ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)


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Podlazov A. V. Two-dimensional self-organized critical sandpile models with anisotropic dynamics of the activity propagation. Izvestiya VUZ. Applied Nonlinear Dynamics, 2012, vol. 20, iss. 6, pp. 25-46. DOI: 10.18500/0869-6632-2012-20-6-25-46

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Language: 
Russian
Article type: 
Article
UDC: 
519.6

Two-dimensional self-organized critical sandpile models with anisotropic dynamics of the activity propagation

Autors: 
Podlazov Andrej Viktorovich, Keldysh Institute of Applied Mathematics (Russian Academy of Sciences)
Abstract: 

We numerically and analytically investigate two self-organized critical sandpile models with anisotropic dynamics of the activity propagation – Dhar–Ramaswamy and discrete Feder–Feder models. The full set of critical indices for these models is theoretically determined. We also give systematical statement of the finite-size scaling ansatz and of its use for the solving of self-organized critical systems. Studying the discrete Feder–Feder model we find and explain a number of nontrivial phenomena, such as spontaneous anisotropy, anomalous diffusion and the appearance of midline ditch of filling. 

Reference: 
  1. Bak P, Tang C, Wiesenfeld K. Self-organized criticality: An explanation of 1/f-noise. Phys. Rev. Lett. 1987;59(4):381–384. DOI: 10.1103/physrevlett.59.381.
  2. Bak P, Tang C, Wiesenfeld K. Self-organized criticality. Phys. Rev. A. 1988;38(1):364–374. DOI: 10.1103/PhysRevA.38.364.
  3. Ivashkevich EV. Critical behavior of the sandpile model as a self-organizing branching process. Phys. Rev. Lett. 1996;76(18):3368–3371. DOI: 10.1103/physrevlett.76.3368.
  4. Dhar D, Ramaswamy R. Exactly solved model of self-organized critical phenomena. Phys. Rev. Lett. 1989;63(16):1659–1662. DOI: 10.1103/PhysRevLett.63.1659.
  5. Christensen K, Olami Z. Sandpile models with and without an underlying spatial structure. Phys. Rev. E. 1993;48(5):3361–3372. DOI: 10.1103/PhysRevE.48.3361.
  6. Dhar D, Majumdar SN. Abelian sandpile model on the Bethe lattice. J. Phys. A. Math. Gen. 1990;23:4333–4351. DOI: 10.1088/0305-4470/23/19/018.
  7. Ma SK. Modern Theory of Critical Phenomena. Routledge; 2000. 561 p.
  8. Manna SS. Two-state model of self-organized criticality. L. Phys. A. Math. Gen. 1991;24(7):L363–L371. DOI: 10.1088/0305-4470/24/7/009.
  9. Podlazov AV. Two-dimensional self-organized critical Manna model. Keldysh Preprint. No. 42. Moscow: Keldysh Institute of Applied Mathematics; 2012. 20 p. (in Russian). Available from: http://library.keldysh.ru/preprint.asp?id=2012-42.
  10. Podlazov AV. Comparison of two-dimensional isotropic conservative SOC sandpile models. Keldysh Preprint. No. 43. Moscow: Keldysh Institute of Applied Mathematics; 2012. 12 p. (in Russian). Available from: http://library.keldysh.ru/preprint.asp?id=2012-43.
  11. Malinetskii GG, Podlazov AV. Comparison of two-dimensional isotropic conservative self-organized-critical sand-heap models. Herald of the Bauman Moscow State Technical University. Series Natural Sciences. Special Issue «Mathematical Modeling in Engineering». 2012;(2):119–128 (in Russian).
  12. Kadanoff LP, Nagel SR, Wu L, Zhou S. Scaling and universality in avalanches. Phys. Rev. A. 1989;39(12):6524–6537. DOI: 10.1103/PhysRevA.39.6524.
  13. Bak P. How Nature Works: The Science of Self-Organized Criticality. Springer-Verlag, New York; 1996. 212 p. DOI: 10.1007/978-1-4757-5426-1.
  14. Sornette D, Johansen A, Dornic I. Mapping self-organized criticality onto criticality. J. Phys. I France. 1995;5(3):325–335. DOI: 10.1051/jp1:1995129.
  15. Clar S, Drossel B, Schwabl F. Forest fires and other examples of self-organized criticality. J. Phys. Condens. Matter. 1996;8(37):6803–6825. DOI: 10.1088/0953-8984/8/37/004.
  16. Feder HJS, Feder J. Self-organized criticality in a stick-slip process. Phys. Rev. Lett. 1991;66(20):2669–2672. DOI: 10.1103/physrevlett.66.2669.
Received: 
13.04.2012
Accepted: 
28.11.2012
Published: 
29.03.2013
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