Dynamics of an elongated magnetic droplet in a rotating field

A model is proposed for the dynamics of an elongated droplet under the action of a low frequency rotating magnetic field. This model determines a set of critical frequencies at which the transitions to more complex bent shapes take place. These transitions occur through propagation of jumps of the droplet's axial tangent angle described by a nonlinear singularly perturbed partial differential equation with the intrinsic viscosity of the droplet playing the regularizing role.