{"paper":{"title":"Turbulent stretching of FENE dumbbell polymer model via special stochastic scaling and singular limits","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Under a scaling where turbulent eddies shrink as one over N, the stochastic density equation for FENE polymers converges pathwise to a deterministic equation with an added second-order operator for average turbulent stretching.","cross_cats":["math-ph","math.AP","math.MP"],"primary_cat":"math.PR","authors_text":"Federico Butori, Yassine Tahraoui","submitted_at":"2026-05-15T08:52:04Z","abstract_excerpt":"We investigate the stretching mechanism of Finitely Extensible Nonlinear Elastic (FENE) model of polymers in a random turbulent flow. The turbulent model includes a dominant space-scale $\\ell\\sim N^{-1}$, a dominant time-scale $\\tau$, and is white in time. Under suitable scaling assumption, the polymer density equation, initially a stochastic Fokker-Planck equation in the presence of transport-stretching noise, converges weakly as $N\\uparrow \\infty$ to a limit deterministic equation with a new extra term, a second order operator. This operator, whose shape has been predicted in the physical li"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Under suitable scaling assumption, the polymer density equation, initially a stochastic Fokker-Planck equation in the presence of transport-stretching noise, converges weakly as N↑∞ to a limit deterministic equation with a new extra term, a second order operator. This operator express a sort of average 'turbulent stretching' effect. The deterministic limit is obtained pathwise, without having to take averages with respect to different realizations of the random flow.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The suitable scaling assumption on the turbulent model (dominant space-scale ℓ∼N^{-1}, time-scale τ, white in time) together with the choice of weighted spaces that handle the FENE force singularity near the boundary and the no-flux boundary condition; if these do not hold the convergence to the claimed deterministic limit with the second-order operator may fail.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Derives pathwise deterministic limit for FENE polymer density in white-in-time turbulent flow via stochastic scaling, adding a second-order stretching operator, then takes singular limit for stationary polymer length distribution.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Under a scaling where turbulent eddies shrink as one over N, the stochastic density equation for FENE polymers converges pathwise to a deterministic equation with an added second-order operator for average turbulent stretching.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"e97c1dfe57407cc9ed357e4d03160a68272419d696c01e2056af079f2f40ab7a"},"source":{"id":"2605.15742","kind":"arxiv","version":1},"verdict":{"id":"2a18bb73-367d-4f63-8530-29d255951486","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T19:43:43.922841Z","strongest_claim":"Under suitable scaling assumption, the polymer density equation, initially a stochastic Fokker-Planck equation in the presence of transport-stretching noise, converges weakly as N↑∞ to a limit deterministic equation with a new extra term, a second order operator. This operator express a sort of average 'turbulent stretching' effect. The deterministic limit is obtained pathwise, without having to take averages with respect to different realizations of the random flow.","one_line_summary":"Derives pathwise deterministic limit for FENE polymer density in white-in-time turbulent flow via stochastic scaling, adding a second-order stretching operator, then takes singular limit for stationary polymer length distribution.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The suitable scaling assumption on the turbulent model (dominant space-scale ℓ∼N^{-1}, time-scale τ, white in time) together with the choice of weighted spaces that handle the FENE force singularity near the boundary and the no-flux boundary condition; if these do not hold the convergence to the claimed deterministic limit with the second-order operator may fail.","pith_extraction_headline":"Under a scaling where turbulent eddies shrink as one over N, the stochastic density equation for FENE polymers converges pathwise to a deterministic equation with an added second-order operator for average turbulent stretching."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.15742/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T20:01:19.194092Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T19:51:28.992586Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T19:33:23.894132Z","status":"skipped","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T17:21:55.979975Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"802ff3a58dc937bae9fc3b3c4c718a7a2a5bc3e27dd864ea0ac647a0a518171c"},"references":{"count":41,"sample":[{"doi":"","year":2005,"title":"Nonlinear elastic polymers in random flow","work_id":"fa0c11ff-49a8-4b1f-ac5f-2730f3a3e3b0","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2026,"title":"A. 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