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 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 | 0.000 | 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 | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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".