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Exploration of Gibbs-Laguerre tessellations for three-dimensional stochastic modeling | | F. Seitl
; L. Petrich
; C.E. Krill III
; V. Schmidt
; J. Staněk
; V. Beneš
; | | Date: |
10 May 2019 | | Abstract: | Random tessellations are well suited for the probabilistic modeling of
three-dimensional (3D) grain microstructure of polycrystalline metals. The
present paper deals with so-called Gibbs-Laguerre tessellations where the
generators of a Laguerre tessellation form a Gibbs point process. The goal is
to construct an energy function of the Gibbs point process from a suitable set
of potentials, such that the resulting Gibbs-Laguerre tessellation matches some
desired geometrical properties. Since the model is analytically hardly
tractable, our main tool of analysis are stochastic simulations based on Markov
chain Monte Carlo. These enable us to investigate the properties of the models,
and, in the next step, to apply the thus gained knowledge to do a statistical
reconstruction of an aluminum alloy based on 3D tomographic image data. | | Source: | arXiv, 1905.4252 | | Services: | Forum | Review | PDF | Favorites | |
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