Glimm’s Method for Relativistic Hydrodynamics
Bibliographic record
Abstract
We present the results of standard one-dimensional test problems in relativistic hydrodynamics using Glimm's (random choice) method and compare them to results obtained using finite differencing methods. For problems containing profiles with sharp edges, such as shocks, we find Glimm's method yields global errors ~1-3 orders of magnitude smaller than the traditional techniques. The strongest differences are seen for problems in which a shear field is superposed. For smooth flows, Glimm's method is inferior to standard methods. The location of specific features can be off by up to two grid points with respect to an exact solution in Glimm's method, and furthermore, curved states are not modeled optimally, since the method idealizes solutions as being composed of piecewise constant states. Thus, although Glimm's method is superior at correctly resolving sharp features, especially in the presence of shear, for realistic applications in which one typically finds smooth flows plus strong gradients or discontinuities, standard finite-difference methods yield smaller global errors. Glimm's method may prove useful in certain applications such as GRB afterglow shock propagation into a uniform medium.
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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 | 0.002 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.010 | 0.005 |
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".