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General framework for testing Poisson‐Voronoi assumption for real microstructures

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  • Martina Vittorietti
  • Piet J. J. Kok
  • Jilt Sietsma
  • Wei Li
  • Geurt Jongbloed

Abstract

Modeling microstructures is an interesting problem not just in materials science, but also in mathematics and statistics. The most basic model for steel microstructure is the Poisson‐Voronoi diagram. It has mathematically attractive properties and it has been used in the approximation of single‐phase steel microstructures. The aim of this article is to develop methods that can be used to test whether a real steel microstructure can be approximated by such a model. Therefore, a general framework for testing the Poisson‐Voronoi assumption based on images of two‐dimension sections of real metals is set out. Following two different approaches, according to the use or not of periodic boundary conditions, three different model tests are proposed. The first two are based on the coefficient of variation and the cumulative distribution function of the cells area. The third exploits tools from to topological data analysis, such as persistence landscapes.

Suggested Citation

  • Martina Vittorietti & Piet J. J. Kok & Jilt Sietsma & Wei Li & Geurt Jongbloed, 2020. "General framework for testing Poisson‐Voronoi assumption for real microstructures," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 36(4), pages 604-627, July.
    • Handle: RePEc:wly:apsmbi:v:36:y:2020:i:4:p:604-627
    DOI: 10.1002/asmb.2517
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    Cited by:

    1. Cipriani, Alessandra & Hirsch, Christian & Vittorietti, Martina, 2023. "Topology-based goodness-of-fit tests for sliced spatial data," Computational Statistics & Data Analysis, Elsevier, vol. 179(C).

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