Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2012-02-12
Physics
Condensed Matter
Disordered Systems and Neural Networks
Scientific paper
We consider a fiber bundle model with a equal load sharing and uniformly distributed breakdown thresholds. A unified probability-theoretic approach was used to describe bundle under continuous and discrete load increase. It was shown that the ratio of distribution D(d) of avalanches of sizes d to the number of bundle load steps exactly corresponds to burst probability of size d. Evolution of s - power law distribution exponent of D(d) was studied as a function of loading step and bundle size. It was shown that s does not depend on bundle size. In the numerical experiment, dependence s on loading step was obtained with fiber bundle size up to N=10^10. The regions of s values constancy and the transition region were found. A distribution of fiber bursts on each loading step was recovered in the numerical simulations. It was shown that a change in the type of this distribution is the reason for evolution of s values in the range of -3 - -5/2.
Bezsudnov I. V.
Snarskii A. A.
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