Defects in self-organized criticality: a directed coupled map lattice model

Tadic', Bosiljka ; Ramaswamy, Ramakrishna (1996) Defects in self-organized criticality: a directed coupled map lattice model Physical Review E - Statistical, Nonlinear and Soft Matter Physics, 54 (4). pp. 3157-3164. ISSN 1539-3755

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Official URL: http://pre.aps.org/abstract/PRE/v54/i4/p3157_1

Related URL: http://dx.doi.org/10.1103/PhysRevE.54.3157

Abstract

We study a directed coupled map lattice model in d=2 dimensions, with two degrees of freedom associated with each lattice site. The two freedoms are coupled at a fraction c of lattice bonds acting as quenched random defects. The system is driven (by adding "energy," say) in one of the degrees of freedom at the top of the lattice, and the relaxation rules depend on the local difference between the two variables at a lattice site. In the case of conservative dynamics, at any concentration of defects the system reaches a self-organized critical state with universal critical exponents close to the mean-field values Τt=1, Τs=2/3, and Τn=½, for the integrated distributions of avalanche durations (t), size (s), and released energy (n), respectively. The probability distributions follow the general scaling formP(X,L)=L−αP(XL-D), where α?1 is the scaling exponent for the distribution of avalanche lengths, X stands for t, s, or n, and DX is the (independently determined) fractal dimension with respect to X. The distribution of current through the system is, however, nonuniversal, and does not show any apparent scaling form. In the case of nonconservative dynamics-obtained by incomplete energy transfer at the defect bonds-the system is driven out of the critical state. In the scaling region close to c=0 the probability distributions exhibit the general scaling formP(X,c,L)=X-ΤXP[X/ξX(c),XL-DX],here αX=α/DXand the corresponding coherence length ξX(c) depends on the concentration of defect bonds c as ξX(c)∼c-DX.

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