Comparative grain topology

Space-filling polyhedral networks are commonly studied in biological, physical, and mathematical disciplines. The constraints governing the construction of each network varies considerably under each context, affecting the topological properties of the constituents. A method for mapping the topologi...

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Bibliographic Details
Published inActa materialia Vol. 66; pp. 414 - 423
Main Authors Keller, Trevor, Cutler, Barbara, Lazar, Emanuel A., Yauney, Gregory, Lewis, Daniel J.
Format Journal Article
LanguageEnglish
Published Kidlington Elsevier Ltd 01.03.2014
Elsevier
Subjects
Applied sciences
Computer simulation
Ellipsoids
Exact sciences and technology
Grain growth
Metals. Metallurgy
Microstructure
Monte Carlo methods
Networks
Phase-field method
Polyhedra
Polyhedrons
Topology
Topology
Computer simulation
Grain growth
Microstructure
Phase-field method
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Summary:Space-filling polyhedral networks are commonly studied in biological, physical, and mathematical disciplines. The constraints governing the construction of each network varies considerably under each context, affecting the topological properties of the constituents. A method for mapping the topological symmetry of a space-filling population of polyhedra is presented, relative to all possible polyhedra. This method is applied to the topological comparison of populations generated by seven different processes: (i) natural grain growth in polycrystalline metal, ideal grain growth simulated by (ii) interface-tracking and (iii) phase-field methods, (iv) Poisson–Voronoi and (v) ellipsoid tessellations, and (vi) graph-theoretic and (vii) Monte Carlo enumerations of individual polyhedra. Evidence for topological bias in these populations is discussed.
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ISSN:1359-6454
1873-2453
DOI:10.1016/j.actamat.2013.11.039