Bibliographic record
Abstract
The notion of barycentric velocity appears in irreversible thermodynamics and fluid mechanics, in which it is a field variable obeying the hydrodynamic equations or, more specifically, the momentum balance equation, which is coupled to the rest of hydrodynamic equations. Therefore, its behavior is not known until the hydrodynamic equations are solved for the flow problem of interest. Unlike diffusion fluxes, heat fluxes, or stresses, it does not have its own constitutive relation similar to Fick's law, Fourier's law, and Newton's law of viscosity. In this work, the constitutive equation is derived for it. In parallel to the phenomenological notion of barycentric velocity, the notion of mean fluid velocity appears in statistical mechanics of irreversible dynamic processes according to the theory of Irving and Kirkwood [J. Chem. Phys. 18, 817 (1950)], and plays the same role of the phenomenological counterpart. In this work, we investigate the statistical mechanical meanings of the mean fluid velocity of a fluid in flow beyond its formal connection with the barycentric velocity. We show that it consists of two components; the center-of-gravity velocity of the packet of fluid molecules, which may be identified with the barycentric velocity in the phenomenological theory, and the diffusive contribution of its collective modes relative to the center of gravity. If the fluid is uniform in space or if the packet of fluid mass is rigid, the diffusive component vanishes. The statistical mechanical (molecular theory) formula for the mean fluid velocity provides the constitutive relation for it in terms of density and temperature gradients present in the fluid in flow. The constitutive relation obtained for the mean fluid velocity can be an important component in the theory of transport processes in liquids. Its significance to fluid mechanics is briefly discussed.
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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".