Model for dynamic self-assembled magnetic surface structures

We propose a first-principles model for the dynamic self-assembly of magnetic structures at a water-air interface reported in earlier experiments. The model is based on the Navier-Stokes equation for liquids in shallow water approximation coupled to Newton equations for interacting magnetic particles suspended at a water-air interface. The model reproduces most of the observed phenomenology, including spontaneous formation of magnetic snakelike structures, generation of large-scale vortex flows, complex ferromagnetic-antiferromagnetic ordering of the snake, and self-propulsion of bead-snake hybrids.