Stability Analysis of an Array of Magnets: When Will It Jump?

Physical Review Letters
Nicolas TaberletNicolas Plihon

Abstract

A bidimensional array of magnets whose magnetic moments share the same vertical orientation, and lying on a planar surface, can be gradually compacted. As the density reaches a threshold, the assembly becomes unstable, and the magnets violently pop out of plane. In this Letter, we investigate experimentally and theoretically the maximum packing fraction (or density) of a bidimensional planar assembly of identical cylindrical magnets. We show that the instability can be attributed to local fluctuations of the altitude of the magnets on the planar surface. The maximum density is theoretically predicted assuming dipolar interactions between the magnets and is in excellent agreement with experimental results using a variety of cylindrical magnets.

References

May 1, 1992·Physical Review. a·M G RaizenD J Wineland
Mar 5, 2004·Physical Review Letters·V NosenkoB Liu
Sep 26, 2012·Physical Review Letters·Sheng ZhangPeter Schiffer
Feb 2, 2013·Physical Review Letters·Paula MelladoL Mahadevan
Aug 21, 2013·Physical Review Letters·A FarhanL J Heyderman
Aug 31, 2016·Physical Review. E·Nicolas PlihonJean-François Pinton
Jan 20, 2018·Physical Review. E·A MehremV J Sánchez-Morcillo

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