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The initial spheres' density {\\rho} is non-uniform and scales with the distance (from the origin) l as, {\\rho} l^(-a), 0\\leqa\\leq1. An approximation for the N-particle PDF for this problem is derived. From this solution, scaling law analysis and numerical simulations, we show here that the mean square displacement f"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1002.1450","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2010-02-07T14:06:40Z","cross_cats_sorted":["q-bio.QM"],"title_canon_sha256":"cbac050a41571513b0a2f655319ae89400606632e3d5db18d496b3bd65e82159","abstract_canon_sha256":"f55a645087ee431809decd6de7d1e81da734a51401b2757a6cefd3eb92089be9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:24:45.355646Z","signature_b64":"4TqARoP1P71y0QG8PSF4uxgzIlv0gZasDbPNMQV/eyayw3Nc7lq8x3qfI9BBsdJa8o2so6XmLU8D65lBPCTnCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6c43102369adf112e0e87978be6d2cfcdf1b76ade13e6cac339748d141da7e60","last_reissued_at":"2026-05-18T04:24:45.355012Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:24:45.355012Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Dynamics of heterogeneous hard spheres in a file","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-bio.QM"],"primary_cat":"cond-mat.soft","authors_text":"Ophir Flomenbom","submitted_at":"2010-02-07T14:06:40Z","abstract_excerpt":"Normal dynamics in a quasi-one-dimensional channel of length L (\\to\\infty) of N hard spheres are analyzed. 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