Size estimates of an obstacle in a stationary Stokes fluid
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Bibliographic record
Abstract
Abstract In this work we are interested in estimating the size of a cavity D immersed in a bounded domain <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mstyle displaystyle="false"> <mml:mo mathvariant="normal">Ω</mml:mo> <mml:mo>⊂</mml:mo> <mml:mstyle displaystyle="false"> <mml:msup> <mml:mrow> <mml:mrow> <mml:mi mathvariant="double-struck">R</mml:mi> </mml:mrow> </mml:mrow> <mml:mi>d</mml:mi> </mml:msup> </mml:mstyle> <mml:mo>,</mml:mo> </mml:mstyle> </mml:math> d = 2, 3, filled with a viscous fluid governed by the Stokes system, by means of velocity and Cauchy forces on the external boundary <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mstyle displaystyle="false"> <mml:mi mathvariant="normal">∂</mml:mi> <mml:mo mathvariant="normal">Ω</mml:mo> </mml:mstyle> </mml:math> . More precisely, we establish some lower and upper bounds in terms of the difference between the external measurements when the obstacle is present and without the object. The proof of the result is based on interior regularity results and quantitative estimates of unique continuation for the solution of the Stokes system.
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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 | 0.001 |
| Open science | 0.001 | 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