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Philosophical Magazine B Volume 75, 1997 - Issue 4
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Original Articles

The laguerre model for grain growth in three dimensions

Xinjian Xue Department of Mathematics, Ecole Polytechnique Fédérale de Lausanne, CH-1015, Lausanne, Switzerland
,
Franco Righetti Department of Mathematics, Ecole Polytechnique Fédérale de Lausanne, CH-1015, Lausanne, Switzerland
,
Hubert Telley Department of Mathematics, Ecole Polytechnique Fédérale de Lausanne, CH-1015, Lausanne, Switzerland
,
Thomas M. Liebling Department of Mathematics, Ecole Polytechnique Fédérale de Lausanne, CH-1015, Lausanne, Switzerland
&
Alain Mocellin École des Mines de Nancy, F-54042, Nancy, France
Pages 567-585 | Received 04 Sep 1996, Accepted 05 Oct 1996, Published online: 20 Aug 2006

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A. Spettl, T. Brereton, Q. Duan, T. Werz, C. E. Krill$suffix/text()$suffix/text(), D. P. Kroese & V. Schmidt. (2016) Fitting Laguerre tessellation approximations to tomographic image data. Philosophical Magazine 96:2, pages 166-189.
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André Liebscher. (2015) Laguerre approximation of random foams. Philosophical Magazine 95:25, pages 2777-2792.
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Andreas Alpers, Andreas Brieden, Peter Gritzmann, Allan Lyckegaard & Henning Friis Poulsen. (2015) Generalized balanced power diagrams for 3D representations of polycrystals. Philosophical Magazine 95:9, pages 1016-1028.
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Alberto Leonardi, Paolo Scardi & Matteo Leoni. (2012) Realistic nano-polycrystalline microstructures: beyond the classical Voronoi tessellation. Philosophical Magazine 92:8, pages 986-1005.
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J.-A. Ferrez & Th.M. Lieblin3g. (2002) Dynamic triangulations for efficient detection of collisions between spheres with applications in granular media simulations. Philosophical Magazine B 82:8, pages 905-929.
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Articles from other publishers (24)

A. Liebscher & C. Redenbach. (2022) Elastic properties of Laguerre approximations of random foams. International Journal of Solids and Structures 252, pages 111722.
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Dascha Dobrovolskij & Katja Schladitz. (2022) Simulation of Ultrasonic Backscattering in Polycrystalline Microstructures. Acoustics 4:1, pages 139-167.
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Pedro Gómez-Gálvez, Samira Anbari, Luis M. Escudero & Javier Buceta. (2021) Mechanics and self-organization in tissue development. Seminars in Cell & Developmental Biology 120, pages 147-159.
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Zbyněk Pawlas, Iva Karafiátová & Luděk Heller. (2020) Random tessellations marked with crystallographic orientations. Spatial Statistics 39, pages 100469.
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M. Marvi-Mashhadi, C.S. Lopes & J. LLorca. (2018) Effect of anisotropy on the mechanical properties of polyurethane foams: An experimental and numerical study. Mechanics of Materials 124, pages 143-154.
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M. Marvi-Mashhadi, C. S. Lopes & J. LLorca. (2018) Surrogate models of the influence of the microstructure on the mechanical properties of closed- and open-cell foams. Journal of Materials Science 53:18, pages 12937-12948.
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M. Marvi-Mashhadi, C.S. Lopes & J. LLorca. (2018) Modelling of the mechanical behavior of polyurethane foams by means of micromechanical characterization and computational homogenization. International Journal of Solids and Structures 146, pages 154-166.
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Javier Segurado, Ricardo A. Lebensohn & Javier LLorca. 2018. Advances in Crystals and Elastic Metamaterials, Part 1. Advances in Crystals and Elastic Metamaterials, Part 1 1 114 .
A Spettl, R Wimmer, T Werz, M Heinze, S Odenbach, C E KrillIIIIII & V Schmidt. (2015) Stochastic 3D modeling of Ostwald ripening at ultra-high volume fractions of the coarsening phase. Modelling and Simulation in Materials Science and Engineering 23:6, pages 065001.
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A. LIEBSCHER, D. JEULIN & C. LANTUÉJOUL. (2015) Stereological reconstruction of polycrystalline materials. Journal of Microscopy 258:3, pages 190-199.
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Aaron Spettl, Thomas Werz, Carl E. KrillIIIIII & Volker Schmidt. (2013) Parametric Representation of 3D Grain Ensembles in Polycrystalline Microstructures. Journal of Statistical Physics 154:4, pages 913-928.
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Alberto Leonardi, Matteo Leoni & Paolo Scardi. (2013) Atomistic modelling of polycrystalline microstructures: An evolutional approach to overcome topological restrictions. Computational Materials Science 67, pages 238-242.
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Lionel Pournin. (2011) Weakly Regular Subdivisions. Discrete & Computational Geometry 47:1, pages 106-116.
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M. Ferraro & L. Zaninetti. (2011) Statistics of cross sections of Voronoi tessellations. Physical Review E 84:4.
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Emanuel A. Lazar, Jeremy K. Mason, Robert D. MacPherson & David J. Srolovitz. (2011) A more accurate three-dimensional grain growth algorithm. Acta Materialia 59:17, pages 6837-6847.
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Jun Chen Li, Xu Dong Li & Jie Sheng. (2011) Multi-Parameter Design and Simulation of Composite Microstructure. Advanced Materials Research 314-316, pages 1306-1312.
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Allan Lyckegaard, Erik Mejdal Lauridsen, Wolfgang Ludwig, Richard Warren Fonda & Henning Friis Poulsen. (2011) On the Use of Laguerre Tessellations for Representations of 3D Grain Structures. Advanced Engineering Materials 13:3, pages 165-170.
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Claudia Redenbach. (2009) Microstructure models for cellular materials. Computational Materials Science 44:4, pages 1397-1407.
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L. Pournin & Th.M. Liebling. (2007) Constrained paths in the flip-graph of regular triangulations. Computational Geometry 37:2, pages 134-140.
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Eugene S. Machlin. 2007. An Introduction to Aspects of Thermodynamics and Kinetics Relevant to Materials Science. An Introduction to Aspects of Thermodynamics and Kinetics Relevant to Materials Science 289 318 .
Gernot Schaller & Michael Meyer-Hermann. (2004) Kinetic and dynamic Delaunay tetrahedralizations in three dimensions. Computer Physics Communications 162:1, pages 9-23.
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C.E. Krill III & L.-Q. Chen. (2002) Computer simulation of 3-D grain growth using a phase-field model. Acta Materialia 50:12, pages 3059-3075.
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Jean-Albert Ferrez, Thomas M. Liebling & Didier Müller. 2000. Statistical Physics and Spatial Statistics. Statistical Physics and Spatial Statistics 394 409 .
V. Parfait-Pignol, R. Delannay & A. Mocellin. 1999. Foams and Emulsions. Foams and Emulsions 547 562 .

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