{"paper":{"title":"Chapman-Enskog expansion for the Vicsek model of self-propelled particles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.soft","physics.bio-ph","physics.flu-dyn"],"primary_cat":"cond-mat.stat-mech","authors_text":"Thomas Ihle","submitted_at":"2016-05-12T19:52:48Z","abstract_excerpt":"Using the standard Vicsek model, I show how the macroscopic transport equations can be systematically derived from microscopic collision rules. The approach starts with the exact evolution equation for the N-particle probability distribution, and after making the mean-field assumption of Molecular Chaos leads to a multi-particle Enskog-type equation. This equation is treated by a non-standard Chapman-Enskog expansion to extract the macroscopic behavior. The expansion includes terms up to third order in a formal expansion parameter $\\epsilon$, and involves a fast time scale. A self-consistent c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.03953","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"}