Precursors of catastrophe in the Bak-Tang-Wiesenfeld, Manna, and random-fiber-bundle models of failure

2001/07/31 by Srutarshi Pradhan, Bikas K. Chakrabarti · 9 citations
Engineering · Materials Science · Physics and Astronomy · #Granular flow and fluidized beds #Material Dynamics and Properties #Theoretical and Computational Physics #cond-mat.stat-mech

paper · pdf · doi:10.1103/physreve.65.016113

published as Phys. Rev. E 65, 016113 (2001) · 13 pages, 9 figures (eps)

arxiv created 2001/11/12 · openalex publication_date 2001/12/17 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We have studied precursors of the global failure in some self-organized critical models of sandpile [in Bak-Tang-Wiesenfeld (BTW) and Manna models] and in the random-fiber-bundle model (RFB). In both BTW and Manna model, as one adds a small but fixed number of sand grains (heights) to any central site of the stable pile, the local dynamics starts and continues for an average relaxation time \ensuremathτ and an average number of topplings \ensuremathΔ spread over a radial distance \ensuremathξ. We find that these quantities all depend on the average height h_av of the pile and they all diverge as h_av approaches the critical height h_c from below: \ensuremathΔ\ensuremath∼(h_c\ensuremath-h_av)^\ensuremath-\ensuremathδ,\ensuremathτ\ensuremath∼(h_c\ensuremath-h_av)^\ensuremath-\ensuremathγ, and \ensuremathξ\ensuremath∼(h_c\ensuremath-h_av)^\ensuremath-\ensuremathν. Numerically, we find \ensuremathδ\ensuremath≃2.0,\ensuremathγ\ensuremath≃1.2, and \ensuremathν\ensuremath≃1.0 for both BTW and Manna model in two dimensions. In the strained RFB model, we find that the breakdown susceptibility \ensuremathχ (giving the differential increment of the number of broken fibers due to increase in external load) and the relaxation time \ensuremathτ, both diverge as the applied load or stress \ensuremathσ approaches the network failure threshold \ensuremathσ_c from below: \ensuremathχ\ensuremath∼(\ensuremathσ_c\ensuremath-\ensuremathσ)^\ensuremath-1/2 and \ensuremathτ\ensuremath∼(\ensuremathσ_c\ensuremath-\ensuremathσ)^\ensuremath-1/2. These self-organized dynamical models of failure, therefore, show some definite precursors with robust power laws long before the failure point. Such well-characterized precursors should help predicting the global failure point of the systems in advance.

Citations

• The statistical theory of the strength of bundles of threads. I

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