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--- chaosbook:pipes [2011/02/16 10:34]
predrag Ashley makes progress, Predrag none
+++ chaosbook:pipes [2012/02/28 19:23] (current)
predrag
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 Regarding the latest figures - I usually think that time series in dynamics are not too insightful, would be nice to also see the reduced state space projections of the flow on one slice (for now), with segments of trajectory where //dS_z/dt// is large color-coded. Might see more clearly where the inflection hyperplane lies. I am bit worried about the shift velocities that you do see - I would hope there is a closer template in each case. so the singularity is preempted by switching to its neighborhood.
-**2011-02-16 Ash** Using the set of TWs as templates, I've been able to get quite long tracks without jumps.  This has meant that I could do some recurrence checking... Here's another RPO found using the slicing!, //T=45 R/(2U)=11.25 D/U//; the crosses are equally spaced in time.  (S&Rot symmetry has been removed.) The candidate for the long-period orbit I've found difficult to get to converge.. I'm trying multiple shooting at the mo'.
+**2011-02-16 Ash** Using the set of TWs as templates, I've been able to get quite long tracks without jumps.  This has meant that I could do some recurrence checking... Here's another RPO found using the slicing! [pink], //T=45 R/(2U)=11.25 D/U//; the crosses are equally spaced in time.  (S&Rot symmetry has been removed.) The candidate for the long-period orbit I've found difficult to get to converge.. I'm trying multiple shooting at the mo'.
-{{:chaosbook:pipes:2210nd_02.png?400}}{{:chaosbook:pipes:2216m1proj.png?400}}
+{{:chaosbook:pipes:2210nd_02.png?400}}{{:chaosbook:pipes:2514m1proj.png?400}}
 **2011-02-16 Humbledt** you are an angel, but I cannot see what the left figure is. Mea culpa, no doubt. Join us for Marc's Webinar, or be square.
+**2011-02-17 Ash** Sorry I missed the meeting, give me a bit longer warning next time.  I've registered but not found it online - is it recorded anywhere?  **Re yesterday's entry:**  The figure on the LHS shows the relative distance within the slice between states separated by time //dt//.  The signature around //t=3100..3300// suggested that the trajectory shadowed an orbit four or five times.  When plotted, the candidate trajectory looked like it might just be spiralling away from the S2a state (green spot on RH figure), but it proved worthwhile trying with Newton.  The plotted orbit was located within half a dozen iterations.
+**2011-03-31 Ash** Second RPO added to figure on 2011-02-16, the longer one (blue).  //T=37.93 D/U//;  marks on trajectories are //2 D/U// apart.  The orbit wanders roughly equidistant from M1 (lower blue circle) and S2a (green spot), not just around S2a as this particular projection suggests.
+**2011-04-14 Humbledt** Wow! this one will require some thinking. In the spirit of Froehlich & Cvitanovic paper, we will have to add a Poincare section hyperplane through each template point, start looking into local segments of the unstable manifolds to start working out symbolic dynamics for RPOs and making sense of it all. Already the (blue) RPO is too convoluted to interpret without making a stab at symbolic dynamics of longer orbits.
+**2011-04-08 Ash** And another (orange).  Very similar to the first RPO (pink), but having compared energies and friction factors, they are not just different projections of the same orbit.
+**2011-05-29 Humbledt** Got [[http://theanke.posterous.com/excellent-anglo-eu-translation-guide-albertoa|this link]] form Mason Porter, it might be helpful to non-Brits in this collaboration.
+**2011-05-29 Humbledt** Starting this date, the blog has been moved to CNS svn repository `pipes'.

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