= Small-wavelength thermal approximation for a solidification front
{title2=$\sigma=-V^2/\kappa+V\alpha-2\kappa\Gamma\alpha^3/\Delta T$}
Approximating perturbation <temperatures> by harmonic fields decaying as $e^{\pm\alpha\xi}$, while retaining displacement through the base gradient, produces this reduced <dispersion relation>. The <Gibbs--Thomson relation> supplies $\Gamma=\gamma T_m/(\rho L)$. This short-wave reduction suppresses perturbation advection and time dependence; its constant term and a threshold at $\alpha\kappa/V=O(1)$ are not controlled next-order results of the full diffusion problem.
Back to article page
