Generalized q-Analysis of Log-Periodicity: Applications to Critical Ruptures

Details Generalized q-Analysis of Log-Periodicity: Applications to Critical Ruptures Generalized q-Analysis of Log-Periodicity: Applications to Critical Ruptures

2002-01-25

arxiv.org/abs/cond-mat/0201458v1

Phys. Rev. E 66, 046111 (2002) (8 pages)

Physics

Condensed Matter

Statistical Mechanics

12 pages of text (latex) + 47 eps figures + 3 tables (36 pages in total)

Scientific paper

10.1103/PhysRevE.66.046111

We introduce a generalization of the q-analysis, which provides a novel non-parametric tool for the description and detection of log-periodic structures associated with discrete scale invariance. We use this generalized q-analysis to construct a signature called the (H,q)-derivative of discrete scale invariance, which we use to detect the log-periodicity in the energy release rate and its cumulative preceding the rupture of five pressure tanks made of composite carbon-matrix material. We investigate the significance level of the spectral Lomb periodogram of the optimal (H,q)-derivative. We confirm and strengthen previous parametric results that the energy release rate and it cumulative exhibit log-periodicity before rupture. However, our tests to use this method as a scheme for the prediction of the critical value of the stress at rupture are not encouraging.

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