Publication

2D grain growth viewed as a purely topological phenomenon : models and computational results

Thomas Liebling
1989
Journal Articles

Abstract

Grain growth in 2D polycrystals or similar cellular structures is characterized by interface motions and topological transforamtions. Focusing on the topology of such cell complexes only, regardless of their geometry, they become topological graphs of a given type. In this paper, grain growth is viewed as a sequence of discrete transformations of such topological graphs. Simple simulation models using these general features are introduced, and their first results -essentially face coordination distributions- analyzed and compared to both real and theoretical ones.

Official source

https://infoscience.epfl.ch/entities/publication/18c01d84-26bc-4b04-be72-79cc6dd2d6b4

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Thomas Liebling
1989
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/18c01d84-26bc-4b04-be72-79cc6dd2d6b4

About this result

Related concepts (32)

Topological graph theory

In mathematics, topological graph theory is a branch of graph theory. It studies the embedding of graphs in surfaces, spatial embeddings of graphs, and graphs as topological spaces. It also studies immersions of graphs. Embedding a graph in a surface means that we want to draw the graph on a surface, a sphere for example, without two edges intersecting. A basic embedding problem often presented as a mathematical puzzle is the three utilities problem.

Grain boundary

In materials science, a grain boundary is the interface between two grains, or crystallites, in a polycrystalline material. Grain boundaries are two-dimensional defects in the crystal structure, and tend to decrease the electrical and thermal conductivity of the material. Most grain boundaries are preferred sites for the onset of corrosion and for the precipitation of new phases from the solid. They are also important to many of the mechanisms of creep.

Topological sorting

In computer science, a topological sort or topological ordering of a directed graph is a linear ordering of its vertices such that for every directed edge uv from vertex u to vertex v, u comes before v in the ordering. For instance, the vertices of the graph may represent tasks to be performed, and the edges may represent constraints that one task must be performed before another; in this application, a topological ordering is just a valid sequence for the tasks.

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2D grain growth viewed as a purely topological phenomenon : models and computational results

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