Bibliographic record
Abstract
This chapter starts by distinguishing between the primitive and conservative equations of MHD in 1-D, emphasising that the former deal only with continuous flow , whereas the latter admit flow discontinuities . The first application is to MHD waves including Alfvén , slow , fast , and magneto-acoustical waves . An intuitive analogy is given describing what one might experience in an MHD atmosphere when a “thunder clap” occurs. The MHD Rankine–Hugoniot jump conditions for MHD are introduced and solved (using difference theory ) revealing tangential/contact/rotational discontinuities and, most importantly, shock waves including slow , intermediate , and fast shocks . In the context of the not strictly hyperbolic nature of the MHD equations, both the entropy and evolutionary conditions are used to determine the physicality and uniqueness of the shock solution. Finally, discussion of MHD shocks includes the special cases of switch-on/off shocks and Euler shocks .
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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 | 0.000 | 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 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".