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docs:utils:poincare [2009/02/23 11:51]
gibson created
docs:utils:poincare [2010/02/02 07:55] (current)
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 ====== poincare ====== ====== poincare ======
  
-compute ​crossings of a Poincare section in a pre-computed trajectory+Compute ​crossings of a Poincare section in a pre-computed trajectory. The Poincare condition is %%(u(t) - ueqb, e) == 0%%, i.e. the displacement from a given point %%ueqb%% is orthogonal to a direction %%e%%. The program checks for changes in sign in the inner product in the stored trajectory (with large %%dT%%, and when it finds one, goes back and reintegrates with small %%dt%%, and then does quadratic interpolation when the fine-scale trajectory recrosses the section.
  
-===== Options ​=====+===== usage ===== 
 + 
 +<​code>​ 
 +  poincare -T0 0 -T1 400 -d datadir ueqb.ff e.ff 
 +</​code>​ 
 +reads a trajectory u0, u1, ..., u400 stored in %%datadir%%,​ computes the crossings of the Poincare section %%(u(t)-ueqb,​ e) == 0%%, and saves them in a %%poincare/​%% directory.  
 + 
 +===== options ​=====
  
 <​code>​ <​code>​
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 </​code>​ </​code>​
  
-===== Usage examples ​=====+===== Usage example ​=====
  
  
 +Here is the basic idea of usage. Suppose you have an equilibrium ueqb with an unstable complex eigenvalue pair whose eigenfunctions are ef1 and ef2. Integrate a trajectory with initial condition %%u(0) = ueqb + 0.001 ef1%% as follows
 +<​code>​
 +   ​addfields 1 ueqb 0.001 ef1 ueqb_001ef1
 +   ​couette -T0 0 -T1 1000 -o data-ueqb_0001ef1 ueqb_001ef1
 +</​code>​
 +Then you can define a Poincare section as, say, %%(u-ueqb, ef2) = 0%%, that is, the displacement from the equilibrium is orthogonal to the ef2 eigenfunction. To compute crossings of the Poincare section within the
 +previously integrated trajectory, run
 +<​code>​
 +   ​poincare -T0 0 -T1 1000 -d data-ueqb_0001ef1 ueqb ef2
 +</​code>​
 +
 +===== Hiccups =====
  
 +:-) Hey John, I was wondering if there was any particular reason you put the cfpause() line in your code other than it was helpful in writing the code. --- //​[[dustin.spieker@gatech.edu|Dustin Spieker]] 2009-03-02 10:24//
docs/utils/poincare.1235418700.txt.gz · Last modified: 2009/02/23 11:51 (external edit)