{"paper":{"title":"Exact solutions of the Boeder differential equation for macromolecular orientations in a flowing liquid","license":"","headline":"","cross_cats":["physics.gen-ph"],"primary_cat":"physics.chem-ph","authors_text":"A. Hijazi, A. Khater, C. Tannous","submitted_at":"2001-04-09T20:02:04Z","abstract_excerpt":"The Boeder differential equation is solved in this work over a wide range of $\\alpha$, yielding the probability density functions (PDF), that describe the average orientations of rod-like macromolecules in a flowing liquid. The quantity $\\alpha$ is the ratio of the hydrodynamic shear rate to the rotational diffusion coefficient. It characterises the coupling of the motion of the macromolecules in the hydrodynamic flow to their thermal diffusion. Previous analytical work is limited to approximate solutions for small values of $\\alpha$. Special analytical as well as numerical methods are develop"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"physics/0104035","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":""},"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"}