The objective of this research is to discover and quantify the unifying theoretical aspects of morphological stability, a phenomenon concerned with spontaneous changes in shape of some material body under the influence of driving forces, such as capillarity, diffusion, heat flow, and stress. Part I explores the morphological bifurcations of three dimensional shapes for a continuous range of ellipsoidal shapes that include planes, cylinders, and spheres. Recent observations on composite materials relate to this area. Part II looks at global aspects of morphological instability and coarsening. Mathematical relations developed by Gurtin are applied to dendritic solidification and late stage coarsening to characterize quantitatively the evolving morphologies. Computer simulation is employed to study diffusion-limited aggregation of particles.
