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 P\'eclet 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 P\'eclet-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.
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Martine Ben Amar (1990) studied this question.
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