{"paper":{"title":"Shock-Centered Low-Rank Structure and Neural-Operator Representation of Rarefied Micro-Nozzle Flows","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Registering rarefied nozzle flows to shock-centered coordinates collapses their density fields to one dominant mode capturing 98 percent of fluctuation energy.","cross_cats":[],"primary_cat":"physics.flu-dyn","authors_text":"Amirmehran Mahdavi, Ehsan Roohi","submitted_at":"2026-05-12T20:28:41Z","abstract_excerpt":"We examine the structure of Direct Simulation Monte Carlo (DSMC)-resolved internal compression layers in rarefied micro-nozzle flows and show that their apparent parametric complexity is largely a registration and finite-thickness scaling effect. A density-gradient diagnostic identifies the compression-layer station \\(x_s\\), while a jump-based thickness \\(\\delta_j=\\Delta\\rho/\\max|\\partial\\rho/\\partial x|\\) defines a shock-centered coordinate \\(\\xi_j=(x-x_s)/\\delta_j\\). In physical coordinates, the leading proper orthogonal decomposition (POD) mode of the centerline density profiles captures on"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"In the registered (ξ_j, η) frame, the first density mode captures 94.98% and the first two modes capture 99.05% of the fluctuation energy. For held-out back-pressure cases, density, temperature, and pressure errors remain below 6.8%, 4.3%, and 6.8%, respectively, and the hardest case reduces the shock-window mean error from 9.75%–22.27% for standard baselines to 4.51%.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The jump-based thickness δ_j = Δρ / max|∂ρ/∂x| and shock station x_s identified from density-gradient diagnostics remain representative and generalizable beyond the specific DSMC cases and back-pressure range examined.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Shock-centered scaling of DSMC fields in micro-nozzles reveals low-rank density structure, enabling DeepONet surrogates with mean errors reduced to 4.51% on hardest test cases.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Registering rarefied nozzle flows to shock-centered coordinates collapses their density fields to one dominant mode capturing 98 percent of fluctuation energy.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"e4e008d4f903261f5f73643c73b3446924aff0e352a969ab985d3dce55e7c77c"},"source":{"id":"2605.12723","kind":"arxiv","version":1},"verdict":{"id":"9cd486c3-27c4-4ae1-bb8a-c9fdb64757a5","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T19:50:04.024751Z","strongest_claim":"In the registered (ξ_j, η) frame, the first density mode captures 94.98% and the first two modes capture 99.05% of the fluctuation energy. For held-out back-pressure cases, density, temperature, and pressure errors remain below 6.8%, 4.3%, and 6.8%, respectively, and the hardest case reduces the shock-window mean error from 9.75%–22.27% for standard baselines to 4.51%.","one_line_summary":"Shock-centered scaling of DSMC fields in micro-nozzles reveals low-rank density structure, enabling DeepONet surrogates with mean errors reduced to 4.51% on hardest test cases.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The jump-based thickness δ_j = Δρ / max|∂ρ/∂x| and shock station x_s identified from density-gradient diagnostics remain representative and generalizable beyond the specific DSMC cases and back-pressure range examined.","pith_extraction_headline":"Registering rarefied nozzle flows to shock-centered coordinates collapses their density fields to one dominant mode capturing 98 percent of fluctuation energy."},"references":{"count":36,"sample":[{"doi":"10.2514/2.1726","year":2002,"title":"Numerical modeling of axisymmetric and three-dimensional flows in microelec- tromechanical systems nozzles.AIAA journal, 40(5), 897–904 (2002)","work_id":"4a401817-c16b-4019-b375-a8320ad3690e","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1016/j.ast.2015.07.016","year":2015,"title":"doi: 10.1016/j.ast.2015.07.016","work_id":"462e6794-0e91-46d7-b3b2-51daeb6643f8","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1063/5.0237548","year":2024,"title":"Numericalandexperimentalinvestigationofrarefiedhypersonicflowinanozzle.PhysicsofFluids, 36(11), 116131 (2024)","work_id":"652a38ff-4387-41d2-9af6-55a0bdbc2643","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1016/j.ast.2024.109625","year":2024,"title":"Numerical investigation of micropropulsion systems for CubeSats: Gas species and geometrical effects on nozzle performance.Aerospace Science and Technology, 155, 109625 (2024)","work_id":"1519c2d6-799d-486e-b440-7e6d7fda6864","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.2514/1.j064386","year":2025,"title":"Numerical Study of Facility Pressure Effects on Micronozzles for Space Propulsion","work_id":"08cfc6a9-e3ef-469d-b078-aca1458e2d91","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":36,"snapshot_sha256":"479d235213351a9413b065211319c22563af29954534486a36b1f971d0ed6b02","internal_anchors":1},"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"}