Elastic properties of inhomogeneous media with chaotic structure

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 63, Issue 3, 2001, Pages

  Novikov, V V ^a   Wojciechowski, K W ^b   Belov, D V ^a   Privalko, V P ^c  

^a ODESSA NATIONAL POLYTECHNIC UNIVERSITY   (Ukraine)

^b INSTITUTE OF MOLECULAR PHYSICS   (Poland)

^c TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

CHAOS THEORY; CRYSTAL LATTICES; ELASTICITY; FRACTALS; HAMILTONIANS; ITERATIVE METHODS; MATHEMATICAL MODELS; PERCOLATION (FLUIDS); POISSON RATIO;

DIRAC FUNCTIONS; INHOMOGENEOUS MEDIA; ITERATIVE AVERAGING METHOD;

QUANTUM THEORY;

EID: 0035275703     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.63.036120     Document Type: Article

References (31)

1. J. Bernasconi, Phys. Rev. B 18, 2185 (1978).
2. S. Feng and M. Sahimi, Phys. Rev. B 31, 1671 (1985).
3. Y. Kantor and I. Webman, Phys. Rev. Lett. 52, 1891 (1984).
4. D. Y. Bergman and Y. Kantor, Phys. Rev. Lett. 53, 511 (1984).
5. S. Arbabi and M. Sahimi, Phys. Rev. B 38, 7173 (1988).
6. H. J. Herrman and H. E. Stanley, J. Phys. A 21, 1829 (1988).
7. S. Arbabi and M. Sahimi, Phys. Rev. B 47, 695 (1993).
8. M. Sahimi and S. Arbabi, Phys. Rev. B 47, 703 (1993).
9. P. De Gennes, Scaling Concepts in Polymer Physics (Cornell University Press, Ithaca, NY, 1979).
10. M. Sahimi, Phys. Rep. 306, 213 (1998).
11. A. Coniglio and H. E. Stanley, Phys. Rev. Lett. 52, 1068 (1984).
12. D. Stauffer and A. Aharony, Introduction to Percolation Theory, 2nd ed. (Taylor and Francis, London, 1992).
13. P. J. Reynolds, H. E. Stanley, and W. Klein, Phys. Rev. B 21, 1223 (1980).
14. D. A. S. Weitz and M. Oliveira, Phys. Rev. Lett. 52, 1433 (1984).
15. V. P. Privalko and V. V. Novikov, The Science of Heterogeneous Polymers. Structure and Thermophysical Properties (Wiley, Chichester, U.K., 1995).
16. L. Pietronero and E. Tossati, Fractals in Physics (North-Holland, Amsterdam, 1986).
17. V. V. Novikov and V. P. Belov, Zh. Eksp. Teor. Fiz. 79, 428 (1994) [JETP 106, 780 (1994)].
18. V. V. Novikov, O. P. Poznansky, and V. P. Privalko, Sci. Eng. Composite Mater. 4, 49 (1995).
19. V. V. Novikov and O. P. Poznansky, Fiz. Tverd. Tela (St. Petersburg) 37, 451 (1995); [Phys. Solid State 37, 830 (1995)].
20. V. V. Novikov, High Temp. 34, 688 (1969).
21. V. V. Novikov, Phys. Met. Metallogr. 83, 349 (1997).
22. The strict validity of Eq. (6) may be questioned 23 in so far as for a certain spanning rule and boundary condition on the square lattice the probability (Formula presented) turns out to be universal, which is at variance with the nonuniversal value of (Formula presented) A counterargument to this claim was offered by Sahimi and Rassamdana 24, who managed to show that the equation (Formula presented) [where α is any number in (0,1)] provided a sequence of (Formula presented)’s that always converge to (Formula presented) as (Formula presented) with optimal convergence at (Formula presented)
23. R. M. Ziff, Phys. Rev. Lett. 69, 2670 (1992);
24. Phys. Rev. Lett.R. M. Ziff72, 1942 (1994).
25. M. Sahimi and H. Rassamdana, J. Stat. Phys. 78, 1157 (1995).
26. Z. Hashin and S. Shtrikman, J. Mech. Phys. Solids 10, 335 (1962).
27. Z. Hashin, J. Appl. Mech. 50, 481 (1983).
28. J. G. Zabolitzky, D. J. Bergman, and D. Stauffer, J. Stat. Phys. 44, 211 (1986).
29. M. Sahimi, J. Phys. C 19, L79 (1986).
30. S. Arbabi and M. Sahimi, Phys. Rev. Lett. 65, 725 (1990).
31. W. Y. Hsu, M. R. Giri, and R. M. Ikeda, Am. Chem. Soc. Ser. 15, 1210 (1992).