Physical and geometrical percolations of effective conductivity on a lattice

Physical Review B - Condensed Matter and Materials Physics

Volumn 76, Issue 14, 2007, Pages

  Hakobyan, Yeranuhi ^a   Papoulia, Katerina D ^b   Grigoriu, Mircea D ^a  

^a Cornell University   (United States)

^b UNIVERSITY OF WATERLOO   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 35448944408     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.76.144205     Document Type: Article

References (44)

1. S. Kirkpatrick, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.45. 574 45, 574 (1973).
2. I. Webman, J. Jortner, and M. H. Cohen, Phys. Rev. B PLRBAQ 0556-2805 10.1103/PhysRevB.11.2885 11, 2885 (1975).
3. D. C. Hong, H. E. Stanley, A. Coniglio, and A. Bunde, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.33.4564 33, 4564 (1986).
4. S. Kirkpatrick, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.27. 1722 27, 1722 (1971).
5. V. Ambegaokar, B. I. Halperin, and J. S. Langer, Phys. Rev. B PLRBAQ 0556-2805 10.1103/PhysRevB.4.2612 4, 2612 (1971).
6. G. E. Pike and C. H. Seager, Phys. Rev. B PLRBAQ 0556-2805 10.1103/PhysRevB.10.1421 10, 1421 (1974).
7. G. E. Pike and C. H. Seager, Phys. Rev. B PLRBAQ 0556-2805 10.1103/PhysRevB.10.1435 10, 1435 (1974).
8. E. J. Garboczi, L. M. Schwartz, and D. P. Bentz, Adv. Cem. Based Mater. ACATE9 1065-7355 2, 169 (1995).
9. L. M. Schwartz, E. J. Garboczi, and D. P. Bentz, J. Appl. Phys. JAPIAU 0021-8979 10.1063/1.360591 78, 5898 (1995).
10. D. D. L. Chung, Composite Materials for Electronic Functions, Materials Science Foundations Vol. 12 (Trans. Tech., Switzerland, 2000).
11. D. D. L. Chung, Multifunctional Cement-based Materials, Civil and Environmental Engineering Book Series (Dekker, New York, 2003).
12. D. D. L. Chung, J. Electroceram. JOELFJ 1385-3449 6, 75 (2001).
13. D. Stauffer and A. Aharony, Introduction to Percolation Theory, 2nd ed. (Taylor & Francis, London, 1992).
14. B. J. Last and D. J. Thouless, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.27.1719 27, 1719 (1971).
15. L. N. Smith and C. J. Lobb, Solid State Commun. SSCOA4 0038-1098 20, 3653 (1979).
16. I. Balberg and S. Borwski, Solid State Commun. SSCOA4 0038-1098 10.1016/0038-1098(82)90144-2 44, 551 (1982).
17. V. K. S. Shante and S. Kirkpatrick, Adv. Phys. ADPHAH 0001-8732 10.1080/00018737100101261 20, 325 (1971).
18. V. A. Vyssotsky, S. B. Gordon, H. L. Frisch, and J. M. Hammersley, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.123.1566 123, 1566 (1961).
19. H. L. Frisch, J. M. Hammersley, and D. J. A. Welsh, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.126.949 126, 949 (1962).
20. H. Scher and R. Zallen, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1674565 53, 3759 (1970).
21. I. Balberg and N. Binenbaum, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.28.3799 28, 3799 (1983).
22. I. Balberg, N. Binenbaum, and N. Wagner, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.52.1465 52, 1465 (1984).
23. A. L. R. Bug, S. A. Safran, and I. Webman, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.54.1412 54, 1412 (1985).
24. E. J. Garboczi, K. A. Snyder, J. F. Douglas, and M. F. Thorpe, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.52.819 52, 819 (1995).
25. E. J. Garboczi, M. F. Thorpe, M. S. DeVries, and A. R. Day, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.43.6473 43, 6473 (1991).
26. M. E. Fisher and J. W. Essam, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.1703745 2, 609 (1961).
27. J. W. Essam, Phase Transition and Critical Phenomena (Academic, New York, 1972).
28. I. Balberg, C. H. Anderson, S. Alexander, and N. Wagner, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.30.3933 30, 3933 (1984).
29. I. Balberg, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.31.4053 31, 4053 (1985).
30. C. J. Lobb, D. J. Frank, and M. Tinkham, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.23.2262 23, 2262 (1981).
31. D. B. Gingold and C. J. Lobb, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.42.8220 42, 8220 (1990).
32. H. J. Maris and L. P. Kadanoff, Am. J. Phys. AJPIAS 0002-9505 10.1119/1.11224 46, 652 (1978).
33. J. Bernasconi, Phys. Rev. B PLRBAQ 0556-2805 10.1103/PhysRevB.18.2185 18, 2185 (1978).
34. M. F. Sykes and J. W. Essam, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.1704215 5, 1117 (1964).
35. L. D. Landau and E. M. Lifshitz, The Classical Theory of Fields (Pergamon, Oxford, 1971).
36. R. Kikuchi, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1674394 53, 2713 (1970).
37. T. J. R. Hughes, The Finite Elements Method: Linear Static and Dynamic Finite Element Analysis (Prentice-Hall, Englewood Cliffs, NJ, 1987).
38. J. R. Shewchuk, Computational Geometry: Theory and Applications, Vol. 22 (2002), pp. 21-74.
39. L. Bocquet, Am. J. Phys. AJPIAS 0002-9505 10.1119/1.2426354 75, 148 (2007).
40. P. Tong and T. H. H. Pian, Int. J. Solids Struct. IJSOAD 0020-7683 10.1016/0020-7683(73)90082-6 9, 313 (1973).
41. S. E. Benzley, Int. J. Numer. Methods Eng. IJNMBH 0029-5981 10.1002/nme.1620080310 8, 537 (1974).
42. S. A. Vavasis, SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. SJNAEQ 0036-1429 10.1137/0733045 33, 890 (1996).
43. J. F. Douglas and E. J. Garboczi, Intrinsic Viscosity and the Polarizability of Particles Having a Wide Range of Shapes (Wiley, New York, 1995).
44. J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975).