{"paper":{"title":"Blocking of 2D bistable reaction-diffusion fronts by obstacles","license":"http://creativecommons.org/licenses/by/4.0/","headline":"The integral of the reaction term provides an effective driving force that, combined with the one-dimensional traveling wave solution, yields an analytical model for predicting when bistable fronts are blocked by two-dimensional obstacles.","cross_cats":["math.MP","physics.bio-ph"],"primary_cat":"math-ph","authors_text":"B. Sarels, G. Cruz-Pacheco, J. Gatlik, J.-G. Caputo","submitted_at":"2026-04-16T17:22:22Z","abstract_excerpt":"We investigate numerically the blocking of two-dimensional bistable reaction diffusion fronts by geometric obstacles. Our goal is to derive quantitative criteria for front propagation in the presence of spatial heterogeneities. Using a conservation law approach, we show that the integral of the reaction term acts as an effective driving force for the front. Combining this insight with the exact one-dimensional traveling wave solution, we construct a reduced analytical model that predicts blocking thresholds. In particular, we obtain explicit conditions for front propagation in a waveguide conn"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Combining this insight with the exact one-dimensional traveling wave solution, we construct a reduced analytical model that predicts blocking thresholds. In particular, we obtain explicit conditions for front propagation in a waveguide connected to a conical region of angle theta, valid for widths w less than 4. The model captures the influence of both geometry and nonlinearity, and shows good agreement with numerical simulations.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The integral of the reaction term can be treated as an effective driving force that allows reduction of the 2D problem to the 1D traveling-wave solution, with the reduction remaining valid for the waveguide-conical geometry when w < 4.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A conservation-law reduced model yields explicit blocking thresholds for bistable fronts in waveguides connected to conical regions of angle theta (valid for widths w<4) and heuristic rules for complex obstacles, agreeing with simulations.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The integral of the reaction term provides an effective driving force that, combined with the one-dimensional traveling wave solution, yields an analytical model for predicting when bistable fronts are blocked by two-dimensional obstacles.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"727fb0abe1a1072617b907cd4e35522690a430fc5dc9618e17aa52847ffac023"},"source":{"id":"2604.15246","kind":"arxiv","version":3},"verdict":{"id":"39d2b400-4044-4085-aa3c-8e287fbfb98b","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-10T09:39:49.318276Z","strongest_claim":"Combining this insight with the exact one-dimensional traveling wave solution, we construct a reduced analytical model that predicts blocking thresholds. In particular, we obtain explicit conditions for front propagation in a waveguide connected to a conical region of angle theta, valid for widths w less than 4. The model captures the influence of both geometry and nonlinearity, and shows good agreement with numerical simulations.","one_line_summary":"A conservation-law reduced model yields explicit blocking thresholds for bistable fronts in waveguides connected to conical regions of angle theta (valid for widths w<4) and heuristic rules for complex obstacles, agreeing with simulations.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The integral of the reaction term can be treated as an effective driving force that allows reduction of the 2D problem to the 1D traveling-wave solution, with the reduction remaining valid for the waveguide-conical geometry when w < 4.","pith_extraction_headline":"The integral of the reaction term provides an effective driving force that, combined with the one-dimensional traveling wave solution, yields an analytical model for predicting when bistable fronts are blocked by two-dimensional obstacles."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.15246/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"}