The objective of this research, jointly funded by the Divisions of Materials Research and Mathematical Sciences, is to develop reliable theoretical methods for calculating the patterns that result in crystal growth subsequent to morphological instability and to discover and quantify their unifying aspects. Morphological instability pertains to spontaneous changes in shape of some material body under the influence of driving forces such as capillarity, diffusion, and heat flow. Examples include cellular morphologies in semiconductor crystals, dendritic solidification of metallic alloys, and shape changes of phases in composite materials. Research methods include numerical solution of free boundary problems and phase field equations via supercomputing and computer simulation using random walk algorithms. %%% The accurate modeling and physical understanding of patterns which form during the growth of crystals is an extremely difficult problem. However, the growth of solid bodies from the melt is common to most fields of materials science. Thus, any progress made in this field can have broad ramifications. The work is also highly interdisciplinary and requires research at the boundaries of materials science, condensed matter physics and applied mathematics. Consequently, this research in nonlinear science is jointly funded through the Materials Research and Mathematical Sciences Divisions.
