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Linear and weakly nonlinear analysis of the Rosensweig instability
Author(s) -
Lange A.
Publication year - 2002
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/1617-7061(200203)1:1<314::aid-pamm314>3.0.co;2-n
Subject(s) - instability , physics , nonlinear system , magnetic field , wavenumber , multiple scale analysis , wave vector , permeability (electromagnetism) , mathematical analysis , mechanics , mathematics , condensed matter physics , chemistry , optics , quantum mechanics , biochemistry , membrane
The Rosensweig instability of a layer of magnetic fluid with a free surface manifests itself as a stationary pattern of peaks. The pattern is characterized by a wave vector q whose absolute value gives the wave number q = | q |. Within the frame of a linear stability theory a quantitative analysis of the dependence of the wave number on the strength of the magnetic field is presented. The method of multiple scale analysis is applied for a weakly nonlinear analysis of the Rosensweig instability. For magnetic inductions above the critical value, the stability of different patterns are discussed with respect to the relative permeability of the magnetic fluid and the layer thickness.