Selected Applications of Hydrodynamics
Why this work is in the frame
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Bibliographic record
Abstract
By linearising the equations of HD developed in Chapter 1, the wave equation for the propagation of sound is derived. This is examined from two approaches: direct solution of the wave equation and examining normal modes to convert the problem to one of linear algebra. This introduces the very important concepts of eigenvalues ( characteristic speeds ) and eigenkets (right eigenvectors) along with the role they play in examining fluid dynamics in terms of waves . From the 1-D, non-linearised, steady-state equations, the Rankine–Hugoniot jump conditions are derived from which the conditions for tangential/contact discontinuities and shocks are developed. An optional section considers the phenomenon of bores and hydraulic jumps , while the last section introduces concepts such as streamlines and stream tubes culminating with Bernoulli’s theorem applied to an incompressible fluid, a subsonic compressible fluid, and a supersonic compressible fluid.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 it