{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/generalized-q-analysis-of-log-periodicity","title":"Generalized q-Analysis of Log-Periodicity: Applications to Critical Ruptures","arxiv_id":"cond-mat/0201458","date":"2002-01-25","proceeding":null,"authors":["Wei-Xing Zhou","Didier Sornette"],"abstract":"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.","url_abs":"https://arxiv.org/abs/cond-mat/0201458v1","url_pdf":"https://arxiv.org/pdf/cond-mat/0201458v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"generalized-q-analysis-of-log-periodicity","repo_url":"https://github.com/thebubbleindex/thebubbleindex","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}