{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:2BK22QIIG3MQQSONDMO4ME5OOK","short_pith_number":"pith:2BK22QII","schema_version":"1.0","canonical_sha256":"d055ad410836d90849cd1b1dc613ae7294deed821a7bf0c23ca04f5dbd49ee02","source":{"kind":"arxiv","id":"1504.02123","version":1},"attestation_state":"computed","paper":{"title":"Generalized Navier-Stokes equations for active suspensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.soft","authors_text":"Jonasz S{\\l}omka, J\\\"orn Dunkel","submitted_at":"2015-04-08T20:46:58Z","abstract_excerpt":"We discuss a minimal generalization of the incompressible Navier-Stokes equations to describe the solvent flow in an active suspension. To account phenomenologically for the presence of an active component driving the ambient fluid flow, we postulate a generic nonlocal extension of the stress-tensor, conceptually similar to those recently introduced in granular media flows. Stability and spectral properties of the resulting hydrodynamic model are studied both analytically and numerically for the two-dimensional (2D) case with periodic boundary conditions. Future generalizations of this momentu"},"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":"1504.02123","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2015-04-08T20:46:58Z","cross_cats_sorted":[],"title_canon_sha256":"022c16ee5f8b904a8855afe36d9ee1543bf1e1ec2d3fd4e486170d8236e92ead","abstract_canon_sha256":"ebd897bb47c6f0b738200cb7180464dda763fe7a88933cc110556bd14587d839"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:19:15.988093Z","signature_b64":"bClHblALSX8ZlzqGxxJ6O7ATbmnlPSE5PQgzvEoq40KZFd1flr+mVhDe5NP31nXD6rJCkfnN0KqTIrQ/hR/oDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d055ad410836d90849cd1b1dc613ae7294deed821a7bf0c23ca04f5dbd49ee02","last_reissued_at":"2026-05-18T02:19:15.987482Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:19:15.987482Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Generalized Navier-Stokes equations for active suspensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.soft","authors_text":"Jonasz S{\\l}omka, J\\\"orn Dunkel","submitted_at":"2015-04-08T20:46:58Z","abstract_excerpt":"We discuss a minimal generalization of the incompressible Navier-Stokes equations to describe the solvent flow in an active suspension. To account phenomenologically for the presence of an active component driving the ambient fluid flow, we postulate a generic nonlocal extension of the stress-tensor, conceptually similar to those recently introduced in granular media flows. Stability and spectral properties of the resulting hydrodynamic model are studied both analytically and numerically for the two-dimensional (2D) case with periodic boundary conditions. Future generalizations of this momentu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.02123","kind":"arxiv","version":1},"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":"1504.02123","created_at":"2026-05-18T02:19:15.987578+00:00"},{"alias_kind":"arxiv_version","alias_value":"1504.02123v1","created_at":"2026-05-18T02:19:15.987578+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.02123","created_at":"2026-05-18T02:19:15.987578+00:00"},{"alias_kind":"pith_short_12","alias_value":"2BK22QIIG3MQ","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_16","alias_value":"2BK22QIIG3MQQSON","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_8","alias_value":"2BK22QII","created_at":"2026-05-18T12:28:59.999130+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/2BK22QIIG3MQQSONDMO4ME5OOK","json":"https://pith.science/pith/2BK22QIIG3MQQSONDMO4ME5OOK.json","graph_json":"https://pith.science/api/pith-number/2BK22QIIG3MQQSONDMO4ME5OOK/graph.json","events_json":"https://pith.science/api/pith-number/2BK22QIIG3MQQSONDMO4ME5OOK/events.json","paper":"https://pith.science/paper/2BK22QII"},"agent_actions":{"view_html":"https://pith.science/pith/2BK22QIIG3MQQSONDMO4ME5OOK","download_json":"https://pith.science/pith/2BK22QIIG3MQQSONDMO4ME5OOK.json","view_paper":"https://pith.science/paper/2BK22QII","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1504.02123&json=true","fetch_graph":"https://pith.science/api/pith-number/2BK22QIIG3MQQSONDMO4ME5OOK/graph.json","fetch_events":"https://pith.science/api/pith-number/2BK22QIIG3MQQSONDMO4ME5OOK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2BK22QIIG3MQQSONDMO4ME5OOK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2BK22QIIG3MQQSONDMO4ME5OOK/action/storage_attestation","attest_author":"https://pith.science/pith/2BK22QIIG3MQQSONDMO4ME5OOK/action/author_attestation","sign_citation":"https://pith.science/pith/2BK22QIIG3MQQSONDMO4ME5OOK/action/citation_signature","submit_replication":"https://pith.science/pith/2BK22QIIG3MQQSONDMO4ME5OOK/action/replication_record"}},"created_at":"2026-05-18T02:19:15.987578+00:00","updated_at":"2026-05-18T02:19:15.987578+00:00"}