Dynamic grain models via fast heuristics for diagram representations. Issue 10 (19th May 2023)

• Record Type: Journal Article
• Authors: Alpers, Andreas; Fiedler, Maximilian; Gritzmann, Peter; Klemm, Fabian
• Is Part Of: Philosophical magazine. Volume 103:Issue 10(2023)
• Page Start: 948
• Page End: 968
• Publication Date: 2023-05-19
• Subjects: Power diagrams -- generalized balanced power diagrams -- tessellations -- grains -- polycrystals -- grain growth; Condensed matter -- Periodicals; Physics -- Periodicals; Matière condensée -- Périodiques; Physique -- Périodiques; 530.41
• DOI: 10.1080/14786435.2023.2180679
• Languages: English
• ISSNs: 1478-6435

Abstract

ABSTRACT: The present paper introduces a mathematical model for analysing dynamic grain growth. In particular, we show how the characteristic measurements grain volumes, centroids, and central second-order moments at discrete moments in time can be quickly turned 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 give a theoretical analysis of common optimization-free heuristics in terms of discriminant analysis and evaluate the computational behaviour of our algorithm on real-world data.