Dynamic grain models via fast heuristics for diagram representations

TL;DR

This paper presents a fast heuristic-based mathematical model for dynamic grain growth, enabling continuous representation of grain evolution from discrete measurements using geometric diagrams like Voronoi tessellations.

Contribution

It introduces a novel, efficient approach to model dynamic grain growth through geometric diagrams, generalizing traditional tessellations with real-world data evaluation.

Findings

Algorithm performs well on real-world data

Enables continuous modeling from discrete measurements

Generalizes Voronoi and Laguerre tessellations

Abstract

The present paper introduces a mathematical model for studying dynamic grain growth. In particular, we show how characteristic measurements, grain volumes, centroids, and central second-order moments at discrete moments in time can be turned quickly into a continuous description of the grain growth process in terms of geometric diagrams (which largely generalize the well-known Voronoi and Laguerre tessellations). We evaluate the computational behavior of our algorithm on real-world data.