 and see how that changes the poincare section, and maybe looking into working with the some of the other solutions.+====== Table of Solution Properties ======
  
-{{gtspring2009:​gibson.png?​24}} Are you having problems compiling eq2poincare.cpp?​ Skype me, baby! No cause to worry that you might not have thought of everything on your first shot; i surely haven'​t either, and two minds will do better than one.  // John Gibson 2009-05-08 noon EST// 
  
-===== ChaosBook.org reading =====+^ name ^ Re ^ D ^ L2Norm ^ Isotropy Subgroup ^ Σ λ+ ^ 
 +| EQ1 | 400 | 1.42926 | 0.209125 | Rxz | 0.050123 | 
 +| EQ2 | 400 | 3.04367 | 0.385806 | Rxz | 0.13007 | 
 +| EQ3 | 400 | 1.31768 | 0.125884 | Rxz | 0.051762 | 
 +| EQ4 | 400 | 1.45368 | 0.168116 | Rxz | 0.10849 | 
 +| EQ5 | 400 | 2.02013 | 0.218648 | Rxz | 0.24575 | 
 +| EQ6 | 330 | 2.81845 | 0.275125 | Rxz | | 
 +| EQ7 | 400 | 1.25225 | 0.093586 | Rxz x {e,τxz} | 0.080364 | 
 +| EQ8 | 400 | 1.76977 | 0.346590 | Rxz x {e,τxz} |  | 
 +| EQ9 | 400 | 1.40475 | 0.156523 | S3 {e,σxz}| | 
 +| EQ10 | 400 | 2.37207 | 0.328542 | S3 | | 
 +| EQ11 | 400 | 3.43223 | 0.404869 | S3 | | 
 +| EQ12 | 400 | 2.07134 | 0.303660 | S3 | | 
 +| EQ13 | 400 | 3.36118 | 0.404894 | S3 | | 
 +| EQ14 | 400 | 1.60344 | 0.240510 | S3 | 0.033852 | 
 +| EQ15 | 400 | 1.76297 | 0.268269 | S3 | 0.084577 | 
 +| EQ16 | 400 | 3.49153 | 0.333003 | R | 0.49640 | 
 +| EQ17 | 400 | 2.97947 | 0.291661 | R | 0.70251 | 
 +| EQ18 | 400 | 3.65963 | 0.325111 | R | 1.0039 | 
 +| EQ19 | 400 | 5.54202 | 0.427491 | Rz | 1.1758 |
  
 +====== ChaosBook.org reading ======
 +  * [[chaosbook:​discrete|World in a mirror]]
 +  * [[chaosbook:​continuous|Relativity for cyclists]]
   * [[chaosbook:​maps#​sectionpoincare_sections|Poincaré section and return map]]   * [[chaosbook:​maps#​sectionpoincare_sections|Poincaré section and return map]]
   * [[chaosbook:​smale|Chapter:​ Qualitative dynamics, for cyclists]], mostly for Dustin or JohnG, whoever gets there first. ​   * [[chaosbook:​smale|Chapter:​ Qualitative dynamics, for cyclists]], mostly for Dustin or JohnG, whoever gets there first. ​
  
 Please blog in appropriate ChaosBook blog pages whatever conceptual difficulties you have on the way to constructing a return map for the upper branch. Please blog in appropriate ChaosBook blog pages whatever conceptual difficulties you have on the way to constructing a return map for the upper branch.
gtspring2009/spieker_blog.1239206288.txt.gz · Last modified: 2009/04/08 08:58 by wikiadmin