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Dorogovtsev SN, Mendes JF, Pogorelov YG. Bak-sneppen model near zero dimension. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 2000;62(1):295-8doi: 10.1103/physreve.62.295.
Dorogovtsev, S. N., Mendes, J. F., & Pogorelov, Y. G. (2000). Bak-sneppen model near zero dimension. Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 62(1), 295-8. https://doi.org/10.1103/physreve.62.295
Dorogovtsev, et al. "Bak-sneppen model near zero dimension." Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics vol. 62,1 (2000): 295-8. doi: https://doi.org/10.1103/physreve.62.295
Dorogovtsev SN, Mendes JF, Pogorelov YG. Bak-sneppen model near zero dimension. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 2000 Jul;62(1):295-8. doi: 10.1103/physreve.62.295. PMID: 11088462.
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Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 2000 Jul;62(1):295-8. doi: 10.1103/physreve.62.295.

Bak-sneppen model near zero dimension.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

Dorogovtsev, Mendes, Pogorelov

Affiliations

  1. Departamento de Fisica and Centro de Fisica do Porto, Faculdade de Cieinsertion markncias, Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto, Portugal and A. F. Ioffe Physico-Technical Institute, 194021 St. Petersburg, Russia.

PMID: 11088462 DOI: 10.1103/physreve.62.295

Abstract

We consider the Bak-Sneppen model near zero dimension, where the avalanche exponent tau is close to 1 and the exponents &mgr; and sigma are close to 0. We demonstrate that tau-1=&mgr;-sigma=exp-&mgr;(-1)-gamma+ small middle dot small middle dot small middle dot in this limit, where gamma is Euler's constant. The avalanche hierarchy equation is rewritten in a form that makes it possible to find the relation between the critical exponents sigma and &mgr; with high accuracy. We obtain precise values of the critical exponents for the one and two-dimensional Bak-Sneppen model and for the one-dimensional anisotropic Bak-Sneppen model.

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