Noise-induced sidebranching in the boundary-layer model of dendritic solidification

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Abstract
Under certain circumstances, sidebranching in a dendrite may result from the selective amplification of noisy fluctuations in the tip region. This suggestion is based on numerical and analytical studies of the two-dimensional boundary-layer model with both kinetic and surface tension anisotropy. From the dynamical simulations, smooth steady fingers are observed above a critical anisotropy, below which the fingers are unstable. Noise added to a smooth steady tip gives sidebranching. A temperature estimate of the required noise indicates that thermal noise is a candidate. An analytic description of the response of the tail of the dendrite to a perturbation in the tip region is given and this analysis is compared to the numerical results. Comparison is also made to experiment as the undercooling and anisotropy are varied. Implications for the full model are discussed.