Dynamics of a Single Peak of the Rosensweig Instability in a Magnetic Fluid

Details Dynamics of a Single Peak of the Rosensweig Instability in a Magnetic Fluid Dynamics of a Single Peak of the Rosensweig Instability in a Magnetic Fluid

1999-10-05

arxiv.org/abs/patt-sol/9910003v2

Physica D, 140 (2000) 294

Nonlinear Sciences

Pattern Formation and Solitons

21 pages, 9 figures, using elsart, submitted to Physica D; revised version with 2 figures and references added

Scientific paper

10.1016/S0167-2789(00)00018-X

To describe the dynamics of a single peak of the Rosensweig instability a model is proposed which approximates the peak by a half-ellipsoid atop a layer of magnetic fluid. The resulting nonlinear equation for the height of the peak leads to the correct subcritical character of the bifurcation for static induction. For a time-dependent induction the effects of inertia and damping are incorporated. The results of the model show qualitative agreement with the experimental findings, as in the appearance of period doubling, trebling, and higher multiples of the driving period. Furthermore a quantitative agreement is also found for the parameter ranges of frequency and induction in which these phenomena occur.

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