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Characterization of the domain chaos convection state by the largest Lyapunov exponent

Jayaraman, A. and Scheel, J. D. and Greenside, H. S. and Fischer, P. F. (2006) Characterization of the domain chaos convection state by the largest Lyapunov exponent. Physical Review E, 74 (1). Art. No. 016209. ISSN 1539-3755. doi:10.1103/PhysRevE.74.016209.

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Using numerical integrations of the Boussinesq equations in rotating cylindrical domains with realistic boundary conditions, we have computed the value of the largest Lyapunov exponent lambda1 for a variety of aspect ratios and driving strengths. We study in particular the domain chaos state, which bifurcates supercritically from the conducting fluid state and involves extended propagating fronts as well as point defects. We compare our results with those from Egolf et al., [Nature 404, 733 (2000)], who suggested that the value of lambda1 for the spiral defect chaos state of a convecting fluid was determined primarily by bursts of instability arising from short-lived, spatially localized dislocation nucleation events. We also show that the quantity lambda1 is not intensive for aspect ratios Gamma over the range 20<Gamma<40 and that the scaling exponent of lambda1 near onset is consistent with the value predicted by the amplitude equation formalism.

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Additional Information:©2006 The American Physical Society (Received 9 September 2005; published 26 July 2006) The authors thank Michael Cross and Mark Paul for helpful discussions. This work was supported by DOE Grants Nos. DE-FG02-98ER14892, DE-FG03-98ER14891, and DEFG02-98ER14892; and by the Mathematical, Information, and Computational Sciences Division subprogram of the Office of Advanced Scientific Computing Research, U.S. Department of Energy, under Contract No. W-31-109-Eng-38. The numerical code was run on the following supercomputing sites, whom the authors gratefully acknowledge: the National Computational Science Alliance under DMR040001, which utilized the NCSA Xeon Linux Supercluster; the National Energy Research Scientific Computing Center, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC03-76SF00098; and “Jazz,” a 350-node computing cluster operated by the Mathematics and Computer Science Division at Argonne National Laboratory as part of its Laboratory Computing Resource Center.
Subject Keywords:chaos; convection; bifurcation; pattern formation; integration; point defects; nucleation; Lyapunov methods
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:4593
Deposited By: Archive Administrator
Deposited On:29 Aug 2006
Last Modified:08 Nov 2021 20:18

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