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

References

• Abbruzzese , G. and Brozzo , P. , eds. 1992 . Grain Growth in Polycrystalline Materials , Zurich : Trans Tech Publications . Materials Science Forum 94–96
   Google Scholar
• Abbruzzese , G. , Heckelmann , I. and Lucke , K. 1992 . Acta metall. mater. , 40 : 519
   Google Scholar
• Anderson , M. P. , Grest , G. S. and Srolovitz , D. J. 1989 . Phil. Mag. B , 59 : 293
   Web of Science ®Google Scholar
• Aurenhammer , F. 1987 . SIAM J. Comput. , 16 : 78
   Web of Science ®Google Scholar
• Davis , C. 1959 . Scripta math. , 24 : 219
   Google Scholar
• Enomoto , Y. and Kato , R. 1990 . Acta metall. mater. , 38 : 765
   Google Scholar
• Flyvbjerg , H. 1993 . Phys. Rev. E , 47 : 4037
   Web of Science ®Google Scholar
• Fortes , M. A. 1994 . Acta metall. mater. , 42 : 1643
   Google Scholar
• Fradkov , V. E. 1988 . Phil. Mag. Lett. , 58 : 271
   Web of Science ®Google Scholar
• Fradkov , V. E. , Glicksman , M. E. , Palmer , M. and Rajan , K. 1994 . Acta metall. mater. , 42 : 2719
   Google Scholar
• Fradkov , V. E. , Magnasco , M. O. , Udler , D. and Weaire , D. 1993 . Phil. Mag. Lett. , 67 : 203
   Web of Science ®Google Scholar
• Fradkov , V. E. and Shvindlerman , L. S. 1985 . Scripta metall. , 19 : 1285
   Google Scholar
• Fradkov , V. E. and Udler , D. 1995 . Two Dimensional Normal Grain Growths: Topological Aspects , Troy, NY : Rensselaer Polytechnic Institute, Department of Materials Engineering . Technical Report
   Google Scholar
• Fuchizakj , K. , Kusaba , T. and Kawasaki , K. 1995 . Phil. Mag. B , 71 : 333
   Google Scholar
• Fullman , R. L. 1952 . Boundary Migration during Grain Growth, Metal Interfaces , 179 – 207 . Metals Park , Ohio : American Society for Metals .
   Google Scholar
• Glazier , J. A. , Anderson , M. P. and Grest , G. S. 1990 . Phil. Mag. B , 62 : 615
   Web of Science ®Google Scholar
• Hertle , T. and Aref , H. 1992 . J. Fluid Mech. , 241 : 233
   Web of Science ®Google Scholar
• Kawasaki , K. , Nagai , T. and Ohta , S. 1990 . Simulation and Theory of Evolving Microstructures , Edited by: Anderson , M. P. and Rollet , A. D. 65 Warrendale , PA : Minerals, Metals and Materials Society .
   Google Scholar
• Lawson , C. L. 1977 . Math. Software , 111 : 161
   Google Scholar
• Lecar , G. 1991 . J. Phys. A , 24 : 1307 2677 4655
   Google Scholar
• Lewis , F. T. 1928 . Anat. Rec. , 38 : 34
   Google Scholar
• Mullins , W. W. 1986 . J. appl. Phys. , 27 : 1341
   Google Scholar
• Mullins , W. W. and Vinals , J. 1989 . Acta metall. mater. , 37 : 991
   Google Scholar
• Nagai , T. , Kawasaki , K. and Nakamura , K. 1988 . J. phys. Soc. Japan , 57 : 2221
   Google Scholar
• Nagai , T. , Ohta , S. and Kawasaki , K. 1992 . Mater. Sci. Forum , 94–96 : 313
   Google Scholar
• Nakashima , K. , Nagai , T. and Kawasaki , K. 1989 . J. statist. Phys. , 57 : 759
   Web of Science ®Google Scholar
• Peshkin , M. A. , Strandburg , K. J. and Rivier , N. 1991 . Phys. Rev. Lett. , 67 : 1803
   PubMed Web of Science ®Google Scholar
• Righetti , F. 1992 . Ecole polytechnique federale-Lausanne 1016 These
   Google Scholar
• Rivier , N. 1993 . Disorder and Granular Media , Edited by: Bideau , D. and Hansen , A. 55 Amsterdam : Elsevier .
   Google Scholar
• Smith , C. S. 1952 . Metal Interfaces , 65 Metals Park , Ohio : American Society for Metals .
   Google Scholar
• Soares , A. , Ferro , A. C. and Fortes , M. A. 1985 . Scripta metall. , 19 : 1491
   Google Scholar
• Telley , H. 1989 . Ecole polytechnique federale-Lausanne 780 These, 1990, Static and Dynamic Weighted Delaunay Triangulations in the Euclidean Space and in the Flat Torus: Properties, Algorithms and Applications, Report UIUCDCS-R-907ndash;1662, University of Illinois, Urbana-Champaign, p. 11; 1992, Delaunay Triangulations in the Flat Torus, Technical Report RO922909, DMA, EPF, Lausanne
   Google Scholar
• Telley , H. , Liebling , TH. M. and Mocellin , A. 1996 . Phil. Mag. B , 73 : 409
   Web of Science ®Google Scholar
• Thorvaldsen , A. 1993 . Acta metall. mater. , 41 : 1347
   Google Scholar
• Udler , D. G. and Fradkov , V. E. 1987 . Phys. Metals Metallogr. , 64 : 6
   Google Scholar
• Von Neumann , J. 1952 . Metal Interfaces , 108 Metals Park , Ohio : American Society for Metals .
   Google Scholar
• Weaire , D. and Kermode , J. P. 1983 . Phil. Mag. B , 48 : 245 1984, Phil. Mag. B, 50, 379
   Web of Science ®Google Scholar
• Weaire , D. and Rivier , N. 1984 . Contemp. Phys. , 25 : 59
   Web of Science ®Google Scholar