VELOCITY SELECTION AND INSTABILITY SPECTRUM IN 3D DENDRITIC GROWTH

The problem of needle crystal and its stability in dendritic growth is considered. The analytical theory for steady-state growth [4] is exte nded to the case of a nonstationary perturbation. It is shown that, as in the two-dimensional (2D) cast, in the discrete spectrum of steady- state solutions only the unique solution, which corresponds to the hig hest velocity, is stable against the tip splitting perturbations, The instability spectrum for the solutions with lower velocities is enrich ed compared to 2D due to angular modes. The most unstable modes corres pond to the eigensolutions which are localized near the extremum of th e anisotropy of surface energy in the azimuthal direction.