Universal Quake Statistics: From Compressed Nanocrystals to Earthquakes

Creators: Uhl, Jonathan T.; Pathak, Shivesh; Schorlemmer, Danijel; Liu, Xin; Swindeman, Ryan; Brinkman, Braden A. W.; LeBlanc, Michael; Tsekenis, Georgios; Friedman, Nir; Behringer, Robert; Denisov, Dmitry; Schall, Peter; Gu, Xiaojun; Wright, Wendelin J.; Hufnagel, Todd; Jennings, Andrew; Greer, Julia R.; Liaw, P. K.; Becker, Thorsten; Dresen, Georg; Dahmen, Karin A.

Abstract

Slowly-compressed single crystals, bulk metallic glasses (BMGs), rocks, granular materials, and the earth all deform via intermittent slips or "quakes". We find that although these systems span 12 decades in length scale, they all show the same scaling behavior for their slip size distributions and other statistical properties. Remarkably, the size distributions follow the same power law multiplied with the same exponential cutoff. The cutoff grows with applied force for materials spanning length scales from nanometers to kilometers. The tuneability of the cutoff with stress reflects "tuned critical" behavior, rather than self-organized criticality (SOC), which would imply stress-independence. A simple mean field model for avalanches of slipping weak spots explains the agreement across scales. It predicts the observed slip-size distributions and the observed stress-dependent cutoff function. The results enable extrapolations from one scale to another, and from one force to another, across different materials and structures, from nanocrystals to earthquakes.

Additional Information

© 2015 Nature Publishing Group. This work is licensed under a Creative Commons Attribution 4.0 International License. The images or other third party material in this article are included in the article's Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder to reproduce the material. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/. Received: 18 June 2015; Accepted: 14 October 2015; Published: 17 November 2015. We thank Matthew Brinkman for creating Fig. 1. We thank Thomas Goebel for the data on rocks. We thank James Antonaglia, James Beadsworth, Yehuda Ben-Zion, Corey Fyock, Jordan Sickle, and Li Shu for helpful conversations. We acknowledge support from the US National Science Foundation (NSF) DMR 10-05209, DMS 10-69224 (KD), CAREER-award DMR-0748267, ONR Grant-No. N00014-09-1-0883 (JRG), DMR-1042734 (WW), DMR-1107838 (TCH), DMR-0231320, DMR-0909037, CMMI-0900271, CMMI-1100080 (PKL), SCEC, MGA, NSF PHY11-25915, the Kavli Institute for Theoretical Physics at UC Santa Barbara, and the Aspen Center for Physics. KD and PKL acknowledge support from the Department of Energy (DOE), Office of Fossil Energy, National Energy Technology Laboratory (NETL), DE-FE-0011194. PKL acknowledges support from the DOE/NETL (DE-FE-0008855) and the support of the U.S. Army Research Office project (W911NF-13-1-0438). Author Contributions: J.U. and KD devised and led the study. S.P., X.L. and R.S. contributed a large part of the data analysis together with M.L., B.B., G.T. and N.F. D.S. contributed the earthquake data and its analysis. Thomas Goebel, D.S., T.B. and G.D. contributed the data on rocks. W.W., X.G., and T.H. contributed the data on bulk metallic glasses. R.B., D.D. and P.S., contributed the data on granular materials. A.J. and J.R.G. contributed the data on nanocrystals. All authors contributed expertise and ideas to the project. J.U., S.P. and K.D. wrote the manuscript with input from P.L. and all other coauthors. The authors declare no competing financial interests.

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