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Statistics of defect trajectories in spatio-temporal chaos in inclined layer convection and the complex Ginzburg–Landau equation

Chaos 14, 864 (2004); doi:10.1063/1.1778495

Published 16 September 2004

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Cristián Huepe and Hermann Riecke
Engineering Science and Applied Mathematics, Northwestern University, Evanston, Illinois 60208

Karen E. Daniels
Physics Department, Duke University, Durham, North Carolina 27708-0305

Eberhard Bodenschatz
Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York 14850
Max-Planck-Institut für Strömungsforschung, Göttingen 37073, Germany
For spatio-temporal chaos observed in numerical simulations of the complex Ginzburg–Landau equation (CGL) and in experiments on inclined-layer convection (ILC) we report numerical and experimental data on the statistics of defects and of defect loops. These loops consist of defect trajectories in space–time that are connected to each other through the pairwise annihilation or creation of the associated defects. While most such loops are small and contain only a few defects, the loop distribution functions decay only slowly with the quantities associated with the loop size, consistent with power-law behavior. For the CGL, two of the three power-law exponents are found to agree, within our computational precision, with those from previous investigations of a simple lattice model. In certain parameter regimes of the CGL and ILC, our results for the single-defect statistics show significant deviations from the previously reported findings that the defect dynamics are consistent with those of random walkers that are created with fixed probability and annihilated through random collisions. ©2004 American Institute of Physics.
History: Received 9 March 2004; accepted 14 June 2004; published 16 September 2004
Permalink: http://link.aip.org/link/?CHAOEH/14/864/1
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KEYWORDS and PACS

Keywords
PACS
  • 05.45.Pq
    Numerical simulations of chaotic models
  • 05.50.+q
    Lattice theory and statistics including Ising, Potts models, etc
  • 05.40.Fb
    Random walks and Levy flights
  • 47.52.+j
    Chaos in fluid dynamics
  • 02.50.Cw
    Probability theory
  • YEAR: 2004

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PUBLICATION DATA

ISSN:
1054-1500 (print)   1089-7682 (online)
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