{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"66d8198192c14c6fb333bb1c2439611d5174ac31a3f4b51e7585f2aca51a8219","created":"2026-10-03T07:17:57Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"6a8aa8093e1847e16261d8f2bcd4aa7915bf3985af31cc9f654403a92f950a87","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"mechanism","assisted_by":[],"external_id":"bio.granular-rheology.nonlocal-law","kind":"phenomenon","literature_status":"partially-resolved","n":"1","parents":[],"plain":"A simple local friction law describes fast flows of grains well but fails when the flow is slow: grains creep below the expected stopping point and thin layers stop earlier than thick ones. The correct replacement law, and its basis in grain-scale physics, is not established.","posed_since":"","precise":"The local $\\mu(I)$ rheology gives the stress ratio $\\mu = \\tau / P$ as a function of the inertial number $I = \\gamma_{\\mathrm{dot}} d / \\sqrt{P / \\rho_s}$ (shear rate $\\gamma_{\\mathrm{dot}}$, grain diameter $d$, pressure $P$, grain density $\\rho_s$). It fails as $I \\to 0$: creep below the yield ratio $\\mu_s$, thickness-dependent stopping height $h_{\\mathrm{stop}}$ of flowing layers, and flow induced by distant shear. Find a constitutive law (for example a fluidity model with cooperativity length $\\xi \\sim \\mid \\mu - \\mu_s \\mid^{-1/2}$) that predicts all three effects quantitatively for frictional spheres, with parameters derived from grain-scale physics.","problem_ref":null,"references":"","settled_by":"A law with grain-scale-derived parameters that predicts creep profiles, $h_{\\mathrm{stop}}(\\theta)$ and remote-shear fluidization in several geometries within experimental error.","status_note":"Nonlocal fluidity models introduced from 2012 fit several geometries, but their microscopic basis and the cooperativity exponent remain debated (2026).","title":"A nonlocal constitutive law for slow granular 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