The Hydrodynamical Riemann Problem
Bibliographic record
Abstract
This chapter serves as the “practice chapter” for the main goal of Part I: solving the MHD Riemann problem. Lagrangian and Eulerian frames of reference are introduced from which the three Riemann invariants of HD are identified. Space-time diagrams are introduced as a useful visual and conceptual aid in understanding the role of characteristic paths through a continuum, which is in keeping with the text’s underlying approach of treating fluid dynamics as a form of wave mechanics . The Riemann problem for HD is defined and a method of characteristics is introduced whose main purpose is to understand qualitatively how the solution to the HD Riemann problem begins to unfold. In so doing, shocks and contact discontinuities are rediscovered and rarefaction fans are introduced. It is shown how examining the eigenkets leads to profiles of the primitive variables across a rarefaction fan which ultimately leads to a semi-analytic solution to the HD Riemann problem.
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How this classification was reachedexpand
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 | 0.001 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".