Analyse du flux de Poiseuille bidimensionnel via l'équation de Boltzmann
Bibliographic record
Abstract
The two-dimensional Poiseuille flow induced by an external force is analysed in the framework of BoltzmannMaxwell kinetic theory. In the limit of small Knudsen numbers (K n [Formula: see text] 0.1), Boltzmann's nonlinear equation, written in terms of moments, is solved using perturbation theory. In our results, the hydrodynamic variable profiles are determined up to the fourth order in the perturbation parameter. Nonetheless, the method of solution remains valid to obtain all physical quantities of a gas undergoing Poiseuille flow. The major conclusion of our analysis has two elements. First, the profiles of hydrodynamic variables in two dimensions differ quantitatively (and sometimes qualitatively) from those in plane geometry. Thus, the Poiseuille flow representation in a cylindrical pipe is more accurate than in a canal between two parallel planes. Second, a critical comparaison between the theoretical predictions of the kinetic theory and those of NavierStokes shows that the two theories agree only up to the first order of perturbation. Starting at the second order, the difference between the two increases. Thus, within the limit of validity of the present study, the description by NavierStokes remains insufficient to predict the correct profiles for the hydrodynamic variables in the Poisseuille flow. [Journal translation]
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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".