Continuum percolation threshold for interpenetrating squares and cubes

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

Volumn 66, Issue 4, 2002, Pages 5-

  Baker, Don R ^a,b   Paul, Gerald ^a   Sreenivasan, Sameet ^a   Stanley, H Eugene ^a  

^a Boston University   (United States)

^b MCGILL UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

CONTINUUM PERCOLATION; CRITICAL EXPONENTS; NATURAL PHENOMENA; NUMBER DENSITY;

COMPUTER SIMULATION; CONTINUUM MECHANICS; DATA STRUCTURES; POROUS MATERIALS; STATISTICAL MECHANICS; VOLUME FRACTION;

PERCOLATION (SOLID STATE);

ARTICLE;

EID: 41349122168     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.66.046136     Document Type: Article

References (26)

1. D. Ben-Avraham and S. Havlin, Diffusion and Reactions in Fractals and Disordered Systems (Cambridge University Press, Cambridge, 2000).
2. Fractal and Disordered Systems, 2nd ed. edited by A. Bunde and S. Havlin (Springer-Verlag, Berlin, 1996), and references therein.
3. M. Sahimi, Applications of Percolation Theory (Taylor and Francis, London, 1994).
4. D. Stauffer and A. Aharony, Introduction to Percolation Theory (Taylor and Francis, London, 1994).
5. E.J. Garboczi, K.A. Snyder, J.F. Douglas, and M.F. Thorpe, Phys. Rev. E 52, 819 (1995).
6. U. Alon, A. Drory, and I. Balberg, Phys. Rev. A 42, 4634 (1990).
7. E.T. Gawlinski and H.E. Stanley, J. Phys. A 14, L291 (1981).
8. A. Geiger and H.E. Stanley, Phys. Rev. Lett. 49, 1895 (1982).
9. P.L. Leath, Phys. Rev. B 14, 5046 (1976).
10. C.D. Lorenz and R.M. Ziff, J. Chem. Phys. 114, 3659 (2001).
11. Three different sizes of objects were used in the 3D simulations to confirm the independence of the percolation threshold from both object and system size. Unfortunately, our range of system and object size in both 2D and 3D simulations is constrained by computer memory restrictions and CPU time available.
12. P. Bourke, http://astronomy.swin.edu.au/pbourke/geometry/lineline2d
13. P. Bourke, http://astronomy.swin.edu.au/pbourke/geometry/linefacet
14. H.G. Ballesteros, L.A. Fernadez, V. Martin-Mayor, A. Munoz Sudupe, G. Parisi, and J.J. Ruiz-Lorenzo, J. Phys. A 32, 1 (1999).
15. V.K.S. Shante and S. Kirkpatrick, Adv. Phys. 20, 325 (1971).
16. P. R. King, in North Sea Oil and Gas Reservoirs–IIV edited by A. T. Buller (Graham and Trotman, London, 1990).
17. E.J. Garboczi, M.F. Thorpe, M.S. DeVries, and A.R. Day, Phys. Rev. A 43, 6473 (1991).
18. M.A. Dubson and J.C. Garland, Phys. Rev. B 32, 7621 (1985).
19. J. Quintanilla, S. Torquato, and R.M. Ziff, J. Phys. A 33, L399 (2000).
20. M.O. Saar, M. Manga, K.V. Cashman, and S. Fremouw, Earth Planet. Sci. Lett. 187, 367 (2001).
21. I. Balberg, C.H. Anderson, S. Alexander, and N. Wagner, Phys. Rev. B 30, 3933 (1984);
22. S. Sreenivasan, D. R. Baker, G. Paul, and H. E. Stanley, e-print cond-mat/0205665 (2002).
23. I. Balberg, Philos. Mag. B 56, 991 (1987).
24. Here (Formula presented) because the object volume equals 1.
25. I. Balberg, Phys. Rev. B 31, 4053 (1985).
26. T. Kihara, Rev. Mod. Phys. 25, 831 (1953).