Dynamics of self assembly of magnetized disks rotating at the liquid-air interface

This paper is a theoretical study of dynamic self assembly in a system of millimeter-sized magnetized disks floating at a liquid-air interface and spinning under the influence of a rotating magnetic field. Equations of motions are derived that account for the hydrodynamic and magnetic forces acting in the system. Numerical integration of these equations predicts formation of ordered structures of spinning disks: the simulated structures reproduce the patterns observed experimentally.