chaosbook:smale
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chaosbook:smale [2010/02/08 05:38] predrag decay to laminar as extreme event? |
chaosbook:smale [2011/05/06 12:54] (current) predrag link to Creative Research Institute and things more difficult |
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| **Predrag 2009-03-05** added new text on construction of unstable manifolds, arclength parametrization, return maps - still in progress | **Predrag 2009-03-05** added new text on construction of unstable manifolds, arclength parametrization, return maps - still in progress | ||
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| ===== Section: Prune danish ===== | ===== Section: Prune danish ===== | ||
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| [[http://arxiv.org/abs/0906.3572|Extreme fluctuations and the finite lifetime of the turbulent state]] by Nigel Goldenfeld, Nicholas Guttenberg and Gustavo Gioia might be of interest to you. I have no good idea how to set up clones to do this. You could use Channelflow to integrate in a small plane Couette cell reasonably fast (pipe simulations are probably much slower). Keeping track of Lyapunov eigen-exponents is much more costly; Gibson and Viswanath do it by Arnoldi-Krylov methods, for equilibria and periodic orbits. As far as I know, no one yet has implemented it as a covariant Lyapunov vectors calculation. Decay to laminar state is marked by lots of almost marginal eigenvalues; that's presumably the "extreme event" signature. | [[http://arxiv.org/abs/0906.3572|Extreme fluctuations and the finite lifetime of the turbulent state]] by Nigel Goldenfeld, Nicholas Guttenberg and Gustavo Gioia might be of interest to you. I have no good idea how to set up clones to do this. You could use Channelflow to integrate in a small plane Couette cell reasonably fast (pipe simulations are probably much slower). Keeping track of Lyapunov eigen-exponents is much more costly; Gibson and Viswanath do it by Arnoldi-Krylov methods, for equilibria and periodic orbits. As far as I know, no one yet has implemented it as a covariant Lyapunov vectors calculation. Decay to laminar state is marked by lots of almost marginal eigenvalues; that's presumably the "extreme event" signature. | ||
| + | **Predrag Mar 11 2010** | ||
| + | [[http://arxiv.org/abs/1003.2013|Multicanonical sampling of rare trajectories in chaotic dynamical systems]] by Akimasa Kitajima and Yukito Iba: "Multicanonical Monte Carlo" can estimate the probability of initial conditions that lead to trajectories of a given level of chaoticity. They cite references [7, 8, 9, 10, 11] "that discuss sampling of unstable periodic orbits in chaotic systems by dynamic Monte Carlo or related methods". Should have a look at these... | ||
| + | * [7] Sasa, S.-i. and Hayashi, K., EPL (Europhysics Letters) 74 (2006) 156. | ||
| + | * [8] Kawasaki, M. and Sasa, S.-i., Phys. Rev. E 72 (2005) 037202. | ||
| + | * [9] Takeuchi, K. and Sano, M., Phys. Rev. E 75 (2007) 036201. | ||
| + | * [10] Pratt, L. R., J. Chem. Phys. 85 (1986) 5045. | ||
| + | * [11] Cho, A., Doll, J., and Freeman, D., Chemical Physics Letters 229 (1994) 218 | ||
| + | I emailed them the 3 problems above, asked them to test their method on them. | ||
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| + | **Predrag Mar 12 2010** | ||
| + | Akimasa Kitajima reponded: "I will inform you when we get results on them." | ||
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| + | **John Mar 12 2010** Good find, seems entirely relevant, will review. | ||
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| + | **Predrag Mar 13 2010** If you do read any of them, please do me a favor and blog your notes as you read them, either here (this is public) or siminos/blog (that is internal). Helps all of us in figuring what literature to read/not to read. | ||
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| + | **Predrag Apr 21 2010** | ||
| + | [[http://arxiv.org/abs/1004.2654|Identifying rare chaotic and regular trajectories in dynamical systems with Lyapunov weighted path sampling]] | ||
| + | by Philipp Geiger and Christoph Dellago is the next interesting paper in this series, with applications to | ||
| + | yet another set of examples. I emailed them the 3 problems above, asked them to test their method on them. | ||
| + | **Predrag May 6 2011** The monodromy theory of complex dynamical systems approach to the pruning front, [[http://www.cris.hokudai.ac.jp/arai/papers/loops.pdfOn loops in the hyperbolic locus of the complex Henon map and their monodromies]] by the mathematician and [[http://www.ironbarcup.com/irkhtl/|drummer]] [[http://www.cris.hokudai.ac.jp/arai/|Zin Arai]] of the [[http://www.cris.hokudai.ac.jp/cris/en_sousei/|Creative Research Institute]] looks very interesting (but what makes "Non Traditional Science" non-traditional? Go figure). | ||
| ~~DISCUSSION~~ | ~~DISCUSSION~~ | ||
chaosbook/smale.1265636336.txt.gz · Last modified: 2010/02/08 05:38 by predrag
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