A fast contact detection method for ellipsoidal particles
Bibliographic record
Abstract
Abstract This paper presents a fast and robust algorithm for contact detection between elliptical and ellipsoidal particles. The algorithm belongs to the class of geometrical potential methods, which consider the solution of two minimization problems in order to determine a contact point between the particles. The efficiency of the algorithm relies on several ingredients, namely, a transformation that maps the pair of ellipses (ellipsoids) into an ellipse (ellipsoid) centered at the origin and a unit circle (sphere), the construction of an effective initial guess to the solution of the minimization problem, the use of Newton's method for the root finding problem, and the introduction of an additional constraint to guarantee convergence to the desired root. The performance of the new algorithm is compared with that of existing contact detection algorithms on large sets of randomly generated pairs of particles. In particular, the results from several numerical examples show that the present algorithm is several times faster than the existing algorithms for comparable accuracy.
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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 | 0.001 | 0.001 |
| 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".