= First domain length for an unstable Neumann band
{c}
{title2=$L_c=\pi/\sqrt{q_+}$}
If a one-dimensional reaction-diffusion model has a strict unstable squared-<wavenumber> band $(q_-,q_+)$, its nonzero Neumann modes on $[0,L]$ have $q_n=(n\pi/L)^2$. Increasing $L$ from zero first reaches the band with $n=1$ at the displayed threshold. Equality is neutral; the first mode is strictly unstable for $\pi/\sqrt{q_+}<L<\pi/\sqrt{q_-}$. Thus positive growth has an infimum in domain length rather than an attained smallest length. The zero mode must be checked separately through reaction stability.
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