Exact conditions on physically realizable correlation functions of random media

Journal of Chemical Physics

Volumn 111, Issue 19, 1999, Pages 8832-8837

  Torquato, S ^a,b  

^a PRINCETON UNIVERSITY   (United States)

^b Princeton University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001150287     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.480255     Document Type: Article

References (21)

1. J. A. Quiblier, J. Colloid Interface Sci. 98, 84 (1984).
2. P. M. Adler, Porous Media: Geometry and Transport (Butterworth-Heinemann, Boston, 1992).
3. A. P. Roberts and M. Teubner, Phys. Rev. E 51, 4141 (1995); P. Levitz, Adv. Colloid Interface Sci. 76-77, 71 (1998).
4. A. P. Roberts and M. Teubner, Phys. Rev. E 51, 4141 (1995); P. Levitz, Adv. Colloid Interface Sci. 76-77, 71 (1998).
5. C. L. Y. Yeong and S. Torquato, Phys. Rev. E 57, 495 (1998).
6. D. Cule and S. Torquato, J. Appl. Phys. (in press).
7. C. Manwart and R. Hilfer, Phys. Rev. E 59, 5596 (1999).
8. S. Torquato and G. Stell, J. Chem. Phys. 77, 2071 (1982).
9. P. Debye, H. R. Anderson, and H. Brumberger, J. Appl. Phys. 28, 679 (1957).
10. J. G. Berryman, J. Math. Phys. 28, 244 (1987).
11. M. B. Priestley, Spectral Analysis and Time Series (Academic, New York, 1981).
12. G. K. Batchelor, The Theory of Homogeneous Turbulence (Cambridge University Press, Cambridge, 1959).
13. Even if γ(k) does not exist, one can still relate the properties of γ(r) to its spectral properties using the more general Stieltjes representation.
14. B. Lu and S. Torquato, J. Chem. Phys. 93, 3452 (1990).
15. S. Prager, Phys. Fluids 4, 1477 (1961).
16. S. Torquato and J. Rubinstein, J. Chem. Phys. 90, 1644 (1989).
17. 2(r) given in Ref. 4 is for phase 2 (not for phase 1 as in the present work). Moreover, it contains a phase angle which we omitted here.
18. S. Torquato, Ph.D. dissertation, SUNY Stony Brook, New York (1980).
19. G. W. Milton, Phys. Rev. Lett. 46, 542 (1981).
20. G. W. Milton, J. Mech. Phys. Solids 30, 177 (1982).
21. S. Torquato, J. Mech. Phys. Solids 45, 1421 (1997).