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Polarized ferrofluids, lipid monolayers, and magnetic bubbles form domains with deformable boundaries. Stability analysis of these domains depends on a family of nontrivial integrals. We present a closed-form evaluation of these integrals as a combination of Legendre functions. This result allows exact and explicit formulas for stability thresholds and growth rates of individual modes. We also evaluate asymptotic behavior in several interesting limits.
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Miranda et al. (1997) studied this question.
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