= Thin-domain Turing mode selection
{title2=$L_y<\pi/\sqrt{q_+}$}
Suppose a two-species reaction-diffusion instability has an unstable squared-wave-number band $(q_-,q_+)$. On a rectangle with <Neumann boundary conditions>, $q=(n_x\pi/L_x)^2+(n_y\pi/L_y)^2$, with both indices nonnegative. The displayed thin-width condition excludes every $n_y\geq1$ mode but can leave $n_y=0$ modes in the band for sufficiently large $L_x$. Omitting zero indices would incorrectly remove the longitudinal pattern. Linear onset selects allowed directions; it does not alone establish the final nonlinear pattern.
Back to article page
