Onset and breakdown of relaxation oscillations in the torsional Quincke pendulum
Please always quote using this URN:urn:nbn:de:0296-matheon-9686
- In a strong constant electric field, a dielectric particle immersed in a weakly conducting fluid exhibits spontaneous rotations. This phenomenon is known under the name of the Quincke effect. In the original setup the particle was suspended on a silk thread and performed torsional oscillations of remarkably high amplitude. We derive the governing equations for this experiment, and ascertain that onset of oscillations from the quiescent state corresponds to the supercritical Hopf bifurcation. For the case of a soft thread, we characterize the regime of large-scale torsional relaxation oscillations: explicit estimates are derived for their period and amplitude, effects of bifurcation delay are described. In a stronger electric field, these relaxation oscillations yield to small-scale erratic rotations of the pendulum.
Author: | Michael A. Zaks, Mark I. Shliomis |
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URN: | urn:nbn:de:0296-matheon-9686 |
Referee: | Volker Mehrmann |
Document Type: | Preprint, Research Center Matheon |
Language: | English |
Date of first Publication: | 2015/12/23 |
Release Date: | 2015/12/23 |
Tag: | |
Institute: | Humboldt-Universität zu Berlin |
MSC-Classification: | 34-XX ORDINARY DIFFERENTIAL EQUATIONS / 34Dxx Stability theory [See also 37C75, 93Dxx] / 34D20 Stability |
Preprint Number: | 1088 |