{"paper":{"title":"Quantitative Evaluation of Forward and Backward Scattering in Isotropic Turbulence via H\\\"anggi--Klimontovich and It\\^o Stochastic Processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"A drift-free Hänggi-Klimontovich process models the stretch-and-fold mechanism to justify uniform Lagrangian Lyapunov exponents and close the von Karman-Howarth and Corrsin equations without diffusion.","cross_cats":["physics.class-ph"],"primary_cat":"physics.flu-dyn","authors_text":"Nicola de Divitiis","submitted_at":"2026-04-25T01:14:17Z","abstract_excerpt":"This work evaluates the magnitude of the turbulent energy cascade in terms of forward and backward scattering by modeling the \"stretch and fold\" mechanism through a drift-free Hanggi-Klimontovich stochastic process. Mapping this dynamics onto an equivalent Ito process provides a statistical justification for the uniform distribution of the Lagrangian Lyapunov exponent via the associated Fokker-Planck equation. This continuous distribution is shown to be driven by a Lagrangian bifurcation rate significantly higher than the Lyapunov exponents themselves, reflecting the high frequency with which "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"This stochastic formulation, framed within the author's Lyapunov-Liouville analysis, provides a non-diffusive analytical closure of the von Karman-Howarth and Corrsin equations.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The stretch-and-fold mechanism of isotropic turbulence can be represented by a drift-free Hänggi-Klimontovich process whose mapping to an Itô process yields a uniform Lyapunov-exponent distribution without additional fitted drift or diffusion terms.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A drift-free stochastic process for the stretch-and-fold mechanism in isotropic turbulence produces a uniform PDF of Lagrangian Lyapunov exponents that closes the von Kármán-Howarth and Corrsin equations and yields eddy viscosity, thermal diffusivity, and Prandtl number matching numerical data.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A drift-free Hänggi-Klimontovich process models the stretch-and-fold mechanism to justify uniform Lagrangian Lyapunov exponents and close the von Karman-Howarth and Corrsin equations without diffusion.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"1bfbb9b867716457bf34dc006495edb57dacc499e2735cdd5a2e3aa88e1a1037"},"source":{"id":"2604.23092","kind":"arxiv","version":2},"verdict":{"id":"83eb1136-d221-4d1b-b192-5d1cc4d9af7b","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-08T07:31:49.631504Z","strongest_claim":"This stochastic formulation, framed within the author's Lyapunov-Liouville analysis, provides a non-diffusive analytical closure of the von Karman-Howarth and Corrsin equations.","one_line_summary":"A drift-free stochastic process for the stretch-and-fold mechanism in isotropic turbulence produces a uniform PDF of Lagrangian Lyapunov exponents that closes the von Kármán-Howarth and Corrsin equations and yields eddy viscosity, thermal diffusivity, and Prandtl number matching numerical data.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The stretch-and-fold mechanism of isotropic turbulence can be represented by a drift-free Hänggi-Klimontovich process whose mapping to an Itô process yields a uniform Lyapunov-exponent distribution without additional fitted drift or diffusion terms.","pith_extraction_headline":"A drift-free Hänggi-Klimontovich process models the stretch-and-fold mechanism to justify uniform Lagrangian Lyapunov exponents and close the von Karman-Howarth and Corrsin equations without diffusion."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.23092/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-21T09:39:51.096629Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T23:25:59.699253Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"04978bbbe4818381f370d7600e3f8df2e73897ee566c4edc6dca6625f4ca6ebe"},"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"}