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.
Source:  Stability Analysis of an Array of Magnets: When Will It Jump? Nicolas Taberlet, Jérémy Ferrand, and Nicolas Plihon. Phys. Rev. Lett. 120, 264301 – 29 Juin 2018