Modeling the vertical motion of drops bouncing on a bounded fluid reservoir
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Bibliographic record
Abstract
We present a first-principles model of drops bouncing on a liquid reservoir. We consider a nearly inviscid liquid reservoir and track the waves that develop in a bounded domain. Bouncing drops are modeled as vertical linear springs. We obtain an expression for the contact force between drop and liquid surface and a model where the only adjustable parameter is an effective viscosity used to describe the waves on the reservoir’s surface. With no adjustable parameters associated to the drop, we recover experimental bouncing times and restitution coefficients. We use our model to describe the effect of the Bond, Ohnesorge, and Weber numbers on drops bouncing on a stationary reservoir. We also use our model to describe drops bouncing on an oscillated reservoir, describing various bouncing modes and a walking threshold.
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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 it