Second-order analysis by variograms for curvature measures of two-phase structures

European Physical Journal B

Volumn 47, Issue 3, 2005, Pages 397-409

  Arns, C H ^a   Mecke, J ^b   Mecke, K ^c   Stoyan, D ^d  

^a AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

^b FRIEDRICH SCHILLER UNIVERSITY JENA   (Germany)

^c UNIVERSITY OF ERLANGEN NUREMBERG   (Germany)

^d TU BERGAKADEMIE FREIBERG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; CORRELATION METHODS; FOAMS; FUNCTIONS; PHASE SEPARATION; POROUS MATERIALS;

CURVATURE MEASURES; GEOMETRICAL STRUCTURES; SECOND-ORDER ANALYSIS; TWO-PHASE STRUCTURES;

STRUCTURAL ANALYSIS;

EID: 27644531588     PISSN: 14346028     EISSN: 14346036     Source Type: Journal    
DOI: 10.1140/epjb/e2005-00338-5     Document Type: Article

References (50)

1. D. Stoyan, W.S. Kendall, J. Mecke, Stochastic Geometry and its Applications (John Wiley & Sons, Chichester, 1995)
2. S. Torquato, Random Heterogeneous Materials: Microstructure and Macroscopic Properties (Springer-Verlag, New York, 2002)
3. R. Hilfer, Statistical Physics and Spatial Statistics - The Art of Analyzing and Modeling Spatial Structures and Pattern Formation, edited by K.R. Mecke, D. Stoyan, 554 Lect. Notes Phys. (Springer, Berlin, 2000) pp. 203-241
4. K.R. Mecke, Integralgeometrie in der Statistischen Physik: Perkolation, komplexe Flüssigkeiten und die Struktur des Universums (Harry Deutsch, Frankfurt, 1994)
5. K. Mecke, Acta Physica Polonica B, 28, 1747 (1997)
6. K.R. Mecke, Int. J. Mod. Phys. B 12, 861 (1998)
7. K.R. Mecke, Statistical Physics and Spatial Statistics The Art of Analyzing and Modeling Spatial Structures and Pattern Formation, edited by K.R. Mecke, D. Stoyan, 554 Lect. Notes Phys. (Springer, Berlin, 2000) pp. 111-184
8. M. von Laue, Münchener Berichte (1912) p. 303
9. Lord Rayleigh, Proc. Roy. Soc. London Ser. A 84, 25 (1911)
10. A. Guinier, Ann. Phys. 12, 161 (1939)
11. P. Debye, H.R. Anderson, H. Brumberger, J. Appl. Phys. 28, 679 (1957)
12. G. Porod, Kolloid-Zeitschrift 125, 51; 108 (1952)
13. R. Kirste, G. Porod, Kolloid-Zeitschrift 184(1), 1 (1962)
14. J.P. Hansen, I.R. McDonald, Theory of Simple Liquids (Academic Press, 1976)
15. U. Sonntag, D. Stoyan, H. Hermann, Phys. Stat. Sol. 68, 281 (1981)
16. P. Smith, S. Torquato, J. Comp. Phys. 76(1), 176 (1988)
17. K.R. Mecke, J. Stat. Phys. 102, 1343, (2001)
18. C.H. Arns, M.A. Knackstedt, K.R. Mecke, Phys. Rev. Lett. 91, 215506 (2003)
19. P.-M. König, R. Roth, K. Mecke, Phys. Rev. Lett. 93, 1-4 (2004)
20. C.L.Y. Yeong, S. Torquato, Phys. Rev. E 57, 495 (1998)
21. C.L.Y. Yeong, S. Torquato, Phys. Rev. E 58, 224 (1998)
22. J.P. Chilès, P. Delfmer, Geostatistics. Modelling Spatial Uncertainity (J. Wiley and Sons, New York, 1999)
23. R. Schneider, Convex Bodies: The Brunn-Minkowski Theory, Encyclopedia of Mathematics and its Applications, Vol. 44 (Cambridge University Press, Cambridge, 1993)
24. D.A. Klain, G.-C. Rota, Introduction to Geometric Probability (Cambridge University Press, Cambridge, 1997)
25. A. Tscheschel, D. Stoyan, J. Microsc. 211, 80 (2003)
26. A. Bezrukov, M. Bargiel, D. Stoyan, Part. Part. Charact. 19, 111 (2002)
27. S. Torquato, G. Stell, J. Chem. Phys. 79, 1505 (1983)
28. M. Kerscher, K. Mecke, J. Schmalzing, C. Beisbart, T. Buchert, H. Wagner, Astron. Astrophys. 373, 1 (2001)
29. U. Brodatzki, K. Mecke, Computer Physics Communications 147, 218 (2002)
30. Arthur Sakellariou, T.J. Sawkins, T.J. Senden, A. Limaye, Physica A 339(1-2), 152 (2004)
31. M. Saadatfar, M.A. Knackstedt, C H. Arns, A. Sakellariou, T. Senden, A.P. Sheppard, R.M. Sok, H. Steininger, W. Schrof, Physica A 339(1-2), 131, (2004)
32. T. Mattfeldt, D. Stoyan, J. Microsc. 200(2), 158 (2000)
33. D. Marcotte, Computers & Geosciences 22(10), 1175 (1996)
34. K. Koch, J. Ohser, K. Schladitz, Adv. Appl. Prob. 35, 603 (2003)
35. W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery, Numerical, Recipes in Fortran 90 - The Art of Parallel Scientific Computing, Vol. II (Cambridge University Press, Cambridge, 1996)
36. N.A. Seaton, E.D. Glandt, J. Chem. Phys. 85(9), 5262 (1986)
37. M. Knackstedt, G. Arns, M. Saadatfar, T. Senden, A. Sakellariou, A. Sheppard, R. Sok, W. Schrof, H. Steininger, Adv. Eng. Mat. 7(4), 238 (2005)
38. A.P. Sheppard, R.M. Sok, H. Averdunk, Physica A 339(1-2), 145 (2004)
39. P. Spanne, J.F. Thovert, C.J. Jacquin, W.B. Lindquist, K.W. Jones, P.M. Adler, Phys. Rev. Lett. 73, 2001 (1994)
40. P.M. Auzerais, J. Dunsmuir, B.B. Ferrèol, N. Martys, J. Olson, T.S. Ramakrishnan, D.H. Rothman, L.M. Schwartz, Geophys. Res. Lett. 23(7), 705 (1996)
41. J.T. Fredrich, Phys. Chem. Earth (A) 24(7), 551 (1999)
42. J.-F. Thovert, F. Youseflan, P. Spanne, C.G. Jacquin, P.M. Adler, Phys. Rev. E 63, 61307 (2001)
43. W.B. Lindquist, A. Venkatarangan, J. Dunsmuir, T.F. Wong, J. Geophys. Res. B 105, 21509 (2000)
44. C.H. Arns, M.A. Knackstedt, W. Val Pinczewski, W.B. Lindquist, Geophys. Res. Lett. 28(17), 3361 (2001)
45. C.H. Arns, M.A. Knackstedt, K.R. Mecke, Morphology of Condensed Matter - Physics and Geometry of spatially complex Systems, edited by K.R. Mecke, D. Stoyan, Lect. Notes Phys. 600 (Springer, Berlin, 2002) pp. 37-74
46. C.H. Arns, M.A. Knackstedt, W.V. Pinczewski, E.G. Garboczi, Geophys. 67(5), 1396 (2002)
47. C.H. Arns, M.A. Knackstedt, W.V. Pinczewski, N. Martys, J. Petr. Sc. Eng. 45(1-2), 41 (2004)
48. W. Oh, W. Brent Lindquist, IEEE T. Patt. Anal. Machine Intelligence 21, 590 (1999)
49. W.B. Lindquist, A. Venkatarangan, Phys. Chem. Earth (A) 25, 593 (1999)
50. D.J. Bergman, K.-J. Dunn, L.M. Schwartz, P.P. Mitra, Phys. Rev. E 51, 3393 (1995)