Bibliographic record
Abstract
Level set methods are powerful numerical techniques for tracking the motion of an interface. Many applications arise in such areas as fluid flow simulations, medical science, and image processing. In fluid flow simulations, tracking the interface between two fluid flow phases is often difficult. Among the mathematical models that can be used to analyze fluid flow are the shallow water equations and Navier-Stokes equations. An important class of fluid flow problems is known as sloshing problems. These problems are concerned with the sloshing of a fluid in a tank, and they arise in the automotive, aerospace, and ship-building industries. In this thesis we consider the modelling of sloshing problems using shallow water equations and Navier-Stokes equations. Whereas the shallow water equations include a function that models the fluid interface, the Navier-Stokes equations do not. In this latter case, however, one can use the level set approach to track the fluid interface. Given the fluid velocity as obtained from the Navier-Stokes equations, one can use it to evolve the interface using the level set approach. We develop a MATLAB based implementation and provide numerical results to demonstrate this approach. i Acknowledgements It is a pleasure to thank many people who made this thesis possible. I would like to gratefully acknowledge my senior supervisors, Professor Paul Muir (Saint Mary’s University) and Professor Raymond Spiteri (University of Saskatchewan). With their enthusiasm, their inspiration, and their great efforts to explain things clearly and simply, they helped to make mathematics fun for me. Throughout my graduate studies, they provided encouragement, sound advice, good teaching, and lots of good ideas. I would have been lost without them. I am also grateful to my thesis examining committee, Professor Patrick
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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 | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| 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".