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The length scales $R_{\\rm r}=R- 0.5 d$ and $R_{\\rm z}=R+k_2 d$, where $k_2$ is a parameter to be determined and $d$ is the diameter of granule. The effective acceleration, which is derived from $v_{\\rm z}$, follows also a size scaling form $a_{\\rm eff} = v_{\\rm z}^2(0,0;R)R_{\\rm z}^{-1} \\theta (r/R_{\\rm r}, z/R_{\\rm z})$. For granular flow under gravity $g$, there is "},"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":"1708.09647","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2017-08-31T10:08:29Z","cross_cats_sorted":[],"title_canon_sha256":"1d3e51ab871549f9016be01993609e114a4e150592093ed1c578a26975cdf465","abstract_canon_sha256":"ba2b86f213f6bc3b320bbca76a274d79bde57539e03aa12b931ce230ba086bf4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:36:15.896271Z","signature_b64":"wEvXtoaoPBPr7HlIhU0Z0CgUanZV7esr8KJAFnm3rOzqXUg9vWe9Z3AcDYmYC+F4iv4iMhwkE5/XQMUK5cWrCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7e64f8d774dd7f3e36f6e8d3b3048623c48b01562edc7332d37a5db238d0639e","last_reissued_at":"2026-05-18T00:36:15.895518Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:36:15.895518Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Size Scaling of Velocity Field in Granular Flows through Apertures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.soft","authors_text":"Gaoke Hu, Lei Yang, Liangsheng Li, Ping Lin, Xiaosong Chen, Yongwen Zhang","submitted_at":"2017-08-31T10:08:29Z","abstract_excerpt":"For vertical velocity field $v_{\\rm z} (r,z;R)$ of granular flow through an aperture of radius $R$, we propose a size scaling form $v_{\\rm z}(r,z;R)=v_{\\rm z} (0,0;R)f (r/R_{\\rm r}, z/R_{\\rm z})$ in the region above the aperture. The length scales $R_{\\rm r}=R- 0.5 d$ and $R_{\\rm z}=R+k_2 d$, where $k_2$ is a parameter to be determined and $d$ is the diameter of granule. The effective acceleration, which is derived from $v_{\\rm z}$, follows also a size scaling form $a_{\\rm eff} = v_{\\rm z}^2(0,0;R)R_{\\rm z}^{-1} \\theta (r/R_{\\rm r}, z/R_{\\rm z})$. 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