  Polycrystalline materials undergoing coarsening can be represented as
evolving networks of grain boundaries, whose statistical characteristics
determine macroscopic materials properties. The process of formation of various
statistical distributions is extremely complex and is strongly influenced by
topological changes in the network. This work is an attempt to elucidate the
role of these changes by conducting a thorough numerical investigation of one
of the simplest types of grain growth simulation models, called vertex models.
While having obvious limitations in terms of its ability to represent realistic
systems, the vertex model enables full control over topological transitions and
retains essential geometric features of the network. We formulate a
self-consistent vertex model and investigate the role of microscopic parameters
on the mesoscale network behavior. This study sheds light onto several
important questions, such as how statistics are affected by the choice of
temporal and spatial resolution and rules governing topological changes.
Statistical analysis of the data produced by the simulation is performed for
both isotropic and anisotropic grain boundary energy.
