{"paper":{"title":"Iterative bounds on effective transport for advection diffusion in periodic flow fields","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["physics.app-ph","physics.comp-ph","physics.geo-ph"],"primary_cat":"physics.flu-dyn","authors_text":"D. Hallman, E. Cherkaev, J. Xin, K. M. Golden, N. B. Murphy","submitted_at":"2024-04-29T14:52:11Z","abstract_excerpt":"Over three decades ago a Stieltjes integral representation for the effective diffusivity of a tracer in a steady fluid velocity field was developed, involving the spectral measure of a compact self-adjoint operator and the P\\'eclet number of the flow. Rigorous bounds on the homogenized diffusivity could then be obtained from knowledge of the moments of the spectral measure. A recent extension to space-time periodic flows involves an unbounded self-adjoint operator. Though Pad\\'e approximants provide upper and lower bounds in terms of the moments, the lack of a general method for calculating th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.18754","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/2404.18754/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"}