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F. Seitl

Publications and source records attributed to F. Seitl.

2 recordsLinked to original sources
arXiv2022

Fitting the grain orientation distribution of a polycrystalline material conditioned on a Laguerre tessellation

The description of distributions related to grain microstructure helps physicists to understand the processes in materials and their properties. This paper presents a general statistical methodology for the analysis of crystallographic orientations of grains in a 3D Laguerre tessellation dataset which represents the microstructure of a polycrystalline material. We introduce complex stochastic models which may substitute expensive laboratory experiments: conditional on the Laguerre tessellation, we suggest interaction models for the distribution of cubic crystal lattice orientations, where the interaction is between pairs of orientations for neighbouring grains in the tessellation. We discuss parameter estimation and model comparison methods based on maximum pseudolikelihood as well as graphical procedures for model checking using simulations. Our methodology is applied for analysing a dataset representing a nickel-titanium shape memory alloy.

cond-mat.mtrl-sci↗
arXiv2019

Exploration of Gibbs-Laguerre tessellations for three-dimensional stochastic modeling

Random tessellations are well suited for probabilistic modeling of three-dimensional (3D) grain microstructures of polycrystalline materials. The present paper is focused on so-called Gibbs-Laguerre tessellations, in which the generators of the Laguerre tessellation form a Gibbs point process. The goal is to construct an energy function of the Gibbs point process such that the resulting tessellation matches some desired geometrical properties. Since the model is analytically intractable, our main tool of analysis is stochastic simulation based on Markov chain Monte Carlo. Such simulations enable us to investigate the properties of the models, and, in the next step, to apply the knowledge gained to the statistical reconstruction of the 3D microstructure of an aluminum alloy extracted from 3D tomographic image data.

eess.IV↗