Analysis of 3-D network structures

Philosophical Magazine

Volumn 85, Issue 1, 2005, Pages 3-31

  Glicksman, M E ^a  

^a RENSSELAER POLYTECHNIC INSTITUTE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

AMORPHOUS MATERIALS; COMPUTER SIMULATION; FOAMS; POLYCRYSTALS; PROBLEM SOLVING; TISSUE; TOPOLOGY;

INTEGRAL GEOMETRY; NETWORK STRUCTURES; POLYHEDRAL NETWORKS; TRIPLE LINES;

INTEGRAL EQUATIONS;

EID: 21144437136     PISSN: 14786435     EISSN: 14786443     Source Type: Journal    
DOI: 10.1080/14786430412331329892     Document Type: Article

References (57)

1. AVRON, J. E., and LEVINE, D., 1992, Phys. Rev. Lett., 69, 208.
2. BRAKKE, K., 1977, The Motion of a Surface by its Mean Curvature (Princeton, NJ: Princeton University Press).
3. BRAKKE, K., 1992, Exper. Math., 1, 141.
4. BRAKKE, K., 2002, http://geom.umn.edu/software/evolver.
5. COX, S. J., and FORTES, M. A., 2003, Phil. Mag. Lett., 83, 281.
6. COX, S. J., 2003, private communication.
7. COXETER, H. S. M., 1958, Illinois J. of Math.,
8. reprinted in The Kelvin Problem, vol. 2, edited by Denis Weaire, 1996 (London: Taylor & Francis), pp. 109-123.
9. DEHOFF, R. T., 1994, Acta Metall. et Mat., 42, 2633.
10. DESCH, C. H., 1919, Trans. ASM, 22, 241.
11. DREW, D. A., 1990, SIAM J. Appl. Math., 50, 649.
12. FRADKOV, V. E., PALMER, M., NORDBERG J., GLICKSMAN, M. E., and RAJAN, K., 1993, Physica D, 66, 50.
13. FRADKOV, V. E., PALMER, M., GLICKSMAN, M. E., and RAJAN, K., 1994, Acta Metall. et Mat., 42, 2719.
14. GLAZIER, J. A., 1993, Phys. Rev. Lett., 70, 2170.
15. GLICKSMAN, M. E., LUPULESCU, A., and KOSS, M. B., 2003, J. Thermophysics and Heat Transfer, 17, 69.
16. GOLDBERG, M., 1934, Tohoku Math. J., 40, 226.
17. GRANER, F., JIANG Y., JANIAUD, E., and FLAMENT, C., 2001, Phys. Rev. E, 63, 402.
18. GRAY, A., 1997, The Gaussian and Mean Curvature, second edn (Boca Raton: CRC Press).
19. GRAY, A., 1999, Modern Differential Geometry, second edn (Boca Raton: CRC Press).
20. HARKER, D., and PARKER, E., 1945, Trans. ASM, 34, 156.
21. HILGENFELDT, S., KRAYNIK, A. M., KOEHLER, S. A., and STONE, H. A., 2001, Phys. Rev. Lett., 86, 2685.
22. HUISKEN, G., 1984, J. Diff. Geometry, 20, 237.
23. KOENDERINK, J. J., 1991, Solid Shape, second edn (Cambridge: MIT Press).
24. rd EuroConference on Foams, Emulsions and Applications, edited by P. Zitha (Bremen: MIT-Verlag).
25. LEWIS, F. T., 1944, Am. J. Botany, 31, 619.
26. LIPSCHUTZ, M. M., 1981, Differential Geometry, Schaums Outline Series (New York: McGraw-Hill).
27. LORD KELVIN, 1887, Phil. Mag., 24, 503.
28. LORD KELVIN, 1894, Proc. R. Soc., 55, 1.
29. MARSH, S. P., GLICKSMAN, M. E., and ZWILLINGER, D., 1988, Modeling and Control of Casting and Welding Processes, Vol. 4, edited by T. S. Piwonka and H. P. Wang (Warrendale, Pennsylvania: The Metallurgical Society of AIME), pp. 921-928.
30. MARSH, S. P., and GLICKSMAN, M. E., 1996, Metall. Matls. Trans. A, 27A, 557.
31. MARSH, S. P., and GLICKSMAN, M. E., 1997, Mater. Sci. Engn., A238, 140.
32. MATZKE, E. B., and NESTLER, J., 1946, Am. J. Botany, 33, 130.
33. MATZKE, E. B., 1952, Grain Shapes and other Metallurgical Applications of Topology (Cleveland: American Society for Metals), pp. 110-111.
34. MONNEREAU, C., and VIGNES-ADLER, M., 1998, Phys. Rev. Lett., 80, 5228.
35. MONNEREAU, C., PITTET, N., and WEAIRE, D., 2000, Europhys. Lett., 52, 361.
36. MULLINS, W. W., 1956, J. Appl. Phys., 22, 900.
37. MULLINS, W. W., 1986, J. Appl. Phys., 59, 1341.
38. NELSON, D. R., 1983, Phys. Rev., B28, 5515.
39. PALMER, M. A., FRADKOV, V. E., GLICKSMAN, M. E., and RAJAN, K., 1994, Scripta Metall. et Mat., 30, 633.
40. PALMER, M. A., GLICKSMAN, M. E., RAJAN, K., FRADKOV, V. E., and NORDBERG, J., 1995, Metall. and Mat. Trans. A, 26, 1061.
41. PHELAN R., 1996, The Kelvin Problem, edited by Denis Weaire (London: Taylor & Francis), pp. 125-140.
42. RIOS, P., 2004, private communciation.
43. RIVIER, N., 1982, J. Phys. (Paris), 43, 91.
44. ROLLETT, A., 2003, private communication.
45. ROSS, S., 1978, Am. J. Phys., 46, 513.
46. SMITH, C. S., 1952, Grain Shapes and other Metallurgical Applications of Topology (Cleveland: American Society for Metals), pp. 65-109.
47. SPAEPEN, F., 2003, private communication.
48. STREITENBERGER, P., 2003, private communication.
49. STRUIK, D., 1950, Lectures on Classical Differential Geometry (Reading, MA: Addison-Wesley).
50. THOMPSON, D. W., 1948, On Growth and Form, second edn (Cambridge: Cambridge University).
51. VAZ, M. F., FORTES, M. A., and GRANER, F., 2002, Phil. Mag. Lett., 82, 575.
52. VON NEUMANN, J. 1952, Grain Shapes and other Metallurgical Applications of Topology (Cleveland: American Society for Metals), pp. 108-110.
53. WEISSTEIN, E. W., 1999a, World of Mathematics (Boca Raton: CRC Press).
54. WEISSTEIN, E. W., 1999b, http://mathworld.wolfram.com.
55. WEISSTEIN, E. W., 1999c, "Reuleaux Tetrahedron", MathWorld, A Wolfram Web Resource, http://mathworld.wolfram.com/ReuleauxTetrahedron.html.
56. WILLIAMS, W. M., 1952, Metal Interfaces written discussion (Cleveland: American Society for Metals).
57. ZWILLINGER, D., 1995, Spherical Geometry and Trigonometry (Boca Raton: CRC Press).