Katsuya Nakashima

Vertex models for two-dimensional grain growth

Abstract We develop two-dimensional vertex models which are expected to capture the essential ingredients of the long-time behaviour of two-dimensional grain growth and permit efficient large-scale computer simulations. Such simulations are carried out starting with the initial 24 000 randomly chosen Voronoi cells. We confirm the 1/2 power law for the growth of average grain size. We also find the normalized grain-size distribution and the edge number distribution which exhibit stationary behaviour at long times except for small-amplitude oscillatory behaviour for the latter.

Scaling behavior of two-dimensional domain growth: Computer simulation of vertex models

Computer simulations are performed for vertex models which are coarse-grained models for dynamical cellular patterns in two dimensions. By simulating large systems, we obtain conclusive evidence of scaling behavior, that is, a power law for the growth of the average cell size and the scaling properties for the distribution functions of edge number and size of cells. Several versions of the vertex models are obtained by making some approximations for the equation of motion of a vertex, and we compare the statistical properties of the patterns in the scaling regime.

Statistical Physics of Domain Walls and Grain Boundaries in Ordering Kinetics

It is now well recognized that topological defects like domain walls, vortex lines etc. play crucial roles at late stages of ordering Kinetics [1]. However, treatments of generally interconnected and interacting topological defects present formidable problems of cooperative dynamics in complex physical systems. In this talk we take up two concrete examples studied recently in our research group.