Two Dimensional Dendritic Crystal Growth for Weak Undercooling

We discuss the framework and issues brought forth in the recent work of Kunka, Foster & Tanveer, which incorporates small but nonzero surface energy effects in the nonlinear dynamics of a conformal mapping function z(zeta,t) that maps the upper-half zeta plane into the exterior of a dendrite. In this paper, surface energy effects on the singularities of z(zeta,t) in the lower-half plane were examined, as they move toward the real axis from below. In particular, the dynamics of complex singularities manifests itself in predictions on nature and growth rate of disturbances, as well as of coarsening.