메뉴 건너뛰기




Volumn 130, Issue 6, 2008, Pages 1047-1062

From symmetry breaking to poisson point process in 2D voronoi tessellations: The generic nature of hexagons

Author keywords

Desch law; Gaussian noise; Lewis law; Poisson point process; Random geometry; Symmetry breaking; Topological stability; Voronoi tessellation

Indexed keywords


EID: 39149138411     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10955-007-9475-x     Document Type: Article
Times cited : (27)

References (39)
  • 2
    • 84976826673 scopus 로고
    • Voronoi diagrams-a survey of a fundamental geometric data structure
    • Aurenhammer, F.: Voronoi diagrams-a survey of a fundamental geometric data structure. ACM Comput. Surv. 23, 345-405 (1991)
    • (1991) ACM Comput. Surv. , vol.23 , pp. 345-405
    • Aurenhammer, F.1
  • 4
    • 0030764730 scopus 로고    scopus 로고
    • Voronoi tessellation methods to delineate harvest units for spatial forest planning
    • 6
    • Barrett, T.M.: Voronoi tessellation methods to delineate harvest units for spatial forest planning. Can. J. For. Res. 27(6), 903-910 (1997)
    • (1997) Can. J. For. Res. , vol.27 , pp. 903-910
    • Barrett, T.M.1
  • 7
    • 0019563894 scopus 로고
    • Computing Dirichlet tessellations
    • Bowyer, A.: Computing Dirichlet tessellations. Comput. J. 24, 162-166 (1981)
    • (1981) Comput. J. , vol.24 , pp. 162-166
    • Bowyer, A.1
  • 8
    • 0042380129 scopus 로고    scopus 로고
    • Precise formulae for the distributions of the principal geometric characteristics of the typical cells of a two-dimensional Poisson Voronoi tessellation and a Poisson line process
    • Calka, P.: Precise formulae for the distributions of the principal geometric characteristics of the typical cells of a two-dimensional Poisson Voronoi tessellation and a Poisson line process. Adv. Appl. Probab. 35, 551-562 (2003)
    • (2003) Adv. Appl. Probab. , vol.35 , pp. 551-562
    • Calka, P.1
  • 9
    • 0002346911 scopus 로고
    • Random lattice field theory: General formulation
    • Christ, N.H., Friedberg, R., Lee, T.D.: Random lattice field theory: general formulation. Nucl. Phys. B 202, 89-125 (1982)
    • (1982) Nucl. Phys. B , vol.202 , pp. 89-125
    • Christ, N.H.1    Friedberg, R.2    Lee, T.D.3
  • 11
    • 0001533236 scopus 로고
    • The solidification of metals from the liquid state
    • Desch, C.H.: The solidification of metals from the liquid state. J. Inst. Metals 22, 241 (1919)
    • (1919) J. Inst. Metals , vol.22 , pp. 241
    • Desch, C.H.1
  • 12
    • 0001152124 scopus 로고    scopus 로고
    • Cell crystals: Kelvin's polyhedra in block copolymer melts
    • Dotera, T.: Cell crystals: Kelvin's polyhedra in block copolymer melts. Phys. Rev. Lett. 82, 105-108 (1999)
    • (1999) Phys. Rev. Lett. , vol.82 , pp. 105-108
    • Dotera, T.1
  • 13
    • 0002308984 scopus 로고
    • Random geometry and the statistics of two-dimensional cells
    • Drouffe, J.M., Itzykson, C.: Random geometry and the statistics of two-dimensional cells. Nucl. Phys. B 235, 45-53 (1984)
    • (1984) Nucl. Phys. B , vol.235 , pp. 45-53
    • Drouffe, J.M.1    Itzykson, C.2
  • 14
    • 0011036407 scopus 로고    scopus 로고
    • Cambridge University Press Cambridge
    • Finch, S.R.: Mathematical Constants. Cambridge University Press, Cambridge (2003)
    • (2003) Mathematical Constants
    • Finch, S.R.1
  • 15
    • 0016816308 scopus 로고
    • Volume occupation, environment and accessibility in proteins. the problem of the protein surface
    • Finney, J.L.: Volume occupation, environment and accessibility in proteins. The problem of the protein surface. J. Mol. Biol. 96, 721-732 (1975)
    • (1975) J. Mol. Biol. , vol.96 , pp. 721-732
    • Finney, J.L.1
  • 16
    • 33847690144 scopus 로고    scopus 로고
    • The rise of graphene
    • A.K. Geim K.S. Novoselov 2007 The rise of graphene Nat. Mater. 6 183 191 10.1038/nmat1849 Geim, A.K., Novoselov, K.S.: The rise of graphene. Nat. Mater. 6, 183-191 (2007). doi: 10.1038/nmat1849
    • (2007) Nat. Mater. , vol.6 , pp. 183-191
    • Geim, A.K.1    Novoselov, K.S.2
  • 17
    • 0001136015 scopus 로고    scopus 로고
    • Voronoi cell: New method for allocation of space among atoms: Elimination of avoidable errors in calculation of atomic volume and density
    • Goede, A., Preissner, R., Frömmel, C.: Voronoi cell: new method for allocation of space among atoms: elimination of avoidable errors in calculation of atomic volume and density. J. Comput. Chem. 18, 1113-1118 (1997)
    • (1997) J. Comput. Chem. , vol.18 , pp. 1113-1118
    • Goede, A.1    Preissner, R.2    Frömmel, C.3
  • 18
    • 33846348388 scopus 로고    scopus 로고
    • Automated Thiessen polygon generation
    • D. Han M. Bray 2006 Automated Thiessen polygon generation Water Resour. Res. 42 W11502 10.1029/2005WR004365 Han, D., Bray, M.: Automated Thiessen polygon generation. Water Resour. Res. 42, W11502 (2006). doi: 10.1029/2005WR004365
    • (2006) Water Resour. Res. , vol.42 , pp. 11502
    • Han, D.1    Bray, M.2
  • 19
    • 26244446903 scopus 로고    scopus 로고
    • Asymptotic statistics of the n-sided planar Poisson-Voronoi cell, I: Exact results
    • Hilhorst, H.J.: Asymptotic statistics of the n-sided planar Poisson-Voronoi cell, I: exact results. J. Stat. Mech. P09005 (2005). doi: 10.1088/1742-5468/2005/09/P09005
    • (2005) J. Stat. Mech. P09005
    • Hilhorst, H.J.1
  • 20
    • 33744773830 scopus 로고    scopus 로고
    • Planar Voronoi cells: The violation of Aboav's law explained
    • H.J. Hilhorst 2006 Planar Voronoi cells: the violation of Aboav's law explained J. Phys. A: Math. Gen. 39 7227 7243 10.1088/0305-4470/39/23/004 Hilhorst, H.J.: Planar Voronoi cells: the violation of Aboav's law explained. J. Phys. A: Math. Gen. 39, 7227-7243 (2006). doi: 10.1088/0305-4470/39/23/004
    • (2006) J. Phys. A: Math. Gen. , vol.39 , pp. 7227-7243
    • Hilhorst, H.J.1
  • 21
    • 84945017550 scopus 로고
    • Monte Carlo estimates of the distributions of the random polygons of the Voronoi tessellation with respect to a Poisson process
    • Hinde, A.L., Miles, R.E.: Monte Carlo estimates of the distributions of the random polygons of the Voronoi tessellation with respect to a Poisson process. J. Stat. Comput. Simul. 10, 205-223 (1980)
    • (1980) J. Stat. Comput. Simul. , vol.10 , pp. 205-223
    • Hinde, A.L.1    Miles, R.E.2
  • 22
    • 21744433724 scopus 로고    scopus 로고
    • Particles, space and time
    • Icke, V.: Particles, space and time. Astrophys. Space Sci. 244, 293-312 (1996)
    • (1996) Astrophys. Space Sci. , vol.244 , pp. 293-312
    • Icke, V.1
  • 23
    • 34249840947 scopus 로고
    • Properties of a three-dimensional Poisson-Voronoi tessellation: A Monte Carlo study
    • Kumar, S., Kurtz, S.K., Banavar, J.R., Sharma, M.G.: Properties of a three-dimensional Poisson-Voronoi tessellation: a Monte Carlo study. J. Stat. Phys. 67, 523-551 (1992)
    • (1992) J. Stat. Phys. , vol.67 , pp. 523-551
    • Kumar, S.1    Kurtz, S.K.2    Banavar, J.R.3    Sharma, M.G.4
  • 24
    • 84944482551 scopus 로고
    • The correlation between cell division and the shapes and sizes of prismatic cells in the epidermis of Cucumis
    • Lewis, F.T.: The correlation between cell division and the shapes and sizes of prismatic cells in the epidermis of Cucumis. Anat. Rec. 38, 341-376 (1928)
    • (1928) Anat. Rec. , vol.38 , pp. 341-376
    • Lewis, F.T.1
  • 25
    • 34548648594 scopus 로고    scopus 로고
    • Does the Danube exist? Versions of reality given by various regional climate models and climatological data sets
    • V. Lucarini E. Danihlik I. Kriegerova A. Speranza 2007 Does the Danube exist? Versions of reality given by various regional climate models and climatological data sets J. Geophys. Res. 112 D13103 10.1029/2006JD008360 Lucarini, V., Danihlik, E., Kriegerova, I., Speranza, A.: Does the Danube exist? Versions of reality given by various regional climate models and climatological data sets. J. Geophys. Res. 112, D13103 (2007). doi: 10.1029/2006JD008360
    • (2007) J. Geophys. Res. , vol.112 , pp. 13103
    • Lucarini, V.1    Danihlik, E.2    Kriegerova, I.3    Speranza, A.4
  • 26
    • 0003746585 scopus 로고
    • Interface area, edge length, and number of vertices in crystal aggregates with random nucleation: Phillips research reports
    • Meijering, J.L.: Interface area, edge length, and number of vertices in crystal aggregates with random nucleation: Phillips research reports. Philips Res. Rep. 8, 270-290 (1953)
    • (1953) Philips Res. Rep. , vol.8 , pp. 270-290
    • Meijering, J.L.1
  • 28
    • 33344469554 scopus 로고    scopus 로고
    • Hexagonal convection patterns in atomistically simulated fluids
    • Rapaport, D.C.: Hexagonal convection patterns in atomistically simulated fluids. Phys. Rev. E 73, 025301 (2006)
    • (2006) Phys. Rev. e , vol.73 , pp. 025301
    • Rapaport, D.C.1
  • 29
    • 34547555060 scopus 로고    scopus 로고
    • Voronoi neighbor statistics of hard-disks and hard-spheres
    • Senthil Kumar, V., Kumaran, V.: Voronoi neighbor statistics of hard-disks and hard-spheres. J. Chem. Phys. 123, 074502 (2005)
    • (2005) J. Chem. Phys. , vol.123 , pp. 074502
    • Senthil Kumar, V.1    Kumaran, V.2
  • 30
    • 39149089091 scopus 로고    scopus 로고
    • Analytical investigation of intersection-based range-free localization information gain
    • Sortais, M., Hermann, S., Wolisz, A.: Analytical investigation of intersection-based range-free localization information gain. In: Proc. of European Wireless (2007)
    • (2007) Proc. of European Wireless
    • Sortais, M.1    Hermann, S.2    Wolisz, A.3
  • 31
    • 48749144760 scopus 로고
    • A new algorithm for three-dimensional Voronoi tessellation
    • Tanemura, M., Ogawa, T., Ogita, N.: A new algorithm for three-dimensional Voronoi tessellation. J. Comput. Phys. 51, 191-207 (1983)
    • (1983) J. Comput. Phys. , vol.51 , pp. 191-207
    • Tanemura, M.1    Ogawa, T.2    Ogita, N.3
  • 32
    • 33747617010 scopus 로고    scopus 로고
    • Statistical distributions of Poisson-Voronoi cells in two and three dimensions
    • Tanemura, M.: Statistical distributions of Poisson-Voronoi cells in two and three dimensions. Forma 18, 221-247 (2003)
    • (2003) Forma , vol.18 , pp. 221-247
    • Tanemura, M.1
  • 34
    • 20144378087 scopus 로고    scopus 로고
    • Geophysical parameterization and parameter structure identification using natural neighbors in groundwater inverse problems
    • Tsai, F.T.-C., Sun, N.-Z., Yeh, W.W.-G.: Geophysical parameterization and parameter structure identification using natural neighbors in groundwater inverse problems. J. Hydrol. 308, 269-283 (2004)
    • (2004) J. Hydrol. , vol.308 , pp. 269-283
    • Tsai, F.T.-C.1    Sun, N.-Z.2    Yeh, W.W.-G.3
  • 35
    • 0000734331 scopus 로고
    • Nouvelles applications des paramètres continus à la théorie des formes quadratiques. Premier mémoire: Sur quelques propriétées des formes quadritiques positives parfaites
    • Voronoi, G.: Nouvelles applications des paramètres continus à la théorie des formes quadratiques. Premier mémoire: sur quelques propriétées des formes quadritiques positives parfaites. J. Reine Angew. Math. 133, 97-178 (1907)
    • (1907) J. Reine Angew. Math. , vol.133 , pp. 97-178
    • Voronoi, G.1
  • 36
    • 84927514013 scopus 로고
    • Nouvelles applications des parametres continus a la theorie des formse quadratiques. Duesieme memoire: Recherches sur les paralleloderes primitifs
    • Voronoi, G.: Nouvelles applications des parametres continus a la theorie des formse quadratiques. Duesieme memoire: recherches sur les paralleloderes primitifs. J. Reine Angew. Math. 134, 198-287 (1908)
    • (1908) J. Reine Angew. Math. , vol.134 , pp. 198-287
    • Voronoi, G.1
  • 37
    • 0019563697 scopus 로고
    • Computing the n-dimensional tessellation with application to Voronoi polytopes
    • Watson, D.F.: Computing the n-dimensional tessellation with application to Voronoi polytopes. Comput. J. 24, 167-172 (1981)
    • (1981) Comput. J. , vol.24 , pp. 167-172
    • Watson, D.F.1
  • 38
    • 0022721050 scopus 로고
    • On the distribution of cell areas in a Voronoi network
    • Weaire, D., Kermode, J.P., Wejchert, J.: On the distribution of cell areas in a Voronoi network. Philos. Mag. B 53, L101-L105 (1986)
    • (1986) Philos. Mag. B , vol.53
    • Weaire, D.1    Kermode, J.P.2    Wejchert, J.3
  • 39
    • 0035782834 scopus 로고    scopus 로고
    • The geometrical properties of irregular two-dimensional Voronoi tessellations
    • Zhu, H.X., Thorpe, S.M., Windle, A.H.: The geometrical properties of irregular two-dimensional Voronoi tessellations. Philos. Mag. A 81, 2765-2783 (2001)
    • (2001) Philos. Mag. A , vol.81 , pp. 2765-2783
    • Zhu, H.X.1    Thorpe, S.M.2    Windle, A.H.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.