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Volumn 1, Issue 1, 2009, Pages 21-54

Symmetry-break in Voronoi tessellations

Author keywords

Anomalous scaling; Body centred cubic; Cubic crystals; Desch law; Face centred cubic; Fluctuations; Gaussian noise; Isoperimetric quotient; Kelvin's conjecture; Kendall's conjecture; Kepler's conjecture; Lewis law; Numerical simulations; Poisson point process; Random geometry; Simple cubic; Symmetry break; Topological stability; Voronoi tessellation

Indexed keywords


EID: 84860382523     PISSN: None     EISSN: 20738994     Source Type: Journal    
DOI: 10.3390/sym1010021     Document Type: Review
Times cited : (19)

References (67)
  • 1
    • 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. 1907, 133, 97-178.
    • (1907) J. Reine Angew. Math. , vol.133 , pp. 97-178
    • Voronoi, G.1
  • 2
    • 84927514013 scopus 로고
    • Nouvelles Applications des Parametres Continus a la Theorie des Formes Quadratiques. Duesieme Memoire: Recherches sur les Paralleloderes Primitifs
    • Voronoi, G. Nouvelles Applications des Parametres Continus a la Theorie des Formes Quadratiques. Duesieme Memoire: Recherches sur les Paralleloderes Primitifs. J. Reine Angew. Math. 1908, 134, 198-287.
    • (1908) J. Reine Angew. Math. , vol.134 , pp. 198-287
    • Voronoi, G.1
  • 3
    • 0034266827 scopus 로고    scopus 로고
    • Poisson-Voronoi tessellations in three-dimensional hyperbolic spaces
    • Isokawa, Y. Poisson-Voronoi tessellations in three-dimensional hyperbolic spaces. Adv. Appl. Probl. 2000, 32, 648-662.
    • (2000) Adv. Appl. Probl. , vol.32 , pp. 648-662
    • Isokawa, Y.1
  • 5
    • 39149089091 scopus 로고    scopus 로고
    • Analytical Investigation of Intersection-Based Range-Free Localization Information Gain
    • Paris, France, April
    • Sortais, M.; Hermann, S.; Wolisz, A. Analytical Investigation of Intersection-Based Range-Free Localization Information Gain. In Proceedings of European Wireless 2007, Paris, France, April 2007.
    • (2007) Proceedings of European Wireless 2007
    • Sortais, M.1    Hermann, S.2    Wolisz, A.3
  • 6
    • 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. 1975, 96, 721-732.
    • (1975) J. Mol. Biol. , vol.96 , pp. 721-732
    • Finney, J.L.1
  • 7
    • 21744433724 scopus 로고    scopus 로고
    • Particles, space and time
    • Icke, V. Particles, space and time. Astrophys. Space Sci. 1996, 244, 293-312.
    • (1996) Astrophys. Space Sci. , vol.244 , pp. 293-312
    • Icke, V.1
  • 8
    • 0030764730 scopus 로고    scopus 로고
    • Voronoi tessellation methods to delineate harvest units for spatial forest planning
    • Barrett, T. M. Voronoi tessellation methods to delineate harvest units for spatial forest planning. Can. J. For. Res. 1997, 27, 903-910.
    • (1997) Can. J. For. Res. , vol.27 , pp. 903-910
    • Barrett, T.M.1
  • 9
    • 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. Comp. Chem. 1997, 18, 1113-1118.
    • (1997) J. Comp. Chem. , vol.18 , pp. 1113-1118
    • Goede, A.1    Preissner, R.2    Frömmel, C.3
  • 10
    • 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. Phil. Mag. B 1986, 53, L101-L105.
    • (1986) Phil. Mag. B , vol.53
    • Weaire, D.1    Kermode, J.P.2    Wejchert, J.3
  • 11
    • 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. 1999, 82, 105-108.
    • (1999) Phys. Rev. Lett. , vol.82 , pp. 105-108
    • Dotera, T.1
  • 13
    • 1542634760 scopus 로고    scopus 로고
    • Unit cells for micromechanical analyses of particle-reinforced composites
    • Li, S.; Wongsto, A. Unit cells for micromechanical analyses of particle-reinforced composites. Mechanics of Materials 2004, 36, 543-572.
    • (2004) Mechanics of Materials , vol.36 , pp. 543-572
    • Li, S.1    Wongsto, A.2
  • 14
    • 0034287449 scopus 로고    scopus 로고
    • Voronoi tessellation reveals the condensed matter character of folded proteins
    • Soyer, A.; Chomilier, J.; Mornon, J.P.; Jullien, R.; Sadoc, J.F. Voronoi tessellation reveals the condensed matter character of folded proteins. Phys. Rev. Lett. 2000, 85, 3532-3535.
    • (2000) Phys. Rev. Lett. , vol.85 , pp. 3532-3535
    • Soyer, A.1    Chomilier, J.2    Mornon, J.P.3    Jullien, R.4    Sadoc, J.F.5
  • 17
    • 0011637183 scopus 로고
    • Statistics of Voronoi polyhedra in a model silicon glass
    • Tsumuraya, K.; Ishibashi, K.; Kusunoki, K. Statistics of Voronoi polyhedra in a model silicon glass. Phys. Rev. B 1993, 47, 8552.
    • (1993) Phys. Rev. B , vol.47 , pp. 8552
    • Tsumuraya, K.1    Ishibashi, K.2    Kusunoki, K.3
  • 18
    • 28844438403 scopus 로고    scopus 로고
    • Structure analysis methods for crystalline solids and supercooled liquids
    • 051202
    • Yu, D.-Q.; Chen, M.; Han, X.-J. Structure analysis methods for crystalline solids and supercooled liquids. Phys. Rev. E 2005, 72, 051202.
    • (2005) Phys. Rev. E , vol.72
    • Yu, D.-Q.1    Chen, M.2    Han, X.-J.3
  • 19
    • 34547353567 scopus 로고    scopus 로고
    • Statistical mechanics of the glass transition as revealed by a Voronoi tessellation
    • Hentschel, H. G. E.; Ilyin, V.; Makedonska, N.; Procaccia, I.; Schupper N. Statistical mechanics of the glass transition as revealed by a Voronoi tessellation. Phys. Rev. E 2007, 75, 50404(R).
    • (2007) Phys. Rev. E , vol.75
    • Hentschel, H.G.E.1    Ilyin, V.2    Makedonska, N.3    Procaccia, I.4    Schupper, N.5
  • 21
    • 0039037271 scopus 로고
    • Pseudospherical integration scheme for electronic-structure calculations
    • Averill, F. W.; Painter, G. S. Pseudospherical integration scheme for electronic-structure calculations. Phys. Rev. B 1989, 39, 8115.
    • (1989) Phys. Rev. B , vol.39 , pp. 8115
    • Averill, F.W.1    Painter, G.S.2
  • 22
    • 0007037036 scopus 로고    scopus 로고
    • Consistent methodology for calculating surface and interface energies
    • Rapcewicz, K.; Chen, B.; Yakobson, B.; Bernholc, J.; Consistent methodology for calculating surface and interface energies. Phys. Rev. B 1998, 57, 007281.
    • (1998) Phys. Rev. B , vol.57 , pp. 007281
    • Rapcewicz, K.1    Chen, B.2    Yakobson, B.3    Bernholc, J.4
  • 23
    • 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 2006, 73, 025301.
    • (2006) Phys. Rev. E , vol.73 , pp. 025301
    • Rapaport, D.C.1
  • 24
    • 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 (2004). Geophysical parameterization and parameter structure identification using natural neighbors in groundwater inverse problems, J. Hydrology 308, 269-283.
    • (2004) J. Hydrology , vol.308 , pp. 269-283
    • Tsai, F.-C.1    Sun, N.-Z.2    Yeh, W.W.-G.3
  • 25
    • 34548648594 scopus 로고    scopus 로고
    • Does the Danube exist? Versions of reality given by various regional climate models and climatological data sets
    • doi: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. 2007, 112, D13103, doi:10.1029/2006JD008360.
    • (2007) J. Geophys. Res. , vol.112
    • Lucarini, V.1    Danihlik, E.2    Kriegerova, I.3    Speranza, A.4
  • 26
    • 46449135358 scopus 로고    scopus 로고
    • Hydrological Cycle in the Danube basin in present-day and XXII century simulations by IPCCAR4 global climate models
    • doi:10.1029/2007JD009167
    • Lucarini, V.; Danihlik, R.; Kriegerova, I.; Speranza, A. Hydrological Cycle in the Danube basin in present-day and XXII century simulations by IPCCAR4 global climate models. J. Geophys. Res. 2008, 113, D09107, doi:10.1029/2007JD009167.
    • (2008) J. Geophys. Res. , vol.113
    • Lucarini, V.1    Danihlik, R.2    Kriegerova, I.3    Speranza, A.4
  • 27
    • 0000148490 scopus 로고
    • Climatological Data for July, 1911: District No. 10, Great Basin
    • Thiessen, A. H.; Alter, J. C. Climatological Data for July, 1911: District No. 10, Great Basin. Monthly Weather Review 1911, 1082-1089.
    • (1911) Monthly Weather Review , pp. 1082-1089
    • Thiessen, A.H.1    Alter, J.C.2
  • 28
    • 0019563894 scopus 로고
    • Computing Dirichlet tessellations
    • Bowyer, A. Computing Dirichlet tessellations. Computer J. 1981, 24, 162-166.
    • (1981) Computer J , vol.24 , pp. 162-166
    • Bowyer, A.1
  • 29
    • 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, Computer J. 1981, 24, 167-172.
    • (1981) Computer J , vol.24 , pp. 167-172
    • Watson, D.F.1
  • 30
    • 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. Compu. Phys. 1983, 51, 191-207.
    • (1983) J. Compu. Phys. , vol.51 , pp. 191-207
    • Tanemura, M.1    Ogawa, T.2    Ogita, N.3
  • 31
    • 0030381077 scopus 로고    scopus 로고
    • The Quickhull Algorithm for Convex Hulls
    • Barber, C. B.; Dobkin, D. P.; Huhdanpaa, H.T. The Quickhull Algorithm for Convex Hulls. ACM TOMS 1996, 22, 469-483.
    • (1996) ACM TOMS , vol.22 , pp. 469-483
    • Barber, C.B.1    Dobkin, D.P.2    Huhdanpaa, H.T.3
  • 32
    • 33846348388 scopus 로고    scopus 로고
    • Automated Thiessen polygon generation
    • doi:10.1029/2005WR004365
    • Han, D.; Bray, M. Automated Thiessen polygon generation. Water Resour. Res. 2006, 42, W11502, doi:10.1029/2005WR004365.
    • (2006) Water Resour. Res. , vol.42
    • Han, D.1    Bray, M.2
  • 33
    • 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. 1953, 8, 270-290.
    • (1953) Philips Res. Rep. , vol.8 , pp. 270-290
    • Meijering, J.L.1
  • 34
    • 0002346911 scopus 로고
    • Random lattice field theory: General formulation
    • Christ, N. H.; Friedberg, R.; Lee, T. D. Random lattice field theory: General formulation. Nuclear Physics B 1982, 202, 89-125.
    • (1982) Nuclear Physics B , vol.202 , pp. 89-125
    • Christ, N.H.1    Friedberg, R.2    Lee, T.D.3
  • 35
    • 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 1984, 235, 45-53.
    • (1984) Nucl. Phys. B , vol.235 , pp. 45-53
    • Drouffe, J.M.1    Itzykson, C.2
  • 36
    • 0041059889 scopus 로고
    • A synopsis of Poisson Flats In Euclidean Spaces
    • Harding, E. F.; Kendall, D. G., Eds.; Wiley: London, UK
    • Miles, R. E. A synopsis of Poisson Flats In Euclidean Spaces. In Stochastic Geometry, Harding, E. F.; Kendall, D. G., Eds.; Wiley: London, UK, 1974; pp. 202-227.
    • (1974) Stochastic Geometry , pp. 202-227
    • Miles, R.E.1
  • 37
    • 0001831684 scopus 로고
    • Random tessellations in Rd
    • Møller, J. Random tessellations in Rd. Adv. Appl. Prob. 1989, 21, 37-73.
    • (1989) Adv. Appl. Prob. , vol.21 , pp. 37-73
    • Møller, J.1
  • 38
    • 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. 2003, 35, 551-562.
    • (2003) Adv. Appl. Probab. , vol.35 , pp. 551-562
    • Calka, P.1
  • 39
    • 33744773830 scopus 로고    scopus 로고
    • Planar Voronoi cells: the violation of Aboav's law explained
    • doi: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. 2006, 39, 7227-7243 doi:10.1088/0305-4470/39/23/004.
    • (2006) J. Phys. A: Math. Gen. , vol.39 , pp. 7227-7243
    • Hilhorst, H.J.1
  • 40
    • 84860371423 scopus 로고    scopus 로고
    • unpublished. Addendum to Finch S. R., Mathematical Constants. Cambridge University Press: Cambridge, UK
    • Finch, S. R., unpublished. Available on http://algo.inria.fr/csolve/vi.pdf. Addendum to Finch S. R., Mathematical Constants. Cambridge University Press: Cambridge, UK, 2005.
    • (2005)
    • Finch, S.R.1
  • 41
    • 35848971039 scopus 로고    scopus 로고
    • Proof of David Kendall's conjecture concerning the shape of large random polygons
    • Kovalenko, I. N. Proof of David Kendall's conjecture concerning the shape of large random polygons. Cybernetics and Systems Analysis 1997, 33, 461-467.
    • (1997) Cybernetics and Systems Analysis , vol.33 , pp. 461-467
    • Kovalenko, I.N.1
  • 42
    • 37349067188 scopus 로고    scopus 로고
    • Typical cells in Poisson hyperplane tessellations
    • Hug, D.; Schneider, R. Typical cells in Poisson hyperplane tessellations. Discr. Comput. Geom. 2007, 38, 305-319.
    • (2007) Discr. Comput. Geom. , vol.38 , pp. 305-319
    • Hug, D.1    Schneider, R.2
  • 43
    • 2142640516 scopus 로고    scopus 로고
    • The limit shape of the zero cell in a stationary Poisson hyperplane tessellation
    • Hug, D.; Reitzner, M.; Schneider, R. The limit shape of the zero cell in a stationary Poisson hyperplane tessellation. Ann. Probab. 2004, 32, 1140-1167.
    • (2004) Ann. Probab. , vol.32 , pp. 1140-1167
    • Hug, D.1    Reitzner, M.2    Schneider, R.3
  • 44
    • 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. Journal of Statistical Physics 1992, 67, 523-551.
    • (1992) Journal of Statistical Physics , vol.67 , pp. 523-551
    • Kumar, S.1    Kurtz, S.K.2    Banavar, J.R.3    Sharma, M.G.4
  • 45
    • 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. Journal of Statistical Computation and Simulation 1980, 10, 205-223.
    • (1980) Journal of Statistical Computation and Simulation , vol.10 , pp. 205-223
    • Hinde, A.L.1    Miles, R.E.2
  • 46
    • 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. Philosophical Magazine A 2001, 81, 2765-2783.
    • (2001) Philosophical Magazine A , vol.81 , pp. 2765-2783
    • Zhu, H.X.1    Thorpe, S.M.2    Windle, A.H.3
  • 47
    • 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 2003, 18, 221-247.
    • (2003) Forma , vol.18 , pp. 221-247
    • Tanemura, M.1
  • 48
    • 26244446903 scopus 로고    scopus 로고
    • Asymptotic statistics of the n-sided planar Poisson-Voronoi cell: I. Exact results
    • doi:10.1088/1742-5468/2005/09/P09005
    • Hilhorst, H. J. Asymptotic statistics of the n-sided planar Poisson-Voronoi cell: I. Exact results. J. Stat. Mech. 2005, P09005, doi:10.1088/1742-5468/2005/09/P09005.
    • (2005) J. Stat. Mech.
    • Hilhorst, H.J.1
  • 49
    • 34547555060 scopus 로고    scopus 로고
    • Voronoi neighbor statistics of hard-disks and hard-spheres
    • Kumar, V. S.; Kumaran, V. Voronoi neighbor statistics of hard-disks and hard-spheres. J. Chem. Phys. 2005, 123, 074502.
    • (2005) J. Chem. Phys. , vol.123 , pp. 074502
    • Kumar, V.S.1    Kumaran, V.2
  • 51
    • 23344441232 scopus 로고    scopus 로고
    • The Optimal Centroidal Voronoi Tessellations and the Gersho's Conjecture in the Three Dimensional Space
    • Du, Q.; Wang, D. The Optimal Centroidal Voronoi Tessellations and the Gersho's Conjecture in the Three Dimensional Space. Comput. Math. Appl. 2005, 49, 1355-1373.
    • (2005) Comput. Math. Appl. , vol.49 , pp. 1355-1373
    • Du, Q.1    Wang, D.2
  • 53
    • 0000049185 scopus 로고
    • Hydrodynamic fluctuations at the convective instability
    • Swift, J.; Hohenberg, P.C. Hydrodynamic fluctuations at the convective instability. Phys. Rev. A 1977, 15, 319-328.
    • (1977) Phys. Rev. A , vol.15 , pp. 319-328
    • Swift, J.1    Hohenberg, P.C.2
  • 54
    • 22044441063 scopus 로고    scopus 로고
    • A Proof of the Kepler Conjecture
    • Hales, T. C. A Proof of the Kepler Conjecture. Ann. Math. 2005, 162, 1065-1185.
    • (2005) Ann. Math. , vol.162 , pp. 1065-1185
    • Hales, T.C.1
  • 55
    • 33745509190 scopus 로고
    • A Counter-Example to Kelvin's Conjecture on Minimal Surfaces
    • Weaire, D.; Phelan, R. A Counter-Example to Kelvin's Conjecture on Minimal Surfaces. Philos. Mag. Lett. 1994, 69, 107-110.
    • (1994) Philos. Mag. Lett. , vol.69 , pp. 107-110
    • Weaire, D.1    Phelan, R.2
  • 56
    • 68949135171 scopus 로고    scopus 로고
    • A new counter-example to Kelvin's conjecture on minimal surfaces
    • Gabbrielli, R. A new counter-example to Kelvin's conjecture on minimal surfaces. Phil. Mag. Lett. 2009, 89.
    • (2009) Phil. Mag. Lett. , vol.89
    • Gabbrielli, R.1
  • 57
    • 38649115653 scopus 로고    scopus 로고
    • Practical Box Splines for Reconstruction on the Body Centered Cubic Lattice
    • Entezari, A.; van de Ville, D.; Möller, T. Practical Box Splines for Reconstruction on the Body Centered Cubic Lattice. IEEE T. Vis. Comput. Gr. 2008, 14, 313-328.
    • (2008) IEEE T. Vis. Comput. Gr. , vol.14 , pp. 313-328
    • Entezari, A.1    van de Ville, D.2    Möller, T.3
  • 58
    • 0032522023 scopus 로고    scopus 로고
    • Statistics of Voronoi cells of slightly perturbed face-centered cubic and hexagonal close-packed lattices
    • Troadec, J. P.; Gervois, A.; Oger, L. Statistics of Voronoi cells of slightly perturbed face-centered cubic and hexagonal close-packed lattices. Europhy. Lett. 1998, 42, 167-172.
    • (1998) Europhy. Lett. , vol.42 , pp. 167-172
    • Troadec, J.P.1    Gervois, A.2    Oger, L.3
  • 59
    • 39149138411 scopus 로고    scopus 로고
    • From Symmetry Breaking to Poisson Point Process in 2D Voronoi Tessellations: the Generic Nature of Hexagons
    • Lucarini, V. From Symmetry Breaking to Poisson Point Process in 2D Voronoi Tessellations: the Generic Nature of Hexagons. J. Stat. Phys. 2008, 130, 1047-1062.
    • (2008) J. Stat. Phys. , vol.130 , pp. 1047-1062
    • Lucarini, V.1
  • 60
    • 58549111857 scopus 로고    scopus 로고
    • Three-Dimensional Random Voronoi Tessellations: From Cubic Crystal Lattices to Poisson Point Processes
    • Lucarini, V. Three-Dimensional Random Voronoi Tessellations: From Cubic Crystal Lattices to Poisson Point Processes. J. Stat. Phys. 2009, 134, 185-206.
    • (2009) J. Stat. Phys. , vol.134 , pp. 185-206
    • Lucarini, V.1
  • 61
    • 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. 1928, 38, 341-376.
    • (1928) Anat. Rec. , vol.38 , pp. 341-376
    • Lewis, F.T.1
  • 62
    • 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 1919, 22, 241.
    • (1919) J. Inst. Metals , vol.22 , pp. 241
    • Desch, C.H.1
  • 63
    • 0011036407 scopus 로고    scopus 로고
    • Cambridge University Press: Cambridge, UK
    • Finch, S. R. Mathematical Constants; Cambridge University Press: Cambridge, UK, 2003.
    • (2003) Mathematical Constants
    • Finch, S.R.1
  • 64
    • 33847690144 scopus 로고    scopus 로고
    • The rise of grapheme
    • doi:10.1038/nmat1849
    • Geim, A. K.; Novoselov, K. S. The rise of grapheme. Nature Materials 2007, 6, 183-191, doi:10.1038/nmat1849.
    • (2007) Nature Materials , vol.6 , pp. 183-191
    • Geim, A.K.1    Novoselov, K.S.2
  • 66
    • 84860371425 scopus 로고    scopus 로고
    • On the entropy flows to disorder
    • arXiv:math-ph /0811.4318v2
    • Dodson, C. T. J. On the entropy flows to disorder. 2008, arXiv:math-ph /0811.4318v2.
    • (2008)
    • Dodson, C.T.J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.