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Philosophical Magazine B Volume 73, 1996 - Issue 3
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Original Articles

The Laguerre model of grain growth in two dimensions I. Cellular structures viewed as dynamical Laguerre tessellations

Hubert Telley Departement de mathematiques, Ecole polytechnique federale, CH-1015, Lausanne, Switzerland
,
Thomas M. Liebling Departement de mathematiques, Ecole polytechnique federale, CH-1015, Lausanne, Switzerland
&
Alain Mocellin Ecole des mines, Parc de Saurupt, F-54000, Nancy, France
Pages 395-408 | Received 30 Nov 1994, Accepted 14 Jul 1995, Published online: 27 Sep 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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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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N. Vandewalle, B. Delisse, M. Ausloos & R. Cloots. (1998) Foam-like evolution in polycrystalline systems following successive ‘melt and growth’ cycles. Philosophical Magazine B 78:4, pages 397-408.
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Xinjian Xue, Franco Righetti, Hubert Telley, ThomasM. Liebling & Alain Mocellin. (1997) The laguerre model for grain growth in three dimensions. Philosophical Magazine B 75:4, pages 567-585.
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Hubert Telley, Thomasm. Libeling & Alain Mocellin. (1996) The Laguerre model of grain growth in two dimensions II. Examples of coarsening simulations. Philosophical Magazine B 73:3, pages 409-427.
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Y. Schneider, U. Weber, W. Wasserbäch, R. Zielke, S. Schmauder & W. Tillmann. (2020) A numerical method for the generation of hierarchical Poisson Voronoi microstructures applied in micromechanical finite element simulations—part I: method. Computational Mechanics 66:3, pages 651-667.
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Pedro M.C. Carneiro, Pedro V. Gamboa, Carmen Baudín & Abílio P. Silva. (2020) Modelling of elastic modulus of a biphasic ceramic microstructure using 3D representative volume elements. Journal of the European Ceramic Society 40:3, pages 901-910.
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Supanut Chaidee & Kokichi Sugihara. (2019) Laguerre Voronoi Diagram as a Model for Generating the Tessellation Patterns on the Sphere. Graphs and Combinatorics 36:2, pages 371-385.
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Grzegorz Grabowski. (2019) Modelling of thermal expansion of single- and two-phase ceramic polycrystals utilising synthetic 3D microstructures. Computational Materials Science 156, pages 7-16.
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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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Dandan Chen, Kenneth W. Desmond & Eric R. Weeks. (2015) Experimental observation of local rearrangements in dense quasi-two-dimensional emulsion flow. Physical Review E 91:6.
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N. Vajragupta, P. Wechsuwanmanee, J. Lian, M. Sharaf, S. Münstermann, A. Ma, A. Hartmaier & W. Bleck. (2014) The modeling scheme to evaluate the influence of microstructure features on microcrack formation of DP-steel: The artificial microstructure model and its application to predict the strain hardening behavior. Computational Materials Science 94, pages 198-213.
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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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X. Guo, K. Chang, L.Q. Chen & M. Zhou. (2012) Determination of fracture toughness of AZ31 Mg alloy using the cohesive finite element method. Engineering Fracture Mechanics 96, pages 401-415.
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Dandan Chen, Kenneth W. Desmond & Eric R. Weeks. (2012) Topological rearrangements and stress fluctuations in quasi-two-dimensional hopper flow of emulsions. Soft Matter 8:40, pages 10486.
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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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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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I. Kadashevich & D. Stoyan. (2010) Simulation of brittle fracture of autoclaved aerated concrete. Computers & concrete 7:1, pages 39-51.
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Alexey V. Anikeenko, Marina L. Gavrilova & Nikolai N. Medvedev. 2009. Generalized Voronoi Diagram: A Geometry-Based Approach to Computational Intelligence. Generalized Voronoi Diagram: A Geometry-Based Approach to Computational Intelligence 13 45 .
I. Kadashevich & D. Stoyan. (2008) A beam-network model for autoclaved aerated concrete and its use for the investigation of relationships between Young’s modulus and microstructure. Computational Materials Science 43:2, pages 293-300.
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Chao Wang, Guoquan Liu, Guangfu Wang & Wenbin Xue. (2007) On the quasi-stationary grain size distribution from two Gamma size distributions in three-dimensional grain growth. Materials Letters 61:21, pages 4262-4266.
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Yoshihiro Suwa, Yoshiyuki Saito & Hidehiro Onodera. (2007) Three-dimensional phase field simulation of the effect of anisotropy in grain-boundary mobility on growth kinetics and morphology of grain structure. Computational Materials Science 40:1, pages 40-50.
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Luc Oger, Irene Ippolito & Ana M. Vidales. (2007) How disorder can diminish avalanche risks: effect of size distribution. Granular Matter 9:3-4.
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Yoshihiro SuwaYoshiyuki Saito & Hidehiro Onodera. (2007) Computer Simulation of Grain Growth in Three Dimensions by the Phase Field Model with Anisotropic Grain-Boundary Mobilities. Materials Science Forum 539-543, pages 2437-2442.
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N. N. Medvedev, V. P. Voloshin, V. A. Luchnikov & M. L. Gavrilova. (2006) An algorithm for three-dimensional Voronoi S-network. Journal of Computational Chemistry 27:14, pages 1676-1692.
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Ondrej Gedeon & Marek Liška. (2005) Partial volumes and volume fluctuations in potassium-silicate glass: Molecular dynamic simulations. Journal of Non-Crystalline Solids 351:19-20, pages 1682-1687.
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Marina G. Alinchenko, Alexey V. Anikeenko, Nikolai N. Medvedev, Vladimir P. Voloshin, Mihaly Mezei & Pál Jedlovszky. (2004) Morphology of Voids in Molecular Systems. A Voronoi−Delaunay Analysis of a Simulated DMPC Membrane. The Journal of Physical Chemistry B 108:49, pages 19056-19067.
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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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A. Gervois, L. Oger, P. Richard & J. P. Troadec. 2002. Computational Science — ICCS 2002. Computational Science — ICCS 2002 95 104 .
P S Grassia, J J Cilliers & S J Neethling. (2001) The foam geometry "paradox". Canadian Journal of Physics 79:10, pages 1265-1281.
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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 .
Nicolas Rivier. 1999. Foams and Emulsions. Foams and Emulsions 105 126 .
V. Parfait-Pignol, R. Delannay & A. Mocellin. 1999. Foams and Emulsions. Foams and Emulsions 547 562 .

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