Dynamics of labyrinthine pattern formation in magnetic fluids.

A theory is developed for the dynamics of pattern formation in quasi-two-dimensional domains of magnetic fluids (ferrofluidsl in transverse magnetic fields. The pattern formation is treated as a dissipative dynamical process, with the motion derived variationally from a static energy functional using minimal assumptions. This dynamics is one instance of a general formalism applicable to any system that can be modeled as a closed curve in a plane. In applying the formalism to ferrofluids, we present a calculation of the energy of a two-dimensional dipolar domain as a functional of the shape of its boundary