Dynamics of a single peak of the Rosensweig instability in a magnetic fluid

To describe the dynamics of a single peak of the Rosensweig instability a m odel is proposed which approximates the peak by a half-ellipsoid atop a lay er of magnetic fluid. The resulting nonlinear equation for the height of th e peak leads to the correct subcritical character of the: bifurcation for s tatic induction. For a time-dependent induction the effects of inertia and damping are incorporated. The results of the model show qualitative agreeme nt with the experimental findings, as in the appearance of period doubling, trebling, and higher multiples of the driving period. Furthermore, a quant itative agreement is also found for the parameter ranges of frequency and i nduction in which these phenomena occur. (C) 2000 Elsevier Science B.V. All rights reserved.