Geometric growth and character development in large metastable networks

Cellular networks are ubiquitous in nature. They exhibit behavior on many different length and time scales and are generally metastable. Most technologically useful materials are polycrystalline microstructures composed of a myriad of small monocrystalline grains separated by grain boundaries. The energetics and connectivity of the grain boundary network plays a crucial role in determining the properties of a material across a wide range of scales. A central problem in materials science is to develop technologies capable of producing an arrangement of grains - a texture - that provides for a desired set of material properties. Here we discuss briefly the role of energy in texture development, measured by a character distribution, and how this is different from the evolution of geometric features, which we term geometric coarsening. For this purpose we present a critical event model to deepen our understanding of the topological reconfigurations that occur during the growth process.