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- W2214892346 abstract "Chaotic dynamics in extended pattern forming systems like Rayleigh-Benard convection or Taylor vortex flow has drawn considerable interest recently. Most intensely investigated has been the complex Ginzburg-Landau equation describing travelling waves near onset1–3. A remarkable feature of these waves is, that they can be unstable to spatial perturbations for all wave numbers for which they exist, i.e. they are Benjamin-Feir unstable4. This is to be contrasted to the situation obtained for steady patterns close to threshold: in spatially homogeneous quasi-one-dimensional systems they are always stable within a band of wave numbers. Its limits are given by the Eckhaus instability which triggers a ‘phase-slip process’ which destroys (or creates) a roll (or vortex) pair. The situation changes, however, if the system is allowed to be spatially inhomogeneous. More precisely, if a control parameter R. varies in space such that it becomes subcritical, R < R c , in part of the system (‘subcritical ramp’), then the stable band is reduced and - in the limit of infinitely slow variations - shrinks to a single wave number5,6. Of particular interest in the present context is the fact, that the solution need not be stable for the wave number singled out in this way. It has been predicted that this will lead to dynamics resulting from the persistent creation (or destruction) of vortices7. This prediction, which was made quantitative by applying the phase diffusion approach to Taylor vortex flow8,9 (TVF), was recently confirmed in a Taylor system in which the straight cylinders have been replaced by tapered ones10. The resulting dynamics turns out to be periodic and the corresponding frequency agrees well with the results obtained from the phase equation9. In the present contribution we address the following questions. Why is the experimentally observed dynamics periodic? Could one set up a system in which the dynamics becomes more complicated? What kind of dynamics can be found?" @default.
- W2214892346 created "2016-06-24" @default.
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- W2214892346 date "1992-01-01" @default.
- W2214892346 modified "2023-09-23" @default.
- W2214892346 title "Chaotic Phase Diffusion through the Interaction of Phase Slip Processes" @default.
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- W2214892346 doi "https://doi.org/10.1007/978-1-4615-3438-9_6" @default.
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