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Accepted · first revision · record

Title: Universal exponents of plastic avalanches in sheared amorphous solids
Plain: A slowly sheared glass flows in bursts, or avalanches, of all sizes. The numbers describing how often avalanches of each size occur differ from simple mean-field theory, and an exact theory in two or three dimensions is missing.
Precise: In steady athermal quasistatic flow, avalanche sizes S follow $P(S)\sim S^{-\tau}$ with cutoff $S_c\sim L^{d_f}$, and the density of local distances to instability $P(x)\sim x^{\theta}$ at small $x$. Determine $\tau$, $d_f$ and $\theta$ in $d=2\ \text{and}\ 3$, which numerically lie below the mean-field value $\tau=3/2$, and derive them from a controlled theory of elastoplastic dynamics with long-range Eshelby interactions, consistent with the known scaling relations among them.
Settled by: A renormalization-group or exact calculation of $\tau$, $d_{f}$ and $\theta$ in finite $d$ that matches high-precision particle and elastoplastic simulations.
Kind: well-posed
Answer type: value
References: (empty)
Literature status: partially-resolved
Status note: Scaling relations linking $\tau, d_{f} \text{ and } \theta$ were established in 2014, and simulations report $\tau$ of roughly 1.2 to 1.4 in $d = 2, 3$, but a finite-d theory of the exponents is lacking (2026).
Posed since: (empty)