The growth of a free dendrite having a non-axisymmetric morphology with arbitrary symmetry in a pure substance is considered with the interfacial effect of anisotropy and in the absence of convective flow. A stable mode of thermal dendritic growth with the n-fold crystal symmetry is formulated using the solvability theory. A complete set of nonlinear equations, consisting of the undercooling balance condition and the selection criterion, is derived. Theoretical predictions are compared with phase field modeling data in two and three dimensional geometry obtained for ice dendrites growing in pure water.

中文翻译：

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在二维和三维中具有任意对称性的枝晶的非轴对称生长：清晰的界面模型与相场模型

考虑到具有各向异性的界面效应并且在没有对流的情况下，在纯物质中具有任意对称性的具有非轴对称形态的自由枝晶的生长。使用可溶性理论制定了具有n倍晶体对称性的热树突生长的稳定模式。得出了由过冷平衡条件和选择标准组成的一整套非线性方程。将理论预测与在纯水中生长的冰晶的二维和三维几何相场建模数据进行比较。