Preparing a texture suitable for a given purpose is a central problem
in materials science, which presents many challenges for mathematical
modeling, simulation, and analysis. In recent years we have witnessed
a changing paradigm in the materials laboratory with the introduction
of automated data acquisition technologies. This has permitted a more
accurate characterization of materials properties and the collection
of statistics on a vast scale, both of which pave the road to a better
understanding of the way materials evolve in nature and to optimizing
aspects of material behavior to better fit technological needs.

In this talk, I will focus on the mesoscopic behavior of a model grain
boundary system and on understanding the role of topological
reconfigurations during evolution. We have explored several evolution
equations based on pure probabilistic and stochastic descriptions and
compared against the results provided by large-scale simulations and
experiments. The advantages and limitations, numerical characteristics
and possible extensions of these approaches to higher dimensions will
be discussed.