Dendritic growth rate at arbitrary undercooling

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Abstract
We study the growth rate of a dendritic crystal in two and three dimensions in the symmetric model of solidification. We clarify the question of the variation of the ‘‘stability constant’’ with the Péclet number in the regime of moderate to large values. A careful WKB treatment shows that the eigenvalues selected by anisotropy of surface tension are strongly Péclet-number dependent in contradiction with some earlier treatments. We also perform a numerical analysis of this problem and our results are compared with recent experimental data.