Karin Dahmen1 Wendelin Wright2 Dmitry Denisov3 Peter Schall3 Jonathan Uhl4

1, University of Illinois at Urbana Champaign, Urbana, Illinois, United States
2, Bucknell University, Lewisburg, Pennsylvania, United States
3, University of Amsterdam, Amsterdam, , Netherlands
4, Retired, Los Angeles, California, United States

Slowly-compressed nano-crystals, bulk metallic glasses, 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, they also appear to show similar slip dynamics.

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 temporal slip profiles. The analysis draws on tools from statistical physics and the renormalization group. The results enable extrapolations from one scale to another, and from one force to another, across different materials and structures, from nanocrystals to earthquakes. Connections to neuron avalanches in the brain and recent observations on stars will also be discussed, extending the range of scales to 16 decades in length.


[1] Jonathan T. Uhl, Shivesh Pathak, Danijel Schorlemmer, Xin Liu, Ryan Swindeman, Braden A.W. Brinkman,, Michael LeBlanc, Georgios Tsekenis, Nir Friedman, Robert Behringer, Dmitry Denisov, Peter Schall, Xiaojun Gu, Wendelin J. Wright, Todd Hufnagel, Andrew Jennings, Julia R. Greer, P.K. Liaw, Thorsten Becker, Georg Dresen, and Karin A. Dahmen, Universal Quake Statistics: From Compressed Nanocrystals to Earthquakes, Sci. Rep. 5, 16493 (2015).

[2] N. Friedman, A. T. Jennings, G. Tsekenis, J.-Y. Kim, J. T. Uhl, J. R. Greer, and K. A. Dahmen. Statistics of dislocation slip-avalanches in nano-sized single crystals show tuned critical behavior predicted by a simple mean field model, Phys. Rev. Lett. 109, 095507 (2012).

[3] James Antonaglia, Wendelin J. Wright, Xiaojun Gu, Rachel R. Byer, Todd C. Hufnagel, Michael LeBlanc, Jonathan T. Uhl, and Karin A. Dahmen, Bulk Metallic Glasses Deform via Slip Avalanches, Phys. Rev. Lett. 112, 155501 (2014).

[4] N. Friedman, S. Ito, B.A.W. Brinkman, L. DeVille, K. Dahmen, J. Beggs, and T. Butler. Universal critical dynamics in high resolution neuronal avalanche data. Phys. Rev. Lett. 108, 208102 (2012).

[5] Mohammed A. Sheikh, Richard L. Weaver, and Karin A. Dahmen, Avalanche Statistics Identify Intrinsic Stellar Processes near Criticality in KIC 8462852, Phys. Rev. Lett. 117, 261101 (2016).

[6] Dmitry V. Denisov, Kinga A. Loerincz, Wendelin J. Wright, Todd C. Hufnagel, Aya Nawano, Xiaojun Gu, Jonathan T. Uhl, Karin A. Dahmen & Peter Schall, Universal slip dynamics in metallic glasses and granular matter: linking frictional weakening with inertial effects, Sci. Rep. 7, 43376 (2017).