Flooding transition in the topography of toppling surfaces of stochastic and rotational sandpile models

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 85, Issue 3, 2012, Pages

  Ahmed, J A ^a   Santra, S B ^a  

^a INDIAN INSTITUTE OF TECHNOLOGY GUWAHATI   (India)

Author keywords

[No Author keywords available]

Indexed keywords

CONTINUOUS PHASE TRANSITIONS; CRITICAL EXPONENT; CRITICAL POINTS; CRITICAL REGIMES; FINITE-SIZE SCALING THEORY; HURST EXPONENTS; POWER LAW DISTRIBUTION; SAND-PILE MODELS; SELF AFFINITY; STEADY STATE; UNIVERSALITY CLASS;

FRACTAL DIMENSION; PHASE TRANSITIONS; SAND; SOLVENTS; STOCHASTIC SYSTEMS;

STOCHASTIC MODELS;

EID: 84858241836     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.85.031111     Document Type: Article

References (57)

1. P. Meakin, Fractals, Scaling and Growth Far From Equilibrium (Cambridge University Press, Cambridge, 1998).
2. D. L. Turcotte, Fractals and Chaos in Geology and Geo-physics (Cambridge University Press, Cambridge, 1992).
3. S. Lovejoy, Science SCIEAS 0036-8075 10.1126/science.216.4542.185 26, 185 (1982);
4. J. D. Pelletier, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett. 78.2672 78, 2672 (1997).
5. E. Bouchaud, G. Lapasset, and J. Planès, Europhys. Lett. EULEEJ 0295-5075 10.1209/0295-5075/13/1/013 13, 73 (1990).
6. M. J. Alava, P. K. V. V. Nukala, and S. Zapperi, Adv. Phys. ADPHAH 0001-8732 10.1080/00018730300741518 55, 349 (2006); (Pubitemid 43884572)
7. S. Santucci, M. Grob, R. Toussaint, J. Schmittbuhl, A. Hansen, and K. J. Måløy, Europhys. Lett. EULEEJ 0295-5075 10.1209/0295-5075/92/44001 92, 44001 (2010).
8. D. L. Blair and A. Kudrolli, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.166107 94, 166107 (2005). (Pubitemid 40648271)
9. S. V. Buldyrev, S. Havlin, and H. E. Stanley, Physica A PHYADX 0378-4371 10.1016/0378-4371(93)90518-9 200, 200 (1993).
10. J. Schmittbuhl, J.-P. Vilotte, and S. Roux, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/26/22/014 26, 6115 (1993).
11. Z. Olami and R. Zeitak, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.76.247 76, 247 (1996).
12. G. Wagner, P. Meakin, J. Feder, and T. Jøssang, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.55.1698 55, 1698 (1997).
13. V. V. Mourzenko, J.-F. Thovert, and P. M. Adler, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.59.4265 59, 4265 (1999).
14. M. Sahimi, AIChE J. AICEAC 0001-1541 10.1002/aic.690410205 41, 229 (1995).
15. P. Gouze, C. Noiriel, C. Bruderer, D. Loggia, and R. Leprovost, Geophys. Res. Lett. GPRLAJ 0094-8276 10.1029/2002GL016755 30, 1267 (2003).
16. A. A. Saberi, Appl. Phys. Lett. APPLAB 0003-6951 10.1063/1.3502568 97, 154102 (2010).
17. H. J. Jensen, Self-Organized Criticality (Cambridge University Press, Cambridge, 1998).
18. D. Dhar, Physica A PHYADX 0378-4371 10.1016/S0378-4371(99)00149-1 270, 69 (1999).
19. S. B. Santra, S. Ranjita Chanu, and D. Deb, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.75.041122 75, 041122 (2007). (Pubitemid 46686349)
20. P. Bak, C. Tang, and K. Wiesenfeld, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.59.381 59, 381 (1987);
21. P. Bak, C. Tang, and K. Wiesenfeld, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.38.364 38, 364 (1988).
22. J. A. Ahmed and S. B. Santra, Europhys. Lett. EULEEJ 0295-5075 10.1209/0295-5075/90/50006 90, 50006 (2010).
23. S. Lübeck, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.61.204 61, 204 (2000);
24. C. Tebaldi, M. De Menech, and A. L. Stella, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.83.3952 83, 3952 (1999).
25. M. Paczuski and S. Boettcher, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.77.111 77, 111 (1996).
26. A. Vespignani, R. Dickman, M. A. Muñoz, and S.Zapperi, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.81.5676 81, 5676 (1998);
27. R. Dickman, A. Vespignani, and S.Zapperi, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.57.5095 57, 5095 (1998).
28. A. Vespignani, R. Dickman, M. A. Muñoz, and S. Zapperi, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.62.4564 62, 4564 (2000).
29. R. Dickman, M. Alava, M. A. Muñoz, J. Peltola, A. Vespignani, and S. Zapperi, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.64.056104 64, 056104 (2001);
30. M. Alava and M. A. Muñoz, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.65.026145 65, 026145 (2002). (Pubitemid 40619474)
31. M. J. Alava and K. B. Lauritsen, Europhys. Lett. EULEEJ 0295-5075 10.1209/epl/i2001-00189-8 53, 563 (2001);
32. M. Alava, J. Phys. Condens. Matter JCOMEL 0953-8984 10.1088/0953-8984/14/ 9/324 14, 2353 (2002). (Pubitemid 34255465)
33. J. Krug, J. E. S. Socolar, and G. Grinstein, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.46.R4479 46, R4479 (1992).
34. J. G. Oliveira, J. F. F. Mendes, and G. Tripathy, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.69.031105 69, 031105 (2004).
35. D. Stauffer and A. Aharony, Introduction to Percolation Theory, 2nd ed. (Taylor and Francis, London, 1994).
36. A. Chessa, H. E. Stanley, A. Vespignani, and S. Zapperi, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.59.R12 59, R12 (1999).
37. K. Christensen and Z. Olami, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.48.3361 48, 3361 (1993);
38. A.Ben-Hur and O. Biham, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.53.R1317 53, R1317 (1996);
39. S. Lübeck and K. D. Usadel, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.55.4095 55, 4095 (1997).
40. A. A. Saberi, M. D. Niry, S. M. Fazeli, M. R. Rahimi Tabar, and S. Rouhani, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.77.051607 77, 051607 (2008). (Pubitemid 351768338)
41. B. B. Mandelbrot, The Fractal Geometry of Nature (Freeman, New York, 1992).
42. S. B. Ramisetti, C. Campañá, G. Anciaux, J. F. Molinari, M. H. Müser, and M. O. Robbins, J. Phys. Condens. Matter JCOMEL 0953-8984 10.1088/0953-8984/23/21/215004 23, 215004 (2011).
43. A. Hansen and J. Mathiesen, in Modeling Critical and Catastrophic Phenomena in Geoscience: A Statistical Physics Approach, edited by, P. Bhattacharyya, and, B. K. Chakrabarti, Lecture Notes in Physics, Vol. 705 (Springer, Berlin, 2006), pp. 93-110.
44. P. G. de Gennes, Scaling Concepts in Polymer Physics (Cornell University Press, Ithaca, NY, 1979).
45. B. K. Chakrabarti and S. S. Manna, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/16/4/003 16, L113 (1983);
46. S. Redner and I. Majid, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/16/ 9/005 16, L307 (1983).
47. H. J. W. Blöte and H. J. Hilhorst, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/17/3/004 17, L111 (1984);
48. K.Y. Lin, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/18/3/008 18, L145 (1985).
49. H. Hinrichsen, Adv. Phys. ADPHAH 0001-8732 10.1080/00018730050198152 49, 815 (2000), and references therein. (Pubitemid 35381843)
50. S. B. Santra and I. Bose, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/24/10/021 24, 2367 (1991), and references therein.
51. S. Sinha and S. B. Santra, Eur. Phys. J. B EPJBFY 1434-6028 10.1140/epjb/e2004-00224-8 39, 513 (2004), and references therein.
52. D. Dhar and R. Ramaswamy, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.63.1659 63, 1659 (1989).
53. S. Lübeck, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.56.1590 56, 1590 (1997);
54. O. Biham, E. Milshtein, and O. Malcai, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.63.061309 63, 061309 (2001).
55. S. S. Manna, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/24/7/009 24, L363 (1991).
56. J. A. Ahmed and S. B. Santra, Eur. Phys. J. B EPJBFY 1434-6028 10.1140/epjb/e2010-00198-x 76, 13 (2010).
57. Rossi M. Pastor-Satorras R. Vespignani A. Phys. Rev. Lett. 2000 85 1803 PRLTAO 0031-9007 10.1103/PhysRevLett.85.1803.