Capillary instability of a streaming fluid-core liquid jet underself-gravitating forces
Bibliographic record
Abstract
The stability criterion of a fluid cylinder (density ρ (1) ) embedded in a different fluid (density ρ (2) ) is derived and discussed. The model is capillary unstable in the domain 0 < x < 1 as m = 0 where x and m are the axial and transverse wave numbers, while it is stable in all other domains. The densities ratio ρ (2) / ρ (1) decreases the unstable domains but never suppress them. The streaming increases the unstable domains. Gravitationally, in m = 0 mode the model is unstable in the domain 0 < x < 1.0668 as ρ (2) < ρ (1) , while as ρ (2) = ρ (1) it is marginally stable but when ρ (2) > ρ (1) the model is purely unstable for all short and long wavelengths. In m ≠ 0 modes, the self-gravitating model is neutrally stable as ρ (1) = ρ (2) , ordinarily stable as ρ (2) < ρ (1) , but is purely unstable as ρ (2) > ρ (1) . The streaming destabilizing effect makes the self-gravitating instability worse and shrinks the stable domains. The stability analysis of the model under the combined effect of the capillary and self-gravitating forces is performed analytically and verified numerically. When ρ (2) < ρ (1) the capillary force and the axial flow have destabilizing influences but the ratio of the densities ρ (2) / ρ (1) has a stabilizing effect on the gravitating instability. If ρ (1) = ρ (2) , the streaming is destabilizing but the capillary force is strongly stabilizing and could suppress the gravitational instability. When ρ (2) > ρ (1) the capillary force improves the gravitational instability and creates domains of much stability and moreover the instability of the self-gravitating force disappears in several cases of axisymmetric disturbances. PACS No.: 47.17+e
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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".