{"paper":{"title":"Precise Determination of the Long-Time Asymptotics of the Diffusion Spreadability of Two-Phase Media","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.dis-nn","cond-mat.soft","cond-mat.stat-mech"],"primary_cat":"cond-mat.mtrl-sci","authors_text":"Salvatore Torquato, Shaobing Yuan","submitted_at":"2026-02-19T22:18:29Z","abstract_excerpt":"The time-dependent diffusion spreadability $\\mathcal{S}(t)$ is a powerful dynamical probe of the microstructure of two-phase heterogeneous media across length scales [Torquato, S., \\emph{Phys. Rev. E.}, 104 054102 (2021)]. It has been shown that when the spectral density takes the power-law form $\\tilde{\\chi}_{_V}(\\mathbf{k})\\sim |\\mathbf{k}|^\\alpha$ as the wavenumber $|\\mathbf{k}|$ tends to zero, the normalized excess spreadability $\\mathscr{s}^{ex}(t)$ [proportional to $\\mathcal{S}(\\infty)-\\mathcal{S}(t)$] scales as $\\mathscr{s}^{ex}(t)\\sim t^{-\\frac{d+\\alpha}{2}}$ in the long-time limit $t\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.17873","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2602.17873/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}