Search results for "Voronoi diagrams"

showing 4 items of 4 documents

General framework for testing Poisson-Voronoi assumption for real microstructures

2020

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 paper 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 2D sections of real metals is set out. Following two different approaches, according to the use or not of periodic boundary conditions, thre…

FOS: Computer and information sciencesreal microstructuresPoisson-Voronoi diagrams0211 other engineering and technologies02 engineering and technologyManagement Science and Operations ResearchPoisson distribution01 natural sciencesStatistics - ApplicationsMethodology (stat.ME)Set (abstract data type)010104 statistics & probabilitysymbols.namesakehypothesis testingPeriodic boundary conditionsApplied mathematicsApplications (stat.AP)0101 mathematicsStatistics - MethodologyStatistical hypothesis testing021103 operations researchCumulative distribution functionDiagramscalingGeneral Business Management and Accounting62P30 62-00 62-01 62G10persistence landscapeModeling and SimulationsymbolsTopological data analysiscumulative distribution functionVoronoi diagramApplied Stochastic Models in Business and Industry
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Accurate representation of the distributions of the 3D Poisson-Voronoi typical cell geometrical features

2019

Understanding the intricate and complex materials microstructure and how it is related to materials properties is an important problem in the Materials Science field. For a full comprehension of this relation, it is fundamental to be able to describe the main characteristics of the 3-dimensional microstructure. The most basic model used for approximating steel microstructure is the Poisson-Voronoi diagram. Poisson-Voronoi diagrams have interesting mathematical properties, and they are used as a good model for single-phase materials. In this paper we exploit the scaling property of the underlying Poisson process to derive the distribution of the main geometrical features of the grains for ev…

General Computer SciencePoisson-Voronoi diagramsMonte Carlo methodVoronoiGeneral Physics and Astronomy02 engineering and technology010402 general chemistryPoisson distribution01 natural sciencesParametric representationsymbols.namesakeGeneral Materials ScienceStatistical physicsRepresentation (mathematics)ScalingParametric statisticsDiagramGeneral Chemistry021001 nanoscience & nanotechnology0104 chemical sciencesComputational MathematicsDistribution (mathematics)Mechanics of Materialssymbols0210 nano-technologyVoronoi diagram3D grain sizeComputational Materials Science
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Space partitioning of exchange-correlation functionals with the projector augmented-wave method

2018

We implement a Becke fuzzy cells type space partitioning scheme for the purposes of exchange-correlation within the GPAW projector augmented-wave method based density functional theory code. Space partitioning is needed in the situation where one needs to treat different parts of a combined system with different exchange-correlation functionals. For example, bulk and surface regions of a system could be treated with functionals that are specifically designed to capture the distinct physics of those regions. Here, we use the space partitioning scheme to implement the quasi-nonuniform exchange-correlation scheme, which is a useful practical approach for calculating metallic alloys on the gene…

Surface (mathematics)Correctnessprojector augmented wave methodFOS: Physical sciencesGeneral Physics and Astronomy010402 general chemistry01 natural sciencesFuzzy logiclaw.inventionSet (abstract data type)alloyslaw0103 physical sciencesmetalliseoksetPhysical and Theoretical ChemistrySpace partitioningta116density functional theoryPhysicsCondensed Matter - Materials Scienceta114010304 chemical physicsgeneralized gradient approximationsPartitions (building)tiheysfunktionaaliteoriaMaterials Science (cond-mat.mtrl-sci)0104 chemical sciencesexchange correlation functionalsProjectorVoronoi diagramsDensity functional theoryProjector augmented wave methodDensity functional theoryapproksimointiAlgorithmThe Journal of Chemical Physics
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A Data-Driven Approach for Studying the Influence of Carbides on Work Hardening of Steel

2022

This study proposes a new approach to determine phenomenological or physical relations between microstructure features and the mechanical behavior of metals bridging advanced statistics and materials science in a study of the effect of hard precipitates on the hardening of metal alloys. Synthetic microstructures were created using multi-level Voronoi diagrams in order to control microstructure variability and then were used as samples for virtual tensile tests in a full-field crystal plasticity solver. A data-driven model based on Functional Principal Component Analysis (FPCA) was confronted with the classical Voce law for the description of uniaxial tensile curves of synthetic AISI 420 ste…

TechnologyMicroscopyQC120-168.85FPCATQH201-278.5stress–strain diagramlinear mixed-effects modelEngineering (General). Civil engineering (General)TK1-9971Descriptive and experimental mechanicsVoronoi diagramssynthetic microstructure; stress–strain diagram; FPCA; Voronoi diagrams; Voce law; linear mixed-effects modelGeneral Materials ScienceElectrical engineering. Electronics. Nuclear engineeringTA1-2040Voronoi diagramsynthetic microstructureVoce law
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