Percolation theory: Topology and structure

Lecture Notes in Physics

Volumn 771, Issue , 2009, Pages 1-36

  Hunt, Allen ^a   Ewing, Robert ^b  

^a WRIGHT STATE UNIVERSITY   (United States)

^b IOWA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 62849116957     PISSN: 00758450     EISSN: None     Source Type: Book Series    
DOI: 10.1007/978-3-540-89790-3_1     Document Type: Article

References (54)

1. Diestel, R., 2000, Graph Theory, 3rd edition. Springer-Verlag, Heidelberg, Graduate Texts in Mathematics, Volume 173.
2. Du, D.-Z., and F. Hsu, 1995, Combinatorial Network Theory (Applied Optimization) Springer, Heidelberg.
3. Fatt, I., 1956, The network model of porous media, Trans. Am. Inst. Min. Metall. Pet. Eng., 207: 144-177.
4. Chalupa, J., P. L. Leath, and G. R. Reich, 1979, Bootstrap percolation on a Bethe lattice, J. Phys. C. Solid State Physics 12: L31-L35.
5. Rosso, M., J. F. Gouyet, B. Sapoval, 1986, Gradient percolation in 3 dimensions and relation to diffusion fronts, Phys. Rev. Lett. 57: 3195-3198.
6. Chandler, R., J. Koplik, K. Lerman, and J. F. Willemsen, 1982, Capillary displacement and percolation in porous media, J. Fluid Mech., 119, 249-267.
7. Nickel, B., and D. Wilkinson, 1983, Invasion percolation on the Cayley tree - exact solution of a modified percolation model, Phys Rev Lett. 51(2): 71-74.
8. Wilkinson, D., and J. Willemsen, 1983, Invasion percolation: A new form of percolation theory, J. Phys. A: Math. Gen. 16: 3365-3376.
9. Flory, P. J., 1941, Molecular size distribution in three dimensional polymers, J. Am. Chem. Soc. 63: 3083-3100.
10. Broadbent, S. R. and J. M. Hammersley, 1957, Percolation processes, 1. Crystals and mazes, Proc. Cambridge Philos. Soc. 53: 629-641.
11. Gandolfi, A., G. Grimmett, and L. Russo, 1988, On the uniqueness of the infinite cluster in the percolation model, Commun. Math. Phys. 114: 549-552.
12. Kesten, H., 1982, Percolation Theory for Mathematicians. Progress in Probability and Statistics, vol. 2, Birkhauser, Boston, MA, 423 pp. ISBN 3-7643-3107-0.
13. Aizenman M., H. Kesten, and C. M. Newman, 1987, Uniqueness of the infinite cluster and continuity of connectivity functions for short and long-range percolation, Commun. Math. Phys. 111(4): 505-531.
14. Pike, G. E., 1978, Conductivity of thick film (cermet) resistors as a function of metallic particle volume fraction, In: Electrical Transport and Optical Properties of Inhomogeneous Materials, Ed. J. C.Garland and D. B.Tanner, Vol. 40, AIP, New York, pp. 366-371.
15. Kogut, P. M. and J. Straley, 1979, Distribution-induced non-universality of the percolation conductivity exponents, J. Phys. C. Solid State Phys. 12: 2151-2159.
16. Balberg, I., 1987, Recent developments in continuum percolation, Philos. Mag. B 30: 991-1003.
17. Gaillard-Groleas, G., M. Lagier, and D. Sornette, 1990, Critical behaviour in piezoelectric ceramics, Phys. Rev. Lett. 64, 1577.
18. Sornette, D., M. Lagier, S. Roux, and A. Hansen, 1989, Critical piezoelectricity in percolation, J. Phys. France, 50: 2201-2216.
19. Stauffer, D., 1979, Scaling theory of percolation clusters, Phys. Rep. 54: 1-74.
20. Stauffer, D., and A. Aharony, 1994, Introduction to Percolation Theory, 2nd edition, Taylor and Francis, London. 3
21. Berkowitz, B., and I. Balberg, 1993, Percolation theory and its application to groundwater hydrology, Water Resour. Res. 29: 775-794.
22. Sahimi, M., 1993, Fractal and superdiffusive transport and hydrodynamic dispersion in heterogeneous porous media, Transp. Porous Media 13: 3-40.
23. Sahimi, M., 1993, Flow phenomena in rocks - from continuum models to fractals, percolation, cellular automata, and simulated annealing, Rev. Mod. Phys. 65(4): 1393-1534.
24. Sahimi, M., and Y. C. Yortsos, 1990, Applications of fractal geometry to porous media: A review, Paper presented at the 1990 Annual Fall Meeting of the Society of Petroleum Engineers, New Orleans, LA.
25. Bunde, A., and S. Havlin, 1996, Fractals and Disordered Systems, Springer, Berlin.
26. Kunz, H., and B. Souillard, Essential singularity in percolation model, 1978, Phys. Rev. Lett. 40: 133-135.
27. Skal, A. S., and B. I. Shklovskii, 1975, Topology of an infinite cluster in the theory of percolation and its relationship to the theory of hopping conduction, Sov. Phys. Semicond. 8: 1029-1032.
28. Shklovskii, B. I., and A. L. Efros, 1984, Electronic Properties of Doped Semiconductors, Springer, Heidelberg.
29. Pollak, M., 1987, In. Non-Crystalline Semiconductors, CRC Press, Boca Raton, FL, Chapter 5ab.
30. Stauffer, D., 1985, Introduction to Percolation Theory, Taylor and Francis, London.
31. Stanley, H. E., 1971, Introduction to Phase Transitions and Critical Phenomena, Oxford University Press, New York.
32. De 'Bell, K., J. W. Essam, and A. J. Guttman, 1988, On Two Dimensional Directed Percolation, University of Melbourne, Dept. of Mathematics, Parkville.
33. Benfatto, G., and G. Gallavotti, 1995, Renormalization Group, Princeton University Press, Princeton, NJ.
34. Domb, C., and J. L. Lebowitz, 1988, Phase Transitions and Critical Phenomena, Academic, London.
35. Lesne, A., 1998, Renormalization Methods, J. Wiley, New York.
36. Sornette, D., 2004, Critical Phenomena in Natural Sciences: Chaos, Fractals, Selforganization and Disorder: Concepts and Tools, Springer, Heidelberg.
37. Essam, J. W., 1980, Percolation theory, Rep. Prog. Phys. 43: 833-912.
38. Middlemiss, K. M., S. G. Whittington, and D. C. Gaunt, 1980, Monte-Carlo study of the percolation cluster for the square lattice problem, J. Phys. A 13: 1835-1840.
39. Alexandrowizc, Z., 1980, Critically branched chains and percolation clusters, Phys. Lett. A 80: 284-286.
40. Pike, R., and H. E. Stanley, 1981, Order propagation near the percolation threshold, J. Phys. A 14: L169-L177.
41. Fisher, M. E., Theory of condensation and critial point, 1967, Physics 3: 255.
42. Toulouse, G., Perspectives from theory of phase transitions, 1974, Nuovo Cimento B 23: 234-240.
43. Reynolds, P. J.,W. Klein, and H. E. Stanley, 1977, A real-space renormalization group for site and bond percolation, J. Phys. C 10: L167.
44. Miyazima, S., 2005, An exact percolation point for surface filing in a four-dimensional hypercubic lattice, Prog Theor. Phys. 113: 1159-1163.
45. Vyssotsky, V. A., S. B. Gordon, H. L. Frisch, and J. M. Hammersley, 1961, Critical percolation probabilities (bond problem), Phys. Rev. 123: 1566-1567.
46. Essam, J.W., D. S. Gaunt, and A. J. Guttmann, 1978, Percolation theory at critical dimension, J. Phys. A 11: 1983-1990.
47. Sykes, M. F., and M. K. Wilkinson, 1986, Derivation of series expansions for a study of percolation processes, J. Phys. A 19: 3415-3424.
48. Adler, J., Y. Meir, A. B. Harris, and A. Aharony, 1989, Bull Isr. Phys. Soc. 35: 102
49. Ziff, R. M., and B. Sapoval, 1987, The efficient determination of the percolation threshold by a frontier-generating walk in a gradient, J. Phys. A 19: L1169-L1172.
50. Strenski, P. N., R. M. Bradley, J. M. Debierre, 1991, Scaling behavior of percolation surfaces in three dimensions, Phys. Rev. Lett. 66, 1330-1333.
51. Galam, S., and A. Mauger, 1997, A universal formula for percolation thresholds II. Extension to anisotropic and aperiodic lattices, Phys. Rev E. 56: 322.
52. Scher, H., and R. Zallen, 1970, Critical density in percolation processes, J. Chem. Phys. 53: 3759.
53. Shante, V. K. S., and S. Kirkpatrick, 1971, Introduction to percolation theory, Adv. Phys. 20: 325.
54. Garboczi, E. J., K.A. Snyder, J. F. Douglas, and M. F. Thorpe, 1995, Geometrical percolation threshold of overlapping ellipsoids, Phys. Rev. E 52, 819-828.