Uniqueness of reconstruction of multiphase morphologies from two-point correlation functions

Physical Review Letters

Volumn 89, Issue 13, 2002, Pages 1355011-1355014

  Rozman, M G ^a   Utz, Marcel ^a  

^a UNIVERSITY OF CONNECTICUT   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; BOUNDARY CONDITIONS; COMPUTER SIMULATION; CORRELATION METHODS; CRYSTAL MICROSTRUCTURE; CRYSTALLOGRAPHY; FOURIER TRANSFORMS; INTEGRATION; INVERSE PROBLEMS; PHASE TRANSITIONS; RANDOM PROCESSES; VOLUME FRACTION;

MULTIPHASE MORPHOLOGY;

PHASE SEPARATION;

EID: 0037163783     PISSN: 00319007     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevLett.89.135501     Document Type: Article

References (41)

1. J.W. Cahn, J. Chem. Phys. 42, 93 (1965).
2. J.A. Quiblier, J. Colloid Interface Sci. 98, 84 (1984).
3. N.F. Berk, Phys. Rev. Lett. 58, 2718 (1987).
4. M. Teubner, Europhys. Lett. 14, 403 (1991).
5. A.P. Roberts and M. Teubner, Phys. Rev. E 51, 4141 (1995).
6. A.P. Roberts and S. Torquato, Phys. Rev. E 59, 4953 (1999).
7. P.M. Adler, Porous Media: Geometry and Transport (Butterworth-Heinemann, Boston, 1992).
8. P. Levitz, Adv. Colloid Interface Sci. 76-77, 71 (1998).
9. C.L.Y. Yeong and S. Torquato, Phys. Rev. E 57, 495 (1998).
10. D. Cule and S. Torquato, J. Appl. Phys. 86, 3428 (1999).
11. C. Manwart, S. Torquato, and R. Hilfer, Phys. Rev. E 62, 893 (2000).
12. J.M. Drake, J. Klafter, and P. Levitz, Science 251, 1574 (1991).
13. P. Robyr and R. Bowtell, J. Chem. Phys. 107, 702 (1997).
14. S. Torquato, Random Heterogeneous Materials (Springer, New York, 2001).
15. C. Chubb and J.I. Yellott, Vis. Res. 40, 485 (2000).
16. M.G. Rozman and M. Utz, Phys. Rev. E 63, 066701 (2001).
17. U. Breiner, U. Krappe, E.L. Thomas, and R. Stadler, Macromolecules 31, 135 (1998).
18. S.S. Sheiko, Adv. Polym. Sci. 151, 62 (2000).
19. Color and animated version of figures are available from the authors' web site http:/giotto.ims.uconn.edu/.
20. The simulation box used for the reconstruction is much larger than the characteristic decay length of the correlation functions.
21. A.L. Patterson, Phys. Rev. 65, 195 (1944).
22. Patterson and Pattersons: Fifty Years of the Patterson Function, edited by J.P. Glusker, B.K. Patterson, and M. Rossi, International Union of Crystallography (Oxford University Press, New York, 1987).
23. A.M. Finkelstein, O.M. Kosheleva, and V.J. Kreinovic, Astrophys. Space Sci. 92, 31 (1983).
24. J. John and I. Yellott, J. Opt. Soc. Am. A 10, 777 (1993).
25. S.S. Skiena, W.D. Smith, and P. Lemke, in Proceedings of the Sixth Annual Symposium on Computational Geometry (ACM, New York, 1990), pp. 332-339.
26. H. Hauptman and J. Karle, Solution of the Phase Problem. (American Crystallographic Association, 1953).
27. L.A. Santaló, Integral Geometry and Geometric Probability (Addison-Wesley, Reading, Massachusetts, 1976).
28. J. Serra, Image Analysis and Mathematical Morphology (Academic Press, London, 1982).
29. W. Nagel, J. Appl. Probab. 30, 730 (1993).
30. E. Marinari, G. Parisi, and F. Ritort, J. Phys. A 27, 7615 (1994).
31. W. Krauth and M. Mezard,Z. Phys. B 97, 127 (1995).
32. S. Mertens, J. Phys. A 29, L473 (1996).
33. S. Mertens and C. Bessenrodt, J. Phys. A 31, 3731 (1998).
34. W. Wenzel and K. Hamacher, Phys. Rev. Lett. 82, 3003 (1999).
35. J. Bernasconi, J. Phys. (Paris) 48, 559 (1987).
36. J.W. Cahn and H.E. Hilliard, J. Chem. Phys. 28, 258 (1958).
37. J.D. Gunton, M. San Miguel, and P.S. Sahni, in Phase Transitions and Critical Phenomena, edited by C. Domb and J.L. Lebowitz (Academic, New York, 1983).
38. A.J. Bray, Adv. Phys. 43, 357 (1994).
39. K. Binder, in Phase Transformations in Materials, Materials Science and Technology, edited by R.W. Cahn, P. Haasen, and E.J. Kramer (VCH, Weinheim, 1991), Vol. 5.
40. K.R. Mecke and V. Sofonea, Phys. Rev. E 56, R3761 (1997).
41. S. Puri, A.J. Bray, and J.L. Lebowitz, Phys. Rev. E 56, 758 (1997).