= Merger at a magnetoconvection neutral-curve minimum
{title2=$k_s^2=\pi^2(\sigma+\zeta)/[2\sigma(1-\zeta)],\quad k_o^2=\pi^2/[2(1-\zeta^2)]$}
At a steady-curve minimum, differentiation and the <steady-Hopf merger in vertical-field magnetoconvection> give the first displayed wavenumber. At an oscillatory-curve minimum they give the second. For fixed positive <Prandtl number> $\sigma$ and large $Q_\kappa$, the corresponding merger diffusivity deficits are $1-\zeta_s\sim[(1+\sigma)/\sigma](\pi^2/(4Q_\kappa))^{1/3}$ and $1-\zeta_o\sim[(1+\sigma)\pi^2/(16\sigma Q_\kappa)]^{1/3}$. The two parameter surfaces are distinct: coincidence of neutral curves at one wavenumber does not imply coincidence of their minimizing wavenumbers.
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