The deformation of many solid
materials is not continuous, but discrete, with intermittent slips similar to
earthquakes. Here, we suggest that the statistical distributions of the slips,
such as the slip-size distributions, reflect tuned criticality, with
approximately the same regular (power-law) functions, and the same tunable
exponential cutoffs, for systems spanning 13 decades in length, from tens of
nanometers to hundreds of kilometers; for compressed nano-crystals, to
amorphous materials, to earthquakes. The similarities are explained by a
simple analytic model, which suggests that results are transferable across
scales. This study provides a unified understanding of fundamental properties
of shear-induced deformation in systems ranging from nanocrystals to
earthquakes. It also provides many new predictions for future experiments and
simulations. The studies draw on methods from the theory of phase transitions,
the renormalization group, and numerical simulations. Connections to other
systems with avalanches, such as magnets and neuron firing avalanches in the
brain are also discussed.
This Colloquium is jointly sponsored by Fields Institute for Research in Mathematical Sciences and the Department of Phyics.