Simple Cubic Random-Site Percolation Thresholds for Complex Neighbourhoods

Reports on Mathematical Physics

Volumn 70, Issue 2, 2012, Pages 163-169

  Kurzawski, Łukasz ^a   Malarz, Krzysztof ^a  

^a AGH UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Poland)

Author keywords

Computer simulations; Percolation thresholds; Site percolation

Indexed keywords

EID: 84870328653     PISSN: 00344877     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0034-4877(12)60036-6     Document Type: Article

References (68)

1. Broadbent S.R., Hammersley J.M. Proc. Cambridge Phil. Soc. 1957, 53:629-641.
2. Hammersley J.M. Proc. Cambridge Phil. Soc. 1957, 53:642-645.
3. Frisch H.L., Hammersley J.M., Welsh D.J.A. Phys. Rev. 1962, 126:949-951.
4. Sykes M.F., Glen M. J. Phys. A 1976, 9:87-95.
5. Sykes M.F., Gaunt D.S., Glen M. J. Phys. A 1976, 9:97-103.
6. Sykes M.F., Gaunt D.S., Glen M. J. Phys. A 1976, 9:715-724.
7. Sykes M.F., Gaunt D.S., Glen M. J. Phys. A 1976, 9:725-730.
8. Gaunt D.S., Sykes M.E. J. Phys. A 1976, 9:1109-1116.
9. Wierman J.C., Naor S.P., Cheng R. Phys. Rev. E 2005, 72:066116.
10. Rosowsky A. Eur. Phys. J. B 2000, 15:77-86.
11. Halperin B.I., Bergman D.J. Physica B 2010, 405:2908-2914.
12. Shearing P.R., Brett D.J.L., Brandon N.P. International Materials Reviews 2010, 55:347-363.
13. Silva J., Simoes R., Lanceros-Mendez S., Vaia R. EPL 2011, 93:37005.
14. Suzuki S.U., Sasaki A. J. Theor. Biol. 2011, 276:117-125.
15. Lindquist J., Junling Ma, van den Driessche P., et al. J. Math. Biol. 2011, 62:143-164.
16. Naumova E.N., Gorski J., Naumov Yu.N. Annales Zoologici Fennici 2008, 45:369-384.
17. Floyd W., Kay L., Shapiro M. Bull. Math. Biol. 2008, 70:713-727.
18. Camelo-Neto G., Coutinho S. J. Stat. Mech. 2011, P06018.
19. Guisoni N., Loscar E.S., Albano E.V. Phys. Rev. E 2011, 83:011125.
20. Simeoni A., Salinesi P., Morandini F. Int. J. Wildland Fire 2011, 20:625-632.
21. Malarz K., Kaczanowska S., Kulakowski K. Int. J. Mod. Phys. C 2002, 13:1017-1031.
22. Malarz K., Kaczanowska S., Kulakowski K. Frontiers on Nonlinear Dynamics 2004, 3:334-343.
23. Amiaz Y., Sorek S., Enzel Y., et al. Water Resources Research 2011, 47:W10513.
24. Bolandtaba S.F., Skauge A. Transport in Porous Media 2011, 89:357-382.
25. Mourzenko V.V., Thovert J.-F., Adler P.M. Phys. Rev. E 2011, 84:036307.
26. Stauffer D., Aharony A. Introduction to Percolation Theory 1994, Taylor and Francis, London.
27. Kesten H. Percolation Theory for Mathematicians 1982, Brikhauser, Boston.
28. Sahimi M. Applications of Percolation Theory 1994, Taylor and Francis, London.
29. Stauffer D. Physica A 1997, 242:1-7.
30. Landau D.P., Binder K. A Guide to Monte Carlo Simulation in Statistical Physics 2005, Cambridge University Press, Cambridge.
31. Ł. Kurzawski: M.Sc. Thesis, AGH University of Science and Technology, Kraków 2011.
32. Hoshen J., Kopelman R. Phys. Rev. B 1976, 14:3438-3445.
33. Malarz K., Galam S. Phys. Rev. E 2005, 71:016125.
34. Galam S., Malarz K. Phys. Rev. E 2005, 72:027103.
35. Majewski M., Malarz K. Acta Phys. Pol. B 2007, 38:2191-2199.
36. Finite Size Scaling and Numerical Simulation of Statistical Systems 1990, World Scientific, Singapore. V. Privman (Ed.).
37. Newman M.E.J., Ziff R.M. Phys. Rev. E 2001, 85:016706.
38. Lima F.W.S., Mostowicz J., Malarz K. Commun. Conzput. Phys. 2011, 10:912-919.
39. Santos J.C., Lima F.W.S., Malarz K. Physica A 2011, 390:359-364.
40. Lima F.W.S., Malarz K. Int. J. Mod. Plzys. C 2006, 17:1273-1283.
41. Lima F.W.S., Sousa A.O., Sumuorc M.A. Physica A 2008, 387:3503-3510.
42. Stauffer D., Sousa A.O., Moss de Oliveira S. Int. J. Mod. Phys. C 2000, 11:1239-1245.
43. Moreira A.A., Andrade J.S., Stauffer D. Int. J. Mod. Phys. C 2001, 12:39-42.
44. Sousa A.O. Physica A 2005, 348:701-710.
45. ISO Technical Advisory Group, Working Group 3 Guide to the Expression of Uncertainty in Measurement 1993, International Organisation for Standardization, Geneva.
46. Gleser L.J. Statist. Sci. 1988, 13:277-290.
47. Grassberger P. J. Phys. A 1992, 25:5867-5888.
48. Lorenz C.D., Ziff R.M. J. Phys. A 1998, 31:8147-8157.
49. Jan N., Stauffer D. Int. J. Mod. Phys. C 1998, 9:341-347.
50. Ballesteros P.N., Fernandez L.A., Martin-Mayor V., et al. J. Phys. A 1999, 32:1-13.
51. Deng Youjin, Blöte H.W.J. Phys. Rev. E 2005, 72:016126.
52. Acharyya M., Stauffer D. Int. J. Mod. Phys. C 2009, 9:643-647.
53. Škvor J., Nezbeda I. Phys. Rev. E 2009, 79:041141.
54. Domb C., Dalton N.W. Proc. Phys. Soc. 1966, 89:859-871.
55. R. M. Ziff and S. Torquato: priv. commun.
56. Vyssotsky V.A., Frisch H.L., Sonnenblick E., Hammersley J.M. Phys. Rev. 1961, 124:1021-1022.
57. Silverman A., Adler J. Phys. Rev. B 1990, 42:1369-1373.
58. van der Marck S.C. Int. J. Mod. Phys. C 1998, 9:529-540.
59. Lorenz C.D., May R., Ziff R.M. J. Stat. Phys. 2000, 98:961-970.
60. Bradley R.M., Strenski P.N., Debierre J.-M. Phys. Rev. B 1991, 44:76-84.
61. Gaunt D.S., Sykes M.F. J. Phys. A 1983, 16:783-799.
62. Lorenz C.D., Ziff R.M. J. Phys. A 1998, 31:8147-8157.
63. Tahir-Kheli J., Goddard W.A. Phys. Rev. B 2007, 76:014514.
64. Sahimi M., Hughes B.D., Scriven L.E., Davis T. J. Phys. A 1983, 16:L67-L71.
65. Galam S., Mauger A. J. Appl. Phys. 1994, 75:5526-5528.
66. Galam S., Mauger A. Physica A 1994, 205:502-510.
67. van der Marck S.C. Phys. Rev. E 1997, 55:1228-1229.
68. http://www.rubiks.com/.