On the Self-Recovery Phenomenon for a Cylindrical Rigid Body Rotating in an Incompressible Viscous Fluid
Bibliographic record
Abstract
The damping-induced self-recovery phenomenon is well understood for finite-dimensional mechanical systems. In this paper, we discover a self-recovery phenomenon in a composite system that consists of a cylindrical vessel and a surrounding fluid, where the vessel is equipped with an internal rotor and the fluid is incompressible and viscous. In the system dynamics, interactions between the vessel and the ambient fluid are fully taken into account. A combination of the Lyapunov method and the final-value theorem is applied for analysis of the dynamics. It is mathematically shown that after the spin of the rotor comes to a complete stop in finite time or exponentially as time tends to infinity, the vessel, which has deviated from its initial position due to the reaction to rotor spinning, converges back to its initial position as time tends to infinity, and so does every fluid particle. An experimental test is conducted to verify the occurrence of this phenomenon. The simultaneous self-recovery of the vessel and the fluid to the initial configuration is induced by the fluid viscosity as if the viscosity has a memory of the initial configuration. We envision that our discovery may be useful in designing and operating mechatronic systems interacting with fluids such as underwater vehicles.
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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 | 0.002 | 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".