Thin silicon films on a cooled substrate are often found to develop two-phase lamellar structures upon radiative heating. Jackson and Kurtz developed a two-dimensional model for the process in which the heated film consists of alternating parallel bands of liquid and solid phases separated by straight solid-liquid interfaces. To understand the cellular or dendritic structures that sometimes are observed in these interfaces, they also performed a linearized morphological stability analysis and obtained the conditions for the growth or decay of infinitesimal perturbations to the interface. In this work we extend that analysis to finite amplitudes by developing a boundary integral representation of the thermal field, and obtain numerical solutions for nonplanar solid-liquid interfaces.

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