Universality class of dislocation avalanches in microcrystals
In plain words
Small metal crystals deform in sudden jumps called avalanches, whose sizes follow a power law, much like earthquakes. Whether these jumps obey the same simple theory as other avalanche systems, and what sets the largest size, is unsettled.
Precise statement
Compression of micropillars (Dimiduk et al. 2006) and acoustic emission in ice and metals give slip-size distributions $P(S) \sim S^{-\tau} \operatorname{exp}(-S/S_{0})$ with $\tau \sim 1.5 \text{ to } 1.6$. Determine whether the critical behavior is mean-field depinning ($\tau = 3/2, S_{0} \sim (\sigma_{c} - \sigma)^{-2}$), a distinct class set by long-range dislocation interactions, or criticality without a tuning parameter, and how $\tau$ depends on crystal structure (FCC versus BCC) and temperature. An answer is a classification with $\tau$, cutoff scaling and average avalanche shape.
What would settle it
Stress-resolved avalanche statistics and avalanche shapes from experiments and 3D dislocation dynamics agreeing on exponents and cutoff scaling.