Reduced Models for Chaotic Dynamics of a Fluid-Conveying Pipe
Bibliographic record
Abstract
A high-dimensional model for chaotic vibration of a cantilever conveying fluid having an end-mass is investigated. The nonlinear partial differential equation describing the oscillations of the pipe is converted into a finite set of coupled nonlinear ordinary differential equation (ODEs) using a Galerkin projection with the uniform cantilever-beam modes as basis. Depending on the parameter range of interest, it turns out that the order of the coupled set of ODEs is much larger (up to 18 degree-of-freedom) in order to obtain a convergent solution. In order to construct a bifurcation diagram with the non-dimensional flow velocity as unfolding parameter, a prohibitive amount of computational effort is necessary in a single-processor (serial) personal computer. To alleviate this computational limitation, such bifurcation diagrams for high-order chaotic system are constructed in parallel computer simulation using multi-threading (i.e. auto-parallelism). A significant computational gain is achieved in terms of time-saving through parallel-processing. The computational gain permits a reliable construction of bifurcation diagrams in the chaotic regime within a reasonable time frame. Subsequently, the efficacy of a reduced-order model based on proper orthogonal mode (POD) is contrasted with the high-dimensional model (with uniform cantilever-beam mode as basis). Numerical results demonstrate the merits and drawbacks of the POD-based bifurcation diagram, depending on the non-dimensional flow-velocity chosen to construct the POD.
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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".