1202.2553 (I. V. Bezsudnov et al.)

Evolution of burst distribution in fiber bundle model    [PDF]

I. V. Bezsudnov, A. A. Snarskii

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.

View original: http://arxiv.org/abs/1202.2553