Nonmagnetic microspheres dispersed in a ferrofluid are denoted magnetic holes. When the spheres are confined to a monolayer between two plane, parallel plates and subjected to AC magnetic fields, they show a variety of dynamical behaviors and assemblages. The magnetic interactions between the particles and their dynamical behavior are influenced by the boundaries and the degree of confinement. We have derived analytical results for the pair-wise competing interactions, and these compare favorably with experimental results.
It is also possible to characterize the self-assembly and dynamics of the spheres by the theory of braids. It involves classifying different ways of tracing curves in space. The essentially two-dimensional motion of a sphere can be represented as a curve in a three-dimensional space-time diagram, and so several spheres in motion produce a set of braided curves. The dynamical modes can then be described in terms of braid-words. We also present a few other examples on how this system can be used to study dynamical processes.