Random Two-Dimensional Cellular Structures

  • D. Weaire
Conference paper
Part of the Springer Series in Solid-State Sciences book series (SSSOL, volume 46)

Abstract

Two-dimensional cellular structures abound in nature and they crop up in a variety of contexts in the scientific literature. An early example [1] is shown in Fig. 1. D’A. W. THOMPSON described this and numerous other interesting examples in his classic work On Growth and Form [2]. He sensed that such patterns often have much in common, even when they are formed in very different systems. In this and other areas he set out to “show the mathematician a field for his labour — a field which few have entered and no man has explored”

Keywords

Entropy Anisotropy Argon 

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References

  1. 1.
    S. Foley, Trans. Roy. Soc. London,18, 170 (1694).Google Scholar
  2. 2.
    D’A. W. Thompson, On Growth and Form, 2nd Edition (Cambridge University Press, 1942 ).Google Scholar
  3. 3.
    F.T. Lewis, Amer. J. Bot. 30, 766 (1943).CrossRefGoogle Scholar
  4. 4.
    F.T. Lewis, Anat. Rec. 56, 235 (1 931).Google Scholar
  5. 5.
    C.S. Smith, in Metal In Terfaces (Cleveland: American Society for metals, 1952 ) p. 65.Google Scholar
  6. 6.
    C.S. Smith, Metallurgical Review, 9, 1 (1964).Google Scholar
  7. 7.
    A. Getis and B. Boots, Models of Spatial Processes (Cambridge University Press, 1979 ).Google Scholar
  8. 8.
    W. Krommenhoek, J. Sebus and G.J. van Esch, Biological Structures ( Hertogenbosch: Malmberg B.V., 1979 ).Google Scholar
  9. 9.
    J.P. O’Reilly, Trans. Roy. Ir. Acad. 26, 641 (1879).Google Scholar
  10. 10.
    D. Weaire and J.P. Kermode, to be published (1983).Google Scholar
  11. 11.
    L. Bragg and J.F. Nye, Proc. Roy. Soc. London A, 196, 171 (1949).CrossRefADSGoogle Scholar
  12. 12.
    A.S. Argon and L.T. Shi, Phil. Mag. 46, 275 (1982).CrossRefGoogle Scholar
  13. 13.
    J.F. Shackl ef ord, J. Non-Cryst. SolicTs, 49, 19 (1 982).Google Scholar
  14. 14.
    I. K. Crain, Search, 3, 220 (1972).Google Scholar
  15. 15.
    I.J. Smalley, Geol. Mag. 103, 110 (1966).CrossRefGoogle Scholar
  16. 16.
    M. Tanemura and T. Ogawa, J. Comp. Phys, to be published (1983).Google Scholar
  17. 17.
    J.L. Meijering, Philips Res. Rep. 8, 270 (1953).MATHGoogle Scholar
  18. 18.
    K. J. Dormer, Fundamental Tissue Geometry for Biologists (Cambridge University Press 1980)Google Scholar
  19. 19.
    D.A. Aboav, Meta11ography 3, 383 (1970).CrossRefGoogle Scholar
  20. 20.
    S.K. Kurtz and F.M.A. Carpay, J. Appl. Phys. 51, 5725 (1981).CrossRefADSGoogle Scholar
  21. 21.
    T. Kiang, Zeitschrift fur Astrophysik, 64, 433 (1966).ADSGoogle Scholar
  22. 22.
    N. Rivier and A. Lissowski, J. Phys. A 15, L143 (1982).CrossRefADSMathSciNetGoogle Scholar
  23. 23.
    D. Weaire, Metallography 7, 157 (1974).CrossRefGoogle Scholar
  24. 24.
    D.A. Aboav, Meta11ography, 13, 43 (1980).CrossRefGoogle Scholar
  25. 25.
    B.N. Boots, Canadian Geographer, 24, 406 (1980).CrossRefGoogle Scholar
  26. 26.
    C.J. Lambert and D. Weaire, Metallography, V4, 307 (1981).CrossRefGoogle Scholar
  27. 27.
    C.J. Lambert and D. Weaire, Phil. Mag. to be published (1983).Google Scholar
  28. 28.
    B.N. Boots, Metallography, 14, 319 (1981).CrossRefGoogle Scholar
  29. 29.
    J. Von Neumann, in Meta1 Interfaces (Cleveland: American Society for Metals, 1952) p.108.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1983

Authors and Affiliations

  • D. Weaire
    • 1
  1. 1.Department of PhysicsUniversity CollegeDublinIreland

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