Self-assembled clusters of magnetically tilted dipoles

TL;DR

This paper presents a macroscopic experiment with floating magnets that self-assemble into clusters, supported by a mathematical model that explains their stability and ordering, offering insights into complex systems with repulsive particles.

Contribution

It introduces a modified experimental setup and a new mathematical model to analyze self-assembled magnetic clusters, revealing conditions for their stability and alternative orderings.

Findings

Empirical observations of stable magnetic clusters under external fields.

A mathematical model reproduces and explains the observed cluster behaviors.

Conditions for cluster stability and collapse are established.

Abstract

Motivated by the idea of using simple macroscopic examples to illustrate the physics of complex systems, we modify a historic experimental setup in which interacting floating magnets spontaneously self-assemble into ordered clusters. By making the cluster components mechanically stable against their natural tendency to flip and coalesce, we can monitor the torque experienced by individual magnets through the macroscopic tilt angles they acquire when exposed to non-collinear external fields. A mathematical model that reproduces the empirical observations is introduced, enabling us to go beyond the experimental cases considered. The model confirms the existence of alternative orderings as the number of objects increases. Furthermore, a simpler and more mathematically transparent version of our model enables us to establish the conditions under which the cluster structure is stable and when it will collapse. We argue that our simple experimental setup combined with the accompanying models may be useful to describe general features seen in systems composed of mutually repulsive particles in the presence of modulating confining fields.