{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"bb8e788670d3bb6136481e83de064c79fe0e8dc774dde2d1420734cffc956420","created":"2026-10-03T07:17:56Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"f247520f893e0370db3c03a431c82af54788549bdde81f32fce8aa18246c76a0","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"value","assisted_by":[],"external_id":"bio.amorphous-plasticity.avalanche-exponents","kind":"well-posed","literature_status":"partially-resolved","n":"1","parents":[],"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.","posed_since":"","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.","problem_ref":null,"references":"","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.","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).","title":"Universal exponents of plastic avalanches in sheared amorphous 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