Abstract
Selection of steady needle crystals in the symmetric model of dendritic growth is considered. The diffusion equation and associated kinematic and thermodynamic boundary condition are recast into a nonlinear equation through the use of boundary integral methods. The equation is solved numerically and for the range of Péclet numbers considered it is found that a smooth solution exists only if anisotropy is included in the capillarity term of the Gibbs-Thompson condition. The behavior of the selected velocity and tip radius as a function of undercooling is also examined. A linear integral equation is also derived to examine the stability of the steady state.
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