Wolfram Computation Meets Knowledge

Wolfram Summer School


Jiri Kroc

Summer School

Class of 2004


Jiri Kroc is a visiting professor at Helsinki School of Economics, Mikkeli, in Finland and a researcher at the Research Centre of West Bohemia University in the Czech Republic. His main research activities are quite diverse and range from solid-state physics to computational science and biology. The theory of complex systems is used to formulate everything he investigates. Cellular automata (CA) are used to express and to simulate their behavior. His use of CA can be traced to his Ph.D. studies carried at Charles University in the Czech Republic. His thesis was “Simulation of dynamic recrystallization by cellular automata.” Since that time, his research tool remains the same, but the number of fields has slowly increased.

His work within the last two years has been mainly focused on the following: teaching complex systems and calculus, modeling tumor growth and grain boundary migration, and studying the influence of lattice anisotropy on grain growth models, domain decomposition performed by CA, coloring of tiled planes, and other algorithms expressed by CAs. Recently he presented at the NKS conference with a paper about coloring tiled planes.

Project: Modeling of Crystal Growth Using Boundary Migration

Crystal growth in polycrystalline materials (NKS 369-373) has been of great interest since the industrial use of alloys and metals. The shape of grains is strongly affected by the underlying crystallographic structure. Experimental observations of grain growth use optical microscopes and X-ray crystallography (NKS 993). The Hall-Petch relationship of normal polycrystals displays the dependence of hardness with respect to grain size: hardness increases with decreasing grain size. Contrary to this, decreasing hardness with decreasing grain size is observed for nanocrystals. Therefore, the size of grains matters.

Modeling of crystal growth and grain boundary migration has a long history (NKS 993). A polycrystalline microstructure of polycrystalline material could be produced by, for example, a Voronoi diagram, or a simulation of recrystallization. Despite a substantial effort, there are still certain effects that are not theoretically explained. Among others, one of the biggest problems is related to the presence of anisotropy of any computational lattice, which is in contrast with the lack of experimentally observed anisotropy of the material itself.

The main goal of this project is to propose and to study rules describing grain growth using purely deterministic rules, from the New Kind of Science point of view. Properties of such rules are of great interest. So far, only modifications of the probabilistic approach have been used to model grain growth. The question is simple but the answer is still incomplete. There are systems, such as bismuth (NKS 993), that crystallize in a quite complex manner despite the lack of global information. In other words, there is a simple rule that could and for sure does produce really spatially complicated structures.

Favorite Two-Color, Radius-2 Rule

Rule chosen: 20040424