Bibliographic record
Abstract
A mathematical relation is formulated to calculate the properties of oblique shocks generated from swept ramps. Ramp-sweep extends the oblique shock relations from 2D to 3D in a manner analogous to the way ramp-deflection extends the Rankine-Hugoniot shock relations from 1D to 2D. A new Theta-Beta-Mach-Sweep (θ-β-Mach-Sweep) relation is formulated, which reduces to the standard Theta-Beta-Mach (θ-β-Mach) relation for the special case of 2D shocks from unswept ramps. The swept formulation may be expressed as a cubic equation with coefficients that are simple modifications of the cubic coefficients for the standard unswept formulation. The solution of this swept cubic equation allows the shock-angle and downstream properties to be determined directly from the upstream Mach number, geometric ramp-angle and sweep. Several notable properties of sweep on the “strong” and “weak” solutions are depicted and discussed. The new formulation simplifies the process of placing, aligning and focusing shocks for a sequence of swept ramps.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.008 | 0.002 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".