Regensburg 2004 – wissenschaftliches Programm
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DY: Dynamik und Statistische Physik
DY 11: Ferrofluids
DY 11.5: Vortrag
Montag, 8. März 2004, 11:30–11:45, H3
Nonlinear oscillations of a torsional pendulum filled with ferrofluid — •Michael Zaks1 and Mark Shliomis2 — 1Institut für Physik, Humboldt-Universität Berlin — 2University of Beer-Sheva, Israel
We consider torsional motions of a sphere filled with ferrofluid and suspended on an elastic fiber. In presence of the linearly polarized horizontal magnetic field microscopic rotational motions of magnetic grains can sum up into a collective motion of the ferrofluid. Dynamics of the fluid magnetization and the angle of pendulum deflection is governed by a non-autonomous differential equation of the 4th order. We perform the detailed bifurcation analysis of this system.
If the frequency of the magnetic field strongly exceeds the pendulum eigenfrequency, separation of timescales reduces the problem to the 2nd order equation of the Van-der-Pol type with supercritical or subcritical onset of oscillations. If two frequencies are of the same order, bifurcation scenarios are more complicated. In contrast to the conventional picture of Arnold tongues, presence of physical symmetries causes a hysteresis near the resonances: coexistence of periodic states which correspond to “phase-locked” torsional motions with quasiperiodic oscillations. Our estimates show that these effects can be observed in experiments with moderate magnetic fields.