13-moment-equations from nonequilibrium thermodynamics and kinetic theory: Comparison for non-linear one-dimensional flows
Bibliographic record
Abstract
The GENERIC-13 moment equations (general equation for the non-equilibrium reversible-irreversible coupling) [Struchtrup & Öttinger, Phys. Fluids 34, 017105 (2022)] were developed to have complete thermodynamic structure, in contrast to Grad's 13-moment equations which are not accompanied by a suitable formulation of the second law of thermodynamics and loose hyperbolicity for larger deviations from equilibrium. With GENERIC-13 constructed to agree with Grad-13 to second order in the Knudsen number, both sets are considered and compared for hyperbolicity and plane heat transfer, and Couette and Poiseuille flows. It is shown that the GENERIC-13 equations are unconditionally hyperbolic. Jump and slip boundary conditions for GENERIC-13 are developed from the second law with coefficients adapted from kinetic theory. Additional asymptotically vanishing boundary conditions are constructed such that solutions of the GENERIC-13 equations reduce to those of Grad-13 to second and of Navier–Stokes–Fourier equations to first order in the Knudsen number.
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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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".