Stability analysis of polarized domains

TL;DR

This paper provides a mathematical analysis of the stability of polarized domains in ferrofluids, lipid monolayers, and magnetic bubbles, deriving explicit formulas for stability thresholds and growth rates.

Contribution

It introduces a closed-form evaluation of complex integrals using Legendre functions, enabling precise stability analysis of deformable polarized domains.

Findings

Explicit formulas for stability thresholds and growth rates.

Asymptotic behaviors in various limits derived.

Enhanced understanding of domain stability in polarized fluids.

Abstract

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 formulae for stability thresholds and growth rates of individual modes. We also evaluate asymptotic behavior in several interesting limits.