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Linear and nonlinear approach to the Rosensweig instability
Author(s) -
Lange Adrian,
Richter Reinhard,
Tobiska Lutz
Publication year - 2007
Publication title -
gamm‐mitteilungen
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.239
H-Index - 18
eISSN - 1522-2608
pISSN - 0936-7195
DOI - 10.1002/gamm.200790006
Subject(s) - instability , nonlinear system , wavenumber , bifurcation , bistability , physics , amplitude , metastability , pulse (music) , bifurcation diagram , statistical physics , linear stability , stability (learning theory) , mechanics , optics , computer science , quantum mechanics , detector , machine learning
We report on recent efforts to improve the understanding of the Rosensweig instability in the linear as well as in the nonlinear regime. In the linear regime we focus on the wavenumber of maximal growth and the oscillatory decay of metastable magnetic liquid ridges, accessible via a new pulse technique. We compare the measurements with the predictions of the linear stability analysis. In the nonlinear regime the fully developed Rosensweig pattern was successfully estimated by the method of finite elements, taking into account the nonlinear magnetization law. For a comparison with these results the three‐dimensional surface profile is recorded by a radioscopic measurement technique. The bifurcation diagram measured in this way can be fitted by the roots of an amplitude equation. Eventually we investigate ferrosolitons, which were recently uncovered in the bistability interval of the Rosensweig instability. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)