INTERFACE MODELS OF DENDRITIC GROWTH.

In order to understand the dynamics of pattern selection and sidebranch emission in dendritic growth, we develop two models which describe the time-evolution of the dendrite boundary. In the first model, the motion of the interface is strictly a function of the local geometry of the interface. The model, designed to mimic the physics of the diffusion-controlled growth, is however much simpler to analyze due to its essentially one-dimensional nature. Authors construct an algorithm to simulate the time development of interfaces in the model. These simulations show that our model grows dendritic-like shapes upon the introduction of sufficient anisotropy, and corroborate our analytic demonstration of velocity selection via a global solvability condition. The second model examined is the infinite diffusion length limit of a more realistic diffusion model. The algorithm developed for the local model can be easily extended to treat this model. Simulations reveal that this model also exhibits dendritic behaviour, with a tip-splitting instability for insufficient anisotropy.