{"paper":{"title":"Transit-Length Distribution for Particle Transport in Binary Markovian Mixed Media","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.MP","physics.comp-ph"],"primary_cat":"math-ph","authors_text":"Brian C. Kiedrowski, Emily H. Vu","submitted_at":"2024-12-26T21:46:14Z","abstract_excerpt":"The correspondence between the telegraph random process and transport within a binary stochastic Markovian mixture is established. This equivalence is used to derive the distribution function for the transit length, defined as the distance a particle moving along a straight-line trajectory travels through a specific material zone within the random mixture. A numerically robust asymptotic form of this distribution is obtained for highly mixed materials and the convergence to the atomic-mix limit is shown. The validity of the distribution is verified using a Monte Carlo simulation of the transpo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.19359","kind":"arxiv","version":1},"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/2412.19359/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"}