Accurate solution for acceleration motion of a vertically falling spherical particle in incompressible newtonian media
Bibliographic record
Abstract
Abstract In this paper, the acceleration motion of a vertically falling spherical particle in incompressible Newtonian media was investigated. The instantaneous velocity and acceleration were carried out using analytical solution technique i.e. the differential transformation method (DTM). Using the DTM, the non‐linear constrained governing equations were reduced to recurrence relations and related initial conditions were transformed into a set of algebraic equations. The solutions were subsequently solved by a process of inverse transformation. The results were also compared with those derived from the homotopy perturbation method (HPM), closed‐form solution, the established fourth order Runge–Kutta method and experimental data in order to verify the accuracy of the proposed method. It was found that this method can achieve more accurate results compared with the HPM. © 2012 Canadian Society for Chemical Engineering
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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 | 0.002 |
| 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".