Jackson, David P., and Brennan Gantner. Energetics of Interacting Magnetized Domains. Physical Review E 64, no. 5 (2001): e056230. https://journals.aps.org/pre/abstract/10.1103/PhysRevE.64.056230

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Many of the pattern forming features of ferrofluids, lipid monolayers, type-I superconductors, and magnetic bubbles can be understood by treating them as dipolar (uniformly magnetized or polarized) domains. Here, we investigate the early stages of pattern formation in a system consisting of two quasi-two-dimensional dipolar domains. We calculate the linearized interaction energy for these domains and find that the lowest energy states are those for which each drop has an indentation directed toward the other. These theoretically preferred states compare favorably with results of experiments performed with ferrofluids.

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