Critical Role of Crystalline Anisotropy in the Stability of Cellular Array Structures in Directional Solidification

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Abstract
We calculate numerically the full Floquet-Bloch stability spectrum of cellular array structures in a symmetric model of directional solidification. Our results demonstrate that crystalline anisotropy critically influences the stability of these structures. Without anisotropy, the stability balloon of cells in the plane of wave number and velocity closes near the onset of morphological instability. With a finite, but even small, amount of anisotropy this balloon remains open and a band of stable solutions persists for higher velocities into a deep cell regime. The width of the balloon depends critically on the anisotropy strength.