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Stability Limits of Defects and Spatio-Temporal Chaos in Nonequilibrium Media

Title data

Aranson, Igor ; Kramer, Lorenz ; Weber, Andreas:
Stability Limits of Defects and Spatio-Temporal Chaos in Nonequilibrium Media.
In: Tirapegui, E. ; Zeller, W. (ed.): Instabilities and Nonequilibrium Structures IV. - Dordrecht : Springer Netherlands , 1993 . - pp. 259-272 . - (Mathematics and its Applications ; 267 )
ISBN 978-94-010-4842-2
DOI: https://doi.org/10.1007/978-94-011-1906-1_25

Abstract in another language

We show that the Eckhaus instability for traveling waves is of convective nature and does not lead directly to absolute instability. As a consequence spiral waves and hole solutions remain stable in a larger range than expected previously and the transition to spatio-temporal chaos can be delayed in some parameter range even beyond the Benjamen-Feir limit. We calculate the onset of absolute instability using the complex Ginzburg-Landau equation (CGLE ) and verify the results by detailed simulations. For the 1d CGLE we show that stable localized oscillating hole solutions exist in a region of parameters preceding the appearance of spatio-temporal chaos. These solutions oscillate in the depth and position of the hole. They can be described in terms of a supercritical Hopf bifurcation of the stationary hole solutions. The analytical results have been verified numerically by direct simulations of the CGLE.

Further data

Item Type: Article in a book
Refereed: Yes
Institutions of the University: Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Physics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Physics > Chair Theoretical Physics II
Result of work at the UBT: Yes
DDC Subjects: 500 Science
500 Science > 530 Physics
Date Deposited: 04 May 2016 07:35
Last Modified: 08 Jun 2016 06:39
URI: https://eref.uni-bayreuth.de/id/eprint/32320