{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:VQOMQBO55MR6MYVNU2DKXVT7CB","short_pith_number":"pith:VQOMQBO5","schema_version":"1.0","canonical_sha256":"ac1cc805ddeb23e662ada686abd67f105b2cd6ef06d87a29a840fd0110289e5b","source":{"kind":"arxiv","id":"1905.08052","version":2},"attestation_state":"computed","paper":{"title":"Analytical steady-state solutions for pressure with a multiscale non-local model for two-fluid systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.flu-dyn","authors_text":"Alexandre M. Tartakovsky, Amanda A. Howard, Yongcheng Zhou","submitted_at":"2019-05-16T21:39:56Z","abstract_excerpt":"We consider the nonlocal multiscale model for surface tension \\citep{Tartakovsky2018} as an alternative to the (macroscale) Young-Laplace law. The nonlocal model is obtained in the form of an integral of a molecular-force-like function with support $\\varepsilon$ added to the Navier-Stokes momentum conservation equation. Using this model, we calculate analytical forms for the steady-state equilibrium pressure gradient and pressure profile for circular and spherical bubbles and flat interfaces in two and three dimensions. According to the analytical solutions, the pressure changes continuously a"},"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":"1905.08052","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2019-05-16T21:39:56Z","cross_cats_sorted":[],"title_canon_sha256":"c9f426406c4699e942e33a9750753928e03a012e10209d0a64e1fce7fd13994d","abstract_canon_sha256":"440ef946073e4f95ee711cf0eab42e3fb206286388670deb23f15a3530745209"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:45:43.877639Z","signature_b64":"GXTl76RXfQYa+kbg8a8vfsEuRuof0RmtLZ28jRagDO71IPYtKjufFcu8+B4WdgTxpWX0bKoNv3xuCiHoKpIhDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ac1cc805ddeb23e662ada686abd67f105b2cd6ef06d87a29a840fd0110289e5b","last_reissued_at":"2026-05-17T23:45:43.877128Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:45:43.877128Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Analytical steady-state solutions for pressure with a multiscale non-local model for two-fluid systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.flu-dyn","authors_text":"Alexandre M. Tartakovsky, Amanda A. Howard, Yongcheng Zhou","submitted_at":"2019-05-16T21:39:56Z","abstract_excerpt":"We consider the nonlocal multiscale model for surface tension \\citep{Tartakovsky2018} as an alternative to the (macroscale) Young-Laplace law. The nonlocal model is obtained in the form of an integral of a molecular-force-like function with support $\\varepsilon$ added to the Navier-Stokes momentum conservation equation. Using this model, we calculate analytical forms for the steady-state equilibrium pressure gradient and pressure profile for circular and spherical bubbles and flat interfaces in two and three dimensions. According to the analytical solutions, the pressure changes continuously a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.08052","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1905.08052","created_at":"2026-05-17T23:45:43.877211+00:00"},{"alias_kind":"arxiv_version","alias_value":"1905.08052v2","created_at":"2026-05-17T23:45:43.877211+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.08052","created_at":"2026-05-17T23:45:43.877211+00:00"},{"alias_kind":"pith_short_12","alias_value":"VQOMQBO55MR6","created_at":"2026-05-18T12:33:30.264802+00:00"},{"alias_kind":"pith_short_16","alias_value":"VQOMQBO55MR6MYVN","created_at":"2026-05-18T12:33:30.264802+00:00"},{"alias_kind":"pith_short_8","alias_value":"VQOMQBO5","created_at":"2026-05-18T12:33:30.264802+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/VQOMQBO55MR6MYVNU2DKXVT7CB","json":"https://pith.science/pith/VQOMQBO55MR6MYVNU2DKXVT7CB.json","graph_json":"https://pith.science/api/pith-number/VQOMQBO55MR6MYVNU2DKXVT7CB/graph.json","events_json":"https://pith.science/api/pith-number/VQOMQBO55MR6MYVNU2DKXVT7CB/events.json","paper":"https://pith.science/paper/VQOMQBO5"},"agent_actions":{"view_html":"https://pith.science/pith/VQOMQBO55MR6MYVNU2DKXVT7CB","download_json":"https://pith.science/pith/VQOMQBO55MR6MYVNU2DKXVT7CB.json","view_paper":"https://pith.science/paper/VQOMQBO5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1905.08052&json=true","fetch_graph":"https://pith.science/api/pith-number/VQOMQBO55MR6MYVNU2DKXVT7CB/graph.json","fetch_events":"https://pith.science/api/pith-number/VQOMQBO55MR6MYVNU2DKXVT7CB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VQOMQBO55MR6MYVNU2DKXVT7CB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VQOMQBO55MR6MYVNU2DKXVT7CB/action/storage_attestation","attest_author":"https://pith.science/pith/VQOMQBO55MR6MYVNU2DKXVT7CB/action/author_attestation","sign_citation":"https://pith.science/pith/VQOMQBO55MR6MYVNU2DKXVT7CB/action/citation_signature","submit_replication":"https://pith.science/pith/VQOMQBO55MR6MYVNU2DKXVT7CB/action/replication_record"}},"created_at":"2026-05-17T23:45:43.877211+00:00","updated_at":"2026-05-17T23:45:43.877211+00:00"}