Complexity of Fracturing in Terms of Non-Extensive Statistical Physics: From Earthquake Faults to Arctic Sea Ice Fracturing

Fracturing processes within solid Earth materials are inherently a complex phenomenon so that the underlying physics that control fracture initiation and evolution still remain elusive. However, universal scaling relations seem to apply to the collective properties of fracturing phenomena. In this a...

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Bibliographic Details
Published in:Entropy
Main Authors: Filippos Vallianatos, Georgios Michas
Format: Article in Journal/Newspaper
Language:English
Published: MDPI AG 2020
Subjects:
Q
Online Access:https://doi.org/10.3390/e22111194
https://doaj.org/article/1ef7e3a85c3a4bb5866281dde20254f2
Description
Summary:Fracturing processes within solid Earth materials are inherently a complex phenomenon so that the underlying physics that control fracture initiation and evolution still remain elusive. However, universal scaling relations seem to apply to the collective properties of fracturing phenomena. In this article we present a statistical physics approach to fracturing based on the framework of non-extensive statistical physics (NESP). Fracturing phenomena typically present intermittency, multifractality, long-range correlations and extreme fluctuations, properties that motivate the NESP approach. Initially we provide a brief review of the NESP approach to fracturing and earthquakes and then we analyze stress and stress direction time series within Arctic sea ice. We show that such time series present large fluctuations and probability distributions with “fat” tails, which can exactly be described with the q -Gaussian distribution derived in the framework of NESP. Overall, NESP provide a consistent theoretical framework, based on the principle of entropy, for deriving the collective properties of fracturing phenomena and earthquakes.