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Philosophical Magazine B Volume 58, 1988 - Issue 6
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Original Articles

Distribution of cell volumes in a Voronoi partition

P. N. Andrade Departamento de Engenharia de Materiais, Instituto Superior Técnico, Av. Rovisco Pais, 1000, Lisboa, Portugal
&
M. A. Fortes Departamento de Engenharia de Materiais, Instituto Superior Técnico, Av. Rovisco Pais, 1000, Lisboa, Portugal
Pages 671-674 | Received 14 May 1988, Accepted 05 Jul 1988, Published online: 20 Aug 2006

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L. Oger, A. Gervois, J.P. Troadec & N. Rivier. (1996) Voronoi tessellation of packings of spheres: Topological correlation and statistics. Philosophical Magazine B 74:2, pages 177-197.
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Articles from other publishers (19)

M. Shepilov. (2023) Anomalous light scattering in nanostructured glasses formed by simultaneous nucleation and diffusion-limited growth of particles: Modelling. Journal of Non-Crystalline Solids 600, pages 121958.
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Supti Sadhukhan, Ankush Kumar, Giridhar U Kulkarni, Sujata Tarafdar & Tapati Dutta. (2019) A spring network simulation in three dimensions for designing optimal crack pattern template to fabricate transparent conducting electrodes. Bulletin of Materials Science 42:5.
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R. Mahjoub, K.J. Laws, J.P. Scicluna, J.E. Daniels & M. Ferry. (2015) A first principles molecular dynamics study of the relationship between atomic structure and elastic properties of Mg–Zn–Ca amorphous alloys. Computational Materials Science 96, pages 246-255.
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H.X. Zhu, P. Zhang, D. Balint, S.M. Thorpe, J.A. Elliott, A.H. Windle & J. Lin. (2014) The effects of regularity on the geometrical properties of Voronoi tessellations. Physica A: Statistical Mechanics and its Applications 406, pages 42-58.
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Emanuel A. Lazar, Jeremy K. Mason, Robert D. MacPherson & David J. Srolovitz. (2013) Statistical topology of three-dimensional Poisson-Voronoi cells and cell boundary networks. Physical Review E 88:6.
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. 2013. Stochastic Geometry and its Applications. Stochastic Geometry and its Applications 453 505 .
P. Zhang, M. Karimpour, D. Balint & J. Lin. (2012) Three-dimensional virtual grain structure generation with grain size control. Mechanics of Materials 55, pages 89-101.
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Somnath Ghosh. 2011. Micromechanical Analysis and Multi-Scale Modeling Using the Voronoi Cell Finite Element Method. Micromechanical Analysis and Multi-Scale Modeling Using the Voronoi Cell Finite Element Method 537 584 .
Nuno Reis, Alberto C. Ferro & José Carlos Pereira. (2006) Geometry and Topology of 3D Voronoi Partitions. Materials Science Forum 514-516, pages 1488-1492.
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V. Senthil Kumar & V. Kumaran. (2005) Voronoi cell volume distribution and configurational entropy of hard-spheres. The Journal of Chemical Physics 123:11.
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Eloi Pineda, Pere Bruna & Daniel Crespo. (2004) Cell size distribution in random tessellations of space. Physical Review E 70:6.
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Francis W. Starr, Srikanth Sastry, Jack F. Douglas & Sharon C. Glotzer. (2002) What Do We Learn from the Local Geometry of Glass-Forming Liquids?. Physical Review Letters 89:12.
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Haibo Yu, Guoquan Liu & Xiaoyan Song. (1998) On the relation between the number-weighted and volume-weighted grain volume distribution parameters. Metallurgical and Materials Transactions A 29:12, pages 3081-3086.
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Viggo Tarnow. (1997) Calculation of the dynamic air flow resistivity of fiber materials. The Journal of the Acoustical Society of America 102:3, pages 1680-1688.
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A. Thorvaldsen. (1997) The intercept method—1. Evaluation of grain shape. Acta Materialia 45:2, pages 587-594.
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Knut Marthinsen. (1996) Comparative analysis of the size distributions of linear, planar, and spatial Poisson Voronoi cells. Materials Characterization 36:2, pages 53-63.
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Susmit Kumar & Stewart K. Kurtz. (1995) Monte-Carlo study of angular and edge length distributions in a three-dimensional Poisson-Voronoi tesselation. Materials Characterization 34:1, pages 15-27.
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Susmit Kumar & Stewart K. Kurtz. (1994) A Monte Carlo study of size and angular properties of a three-dimensional Poisson-Delaunay cell. Journal of Statistical Physics 75:3-4, pages 735-748.
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Susmit Kumar, Stewart K. Kurtz, Jayanth R. Banavar & M. G. Sharma. (1992) Properties of a three-dimensional Poisson-Voronoi tesselation: A Monte Carlo study. Journal of Statistical Physics 67:3-4, pages 523-551.
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